Electronic Structure and Surfaces of Sulfide Minerals: Density Functional Theory and Applications 0128179740, 9780128179741

Table of contents :
Cover
Electronic Structure and Surfaces of Sulfide Minerals: Density Functional Theory and Applications
Copyright
Preface
Prologue
1 - Introduction of density functional theory
1.1 Introduction
1.2 Thomas−Fermi model
1.3 Hohenberg−Kohn theorem
1.4 Kohn−Sham equation
1.5 Exchange-correlation energy functional
1.5.1 Local density approximation
1.5.2 Generalized gradient approximation
1.6 Energy band theory
1.6.1 Bloch's theorem
1.6.2 The first Brillouin zone
References
2 - Electronic properties of sulfide minerals and floatability
2.1 Crystal structure and electronic properties of copper sulfide minerals
2.1.1 Crystal structure of copper sulfides
2.1.2 Computational methods
2.1.3 The electronic properties of copper sulfide
2.1.4 Bonding analysis of copper sulfide minerals
2.1.5 Frontier orbitals
2.1.6 Floatability and electronic properties for copper sulfide minerals
2.2 Crystal structure and electronic properties of iron sulfide minerals
2.2.1 Crystal structure and floatability of iron sulfides
2.2.2 Band structure of iron sulfides
2.2.3 Spin polarization of iron sulfide
2.2.4 Bonding between S and Fe atoms
2.2.5 Bond Mulliken population
2.2.6 Frontier molecular orbital
2.3 Crystal structure and electronic properties of lead–antimony sulfide minerals
2.3.1 Computational methods
2.3.2 Effects of crystal structures
2.3.3 DOS analysis of jamesonite, galena, and stibnite
2.3.4 Analysis of frontier orbital
2.4 Electronic and chemical structures of pyrite and arsenopyrite
2.4.1 Crystal structure
2.4.2 Computational methods
2.4.3 Crystal structure differences between pyrite and arsenopyrite
2.4.4 Electronic structures
2.4.5 Fermi level of pyrite and arsenopyrite
2.4.6 Frontier molecular orbital of pyrite and arsenopyrite
2.5 Electronic structure and flotation behavior of monoclinic and hexagonal pyrrhotite
2.5.1 Introduction
2.5.2 Computational methods and models
2.5.3 Energy band and density of states
2.5.4 The electrons density of monoclinic and hexagonal pyrrhotite
2.5.5 Frontier orbital calculations
2.5.6 Flotation behavior of monoclinic and hexagonal pyrrhotite
2.6 Galvanic interaction between pyrite and galena
2.6.1 Introduction
2.6.2 Effect of galvanic interaction on mineral flotation
2.6.3 Effect of contact distance on the galvanic interaction
2.6.4 Electron transfer between mineral surface atoms
2.6.5 Nucleophilicity and electrophilicity of surfaces
2.6.6 Orbital coefficients of surface atoms
2.6.7 DOS of surface atoms
2.6.8 Effect of H2O and N2 molecules at the interface of pyrite and galena on the galvanic interaction
References
3 - Surface relaxation and electronic properties of sulfide minerals
3.1 Development of surface electronic states
3.1.1 Startup period
3.1.2 Comprehensive development period
3.1.3 Mature period
3.2 Surface relaxation and surface states: foundation
3.2.1 Surface relaxation
3.2.2 Surface state
3.2.3 Slab model
3.3 Surface relaxation and surface state of sulfide minerals
3.3.1 Surface relaxation of sulfide mineral
3.3.2 Surface state energy level of sulfide mineral surface
3.4 Density of states of sulfide minerals surface
3.4.1 Density of states of surface
3.4.2 Charge distribution of surface atoms
3.5 Effect of surface structure on the electronic properties
3.6 Surface atomic reactivity on sulfide minerals
3.6.1 Frontier orbital coefficient
3.6.2 Fukui functions
References
4 - Interaction of water and oxygen with sulfide mineral surface
4.1 Effect of water molecule on surface relaxation
4.1.1 Computational method
4.1.2 Relaxation of minerals surfaces after adsorption of H2O molecule
4.1.3 Effect of density of states on sulfide minerals surfaces in presence of H2O molecule
4.1.4 Effect of Mulliken populations on sulfide minerals surfaces in presence of H2O molecule
4.2 Adsorption of multilayer water molecules on galena and pyrite surfaces
4.2.1 Computational methods
4.2.2 Adsorption of isolated water molecule
4.2.3 Excess water molecules adsorption
4.2.4 Structure and electronic properties of galena and pyrite surfaces
4.3 Interaction of water and oxygen on the pyrite surface
4.3.1 Computational methods
4.3.2 Isolated H2O/O2 molecule adsorption
4.3.3 Coadsorption of H2O–O2 on pyrite surface
4.4 Coadsorption of water and oxygen on the galena surface
4.4.1 Computational models and methods
4.4.2 Adsorption of a single oxygen molecule
4.4.3 Adsorption of a single water molecule
4.4.4 Sequential coadsorption of water and oxygen on the PbS (100) surface
4.4.5 Simultaneous coadsorption of water and oxygen on the PbS (100) surface
References
5 - Structure and reactivity of flotation reagents
5.1 Density states of collector molecules
5.1.1 Methods
5.1.2 Xanthate-type collector
5.1.3 Bonded atoms of xanthate-type collector
5.1.4 Aerofloat collector
5.1.5 Thiocarbamate collector
5.2 Structure–activity of chelating collectors
5.2.1 Computational details
5.2.2 Frontier orbital results
5.2.3 Interactions of metals with chelating collectors
5.3 Azo compound depressants
5.3.1 Computational methods
5.3.2 Effect of azo reagents on sulfide minerals flotation
5.3.3 Relationship between molecular structure and depression properties of azo agents
5.3.4 Frontier orbital energy of azo agents and minerals
5.4 Frothers adsorption at water–gas interface
5.4.1 Computational method
5.4.2 Frother molecule in water phase
5.4.3 Frother molecule adsorbing at the gas–liquid interface
5.4.3.1 α-terpineol
5.4.3.2 MIBC
5.4.3.3 DF200
5.4.4 Frother adsorption layer at the gas–liquid interface
References
6 - Interaction of flotation reagents with mineral surface
6.1 Interaction of xanthate on galena and pyrite surfaces
6.1.1 Computational details
6.1.2 Adsorption of xanthate on minerals surfaces in the absence of oxygen
6.1.3 Adsorption of xanthate on minerals surfaces in the presence of oxygen
6.1.4 Formation of dixanthogen
6.2 Adsorption of xanthate, dithiophosphate, and dithiocarbamate on galena and pyrite surfaces
6.2.1 Experimental and computational methods
6.2.2 The electronic structure and properties of galena (100) and pyrite (100) surfaces
6.2.3 The geometry and electron density of collector adsorption
6.2.4 The analysis of density of states
6.2.5 The heat of adsorption of collectors on galena and pyrite surfaces
6.2.6 Kinetics of collector adsorption on galena and pyrite surface
6.3 Copper activation of sphalerite and pyrite surfaces
6.3.1 Activation model of sphalerite and its electronic properties
6.3.2 Activation model of pyrite and its electronic properties
6.4 Interaction of lime with pyrite surface
6.4.1 Methods
6.4.2 Adsorption of OH– and CaOH+on pyrite surface
6.4.3 Copper activation of pyrite depressed by NaOH and CaO
6.5 The adsorption of cyanide on pyrite, marcasite, and pyrrhotite
6.5.1 Computational methods and models
6.5.2 Adsorption of CN– on pyrite, marcasite, and pyrrhotite surfaces
6.5.3 Effect of sodium cyanide dosage on the grade and recovery of iron
6.6 Effect of water molecules on the thiol collector interaction on galena and sphalerite surfaces
6.6.1 Computational methods
6.6.2 Effect of water molecule on the surface properties of ZnS (110) and PbS (100)
6.6.3 Effect of water molecule on the sphalerite surface reagent adsorption
6.6.4 Effect of water molecule on galena surface adsorption
6.6.5 Effect of water molecule on the selectivity of collector in the separation of lead and zinc sulfide
References
7 - Electronic structures and surface adsorption of impurity-bearing sulfide minerals
7.1 Effect of impurities on the floatability of sulfide minerals
7.2 Effect of impurities and defects on the lattice constants of sulfide minerals
7.3 Effect of impurities and defects on the band gap
7.4 Impurities contribution on the properties of sulfide mineral: the frontier orbital coefficient studies
7.5 Occurrences and correlation of Au and As in pyrite
7.5.1 Computational details
7.5.2 Correlation of Au and As in pyrite
7.5.3 Crystal structure of pyrite containing Au and As
7.5.4 Electronic structures of Au- and As-bearing pyrite
7.6 Effect of impurities on the band structure and oxidation of galena
7.6.1 Computational methods
7.6.2 Effects of impurity on electronic band structure of galena
7.6.3 Adsorption energy and structure
7.6.4 DOS analysis of oxygen with galena surface bearing impurities
7.6.5 Electron density map
7.6.6 Cyclic voltammetry examination
7.7 Activation and collecting of impurity-bearing sphalerite
7.7.1 Effect of impurities on the band structure of sphalerite surface
7.7.2 Effect of impurities on flotation behavior of sphalerite
7.8 Effect of impurities on the interaction between galena and xanthate
References
Subject index
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Author index
A
B
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Back Cover

Citation preview

Electronic Structure and Surfaces of Sulfide Minerals Density Functional Theory and Applications Jianhua Chen Zhenghe Xu Ye Chen

Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States Copyright © 2020 Central South University Press. Published by Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-12-817974-1 For information on all Elsevier publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Candice Janco Acquisitions Editor: Amy Shapiro Editorial Project Manager: Emerald Li Production Project Manager: Sruthi Satheesh Cover Designer: Miles Hitchen Typeset by TNQ Technologies

Preface Flotation is a process of separating fine valuable mineral particles from their associated gangues. In flotation, hydrophobic minerals of interest are attached to air bubbles, floated under the buoyancy force of bubbles to the top of pulp, and collected as products referred to as concentrate, leaving hydrophilic particles in the pulp as tailings. Flotation has been used in large-scale mineral processing industry since the 1920s. In 1921, Perkins first patented the slightly soluble thiocarbamate as a nonoil chemical collector for sulfide mineral flotation, followed by Keller who invented in 1925 water-soluble xanthates and Whitworth who developed in 1926 dithiophosphate, which revolutionized flotation. During 1930s, the application of soaps and cationic amine collectors industrialized processing of nonmetallic ores. Due to its high efficiency and low cost, flotation is currently used to process annually over billions of tons of ores, in addition to its widely expanding application to wastewater treatment and recycling of various types of valuables from electronic wastes, metallurgical slugs, used batteries, etc. The importance of the froth flotation to the economy of the industrial world has been considered to be enormous. Many early efforts at understanding flotation were directed toward explaining differential flotation in terms of the relative occlusion of gases. In 1916, bubbles were considered to be at the heart of flotation science. The role of interfaces in flotation had been considered by Sulman by 1912. The first direct application of thermodynamics to systems similar to flotation was that of von Reinders, who deduced how fine solid particles would be distributed between oil and water phases based on Maxwell’s capillarity equations in 1913. In 1915, Ralston suggested that flotation might result from the electrical attraction between negatively charged air bubbles and positively charged mineral particles. In 1917, Taggart and Beach fairly lucidly applied thermodynamics concepts directly to flotation. At present, thermodynamics has become a fairly widely used tool for the analysis of flotation phenomena. In 1917, Anderson suggested that adsorption might play a dominant role in flotation and used the Gibbs adsorption equation to discuss the frother adsorption at the airewater interface. In 1920, Langmuir found the correlation between adsorption and hydrophobicity. He reported that oleic acid created large contact angles on cleaved calcite and galena but only small angles on clean glass and cleaved mica. In 1928, Taggart described the results of adsorption tests on sulfide minerals that related the structure of the adsorbate to its ability to

xi

Preface act as a flotation collector. Taggart formulated the definition of the molecular structure needed for a soluble flotation collector, namely, that it must possess both a polar group that binds it to the surface and a nonpolar group that can orient away when adsorbed at a mineralewater interface. Although such early researchers as Fahrenwald, Sulman, and Taggart carried out a number of experiments to elucidate flotation phenomena, the founder of the scientific basis of flotation was A.M. Gaudin and his colleagues, who opened the beginning of the modern approach to research in flotation chemistry. Major advances, particularly starting in the 1950s, were achieved to flotation systems through better understanding and application of the fundamental principles of surface and colloid chemistry, particularly electrical double-layer phenomena. Since most of natural minerals are originally not sufficiently hydrophobic for effective attachment to air bubbles, a key for separating valuable minerals from gangue minerals is therefore to render the target minerals hydrophobic by selective adsorption of added chemicals known as collectors in mineral processing. Collectors can adsorb on mineral surfaces by electrostatic attraction, electrochemical reaction, chemical binding, hydrogen bonds, etc. To achieve selective adsorption of collectors on target minerals requires designing special structures of collectors to suit particular mineral surfaces. A number of theories have been proposed to explain the selectivity of collector adsorption at mineral surfaces in flotation. In 1930, for example, the solubility product theory of solutions was suggested by Taggart that the smaller the solubility product of the compounds formed by reagent and metallic ions is, the stronger is the adsorption of the reagents on the corresponding minerals, hence the more effective flotation. This theory has provided satisfactory explanation on some flotation phenomena, such as strong flotation of calcium minerals and weaker or negligible collecting power of silicate minerals by oleic acids. Similarly, the product solubility theory has been used to explain selective flotation of metal sulfide minerals from gangue minerals by xanthate. Other theories based on chemical reactions, chelation, and coordination of collectors with metal ions in solutions have also been proposed to explain selective flotation. In these theories, the potency of metal ions to react with collectors in bulk solutions is used to infer their interactions on mineral surfaces. Clearly the influence of the mineral surface structure and the properties of adjacent coordination atoms on their interactions with collectors are not considered in these theories. Therefore, they cannot explain why copper, lead, and iron sulfides can be effectively floated by xanthate, but not their corresponding oxidized minerals. The atoms (ions) in mineral crystal structure and on mineral surfaces are known to interact with each other, which greatly affects their reactivity with collectors. For example, the reactivity of iron in hematite (Fe2O3) and in pyrite (FeS2) with collectors is drastically different, leading to the use of completely different collectors for hematite flotation and pyrite flotation. Pradip suggested that the selectivity of flotation reagents depends greatly on the “structural/stereochemical compatibility” between the molecular architecture of the adsorbing collector and the specific structure of mineral surface. More accurate prediction of interactions between the flotation reagent molecule and the mineral surface requires better understanding of spatial effect of mineral surfaces. Although Langmuir noticed the effect of solid surface structure on adsorption as early as 1917, actual effect of mineral surface structure on collector xii

Preface adsorption remains unknown. M.C. Furstenau et al. wrote in The Froth Flotation Century that “We are now at a stage where the further improvement of the flotation process requires a deeper understanding of its fundamental theory.” In 1925, Schro¨dinger put forward the wave function equation of electrons to describe the behavior of microscopic particles. In 1927, Hitler and London made the first attempt to describe the structure of hydrogen molecules using the Schro¨dinger equation, which laid the foundation of modern quantum chemistry. In 1991, K. Takahashi calculated the electronic properties of reagent molecules by adopting extended Hu¨kel molecular orbital (EHMO) method to predict their reactivity. D. Z. Wang focused on the structureeactivity relationship of the reagent by using semiempirical LCAO-MO method. However, the calculation using atomic orbital-based MO method is very difficult. For a molecule of 100 electrons, for example, resolving the RHF equation using MO methods requires integration of 100 million double-electron equations. It is therefore almost impossible to calculate mineral surfaces by MO approach. Density functional theory (DFT) using electron density distribution as a basic variable is a new revolutionary approach for studying the ground state properties of multi-particle systems, which greatly reduce the intensity of calculations. With the recent development of supercomputing power, a wide range of software for DFT calculation has been developed and available for various applications. As a result, DFT is now being rapidly used to calculate the crystal structure of minerals, lattice impurity, mineral surface and interface properties, and reagent adsorption. The solid physical properties of minerals are of particular importance for sulfide flotation. First, sulfide minerals have semiconducting properties, and the flotation of sulfide mineral is an electrochemical process. Electrochemistry is the basic feature of sulfide mineral flotation. Secondly, electrochemical reactions or electrochemical interactions are common in the sulfide ore processing from grinding to flotation separation, such as galvanic interaction between sulfide minerals and grinding media, the electrochemical interactions between flotation reagents and sulfide mineral surfaces, the galvanic corrosion between different sulfide mineral particles, and the electrochemical reaction between the sulfide mineral surface and the oxygen and water medium, all of which involve the semiconductor band structure and electronic properties of sulfide minerals. Therefore, the semiconducting properties of sulfide minerals are the foundation of electrochemistry of sulfide mineral flotation. Studying the solid physical properties of sulfide minerals (energy band structure, electron state, and electron transfer) could provide theoretical explanation to the electron transfer mechanisms during sulfide mineral flotation. This book systematically summarizes the research results of the authors in recent years and expounds the relationship between the crystal properties and the floatability of sulfide minerals from solid physics, crystal chemistry, surface science, and quantum mechanics. The research works of this book have been funded by the National Natural Science Foundation of China (50864001, 51164001, 51864003, 51304054). The authors are thankful for these supports. We would also like to thank Dr. Li Yuqiong, Dr. Zhao Cuihua, Dr. Lan Lihong, and others for their contributions to this book.

xiii

Prologue This book systematically studies the electronic structure of sulfide minerals, surface properties, and interaction of reagents with mineral surfaces. The book is structured in seven chapters. The first chapter introduces density functional theory (DFT), and some important concepts of solid state physics are also introduced. The second chapter deals with the crystal structure and electronic properties of sulfide minerals and their applications in flotation. The relationships between the floatability and their crystal structure, band structure, density of states, and frontier orbitals are provided. The third chapter presents the surface relaxation and electronic structure of sulfide minerals surfaces. The difference in charge distribution between surface atoms and bulk atoms, as well as the correlation between surface atomic coordination and reactivity is discussed. In the fourth chapter the adsorption of flotation reagents on mineral surfaces at the solideliquid interface was studied. In addition, the effect of water and oxygen molecule on the surface properties and reagent adsorption are discussed. The fifth chapter explores the electronic properties of flotation reagents by DFT, and structureeactivity of reagents is discussed. In the sixth chapter the mechanism of flotation reagent interacting with mineral surfaces was studied by DFT calculation and microcalorimetry tests. The seventh chapter reports the effects of lattice defects on the properties of sulfide minerals, surface structure, and adsorption behaviors of reagents.

xv

CHAPTER 1

Introduction of density functional theory 1.1 Introduction In 1926 and 1927, physicists Schrodinger and Heisenberg, respectively, put forward the Schrodinger equation and uncertainty principle, which marked the birth of quantum mechanics. After that, a new world that is completely different from classical physics was shown in front of the physicist. Meanwhile, a new theoretical tool for understanding the chemical structure of matter was provided for the chemist too. In 1927 the physicists Heitler and London applied the approach of quantum mechanics to atomic structure to study H2 molecule [1], successfully explaining the bonding mechanism in a homonuclear molecule. Their success marked the interdisciplinary science of quantum mechanics and chemistry: the birth of quantum chemistry. After Heitler and London, chemists have also begun to apply quantum mechanics theory to study. On the basis of the study of hydrogen molecule by the two physicists, three theories of molecular structure were established by chemists, namely valence bond theory, molecular orbital theory, and ligand field theory. Pauling developed the valence bond theory on the basis of the earliest hydrogen molecular model [2] and won the Nobel Prize in Chemistry in 1954. In 1928, the physicist Mulliken put forward the earliest molecular orbital theory [3e5]. In 1931, Hu¨ckel developed the molecular orbital theory of Mulliken and applied it to conjugated and aromatic hydrocarbons [6]. In 1929, Bethe proposed the theory of ligand field and applied it to the theoretical research on the transition metal complexes [7]. Later, the theory of ligand field and molecular orbital theory developed into a modern ligand field theory. The valence bond theory, molecular orbital theory, and ligand field theory are the three basic theories of quantum chemistry used to describe molecular structure. In the early stages, due to the limitation of calculation method and relatively small calculation amount, the more intuitive valence bond theory dominated the study of quantum chemistry. After the 1950s, with the invention and rapid development of the computer, a huge amount of computation became an easy task. The advantages of molecular orbital theory were highlighted at this background, which gradually replaced the valence bond theory.

Electronic Structure and Surfaces of Sulfide Minerals. https://doi.org/10.1016/B978-0-12-817974-1.00001-6 Copyright © 2020 Central South University Press. Published by Elsevier Inc. All rights reserved.

1

2 Chapter 1 In 1928, Hartree proposed the Hartree equation [8], which assumed that the charge distribution of each electron was the solution of the Schro¨dinger equation for an electron in a potential n(r), derived from the field. In 1930, Hartree’s students, Fock and Slater, proposed a self-consistent field iterative equation considering the Pauli principle, called the Hartree-Fock equation, which further improved the Hartree equation [9e11]. To solve the Hartree-Fock equation, in 1951, Roothaan further proposed that molecular orbitals could be expressed as the linear combination of atomic orbitals that composed the molecule and developed the famous Roothaan-Hartree-Fock (RHF) equation [12]. This equation along with the method based on the further development of this equation is the fundamental method of modern quantum chemistry. In 1952, Japanese chemist Kenichi Fukui proposed a frontier molecular orbital theory [13]. In 1965, the American organic chemist Woodward and the quantum chemist Hoffmann jointly proposed the theory of conservation of molecular orbital symmetry in organic reactions. The theories proposed by Fukui, Woodward, and Hoffman use simple models that are based on the simple molecular orbital theory to avoid complex mathematical operations and apply quantum chemistry theory to qualitative treatment of chemical reactions in an intuitive form. Through their theory, experimental chemists can intuitively understand the abstract concepts of molecular orbital wave functions. In 1981, Fukui and Hoffman won the Nobel Prize in Chemistry for their contributions. Although the quantum theory had been established as early as the 1930s, the Schrodinger equation is very complex and still difficult to obtain the exact solution. Even for the approximate solution by molecular orbital, the required computations are enormous. For example, for a small molecule with 100 electrons, there are over 100 million of the double-electron integrals in the process of solving the RHF equation. This calculation is obviously impossible to complete by humans. Hence, in the next decades, quantum chemistry progressed slowly, and was even rejected by experimental chemists. In the study of solid state physics, it is almost impossible to calculate the crystal and the surface from the classical molecular orbital due to the periodic structure of the crystal and 1023 order magnitude of nuclei and electrons per cubic centimeter, thus the theoretical calculation of solid physics has been developing slowly. It was not until the 1990s that the maturity of density functional theory (DFT) and the development of computer hardware provided an effective theoretical tool for the calculation of solids and their surfaces. DFT is one of the solutions based on quantum mechanics and the ab initio method of BorneOppenheimer approximation. Distinguished with many methods based on molecular orbital theory, which constructs wave functions of multielectron systems (e.g., HartreeeFock methods), this method is based on electron density function and solves the single-electron many-body Schrodinger equation by KohneSham

Introduction of density functional theory 3 self-consistent field (KS-SCF) iteration to obtain the electron density distribution. This operation reduces the number of free variables and the degree of systematic oscillation, thus improving the rate of convergence. In 1964, Hohenberg and Kohn put forward an important computational idea and proved that the electron energy was determined by the electron density [14]. Thus, the electronic structure can be obtained by electron density without dealing with complex many-body electron wave functions. The electronic structure can be described by only three spatial variables. This method is called as density functional theory (DFT). According to this theory, the Hamiltonian of the particle is determined by the local electron density, and the local density approximation (LDA) method is derived. This method has achieved great success in the simulation of solid materials such as metal and semiconductors through the combination of metal electron theory, periodic boundary condition, and energy band theory. LDA was later extended to several other fields, in particular to study the property of molecules and condensed matter. Now it is one of the most commonly used methods in the field of condensed matter physics and computational chemistry. Walter Kohn received the Nobel Prize in Chemistry for the great contributions in the developments of density functional theory. In view of the extensive application and great achievements of DFT, this theory is taken as the second revolution of quantum chemistry. At present, DFT is the main method to calculate the structure and electronic properties of solids, and the selfconsistent calculation based on this method is called the first principle method. Since 1970, DFT has been widely used in the calculation of solid state physics. In most cases, DFT with LDA gives very satisfying results compared with other methods of solving the many-body problem of quantum mechanics, and the computational cost is less than that of the experiment. It was generally considered that quantum chemistry calculations cannot give sufficient precise results, until the 1990s, when the approximation used in the DFT was refined into a better exchange correlation model. However, DFT is still not perfect. DFT is mainly achieved through the Kohn-Sham method. In the framework of Kohn-Sham DFT, the intractable many-body problem (due to the interacting electrons in a static external potential) is simplified to a tractable problem of non-interacting electrons moving in an effective potential. The effective potential includes the external potential and the effect of Coulomb interactions between the electrons, e.g., the exchange and correlation interactions. Modeling the latter two interactions becomes the difficulty within Kohn-Sham DFT. At present, there is no precise solution to calculate the exchange correlation energy; the simplest approximation is the local-density approximation (LDA). LDA approximation uses a simple homogeneous electron gas model to calculate the exchange energy of the system, and the correlation

4 Chapter 1 energy is treated by fitting free electron gas. Although DFT has been greatly improved, it is hard to accurately describe the intermolecular interactions, especially van der Waals forces and in calculations of the band gap in semiconductors. For example, the experimental band gap of zinc sulfide (ZnS) is of 3.6 eV, but the calculated result based on DFT is only 2.0 eV, which is far away from the experimental value.

1.2 Thomas¡Fermi model As early as 1927, Thomas and Fermi first realized that statistical methods could be used to approximate the distribution of electrons in an atom [15,16]. They proposed a homogeneous electron gas model based on the kinetic energy as an electron density functional expression, which is called as the ThomaseFermi model. According to the Thomas
Fermi model, the total kinetic energy of the electrons (TTF) can be expressed as shown in Eq. (1.1): Z (1.1) TTF ½r ¼ CF r5=3 ðrÞdr   3 3p2 2=3 ¼ 2:817. where CF ¼ 10 The integrand rðrÞ is an undetermined function, so TTF ½r is a functional. For the manyelectron system, in considering only the interactions between nuclei and electrons and between electrons and electrons, the total energy of the electrons can be expressed as shown: ZZ Z Z rðrÞ 1 rðr1 Þrðr2 Þ 5=3 dr þ ETF ½rðrÞ ¼ CF r ðrÞdr
Z (1.2) dr1 dr2 r 2 jr1
r2 j Eq. (1.2) needs to be solved under equivalent periodic conditions: Z N ¼ N½rðrÞ ¼ ½rðrÞdr

(1.3)

The ThomaseFermi model does not consider the atomic exchange energy, so the calculation accuracy is lower than other methods. Although the treatment of molecules by the ThomaseFermi method is not successful, the ThomaseFermi method opens a new method for DFT. Since then, the calculation accuracy of the model has been the focus of research in this field, but the results are not unsatisfactory. This situation keeps unchanged until the emergence of HohenbergeKohn’s theorem.

Introduction of density functional theory 5

1.3 Hohenberg¡Kohn theorem In 1964, based on the inhomogeneous electron gas theory, Hohenberg and Kohn proposed a multi-electron system in an external potential VðrÞ, whose ground state physical properties can be determined by the electron density distribution function rðrÞ. This theory proposed that the energy of the system is the functional of the electron density distribution function, and the ground state is the minimum [14]. Z (1.4) EV ½r ¼ T½r þ Vne ½r þ Vee ½r ¼ rðrÞVðrÞdr þ FHK ½r where FHK ½r ¼ T½r þ Vee ½r Vee ½r ¼ J½r þ Non
classic item ZZ 1 1 J½r ¼ rðr1 Þrðr2 Þdr1 dr2 2 r12

(1.5) (1.6) (1.7)

J½r is the classic electron repulsion energy, Vne is the potential energy between nuclear and electrons, and Vee is the potential energy between electrons and electrons. Nonclassical term very important but difficult to understand quantity. In this nonclassical term, exchange-correlation energy (Exc ½rðrÞ) is the main part of it. HohenbergeKohn’s theorem is about the variational principle of EV ½rðrÞ. It is assumed that EV ½r in this equation is differentiable. Under the condition that the number of particles is conserved, the condition for the extreme value of functional EV ½r is as follows: Z   (1.8) rðrÞdr
N g ¼ 0 dJ ¼ d EV ½r
m m¼

dEV ½r dr

(1.9)

Substituting Eq. (1.4) into Eq. (1.9) yields this: m¼

dEV ½r dFHK ¼ VðrÞ þ dr dr

(1.10)

Eq. (1.10) is the Euler
Lagrange equation of EV ½r. Where FHK is independent of external potential VðrÞ, it is a universal functional of rðrÞ. If we can find its approximate form, the EulereLagrange equation can be applied to any system. Therefore, Eq. (1.10) is the basic equation of the DFT.

6 Chapter 1 However, although the HohenbergeKohn theorem clearly states that the total energy of the system can be obtained by solving the ground state electron density distribution function, it does not indicate how to determine the electron density distribution function rðrÞ, the kinetic energy functional T½rðrÞ, and the exchange-correlation energy functional Exc ½rðrÞ. It was not until the KohneSham equation was proposed in 1965 that DFT was introduced into practical application.

1.4 Kohn¡Sham equation Kohn and Sham proposed in 1965 that the electron density function of a multiparticle system can be obtained by a simple single-particle wave equation [17]. This simple singleparticle equation is the KohneSham equation (KeS equation for short). In the KohneSham equation, the electron density function of the system can be expressed by the sum of the squares of the single electron wave functions: rðrÞ ¼

N X

jji ðrÞj2

(1.11)

i¼1

and the KohneSham equation can be written as:  
V2 þ VKS ½rðrÞ ji ðrÞ ¼ Ei ji ðrÞ Z 0 0 r ðr Þ 0 dExc ½r0 ðr 0 Þ dr þ VKS ¼ VðrÞ þ drðrÞ jr
r 0 j

(1.12) (1.13)

The problem of the ground state eigenvalues of the multi-electron system can be transformed into a single electron problem. The Kohn
Sham equation finds its selfconsistent solution obtained through an iterative equation.

1.5 Exchange-correlation energy functional The exchange-correlation functional EXC ½r is very important in DFT, but so far, there is no accurate expression for EXC ½r. If a more accurate expression can be found, the DFT calculation will be more practical. Various approximation methods have been proposed, including LDA, LSDA (local spin density approximation), GGA (generalized gradient approximation), and BLYP (hybrid density functional). At present, LDA and GGA are widely used.

Introduction of density functional theory 7

1.5.1 Local density approximation The basic idea of LDA proposed by Kohn and Sham in 1965 is to divide the entire inhomogeneous electron region in the system into multiple small regions, and to approximate these small regions as a homogeneous electron gas. The specific form of the system nonuniform electron gas exchange-correlation functional is obtained by the density function rðrÞ of the uniform electron gas, and then the self-consistent calculation is performed by the KeS equation and the VKS equation: Z LDA EXC ½r ¼ rðrÞεXC ½rðrÞdr (1.14) where εXC ½rðrÞ is the exchange-correlation energy of each particle in a uniform electron gas of density. The LDA potential function is the exchange correlation potential based on the local charge density in the system. The LDA has been very successful in dealing with the electronic energy bands and related physicochemical properties of metals and semiconductors, but there are also deficiencies in calculating the metal d-band and the band gap of semiconductor. Considering the electron spin state on the basis of the LDA, LSDA is developed. Its exchange-correlation energy is calculated: Z



Exc ½r ¼ dr r[ ðrÞ þ rY ðrÞ εxc r[ ðrÞ; rY ðrÞ (1.15) Where, r[ ðrÞ and rY ðrÞ are the spin-up  electron density and the spin-down electron density, respectively, and εxc r[ ; rY is the exchange-correlation energy equivalent to the homogeneous electron gas single electron in the presence of spin polarization, which is related to the spin orientation.

1.5.2 Generalized gradient approximation Based on LDA, Perdew and Wang proposed in 1986 that in addition to electron density, the exchange energy and correlation energy of the system also depend on the density gradient [18]. Based on this theory, the exchange-correlation functional can be expressed as a function of charge density and gradient: Z GGA Exc ½r ¼ rðrÞεXC ðrðrÞÞdr þ EXC ðrðrÞ; VrðrÞÞ (1.16)

8 Chapter 1 Due to its rationality and accuracy, many functionals such as PBE, RPBE, and PW91 have been developed under the framework of GGA [19e23]. At present, LDA and GGA have been widely used in the calculation of solid physics and material chemistry and have achieved great success.

1.6 Energy band theory 1.6.1 Bloch’s theorem Bloch’s theorem is the foundation of energy band theory of solid physics. It is based on a basic assumption that the atoms in the crystal are periodically arranged and that the potential field in the crystal is translational. In the periodic potential, the single-electron Schrodinger differential equation can be written as: Z2 2 V JðxÞ þ ½VðxÞ
EJðxÞ ¼ 0 2m where VðxÞ is the periodic potential, which is translational


Vðx þ a1 Þ ¼ Vðx þ a2 Þ ¼ Vðx þ a3 Þ ¼ VðxÞ

(1.17)

(1.18)

Here, a1, a2, and a3 are the three lattice basis vectors of the crystal. The Bloch theorem states that the electronic states in the crystal have the following properties: Jðk; x þ ai Þ ¼ eik$ai Jðk; xÞ;

i ¼ 1; 2; 3;

(1.19)

where k is the real wave vector of k-space, and function Jðk; xÞ is also called Bloch function or Bloch wave, which is the most basic function in modern solid state physics. In order to make the eigenfunction and eigenvalue, one-to-one correspondence, which is the electronic wave vector k and the intrinsic value of E (k), must limit the wave vector k values in an inverted primitive cell interval, and the interval is called the first Brillouin zone. The electronic wave vector number in the first Brillouin zone is equal to the primitive cell number of the crystal. When k changes in the Brillouin zone, the energy of the corresponding Bloch wave, i.e., the eigenvalue E of the equation (1.17), also changes within a certain range. These allowable energy ranges are called energy bands, or it can be written as En ðkÞ (where n is the energy band indicator), and they can be arranged in order of increasing energy: E0 ðkÞ  E1 ðkÞ  E2 ðkÞ  /  En ðkÞ

Introduction of density functional theory 9 The corresponding eigenfunctions can be represented by Jn ðk; xÞ, which can be written as follows: Jn ðk; xÞ ¼ eik$x un ðk; xÞ;

(1.20)

where k is the wave vector and un ðk; xÞ is the function with the same periodicity as the lattice: un ðk; x þ a1 Þ ¼ un ðk; x þ a2 Þ ¼ un ðk; x þ a3 Þ ¼ un ðk; xÞ:

(1.21)

The energy band formed by crystal valence electrons plays an important role in the physical properties of the crystal and the physical processes involved. The crystal has a band gap between its highest occupied energy band and the lowest unoccupied energy band. The crystal has only a small number of conductive electrons at low temperatures, which is a semiconductor or an insulator, depending on the band gap. If a crystal has no band gap between its highest occupied band and the lowest unoccupied band, there will still be a significant number of conductive electrons, even at very low temperatures, which is metal. The band theory of crystals explains the conductivity of solids well, and the hypothesis is reasonable. The band theory has been valued by solid physicists. Although there are still some problems that cannot be explained well, the band theory is still the most effective means of studying solid state physics.

1.6.2 The first Brillouin zone Brillouin zone is a part of space centered on the origin in the reciprocal lattice. The first Brillouin zone can be obtained by bisecting with perpendicular planes nearest neighbors reciprocal lattice vectors, second nearest neighbors, and considering the smallest volume enclosed. Similarly, the second Brillouin zone is obtained by continuing the bisecting operations and delimiting the second volume enclosed. The volume adjacent to the second Brillouin zone and equal in volume to the first Brillouin zone is the third Brillouin zone. The first Brillouin area is also called as the simply Brillouin zone, referred to as the Brillouin zone (BZ). Brillouin zone is a symmetric primitive cell in wave vector space, which has all the symmetries of the point group of the reciprocal lattice. The shape of the reciprocal lattice of crystal lattice of simple cube is still simple cube, and its shape of the Brillouin zone is still simple cube. The shape of the reciprocal lattice of crystal lattice of body-centered cube is face-centered, and its shape of the Brillouin zone is rhombic dodecahedron. The shape of the reciprocal lattice of crystal lattice of facecentered cube is body-centered, and its shape of the Brillouin zone is truncated octahedron. The volume of the Brillouin zone is equal to the volume of the primitive unit cell.

10 Chapter 1 The primitive translation vectors of a two-dimensional lattice are a1 ¼ ai, a2 ¼ aj; then the primitive translation vectors of reciprocal lattice are: b1 ¼

2p 2p i; b2 ¼ j a a

There are four reciprocal points closest to the origin: b1,
b1, b2,
b2. The space enclosed by their perpendicular bisectors is the simply Brillouin zone, that is, the first Brillouin zone. As shown in Fig. 1.1, the square in this reciprocal lattice space is the first Brillouin zone of the square lattice. By connecting the coordinate origin with the second nearest neighbor reciprocal points and drawing the vertical bisector of these lines, the space adjacent to the first Brillouin zone and equal in volume to the first Brillouin zone is the second Brillouin zone, which is the shaded area of the four isosceles right triangles as shown in Figure 1.1. By connecting the coordinate origin with the third nearest neighbor reciprocal points and drawing the vertical bisector of these lines, the space adjacent to the second Brillouin zone and equal in volume to the second Brillouin zone is the third Brillouin zone, which is the region of the eight isosceles right triangles in Figure 1.1.

2π a 3

2

1 2π a

O

2π a

2π a

Figure 1.1 Two-dimensional square lattice Brillouin zone.

Introduction of density functional theory 11 k

L Λ

Γ Δ i

X

Σ K

j

Figure 1.2 The first Brillouin zone of the face-centered cubic lattice.

The first Brillouin zone of the face-centered cubic lattice is more complex. It is a tetrakaidecahedron with eight regular hexagons and six squares, often called truncated octahedron. Fig. 1.2 shows the shape of this truncated octahedron. The coordinates of the typical symmetry point in the first Brillouin zone of the facecentered cubic lattice are as follows: G X 2p 2p ð0; 0; 0Þ ð1; 0; 0Þ a a

K L   2p 3 3 2p 1 1 1 ; ;0 ; ; a 4 4 a 2 2 2

References [1] Heitler W, London F. Wechselwirkung neutraler Atome und homo¨opolare Bindung nach der Quantenmechanik. Z Phys 1927;44(6e7):455e72. [2] Pauling L. The nature of the chemical bond. Cornell University Press; 1960. [3] Mullike RS. The assignment of quantum numbers for electrons in molecules, I. Phys Rev 1928;32(2):186e222. [4] Mullike RS. The assignment of quantum numbers for electrons in molecules. II. Correlation of molecular and atomic electron states. Phys Rev 1928;32(5):761e72. [5] Mullike RS. The assignment of quantum numbers for electrons in molecules. III. Diatomic hydrides. Phys Rev 1929;33(5):730e47. [6] Hu¨ckel E. Quanstentheoretische Beitra¨ge zum BenzolproblemII. Quantentheorie der induzierten Polarita¨ten. Z Phys 1931;72(5e6):310e35. [7] Bethe H. Splitting of terms in crystals. Ann Phys 1929;3:133. [8] Hartree DR. The wave mechanics of an atom with a non-Coulomb central field. Part I. Theory and methods. Proc Camb Philos Soc 1928;24(01):89.

12 Chapter 1 [9] Fock V. Na¨herungsmethode zur Lo¨sung des quantenmechanischen Mehrko¨rperproblems. Z Phys 1930;61(1e2):126e48. [10] Slater JC. Note on Hartree’s method. Phys Rev 1930;35(2):210e1. [11] Slater JC. Atomic shielding constants. Phys Rev 1930;36(1):57e64. [12] Roothaan CCJ. New developments in molecular orbital theory. Rev Mod Phys 1951;23(2):69e89. [13] Fukui K, Yonezawa T, Shingu H. A molecular orbital theory of reactivity in aromatic hydrocarbons. J Chem Phys 1952;20:722. [14] Hohenberg P, Kohn W. Inhomogeneous electron gas. Phys Rev 1964;136(3B):B864e71. [15] Thomas LH. The calculation of atomic fields. Proc Camb Philos Soc 1927;23:542. [16] Fermi E. Un metodo statistico per la determinazione di alcune priorieta dell’atome. Rend. Accad Naz Lincei 1927;6:602e7. [17] Kohn W, Sham LJ. Self-consistent equations including exchange and correlation effects. Phys Rev 1965;140(4A):A1133e8. [18] Perdew JP, Wang Y. Accurate and simple density functional for the electronic exchange energy: generalized gradient approximation. Phys Rev B 1986;33(12):8800e2. [19] Perdew PJ, Burke K, Emezerhof M. Generalized gradient approximation made simple. Phys Rev Lett 1996;77(18):3865e8. [20] Hammer B, Hansen LB, Norskov JK. Improved adsorption energetics within density functional theory using revised PBE functionals. Phys Rev B 1999;59:7413. [21] Wu Z, Cohen RE. More accurate generalized gradient approximation for solids. Phys Rev B 2006;73(23):235116e21. [22] Perdew JP, Chevary JA, Vosko SH, Jackson KA, Pederson MR, Singh DJ, Fiolhais C. Atoms, molecules, solids, and surfaces: applications of the generalized gradient approximation for exchange and correlation. Phys Rev B 1992;46(11):6671e87. [23] Vanderbilt D. Soft selfeconsistent pseudopotentials in a generalized eigenvalue formalism. Phys Rev B 1990;41(11):7892e5.

CHAPTER 2

Electronic properties of sulfide minerals and floatability Sulfide minerals are characteristic of semiconducting, and electron transfer and electrochemical reactions would occur in the process of flotation. The electronic properties of sulfide minerals determine the basic flotation behaviors. The electrochemical reaction is not only carried out on the surface of sulfide minerals, but it also is involved in bulk electrons. For example, the rest potential is a bulk parameter, which can be used to explain the collector’s products on the sulfide surface. The study of the electronic structure and properties of sulfide minerals can give an insight to understand the electrochemical behavior of flotation. This chapter discusses the effects of crystal structure and electronic properties of sulfide minerals and attempts to establish the relationship between electronic structure and floatabillity of sulfide minerals.

2.1 Crystal structure and electronic properties of copper sulfide minerals 2.1.1 Crystal structure of copper sulfides Copper sulfide ore, which accounts for 80% of the copper resource, is the major source for the metallic copper [1]. The major copper sulfide ores contain chalcopyrite (CuFeS2), bornite (Cu5FeS4), covellite (CuS), and chalcocite (Cu2S). The concentrates of copper from sulfides ores are generally performed by flotation and then processed by pyrometallurgic or hydrometallurgic routes to extract copper from the concentrates. Although the pyrometallurgic process is the major route to produce copper, more and more attention has been paid to hydrometallurgic and bioleaching processing routes due to their economic and environmental benefits, especially for the low-grade ores and copper-rich tailings [2]. It is well accepted that the hydrometallurgy, bioleaching, and flotation of metal sulfides are electrochemical processes, which are dependent on the composition and morphology of the mineral. The differences in crystal structure between copper sulfides lead to differences in dissolution, oxidative, and flotation behaviors. For example, the dissolution of metal components from chalcopyrite is slow in both chemical and biologic leaching reaction [3,4]. The bioleaching rates of other copper sulfides such as covellite (CuS) and chalcocite (Cu2S) are relatively high in the presence of iron oxidizing bacteria [5]. Electronic Structure and Surfaces of Sulfide Minerals. https://doi.org/10.1016/B978-0-12-817974-1.00002-8 Copyright © 2020 Central South University Press. Published by Elsevier Inc. All rights reserved.

13

14 Chapter 2 Bornite is known to oxidize rapidly on exposure to air at room temperature [6]. Therefore, the differences in crystal structure of these copper sulfides could result in different electronic properties, and consequently have great influence on the electrochemical and oxidative behaviors. Different copper sulfide minerals are of similar chemical composition, but of totally different crystal structure, and consequently different characteristics. The models for crystal structures of the four kinds of copper sulfides are shown in Fig. 2.1. Chalcopyrite crystallizes in the tetragonal system, and the unit cell is Cu4Fe4S8 (Fig. 2.1A). Each metal atom (Cu and Fe) is coordinated by a tetrahedron of S atoms, and each S atom is coordinated by two Cu and two Fe atoms. The calculated bond lengths are ˚ , dFe‒S ¼ 2.216 A ˚ , dCueCu ¼ dFe‒Fe ¼ 3.695 A ˚, as follows: dCueS ¼ 2.323 A ˚ , and dSeS ¼ 3.631/3.853 A ˚ , which are in a good agreement with the dCueFe ¼ 3.695 A ˚ [7]. experimental values of 2.302, 2.257, 3.713, 3.740, and 3.685/3.795 A Covellite belongs to a hexagonal crystal, and the unit cell formula is Cu6S6 (Fig. 2.1B). The covellite Cu atoms are three- and fourfold coordination, and S atoms are four and

Figure 2.1 Schematic views of the structure for (A) chalcopyrite (Cu4Fe4S8), (B) covellite (Cu6S6), (C) bornite (Cu32Fe16S32), and (D) chalcocite (Cu96S48). (Numbers are the coordination value of the atom.)

Electronic properties of sulfide minerals and floatability 15 fivefold coordination. The four-coordinated Cu atom bonds to the four-coordinated S atom, and the three-coordinated Cu bonds to the five-coordinated S atom with the bond lengths ˚ [8], respectively. of 2.340 and 2.181 A Bornite, Cu5FeS4, occurs in three polymorphic forms: low-, intermediate-, and hightemperature structural forms [9]. The high form is stable above 228 C and has cubic ˚ and space group Fm3m; and the low form is tetragonal with symmetry with a ¼ 5.50 A ˚ and space group P421c [10]. The intermediate form occurs a ¼ 10.94 and c ¼ 21.88 A  ˚ [11]. Sulfur atoms form an below 228 C and has the space group Fd3m with a ¼ 10.94 A ideal face-centered cubic closest packing, and metal atoms are distributed statistically in the tetrahedral sites of sulfur atoms. The superstructure cell for bornite is Cu32Fe16S32 ˚ and (Fig. 2.1C), and S atom has four-coordinate Cu atom with the bond length of 2.234 A ˚ eight-coordinate Fe atom with the bond length of 2.230 A. The crystal structure of chalcocite (Cu2S) is complex with three phases [12], a monoclinic phase called low chalcocite below 103.5 C, a hexagonal phase called high chalcocite between the previous temperature and 436 C, and a cubic phase above this temperature. The unit cell of low chalcocite contains 48 Cu2S with 144 atoms (Fig. 2.1D). The coordination number of chalcocite Cu atom varies from three to six. The S atoms are mainly in sixfold coordination and partly in fivefold coordination. The fourfold and threefold coordinated Cu atoms are coordinated with sixfold S atoms, and the fivefold and sixfold coordination Cu atoms are coordinated with sixfold and fivefold S atoms.

2.1.2 Computational methods The four copper sulfides have several polymorphs; here, we choose the common polymorph in nature to simulate. Chalcopyrite (CuFeS2) crystallizes in the tetragonal ˚ and group (space group of I42d) with the lattice parameters of a ¼ b ¼ 5.289 A ˚ [13]. The space group of bornite (Cu5FeS4) is Fd3m and the lattice c ¼ 10.423 A ˚ and a ¼ b ¼ g ¼ 90 [10]. Covellite (CuS) has a parameters are a ¼ b ¼ c ¼ 10.940 A ˚ and c ¼ 16.341 A ˚ [8]. Chalcocite (Cu2S) space group of P63/mmc with a ¼ b ¼ 3.794 A ˚ , b ¼ 11.884 A ˚, crystallizes in space group of P21/c with lattice parameters of a ¼ 15.246 A  ˚ , and b ¼ 116.35 [14]. c ¼ 13.494 A Geometry optimizations of four copper sulfides were performed using the Cambridge Serial Total Energy Package (CASTEP) [15] and DMol3 [16], which are first-principle pseudopotential methods based on density functional theory (DFT). The interactions between valence electrons and the ionic core were represented by ultrasoft pseudopotentials. After testing, the exchange correlation function and the cutoff energy of the plane wave basis were determined, and the optimized results of four copper sulfides are shown in Table 2.1. It is found that the calculated lattice parameters agree well with the experimental values.

16 Chapter 2 Table 2.1: Lattice parameters of the bulk copper sulfide. Calculated ˚) values (A

Functions Chalcopyrite (Cu4Fe4S8) Bornite (Cu32Fe16S32) Covellite (Cu6S6)

GGA-PW91 [17] (280 eV) GGA-PW91 (280 eV) GGA-WC [18] (270 eV) GGA-PW91 (300 eV)

Chalcocite (Cu96S48)

a ¼ b ¼ 5.262 c ¼ 10.379 a ¼ b ¼ c ¼ 10.698 a ¼ b ¼ 3.778 c ¼ 16.363 a ¼ 15.267 b ¼ 12.035 c ¼ 13.498 b ¼ 116.29

˚) Experimental values (A a ¼ b ¼ 5.289 [13] c ¼ 10.423 a ¼ b ¼ c ¼ 10.940 [10] a ¼ b ¼ 3.796 [8] c ¼ 16.360 a ¼ 15.246 [14] b ¼ 11.884 c ¼ 13.494 b ¼ 116.35

2.1.3 The electronic properties of copper sulfide The band structures and density of states (DOS) for the four kinds of copper sulfides are shown in Figs. 2.22.5, and the Fermi level (EF) is set to the zero point. The calculated result indicates that there is no spin DOS for chalcopyrite and bornite. For chalcopyrite, it is found from Fig. 2.2 that both the valence band maximum and conduction band minimum of the ideal chalcopyrite are located at the G point, which suggests that chalcopyrite is a p-type semiconductor. As the Fermi level enters into the valence band, it indicates that chalcopyrite is a degenerate semiconductor, which is consistent with the report of Fujisawa [19].

Energy (eV)

10

10

5

5

0

0

–5

–5

–10

–10

–15

–15

–20

Z

A

M

G

Z

R

X G

s p d

EF

–20 0

2 4 6 8 10 Density of States (electrons/eV)

Figure 2.2 Band structure and DOS of chalcopyrite.

Electronic properties of sulfide minerals and floatability 17

Figure 2.3 Band structure and DOS of covellite.

6

0

0

–6

–6

–12

–12

Energy (eV)

6

–18

X

R

M

G

R

s p d EF

–18 0

5 10 15 20 25 30 35 Density of States (electrons/eV)

Figure 2.4 Band structure and DOS of bornite.

18 Chapter 2 6

0

0

–6

–6

–12

–12

Energy (eV)

6

–18

s p d

X

R

M

G

R

EF

–18 0

5 10 15 20 25 30 35 Density of States (electrons/eV)

Figure 2.5 Band structure and DOS of chalcocite.

The DOS shown in Fig. 2.2 indicates that the conduction bands of chalcopyrite are derived from Cu 4s and Fe 4s states. The lower valence bands located from 14.5 to 12.5 eV are composed of S 3s states, and the upper parts from 6.5 to 2.4 eV are mainly composed of Cu 3d states, mixed with Fe 3d and S 3p states. The DOS of covellite is shown in Fig. 2.3. The deep valence bands consist of three parts: (a) bands from 16.3 to 12.3 eV are contributed by the 3s states of S2f and S3f atoms; (b) bands from 7.6 to 1.1 eV are composed mainly of Cu 3d states, mixed with S 3p states; and (c) bands from 2.6 to 7.4 eV are derived from 4s states of Cu1 atom and 3p states of S2 atom. The bands locate at 1.1e2.7 eV connecting the conduction and valence bands are composed mainly of 3p states mixed with 2s states of S2 atom, which greatly improves the electrical conductivity of covellite. The band structure and DOS of bornite are shown in Fig. 2.4. In the valence band, the bands from 16.7 to 11.9 eV are derived from S 3s states, and the bands from 8.7 to 3.9 eV are derived from S 3p states. In addition, the bands from 3.9 to 1.8 eV mainly consist of Cu 3d and Fe 3d states and partly of S 3p states. The conduction bands are from 1.8 to 4.5 eV. As previously pointed out, the copper atoms in the unit cell of chalcocite have fivefold and sixfold coordination, called as Cu1 and Cu2, respectively. It is found from Fig. 2.5 that the lower part of the valence bands from 8.7 to 0 eV is derived from S 3s states. The upper valence bands from 15.4 to 12.9 eV are mainly composed of the hybridization state of Cu2 3d, Cu1 3d, and S 3p states. The conduction bands consist of Cu 4s and S 3p states.

Electronic properties of sulfide minerals and floatability 19 The calculated band structures of chalcocite, covellite, and bornite show that their conduction band and the valence band intersect, indicating that they are conductors with good electrical conductivity [6,14,20,21], while chalcopyrite is a narrow band gap semiconductor exhibiting a similar property with metallic. The research [22]shows that electrons near the Fermi level are more active, and the important physical and chemical reactions often occur near the Fermi level. It is noted that for chalcopyrite the bands near the Fermi energy level are contributed by S 4p and Fe 3d orbital, for covellite that are mainly composed of S 3p states mixed with Cu 3d states, for bornite that are derived from Cu 3d and S 3p states, and for chalcocite that are mainly composed of Cu 4s states mixed with S 3p states. It could be concluded that in chalcopyrite, iron and sulfur atoms exhibit more reactivity than copper atom, and in chalcocite, copper atom will show the greatest reactivity, and in covellite the most reactive atom is the sulfur atom, and in bornite, copper and sulfur atoms are the most reactive atoms.

2.1.4 Bonding analysis of copper sulfide minerals The bonding energy level generally appears around the Fermi level, and the contribution of deeper energy level to the bonding is relatively weak. In addition, it is observed that d orbital splits into t2g and eg orbitals in the crystal field, especially at the Fermi level. Therefore, the analysis of the DOS near the Fermi level would give a better understanding of the interaction between orbitals and the strength of the bonding. For chalcopyrite, the DOS for CueS and FeeS bonding are shown in Fig. 2.6. The tetrahedral field results in the split of Cu 3d and Fe 3d orbitals into two terms, e and t2, and the split of Cu 3d orbital is weaker than that of Fe 3d orbital as the bands of Cu 3d orbital are located far away from the Fermi level, while bands of Fe 3d orbital are concentrated at the Fermi level. For the CueS bonding, the lower valence bands, from 6.71 to 3.74 eV, are the Cu 4s and S 3p bonding states. The resonance of Cu 3d (e) with S 3p orbital is weak at energies between 4.0 and 4.5 eV, and the bonding of Cu 3d (e) and S 3p is weakened. The upper valence bands from 3.38 to e1.0 eV are the Cu 3d (t2) and S 3p states, and bands from e1.0 to e0.4 eV are the Cu 3d (e*) and S 3p antibonding states. For the FeeS bonding, the Fe 3d (eg) and S 3p bonding states appear from 6.63 to 3.72 eV, and a hybridized peak located at 4.5 eV strengthens the bonding effect between Fe 3d (eg) and S 3p orbitals. Bands from 3.01 to 0.37 eV are the weak Fe 3d (t2g) and S 3p bonding states. The strong antibonding states of Fe 3d (eg*) and S 3p are observed from 0.37 to 1.56 eV.

20 Chapter 2 4 Cu-S

Cu 4s S 3p Cu 3d

Density of States (electrons/eV)

3

EF

t2g

2 eg 1 eg* 0 –10

–8

–6

–4

–2

0

2

4 Fe-S 3 2

Fe 4s S 3p Fe 3d eg

eg*

t2g

1 0 –10

–8

–6

–4 Energy (eV)

–2

0

2

Figure 2.6 DOS of the bonding atoms in chalcopyrite.

In chalcopyrite (Fig. 2.6), the bonding between Cu and S is mainly contributed by S 3p and Cu 3d orbitals, and partly by Cu 4s orbitals, while that for FeeS bonding is mainly contributed by S 3p and Fe 3d orbitals. Since the outer electron configuration for Cu atom is 3d104s1 and the half-full of 4s orbital makes it easy to participate in the bonding process, and since the outer electron configuration of Fe atom is 3d64s2 with a full-filled 4s orbital, Fe 4s orbital has to participate in the bonding process. Both the bonding and antibonding for the CueS bond are relatively weak, while for FeeS bond the bonding and antibonding are strong. The bond length and value of Mulliken population of CueS bond ˚ and 0.34, and that of FeeS bond are 2.159 A ˚ and 0.46. It is suggested that the are 2.329 A covalent characteristic of CueS bond is weaker than FeeS bond, so in the crush and grinding process of chalcopyrite, the CueS bond is easier to break than FeeS bond, which results in a chalcopyrite surface with a relatively strong hydrophobic property. The covellite belongs to the hexagonal system. In the structure of covellite, the coordination numbers for copper atoms are three and four, and the threefold Cu atom is coordinated with fivefold S atom, and the fourfold Cu atom is coordinated with fourfold S atom. The DOS for two kinds of bonding are shown in Fig. 2.7. An apparent split of Cu 3d orbital is observed, and bands from 7 to 4.0 eV are Cu 3d (eg) and S 3p bonding

Electronic properties of sulfide minerals and floatability 21 EF

8 6

Cu 4s S 3p p Cu 3d

CU(3)-S(5)

t2g

Density of States (electrons/eV)

4 eg 2 0 –10 8 6

e*g

–8

–6

CU(4)-S(4)

Cu 4s S 3p p Cu 3d

4

–2

–8

–6

0

2

0

2

t2g

eg

2 0 –10

–4

–4 Energy (eV)

e*g

–2

Figure 2.7 The DOS of CueS bonding with different coordination for covellite. (The numbers given in brackets are coordination numbers.)

states, and bands from 1.8 to 1.0 eV are Cu 3d (eg*) and S 3p antibonding states. The Cu t2g orbital is a nonbonding orbital. In the case of fourfold Cu atom, the split of Cu 3d is smaller than that of threefold Cu atom, and the overlap of Cu 3d (eg) and S 3p states between 7 and e3 eV is not very good. It is indicated that the strength of Cu4feg e S 3p is weaker than that of Cu3feg e S 3p, and consequently, the bond length of Cu4f e S is ˚ ) longer than that of Cu3f e S (2.181 A ˚ ). (2.340 A Considering the strength of CueS bonding in covellite, it is inferred that in the flotation process, there will be more fourfold Cu atoms exposing to the surface than threefold Cu atoms due to the weak bonding of Cu4fdS, which results in a relative strong hydrophobic feature of the surface. In the bornite crystal, the coordination numbers of copper atom and iron atom are four and seven, respectively, and the density of states for CueS bonding and FeeS bonding are shown in Fig. 2.8. Notice that an obvious split of four-coordinated Cu d orbital in the tetrahedron field and a weak bonding between Cu 3d eg and S 3p orbital appears around 7.0 to 4.0 eV. The bands from 4.0 to 2.5 eV are the antibonding of Cu 3dt2g. The antibonding between Cu eg* antibonding orbital and S 3p orbital appears around 2.5 to

22 Chapter 2 Bornite (Cu5FeS4) 4 Cu-S

Density of States (electrones/eV)

EF

Cu 4s S 3p Cu 3d

3 2 1 0 –10 2.5

–8 Fe-S

–6

–4

–2

0

2

–2

0

2

Fe 4s S 3p Fe 3d

2.0 1.5 1.0 0.5 0.0 –10

–8

–6

–4 Energy (eV)

Figure 2.8 The DOS of CueS and FeeS bonding for bornite.

1.0 eV, which shows an obvious hybrid peak enhancing the antibonding between Cu and S atoms. Consequently, the bonding between Cu and S atoms is relatively weak in bornite crystal. A greater split of d orbital of the seven-coordinated Fe atom is observed in the pentagonal double cone coordination field. The bands from around 7.0 to 4.0 eV are the bonding states of Fe 3d e S 3p, and bands from 4.0 to 2.0 eV are the antibonding states of Fe 3d e S 3p. Several hybridized peaks are found in the antibonding region, suggesting that the FeeS antibonding is relatively strong. According to the preceding analysis, it is concluded that the CueS bonding is weaker than the FeeS bonding in the bornite crystal, indicating that in the grinding process the breaking of CueS bond occurs more easily. As previously pointed out, the crystal structure for chalcocite is very complicated, as the coordination number of copper atom varies from three to six and the unit cell of chalcocite contains as many as 144 atoms. The DOS of CueS bonding between sixfold S and Cu atom with different coordination numbers is shown in Fig. 2.9. In a ligand field view, different coordination numbers correspond to different symmetric fields; for example, the three coordination corresponds to a triangle symmetry field; the four coordination represents a tetrahedron symmetry field; the five coordination corresponds to a pentagon double cone or tetragonal pyramid; and the six coordination has an octahedral field.

Electronic properties of sulfide minerals and floatability 23 6 Cu 4s S 3p Cu 3 d

4

Cu(6)-S

2

Density of States (electrons/eV)

0 –8

–6

–4

–2

0

–8

–6

–4

–2

0

Cu(4)-S

2

0 6 –8

–6

–4

–2

0

Cu(3)-S

2

–6

–4

–2

0

4

Cu(5)-S

2

2 0 4 2

4 2 0 –8

2

Energy (eV)

Figure 2.9 DOS of CueS bonding with different coordination number of Cu atoms in chalcocite. (The numbers given in brackets are coordination numbers.)

Generally, the lower the symmetry is, the greater the split of d orbital. Beside the effect of ligand field, atoms in the chalcopyrite crystal will be affected by the crystal field at the same time. Hence, the split of d orbital in chalcopyrite will be affected in combination of ligand field with the crystal field. It is noted from Fig. 2.9 that the splits of Cu d orbital with different coordination numbers are roughly identical, and the split of Cu d orbital in triangle and octahedral field are relatively weak, while that in hexagonal and threepentagon double cone fields is relatively strong. It is shown in Fig. 2.9 that bands from 7.0 to 6.03 eV are the bonding states of Cu (4s) and S (3p). The bands around 6.0 to 4.0 eV are the bonding states of Cu 3d (eg) and S (3p). The bands from 4.0 to 2.0 eV are derived from the Cu 3d t2g nonbonding states. The upper valence bands, from 2.0 to 0 eV, are the Cu 3d (eg*) and S (3p) antibonding states.

2.1.5 Frontier orbitals The atomic orbital coefficients of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the four copper sulfides are presented in

24 Chapter 2 Table 2.2: Frontier orbital coefficients of four copper sulfides. Frontier orbital Chalcopyrite (Cu4Fe4S8) Bornite (Cu32Fe16S32) Covellite (Cu6S6) Chalcocite (Cu96S48)

HOMO LUMO HOMO LUMO HOMO LUMO HOMO LUMO

Atomic orbital coefficient of HOMO and LUMO 0.436 Fe þ 0.141 S þ 0.107 0.358 Fe þ 0.276 S þ 0.107 0.146 Fe  0.124 S þ 0.079 0.189 S  0.103 Fe  0.091 0.381 S þ 0.223 Cu 0.424 S þ 0.418 Cu 0.075 S  0.063 Cu 0.061 S þ 0.091 Cu

Cu Cu Cu Cu

Table 2.2. Here, the positive and the negative sign represent bonding and antibonding between the atoms, but we only concerned with the absolute value of the coefficient: the greater the coefficient, the greater the contribution of the atom to orbital reactivity. It is found from Table 2.2 that for the Fe-containing copper sulfide (chalcopyrite and bornite), Fe atoms have the greatest coefficient in HOMO orbital, suggesting that Fe atoms would exhibit greater reactivity than Cu atoms. For the copper sulfide without Fe element (covellite and chalcocite), the coefficients of S atoms are the greatest for the HOMO orbital, indicating that S atoms are easy to be oxidized to form element sulfur, which would enhance the surface hydrophobicity. Hence, covellite and chalcocite have better floatability than chalcopyrite and bornite. For the LUMO orbital of chalcopyrite, the coefficient of Fe atom is still the greatest, implying that the Fe atom may show reducibility. The X-ray absorption near-edge structure (XANES) spectra of chalcopyrite implies that some part of copper and iron is divalent [23]. For the LUMO orbital of bornite, the S atom has the greatest coefficient, which may be related to the oxidation state of S atoms. For the LUMO of covellite, the contribution of S and Cu atoms is similar. This may ascribe to the two types of valence state of S and Cu atoms in the covellite [8,24]: Cuþ, Cu2þ, S2, and [S2]2. For the chalcocite, the coefficients for both Cu and S atoms are small, which is ascribed to the large supercell structure with 144 atoms. The contribution of the S atom in the HOMO orbital is the greatest, and that of the Cu atom in the LUMO orbital is the greatest. The bonding in copper sulfides cannot be correctly described in terms of a simple oxidation state formalism because the CueS bonds are somewhat covalent rather than ionic in character, and they have a high degree of delocalization resulting in complicated electronic band structures. Although many textbooks give the mixed valence formula (Cuþ) (Cu2þ) (S2) (S2)2 for CuS, X-ray photoelectron spectroscopic data [25] give strong evidence that, in terms of the simple oxidation state formalism, all the known copper sulfides should be considered purely monovalent copper compounds, and more appropriate formulae would be (Cuþ)3(S2) (S2) for CuS, and

Electronic properties of sulfide minerals and floatability 25 Table 2.3: Frontier molecular orbital energies for copper sulfide minerals and oxygen. Energy/eV Chalcopyrite Chalcocite Covellite Bornite Oxygen

HOMO LUMO HOMO LUMO HOMO LUMO HOMO LUMO HOMO LUMO

DE1/eV 5.622 4.883 4.602 1.538 3.096 1.887 4.696 4.098 6.900 4.610

DE2/eV

1.022

2.017

0.002

5.362

1.504

5.013

0.096

2.802

O O2 Mineral 2 Annotation: DE1 ¼ EMineral HOMO ELUMO ; and DE2 ¼ EHOMO ELUMO

(Cuþ) (S2) for CuS2, respectively [26]. However, copper atom coefficients in HOMO and LUMO shown in Table 2.2 indicate that copper atom shows oxidative (LUMO) and reductive (HOMO) states, suggesting that the Cu atom should be mixed valence. Frontier molecular orbital (FMO) theory simplifies reactivity into interactions between the HOMO of one species and the LUMO of the other, and the lower the absolute DE between HOMO and LUMO, the stronger the interaction. Table 2.3 indicates that the values of DE1 are less than DE2, suggesting that oxidation of copper sulfide occurs between HOMO of mineral and LUMO of oxygen. DE1 values suggest that the interaction between chalcocite and oxygen molecules is the strongest, followed by bornite, and then chalcopyrite, and covellite is the weakest. It has been reported in the literature [27] that the oxidation order for copper sulfide minerals is chalcocite > bornite > chalcopyrite > covellite, which is in agreement with the FMO prediction.

2.1.6 Floatability and electronic properties for copper sulfide minerals Energy band structure calculation results suggest that the covellite, bornite, chalcocite, and chalcopyrite are narrowband semiconductors, having metal characteristic. In general, electrons near Fermi level are the most reactive, and the most important physical and chemical reactions always occur near Fermi level of metal [22]. In the process of flotation, electrons near the Fermi level have a high chemical activity and are easily involved in the surface reaction, such as collector adsorption and oxidation reactions. The DOS near Fermi level for copper sulfide minerals are shown in Fig. 2.10. From Fig. 2.10, the following is found: (1) For copper sulfide minerals containing iron, chalcopyrite, and bornite, the electronic DOS near the Fermi level is mainly composed by Fe 3d states, which have stronger reactivity, so copper sulfide minerals containing iron have similar properties with iron

26 Chapter 2 Cu 3d

2

Density of states /electrons.eV-1

Fe 3d

Chalcopyrite CuFe2S2

S 3p

0 2

Bornite Cu5FeS5

Cu 3d Fe3d S 3p

0 2

Cu 3d

Chalcite Cu2S

S 3p

0 2

Covellite

Cu 3d

CuS S 3p

0 -2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Energy/eV

Figure 2.10 Density of states near Fermi level for copper sulfide minerals.

sulfide minerals. For example, chalcopyrite and bornite are easily depressed by lime and cyanide. This is mainly because the outer electrons of the copper atom are 3d10, which is full, so copper atom has low reactivity. For iron atom, the outer electrons are 3d6, which has an unoccupied orbital, so iron atom shows more reactivity. (2) For copper sulfide minerals not containing iron, near the Fermi level, electronic DOS of copper atoms in chalcocite and covellite are higher than that of in chalcopyrite and bornite, suggesting that copper atoms in chalcocite and covellite are more reactive than that of in chalcopyrite and bornite, thus chalcocite and covellite show better floatability than chalcopyrite and bornite. From the distribution of Cu 3d DOS, chalcocite and covellite have a similar Cu 3d state, which may result in similar floatability. Cu 3d state of bornite locates in the deeper energy region, indicating the most stable electronic state and weakest reactivity. The literature [28] has reported its floatability is poorer than chalcocite, chalcopyrite, and covellite (3) DOS of S atom near the Fermi level shows that S 3p states of chalcopyrite, bornite, and covellite are higher than that of chalcocite, suggesting that S atom of chalcocite exhibits lowest reactivity. It has been found that the following oxidation reactions occur for chalcopyrite, chalcocite, and covellite [29]: CuFeS2 þ 3H2O ¼ CuS þ Fe(OH)3 þ S0 þ 3Hþ þ 3e CuS þ 2H2O ¼ Cu(OH)2 þ S0 þ 2Hþ þ 2e Cu2S þ 2H2O ¼ Cu(OH)2 þ CuS þ 2Hþ þ 2e

ð2:1Þ ð2:2Þ ð2:3Þ

Electronic properties of sulfide minerals and floatability 27 Table 2.4: Fermi level of copper sulfide. Minerals EF/eV

Chalcopyrite 5.4

Chalcocite 4.6

Covellite 2.9

Bornite 4.6

According to these reactions, it is found that sulfur atoms in chalcopyrite and covellite both are oxidized, from S2 to S0; however, the valence state of sulfur in chalcocite stays the same, which is still e2. The Fermi level is the total chemical potential for electrons and is usually denoted by m or EF Fermi level is the average electrochemical potential of electrons; from the statistical point of view, the Fermi level is the sign that the quantum state is occupied or unoccupied by electrons. The position of the Fermi level with the relationship to the band energy levels is a crucial factor in determining electrical properties. According to the chemical potential definition, electrons always flow from high Fermi level to low Fermi level. Table 2.4 lists the Fermi level for chalcopyrite, chalcocite, covellite, and bornite. It is found from Table 2.4 that chalcopyrite has the lowest Fermi level, suggesting that chalcopyrite is the easiest to obtain electrons. Covellite has the highest Fermi level, indicating that covellite is the easiest to lose electrons. The Fermi level of n-butyl xanthate is calculated as 5.2 eV, which is higher than that of chalcopyrite, and lower than that of chalcocite, bornite, and covellite. These suggest that electrons of xanthate are easily transferred to chalcopyrite, resulting in the formation of dixanthogen on chalcopyrite surface; however, due to the higher Fermi level of xanthate, the electrons cannot be transferred to other copper sulfide minerals, indicating that dixanthogen cannot form on chalcocite, bornite, or covellite surface. Tests show that surface product of xanthate on chalcopyrite is dixanthogen, and copper xanthate on chalcocite, bornite, and covellite [28,29].

2.2 Crystal structure and electronic properties of iron sulfide minerals There are three kinds of iron sulfides in nature: pyrite, marcasite, and pyrrhotite, which exist widely in the nonferrous metal ore and coal containing sulfur. Although they have the same Fe and S atoms in lattice, it is found that their lattice structure and physical and chemical properties are completely different. In flotation practice, marcasite shows the best floatability in the presence of xanthate, followed by pyrite, and pyrrhotite is the worst. In addition, there are different oxidation behaviors for pyrite, marcasite, and pyrrhotite. Of them, pyrrhotite is most easy to be oxidized, followed by marcasite, and pyrite is most difficult to be oxidized. As we know, marcasite and pyrite have the same chemical formula: FeS2, and the chemical formula of pyrrhotite is Fe1xS; they have the same cationic atoms, Fe atom. It would be difficult to explain the different flotation behaviors only from the chemical reaction between xanthate and iron atom. The most difference derives from the lattice structure. In this section, the floatability of iron sulfides is discussed from the lattice structure and electron properties.

28 Chapter 2

2.2.1 Crystal structure and floatability of iron sulfides Pyrite crystallizes in the cubic structure and belongs to the space group Pa3. Under thermodynamic standard conditions, the lattice constant of stoichiometric iron pyrite FeS2 ˚ . The unit cell is composed of a Fe face-centered cubic sublattice into amounts to 5.412 A which the S ions are embedded. In the first bonding region, the Fe atoms are surrounded by six S nearest neighbors, in a distorted octahedral arrangement. The material is a diamagnetic semiconductor, and the Fe ions should be considered to be in a low-spin divalent state rather than a tetravalent state as the stoichiometry would suggest the S ions in FeS2 are shifted from these high symmetry positions along axes to reside on (uuu) and symmetry-equivalent positions. Here, the parameter u should be regarded as a free atomic parameter that takes different values in different pyrite-structure compounds. Both low-spin Fe2þ and the disulfide S2 2 moieties are closed shell entities, explaining the diamagnetic and semiconducting properties. The S atoms have bonds with three Fe and one other S atom. The site symmetry at Fe and S positions is accounted for by point symmetry groups C3i and C3, respectively. The missing center of inversion at S lattice sites has important consequences for the crystallographic and physical properties of iron pyrite. These consequences derive from the crystal electric field active at the sulfur lattice site, which causes a polarization of S ions in the pyrite lattice. The mineral marcasite, sometimes called white iron pyrite, is iron sulfide (FeS2) with orthorhombic crystal structure. It is physically and crystallographically distinct from pyrite, which is iron sulfide with cubic crystal structure. Both structures do have in common that they contain the disulfide S2 2 ion having a short bonding distance between the sulfur atoms. The structures differ in how these dianions are arranged around the Fe2þ cations. Marcasite is lighter and more brittle than pyrite. Specimens of marcasite often crumble and break up due to the unstable crystal structure. Pyrrhotite is an iron sulfide mineral with the formula Fe(1x)S (x ¼ 0 e 0.2). Pyrrhotite is also called magnetic pyrite, because the color is similar to pyrite and it is weakly magnetic. Pyrrhotite exists as a number of polytypes of hexagonal or monoclinic crystal symmetry; several polytypes often occur within the same specimen. Their structure is based on the NiAs unit cell. As such, Fe occupies an octahedral site and the sulfide centers occupy trigonal prismatic sites. The ideal FeS lattice is nonmagnetic. Magnetic properties vary with Fe content. More Fe-rich, hexagonal pyrrhotites are antiferromagnetic. However, the Fe-deficient, monoclinic Fe7S8 is ferrimagnetic. The ferromagnetism that is widely observed in pyrrhotite is therefore attributed to the presence of relatively large concentrations of iron vacancies (up to 20%) in the crystal structure. Vacancies decrease the crystal symmetry. Therefore, monoclinic forms of pyrrhotite are in general more defect-rich than the more symmetrical hexagonal forms, and thus are more magnetic. Unit cell models for pyrite, marcasite, and pyrrhotite are shown in Fig. 2.11.

Electronic properties of sulfide minerals and floatability 29

Figure 2.11 Unit cell structures of pyrite (A), marcasite (B), and pyrrhotite (C).

Oxygen consumption/(mL•g–1)

12 11

40°C

10 9 pyrrhotite

8 7

marcasite

6 5 4 3

pyrite

2 1 0

2 3 4 Oxidation time/h

5

Figure 2.12 Relationship between oxidation time and oxygen consumption for pyrite, marcasite, and pyrrhotite [30].

Fig. 2.12 shows that pyrrhotite has the maximum oxygen consumption, followed by white iron; the worst is pyrite, which suggests that pyrrhotite is most likely to be oxidized, followed by marcasite, and the oxidation of pyrite is weakest. Fig. 2.13 shows the results of flotation of pyrite, marcasite, and pyrrhotite in a humid atmosphere of 40 C after the interaction of these three minerals with oxygen. The samples

30 Chapter 2 100

Flotation recovery/%

90 80

pyrite

70 60

marcasite

50 40 30

pyrrhotite

20 10 0

0

0.1 0.2 0.3 0.4 0.5 Oxygen concentration/(mg•L–1)

Figure 2.13 The effect of oxidation on the recovery of pyrite, marcasite, and pyrrhotite under moist air [30].

were transferred to a vacuum dryer to remove water, and then flotation was carried out with xanthate. Higher concentration of oxygen indicates the stronger oxidation of mineral surface. Results suggest that moderate oxidation is favorable for the flotation of iron sulfides, but excess oxidation is detrimental. As shown in Fig. 2.13, the flotation recovery of three kinds of iron sulfides is increased with the increase of oxygen concentration. The flotation recovery begins to decrease when oxygen concentration is up to a certain concentration. Further, it is found that moist air has the greatest influence on the pyrite recovery, followed by marcasite, with the last being pyrrhotite. The interacting products of xanthate on pyrite, marcasite, and pyrrhotite surface have been found to be dixanthogen. Generally, moderate oxidation could cause the surface electrons to be depleted, which is favorable for the adsorption of xanthate; the excess oxidation would destroy the mineral surface as well as result in the formation of hydrophilic chemicals, hence decrease the adsorption of xanthate.

2.2.2 Band structure of iron sulfides Band structures of pyrite, marcasite, and pyrrhotite are shown in Fig. 2.14, Figs. 2.15 and 2.16, respectively. Results suggest that pyrite is an indirect band gap semiconductor, and the calculated gap is 0.58 eV, less than the experimental value of 0.95 eV [31]; marcasite is also an indirect band gap semiconductor, and the calculated gap is 0.98 eV, greater than the experimental value of 0.40 eV [32]; The conducting band intersects with the valence band for pyrrhotite, which is a conductor and easy to interact with oxygen. The band structure of pyrite is shown in Fig. 2.14. It is found that the band of pyrite is divided into five parts: two groups of valence bands from 17eV to 10 eV are composed of a large number of S 3s and only a small amount of S 3p orbitals; The band from 7.5 to e1.5 eV is composed of a large amount of S 3p orbitals and a few Fe 3d

Engery/eV

Electronic properties of sulfide minerals and floatability 31 5

5

0

0

-5

-5

-10

-10

-15

-15

-20

X

R

M

G

R

EF

S 3s S 3p Fe 4s Fe 3d

-20 0

2

4

6

Density of states /electron. eV-1

Figure 2.14 Band structure and DOS of pyrite. 10

5

5

0

0

-5

-5

-10

-10

-15

-15

Energy/eV

10

-20

G

Z

T

Y X

S

U

R

EF S 3s S 3p Fe 4s Fe 3d

-20 0

2

4

Density of states/electrons. eV

6 -1

Figure 2.15 Band structure and DOS of marcasite.

orbitals. The top valence band is mainly composed of S 3p orbitals and Fe 3d orbitals; Conduction bands are mainly composed of S 3p and Fe 3d orbitals, and a few S 3s and Fe 4p orbitals are also found in conduction bands. The band structure near the Fermi level is mainly composed of Fe 3d orbitals. In addition, Fe 4s orbitals have very small contribution to the band structure.

Energy/eV

32 Chapter 2

0

0

-5

-5

-10

-10

-15

GA

H K

G

M L H

EF

S 3s S 3p Fe 4s Fe 3d

-15 0

2

4

6

Density of states/electrons . eV-1

Figure 2.16 Band structure and DOS of pyrrhotite.

Band structure of marcasite is shown in Fig. 2.15. It is found that two groups of valence bands from 17 to 11.5 eV are almost composed of S 3p orbitals, and a small amount of S 3p orbital is also found here. The band structure below the top of valence, also called Fermi level, is composed of S 3p and Fe 3d orbitals; conduction band from 0.5 to 4 eV is composed of S 3p and Fe 3d orbitals; the conduction band from 5.0 to 11 eV is mainly composed of Fe 4s, Fe 4p orbitals. The band structure near Fermi level is mainly composed of Fe 3d orbitals. The band structure of pyrrhotite is shown in Fig. 2.16. It is found that band structure of pyrrhotite is divided into two parts: The band located from 15 to 12 eV is almost composed of S 3s orbitals, and the band located from 7.5 to 2.5 eV is largely composed of S 3p and Fe 3d orbitals, and a very small amount of Fe 4s and Fe 4p orbitals are also found here. The band structure near Fermi level is composed of a large amount of Fe 3d orbitals and a very small amount of S 3p orbitals. Generally, the reactivity of electrons near the Fermi level is the highest. From the DOS shown in Fig. 2.14, Figs. 2.15 and 2.16, it is found that Fe 3d orbitals of pyrite, marcasite, and pyrrhotite all have the largest contribution near the Fermi level, and Fe 3d orbital of pyrite has the greatest contribution, followed by marcasite, with the last being pyrrhotite. Therefore, the Fe atom of pyrite is most reactive, and reactivity of pyrrhotite Fe atom is the weakest. In the flotation process, pyrite is easy to be depressed by cyanide and lime, while pyrrhotite is difficult to be depressed.

Electronic properties of sulfide minerals and floatability 33

2.2.3 Spin polarization of iron sulfide Spin DOS of pyrite, marcasite, and pyrrhotite is shown in Fig. 2.17, respectively. It is found that pyrite and marcasite both are low-spin state, but pyrrhotite is spin polarization state, which is mainly composed of Fe 3d orbitals near the Fermi level. Compared with pyrite and marcasite, pyrrhotite with spin polarization state is easier to react with paramagnetic oxygen molecule, so pyrrhotite is the easiest to be oxidized for all iron sulfide minerals.

2.2.4 Bonding between S and Fe atoms Fig. 2.18 shows that DOS in deep level in range of 17 to 10 eV are mainly composed of S atoms. Due to the presence of disulfide S2 2 in the pyrite and marcasite lattice, we can find bonding and antibonding between two sulfur atoms in the range of 17 to 10 eV, however there is no bonding interaction for pyrrhotite due to only single sulfur atoms in the lattice. For pyrite, interaction between S 3p and Fe 3d orbitals in the range of 5.0 to 1.5 eV is the bonding interaction between S 3p orbital and eg orbital of Fe 3d, where the antibonding state is in the range of 1.2 to 4.0 eV. The t2g nonbonding orbital of Fe 3d is found in the range of 1.0 to 0.5 eV. Marcasite has similar bonding states with pyrite except for t2g splitting and broadening near the Fermi level, which suggests that Fe 3d orbital in the orthorhombic system (marcasite) splits easier than that in cubic system (pyrite). (A)

(B)

Density of states (electrons/eV)

30

(C)

30

Ef

sum alpha sum beta d alpha d beta

20

20

30

Ef

sum alpha sum beta d alpha d beta

20

10

10

10

0

0

0

-10

-10

-10

-20

-20

-20

-30

-30

-30

-20

-15

-10

-5

Energy/eV

0

5

10

-20 -15 -10

-5

0

Energy/eV

5

10

15

-20

Ef

sum alpha sum beta d alpha d beta

-15

-10

-5

Energy/eV

Figure 2.17 Spin density of states of (A) pyrite, (B) marcasite, and (C) pyrrhotite.

0

5

34 Chapter 2 6

S 3s S 3p Fe 4s Fe 3d

Pyrite

Density of states / electrons. eV-1

4

4

-15

-10

-5

4

0

Marcacite

e*g

eg -15

5

t2g

2 0 -20 6

e*g

eg

2 0 -20 6

EF

t2g

-10

-5

0

5

-5

0

5

Pyrrhotite

2 0 -20

-15

-10

Energy/eV

Figure 2.18 Density of states between FeeS bond of pyrite, marcasite, and pyrrhotite.

Fe 3d orbitals of pyrrhotite are very different from those in pyrite and marcasite: at first, Fe 3d orbitals of pyrrhotite split incompletely; then, bonding and antibonding states between S 3p and Fe 3d orbital split incompletely, suggesting weak bonding interaction. From the preceding analysis, FeeS bonding in the pyrite lattice is the strongest, and SeFe antibonding in marcasite lattice is the strongest; moreover the gap between SeFe bonding and antibonding in marcasite lattice is less than that of pyrite, so SeFe bonding in marcasite is less than that in pyrite. The SeFe bonding in pyrrhotite lattice is the weakest. ˚ SeFe bond lengths in pyrite, marcasite, and pyrrhotite are 2.191, 2.231, and 2.271 A respectively, which is the corresponding order with the SeFe bonding strength. From bonding strength, it can be concluded that pyrite has the maximum hardness (Mohs hardness: 6e6.5), followed by marcasite (Mohs hardness: 5e6), and the last is the pyrrhotite (Mohs hardness: 3.5e4.5). Pyrrhotite is fragile and easy to slime in mineral processing, so magnetic separation is good to use to remove the pyrrhotite to prevent the sliming of pyrrhotite in the process of grinding, which would worsen the flotation concentrate quality result when pyrrhotite content is high.

2.2.5 Bond Mulliken population The bond overlap population may be used to assess the covalent or ionic nature of a bond. A large value of the bond population indicates a covalent bond, while a small value

Electronic properties of sulfide minerals and floatability 35 Table 2.5: Bond overlap populations of pyrite, marcasite, and pyrrhotite. Minerals Pyrite Marcasite Pyrrhotite

Bond type FeeS SeS FeeS SeS FeeFe FeeS

˚ Bond length/A

Population 0.34 0.22 0.28, 0.66 0.08 0.11 e 0.20 0.11e0.44

2.191 2.258 2.231, 2.247 2.279 0.2812e0.2972 2.271e2.905

indicates an ionic interaction. A value of zero indicates a perfectly ionic bond, while values greater than zero indicate an increased covalency. The Mulliken overlap populations of pyrite, marcasite, and pyrrhotite are listed in Table 2.5. It is found that the FeeS bond population in pyrite is greater than SeS bond, so FeeS bond has stronger covalence than SeS bond, which can be confirmed by the shorter bond length of FeeS ˚ ) than that of SeS bond (2.258 A ˚ ). There are two FeeS bond populations in (2.191 A marcasite, 0.28 and 0.66, which are both greater than that of SeS bond (0.08), suggesting stronger covalence of FeeS bond than SeS bond, and FeeS bond lengths are less than that of SeS bond. Due to the complicated lattice structure, there are many overlap population values in the same bond. It can be found that the FeeS bond population is in the range of 0.11e0.44, and FeeFe bond population is in the range of 0.11 to about 0.20, suggesting that FeeS bond covalence is generally greater than FeeFe bond. ˚ are relatively smaller than Consequently, FeeS bond lengths ranging from 2.271e2.905 A ˚ those of FeeFe bond lengths ranging from 2.812e2.972 A.

2.2.6 Frontier molecular orbital FMO suggests that the smaller the absolute DE between HOMO and LUMO, the stronger the interaction. Table 2.6 indicates that oxidation occurs between HOMO of mineral and LUMO of oxygen, and interaction of xanthate with mineral occurs between HOMO of xanthate and LUMO of mineral. In addition, the products of xanthate adsorbing on pyrite, marcasite, and pyrrhotite are all dixanthogen, so butyl dixanthogen is used to calculate Table 2.6: The frontier orbital energy of minerals and xanthate. Frontier orbital energy/eV HOMO Pyrite Marcasite Pyrrhotite Oxygen Butyl dixanthogen药

6.295 5.664 5.027 6.908 5.215

LUMO 5.923 4.795 4.987 4.610 2.62

xanthate O2 Mineral DE1 ¼ EMineral HOMO ELUMO ; DE2 ¼ EHOMO ELUMO

Orbital energy difference/eV jDE1j 1.685 1.054 0.417 / /

jDE2j 0.708 0.420 0.228 / /

36 Chapter 2 FMO. It is found that jDE1j, the difference between pyrrhotite HOMO and oxygen LUMO (0.417 eV), is the smallest, followed by marcasite (1.054 eV) and pyrite (1.685 eV), suggesting that the interaction of pyrrhotite with oxygen is the strongest, followed by marcasite, and the interaction of pyrite with oxygen is the weakest. Experimental results shown in Figs.2.12 and 2.13 suggest that the order of oxidation for iron sulfides is pyrrhotite > marcasite > pyrite. It can be seen from the oxygen molecular orbital that there are two lone pair electrons in two antibonding p orbitals, so the oxygen molecule is paramagnetic. The spin DOS suggests that pyrite and marcasite are low-spin state, while pyrrhotite is spin polarized, so the oxygen molecule interacts easier with pyrrhotite than pyrite and marcasite. In the industrial operation, when the ore contains pyrrhotite, oxygen will react with pyrrhotite preferentially, thus consuming a large amount of oxygen in the pulp, leading to the poor floatability of other sulfide minerals. [33]. The product of xanthate interacting with three minerals: marcasite, pyrite, and pyrrhotite, is the same as dixanthogen. The flotation test shows that by using xanthate as collector, the floatability of the three iron sulfide minerals is in the order of marcasite > pyrite > pyrrhotite. It can be seen from Table 2.6 that the frontier orbital energy of pyrite and xanthate j DE2 j is the largest (0.708 eV), followed by marcasite (0.420 eV), and the smallest one is that of pyrrhotite (0.228 eV), which indicates that the interaction between xanthate and marcasite is stronger than that of pyrite, so the floatability of marcasite is better than pyrite. Although pyrrhotite has the strongest effect with xanthate, in the flotation system containing oxygen, as mentioned earlier, because pyrrhotite can easily react with oxygen, it results in excessive oxidation of pyrrhotite, which leads to the formation of soluble film on its surface, which is harmful to the adsorption of dixanthogen. Therefore, the floatability of pyrrhotite in an oxygen-containing flotation system is worse than that of marcasite and pyrite.

2.3 Crystal structure and electronic properties of leadeantimony sulfide minerals Lead and antimony have similar properties: the outer electron configuration of lead atom is 5d106s26p2, and that of antimony atom is 4d105s25p3. The main sulfide minerals that contain lead and antimony are galena (PbS), stibnite (Sb2S3), and jamesonite (Pb4FeSb6S14). Jamesonite is a kind of complex multimetal sulfide mineral, with the crystal morphology of columnar or needle-like, usually in the form of feather-like aggregates, so it is called “feather mine” The reserve of jamesonite in antimony ore is quite limited. Guangxi Dachang in China is the world’s famous production base, which has a rich deposit of jamesonite. Jamesonite also exists in Mexico’s Hidalgo, Cornwall of United Kingdom, and so on. In addition, jamesonite also exists in low temperature lead and zinc deposits in Hunan, Jilin, Liaoning, Gansu, Jiangxi, and other provinces of China, and there is a small amount of production of jamesonite in Bolivia and Nevada, USA.

Electronic properties of sulfide minerals and floatability 37

Figure 2.19 Flotation recoveries of jamesonite, galena, and stibnite at various pH in the presence of xanthate.

The floatability of three leadeantimony minerals is quite different, in which galena has a good floatability under a wide range of pH conditions. Antimony has a good floatability under acidic conditions. while it could not be floated in alkaline conditions, and it is sensitive to lime. The crystal of jamesonite contains lead, antimony and iron elements, so its floatability is between galena and antimony, and lime has strong depressing effect on its floatability. Fig. 2.19 shows the flotation recovery of jamesonite, galena, and stibnite at various pH in the presence of xanthate. The concentration of xanthate was 5  105 mol/L. Galena has the highest flotation recovery, followed by jamesonite and stibnite. The flotation recoveries of jamesonite at various pH are close to that of stibnite, indicating good floatability at pH below 6. However, its flotation recoveries are greatly reduced with increasing pH to above 6. As for galena, pH has little effect on its flotation recovery compared with those of jamesonite and stibnite.

2.3.1 Computational methods Jamesonite is a sulfosalt mineral containing lead, iron, and antimony sulfide with formula Pb4FeSb6S14. It is a dark gray metallic mineral that forms acicular prismatic monoclinic crystals with space group P 21/a. Each Sb atom coordinates with the adjacent three or four S atoms, as shown in Fig. 2.20A. Jamesonite is one of the few sulfide minerals to form fibrous or needle-like crystals. It can also form large prismatic crystals similar to stibnite, with which it can be associated. It is usually found in low to moderate temperature hydrothermal deposits. Stibnite crystallizes in an orthorhombic space group (Pnma). Each S atom coordinates with three Sb atoms, as shown in the model of Fig. 2.20B. Galena belongs to cubic crystal structure with a space group of Fm3m. Each Pb atom coordinates with six S atoms (Fig. 2.20C).

38 Chapter 2

Figure 2.20 Models of Pb4FeSb6S14, Sb2S3, and PbS.

All calculations were performed using the programs CASTEP [15] and Dmol3 [16], which is a first-principle pseudopotential method based on DFT. The calculations of geometry optimization and electronic structures on jamesonite, galena, and stibnite were performed using functional of GGA-PW91 [17]. Based on the test results, plane wave cutoff energies of jamesonite, galena, and stibnite were found to be 270, 280, and 300 eV, respectively, which are the most stable conditions. The valence electron configurations considered in this study included Fe 3d64s2, Pb 5d106s26p2, Sb 5s25p3, and S 3s23p4 states. The convergence tolerances for geometry optimization calculations were set to the ˚ , the maximum force of 0.04 eV/A ˚ , and the maximum maximum displacement of 0.005 A 5 energy change of 2.0  10 eV/atom. The self-consistent field (SCF) convergence ˚ . The calculated tolerance was set to 1.0  105 eV/atom with a global cutoff of 4.4 A ˚ , b ¼ 19.98 A ˚ , and c ¼ 3.98 A ˚, lattice parameters of perfect jamesonite were a ¼ 15.92 A which are close to the experimental values. The values indicate that our calculated results agree well with the experimental data. The atomic orbital coefficients of the HOMO, the LUMO, and the energies of the frontier orbitals of jamesonite, galena, pyrite, and stibnite were calculated using DMol3 program, followed by optimization by CASTEP program. The calculations were performed using GGA-PW91 with fine quality, effective core potentials, an atomic orbital basis set of DNP, and SCF convergence threshold of 1.0  106 eV/atom.

2.3.2 Effects of crystal structures Although Pb atoms in jamesonite and galena are six-coordinated, their structures are completely different, as shown in Fig. 2.21. The Pb atoms in galena coordinate with six symmetrical S atoms, whereas six S atoms coordinated with Pb atoms of jamesonite have

Electronic properties of sulfide minerals and floatability 39

Figure 2.21 Coordination structures of Pb atoms in jamesonite and galena. (A) Coordination structure of Pb atoms. (B) Octahedron crystal field of six-coordinated Pb atoms.

different structures (Fig. 2.21A). In jamesonite structure, two S atoms (S1 and S4) are connected with two Sb atoms, two S atoms (S2 and S6) are connected with 3 Pb atoms and one Sb atom, and two S atoms (S3 and S5) are connected with one Sb atom, one Fe, and another Pb atom. Therefore, the coordination structure of Pb atoms in jamesonite is more complex than that in galena. According to crystal field theory, the different ligand fields have different effects on central atoms. Fig. 2.21B shows a ligand field model of Pb atoms in jamesonite and galena. It indicates that Pb atoms and corresponding coordination S atoms in jamesonite and galena form the octahedron crystal field, but their structures have a big difference. The octahedron crystal field formed by ligand field of Pb atom for jamesonite has an asymmetric structure, while that for galena possess a symmetrical structure. As a result, Pb atoms in jamesonite and in galena are different concerning their stability, electronic property, activity, and other properties. Sb atoms of jamesonite have two coordinated modes: one is three-coordinated and the other one is four-coordinated; though, Sb atoms of stibnite are only three-coordinated, as shown in Fig. 2.22. Compared with three-coordinated Sb atoms of stibnite and jamesonite, the structures of their coordination S atoms are largely different. In stibnite, one S atom (S1) coordinated by Sb atom is a single atom; the other two S atoms (S2 and S3) are

40 Chapter 2

Figure 2.22 Coordinated modes of Sb atoms for jamesonite and stibnite: (A) three-coordinated Sb of jamesonite; (B) four-coordinated Sb of jamesonite; (C) three-coordinated Sb of stibnite.

connected with three Sb atoms (Fig. 2.22C); whereas three S atoms coordinated by Sb atom for jamesonite (Fig. 2.22A) are different than those of stibnite. S1 atom is connected with two Pb atoms, and S2 and S3 atoms are connected with one Pb and one Sb atom. The structure of four-coordinated Sb atom of jamesonite (Fig. 2.22B) is more complex than that of three-coordinated Sb atom. There are two states for four S atoms coordinated by Sb atom. S1 and S4 are connected with one Pb, one Fe, and the other Sb atoms. S2 atom is only connected with one Pb and the other Sb atoms. S3 atom is connected with one Fe and two Pb atoms. Therefore, the properties and activities between three-coordinated Sb atoms and four-coordinated Sb atoms are different.

2.3.3 DOS analysis of jamesonite, galena, and stibnite To understand the relationships and differences of electronic structures among jamesonite, galena, and stibnite, the density of states of Pb and Sb atoms of jamesonite and corresponding atoms of galena and stibnite were studied. The results are presented in Figs. 2.23 and 2.24.

Figure 2.23 DOS of Pb atoms for Pb4FeSb6S14 and PbS.

Electronic properties of sulfide minerals and floatability 41

Figure 2.24 DOS of Sb atoms for Pb4FeSb6S14 and Sb2S3.

Fig. 2.23 shows the DOS of Pb atom for Pb4FeSb6S14 and PbS. The conduction band is mainly formed from Pb 6p with a few contributions from Pb 6s. The valence band is composed of Pb 6s and Pb 6p. DOS of Pb 6s for jamesonite is located in the range of 10 to 7 eV, which shifts to low energy level compared with that of galena with strong peak localization. Compared with galena, DOS of Pb 6s and Pb 6p at Fermi level are small. These results indicate that Pb of jamesonite is inactive. On the other hand, the DOS curve of jamesonite shifts to lower energy in contrast to that of galena, indicating that Pb in jamesonite is more stable than that in galena. According to the electronic structure, it is very easy for PbS to lose electrons (S2eS0), so PbS shows a good floatability. As a result, PbS flotation is far easier than that of jamesonite and can be performed even in collector-free conditions, which is in good agreement with the flotation practice of jamesonite and galena (Fig. 2.19). Fig. 2.24 shows the DOS of Sb atom for Pb4FeSb6S14 and Sb2S3. DOS curve of three-coordination Sb atom in jamesonite is similar to that of Sb atoms (threecoordination) in stibnite. However, Sb 5s and Sb 5p peaks of jamesonite are narrower than those of stibnite, and DOS of Sb 6s and Sb 6p at Fermi level are small, indicating that Sb (three-coordination) of jamesonite is inactive in contrast to that of stibnite. The DOS curve of four-coordination Sb atoms for jamesonite is different from that of three-coordination Sb. Peaks of Sb 5s and Sb 5p are lower than those of threecoordination; however, DOS of Sb 5p for four-coordination Sb atoms near the Fermi energy is large. Hence, four-coordination Sb is more active than three-coordination Sb. On the other hand, DOS curves of jamesonite also shift to lower energy in contrast to that of stibnite. As a result, jamesonite is more stable than stibnite.

42 Chapter 2

2.3.4 Analysis of frontier orbital Table 2.7 presents the atomic orbital coefficients of HOMO and LUMO of Pb4FeSb6S14, PbS, Sb2S3, and FeS2. A large value of coefficient (absolute value) indicates a great contribution of atoms to the frontier orbitals, whereas a small value (absolute value) indicates a small contribution of atoms. Moreover, the positive sign of coefficient denotes the bonding between atoms, while the negative sign of coefficient denotes the antibonding state between atoms. Here, only the absolute and maximum values are concerned. According to data in Table 2.7, the content of Fe in jamesonite is low, but it is very active. The HOMO orbital of jamesonite consists of Fe, S, Sb, and Pb atoms, but the main contributing atoms are Fe and S, and contributions of Sb and Pb are small. The main contribution of LUMO orbital for jamesonite is from Fe, S, and Sb atoms, but Pb atom contributes less. Comparing the frontier orbital coefficients of jamesonite, galena, stibnite, and pyrite, the LUMO orbital of jamesonite is similar to that of stibnite, which is easy to react with collectors and has good floatability. However, the HOMO orbital of jamesonite is similar to those of pyrite and stibnite, which means it is easy to be depressed in alkaline medium, especially in solutions containing lime. Fig. 2.25 shows the flotation behavior of jamesonite, galena, stibnite, and pyrite with various lime contents. Generally, the highest occupied orbitals easily lost electrons, whereas lowest unoccupied orbital easily gain electrons. The frontier orbitals can be simply summarized as nucleophilic HOMO and electrophilic LUMO orbitals. For instance, it is found from Table 2.7 that for frontier orbitals of galena, the main contribution of HOMO orbital is from S atoms, but that of LUMO orbital depends on Pb atoms. Therefore, it is easy for S atoms of galena to lose electrons and be oxidized. The Pb ion reacts easily with xanthate anion to form lead xanthate. The HOMO orbitals of jamesonite, stibnite, and pyrite contain metal atoms. The configurations of metal atoms in HOMO orbitals are due to the low valence of Fe atoms of jamesonite (þ2), Sb atoms of stibnite (þ3), and Fe atoms of Table 2.7: Frontier orbital coefficients of Pb4FeSb6S14, PbS, Sb2S3, and FeS2. Mineral Pb4FeSb6S14 PbS Sb2S3 FeS2

Frontier orbital HOMO LUMO HOMO LUMO HOMO LUMO HOMO LUMO

Atomic orbital coefficient of HOMO and LUMO e 0.341Fe(3d) þ 0.287S(3p) e 0.077Sb(5p) e 0.038Pb(6p) e 0.316 Fe(3d) e 0.240S(3p) e 0.113Sb(5p) e 0.068Pb(6p) e 0.493S(3p) þ 0.038Pb(6p) 0.484Pb(6p) þ 0.203S(3p) 0.484Sb(5p) þ 0.321S(3p) e 0.529Sb(5p) e 0.283S(3p) 0.238Fe(3d) e 0.068S(3p) e 0.004Fe(3d) e 0.124S(3p)

Electronic properties of sulfide minerals and floatability 43

Figure 2.25 Flotation behaviors of jamesonite, galena, stibnite, and pyrite in different lime concentrations.

pyrite (þ2), which have both electrons and empty orbitals and can lose electrons to become high valence. As a result, these metal atoms in HOMO orbitals act as electron occupants. Now, let us discuss how metal atoms in HOMO orbitals relate to the depression effect of lime. According to Fig. 2.25, the flotation of galena is insensitive to lime, although those of jamesonite, pyrite, and stibnite are easily depressed by lime. The effective component in lime is CaOHþ that easily reacts with nucleophilic HOMO orbitals. The depression model of pyrite [35] shows that the adsorption of CaOHþ on pyrite surface mainly via the bondings of Fe-OH- and Ca-S. Therefore, metal atoms in HOMO orbitals favors the adsorption of CaOHþ in the flotation of jamesonite, stibnite, and pyrite which are easily depressed by lime. If there are no metal atoms in HOMO orbital, it is not favorable for the absorption of CaOHþ. For example, galena has no metal atoms in HOMO orbital, which is not easily depressed by lime.

2.4 Electronic and chemical structures of pyrite and arsenopyrite Pyrite (FeS2) and arsenopyrite (FeAsS) are two major sulfides, and they are often found dissociated in nature. They show many similar properties, such as crystal structures, oxidation behaviors, flotation behaviors, etc. In mineral processing, the separation of these two minerals is difficult. It can be seen from Fig. 2.26 that the flotation behavior of arsenopyrite and pyrite is close in broad pH range, and the separable interval could not be found. Flotation separation of arsenopyrite and pyrite is considered to be representative of the difficulty of arsenic sulfide ore flotation separation.

44 Chapter 2 100 pyrite

Recovery/%

arsenopyrite 450

50 300

Eh(vs.SHE)/mV

600 75

25 [NBX]=10–4mol • L–1

150

0 2

4

6

8

10

12

Pulp pH

Figure 2.26 The relationship between recovery of pyrite and arsenopyrite and pulp pH [72] (butyl xanthate: 1  104 mol/L).

2.4.1 Crystal structure The crystal structures of pyrite and arsenopyrite have been studied widely [36e44]. Earlier workers suggested that an excess of sulfur tends to lower the symmetry of arsenopyrite to triclinic, and a large amount of arsenic precludes monoclinic symmetry. It is concluded that most natural arsenopyrites are sulfur-rich. However, a study by Bindi et al. [45] showed that stoichiometric arsenopyrite is monoclinic with space group P21 =c. Pyrite is diamagnetic with Fe2þ in a low-spin configuration (t62g eg0). This configuration supports the 3 cubic symmetry of pyrite. In addition to Fe ions, dianion groups (S2 2 , AsS ) occur in the crystal structures of pyrite and arsenopyrite. Eyert et al. [46] confirmed that the chemical stability results mainly from FeeS bonding. Goodenough [47] found that the structuredetermining interactions were cationeanion interactions and not cationecation interactions. However, Tossell et al. [48] suggested that, to fully understand the structural and spectral properties of the disulfides and related compounds, the sulfuresulfur structural units must be considered in addition to the metalesulfur structural units. Electronic interactions play a significant role in the structural and chemical properties of crystals. Nickel [49] and Hulliger [50] explained the structural variations as a function of the interactions of the d electrons on the metals. Tossell et al. [48] proposed that the systematic increase in unit cell dimension across the series from FeS2 to ZnS2 could be explained by the increasing occupancy of the antibonding eg* orbitals of the metal 3d. Finklea et al. [51] found that a very small amount of electron delocalization was enough to cause the quadrupole splitting observed in the Mo¨ssbauer effect due to the strong effects of the valence electrons on the iron in pyrite. Using quantitative molecular orbital (MO) calculations, Tossell et al. [48] suggested that the structural preferences could be

Electronic properties of sulfide minerals and floatability 45 understood by considering the electron occupations of a set of MOs. The study by Eyert et al. [46] also showed that the S 3p state at the conduction band minimum is very important to the properties of pyrite, and small deviations in the sulfur pair bond lengths resulted in drastic changes in the near-gap electronic states. The electronic structures of pyrite have been studied widely [37,46,52e55]. It has been suggested that arsenic could be present at the sulfur site in pyrite, resulting in the formation of AsS3 dianions within the lattice [56,57]. However, there have been few studies on arsenopyrite [58]. The exact electronic structure of arsenopyrite is still insufficiently studied and understood. Moreover, no comparison results have been published. It is believed that the crystal properties play a critical role in the processing of this mineral, and just small differences in crystal properties may lead to great differences in their flotation behaviors. For example, Chanturiya et al. [59] found that the pyrite with high content of copper, arsenic, and gold impurities can be effectively floated even in strongly alkaline conditions at pH 11.8e12.2, while the recovery of pyrite with low content of copper and high content of sulfur vacancies does not exceed 25% under this high pH condition. To understand the various differences between pyrite and arsenopyrite, it is necessary to investigate their electronic and chemical structures. The flotation behavior of arsenopyrite and pyrite is closely related to its crystal structure and the electrochemical properties of the semiconductor. The electronic structure of pyrite has been reported [37,46,52e55], and the study of the electronic structure of arsenopyrite is less [58]. Understanding the crystal structure and the electronic properties of arsenopyrite and pyrite helps us to further understand the difficulties of the separation of arsenopyrite and pyrite from the theoretical point of view, as well as providing a theory basis for efficient flotation separation of arsenopyrite and pyrite.

2.4.2 Computational methods Based on DFT, structural optimizations and electronic calculations were performed using CASTEP [15], GGA-PW91 [17] (Perdew et al. 1992). Only the valence electrons (Fe 3d6 4S2, S 3s2 3p4, and As 4s2 4p3) were considered explicitly through the use of ultrasoft pseudopotentials [60]. A plane wave cutoff energy of 300 eV was used. A MonkhorstPack [61] k-point sampling density of 4  4  4 mesh was used for both pyrite and arsenopyrite. The convergence tolerances for the geometry optimization calculations ˚ , a maximum force of 0.05 eV/A ˚, a were set to a maximum displacement of 0.002 A 5 maximum energy change of 2.0  10 eV/atom, and a maximum stress of 0.1 GPa. The SCF convergence tolerance was set to 2.0  106 eV/atom. The frontier orbital calculations were performed using DMol3, a single-point energy method, the GGAPW91, DNP basis set, effective core potentials, a fine quality, and an SCF convergence of 1.0  106 eV/atom. The spin calculation was performed during the simulation. The calculation was performed using different wavefunctions for different spins [62e66].

46 Chapter 2

2.4.3 Crystal structure differences between pyrite and arsenopyrite 

Pyrite (cubic symmetry, FeS2) belongs to the space group Pa3 . As stated previously, arsenopyrite has two possible symmetries: monoclinic and triclinic. To obtain a reasonable structure for the present calculation, we calculated and compared the monoclinic and triclinic arsenopyrite results. The results for triclinic arsenopyrite and monoclinic arsenopyrite are almost identical, including the unit cell dimensions, the angle (b) of the unit cell, interatomic distance, Fermi level, and orbital coefficients for the frontier orbitals. In addition, we also calculated the total energies of these two unit cells. The values for triclinic and monoclinic arsenopyrite were found to be similar, e5278.119 and 5278.120 eV, respectively. The recent report by Bindi et al. [45] suggests that stoichiometric arsenopyrite has monoclinic symmetry with the space group P21 =c. Because the crystal cell (Fe4As4S4) used in our calculation had an ideal chemical composition, the monoclinic pattern was used in the present calculation. The unit cells of pyrite and arsenopyrite are shown in Fig. 2.27. The pyrite unit cell contains four FeS2 units with the formula Fe4S8, and the arsenopyrite unit cell also contains four FeAsS units with the formula Fe4As4S4. The dianions in pyrite and 3 arsenopyrite are S2 2 and AsS , respectively. For each mineral, the cation (Fe) is octahedrally coordinated by six anions, and each of the anions is tetrahedrally coordinated by three Fe ions and one other anion (Fig. 2.29). Table 2.8 lists the calculated crystal structural parameters of pyrite and arsenopyrite, which are compared with the literature results. It is found that the calculated results are consistent with the experimental values (less than 1% error), suggesting that the calculation method for this study is reliable. By comparing the SeFeeS angles in pyrite with those in arsenopyrite, it is found that the SeFeeS angle is close to a right angle in pyrite and an obtuse angle in arsenopyrite, implying a greater distortion of the octahedral symmetry of Fe in arsenopyrite than in pyrite, which is related to the internal bonding of the crystal, which will be discussed later.

Figure 2.27 Unit cells of pyrite (A) and arsenopyrite (B).

Electronic properties of sulfide minerals and floatability 47

Figure 2.28 (A) Electron density plots of pyrite SeS and FeeS bonds; (B) electron density plots of arsenopyrite FeeS and AseS bonds. Table 2.8: Unit cell parameters and bond angles of pyrite and arsenopyrite. Calculated results ˚) Unit cell parameters (A Pyrite Arsenopyrite

a ¼ b ¼ c ¼ 5.386 a ¼ 5.701 b ¼ 5.636 c ¼ 5.720

b ( ) 90.0 111.8

Reported results ˚) Unit cell parameters (A a ¼ b ¼ c ¼ 5.417 a ¼ 5.761 b ¼ 5.684 c ¼ 5.767

Refs. b ( ) 90.0 111.7

[27] [31]

It was confirmed by Buerger [67] that the interatomic distances in the arsenopyrite group were quite different from those derived from the pyrite group minerals. Table 2.9 lists the interatomic distances and Mulliken bond populations in pyrite and arsenopyrite. In pyrite, ˚ ) are equivalent, whereas for arsenopyrite the the lengths of the six FeeS bonds (2.247 A lengths of the three FeeAs bonds and the three FeeS bonds are different, ranging from ˚ and 2.174 to 2.209 A ˚ , respectively. The interatomic distances of SeS in 2.366 to 2.403 A Table 2.9: Bond lengths and Mulliken population of pyrite and arsenopyrite. Pyrite Bond type FeeS S1eS2 FeeFe

˚) Bond length (A 2.247 2.186 3.808

Arsenopyrite Mulliken population 0.34 0.22 

Bond type

˚) Bond length (A

Mulliken population

FeeS1 FeeS2 FeeS3 FeeAs1 FeeAs2 FeeAs3 SeAs FeeFe

2.174 2.189 2.209 2.366 2.384 2.403 2.396 2.657, 3.746

0.40 0.43 0.44 0.24 0.26 0.17 0.28 

48 Chapter 2

Figure 2.29 Atomic coordination structures of pyrite Fe (A), S (B) and arsenopyrite Fe (C), S (D) atom.

˚ , respectively. The FeeFe distance pyrite and AseS in arsenopyrite are 2.186 and 2.396 A ˚ , which is much longer than that in arsenopyrite (short distance of in pyrite is 3.808 A ˚ ˚ ). 2.657 A and long distance of 3.746 A Hulliger and Mooser [50] and Tossell et al. [48] showed that two neighboring Fe have a common corner in pyrite, while they share an edge in arsenopyrite (Fig. 2.30). It was noted by Goodenough [68] that the interactions between two octahedral cations will be cationeanionecation interactions if the two octahedra share a common corner, but may be cationecation interactions if the two octahedra share a common edge. These

Figure 2.30 Atomic coordination structures of (A) two adjacent octahedral-pyrite and (B) two adjacent octahedral-arsenopyrite.

Electronic properties of sulfide minerals and floatability 49 configurations support the low-spin states of pyrite and arsenopyrite. Pyrite Fe has 6d electrons with a low-spin configuration of t62g eg0, while in arsenopyrite, the Fe atom has a high-spin d5 configuration, which cannot be fully paired in the three t2g orbitals. However, spin-pairing can be achieved if the unpaired electron in one of the t2g orbitals of the one atom is paired with the unpaired electron of the adjacent metal atom across the octahedral edge [49,50]. Consequently, in arsenopyrite, the FeeFe distances are alternately lengthened and shortened. A magnetic moment of zero supports this low-spin configuration for the arsenopyrite structure [50]. Our calculation also obtains a low spin density for the Fe d electrons in both pyrite and arsenopyrite. The bond population result shows that the covalent interactions of SeS in pyrite (bond population of 0.22) are weaker than those of AseS in arsenopyrite (bond population of 0.28). It is interesting that the population value of the FeeAs bond is negative, suggesting an antibonding interaction occurring between Fe and As atoms. This situation will result in Fe atoms being repelled toward S atoms to stabilize the antibonding orbitals. According to Goodenough [47], these cationeanion repulsive forces may cause distortion in the arsenopyrite structure. The population value of FeeS in pyrite (0.34) is smaller than that in arsenopyrite (0.40e0.44), suggesting that the covalent interaction in the former is weaker than in the latter. This apparently greater covalent interaction is clearly shown in the electron density map (Fig. 2.28A,B), from which it is clear that the electron density in the arsenopyrite FeeS region is greater than that between the pyrite FeeS region. Based on the arsenopyrite map, there is no electron density present between FeeFe (for both short and long separations), which indicates that the cationecation interaction is very weak even at this distance and the cationeanion interactions are dominant in arsenopyrite. This result is consistent with the view of Goodenough [68] and Tossell et al. [48] that structure-determining interactions are attributed to be cationeanion not cationecation interactions.

2.4.4 Electronic structures The electronic band structures and corresponding DOS of pyrite and arsenopyrite are shown in Fig. 2.31 (the zero point energies were set at the Fermi level, EF). There are DOS at the Fermi energy level for pure pyrite or arsenopyrite, indicating they are insulating materials. This result is caused by the Gaussian broadening used in the DOS calculation. The electronic band structure of pyrite splits into five energy intervals between 17 and 5 eV. The two band groups between 17 and 10 eV have almost entirely S 3s character. The lower group of these two bands consists of the SeS bonding state, and the higher group of these two bands consists of the SeS antibonding state. The band in the range from 7.5 to 1.5 eV, below the valence band maximum (VBM), is mainly formed from bonding Fe 3d and S 3p states. The band just below the Fermi level is formed from nonbonding S 3p and Fe 3d states. The conduction band is mainly formed

50 Chapter 2

Figure 2.31 Band structures and density of states (DOS) of pyrite and arsenopyrite.

from antibonding Fe 3d and S 3p states. These results are very consistent with the published studies [37,46,52e54]. For arsenopyrite, there are four groups of bands in the energy range between 17 and 5 eV. The two groups between 17 and 10 eV are similar to those in pyrite. The lower group of these two bands is mainly derived from AseS bonding states, and the higher group of these two bands is formed from AseS antibonding states. The VBM is mainly derived from Fe 3d, As 4p, and S 3p states with some contribution from As 4s and Fe 4s states. The conduction band is composed of S 3p, As 4p, and Fe 3d states, with some contributions from S 3s and As 4s states. Comparing the electronic structures of pyrite with arsenopyrite, it is clear that the pyrite valence band ranging from 7.5 to 0 eV splits at energy of 1.25 eV, while this part of the valence band in arsenopyrite is continuous. Although the Fe 3d electrons are essentially localized in both pyrite and arsenopyrite, the pyrite Fe 3d orbital splits below the Fermi level, whereas the arsenopyrite Fe 3d orbital doesn’t split, which is consistent with the Fe L-edge XANES observation of arsenopyrite by Mikhlin and Tomashevich [69], which demonstrated an almost unsplit 3d, e.g., a band of singlet Fe2þ. This result could be attributed to the stronger interatomic bonding effects between FeeS atoms in pyrite than in arsenopyrite.

Electronic properties of sulfide minerals and floatability 51

Figure 2.32 Energy bands of pyrite and arsenopyrite.

Fig. 2.32 shows the electronic band structures of pyrite and arsenopyrite near the Fermi level. It is shown that both pyrite and arsenopyrite are p-type semiconductors with indirect band gaps. The lowest points of the conduction bands for pyrite and arsenopyrite are located at the high symmetry G point. The calculated band gaps for pyrite and arsenopyrite are 0.54 and 0.78 eV, respectively. The calculated band gap of pyrite is smaller than the experimental value of 0.95 eV [31] due to the GGA method, which commonly results in a smaller gap value. Few reports on the optical band gap of arsenopyrite were found. Using the diffuse reflectance technique, Wood and Strens [70] found that the band gap of arsenopyrite is less than 0.5 eV, slightly lower than our calculated result. The interactions between the orbital electrons can be obtained by plotting the atomic DOS, as shown in Fig. 2.33. Fig. 2.33A plots the ped interaction between SeFe atoms in pyrite. It is shown that, in the Fe octahedral ligand field, the 3d orbitals split at the Fermi level into fully occupied nonbonding t2g states and empty antibonding eg states. The t2g state peak is sharp, and the localization of the electrons is very strong. In addition, below the t2g states, there exist nonlocal, bonding 3d eg states that are separated from the t2g states at 1.5 eV. These eg states interact with the S 3p states and form bonding states, while antibonding interactions occur between the eg state with the S 3p state in the conduction band. Fig. 2.33B shows the ped interaction between the FeeS atoms in arsenopyrite. The first distinct difference between the pyrite FeeS atoms and the arsenopyrite FeeS atoms is that the p-d orbitals of the latter do not split in the range of 7.5 to 0 eV, i.e., the bonding 3d eg states and the nonbonding 3d t2g states are connected together. Another difference is that the bonding range between pyrite FeeS atoms (from 7.5 to 1.5 eV) is wider than

52 Chapter 2

Figure 2.33 DOS of pyrite Fe and S atoms (A), DOS of arsenopyrite Fe and S atoms (B), DOS of arsenopyrite As and Fe atoms (C), and DOS of arsenopyrite As and S atoms (D).

that between arsenopyrite FeeS atoms (from 7.5 to 3 eV). However, the antibonding effect between pyrite FeeS atoms is stronger than that between arsenopyrite FeeS atoms, which causes the larger distance and weaker covalent bonds between FeeS in pyrite than in arsenopyrite. The AseS covalent interaction in arsenopyrite is also found to be greater than the SeS covalent interaction in pyrite. Fig. 2.33C shows the ped interaction between AseFe atoms in arsenopyrite. It is clearly shown that the bonding interaction between the As 4p and Fe 3d orbitals is very weak, while their antibonding effect is very strong, indicating antibonding interactions between the As and Fe atoms, which is consistent with the calculated negative Mulliken population of the AseFe bond. Fig. 2.33D shows the orbital interactions between the As and S atoms in arsenopyrite. The pep orbital interaction occupies the predominant position during the AseS bonding

Electronic properties of sulfide minerals and floatability 53 process, and the s orbital electrons have little contribution to the interatomic bonding. The pep bonding region is between 7.5 and 3 eV, and the antibonding region locates in the range of 3 to 0 eV.

2.4.5 Fermi level of pyrite and arsenopyrite The calculated Fermi levels (EF) and orbital coefficients of pyrite and arsenopyrite are shown in Table 2.10. Statistical theory has proven that the Fermi level is the chemical potential of electrons in the system, expressed by the following equation:   vG (2.4) EF ¼ m ¼ vN T where m and G are the chemical potential and free energy of the system, respectively, N is the total number of electrons, and T is the temperature. According to the calculated Fermi levels of the minerals (Table 2.10), we could know that the EF of pyrite (5.99 eV) and arsenopyrite (5.92 eV) are very close to each other, which suggests that the electrochemical activities of these two minerals are very similar, resulting in difficult separation via simple electrochemical methods. Allison’s [72] studies have shown that the electrostatic potential of pyrite and arsenopyrite is 0.22 V, which is consistent with the Fermi level. In addition, the products of xanthate on the surface of arsenopyrite and pyrite are dixanthagen, which also shows that xanthate has similar electrochemical effects with pyrite and arsenopyrite. It can be seen from the results in Fig. 2.34 that the flotation recoveries of arsenopyrite and pyrite are very close at different pulp potentials, indicating that arsenopyrite and pyrite have similar electrochemical flotation behavior. From the preceding discussion, it can be seen that the electronic chemical potential of arsenopyrite and pyrite is almost the same, so it is difficult to perform the electrochemical flotation separation of arsenopyrite and pyrite under thermodynamic conditions, while we can find their differences in dynamics. The results show that the oxidation rate of arsenopyrite is significantly accelerated in the presence of sodium carbonate (Na2CO3) and sodium sulfate (Na2SO4) [29,73], which provides the kinetic conditions for the separation of arsenopyrite and pyrite. Table 2.10: Fermi levels and orbital coefficients of pyrite and arsenopyrite. Mineral

Fermi level (eV)

Pyrite

5.99

Arsenopyrite

5.92

Frontier orbital HOMO LUMO HOMO LUMO

Orbital coefficient 0.292Fe 3d, 0.035S 3p 0.009Fe 3d, 0.242S 3p 0.323Fe 3d, 0.126S 3p, 0.264As 4p 0.401Fe 3d, 0.200S 3p, 0.090As 4p

54 Chapter 2 100

80

Recovery/%

pyrite 60

arsenopyrite

40 pH 6.0

pyrite 20

pH 11.0

arsenopyrite 0 100

200

300

400

500

600

Pulp potential/mV

Figure 2.34 Flotation behaviors of pyrite and arsenopyrite under different pulp potentials [72] (butyl xanthate: 1  104 mol/L).

2.4.6 Frontier molecular orbital of pyrite and arsenopyrite According to FMO theory, the interactions between molecules involve the HOMO and the LUMO. Moreover, the selectivity is controlled by the orbital coefficients. A large value of the coefficient indicates a large contribution of the atom to the frontier orbital, while a small value indicates a small contribution from the atom. For pyrite, it is indicated that the Fe 3d orbital coefficient (0.292) in the HOMO is far greater than that of S 3p (0.035), whereas the opposite situation occurs for the LUMO (0.009 for Fe 3d and 0.242 for S 3p). In the case of arsenopyrite, the Fe 3d orbital coefficient (0.323) in the HOMO is the largest, followed by the As 4p (0.265) and then the S 3p (0.124). For the LUMO, the Fe 3d orbital coefficient remains the largest, while the magnitude of the S 3p orbital coefficient is greater than that of the As 4p. It has been mentioned earlier that the surface effect of lime and sulfide minerals appears to be related to the HOMO orbital of minerals, especially the contribution of cations in the HOMO, and the greater the orbital coefficient of the cations in the HOMO, the more likely the minerals to be depressed by lime. From Table 2.10, it can be seen that the orbital coefficient of Fe 3d in the HOMO of arsenopyrite is 0.323, which is larger than that of in the HOMO of pyrite (0.292), indicating that the arsenopyrite should be easier depressed by lime than pyrite. The results in Fig. 2.35 confirm the prediction of the frontier orbital coefficients. It is suggested that the LUMO of the oxygen (O2) molecule and the HOMO of the mineral will take part in interactions between O2 molecules and the sulfide mineral

Electronic properties of sulfide minerals and floatability 55 100

Recovery/%

75

pyrite

50

25

arsenopyrite

0 7

8

9

10

11

12

13

Pulp potential/mV

Figure 2.35 Flotation behaviors of arsenopyrite and pyrite under different pH adjusted by lime [13].

surface. Based on the orbital coefficients for the HOMO, it is shown that Fe atoms would be the most reactive sites for the interactions of pyrite and oxygen, while Fe, S, and As (even more reactive than S) atoms all have potential as the reactive site for the interactions of arsenopyrite and oxygen. Therefore, in addition to iron oxides and sulfate, the oxidation products on arsenopyrite may include arsenate. In addition, it is apparent from the orbital coefficients that the oxidation of arsenopyrite by oxygen would be stronger than pyrite. Studies by Corkhill et al. [58] and Schaufuss et al. [74] confirmed that As was more reactive than Fe in an oxidizing environment, and the reaction of oxygen with FeAsS surfaces indicated a fast oxidation of surface As therefore, As was likely to be the most favorable atom at the surface for the adsorption of oxidizing species, such as O2 and H2O, thus promoting the production of As oxides and acids of As, such as H3AsO3 and H3AsO4. Based on these results, we can conclude that the selective separation of arsenopyrite from pyrite may be possible using an oxidation mechanism. However, the oxidation process may be difficult to control. In addition to the oxidation of the mineral, the interaction of the collector with the mineral surface is also very important for the flotation. Generally, the interactions of collectors with sulfide minerals occur between the HOMO of the collectors and the LUMO of the minerals, and the Fe atoms are the reactive sites. It is noted from Table 2.10 that the iron atomic coefficient in LUMO of pyrite (0.009) is much smaller than that of arsenopyrite (0.401), suggesting that the electrophilicity of iron atoms in pyrite is weaker than that of arsenopyrite. Consequently, the separation of arsenopyrite and pyrite could be achieved by utilizing the difference in chemical reactivities of iron in these two minerals. Iron can often form stable compounds with amines; however, some amines species, such as EDTA and ethylenediamine bipyridine, can form stable

56 Chapter 2 compounds with iron in aqueous solutions. Using hexyl thioethylamine as a collector, Sirkeci [75] performed a flotation separation of pyrite from arsenopyrite. Using an unconventional anionic collector, sodium dodecylsulfonate, Kydros et al. [76] performed the selective flotation of arsenopyrite from pyrite in the pH range of approximately 4 in a Hallimond cell from an industrial auriferous bulk pyriteearsenopyrite concentrate.

2.5 Electronic structure and flotation behavior of monoclinic and hexagonal pyrrhotite 2.5.1 Introduction Pyrrhotite is one of the main iron sulfide minerals and often accompanies base metal sulfides in ore deposits. Massive sulfide deposits containing pyrrhotite can be found all around the world, specifically in China, Russia, Australia, and Canada. The pyrrhotite minerals (Fe1xS with 0  x  0.125) vary from the cation-deficient, monoclinic NiAs structure Fe7S8 to the slightly distorted NiAs-like structure troilite (the FeS end member, where x ¼ 0). The nonstoichiometry is due to a system of ordered vacancies within the Fe lattice [77e80]. The formula of pyrrhotite minerals can also be expressed as Fen1Sn with n  8 to give structures from Fe7S8 to Fe11S12. The most iron Fe-deficient end member, Fe7S8, has a monoclinic symmetry, whereas the intermediate (Fe1xS) and equimolar (FeS) members have hexagonal and orthorhombic structures, respectively [80,81]. Orlova et al. [82] noted that hexagonal pyrrhotite is more reactive than monoclinic pyrrhotite. The pyrrhotite minerals demonstrate a variety of magnetic behavior depending on the stoichiometry. The monoclinic form shows ferrimagnetism, while hexagonal pyrrhotite (Fe11S12) has an antiferromagnetic nature [83]. On the other hand, the chemical composition, physical properties, and crystal structure of pyrrhotite determine its floatability. Over the last few decades, many studies have been performed on the floatability of pyrrhotite minerals with different crystal structures, but different researchers drew different conclusions [84e87]. Becker [84] suggested that nonmagnetic Sudbury pyrrhotite was less reactive in terms of its oxygen uptake and showed the best collector-free flotation recovery. Magnetic Phoenix pyrrhotite was more reactive and showed poor collector-free flotation, which was significantly improved with the addition of xanthate and copper activation. These differences in reactivity and flotation performance are interpreted to be a result of the pyrrhotite mineralogy. Hong [85] showed that monoclinic pyrrhotite is richer in sulfur than the hexagonal pyrrhotite, and the recovery variation of the two kinds of pyrrhotites with pH is similar, but the recovery of monoclinic pyrrhotite is higher and the floatability is better than that of hexagonal pyrrhotite. In the acidic condition, the hexagonal is easier to be activated by Cu2þ than monoclinic pyrrhotite. Lime shows a certain depression on hexagonal pyrrhotite, but no obvious depressing effect on

Electronic properties of sulfide minerals and floatability 57 monoclinic pyrrhotite. Kalahdoozan [86] showed that synthetic “hexagonal” pyrrhotite exhibited better xanthate adsorption and flotation recovery at a higher pH (10), whereas at a lower pH (7e8.5), monoclinic pyrrhotite was more floatable. He et al. [87] also showed that monoclinic pyrrhotite was more floatable than hexagonal pyrrhotite. Lawson et al. [88] showed a difference in pyrrhotite recovery between nonmagnetic and magnetic circuits of the Sudbury ore where pyrrhotite depression was targeted. Similarly, results of batch flotation tests performed on Bushveld Merensky Reef ores by Wiese et al. [89] have shown that the recovery of pyrrhotite from Merensky Reef ore from one location was greatly increased when copper sulfate was used as an activator during flotation, whereas for ore from another location the effect of copper sulfate addition on pyrrhotite recovery was minor. Gerson and Jasieniak [90] also showed that the copper activation of magnetic pyrrhotite and nonmagnetic pyrrhotite differed according to pyrrhotite type. Although different flotation behaviors of different crystal structures for pyrrhotite were studied, there are no detailed reports on the effect of electronic structure of pyrrhotite on the floatability.

2.5.2 Computational methods and models All calculations were performed using CASTEP developed by Payne et al. [15], which is a first-principle pseudopotential method based on the DFT. DFT calculations employing plane wave (PW) basis sets and ultrasoft pseudopotentials have been performed. The exchange correlation functional used was the generalized gradient approximation (GGA) developed by Perdew Wang (PW91) [17]. The interactions between valence electrons and ionic core were represented by ultrasoft pseudo-pseudo-potentials. Valence electron configurations considered in this study included Fe 3d64s2, S 3s23p4 states. Based on the test results, a PW cutoff energy of 270 eV was used for all calculations, which is the most stable. The convergence tolerances for geometry optimization calculations were set to the maximum ˚ , the maximum force of 0.08 eV/A ˚ , the maximum energy change of displacement of 0.002 A 5 2.0  10 eV/atom, and the maximum stress of 0.1 GPa, and the SCF convergence tolerance was set to 2.0  106 eV/atom. In addition, the spin was used for all calculations. Pyrrhotite is a nonstoichiometric compound, of general formula Fe1xS, based on Fe(II) and S2 ions. Values for x vary from 0 (FeS) to 0.125 (Fe7S8). Each metal atom is in a distorted octahedral coordination with six sulfur atoms, but the six iron neighbors of a sulfur atom are displaced at the corners of a trigonal prism. Pyrrhotite exists in a ˚ with hexagonal or monoclinic form. The FeeS distance is in the range of 2.37e2.72 A ˚ an average of 2.50 A [77]. The iron content ranges between 46.5% and 46.8% in Fe (on a mole basis) in monoclinic pyrrhotite and between 47.4% and 48.3% in hexagonal forms [91]. Monoclinic pyrrhotite (Fe7S8) has a crystal structure based upon the NiAs structure (hence with a slightly distorted hexagonal close-packed array of anions) arising

58 Chapter 2

Figure 2.36 Unit cells of monoclinic and hexagonal pyrrhotite: (A) monoclinic pyrrhotite; (B) hexagonal pyrrhotite.

from the ordering of Fe vacancies. Monoclinic pyrrhotite has low symmetry and is ferromagnetic at room temperature [83]. The monoclinic forms are stable at temperatures below 254 C, whereas the hexagonal forms are stable above that temperature. The exception is for those with high iron content, close to the troilite composition (47% e50% atomic percent iron) that exhibit hexagonal symmetry. The models of monoclinic and hexagonal pyrrhotite are shown in Fig. 2.36A,B.

2.5.3 Energy band and density of states Figs. 2.37 and 2.38 show the band structures of monoclinic pyrrhotite (Fig. 2.37A) and hexagonal pyrrhotite (Fig. 2.37B), and the corresponding DOS (Fig. 2.38A,B). The zero of energy was set at the Femi level (EF). According to Fig. 2.38A,B, monoclinic pyrrhotite and hexagonal pyrrhotite are conductors. For monoclinic pyrrhotite, the band structure splits into two groups of bands in the range between 17 and 2 eV. The character of bands can be evaluated using the DOS shown in Fig. 2.38A. It is seen that the band in the range from 17 to 12.5 eV is from S 3s, and the band from 8 to 2 is mainly from Fe 3d and S 3p. For metal and narrow gap semiconductors, significant physical processes occur in the vicinity of the Fermi level. In other words, DOS near Fermi level represents atomic reaction activity. So the main contribution of monoclinic pyrrhotite is from Fe 3d with few contributions from S 3p. The band structures and DOS of hexagonal pyrrhotite are

Electronic properties of sulfide minerals and floatability 59

Figure 2.37 Band structures of monoclinic and hexagonal pyrrhotite: (A) monoclinic pyrrhotite; (B) hexagonal pyrrhotite.

different from those of monoclinic pyrrhotite. It is seen from Figs. 2.37B and 2.38B that all orbitals (S 3s, S 3p, Fe 3d, Fe 4s, and Fe 3p) are cross-distributed in the conduction band and the valence band. The contributions near the Fermi level are mainly from Fe 3d, Fe 3p, and S 3s with a few contributions from Fe 4s. The hexagonal pyrrhotite is more reactive than monoclinic pyrrhotite because of large DOS near the Fermi level, which is in good agreement with the results of Orlova [82]. The differences may result in different properties and flotation behaviors. The results show that “the hardness of the covalent material is equal to the resistance of the chemical bond per unit area to the diamond indenter” [92]. The hardness formula of the pure covalent bond is this: HðGPaÞ ¼ ANa Eg

(2.5)

60 Chapter 2

Figure 2.38 Density of states of monoclinic and hexagonal pyrrhotite: (A) monoclinic pyrrhotite; (B) hexagonal pyrrhotite.

where A is a proportional coefficient, Eg is the energy gap, and Na is the covalent bond number per unit area. Most crystals are polar covalent crystals whose hardness formula is this:
(2.6) Hv ðGPaÞ ¼ A Na e1:19fi Eh where Eg is the covalent energy gap of the same poles outside the heterogeneous energy gap, which is subtracted from the ionic bond, and fi is ionic. According to the electronic state, density of the bonding effect can predict the hardness of minerals. The effect of monoclinic pyrite is greater than that of hexagonal pyrrhotite, so the hardness of monoclinic pyrite crystals should be larger than that of hexagonal pyrrhotite crystals. The microhardness test results show that the microhardness of monoclinic pyrite is

Electronic properties of sulfide minerals and floatability 61

Figure 2.39 Spin DOS of monoclinic pyrrhotite.

280e362 kg/mm2, the microhardness of hexagonal pyrrhotite is 218e278 kg/mm2, and the hardness of monoclinic pyrite is obviously larger than that of hexagonal pyrrhotite. Fig. 2.39 shows the spin DOS of monoclinic pyrrhotite. Alpha and beta are spin-up and spin-down. It is seen from Fig. 2.39 that monoclinic pyrrhotite produces a spin polarized state, which is consistent with the study that the monoclinic pyrrhotite is ferrimagnetism [83]. The magnetic behavior of the pyrrhotite minerals depends on the stoichiometry. The hexagonal pyrrhotite shows antiferromagnetism.

2.5.4 The electrons density of monoclinic and hexagonal pyrrhotite Fig. 2.40 shows the electron density maps of monoclinic pyrrhotite and hexagonal pyrrhotite. According to Fig. 2.40A, SeFe in monoclinic pyrrhotite has the overlap of electron cloud, while FeeFe has hardly the overlap, which shows SeFe bonds mainly exist as covalent bond in monoclinic pyrrhotite. As for hexagonal pyrrhotite, it is seen that SeFe does not have the overlap of electron cloud, indicating it has no covalency. The covalency of SeFe in monoclinic pyrrhotite can be proven by Mulliken populations. Table 2.11 presents Mulliken bond population values of monoclinic pyrrhotite. According to the Mulliken bond population, the bonding ionicity and covalency between atoms can be judged. Large Mulliken bond population values show strong covalency, while small Mulliken bond population values show strong ionicity. If the values are equal to zero, it means a perfect ionic bond. If the values are less than zero, it indicates no bonding. According to Fig. 2.40, all SeFe bonds have certain extent covalency; however, the SeFe bonds with different coordination structures have different covalency.

62 Chapter 2

Figure 2.40 Electron density maps of monoclinic and hexagonal pyrrhotite: (A) monoclinic pyrrhotite; (B) hexagonal pyrrhotite. Table 2.11: Mulliken bond population of monoclinic pyrrhotite. Bond SeFe

Population 0.56 0.54 0.48 0.42 0.37 0.43 0.45 0.37 0.39 0.26 0.07

˚ Length/A 2.05 2.08 2.11 (2.14) 2.18 (2.19) 2.20 2.20 2.26 2.46 2.51 2.69 2.98

2.5.5 Frontier orbital calculations Table 2.12 shows the atomic orbital coefficients of HOMO and LUMO of monoclinic and hexagonal pyrrhotite. It is shown that the coefficient of Fe atom is very close to that of S atoms of HOMO and LUMO for monoclinic pyrrhotite, indicating that the main contribution of HOMO and LUMO for monoclinic pyrrhotite is generated from Fe and S atom. The coefficient of Fe atoms (0.7448) is much larger than that of S atoms (0.0002) of HOMO for hexagonal pyrrhotite, indicating that the main contribution of HOMO for hexagonal pyrrhotite is generated from Fe atom. The coefficient of S atom (0.6308) is larger than that of Fe atoms (0.3783) of LUMO for hexagonal pyrrhotite, indicating that the main contribution of HOMO for hexagonal pyrrhotite is generated from S atom with few contributions from Fe atom.

Electronic properties of sulfide minerals and floatability 63 Table 2.12: Frontier orbital coefficients of monoclinic and hexagonal pyrrhotite. Mineral

Frontier orbital

Atomic orbital coefficient of HOMO and LUMO

Monoclinic pyrrhotite

HOMO LUMO HOMO LUMO

þ0.1252Fe(3d) þ 0.1064S(3p) þ0.1169Fe (3d)  0.1149S(3p) þ0.7448Fe(3d)  0.0002S(3p) þ0.6308S(3p) þ 0.3783Fe(4p)

Hexagonal pyrrhotite

Table 2.13: The energy difference of frontier orbital between reagents (xanthate) and minerals. Frontier orbital energy (eV) Mineral Monoclinic pyrrhotite Hexagonal pyrrhotite

Emineral

(LUMO)

5.18 5.05

Exanthate

(HOMO)

5.40 5.40

jDEj 0.22 0.35

DE ¼ Emineral (LUMO)Exanthate (HOMO).

The difference (DE) between frontier orbitals reflects the extent of interaction between molecules. Table 2.13 presents the calculation results of DE between reagents and minerals. The frontier orbital theory proposed that the energy differences DE between the HOMO and the LUMO should be small enough to cause the reaction easily. The calculation results using DMol3 program show that the ELUMO values of monoclinic and hexagonal pyrrhotite are 5.18, and 5.05 eV, respectively. The EHOMO value of xanthate is 5.4 eV. Based on the frontier orbital theory, the smaller the absolute difference (jDEj) between EHOMO of reagents and ELUMO of mineral, the stronger the interaction of reagents with the mineral. It is shown in Table 2.13 that the jDEj values between EHOMO of xanthate and ELUMO of monoclinic pyrrhotite (0.22 eV) are smaller than those between EHOMO of xanthate and ELUMO of hexagonal pyrrhotite of xanthate (0.35 eV). Therefore, it is easier for monoclinic pyrrhotite to react with xanthate in contrast with hexagonal pyrrhotite.

2.5.6 Flotation behavior of monoclinic and hexagonal pyrrhotite The floatability of minerals is related to the crystal structure. Fig. 2.41 shows the flotation recovery of monoclinic and hexagonal pyrrhotite with different content of lime in the presence of xanthate used as a collector. It is seen from Fig. 2.41 that the recovery of monoclinic pyrrhotite is greater than that of hexagonal pyrrhotite, and the floatability of monoclinic pyrrhotite is better than that of hexagonal pyrrhotite. On the other hand, hexagonal pyrrhotite is very sensitive to lime; however, the depression effects of lime on monoclinic pyrrhotite are not obvious.

64 Chapter 2

Figure 2.41 Flotation recovery of monoclinic and hexagonal pyrrhotite with different content of lime in the presence of xanthate (collector).

Generally, the highest occupied orbitals tend to lose electrons, while the lowest unoccupied orbitals tend to gain electrons. Because the HOMO and LUMO coefficient of Fe and S in monoclinic pyrrhotite are very close the main contributions of two orbitals come from Fe and S atoms. S atoms in monoclinic pyrrhotite LUMO lose electrons and undergo oxidation reaction. Therefore, monoclinic pyrrhotite reacts easily with xanthate. HOMO orbitals of hexagonal pyrrhotite contain metal (Fe) atoms, and the orbital coefficient of Fe is larger than that of S. And Fe atom in hexagonal pyrrhotite exists in low valence (þ2), which could lose electrons to become high valence. According to Fig. 2.42, the flotation of monoclinic pyrrhotite is insensitive to lime, while that of hexagonal pyrrhotite is easily depressed by lime. As discussed previously, it has been suggested that the HOMO orbital of sulfide minerals is related to the depression of lime, especially when the greater the contribution of cationic atom to the HOMO orbital, the more easily the mineral is depressed by lime. It is found from Table 2.12 that Fe atoms contribute greatly to the HOMO orbital of hexagonal pyrrhotite, which is easily depressed by lime, whereas they contribute relatively less to the HOMO orbital of monoclinic pyrrhotite, which is not easily depressed by lime. As mentioned before, the adsorption of CaOHþ on sulfide minerals is mainly via the bonding between metal atom-O and Ca-S. It is known that CaOHþ has an empty p orbital, and most cations of sulfide mineral have dorbitals, which could provide electrons to empty p orbital of CaOHþ to form a backbonding. Therefore, the greater the coefficient of metal atom in HOMO orbital of sulfides, the easier the formation of back-bonding with the lime, thus the easier the depression by lime.

Electronic properties of sulfide minerals and floatability 65 (A)

H2S+Fe2+ Fe(OH)2

Fe2+

Fe(OH)3

steel ball

e– mineral

H2O+O2 OH–

(anode)

(B)

S0

(cathode) SO42–+H–

Me2+

inert mineral

(anode)

S0 Me2+

OH–

(cathode)

SO42–+H–

active mineral e– Fe2+

O2

e–

active mineral

(C)

H 2O

steel ball

(anodic domain)

H 2O O2 e– inert mineral

OH–

(cathode domain)

Figure 2.42 Galvanic corrosion model in sulfide mineral pulp: (A) grinding steel medium and sulfide ore; (B) between sulfide minerals; (C) grinding steel medium and two sulfide mines.

2.6 Galvanic interaction between pyrite and galena 2.6.1 Introduction Sulfide ore flotation is a complex electrochemical system. Electron transfer not only occurs between the sulfide minerals and flotation reagent molecules, but it also happens among different sulfide minerals. Many sulfide minerals are narrow band gap semiconductors. Galvanic interactions usually occur when sulfide minerals contact each other due to their different electrode potential. Sulfide minerals are often recovered by froth flotation where the galvanic interaction would occur, causing the electrons to transfer between them and making significant influence on the flotation process [93]. The electron transfer would change surface properties of sulfides, so the recovery of mineral would be promoted or depressed [94]. Ekmekci and Demirel [95] indicated that galvanic interactions between pyrite and

66 Chapter 2 chalcopyrite significantly decrease the recovery of chalcopyrite and activate pyrite. The research of Pecina-Trevino et al. [93] reported that the floatability of galena when contacted with pyrite slightly decreases compared with that of galena alone in the whole range of pH. When two different metals are in contact, a galvanic battery is formed. The metal corrosion caused by galvanic interaction is called galvanic corrosion. During the process of flotation, the galvanic effect occurs between a steel ball and the sulfide minerals during the grinding process. During the process of flotation, the different sulfide mineral particles also have galvanic interaction. These galvanic effects alter the sulfide mineral semiconducting properties and electrochemical reactivity, thereby affecting the electrochemical flotation behavior of sulfide minerals. Sulfide minerals are semiconducting, and different sulfide minerals have different electrostatic potentials. When two sulfide minerals are in contact, the electrons transfer from the minerals with low electrostatic potential to the minerals with high electrostatic potential to form the galvanic cells. The galvanic corrosion in galvanized ore pulp can be summarized in three cases shown in Fig. 2.42. Fig. 2.42C shows the galvanic model during grinding in the presence of two kinds of sulfide ore. Due to the difference of electrostatic potential between two kinds of sulfide minerals, the sulfide mineral with high electrostatic potential is inert, working as the cathode, and the lower one has greater electrochemical activity, combined with the ball media, so it mainly works as an anode. Fig. 2.42B represents the galvanic corrosion behavior between two kinds of sulfide minerals in the flotation process: sulfide minerals with lower electrostatic potential work as the anode undergoing the oxidation reaction, and the sulfide minerals with higher electrostatic potential acts as the cathode undergoing reduction reaction. The electrostatic potential of the sulfide minerals is related with their Fermi level: the higher the mineral Fermi level, the lower the electrostatic potential; on the contrary, the lower the mineral Fermi level, the higher the electrostatic potential. When the two minerals are in contact, the electrons flow from the minerals with higher Fermi level to the minerals with lower Fermi level until the Fermi level is equal. The galvanic effect (or galvanic corrosion) between the sulfide minerals is derived from the electronic Fermi level difference between the two minerals, and the greater the Fermi energy level difference between the two minerals, the more significant the galvanic interaction between them. In the sulfide mineral flotation, galena and pyrite are two typical sulfide minerals. First, galena has the lowest electrostatic potential in sulfide minerals, and the electrostatic potential of pyrite is the highest. Secondly, the adsorbed product of xanthate on pyrite surface is dixanthogen, and that of on galena surface is lead xanthate, which represents

Electronic properties of sulfide minerals and floatability 67 two typical electrochemical mechanisms of the interaction between collector and sulfide minerals. In addition, pyrite is widely found in various sulfide ores. In the galvanic corrosion in the pulp, pyrite always acts as the cathode, while other minerals with low electrostatic potential act as the anode. Therefore, the galvanic interaction between pyrite and galena is typical and representative in sulfide flotation. The following discussion focuses on galena and pyrite as representative minerals to study the effect of galvanic interaction on mineral flotation behavior and electronic structure.

2.6.2 Effect of galvanic interaction on mineral flotation The collector-free flotation recoveries of single galena, single pyrite, and artificial mixed minerals of galena-pyrite are shown in Fig. 2.43. It can be seen that the flotation behavior of mixed minerals (galena and pyrite) and that of a single mineral are different, which shows that galena and pyrite in the mixed system have the galvanic interaction due to the collision between the particles, leading to changes in mineral surface mineral surface properties, affecting the flotation behavior of collector-free flotation. Both galena and pyrite have good floatability in collector-free flotation under acidic conditions. With the increase of pH, the floatability of pyrite decreases, while galena remains good floatability. This is because the natural floatability of pyrite is poor. Under acidic conditions, the surface of pyrite can be oxidized to form elemental sulfur and lead to a high flotation recovery. With the increase of pH, the formation of hydroxyl iron on pyrite surface reduces the hydrophobicity of mineral surface and results in poor recovery. Galena itself has a very good natural floatability, which maintains a high recovery in a wide range of pH.

Figure 2.43 Effect of Galvanic action on the recovery of galena and pyrite under collector-free flotation with different pH.

68 Chapter 2 When galena and pyrite contact with each other, reduction reaction will occur on pyrite surface as the cathode and oxidation reaction will occur on galena surface as the anode due to galvanic interaction. Under the acidic condition, the recovery of pyrite decreases under collector-free flotation, because in the pyrite-galena galvanic system, electrons of galena flow to pyrite, thus depressing the formation of hydrophobic elemental sulfur on pyrite surface, thereby reducing the floatability; and galena is favorable to sulfur oxidation on surface due to the loss of electrons, so floatability becomes better. When the pH increases to about 7, galena shows the best floatability and the flotation recovery is close to 100%. This is due to the galvanic effect of pyrite to promote the formation of hydrophobic elemental sulfur, which improves the surface hydrophobicity of galena. In addition, the floatability of pyrite is also improved, and the recovery of pyrite is about 70%, which is higher than that of a single mineral system. Ball et al. found that the minimum flotation recovery of pyrite at pH 6 was due to the formation of a large number of Fe (OH)3 colloids on the surface of pyrite [96]. After the contact between pyrite and galena, pyrite works as the cathode to obtain electrons from the surface of galena, which depresses the formation of ferric iron on the surface of the pyrite, thus hindering the formation of Fe (OH)3 on the pyrite surface and improving the surface hydrophobicity of pyrite. When the pH exceeds 9, the recovery of galena decreases, which is due to the strong galvanic interaction of pyrite and galena, resulting in the oxidation reaction on galena surface to form Pb(OH)2 and sulfite, and the hydrophilicity of galena surface increases. Under the alkaline condition, the surface of pyrite obtains electrons due to the galvanic interaction, which reduces the electrophilicity of iron and is not conducive to the formation of Fe (OH)3, but improves the hydrophobicity of pyrite surface. It can be seen from Fig. 2.43 that the flotation behavior of pyrite and galena is similar. This is because the Fermi energy level tends to be the same after the contact between pyrite and galena, which leads to their similar electrochemical flotation behavior. Therefore, it can be inferred that for the sulfide minerals with electrochemical activity, their electrochemical flotation behavior tends to be similar due to galvanic action. Pecina-Trevino et al. reported the results of the interaction of the collector 3418 (sodiumdi-isobutyl dithiophosphinate) with pyrite and galena [93]. It can be seen from Fig. 2.44 that after the mixture of pyrite and galena, the recovery of galena decreases and the recovery of pyrite increases, and the flotation behavior of the pyrite and galena is closer than that of a single mineral. It is indicated that the galvanic effect between minerals is the main factor that causes the inconsistency of flotation behavior among the artificial mixed ore, real ore, and single mineral samples.

2.6.3 Effect of contact distance on the galvanic interaction The effect of contact distance on the total Mulliken charge number of pyrite and galena surface was investigated, and seven distances (2.78, 3.82, 4.30, 4.87, 5.98, 7.45, and

Electronic properties of sulfide minerals and floatability 69

Figure 2.44 Effects of galvanic action on flotation of galena and pyrite by 3418 under different pH.

Figure 2.45 Galvanic model of pyriteegalena interaction.

˚ ) were considered. Fig. 2.46 shows the electron transfer number of pyrite and 9.82 A galena after galvanic interaction. It is found that galena surface loses electrons and pyrite surface obtains electrons after galvanic interaction, which is in agreement with the experimental results obtained by Rao and Pecina-Trevino et al. [93,94]. Moreover, the number of electrons transferring between mineral surfaces decreases with the increase of ˚ , galena loses electrons significantly. At a contact distance. At distances shorter than 5 A ˚ ˚ for Pb distance of 2.87 A, which is close to the sum of atomic radii of Pb and S (1.75 A

70 Chapter 2

Figure 2.46 Effect of contact distance on the change in the Mulliken charge number of pyrite and galena surface.

˚ for Fe radius, and 1.04 A ˚ for S), galena loses 0.44 e to pyrite. When the radius, 1.26 A ˚ , the electron transfer number decreases significantly, and at the distance is larger than 5 A ˚ distance of 6 A the electron transfer number is 0.08 e. These results suggest that the galvanic interactions still occur between pyrite and galena, ˚ ) of the atomic radii even though the distance is much greater than that of the sum (z3 A of galena surface atoms (Pb and S atoms) and pyrite surface atoms (Fe and S atoms). ˚ , electrons could not directly transfer by bonding When contact distance is beyond 3 A interaction between pyrite and galena; however the electrons may transfer by quantum tunneling effect. According to quantum mechanics, a particle could tunnel through a barrier higher than the energy of the particle, which, according to classical mechanics, is impossible. The vacuum layer between pyrite and galena could be considered as the barrier, and the contact distance is equal to the width of barrier. The quantum theory indicates that the electron transmission probability is near 1010 when the width of ˚ . Fig. 2.46 shows that when the distance is 9.82 A ˚ , the electron electron barrier is 10 A transfer number is 0 e, so the maximum distance of galvanic interaction between galena ˚. and pyrite surface is about 10 A

2.6.4 Electron transfer between mineral surface atoms By analyzing the surface atomic charges, it is found that significant changes in charge only occur on the top three layers of pyrite surface and the first layer of galena surface (shown in Fig. 2.45). Charge transfer number decreases when far away from the interface, and the other sides of the slabs have slight charge transfer. In addition, the charge changes

Electronic properties of sulfide minerals and floatability 71 ˚. Table 2.14: Mulliken charge of surface atoms at a pyriteegalena distance of 2.78 A

FeS2

Three-coordinated surface S atom Four-coordinated surface S atom Surface Fe atom

PbS

Surface Pb atom Surface S atom

Before After Before After Before After Before After Before After

s

p

1.88 1.87 1.84 1.84 0.46 0.50 1.99 1.73 1.92 1.93

4.39 4.35 4.36 4.33 0.56 0.75 1.44 1.51 4.74 4.66

d 0.00 0.00 0.00 0.00 6.51 6.54 10.00 10.00 0.00 0.00

Charge/e 0.27 0.22 0.20 0.17 þ0.47 þ0.21 þ0.57 þ0.76 0.67 0.59

in metal atoms (Fe and Pb) are greater than nonmetal (S). Table 2.14 lists the Mulliken charge of surface atoms when the galvanic interaction between pyrite and galena is strong ˚ ). (at a distance of 2.78 A For galena, Pb 6s and 6p states lose electrons, and the change in the number of Pb 6p electrons is much less than that of 6s electrons. The number of electrons in Pb 5d has not changed. Pb 6s state loses large numbers of electrons, resulting in the positive charge of Pb atom increases. In addition, S 3p state loses a small number of electrons. This oxidation will produce a hydrophobic surface due to the generation of surface S0 that is favorable to the collector-free flotation of galena. For pyrite, the change in the number of Fe 4p electrons is much greater than that of 4s electrons and 3d electrons. Fe 4p state obtains large numbers of electrons, resulting in the positive charge of Fe atom decreasing. In addition, the 3p state of surface threecoordinated S atom loses a small number of electrons, more than that of four-coordinated S atom, suggesting that the reactivity of surface three-coordinated S atom is greater than four-coordinated S atom. Overall, pyrite acts as the cathode of the galvanic couple, where the oxidation is depressed, leading to pyrite to be passivated and galvanically protected. Hence, the acid mine drainage caused by pyrite can be depressed due to the galvanic interaction. However, surface S atom losing a small number of electrons causes a certain extent of oxidation of pyrite, which may be beneficial to the collector-free flotation of pyrite due to the formation of hydrophobic S element.

2.6.5 Nucleophilicity and electrophilicity of surfaces The galvanic interaction could significantly affect the properties of surfaces, which can be well expressed by the changes of the nucleophilicity or electrophilicity of surface atoms. The nucleophilic or electrophilic strength of a surface can be obtained by calculating the Fukui indices (f þ(r), f(r)) of atoms. The f þ(r) and f(r) are the

72 Chapter 2 electrophilic value and nucleophilic value of the r atom, respectively, and the Fukui indices were calculated by Eqs. (2.7) and (2.8). The r(r) means the charge density of r atom. The r means the atom that was calculated, and every atom could get its value of f þ(r) and f(r), respectively. Moreover, the larger the f þ(r) value is, the more susceptible it is to nucleophilic attack. Similarly, the larger the f(r) value is, the more susceptible it is to electrophilic attack [97]. 1 ðr ðrÞ  rN ðrÞÞ DN NþD 1 f  ðrÞ ¼ ðr ðrÞ  rND ðrÞÞ DN N f þ ðrÞ ¼

(2.7) (2.8)

The single Pb and S atom on the galena surface and single Fe, S3c, and S4c atom on pyrite surface could well reveal the reactivity of galena and pyrite surface region. That is because the same kind of atoms with the same coordination have the same reactivity (the same Fukui indices value and dual descriptor value). It can been seen in Fig. 2.45 that the Pb and S atoms on galena surface and Fe atoms on pyrite surface have the same coordination number, and the S atoms on pyrite surface are three-coordinated and four-coordinated. In addition, the relevant site of the Pb, S, Fe, S3c, and S4c atoms have been shown in Fig. 2.44. S3c means the three-coordinated S atom and S4c means the four-coordinated S atom. For a pyrite surface, shown in Fig. 2.47A, with the decrease of distance from 4.87 to ˚ , the values of f þ(Fe), f þ(S3), and f þ(S4) increase from 0.101 to 0.051, 0.059 2.78 A

Figure 2.47 Fukui indices value of the pyrite and galena surface atoms after galvanic interaction with contact ˚ distance of 2.78, 3.82, and 4.87 A

Electronic properties of sulfide minerals and floatability 73 to 0.039, and 0.065 to 0.035, respectively, while the values of f(Fe) and f(S3) and f  (S4) decrease from 0.157 to 0.079, 0.107 to 0.046, and 0.109 to 0.052, respectively. This indicates that the electrophilicity of surface Fe and S atoms is enhanced due to the galvanic interaction, while their nucleophilicity is weakened. Fig. 2.47B shows that the value of f þ(Pb) and f þ(S) on galena surface decreases significantly from 0.212 to 0.022 and 0.114 to 0.028, respectively, and the value of f(Pb) and f (S) increases obviously from 0.048 to 0.183 and 0.042 to 0.094, ˚ . This result suggests that respectively, with the decrease of distance from 4.87 to 2.78 A due to the galvanic interaction the electrophilic property of surface Pb and S atoms is weakened, while the nucleophilic property is enhanced. The dual descriptor f (2) (r) of surface atoms can be calculated by Fukui indices as follows [97,98]: f (2) (r) ¼ f þ(r) e f (r)

ð2:9Þ

f (2) (r) > 0 suggests that the r atom is electrophilic, and when f (2) (r) < 0, it suggests that the r atom is nucleophilic. The calculated results are shown in Fig. 2.48. The site of the Pb, S, Fe, S3c, and S4c atoms have been shown in Fig. 2.45. Fig. 2.48 shows that the f (2) (r) values of Pb and S atoms on galena surface are changed from positive value to negative value and those of Fe, S3c, and S4c atoms on pyrite surface

Figure 2.48 Dual descriptor value of the pyrite and galena surface atoms after galvanic interaction with ˚ contact distance of 2.78, 3.82, and 4.87 A

74 Chapter 2 are changed from negative value to positive value when the contact distance between ˚ . These suggest that the galena surface is galena and pyrite decreases from 4.87 to 2.78 A changed from electrophilic to nucleophilic, and the pyrite surface is changed from nucleophilic to electrophilic due to the galvanic interactions. Based on the preceding results, it is known that the galvanic interactions could enhance the oxidation of galena caused by contacting with pyrite. The electrophilic surface results in the oxidation inhibition of pyrite, which is consistent with the experimental result by Cruz et al. [99].

2.6.6 Orbital coefficients of surface atoms According to FMO theory, the interactions between molecules involve the HOMO and the LUMO. Moreover, the regioselectivity is controlled by the orbital coefficients. Table 2.15 lists the atomic orbital coefficients of pyrite and galena with and without galvanic interactions. It has been suggested that the HOMO of the mineral will take part in the oxidation process of sulfide minerals. Hence, here only the HOMO orbital is considered. In the system without galvanic interactions, the orbital coefficients of Pb and S atoms are 0.01 and 0.02, respectively, indicating little contribution from the atoms to the frontier orbital. In addition, Fe 3d and S 3s orbitals have coefficients of 0.337 and 0.038, respectively, suggesting a greater contribution of Fe 3d than S 3s to the HOMO orbital. After galvanic interactions, Pb 6s orbital coefficient increases to 0.5, greater than that of Fe 3d orbital (0.197). In addition, the orbital coefficient of Fe 3d decreases. These results suggest that the activity of Pb atoms in HOMO orbital is enhanced after galvanic interactions with pyrite, while the activity of Fe atoms in HOMO orbital is lowered and smaller than Pb atoms. This means that the contribution of galena to the HOMO is greater than pyrite. Consequently, the oxidation (involved HOMO) of galena is enhanced due to the galvanic interactions.

2.6.7 DOS of surface atoms Fig. 2.49 shows the Pb 6s and 6p states of galena surface and Fe 3d states of pyrite surface after galvanic interaction between pyrite and galena surface with the contact Table 2.15: Orbital coefficients in pyriteegalena system. Frontier orbital With galvanic interactions (distance ˚) 2.78 A Without galvanic interactions ˚) (distance 9.82 A

Pyrite Galena Pyrite Galena

HOMO HOMO HOMO HOMO

Orbital coefficient þ0.197Fe 3dþ0.019S 3s þ0.500Pb 6sþ0.109S 3s þ0.337Fe 3dþ0.038S 3s þ0.01Pb 6sþ0.02S 3s

Electronic properties of sulfide minerals and floatability 75

Figure 2.49 The density of states of Pb 6s, Pb 6p, and Fe 3d near Fermi level on galena and pyrite surface ˚ . The zero of after galvanic interaction. The contact distances change at 2.78, 3.82, and 4.87 A the energy has been set at the Fermi level, EF.

˚ . With the decrease of contact distance, it can be seen distances of 2.78, 3.82, and 4.87 A that the Fe 3d DOS reduces at Fermi level, while the Pb 6s and 6p DOS increase at the Fermi level. This indicates that the activity of electrons in Pb 6s and 6p orbitals enhances, while the activity of electrons in Fe 3d orbitals weakens due to the galvanic contact with pyrite. Then, the activity of galena surface Pb atom is enhanced, while that of pyrite surface is weakened due to the galvanic interactions. The Pb and Fe atoms on the mineral surfaces occur in metallic states. For galena, our calculation indicated that the Pb atoms do not occur in metallic states when the contact ˚ , and the metallic states of Pb atoms become more obvious with distance is larger than 6 A the contact distance decreased (the galvanic interaction enhanced). For pyrite, studies [37] indicated that there is no electron state distributed at the Fermi level in the band structure. However, the Fermi energy level is underestimated in the DOS calculation. Hence, a finite value of DOS at the Fermi level is observed.

76 Chapter 2

2.6.8 Effect of H2O and N2 molecules at the interface of pyrite and galena on the galvanic interaction The galvanic interactions often happen in solution, so the effect of H2O molecule on the galvanic interaction has been investigated, and the calculation models are shown in Fig. 2.50. The galvanic interaction with the presence of H2O molecules at the interface has ˚ , and the calculation results been investigated in the contact distances of 5.98 and 7.46 A are shown in Table 2.16. Table 2.16 indicates that the presence of H2O molecule improves the electron transfer between pyrite and galena surface in the contact distance of 5.98 and ˚ ; particularly, the electron transfer number of galena surface is obviously enhanced. 7.46 A N2 is a kind of inert gas that widely exists in the atmosphere. The galvanic interaction with the presence of N2 molecules at the interface has also been investigated, and the calculation results are shown in Table 2.17. It is shown in Table 2.17 that there is no ˚ with the presence of N2. In electron transfer between surfaces in the distance of 7.46 A ˚ , the electron transfer number of galena surface is slightly the distance of 5.98 A enhanced, and the electron transfer number of pyrite is slightly decreased.

Figure 2.50 Computational galvanic interaction model with the presence of H2O and N2 molecules at the interface of pyrite and galena surface. Table 2.16: Effect of H2O molecules at the interface of pyrite and galena on the Mulliken charge ˚. number with the distance of 5.98 and 7.46 A Mulliken charge number/e ˚ Distance/A Presence of H2O Absence of H2O Presence of H2O Absence of H2O

5.98 5.98 7.46 7.46

Galena surface 0.22 0.1 0.16 0.02

Pyrite surface 0.14 0.1 0.08 0.02

H2O molecule 0.08 / 0.08 /

Electronic properties of sulfide minerals and floatability 77 Table 2.17: Effect of N2 molecules at the interface of pyrite and galena on the Mulliken charge ˚. number with the distance of 5.98 and 7.46 A Mulliken charge number/e ˚ Distance/A Presence of N2 Absence of N2 Presence of N2 Absence of N2

5.98 5.98 7.46 7.46

Galena surface 0.15 0.1 0 0.02

Pyrite surface 0.07 0.1 0 0.02

N2 molecule 0.08 / 0 /

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Electronic properties of sulfide minerals and floatability 79 [46] Eyert V, Ho¨ck KH, Fiechter S, Tributsch H. Electronic structure of FeS2: the crucial role of electronlattice interaction. Phys Rev B 1998;57(11):6350e9. [47] Goodenough JB. Energy bands in TX2 compounds with pyrite, marcasite, and arsenopyrite structures. J Solid State Chem 1972;5(1):144e52. [48] Tossell JA, Vaughan DJ, Burdett JK. Pyrite, marcasite, and arsenopyrite type minerals: crystal chemical and structural principles. Phys Chem Miner 1981;7(4):177e84. [49] Nickel EH. Structural stability of minerals with the pyrite, marcasite, arsenopyrite and loellingite structures. Can Mineral 1968;9(3):311e21. [50] Hulliger F, Mooser E. Semiconductivity in pyrite, marcasite and arsenopyrite phases. J Phys Chem Solids 1965;26(2):429e33. [51] Finklea SL, Cathey L, Amma EL. Investigation of the bonding mechanism in pyrite using the Mo¨ssbauer effect and X-ray crystallography. Acta Crystallogr A 1976;32(4):529e37. ˚ , Paul J. Full potential calculations on the electron bandstructures of sphalerite, [52] Edelro R, Sandstro¨m A pyrite and chalcopyrite. Appl Surf Sci 2003;206(1e4):300e13. [53] Oertzen GUV, Skinner WM, Nesbitt HW. Ab initio and x-ray photoemission spectroscopy study of the bulk and surface electronic structure of pyrite (100) with implications for reactivity. Phys Rev B 2005;72. 235427-1e235427-10. [54] Womes M, Karnatak RC, Esteva JM, Lefebvre I, Alla G, Olivier-fourcade J, Jumas JC. Electronic structures of FeS and FeS2: X-Ray absorption spectroscopy and band structure calculations. J Phys Chem Solids 1997;58(2):345e52. [55] Opahle I, Koepernik K, Eschrig H. Full potential band structure calculation of iron pyrite. Comput Mater Sci 2000;17(2e4):206e10. [56] Blanchard M, Alfredsson M, Brodholt J, Wright K, Catlow CRA. Arsenic incorporation into FeS2 pyrite and its influence on dissolution: a DFT study. Geochem Cosmochim Acta 2007;71(3):624e30. [57] Abraitis PK, Pattrick RAD, Vaughan DJ. Variations in the compositional, textural and electrical properties of natural pyrite: a review. Int J Miner Process 2004;74(1):41e59. [58] Corkhill CL, Warren MC, Vaughan DJ. Investigation of the electronic and geometric structures of the (110) surfaces of arsenopyrite (FeAsS) and enargite (Cu3AsS4). Mineral Mag 2011;75(1):45e63. [59] Chanturiya VA, Fedorov AA, Matveeva TN. The effect of auroferrous pyrites non stoichiometry on their flotation and sorption properties. Physicochem Probl Miner Process 2000;34:163e70. [60] Vanderbilt D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys Rev B Condens Matter 1990;41(11):7892e5. [61] Monkhorst HJ, Pack JD. Special points for Brillouin-zone integrations. Phys Rev B 1976;13:5188e92. [62] Rajagopal AK, Callaway J. Inhomogeneous electron gas. Phys Rev B 1973;7(5):864e71. [63] Kohn W, Sham LJ. Self-consistent equations including exchange and correlation effects. Phys Rev 1965;140(4A):A1133e8. [64] Von Barth U, Hedin LA. Local exchange-correlation potential for the spin polarized case. J Phys C Solid State Phys 1972;5(13):1629e42. [65] Vosko SH, Wilk L, Nusair M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can J Phys 1980;58(8):1200e11. [66] Cocula V, Starrost F, Watson SC, Carter EA. Spin-dependent pseudopotentials in the solid-state environment: applications to ferromagnetic and antiferromagnetic metals. J Chem Phys 2003;119(15):7659e71. [67] Buerger MJ. The crystal structure of gudmundite (FeSbS) and its bearing on the existence field of the arsenopyrite structural type. Z fu¨r Kristallogr e Cryst Mater 1939;l0l:290e316. [68] Goodenough JB. Direct cation-vation interactions in several oxides. Phys Rev 1960;117(6):1442e51. [69] Mikhlin Y, Tomashevich Y. Pristine and reacted surfaces of pyrrhotite and arsenopyrite as studied by Xray absorption near-edge structure spectroscopy. Phys Chem Miner 2005;32(1):19e27. [70] Wood BJ, Strens RGJ. Diffuse reflectance spectra and optical properties of some sulphides and related minerals. Mineral Mag 1979;43(328):509e18.

80 Chapter 2 [71] Allison SA, Goold LA, Nicol MJ, Granville A. A determination various solution, products of the products of reaction between sulfide minerals and aqueous xanthate and a correlation of the with electrode rest potentials. Metall Trans 1972;3:2613e8. [72] Zeng K. Study on the flotation behavior and separation of sulfur-arsenic mineral. Master Thesis. Central South University; 2010. [73] Fernandez PG, Linge HG, Wadsley MW. Oxidation of arsenopyrite (FeAsS) in acid part 1: reactivity of arsenopyrite. J Appl Electrochem 1996;26(6):575e83. [74] Schaufuss AG, Nesbitt HW, Scaini MJ, Hoechst H, Bancroft MG, Szargan R. Reactivity of surface sites on fractured arsenopyrite (FeAsS) toward oxygen. Am Mineral 2000;85(11e12):1754e66. [75] Sirkeci AA. The flotation separation of pyrite from arsenopyrite using hexyl thioethylamine as collector. Int J Miner Process 2000;60(3e4):263e76. [76] Kydros KA, Matis KA, Papadoyannis IN, Mavros P. Selective separation of arsenopyrite from an auriferous pyrite concentrate by sulphonate flotation. Int J Miner Process 1933;38(1e2):141e51. [77] Vaughan DJ, Craig JR. Mineral chemistry of metal sulphides. Cambridge, U.K.: Cambridge University Press; 1978. [78] Prosfai M, Dodonay I. Pyrrhotite superstructures. Part I: fundamentals structures of the NC (N¼2, 3, 4 and 5) type. Eur J Mineral 1990:525e8. [79] Thomas JE, Smart RSC, Skinner WM. Kinetic factors for oxidative and non-oxidative dissolution of iron sulfides. Miner Eng 2000;13(10):1149e59. [80] Thomas JE, Skinner WM, Smart RSC. A mechanism to explain sudden changes in rates and products for pyrrhotite dissolution in acid solution. Geochem Cosmochim Acta 2001;65(1):1e12. [81] Janzen MP, Nicholson RV, Scharer JM. Pyrrhotite reaction kinetics: reaction rates for oxidation by oxygen, ferric iron, and for nonoxidative dissolution. Geochem Cosmochim Acta 2000;64(9). 15111-1522. [82] Oriova TA, Stupnikow VM, Krestan AL. Mechanism of oxidative dissolution of sulfides. Zh Prikl Khim 1988;61:2172e7. [83] Becker U, Hunz AW, Lennie AW, Thornton G, Vaughan DJ. The atomic and electronic structure of the (001) surface of monoclinic pyrrhotite (Fe7S8) as studied using STM, LEED and quantum mechanical calculations. Surf Sci 1997;389(s 1e3):66e87. [84] Becker M, Bradshaw D, Villiers JD. The mineralogy of pyrrhotite from Sudbury CCN and Phoenix nickel ores and its effect on flotation performance. Can Metall Q 2011;50(1):10e9. [85] Hong QY, Tang YH, Wang YH, liang DY, Yu LX. Investigation on properties and structure of pyrrhotite and the difference of its floatability. Metal Mine 2011;40:64e7. [86] Kalahdoozan M. Adsorption and flotation characteristics of hexagonal and monoclinic pyrrhotite. PhD Thesis. Queens University; 1996. [87] He MF, Qin WQ, Liz WZ, Chen YJ, Lai CH. Research on flotation performances of polymorphic pyrrhotite. Beijing: International Mineral Processing Congress Science Press; 2008. [88] Lawson V, Kerr AN, Shields Y, Wells PF, Xu M, Dai Z. Improving pentlandite pyrrhotite separation at INCO’s Clarabelle Mill. In: Centenary of flotation symposium. Brisbane: AusIMM; 2005. p. 875e85. [89] Wells PF, Kelebek S, Burrows MJ, Suarez DF. Pyrrhotite rejection at Falconbridge’s Strathcona Mill. In: Finch JA, Rao SR, Holubec I, editors. Processing of Complex Ores: Mineral Processing and the Environment. 1101. CIM: Montreal; 1997. p. 51e62. [90] Gerson AR, Jasieniak M. The effect of surface oxidation on the Cu activation of pentlandite and pyrrhotite. Beijing: International Mineral Processing Congress Science Pres; 2008. 2008. [91] Ward JC. The structure and properties of some iron sulphides. Rev Pure Appl Chem 1970;20:175e206. [92] Gao FM, He JL, Wu ED, Liu SM, Yu DL, Li DC, Zhang SY, Tian YJ. Hardness of covalent crystals. Phys Rev Lett 2003;91(1):0155021. [93] Pecina-Trevin˜o ET, Uribe-Salas A, Nava-Alonso F. Effect of dissolved oxygen and galvanic contact on the floatability of galena and pyrite with Aerophine 3418A. Miner Eng 2003;16(4):359e67. [94] Rao SR, Finch JA. Galvanic interaction studies on sulphide minerals. Can Metall Q 1988;27(4):253e9.

Electronic properties of sulfide minerals and floatability 81 [95] Ekmekci Z, Demirel H. Effects of galvanic interaction on collectorless flotation behaviour of chalcopyrite and pyrite. Colorectal Dis 2016;18(5):496e502. [96] Flotation AM. Gaudin memorial volume. In: Fuerestenau MC, editor. American institute of mining, metallurtical and petroleum engineers, New York; 1976. p. 1341. [97] Liu SB. Conceptual density functional theory and some recent developments. Acta Physico-Chim Sin 2009;25(3):590e600. [98] Geerlings P, De F. Conceptual DFT: the chemical relevance of higher response functions. Phys Chem Chem Phys 2008;10:3028e42. [99] Cruz R, Bertrand V, Monroy M, Gonzalez I. Effect of sulfide impurities on the reactivity of pyrite and pyritic concentrates: a multi-tool approach. Appl Geochem 2001;16(7e8):803e19.

CHAPTER 3

Surface relaxation and electronic properties of sulfide minerals In the formation of surface, the coordination of surface atoms is in an unbalanced state, which leads to the reconstruction of the surface, what is known as surface relaxation. For electronic properties, the discontinuity of periodic Bloch function on the surface leads to the change of surface electronic properties, and the existence of lattice defects will strengthen the discontinuity of this function. In 1932, Tamm proposed that when a crystal has a free surface, it will generate the energy level in the band gap, that is, the Tamm surface state. In 1939, Schockley proposed that dangling bonds on the surface of covalent crystals generate surface electronic states in the band gap, known as Schockley surface states. It has been demonstrated that the wave vector corresponding to the surface state energy level is a complex function, hence the surface state energy level is not permitted to appear in the permissible band of the infinite crystal, but only in the forbidden band. The surface structure and nature of the mineral are the basis of flotation and determine the basic flotation behavior of the mineral and the structure of reagent. This chapter discusses the surface structure and electronic properties of sulfide minerals.

3.1 Development of surface electronic states In 1932, Tamm and Schockley firstly proposed surface electron states based on the theory of quantum mechanics [1,2]. In 1947, Bardeen proposed the relationship between the state density of the semiconductor surface electron state and the electrochemical characteristics of the metal/semiconductor [3], which provided a theoretical foundation for the invention of the transistor. Since then, the research on the electronic state of the semiconductor surface has been closely linked with the development of semiconductor devices. The study of surface electron states can be divided into three stages: startup period, comprehensive development period, and mature period.

Electronic Structure and Surfaces of Sulfide Minerals. https://doi.org/10.1016/B978-0-12-817974-1.00003-X Copyright © 2020 Central South University Press. Published by Elsevier Inc. All rights reserved.

83

84 Chapter 3

3.1.1 Startup period Before 1975 was the beginning of the study of the surface state. The development of experimental testing technology was rapid, a lot of specialized research on surface atoms and electronic structure of the technology had been created. The earliest electronic spectrometer is the electron spectroscopy for chemical analysis developed by Siegbahn of Uppsala University in Sweden, where the light source is a characteristic soft X-ray of metal, X-ray photoelectron spectroscopy (XPS). It has a definite electron shift that is used to determine the chemical environment of the elements in the surface layer. In the 1960s, Auger electron spectroscopy (AES) was developed. The so-called Auger electron is an Xray photoelectric effect in the nonradiation back excitation when the electrons are emitted. This effect was first discovered by the French physicist Auger in 1925, thus being called Auger Electronics, and AES is mainly used to determine the surface layer of atomic composition. Contact potential difference measurement is mainly used to measure the work function of the metal. In 1962, Turner and others of the British Imperial College of London successfully developed a vacuum ultraviolet light photoelectron spectrum, known as ultraviolet photoelectron spectroscopy (UPS). It is mainly used to determine the binding electron energy and state density and the binding energy and state density of the surface state. Surface electron state and surface atomic structure are closely related. After years of efforts, in 1971, Tong and Rhodin for the first time successfully applied the multiple scattering theory to calculate the Al (001) surface of low-energy electron diffraction (LEED), and the result is consistent with Jona’s experimental results. Since then, the LEED spectrum has become an important means to determine the atomic structure of a fixed surface.

3.1.2 Comprehensive development period From 1975 to 1985 was the period of comprehensive development of this field, and the progress of other important technologies has promoted the development of surface state research. The following several new technologies had been developed: (1) Ultra-high vacuum technology is more mature; surfaces cleaned in the 10-14 Pa ultra-high vacuum can be maintained for several days. (2) With greater computer capacity and faster operation, the new data processing technology can quickly obtain experimental results. (3) The application of molecular beam epitaxy (MBE) in 1970 provided more and better research objects. (4) Synchrotron radiation storage ring provided high brightness, good polarization, and the wavelength range from UV to X-ray adjustable new light source. There was new development on the experimental method of surface electronic state, such as angle-resolved photoemission spectroscopy (ARPEC), which can be used to measure the dispersion relationship between the crystal bulk and the surface electrons, as well as

Surface relaxation and electronic properties of sulfide minerals 85 the development of inverse photoemission spectroscopy (IPES), which is made by the physical phenomenon of the photoelectric effect reversal process and can be used to determine the electronic structure of empty energy level of crystal. Due to the variable wavelength of the synchrotron radiation source, several new techniques for photon energy scanning were developed: partial yield spectroscopy (PYS) and constant initial state (CIS) spectra, which can be used to determine below and above states of vacuum level, respectively. And constant final state (CFS) is used to determine the initial density of electrons. In addition, LEED spectrum technology became more mature. At the same time, helium atomic beam scattering technique and high-resolution electron energy loss spectroscopy (HREELS), medium energy and high energy ion beam scattering technology, and surface X-ray absorption edge fine structure technology have become the experimental methods to study the structure of solid surface atoms. The main theoretical achievements of this period are as follows: (1) Moruzzi et al. calculated the work function of about 40 kinds of metals by KKR method, which is in accordance with the experimental results. (2) The study of the relaxation and reconstruction of semiconductors has been carried out successfully. The p bond chain model of Si (111)
2  1 reconstructed surface atomic structure and (110) surface relaxation structure and regularity of surface electronic structure of sphalerite structure semiconductor. (3) A number of physical models have been proposed for the hot topic of Schottky barrier and Si (111)
7  7 surface of metal/semiconductor interface. (4) Due to adsorption, catalytic reaction, and other application need, the research of transition metal surface has become an important hot spot. Also, in 1980, Klitzing et al. found the integer quantum Hall effect and won the 1985 Nobel Prize in Physics. In addition, in 1982, Cuiqi found the fractional quantum Hall effect, which is still an important research field of condensed matter physics.

3.1.3 Mature period After 1985, there were new developments in experimental technology: the scanning tunneling microscope (STM) and scanning tunneling spectroscopy (STS). STM can get the real space image of the surface atomic structure at atomic resolution. Due to its adjustable electronic energy, a real space image of the surface state associated with the surface local structure can be obtained by STS. Secondly, the LEED spectrum can be used to invert the real-space atomic structure image, and the low-energy positron emission spectroscopy (LEPD) is also applied in practice due to the technical improvement, and the atomic structure image produced by LEED spectral inversion is more clear. There was new progress on theoretical research during this period: (1) A complex surface structure of Si (111)
7  7 , which has puzzled people for 27 years, has finally been

86 Chapter 3 found a reasonable model. (2) In the local density functional framework, the electronic structure of the surface can be calculated as the electronic structure of the bulk and can also be included in the relativistic effect and multibody effect. (3) In 1985, Car and Parrinello proposed a new method of combining local density functional and molecular dynamics to give a process for the evolution of GaAs (110) relaxation surface atoms. These results show that the study of surface electronic states is indeed mature and is able to predict the possible structure. (4) In the field of fractional quantum Hall effect, there are new experimental results. In theory, the complex Fermi model and the related theory are proposed. (5) Great achievements have been made in theoretical calculation and experimental determination of Fermi surface structures of high Tc superconductors, and a new situation has been opened up in the experimental study of superconductor energy gap symmetry.

3.2 Surface relaxation and surface states: foundation 3.2.1 Surface relaxation Solid crystal is a stable periodic lattice structure; and the periodically arranged lattice structure of crystals breaks off in one direction to form a surface that is different from the structure of the bulk atoms. This aperiodic surface structure is no longer stressed symmetrically, and the distance between the surface atoms needs to be readjusting to achieve a new equilibrium. This phenomenon is called surface relaxation. Changes in the arrangement and bonding of such surface layers are sometimes referred to as surface reconstruction. The surface, due to the presence of unsaturated bonds and dangling bonds, shows a strong adsorption capacity and reactivity. It can be seen from Fig. 3.1 that there is a minimum between the total energy of the surface atoms and the atomic displacement. When the tungsten atom displacement is 0.018 nm, the total atomic energy of the surface atoms is the smallest, and the surface structure is the most

Figure 3.1 The relationship between the total energy of each surface of the W (001) plane and its distortion [4].

Surface relaxation and electronic properties of sulfide minerals 87 stable. When the surface atomic displacement is too large (more than 0.02 nm), the total surface energy of the surface increases sharply, and the surface is in an unstable state. The results show that the surface relaxation phenomenon occurs from the total energy of the system tending to the minimum, that is, the principle of lowest energy. Therefore, in general, for the surface study, the first thing need to be considered is to relax the surface to obtain the stable surface structure with the lowest surface energy.

3.2.2 Surface state The potential energy of the one-dimensional semiinfinite lattice at the bulk and the surface could be expressed as follows:
Vðz þ naÞ z < 0 (3.1) VðzÞ ¼ z0 V0 As shown in Fig. 3.2, when the semiinfinite lattice z < 0, the potential energy V(z) of the electron is the bulk potential energy, which is periodic, that is, V(z) ¼ V(z þ na), in which a is the lattice period constant; when z  0, the electron potential energy V(z) is the surface potential energy, and V(z) is constant (V0 ). The Schrodinger equation for a single electron:   Z2 d2 þ VðzÞ 4ðzÞ ¼ E4ðzÞ
2m dz2

(3.2)

When z > 0 (surface) and E < V0, the wave function can be written as follows: " pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # 2mðV0
EÞ z 41 ðzÞ ¼ A exp
Z , (z), V(z) Bulk a

(3.3)

Vacuum

V0 z

Figure 3.2 Potential energy (solid line) and surface state wave function (dotted line) of one-dimensional semiinfinite lattice.

88 Chapter 3 When z < 0 (bulk), the wave function can be written as follows: 42 ðzÞ ¼ Buk ðzÞeikz þ Cu
k ðzÞe
ikz

(3.4)

where the wave vector k is a real number in the range of
pa  k < pa . At z ¼ 0, the wave function and its derivative must satisfy continuous condition. As can be seen from the preceding formula, the electron energy level inside the crystal and the surface has different wave functions. In addition, it is necessary to consider the plural wave vector that occurs when the periodic potential field is interrupted at the surface of z ¼ 0: k ¼ k0 þ ik00 0

00

(3.5) 0

42 ðzÞ ¼ B0 uk ðzÞeik z e
k z þ C0 u
k ðzÞe
ik z ek

00

z

(3.6)

Let k00 > 0, when z/
N, to maintain a finite or tend to zero, then get B0 ¼ 0. The condition of the wave function and its derivative continuity at z ¼ 0 is this: C0 u
k ð0Þ ¼ A pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2mðV0
EÞ 0 0 0 C
ik u
k ð0Þ þ u
k ð0Þ ¼
A Z

(3.7) (3.8)

Eliminating the coefficients C0 and B in the preceding two formulas, the surface state level can be obtained: 2  Z2 u0
k ð0Þ 0
ik (3.9) Es ¼ E ¼ V0
2m u
k ð0Þ From Eq. (3.9), it can be seen that the wave vector corresponding to the surface energy level is a complex number, so this energy level cannot be in the permissible band of the crystal (corresponding to the wave vector is a real number) and can only be in the energy gap. The wave function corresponding to the surface state level is the surface wave function, as shown in Fig. 3.2, which is exponentially decaying in the vacuum region; in the crystal is the oscillating decay function. For three-dimensional crystals, the surface atoms are arranged in a two-dimensional periodicity, and the wave functions of two adjacent atoms overlap with each other, which results in interactions between the surface state wave functions, which expending the surface energy level to the surface energy band. The density of surface states is about the same order of magnitude as the number of atoms per unit surface area, about 1015 cm
2. If each surface atom provides a surface state electron, the number of surface electrons density is an order of 1015 cm
2. They form a subsystem that relies on bulk electronic systems and have some

Surface relaxation and electronic properties of sulfide minerals 89 rs = 5

ELECTRON DENSITY

1.0

POSITIVE BACKGROUND 0.5

rs = 2

0 –1.0

–0.5

0

0.5

1.0

DISTANCE (FERMI WAVELENGTHS)

Figure 3.3 Electronic density curves near the surface.

unique properties. Lang and Kohn [5,6] used a uniform-background (jellium) model to study the distribution of electron density on metal surfaces, as shown in Fig. 3.3. As can be seen from Fig. 3.3, the surface electron density distribution has the following characteristics: (1) Electron gas spills from the metal surface into the vacuum zone (z > 0), creating an electrostatic dipole layer on the surface. The potential generated by the dipole layer prevents the electrons from continuing to escape the metal and reach equilibrium. It can be seen from Fig. 3.3 that the electron distribution is continuous near the surface and no abrupt change occurs. This is mainly due to the fact that the actual surface barrier height is limited, and the electron has volatility. At the boundary, to ensure that the wave function and its derivative are continuous, electrons can traverse the surface, so the generation of such surface dipole layer is a reflection of the quantum effect. (2) Along the bulk direction, the electron density oscillating decays and is gradually equal to the electronic density of bulk. This oscillation, also known as Friedel oscillation, is a quantum effect of electronic volatility.

3.2.3 Slab model The surface structure is different from the bulk structure. The periodic structure changes from three-dimensional to two-dimensional. The periodic potential field above the surface layer breaks down and needs to be treated by different wave functions. In 1972,

90 Chapter 3 Appelbaum and Hamann used wave function bonding techniques to deal with the selfconsistent boundary conditions for semiinfinite metal crystal electronic structures [7]. Since both the bulk wave function 4B ðrÞ and the surface wave function 4S ðrÞ have twodimensional periodicity, they can be expanded with the following forms:  X 4ðrÞ ¼ eiðkz þk== Þ$r 4k k== ; z (3.10) k

 In the za point of the vacuum area far from the surface, both the 4Bk k== ; za and  4Sk k== ; za should tend to zero. At the zb point deep inside the bulk phase, the  4Bk k== ; zb must be smoothly coupled to the corresponding Bloch function   eikz zb u k== ; zb . For the surface state, 4Sk k== ; za function should tend to zero. According to the preceding processing, the projection map of the bulk energy band in the surface Brillouin zone and the dispersion curve of the surface state can be obtained. On this basis, the projected density of state of different atomic layers can be calculated. Calculations on the Na(100) surface show that the projected density of states a few atomic layers from the surface can reach that of the corresponding atomic layers in the bulk. This result shows that the electronic structure of the bulk and surface can be obtained by calculating the bulk energy band using the slab model and the supercell method. The concept of a slab is a model consisting of five to ten atomic layers plus a vacuum ˚) layer of a certain thickness. It is also considered that the slab vacuum region (10
20 A repeats infinitely in the z direction of the vertical crystal plane to form a supercell model, as shown in Fig. 3.4. In this way, the electronic structure of the crystal can be calculated by using any kind of band calculation method under the local density approximation. The electronic structure of the core layer of the crystal has the characteristics of bulk or infinite crystal, and the electronic structures of the edge layer and the near edge layer of the crystal represent the electronic structure of the outer surface and the subsurface of the crystal. In other words, the electronic structure of the surface can be obtained by calculating the bulk energy band structure using a model with a surface plus vacuum layer. The thickness of the vacuum layer is mainly to eliminate the mirror effect between the surfaces: too large vacuum layer thickness will increase the calculation, so the thickness is ˚. generally 10e20 A

3.3 Surface relaxation and surface state of sulfide minerals 3.3.1 Surface relaxation of sulfide mineral After cleavage of mineral surface, different surface relaxation or even surface reconstruction will appear. Fig. 3.4 shows the slab models of galena (100) surface, pyrite (100) surface and sphalerite (110) surface.

Surface relaxation and electronic properties of sulfide minerals 91

Figure 3.4 The slab models of mineral surface: (A) galena (100) surface, (B) pyrite (100) surface, and (C) sphalerite (110) surface.

The coordination number and atomic displacement of surface atoms on the relaxed galena (100) and pyrite (100) surfaces are listed in Tables 3.1 and 3.2, respectively, where the negative sign indicates that the atoms relax in the negative direction along the axis and the positive sign indicates the positive direction along the axis. For the galena (100) surface, the first layer sulfur atoms and lead atoms move toward the internal surface direction, and the second layer atoms move toward the external surface along the z-axis direction. The third layer atoms are relaxed to the internal surface with very small atomic displacements. For the pyrite (100) surface, the first layer sulfur atoms move toward the internal surface, and the second layer Fe atoms appear the most obvious relaxation with the atomic Table 3.1: The coordination number and atomic displacement of galena (100) surface atoms. ˚ Atomic displacement/A Atom Pb atom of the 1st layer S atom of the 1st layer Pb atom of the 2nd layer S atom of the 2nd layer Pb atom of the 3rd layer S atom of the 3rd layer

Coordination number 5 5 6 6 6 6

Dx
0.001 0 0 0.001
0.001 0

Dy
0.001 0 0
0.003
0.001 0

Dz
0.082
0.101 0.010 0.128
0.040
0.060

92 Chapter 3 Table 3.2: The coordination number and atomic displacement of pyrite (100) surface atoms. ˚ Atomic displacement/A Atom

Coordination number

S atom of the 1st layer Fe atom of the 2nd layer S atom of the 3rd layer S atom of the 4th layer Fe atom of the 5th layer S atom of the 6th layer S atom of the 7th layer Fe atom of the 8th layer S atom of the 9th layer

3 5 4 4 6 4 4 6 4

Dx

Dy

0.060 0.065 0.021 0.008 0.005 0.003
0.002 0
0.002


0.062 0.065 0.032 0.004
0.010
0.008 0 0.001 0.002

Dz
0.035
0.090 0.093 0.003 0.014 0.003 0.004 0
0.003

˚ to the internal direction. The third layer S atoms are relaxed to the displacement of 0.1 A external surface. The atoms only exhibit significant relaxation at the top three layers, and the fourth to sixth layer atoms undergo a slight displacement, and the relaxation of the seventh to ninth layer atoms is negligible. The results of surface relaxation suggest that surfaces of pyrite and galena undergo relaxation after surface cleavage, but there is no obvious surface reconstruction, and only the top three layers of atoms have relaxation. The calculated structural parameters of perfect sphalerite (110) surface and the results of LEED [8] analysis are shown in Table 3.3. Schematically relaxation is shown in Fig. 3.5, and the structural parameters are also defined in Table 3.3. It is shown that the calculation results are in good agreement with the experimental values. For a surface of certain minerals, apparent reconstruction of surface atoms occurs when the surface relaxes. For chalcopyrite, the cleavage of (001) surface results in a surface reconstruction, as shown in Fig. 3.6. It is found that after surface reconstruction, the first layer of iron and copper atoms moves to the second layer, and the second layer of sulfur atoms moves to the first layer. This is in agreement with the calculated results of Oliveira [9] et al. Similar surface reconstruction occurs on pyrrhotite (001) surface, as demonstrated in Fig. 3.7. After surface reconstruction, the originally located at the second layer of sulfur atoms shift to the first layer, and the first layer of iron atoms move to the second layer. Table 3.3: Structural parameters for the sphalerite (110) surface relaxation. a0 LEED [8] DFT
GGA

5.41 5.50

˚) D1t (A

˚) D1X (A

˚) D2t (A

0.59 0.55

4.19 4.21

0.00 0.00

˚) d12t (A 1.53 1.49

˚) d23t (A 1.91 1.87

˚) d12X (A 3.15 3.12

Surface relaxation and electronic properties of sulfide minerals 93 Δ1,x d12,x

Side view

π-ω Δ1,1 α

d0

γ

d12,1 Δ2,1 Δ3,1

d0

Figure 3.5 Side view of sphalerite (110) surface unit cell (small solid sphere represents Zn, and large hollow sphere represents S).

(A) Cu

Fe Fe S

Cu

(B)

S

S

Cu Fe

Figure 3.6 The reconstruction of chalcopyrite (001) surface (A) before surface reconstruction and (B) after surface reconstruction.

Figure 3.7 The reconstruction of pyrrhotite (001) surface (A) before surface reconstruction and (B) after surface reconstruction.

3.3.2 Surface state energy level of sulfide mineral surface The atoms on the surface layer environment are very different from atoms in the bulk phase and the unsaturated surface atoms exhibit strong surface reactivity. According to

94 Chapter 3 (A)

(B)

2

1

E

0

-1

F

Energy/eV

Energy/eV

1

E

0

F

-1

-2

-2

-3 G

2

-3 F

Q

Z

G

F

Q

Z

G

Figure 3.8 Band structure of bulk and galena (100) surface: (A) bulk galena and (B) galena (100) surface.

energy band theory, due to the discontinuity of the periodic Bloch function in the surface, the surface atomic electron energy level enters the forbidden band, forming a new surface state. Here, we discuss the surface state of galena and pyrite surfaces. The width of the band is very important in the analysis of energy band. The wider the band, that is, the larger the fluctuation in the band diagram, indicating that the smaller the effective mass of the electron in this band, the greater the degree of non-local, and the stronger the extensibility of the atomic orbital that makes up this band. If the shape of the energy band is similar to a parabola, it is generally called sp-like band; conversely, a relatively narrow band indicates that the eigen states of this band are mainly composed of atomic orbitals localized at a lattice point. The electron localization on this band is very strong and the effective mass is relatively large. Band structures of bulk and galena (100) surfaces are shown in Fig. 3.8. It is noted that the energy bands of galena (100) surface are much more than that of bulk galena. This is because the number of atoms in the surface model is larger than that of the bulk model. Compared with the band structure of bulk galena, the band gap of galena (100) surface increases from 0.5 to 0.7 eV, which indicates that the electronic structure of galena (100) surface has changed significantly, and consequently the electron may require more energy to transit from the valence band to the conduction band. In addition, the band structure of galena surface has also changed obviously: (1) The bands of the conduction band on galena surface are separated into two groups, while the bulk conduction bands cross each other into a group of energy bands, indicating that the appearance of the surface leads to the division of the conduction band energy level, and the energy level that is near the Fermi level is more likely to obtain electrons. (2) The top of the valence band on the surface of galena is significantly closer to the Fermi level than the bulk galena.

Surface relaxation and electronic properties of sulfide minerals 95 (A) 2

(B) 1

0

-1

E

Energy/eV

Energy/eV

1

E

0

F

-1 G

F

Q

Z

G

Figure 3.9 Band structures of bulk pyrite and pyrite (100) surfaces.

According to molecular orbital theory, the energy level at the top of the valence band is the easiest to give the electron, so the electrons on the galena surface are more active than the bulk electrons. The band structures of bulk pyrite and pyrite (100) surfaces are shown in Fig. 3.9. Compared with bulk pyrite, the band structure of pyrite surface exhibits obvious differences. First, the band gap of the pyrite surface is narrowed to 0.45 eV, while the bulk band gap is 0.62 eV. This phenomenon is contrary to the galena surface. The forbidden bandwidth of galena surface is larger than that of the bulk phase, which indicates that the pyrite and galena have obvious differences in semiconductor properties. Secondly, the valence band on the pyrite surface shifts downward, indicating that the electronic capability of pyrite surface has been enhanced. The energy band at the bottom of the conduction band is more gentle than that of the bulk, suggesting that the effective electron mass at the bottom of pyrite surface increase, and the localization of electrons becomes stronger. In addition, the valence band on the pyrite surface reaches the Fermi level at G point, indicating that the surface of the pyrite has a certain metallicity, and the electrons easily transit to the conduction band. According to the previous discussion, the band gap of surface galena is larger than the bulk galena, while the band gap of surface pyrite is smaller than the bulk pyrite. Fig. 3.10 shows the variation of the surface energy band between the galena and pyrite minerals. The width of forbidden band is an important characteristic of the semiconductor, and its value is related to the band structure of semiconductor; that is, it is related to the crystal structure and the binding property of atoms. A large number of electrons in semiconductor valence band are electrons on the valence bond, called valence electrons, and they are conductive, which means they are not charge carriers. Only when the valence electrons transit to the conduction band to generate free electrons and free holes can they

F

96 Chapter 3 Pyrite

Galena Conduction band

Conduction band

Bulk Eg

Surface Eg

Bulk Eg

Surface Eg

Valence band Valence band

Figure 3.10 Energy band models of galena and pyrite.

conduct electricity. Therefore, the width of the band gap is actually a physical quantity that reflects the extent of binding of valence electrons, that is, the minimum energy required to generate the intrinsic excitation. According to the previous study on the relaxation of galena and pyrite surfaces, the galena surface has a large relaxation, while the pyrite surface has a small relaxation. Therefore, it can be speculated that the change in the band gap of pyrite and galena is due to different reasons. The decrease of the forbidden bandwidth on the pyrite surface is not caused by the relaxation of the surface, but due to the decrease in the coordination number of the surface atoms and the weakening of the binding ability of surface atoms to valence electrons, thereby reducing the energy of valence electron transitions to the conduction band. The coordination number of the atoms on galena surface is also reduced compared with the bulk atoms. However, due to the larger atomic number of lead atom, the valence electron binding is stronger, which weakens the influence of the coordination number change on the surface properties. The great relaxation of galena surface has a significant effect on the binding of valence electrons, resulting in an increase in the electron transition energy. The difference in surface band gap between galena and pyrite indicates that the galena surface has a stronger valence electron binding capacity than the pyrite surface, so it can be assumed that the electron activity of galena surface is weaker than the pyrite surface. The research results confirm that the adsorption product of sulfydryl collectors on galena surface is metal salts, and there is no electrochemically adsorbed collector product, whereas electrochemical adsorption of xanthate, dithiophosphate, and dithiocarbamate all occur on pyrite surface, and collector dimers are formed.

3.4 Density of states of sulfide minerals surface 3.4.1 Density of states of surface In solid physics, especially metal conductors, the density of states of electrons at the Fermi level is the most important and most active. In terms of the physical sense, the

Surface relaxation and electronic properties of sulfide minerals 97

Figure 3.11 The surface model of pyrite (100) surface. (Numbers are the labels of atoms in different layers.)

Fermi level is the average electrochemical potential of electrons; from the statistical point of view, the Fermi level is the sign that the quantum state is occupied or unoccupied by electrons, and the quantum state below the Fermi level is basically occupied, while that above Fermi energy level is basically unoccupied. Therefore, the electron density distribution near the Fermi level basically represents the ability of electrons to transfer; that is, the electrons near the Fermi level are most active. Fig. 3.11 shows the surface model of pyrite (100) surface, and numbers are the labels of atoms at outer, subsurface, and bulk layers. Figs. 3.12 and 3.13 are the density of states (DOS) of Fe and S atoms at different positions. From Fig. 3.12, it can be seen that compared with the bulk iron atom (Fe12), the coordination number of the subsurface iron atom (Fe7) does not change, and the DOS of electrons also does not change much; the DOS of bonding orbital of Fe 3d eg remains almost unchanged. A peak of antibonding orbital eg appears at the 1e2 eV, which indicates that the bond between the iron atoms of the secondary surface layer is weakened and the activity is enhanced. In addition, the

98 Chapter 3

Density of states/electrons. eV-1

7 6 5 4 3 2 1 0 6 5 4 3 2 1 0 6 5 4 3 2 1 0

EF

t2g Bulk Fe12

Fe 3d

e*g

eg

t2g

Subsurface Fe7

e*g

eg

t2g

Surface Fe3

eg

-4

e*g

-2

0

2

Energy/eV

Figure 3.12 Density of states of Fe atoms at different layers of pyrite (100) surface.

nonbonded orbital of Fe 3d t2g changes comparable to that of the bulk Fe atom, which is due to the decrease in the spatial symmetry of the iron atoms in the subsurface layer. The iron atom on the pyrite surface (Fe3) has only five coordinations due to its bond breakage, which is one coordination less than the six-coordinated bulk iron atom. It can be clearly

2

3p

3s

th

7 layer S (S5)

Density of states/eletrons. eV

-1

1 0 2

3s

3p

th

5 layer S (S5)

1 0 2

3p 3s

Surface bottom S (S3)

1 0 2

3p

3s

Surface top S (S1)

1 0 -14

-12

-10

-8

-6

Energy/eV

-4

-2

0

EF

Figure 3.13 Density of states of S atoms at different layers of pyrite (100) surface.

Surface relaxation and electronic properties of sulfide minerals 99 50

EF

Density of states/electrons. eV -1

surface

s p d

40

30

20

10

0

-18

-15

-12

-9

-6

-3

0

3

Energy/eV

Figure 3.14 Total density of states of pyrite (100) surface.

seen from Fig. 3.12 that the DOS of bonding orbital of Fe 3d eg near 2 eV is obviously enhanced, which indicates that the bonding ability of surface iron atoms becomes stronger, and the 3d states in the conduction band changes from one peak to two peaks. Compared with the bulk hexacoordinated iron atom (Fe12), the band gap of five-coordinated Fe3 atoms in the surface decreases, and the 3d states clearly pass through the Fermi level. Therefore, the pyrite (100) surface has some metal-like features, which are consistent with the physical phenomenon that pyrite samples have an optical reflective surface, and is also consistent with the calculations of Hung et al. [10]. Fig. 3.13 is density of states of S atoms at different layers of pyrite (100) surface. The 3p state of S1 atom on the surface layer contributes most to the DOS between
2.5 and 0 eV, followed by the S3 atom on the third layer, and the DOS of S5 and S7 atoms on the deep layer are almost the same. It is clear that the surface atoms below the top three layers are relatively stable, which is consistent with the result of surface atomic relaxation. Fig. 3.14 shows the total DOS of pyrite (100) surface. Comparing the DOS of iron atoms and sulfur atoms, it is found that the overlap of the 3d state of the surface iron atoms and the 3p state of the sulfur atoms near the Fermi level increases, indicating an increased hybridization effect. In addition, the 3d state of the iron atom on the pyrite surface contributes most to the DOS, and it can be predicted that the surface iron sites will be the reactive sites during the redox reaction. This is in agreement with the STM study and theoretical calculations by Rosso et al. [11]. They calculated using a slab model and found that the surface state of iron atoms enters the band gap due to the lack of surface

100 Chapter 3 coordination, and this surface state was confirmed by STM studies. Furthermore, the DOS of surface iron and sulfur atoms indicates that the highest occupied state is mainly contributed by Fe 3dz2 , and the lowest unoccupied state is the mixed contribution from Fe 3dz2 and S 3p states.

3.4.2 Charge distribution of surface atoms In the process of rebalancing of surface structure, not only the geometric structure will be reconstructed, but the charge of surface atoms will also be redistributed. Table 3.4 shows the surface Mulliken charge distribution of pyrite (100), and the location of atoms is shown in Fig. 3.11. It is found from Table 3.4 that there is a very obvious change in the sulfur and iron atoms from the bulk phase to the surface layer. That is, the sulfur atom changes from the positive charge of the bulk phase to the negative charge of the surface. The iron atom changes from negative charge in the bulk to the positive charge on the surface. From the bulk layer to the surface layer, the number of electrons of S 3s and 3p orbital increases, and the electrons of S 3p orbital increase significantly, indicating that the surface sulfur atoms obtain electrons from the iron atom in the surface reconstruction and charge rebalance process. For iron atoms, from the bulk layer to the surface layer, the number of electrons of Fe 4s and 3d orbitals remains almost constant, and the number of electrons of Fe 4p orbital decreases significantly, decreasing from the bulk 0.64 e to the surface 0.43 e, indicating the decrease of electrons of surface Fe 4p orbital. The lost electrons of Fe 4p corresponds to the electrons of the surface S 3p orbital, suggesting that during surface atomic reconfiguration and charge reequilibrium, the electron transfer between sulfur atoms and iron atoms takes place in the p orbital with similar energy. This phenomenon may be related to the small relaxation of pyrite surface. From the electron changes of the sulfur and the iron atoms, it is known that on the surface of pyrite (100), electrons are transferred from the iron atom to the sulfur atom, which is consistent with the opinion put forward by Nesbitt et al. [12]. That is, on the pyrite surface where the sulfuresulfur bond is broken, a redox reaction occurs, in which the iron atom loses Table 3.4: Mulliken charge of atoms of relaxed pyrite surface. Layer Surface layer Subsurface layer Bulk layer

Number of atoms S1 S4 Fe3 S5 S7 Fe7 S9 Fe12

s

p

d

1.86 1.82 0.34 1.80 1.81 0.35 1.81 0.35

4.25 4.20 0.43 4.10 4.12 0.61 4.11 0.64

0 0 7.15 0 0 7.16 0 7.17

Total Charge/e 6.11 6.02 7.92 5.90 5.93 8.12 5.92 8.16


0.11
0.02 þ0.08 þ0.10 þ0.07
0.12 þ0.08
0.16

Surface relaxation and electronic properties of sulfide minerals 101

Figure 3.15 Sketch map of changes of charge of pyrite from bulk to surface.

electrons to be oxidized and the sulfur atom obtains electrons to be reduced. The study of pyrite (100) surface using XPS method also confirms the transfer of surface charge from iron atom to sulfur atom [13]. In addition, the atomic spin value indicates that both the five-coordinate iron atom on the pyrite (100) surface and the bulk iron atom are spinneutral. In general, the Fermi level of a metal is higher than that of a semiconductor. Analysis of the DOS shows that the pyrite surface has some metal-like characteristics and the bulk phase is a semiconductor. Therefore, electrons have a tendency to flow from the surface to the bulk, where the pyrite surface has electron-withdrawing ability, and the analysis of the surface atomic charge confirms this result. As shown in Fig. 3.15, the number of sulfur and iron atoms is the same for every six atomic layers, so every six atomic layers form a periodic layer. The first six atomic layer from the surface is the surface layer, and the second six atomic layers can be considered as the bulk layer. Numbers in Fig. 3.15 are the total charge of the surface and bulk layers. The results show that the charge on the surface layer is
0.33 e and the charge on the bulk layer is
0.97 e. This indicates that the bulk layer is in an electron-rich state and the surface layer is in an electron-deficient state. Therefore, the surface layer of pyrite has the ability to attract electrons. In the flotation practice, since the pyrite surface has electron-withdrawing properties, the electrons on the xanthate are easily transferred to the pyrite surface, and an oxidation reaction occurs to form dixanthogen.

102 Chapter 3 Table 3.5: Mulliken charge distribution of atoms on the galena after surface relaxation. Layer Surface layer Subsurface layer Bulk layer

Atom Pb S Pb S Pb S

s

p

d

1.98 1.93 1.90 1.92 1.88 1.93

1.41 4.75 1.43 4.73 1.41 4.74

10 0 10 0 10 0

Total 13.39 6.68 13.33 6.65 13.29 6.67

Charge/e 0.61
0.68 0.67
0.65 0.71
0.67

The galena surface has a layered structure, and the lead atoms and sulfur atoms in each layer have the same z-coordinate, and the surface structure is relatively simple. The changes of Mulliken charge of the top three layers of galena after the surface relaxation are shown in Table 3.5. It is found that the charge of sulfur atom changes from
0.67 to
0.68 e from the bulk layer to the surface layer, but the change in the atomic charge of lead atom is notable, from 0.71 e in the bulk layer to 0.67 e in the secondary surface layer and 0.61 e to the outer surface layer. The charges of lead atom of galena have a tendency to decrease from the bulk to the surface. From the orbital distribution of electrons, the valence electron of Pb atom is 5d106s26p2, and the valence electron of S atom is 3s23p4. In the galena crystal, the interaction is mainly between the S 3p orbital and Pb 6p orbital, and the electrons of Pb 6p orbital transfer to S 3p orbital. During the relaxation of the galena surface, the electrons in the sulfur 3p orbital and lead 6p orbital basically did not change, indicating that the relaxation of the galena surface does not substantially change the interaction between sulfur 3p orbital and lead 6p orbital, but the electrons in external surface layer Pb 6s orbital obviously increase from the 1.88 e in the bulk to 1.98 e in the external surface. From the surface electron distribution and charge change of galena, the total number of electrons on the outer surface of galena is larger than that of the bulk layer, and the change in net charge is from 0.04 e in the bulk layer to
0.07 e in the outer layer. It is indicated that the surface of galena has the property of enriching electrons. This property of galena surface is not in favor of the oxidation of xanthate to form dixanthogen. At present, only lead xanthate is detected on the galena surface, and no dixanthogen is found. The surface structure of sphalerite (110) is shown in Fig. 3.16, and the Mulliken charge of sphalerite atoms is listed in Table 3.6. After the geometric reconstruction of sphalerite surface, the atomic charge of surface atoms is redistributed, the charge distribution of zinc atoms changed greatly, and the change of sulfur atoms was small. In the crystal structure of sphalerite, one zinc atom is coordinated with four sulfur atoms and one sulfur atom is coordinated with four zinc atoms, and the zinc and sulfur atoms are four-coordinated. Due to the breakage of surface atomic bonds, the outer surface layer atoms have two structures: the three-coordinated Zn1 and S1 and the four-coordinated Zn2 and S2. Therefore, the electron transfer and distribution of atoms with different coordination numbers are different.

Surface relaxation and electronic properties of sulfide minerals 103

Figure 3.16 Model of sphalerite (110) surface. Table 3.6: Mulliken charge distribution of atoms on the sphalerite after surface relaxation. Layer Surface layer

Subsurface layer

Bulk layer

Atom S1 (three-coordinate) S2 (four-coordinate) Zn1 (three-coordinate) Zn2 (four-coordinate) S3 (four-coordinate) S4 (four-coordinate) Zn3 (four-coordinate) Zn4 (four-coordinate) S5 (four-coordinate) S6 (four-coordinate) Zn5 (four-coordinate) Zn6 (four-coordinate)

s

p

d

1.86 1.82 0.91 0.75 1.82 1.82 0.55 0.46 1.82 1.82 0.50 0.48

4.65 4.67 0.79 0.93 4.65 4.66 0.93 0.93 4.66 4.66 0.94 0.94

0.00 0.00 9.97 9.98 0.00 0.00 9.98 9.98 0.00 0.00 9.98 9.98

Total 6.51 6.49 11.68 11.66 6.47 6.48 11.46 11.37 6.48 6.48 11.41 11.40

Charge/e
0.51
0.49 0.32 0.34
0.47
0.48 0.54 0.63
0.48
0.48 0.59 0.60

104 Chapter 3 The valence electron configuration of sulfur is 3s23p4, and that of zinc is 3d104s24p0. The 3s orbital of bulk sulfur atom loses electrons and the bulk S 3p orbital obtains electrons. The 4s and 4p orbitals of bulk zinc atoms are hybridized and lose their electrons. Zinc 3d orbital is not involved in the reaction because it is in a deeper energy level and is a filled stable structure. Therefore, the electron transfer of sulfur atoms and zinc atoms in the bulk sphalerite occurs mainly in the s orbital and p orbital. Although the atoms in the subsurface layer are all four-coordinated, as in the bulk phase, they have an asymmetrical structure in the z direction due to the attachment to the outer surface layer. The sulfur atom charge at different positions in the subsurface layer does not change much, but the zinc atoms in different positions have large differences. The 3d and 4p orbital electrons of the Zn3 and Zn4 atoms did not change, but there was a large difference in the 3s orbital. Compared to bulk zinc atoms, the 4s orbital of Zn4 atom in the subsurface layer loses electrons and the 4s orbital of Zn3 atom obtains electrons, showing the influence of the spatial structure on the ability of the zinc atom to acquire electrons (the zinc 4s orbital is an active outer orbital). For the zinc and sulfur atoms on the outermost surface of sphalerite, the Zn1 and S1 atoms are three-coordinated due to the bond breaking, and the Zn2 and S2 atoms are still tetracoordinated. It is clear that the decrease in the coordination number would cause a large change in the distribution of electrons. Three-coordinated sulfur atom (S1) has more electrons in the 3s orbital, and the charge of surface S1 atom is also more negative than that of the bulk S. The coordination number of S2 atom (fourcoordinated) does not change, but the symmetry of the spatial structure changes. Therefore, there is only a small change in the charge of S2 atom, which is basically close to the bulk charge. For zinc atoms, the charges of three-coordinated zinc atoms and tetracoordinate zinc atoms undergo large changes. Compared with bulk zinc atoms, the electrons of Zn 4s orbital all increase, and the electrons of 4p orbitals are different. The 4p orbital of Zn1 atom loses electrons, and that of Zn2 (tetracoordinate) atom does not change, indicating that the electron distribution of three-coordinated zinc atom is most affected. From the preceding analysis, it is found that the electrons on the outer surface of the sphalerite have more electrons than the bulk layer, indicating that the surface of the sphalerite has been enriched in electrons. The electrons of 4s orbital of the three-coordinated zinc atom increase obviously, suggesting a reduced nucleophilicity of three-coordinated zinc atom, which is not favorable for the interaction with the collector that has a nucleophilic sulfhydryl group.

3.5 Effect of surface structure on the electronic properties Theoretically, the smaller the atomic coordination number, the smaller the binding effect on valence electrons, the reduced localization of electrons, the enhanced delocalization of electrons, and the stronger the atomic reactivity. Due to the asymmetry of the surface

Surface relaxation and electronic properties of sulfide minerals 105 8 4

DOS/electrons. eV

-1

0 4 0 4 0

(110) surface three-coordination Fe atom Fe 3d (210) surface four-coordination Fe atom Fe 3d

Fe 4p

(100) surface five-coordination Fe atom Fe 3d Bulk six-coordination Fe atom

4

Fe 3d

0 4

Fe 3d

Free Fe atom

0 -10

Fe 4s 0

-5

Fe 4p 5

Energy/eV

Figure 3.17 DOS of pyrite iron atom with different coordination number.

structure, with the relaxation of the surface structure, the surface electrons will also be redistributed to form surface electronic states. As early as 1932, Tamm proposed that the existence of a surface will give rise to surface states with energies different from the energies of the bulk states. For a surface with d electrons (most of the sulfide minerals have d electrons), the coordination number of atoms in the outermost layer of the surface is smaller than that of atoms in the bulk phase, which causes the increasing of potential energy of d electrons. This causes the originally localized d-state to produce a d electron surface energy level higher than that of bulk energy level, which is the surface Tamm state. Fig. 3.17 shows the DOS of iron atoms with different coordination numbers in the pyrite bulk and surface. The free iron atom can be considered a special case with zero coordination number. For free iron atoms with zero coordination number, the DOS at the Fermi level are mainly composed of 3d and 4s orbitals. When the coordination number of iron atom increases from 3 to 6, the electron states of p and s orbital near the Fermi level disappear, leaving only the 3d state. It is indicated that due to the the increase of coordination number of iron atom, the degree of binding electrons is enhanced. In addition, as far as the 3d electronic state of iron atoms is concerned, the 3d states of iron atoms with different coordination numbers are very different. The 3d electron state of tricoordinated iron atom on (110) plane has the strongest delocalization, and the states of 3d orbital do not split. The 3d orbital states of iron atoms, whose coordination is tetracoordinated, pentacoordinated, or hexacoordinated, are clearly divided into three parts, where the Fermi level is t2g nonbonding orbital, and the other two parts are eg bonding orbital and eg antibonding orbital. From the surface state of the iron atom, the DOS of the surface iron atoms decrease with the decrease of coordination number, and the 3d state moves toward the positive energy level; that is, the coordination number

106 Chapter 3 decreases, resulting in an increase in the d electron energy level and forming surface state energy levels.

3.6 Surface atomic reactivity on sulfide minerals 3.6.1 Frontier orbital coefficient In the mineral flotation process, the interaction between reagent molecules and minerals occurs on the mineral’s surface, and the chemical reactivity of mineral surface atoms is related to their environment, which referrs to the type of the adjacent atoms, the coordination number of the atoms and the spatial structure of the atoms. Any change in any of these three environmental factors will cause the change of the activity of surface atoms. For example, for galena and cerussite, their lead atoms are in different spatial structures and have different coordination, and their reactivity is also different. Xanthate can easily float galena, but it cannot float cerussite. For pyrite, marcasite, and pyrrhotite, they have the same coordinating atom, i.e., a sulfur atom, but the surface space structure for the iron atom is different. Therefore, the iron atoms on the surface of the three iron sulfides have different reactivity as well as different floatability. Fig. 3.18 is the surface structure of pyrite (100) surface. It is found that the iron atoms on the pyrite (100) surface are all tetracoordinated (Fe1, Fe2, Fe3, Fe4) and have the same coordination number as that of bulk iron atom; while sulfur atoms have two types: tricoordinated sulfur atoms (S1, S2, S3, and S4) and tetracoordinated sulfur atoms (S5, S6, S7, and S8) (having the same coordination number as the bulk sulfur atom). From the previous discussion, it is known that the tricoordinated sulfur atom (S1) is more active than the tetracoordinated sulfur atom (S2), and it is generally believed that the oxidation of sulfur occurs preferentially at the tricoordinated sulfur atom. The determination of the reactivity of atoms at different positions on the mineral surface is of great significance for further understanding of the mechanism of mineral surface adsorption. In the discussion of the frontier orbital in Chapter 2, it has been pointed out that the atom’s contribution to the frontier orbital can be known by comparing the frontier orbital coefficients of the atom, and the atom that contributes most to the frontier orbital is the most reactive atom. The effect of lattice impurities on the properties of sphalerite, galena, and pyrite was studied using the frontier orbital coefficients [14e16]. Similarly, we

Figure 3.18 Surface structure of pyrite (100) plane.

Surface relaxation and electronic properties of sulfide minerals 107

Figure 3.19 Model of galena (100) surface. (Numbers in the figure label different atoms.)

use the frontal orbital coefficients to study the reactivity of surface atoms. The frontier orbital coefficients of galena surface atoms were calculated by using slab model. The galena (100) surface model and atom number are shown in Fig. 3.19. It is known from the previous description that the slab model is separated by a vacuum layer in the z direction and has periodicity in the x and y directions. Therefore, the upper and lower three layers in Fig. 3.19 are symmetrical and the same. It can be inferred that the bulk atoms are completely coordinated, and there is no excess valence bond, so the reaction activity should be the lowest. The outer surface atoms are unsaturated and have valence bonds, and the reaction activity would be the highest. However, the calculation results show that the atoms with the largest HOMO orbital and LUMO orbital coefficients on the galena surface are not atoms on the external surface, but appear in the subsurface and bulk layers, respectively. The atoms with the largest HOMO orbital coefficient are S43 (0.2473) atoms and Pb16 (0.2445). The atoms with the largest LUMO orbital coefficients are S11 (0.2953) and Pb38 (0.2774). The HOMO orbital coefficients of the outer surface layer atoms S21 and Pb18, which are the inferred most active atoms, are only 0.03367 and 0.1203, and the LUMO orbital coefficients of S45 and Pb42 are only 0.1044 and 0.05921, respectively. This result does not correctly reflect the surface structure of the mineral and

108 Chapter 3 the reactivity of the surface atoms and is therefore unreasonable. For mineral surfaces, only atoms on the outer surface have unsaturated bonds and thus have adsorption reactivity, while the subsurface and bulk layer atoms are in a saturated coordination state which are impossible to have adsorption reactivity. The reason for this result is that the frontier molecular orbital theory is based on molecular theory, which treats the mineral surface as a molecular structure in which any atom can be reactive. However, the atoms with adsorptive activity in minerals can only be atoms on the outer surface, not inside of the mineral. Therefore, the frontier orbital theory is not suitable for studying mineral surfaces with periodic structures.

3.6.2 Fukui functions The chemical potential, chemical hardness and softness, and reactivity indices have been used by a number of researchers to evaluate the reactivity of molecules or atoms. Various methods include atomic charge computation, free valency, spin populations, and the charge of density had been adopted. Among these methods, the most successful and best-known method is the frontier orbital theory. However, our previous results indicate that the frontier orbital theory is not suitable for characterizing the reactivity of mineral surface atoms. Another method, the Fukui function, relates the reactivity of a molecule with respect to electrophilic and nucleophilic attack to the charge density [17e21], is introduced. These so-called Fukui functions (FFs) are a qualitative way of measuring and displaying the reactivity of a molecule. The FF measures the sensitivity of the charge density, r(r), with respect to the loss or gain of electrons via the expressions: 1 ðrÞ
rN ðrÞÞ (3.11) ðr DN NþD 1 (3.12) ðr ðrÞ
rN
D ðrÞÞ f
ðrÞ ¼ DN N  1

(3.13) f 0 ðrÞ ¼ f þ ðrÞ þ f
ðrÞ 2 Where N is the number of electrons, DN is the number of gains and losses of electrons, and r is charge density. The nucleophilic index reflects the degree of change in charge density of a molecule or atom. The expression fþ(r) measures changes in the density when the molecule gains electrons and, hence, corresponds to reactivity with respect to nucleophilic attack. Conversely, f
(r) corresponds to reactivity with respect to electrophilic attack (loss of electrons). f 0 ðrÞ is simply the average of these two. f þ ðrÞ ¼

FF was used to study the reactivity of atoms in different layers on the surface of sulfide minerals. The results are listed in Table 3.7. It is found that the nucleophilic and

Surface relaxation and electronic properties of sulfide minerals 109 Table 3.7: The nucleophilic and electrophilic indices of different layers of atoms on the surface of sulfide minerals. Nucleophilic index fþ

Electrophilic index f¡

S(1)0.079 S(3)0.079 S(6)0.004 S(8)0.004 S(9)0.005 S(11)0.005

Zn(2)0.043 Zn(4)0.043 Zn(5)0.022 Zn(7)0.022 Zn(10)0.03 Zn(12)0.03

S(1)0.101 S(3)0.101 S(6)0.025 S(8)0.025 S(9)0.027 S(11)0.027

Zn(2)0.021 Zn(4)0.021 Zn(5)0.001 Zn(7)0.001 Zn(10)0.007 Zn(12)0.007

Pb(18)0.07 Pb(30)0.07 Pb(6)0.069 Pb(42)0.069 Pb(3) 0.001 Pb(16)0.001 Pb(39)0.001 Pb(27)0.001 Pb(6) 0 Pb(29)0 Pb(41)0 Pb(12) 0

S (9) 0.009 S (21)0.009 S (33)0.009 S (45)0.009 S(12) 0.002 S(24) 0.002 S(36) 0.002 S(48) 0.002 S (8) 0.009 S (32)0.009 S (20)0.009 S (44)0.009

Pb(6) 0.069 Pb(18)0.069 Pb(30)0.069 Pb(42)0.069 Pb(3) 0.015 Pb(16)0.015 Pb(27)0.015 Pb(39)0.015 Pb(6) 0.05 Pb(29)0.05 Pb(41)0.05 Pb(32)0.05

S (9) 0.017 S(21) 0.017 S(33) 0.017 S(45) 0.017 S(12) 0.002 S(24) 0.002 S(36) 0.002 S(48) 0.002 S (8) 0.012 S(20) 0.012 S(32) 0.012 S(44) 0.012

S (1)0.066 S (2)0.066 S (3)0.066 S (4)0.066 S (5) 0.015 S (6)0.015 S (7)0.015 S (8)0.015 S (9)0.02 S (10)0.02 S (11)0.02 S (12)0.02

Mo(1)0.002 Mo(2)0.002 Mo(3)0.002 Mo(4)0.002

S (1)0.064 S(2)0.064 S(3)0.064 S(4)0.064 S (5)0.017 S(6)0.017 S(7)0.017 S(8)0.017 S(9) 0.046 S(10) 0.046 S(11) 0.046 S(12) 0.046

Mo(1)0.007 Mo(2)0.007 Mo(3)0.007 Mo(4)0.007

Sphalerite surface

Galena surface

Molybdenite surface

Mo(5)0.01 Mo(6)0.01 Mo(7)0.01 Mo(8)0.01

Mo(5)0.007 Mo(6)0.007 Mo(7)0.007 Mo(8)0.007

110 Chapter 3 electrophilic indices of the outermost surface atoms are the largest, and that of the subsurface layer atoms sharply reduce, and the atomic reactivity is worse, indicating that the FF better reflects the activity of atoms on the mineral surface. However, the calculated value of sulfur atoms on the surface is relatively large. For galena, stibnite, and molybdenite, the atoms with the highest nucleophilic and electrophilic indices are all sulfur atoms. If only the relative value is considered, i.e., the nucleophilicity is only concerned with the activity of the sulfur atom, the electrophilicity is only concerned with the activity of the metal cation, and the FF can be used to characterize the reactivity of the mineral surface atoms.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

[12] [13] [14] [15] [16] [17] [18]

Tamm IE. On the possible bound states of electrons on a crystal surface. Phys Z Soviet 1932;1:733e46. Shockley W. On the surface states associated with a periodic potential. Phys Rev 1939;56:317e23. Bardeen J. Surface states and rectification at a metal semi
conductor contact. Phys Rev 1947;71:717e27. Fu CL, Freeman AJ, Wimmer E, Weinert M. Frozen
Phonon total
energy determination of structural surface phase transitions: W(001). Phys Rev Lett 1985;54(20):2261e4. Lang ND, Kohn W. Theory of metal surfaces: charge density and surface energy. Phys Rev B 1970;1(12):4555e67. Lang ND. Density
functional studies of metal surfaces and metal
adsorbate systems. Surf Sci 1994;299/ 300:284e97. Appelbaum JA, Hauman DR. Variational calculation of the image potential near a metal surface. Phys Rev B 1972;6(4):1122e30. Duke CB, Wang YR. Surface structure and bonding of cleavage faces of tetrahedrally coordinated IIeIV compounds. J Vac Sci Technol B 1988;6(4):1440e3. Oliveira C, Lima GF, Abreu HA, Duarte HA. Reconstruction of the chalcopyrite surfacesda DFT study. J Phys Chem C 2012;116:6357e66. Hung A, Muscat J, Yarovsdy I, Russo SP. Density
functional theory studies of pyrite FeS2 (100) and (110)surfaces. Surf Sci 2002;513(3):511e24. Rosso KM, Becker U, Hochella Jr MF. Atomically resolved electronic structure of pyrite (100) surfaces: an experimental and theoretical investigation with implications for reactivity. Am Mineral 1999;84:1535e48. Nesbitt HW, Bancroft GM, Pratt AR, Scaini MJ. Sulfur and iron surface states on fractured pyrite surfaces. Am Mineral 1998;83(9/10):1067e76. Von Oertzen GU, Skinner WM, Nesbitt HW. Ab initioand XPS studies of pyrite (100) surface states. Radiat Phys Chem 2006;75(11):1855e60. Chen Y, Chen JH, Guo J. A DFT study of the effect of lattice impurities on the electronic structures and floatability of sphalerite. Miner Eng 2010;23:1120e30. Chen JH, Wang L, Chen Y, Guo J. A DFT study on the effect of natural impurities on the electronic structures and flotation behavior of galena. Int J Miner Process 2011;98:132e6. LI YQ, Chen JH, Chen Y, Guo J. Density functional theory study of the influence of impurity on electronic properties and reactivity of pyrite. Trans Nonferrous Metals Soc China 2011;21(8):1887e95. Ayers PW, Parr RG, Pearson RG. Elucidating the hard/soft acid/base principle: a perspective based on half
reactions. J Chem Phys 2006;124(19):194107. Parr RG, Bartolotti LJ. On the geometric mean principle for electronegativity equalization. J Am Chem Soc 1982;104(14):3801e3.

Surface relaxation and electronic properties of sulfide minerals 111 [19] Zhang YK, Yang WT. Perspective on density
functional theory for fractional particle number: derivative discontinuities of the energy. Theor Chem Acc 2000;103(3
4):346e8. [20] Gyftopoulos EP, Hatsopoulos GN. Quantum
thermodynamic definition of electronegativity. Proc Natl Acad Sci USA 1968;60(3):786e93. [21] Yang WT, Zhang YK, Ayers PW. Degenerate ground states and a fractional number of electrons in density and reduced density matrix functional theory. Phys Rev Lett 2000;84(22):5172e5.

CHAPTER 4

Interaction of water and oxygen with sulfide mineral surface 4.1 Effect of water molecule on surface relaxation Mineral flotation is a complicated physicochemical process, involving solid, liquid, and gas phases. Reactions in the process of flotation occur on the interface between minerals. Hence, the structure and properties of the solideliquid interface play an important role in the flotation that determines the adsorption of flotation reagent on the mineral surface. It is reported that the flotation behavior and the reagent adsorption are influenced by the water molecule. Zhu et al. [1,2] found that magnetized water was a benefit to hematite flotation using sodium oleate as collector and can reduce the activation of quartz by calcium ion. The proton adsorption was studied at hydrous sulfide mineral surfaces by Sun et al. [3] and Ro¨nngren et al. [4]. The results showed that the exchange between protons and surface metal ions resulted in quite high metal ion concentrations, which indicated that the hydration influenced the chemical reactions and ion exchange on the surfaces of galena and sphalerite. Ro¨nngren et al. [5] investigated the complexation of sulfide ions at the ZnSeH2O and PbSeH2O interfaces and built a surface complexes model. The results explained part of the mechanism behind depression of sulfide minerals in the flotation process. Weerasooriya and Tobschall [6] suggested that the interfacial properties affected the surface charging of pyrite in pyriteewater suspensions. Wen and Zhang [7] explored the arrangement of the reagent layers adsorbed on the mineral surfaces and established a theoretical model of water stability. Catalano [8] examined relaxations and interfacial water ordering occurring at the corundum (110)ewater interface, which demonstrated the stability of aluminum through the hydrogen bonding interactions of their surface functional groups. Chen et al. [9,10] investigated the interaction energy between flotation reagent and mineral surface and built an adsorption model in the presence of water molecule. Meanwhile, they calculated the adsorption heat of butyl xanthate and galena surface. The results were much closer to the experimental values. Recently, quantum theory has been paid more and more attention due to advantages in acquiring the micro information of minerals. Stirling et al. [11] simulated the adsorption of H2O molecule on the surface (110) of pyrite. The results manifested that the H2O

Electronic Structure and Surfaces of Sulfide Minerals. https://doi.org/10.1016/B978-0-12-817974-1.00004-1 Copyright © 2020 Central South University Press. Published by Elsevier Inc. All rights reserved.

113

114 Chapter 4 molecule was preferably adsorbed on the Fe atom and the chemisorption of H2O molecule was unstable. The water adsorption on the sphalerite (110) surface was modeled to study the possible interaction modes of Pb2þ ions and the (110) surface by Steele et al. [12]. It was found that adsorption of hydrated PbO and PbOHþ is energetically feasible and leads to PbeO distances compatible with REFLEXAFS data. Chen et al. [13e18] calculated the effects of vacancy defect and impurities on the electronic structure and surface properties of sphalerite, pyrite, and galena by the density functional theory (DFT); then, they investigated the influence of vacancy defect and impurities of these sulfide minerals on the activation of copper ion and the adsorption of O2, xanthate and CN molecule; and finally, the quantum chemistry model was established to explain the effect of lattice defects on the sulfide mineral properties and flotation behavior. At present, most of the researches were focused on the reaction between the flotation reagent and mineral surface. However, the reaction occurs on the interface of mineralewater in the flotation processing. The influence of H2O molecule, therefore, should be investigated. In this work, we modeled the MoS2 (001), Sb2S3 (010), Cu2S (100), ZnS (110), PbS (100), and FeS2 (100) surfaces in the presence of H2O molecule and studied the effects of H2O adsorption on these surfaces. The results can provide important insight into the structures and properties of mineral surfaces, the mechanism of reagent adsorption, and the subsequent flotation behavior of sulfide minerals.

4.1.1 Computational method Calculations have been done using Cambridge Serial Total Energy Package (CASTEP) [19,20], which is a first-principle pseudopotential method based on DFT [21e24]. DFT calculations employ plane wave (PW) basis sets and ultrasoft pseudopotentials [25]. The exchange correlation functional used is the generalized gradient approximation (GGA) developed by Perdew-Wang generalized gradient approximation (PW91) [26]. The kinetic energy cutoff (300 eV) of the PW basis is used throughout, and the Brillouin zone is sampled by Monkhorst and Pack [27,28] special k-points of a 4  4  1 grid for all structure calculations, which shows that the cutoff energy and the k-points meshes are sufficient for the system. The convergence tolerances for geometry optimization ˚ , the maximum force calculations are set to the maximum displacement of 0.002 A 5 ˚ , the maximum energy change of 2.0  10 eV/atom, and the maximum of 0.08 eV/A stress of 0.1 GPa, and the self-consistent field (SCF) convergence tolerance is set to be 2.0  106 eV/atom. The valence electron configurations considered in the work are H 1s1, O 2s22p4, S 3s23p4, Mo 4s24p64d55s1, Sb 5s25p3, Cu 3d104s1, Pb 5d106s26p2, Fe 3d64s2, and Zn 3d104s2. Before adsorption, the H2O molecule is placed in a ˚ is ˚ 3 cubic cell for optimization. In addition, a vacuum thickness of 10 A 10  10  10 A placed between the surface’s slabs.

Interaction of water and oxygen with sulfide mineral surface

115

Molybdenite (MoS2) is a hexagonal crystal with a space group of P63/mmc, whose cleavage plane is (001). A slab model of molybdenite is shown in Fig. 4.1A. Stibnite (Sb2S3) is an orthorhombic space group (Pnma). Common cleavage plane is (010) surface, whose slab model is shown in Fig. 4.1B. S atom of surface coordinates with two Sb atoms or three Sb atoms, and each Sb atom coordinates with three S atoms. Chalcocite (Cu2S) has an orthorhombic unit cell with a space group of Abm2, whose slab model (100) surface is shown in Fig. 4.1C. S atom of surface coordinates with four Cu atoms or three

Figure 4.1 Slab models of sulfide minerals surfaces: (A) MoS2 (001); (B) Sb2S3 (010); (C) Cu2S (110); (D) ZnS (110); (E) PbS (100); (F) FeS2 (100).

116 Chapter 4 Cu atoms, and Cu atom coordinates with three S atoms and one Cu atom, or two S atoms and two Cu atoms, or three S atoms and two Cu atoms. Sphalerite (ZnS) has cubic crystal  structure, whose space group is F4 3m with (110) surface. Each Zn atom of the surface coordinates with three S atoms, while each S atom coordinates with two Zn atoms and one S atom (Fig. 4.1D). Galena (PbS) also belongs to cubic crystal structure with a space group of Fm3m. Common cleavage plane is (100) face along PbeS bond. Each Pb atom of the surface coordinates with adjacent five S atoms, and each S atom coordinates with five Pb atoms (Fig. 4.1E). Pyrite (FeS2) possesses a cubic crystal structure and has a space group of Pa3. The common cleavage plane is (100) face along FeeS bond. Each Fe atom of the surface coordinates with adjacent five S atoms, while each S atom coordinates with adjacent two Fe atoms and one S atom (Fig. 4.1F). All surfaces are obtained from the bulk sulfides with the optimum unit cell volume and are modeled using a supercell approach (2  2  1) except for chalcocite, where the central cell, periodic in 3D, contains a slab that has two surfaces and a vacuum gap above and below the surfaces separating adjacent mirror images of the slab. The adsorption energy of adsorbate on sulfide’s surface is calculated as follows: Eads ¼ Eadsorbate=surface  ðEadsorbate þ Esurface Þ

(4.1)

where Eads is the adsorption energy, Eadsorbate is the energy of the H2O or N2 molecules, Esurface is the energy of the pyrite, sphalerite, galena, chalcocite, stibnite, or molybdenite slab, and Eadsorbate=surface is the energy of the adsorbate molecule adsorbed on mineral surface. A larger negative value of Eads indicates stronger adsorption of molecule on the surface.

4.1.2 Relaxation of minerals surfaces after adsorption of H2O molecule Fig. 4.2 shows the adsorption model of an H2O molecule on the top layer of various sulfide surfaces. The atomic displacements and coordination of mineral surfaces are listed in Table 4.1. The corresponding atomic numbers are shown in Fig. 4.2. It is found that the displacement of surface atoms changes after water adsorption. Surface atoms move outward or toward the bulk in the direction of X, Y, and Z axes. Especially, the displacement of atoms on molybdenite surface moves dramatically toward the bulk along the direction of Z axis, and it is the most obvious one in all mineral’s surfaces. It is well known that molybdenite possesses a layered structure, and the atoms between each layer bond relatively weakly, which makes relaxation more easy and obvious. The effect of H2O molecule, therefore, is significantly for the surface of molybdenite. For stibnite,

Interaction of water and oxygen with sulfide mineral surface

117

Figure 4.2 Optimized geometries for the adsorption of a single water molecule on sulfide mineral surfaces: (A) MoS2 (001), (B) Sb2S3 (010), (C) Cu2S (110), (D) ZnS (110), (E) PbS (100), and (F) FeS2 (100).

the atoms on the top layer have relaxed after H2O adsorption, particularly in the Z axis direction. With regard to the sphalerite surface, Zn atoms on the top surface layer move outward from the bulk and S atoms move outward. It is notable that there is a large relaxation on the surface of the sphalerite, which indicates that the adsorption of H2O molecules has a significant effect on the surface structure of the sphalerite. For pyrite, the atomic relaxation on the top layer of surface is not very obvious. However, it is worth noting that the displacement of surface atoms (i.e., Fe1, Fe2, S1, and S2) that react with H2O molecule is much larger than that of other surface atoms. The surfaces of chalcocite and galena are only slightly relaxed. The dangling bonds resulted from cleavage are exceedingly active on the top layer of the mineral surface. Consequently, such surfaces react with the H2O molecule more easily. After adsorbing H2O, the structure of the mineral surfaces is different from the previous ones. To confirm the effect of H2O molecule on the property of mineral surfaces, we calculate the densities of states (DOS) of mineral surfaces.

118 Chapter 4 Table 4.1: Atomic displacement and coordination of sulfide mineral surfaces. ˚ Atomic displacement/A Mineral Molybdenite (MoS2)

Stibnite (Sb2S3)

Chalcocite (Cu2S)

Sphalerite (ZnS)

Galena (PbS)

Pyrite (FeS2)

Atomic number Mo1 Mo2 Mo3 Mo4 S1 S2 S3 S4 Mo1 Mo2 Sb1 Sb2 S1 S2 S3 S4 Cu1 Cu2 Cu3 Cu4 S1 S2 S3 S4 Zn1 Zn2 Zn3 Zn4 S1 S2 S3 S4 Pb1 Pb2 S1 S2 Fe1 Fe2 Fe3 S1 S2 S3 S4 S5

Coordination 6 6 6 6 3 3 3 3 6 6 3 3 2 2 3 3 4 4 6 5 3 5 5 4 3 3 4 4 3 3 4 3 5 5 5 5 5 5 5 3 4 4 3 4

Dx e0.002 e0.002 e0.002 e0.002 e0.002 e0.002 e0.004 e0.003 e0.002 e0.002 0.002 0.003 0.002 0.012 0.010 0.011 0.010 0.002 e0.014 e0.002 0.029 e0.005 0.000 e0.009 0.015 e0.007 e0.006 e0.006 e0.002 e0.002 e0.001 e0.008 0.000 0.000 e0.004 0.006 e0.019 e0.002 e0.001 e0.007 e0.002 e0.001 e0.003 e0.002

Dy 0.008 0.007 0.008 0.008 0.008 0.009 0.008 0.009 0.008 0.007 e0.018 0.018 0.017 0.017 0.010 0.012 0.009 0.000 e0.001 0.000 0.018 0.006 0.000 0.005 0.010 0.000 0.002 e0.003 0.002 e0.002 0.005 0.002 e0.014 e0.007 0.003 0.002 0.000 0.000 0.000 e0.002 e0.001 e0.001 e0.005 e0.001

Dz e0.011 e0.011 e0.011 e0.011 e0.012 e0.012 e0.012 e0.012 e0.011 e0.011 0.012 0.012 0.014 0.014 0.012 0.014 0.005 e0.001 0.001 0.000 0.000 0.002 0.000 e0.002 0.017 0.000 e0.004 e0.004 e0.001 e0.002 0.003 e0.002 e0.012 0.015 e0.014 e0.015 0.003 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Interaction of water and oxygen with sulfide mineral surface

119

4.1.3 Effect of density of states on sulfide minerals surfaces in presence of H2O molecule Figs. 4.3e4.8 shows the DOS of the atoms on the top surface layers before and after adsorbing H2O molecule. The zero of energy has been set at the Fermi level (EF). We only consider the details near Fermi surface because significantly physical processes occur in the vicinity to Fermi level. It is seen that the DOS of FeS2 (see Fig. 4.3) has an evident change after H2O adsorption, and the Fe 3d states occupy in the vicinity of the Fermi level (EF), which indicates that the structure of FeS2 is changed, and the activity becomes more effective in presence of the H2O molecule. For ZnS (see Fig. 4.4), there is no significant change on the DOS after adsorbing H2O molecule. Similarly, the DOS of PbS becomes EF

Before adsorption of H2O molecule

s

Density of States (electrons/eV)

p d

After adsorption of H2O molecule

Energy /eV

Figure 4.3 Density of states of FeS2 (100) surface before and after adsorption of a single H2O molecule.

Density of States (electrons/eV)

Before adsorption of H2O molecule

EF

s p d

After adsorption of H2O molecule

Energy /eV

Figure 4.4 Density of states of ZnS (110) surface before and after adsorption of a single H2O molecule.

Density of States (electrons/eV)

Before adsorption of H2O molecule

EF

s p

After adsorption of H2O molecule

Energy /eV

Figure 4.5 Density of states of PbS (100) surface before and after adsorption of a single H2O molecule.

Density of States (electrons/eV)

Before adsorption of H2O molecule

EF

s p d

After adsorption of H2O molecule

Energy /eV

Figure 4.6 Density of states of MoS2 (001) surface before and after adsorption of a single H2O molecule.

Density of States (electrons/eV)

Before adsorption of H2O molecule

EF

s p

After adsorption of H2O molecule

Energy /eV

Figure 4.7 Density of states of Sb2S3 (010) surface before and after adsorption of a single H2O molecule.

Interaction of water and oxygen with sulfide mineral surface

Density of States(electrons/eV)

Before adsorption of H2O molecule

EF

121

s p d

After adsorption of H2O molecule

Energy /eV

Figure 4.8 Density of states of Cu2S (110) surface before and after adsorption of a single H2O molecule.

different before and after H2O adsorption. A newly apparent state peak generated from S 3s orbital is obtained at 3 eV, which is shown in Fig. 4.5. It is seen that the DOS peak near 7 eV, in presence of H2O molecule, splits into two peaks at 7.7 and 5.7 eV, respectively. Whereas the DOS of Cu2S appears a new peak located at 4 eV in presence of H2O, which is formed by S 4p state (see Fig. 4.8). Meanwhile, the DOS peak moves from 2.8 to 1.6 eV, which suggests that the surface of chalcocite becomes more active. In addition, the DOS peaks change slightly for the surfaces of molybdenite and stibnite (see Figs. 4.6 and 4.7). In a word, the DOS of mineral surfaces have been influenced in presence of H2O. To study deeply the electronic structures and properties and to obtain comprehensively the changes of mineral surfaces after adsorbing H2O molecule, we calculate the Mulliken populations on the surface’s layers in presence and absence of H2O molecule.

4.1.4 Effect of Mulliken populations on sulfide minerals surfaces in presence of H2O molecule The Mulliken atomic charges and bonds populations of mineral surface layers are listed in Tables 4.2-4.7 respectively. It is seen that the Mulliken atomic charges populations of ZnS, PbS, and FeS2 surface layers are different before and after H2O absorption; i.e., the charges of Zn1 and Pb1 atoms increase from þ0.35 to þ0.45 e and þ0.61 to þ0.75 e, respectively. The charges of Fe2 atom reduce from þ0.13 to þ0.08 e, which indicates that the Zn1 and Pb1 atoms become more positive and the Fe2 atom becomes more negative. In addition, there are changes in the charges of S atoms on ZnS and PbS surface layers before and after H2O absorption; that is, the charge of S atom on the surface layers of ZnS becomes more negative, such as S1 (from 0.50 to 0.51 e) and S2 (from 0.51 to

122 Chapter 4 Table 4.2: Mulliken atomic charge of ZnS (110) surface layers before and after H2O adsorption. Atomic label Zn1 Zn2 Zn3 Zn4 S1 S2 S3 S4

Adsorption situation Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption

s

p

d

0.90 0.81 0.92 0.90 0.80 0.77 0.80 0.80 1.85 1.86 1.86 1.85 1.84 1.82 1.83 1.85

0.77 0.75 0.82 0.77 0.91 0.91 0.91 0.89 4.65 4.65 4.65 4.68 4.67 4.67 4.67 4.69

9.98 9.98 9.97 9.98 9.98 9.98 9.98 9.98 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Total 11.65 11.55 11.71 11.65 11.69 11.66 11.69 11.67 6.50 6.51 6.51 6.53 6.49 6.49 6.54 6.49

charge /eV +0.35 +0.45 +0.29 +0.35 +0.31 +0.34 +0.31 +0.33 e 0.50 e 0.51 e 0.51 e 0.53 e 0.49 e 0.49 e 0.50 e 0.49

Table 4.3: Mulliken atomic charge of PbS (100) surface layers before and after H2O adsorption. Atomic label Pb1 Pb2 S1 S2

Adsorption situation Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption

s

p

1.99 1.93 1.90 1.90 1.92 1.92 1.92 1.92

1.41 1.32 1.42 1.42 4.76 4.76 4.76 4.76

d 10.00 10.00 10.00 10.00 0.00 0.00 0.00 0.00

Total 13.39 13.25 13.32 13.32 6.68 6.69 6.68 6.69

charge /eV 0.61 0.75 0.68 0.68 e 0.68 e 0.69 e 0.68 e 0.69

Table 4.4: Mulliken atomic charge of FeS2 (100) surface layers before and after H2O adsorption. Atomic label Fe1 Fe2 Fe3 S1 S2 S3

Adsorption situation Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption

s

p

d

0.39 0.36 0.39 0.40 0.39 0.40 1.86 1.85 1.81 1.81 1.81 1.81

0.36 0.36 0.35 0.39 0.35 0.37 4.25 4.27 4.19 4.17 4.19 4.19

7.12 7.15 7.13 7.13 7.13 7.11 0.00 0.00 0.00 0.00 0.00 0.00

Total 7.87 7.88 7.87 7.92 7.87 7.88 6.11 6.12 6.00 5.98 6.00 5.99

charge /eV 0.13 0.12 0.13 0.08 0.13 0.12 0.11 0.12 0.00 0.02 0.00 0.01

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Table 4.5: Mulliken atomic charge of Cu2S(110) surface layers before and after H2O adsorption. Atomic label Cu1 Cu2 Cu3 Cu4 S1 S2 S3 S4

Adsorption situation Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption

s

p

d

0.66 0.67 0.62 0.62 0.67 0.67 0.56 0.57 1.81 1.82 1.81 1.82 1.80 1.80 1.85 1.86

0.24 0.24 0.44 0.45 0.38 0.38 0.47 0.47 4.44 4.44 4.48 4.46 4.52 4.52 4.52 4.48

9.72 9.72 9.76 9.77 9.74 9.74 9.71 9.71 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Total 10.62 10.63 10.82 10.84 10.79 10.78 10.74 10.75 6.25 6.25 6.29 6.28 6.32 6.31 6.36 6.33

charge /eV 0.38 0.37 0.18 0.16 0.21 0.22 0.26 0.25 e 0.25 e 0.25  0.29  0.28  0.32  0.31  0.36  0.33

Table 4.6: Mulliken atomic charge of MoS2(001) surface layers before and after H2O adsorption. Atomic label Mo1 S1 S2 S3

Adsorption situation Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption

s

p

d

2.46 2.47 1.86 1.86 1.85 1.86 1.87 1.86

6.46 6.45 4.17 4.16 4.18 4.16 4.11 4.16

5.03 5.03 0.00 0.00 0.00 0.00 0.00 0.00

Total 13.96 13.95 6.03 6.02 6.03 6.02 5.98 6.02

charge /eV 0.04 0.05  0.03  0.02  0.03  0.02  0.02  0.02

Table 4.7: Mulliken atomic charge of Sb2S3(010) surface layers before and after H2O adsorption. Atomic label Sb1 S1 S2 S6

Adsorption situation Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption

s

p

d

1.93 1.94 1.92 1.92 1.92 1.92 1.92 1.92

2.30 2.28 4.64 4.65 4.64 4.65 4.67 4.66

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Total 4.23 4.22 6.56 6.57 6.56 6.57 6.59 6.57

charge /eV 0.77 0.78  0.56  0.57  0.56  0.57  0.59  0.57

124 Chapter 4 0.53 e), and the similar change happens to the S atom on the surface layers of PbS, i.e., S1 (from 0.68 to 0.69 e) and S2 (from 0.68 to 0.69 e). With regard to Cu2S, the charges of Cu atoms on the surface layers almost decrease (Cu1, Cu2, and Cu4) and are more negatively charged. Meanwhile, the charges of S atoms on the surface layers increase and become more positively charged. For MoS2 and Sb2S3, the results obtained by the Mulliken atomic charge populations change little. It is well known, in general, that the property of ionic or covalent can be determined according to the value of Mulliken bond populations. The large value of populations indicate that the bond is covalent. On the contrary, the small value of populations suggest that the interaction between bonds is ionic. The Mulliken bonds populations of MoS2, Sb2S3, Cu2S, ZnS, PbS, and FeS2 surface layers before and after H2O adsorption are listed in Tables 4.8-4.13, respectively. The results show that the surfaces of ZnS, PbS, and FeS2 are affected remarkably by the H2O molecule. Table 4.8: Mulliken bond population of Mo and S atoms on the MoS2(001) surface before and after H2O adsorption. Bond label Mo1eS1 Mo2eS2 Mo3eS1 Mo3eS3 Mo4eS2 Mo4eS4

Adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption

Bond population 0.43 0.44 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43

˚ Bond length / A 2.4076 2.4098 2.4076 2.4056 2.4076 2.4093 2.4076 2.4058 2.4076 2.4069 2.4076 2.4081

Table 4.9: Mulliken bond population of Sb and S atoms on the Sb2S3(010) surface before and after H2O adsorption. Bond label Sb1eS1 Sb1eS2 Sb1eS3 Sb2eS2 Sb2eS4

Adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption

Bond population 0.24 0.32 0.22 0.29 0.36 0.39 0.32 0.34 0.36 0.37

˚ Bond length / A 2.5633 2.6275 2.6028 2.6622 2.5077 2.5578 2.5633 2.5288 2.5578 2.5536

Interaction of water and oxygen with sulfide mineral surface Table 4.10: Mulliken bond population of Cu and S atoms on the Cu2S (110) surface before and after H2O adsorption. Bond label Cu1eS2 Cu2eS2 Cu2eCu3 Cu2eS3 Cu3eS3 Cu4eS1

Adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption

Bond population 0.49 0.49 0.29 0.27 0.14 0.14 0.38 0.38 0.37 0.36 0.40 0.41

˚ Bond length / A 2.1997 2.2047 2.4613 2.4911 2.6505 2.6456 2.2981 2.2898 2.2029 2.2065 2.3618 2.3383

Table 4.11: Mulliken bond population of Zn and S atoms on the ZnS (110) surface before and after H2O adsorption. Bond label Zn1eS1 Zn1eS2 Zn1eS3 Zn2eS2 Zn2eS4 Zn3eS3

Adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption

Bond population 0.66 0.62 0.67 0.59 0.55 0.48 0.66 0.68 0.55 0.53 0.53 0.56

˚ Bond length / A 2.2835 2.3273 2.2767 2.3373 2.3204 2.3531 2.2835 2.2985 2.3204 2.3449 2.3813 2.3815

Table 4.12: Mulliken bond population of Pb and S atoms on the PbS (110) surface before and after H2O adsorption. Bond label Pb1eS1 Pb1eS5 Pb2eS1 Pb4eS3

Adsorption situation Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption

˚ Bond population Bond length / A 0.07 0.07 0.21 0.11 0.09 0.09 0.09 0.09

2.9878 2.9870 2.7849 2.8550 2.8120 2.8241 2.8095 2.8236

125

126 Chapter 4 Table 4.13: Mulliken bond population of Fe and S atoms on the FeS2 (100) surface before and after H2O adsorption. Bond label Fe1eS1 Fe1eS5 Fe2eS2 Fe3eS3 Fe4eS4

Adsorption situation Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption

˚ Bond population Bond length / A 0.56 0.50 0.48 0.48 0.44 0.42 0.45 0.47 0.46 0.46

2.1030 2.1456 2.1437 2.1579 2.1224 2.1201 2.2332 2.2316 2.1917 2.1924

According to Table 4.11, it can been seen that the Mulliken bond populations on the first layer are almost reduced; i.e., the populations of Zn1eS1, Zn1eS2, and Zn1eS3 decrease from 0.66 to 0.62, 0.67 to 0.59, and 0.55 to 0.48, respectively, which suggests that the bonds become more ionic. Meanwhile, the lengths of bonds on the first layer all increase, which manifests the interaction between bonds gradually weakened. On the contrary, we find that the Mulliken populations and the length between bonds on the second layer are all increasing (such as Zn3eS3), so these bonds become more covalent in the presence of H2O. As for PbS, there is a sharp change at the Mulliken bond populations and length. According to the corresponding image (see Fig. 4.2), we discover that the bond populations of Pb1eS5 connected between the layers, namely the interlayer bonds, change from 0.21 to 0.11 before and after H2O absorption, and the length increases 2.7849e2.8550 nm (see Table 4.12). Hence, this manifests that the Pb1eS5 bond becomes more ionic, and the interaction between layers becomes more greatly enhanced. Meanwhile, the bonds on the same plane layer have no significant changes in the presence of H2O. It is seen that the populations and length on the first layer change with FeS2 surface; that is, the Mulliken bond population of Fe1eS1 reduces from 0.56 to 0.50, and ˚ , respectively (see Table 4.13). This suggests the length increases from 2.1030 to 2.1456 A that the interaction between bonds is more ionic. Whereas, the population and length of Fe3eS3 increase, indicating that the interaction between bonds is weakened. With regard to MoS2, Sb2S3, and Cu2S, the population and the length are affected barely in presence of H2O molecule.

4.2 Adsorption of multilayer water molecules on galena and pyrite surfaces Surface structure and properties of crystal, especially for the hydrophobic and hydrophilic surface, have a great influence on water adsorption and the subsequent interfacial chemical

Interaction of water and oxygen with sulfide mineral surface

127

reaction. Galena (PbS) and pyrite (FeS2) are the most common sulfide minerals and are widely distributed in nonferrous metal deposits. They are totally distinct in their surface characteristics. Galena surface is almost hydrophobic, and its contact angle is 48e52 degrees, and pyrite surface is strongly hydrophilic with the contact angle of 20 degrees [29,30]. The research [31] shows that the outermost layer of both PbS and FeS2 surfaces is electronegative, but PbS carries more negative charge than FeS2 surface. The surface iron atom of pyrite is more reactive than the surface lead atom of galena. Oxidation of pyrite in aqueous solution is the most important factor in the generation of acid mine drainage (AMD), which will decrease the pH of water and devastate rivers, streams, and aquatic life for years [32]. Weathering of galena results in the release of lead, sulfate, and other potentially toxic trace metals in the form of lattice substitution, such as cadmium, mercury, thallium, arsenic, and other trace metals [33]. These dissolved sulfate, lead, and trace metals may enter groundwater, rivers, and oceans and cause heavy metal pollution. For galena and pyrite, it has been confirmed that the oxygen in sulfate is derived from water molecules [33e38]. Accordingly, the adsorption of water molecules participates in the oxidation process and determines the final oxidation product. The difference of water adsorption structure on the hydrophobic/hydrophilic surfaces would result in the obvious variation in the mineral oxidation process. Moreover, galena is the world’s primary ore of lead, while it is also the main carrier mineral of silver. Pyrite is an important raw material for industrial manufacture of sulfuric acid. Both galena and pyrite are generally recovered by froth flotation, which takes advantage of the differences in wettability at particle surfaces to separate different minerals. Generally, suitable reagents are necessary to add to adjust the hydrophobicity or hydrophilicity of the mineral surface to ensure the selective adhesion to the froth. As described by Stirling [11], these reactions occur on a water-covered surface, and they either directly involve the adsorbed water molecules or are initiated by the exchange of the adsorbed water with the reactants to be bound on surface sites. Both galena and pyrite surface have been extensively studied using experimental methods such as X-ray photoelectron spectroscopy (XPS) [39e53], ultraviolet photoelectron spectroscopy (UPS) [44,54,55], Raman spectroscopy [56], scanning tunneling microscopy (STM) [36,40,42,55e59], low-energy electron diffraction [50,55], photoemission of adsorbed xenon [60,61], and temperature-programmed desorption (TPD) [60e62] as well as X-ray standing wave technique (XSW) [63]. These researches devote to describing the surface characteristics of galena and pyrite. Besides, some theoretical studies based on Hartree-Fock (HF) [58,64,68] and DFT methods on cluster or periodic models have been reported [36,44,52,53,55,57,65e88]. Furthermore, a few researches about the water adsorption on galena or pyrite surfaces have been performed. Wright et al. [78,79], studied the adsorption and dissociation of molecular

128 Chapter 4 water on the defective (001) surface of galena using both periodic and embedded cluster electronic structure methods and found that the sorption to steps lead to rapid dissociation of the water molecules. Zhang et al. [80] studied methylamine and water adsorption on PbS by DFT and found that an exceptional strong hydrogen bonding at the solutionesolid interface may lower the surface energy. Zhao et al. [81] conducted a microcalorimetry experiment and the DFT simulations of a single water adsorption on four sulfide mineral surfaces including galena and pyrite. Bryce [66] has explored the adsorption and reactivity of molecular water on the surface of PbS (galena) and its interface with aqueous solution, employing the recently proposed CECILIA [89] method. Philpott et al. [90] found a strong adsorption of water molecules on the pyrite surface by a molecular dynamics simulation. Stirling et al. [11] studied water adsorption on (100) surface of pyrite by using the CarParrinelloab initio molecular dynamics (CPMD) method. Patrick et al. performed a DFT study on the adsorption and reactions of oxygen and water on the pyrite (100) surface. Leeuw et al. [91] introduced a potential model to study the hydration energy of FeS2 surfaces. However, a full understanding of the difference in water adsorption mechanism on both the hydrophobic galena and hydrophilic pyrite surfaces has not been established. To understand the variation in the water adsorption mechanism on the hydrophobic and hydrophilic surfaces at an atomic level, the comparison of a single, mono-, and multilayer water adsorption on the hydrophobic galena (PbS) and hydrophilic pyrite (FeS2) (100) surfaces was performed using the DFT methods. The results may give insight into the nature of the wettability of hydrophobic galena/hydrophilic pyrite surfaces and help to explain the subsequent interfacial reactions on the surfaces.

4.2.1 Computational methods All calculations were performed in the framework of CASTEP developed by Payne et al. [92]. The DFT calculation employed PW basis sets and ultrasoft pseudopotentials. The exchange correlation functional applied was the GGA of Perdew and Wang (PW91) [93]. The interactions between valence electrons and ionic core were represented by ultrasoft pseudopotentials [25]. Valence electron configurations considered in the study included Pb5d106s26p2, S 3s23p4, Fe 3d64s2,O 2s22p4, and H 1s1 states. Based on the test results, the PW cutoff energy of 300 eV was used throughout, and the Brillouin zone was sampled with Monkhorst and Pack special of a 2  2  1 grid for pyrite and a 1  2  1 grid for galena surfaces calculations [27]. For self-consistent electronic minimization, the Pulay density mixing method was employed and with the convergence tolerance of 2.0  106 eV/atom. The convergence criteria for structure optimization and energy calculation were set to (a) energy tolerance of ˚ , and (c) maximum 2.0  105 eV/atom, (b) maximum force tolerance of 0.05 eV/A ˚ displacement tolerance of 0.002 A.

Interaction of water and oxygen with sulfide mineral surface

129

The PbS (100) and FeS2 (100) surfaces are chosen as they are the most stable surfaces [75,79]. Surfaces were cleaved on the basis of the optimized bulk structure. The computed ˚ , respectively, lattice parameters for the bulk galena and pyrite are 6.018 and 5.410 A ˚ 69. After testing the which are very closed to the experimental values of 5.936 and 5.416 A slab thickness, we constructed a (4  2) PbS (100) surface with eight atomic layers (64 Pb and 64 S atoms) and a (2  2) FeS2 (100) surface with 15 atomic layers (40 Fe and 80 S ˚ of vacuum, as shown in Figs. 4.9 and 4.10. The supercells for atoms) separated by 15 A ˚ 3 and the galena and pyrite slabs had the dimensions of 17.01  8.51  36.05 A 3 ˚ , respectively. For the FeS2 surface, the six outermost atomic 10.77  10.77  27.03 A layers of the substrate were allowed to relax, while the nine bottom-most atomic layers of the substrate were fixed to the bulk coordinates, and for the PbS surface the three outermost atomic layers of the substrate were allowed to relax, while the five bottom-most atomic layers of the substrate were fixed to the bulk coordinates in the adsorption calculations. ˚ cubic cell. The The optimization of H2O molecule was performed in a 10  10  10 A ˚ calculated dOeH and :HeOeH of optimized H2O are 0.976 A and 103.8 degrees, ˚ and 104.5 degrees respectively, which are close to the experimental values of 0.958 A [94]. Adsorption energy can be expressed by the following Eq. (4.2): 1 DEads ¼ ½EsurfþnH2 O  Esurf  nEH2 O n

Figure 4.9 The slab model of a (4  2) galena (100) surface: (A) side view and (B) top view.

(4.2)

130 Chapter 4

Figure 4.10 The slab model of a (2  2) pyrite (100) surface: (A) side view and (B) top view.

Where DEads is the adsorption energy, EsurfþnH2 O is the total energy of the surface with the water molecules, Esurf is the total energy of the mineral surface, and EH2 O is the energy of one water molecule, which is calculated in the cell with the same cell size and k-point grid as used in the surface.

4.2.2 Adsorption of isolated water molecule Firstly, an isolated water molecule was placed on the PbS and FeS2 (100) surfaces to simulate a single water adsorption, and the most stable adsorption geometries are shown in Figs. 4.11 and 4.12, respectively. It is shown in Fig. 4.11 that the adsorption of a single water molecule is mainly via its H ˚ . The calculated atoms and surface S atoms with the SeH distance of 2.386 and 2.237 A adsorption energy is 29.1 kJ/mol, which indicates that the interaction between water molecule and galena surface is weak. In an earlier DFT study, Wright et al. [78], found adsorption energies on the PbS (001) surface with ‒31 and ‒44 kJ/mol for an embedded 4  4  2 atom slab and a 2  2  6 atom periodic slab. Moreover, the dissociative

Interaction of water and oxygen with sulfide mineral surface

131

Figure 4.11 Optimized geometry for the adsorption of a single water molecule on PbS surface.

Figure 4.12 Optimized geometries for the adsorption of a single water molecule on FeS2 (100) surface: (A) molecular adsorption and (B) dissociative adsorption.

adsorption of water on the galena (100) surface is not observed in our study, which is similar to the earlier findings of Wright et al. [78]. They suggested that on the perfect surface, no obvious sites would interact with water or facilitate dissociative reactions. However, water would readily dissociate if surface defects were present [79]. The adsorption of water at full coverage was also conducted, and the calculated adsorption energy per molecule is 42.9 kJ/mol. In addition, hydrogen bonds between water molecules are observed. On the FeS2 (100) surface, both the molecular and the dissociative adsorptions have been considered, and the optimized geometries are shown in Fig. 4.12A,B. For the molecular adsorption, it is found that water prefers to adsorb on the surface Fe atom via its O atom ˚ . The calculated adsorption energy is 56.2 kJ/mol, with the FeeO length of 2.108 A which agrees well with the result of 54.4 kJ/mol calculated by Stirling et al. [11] and the result of 54.8 kJ/mol calculated by Zipoli et al. [95]. Other theoretical studies from Leeuw [91] and Rodriguez [85] predicted energies of 47 and ‒45 kJ/mol. These results are consistent with the experimental value of 42 kJ/mol determined by TPD experiments [62]. Other theoretical studies predicted an energy of 65.7 kJ/mol from spin-polarized DFT calculations [35], or 62 kJ/mol using ab initio molecular dynamics simulations [96]. The dissociative adsorption is energetically unfavorable with the energy of 82.4 kJ/mol. This is in accordance with both the experimental [62,97] and theoretical researches

132 Chapter 4 [11,36]. The adsorption of water at full coverage was considered, and the pyrite surface exposed four iron atoms, so we placed four water molecules on the surface. The computed adsorption energy per molecule is 56.8 kJ/mol, which is consistent with the result of 59.8 kJ/mol calculated by Zipoli et al. [95] employing Car-Parrinello FPMD simulations. In previous studies, Stirling et al. [11] found energy of 48.5 kJ/mol using the CPMD, and Leeuw et al. [91] calculated energy of 52.2 kJ/mol using a potential model for FeS2.

4.2.3 Excess water molecules adsorption In aqueous environment, the adsorption of excess water is interesting because both the H bonding and wateresurface interactions are involved in the adsorbed water molecules. Studying these excess water molecules at surfaces may help us understand the competition between the two interactions [95,98,99]. Therefore, we build monolayer and multilayer excess water adsorption models to simulate the influence of two-dimensional hydrogen bonding and three-dimensional hydrogen bonding. In the monolayer excess water adsorption model, the amount of water molecules is more than adsorption sites on the surface and is determined by the surface area of minerals and the hydrogen bonding distance between water molecules. After testing, it is found that nine water molecules are sufficient to cover the (2  2) FeS2 (100) surface, and 18 water molecules are sufficient to cover the (4  2) PbS (100) surface. For PbS (100) surface, the optimized structure of monolayer excess water adsorption is shown in Fig. 4.13A. It is found that the adsorption structure of monolayer water is very different from that of a single water molecule due to the formation of hydrogen bonds ˚ ). Except for the interaction of between water molecules (OeH distances: 1.650e1.812 A S/H bonding, the interaction between O and the surface Pb atoms is also observed with ˚ . Particularly, strong hydrogen bonds are the PbeO distances of 2.933, 2.950, and 3.085 A ˚ formed with the SeH distances of z2.3 A. In the case of FeS2 (100) surface, the optimized configuration of monolayer excess water adsorption is shown in Fig. 4.13B. It is found that the formation of two-dimensional hydrogen bonds influences the adsorption structure of water on the pyrite surface. The bond population of FeeO increases from 0.12 without hydrogen bond to 0.16 with twodimensional hydrogen bonds, suggesting that the two-dimensional hydrogen bonding strengthens the covalent characteristic of FeeO bond. The three-dimensional multilayer water adsorption could provide the information about the influence of hydrogen bond at the z direction on the adsorption of H2O at mineral surface. The adsorption of multilayer water was simulated by placing 54 water molecules on the PbS (100) surface and 27 water molecules on the FeS2 (100) surface, respectively, and the optimized configurations are shown in Fig. 4.14A,B.

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133

Figure 4.13 Optimized structures for the adsorption of monolayer water molecules on (A) PbS and (B) FeS2 surfaces.

For PbS surface, the additional water at the z direction changes the configuration of water ˚ for the adsorption. The average values of S/H bond length increase from 2.468 A ˚ for the multilayer water, indicating that the formation of hydrogen monolayer to 2.524 A bond at the z direction weakens the adsorption of water. This is ascribed to the hydrogen bonding interaction between water molecules at the z direction. It is found from ˚ ) are shorter Fig. 4.14A that the average values of O/H bond at the z direction (1.755 A ˚ ), suggesting a stronger interaction between water than those of S/H bond (2.208 A molecules at the z direction than that of water and galena surface. For FeS2 surface, the distances between the adsorbed H2O molecules and surface Fe atoms ˚ long, indicating become shorter, with the Fe/O distances of 2.074, 2.090, and 2.253 A that the interaction between H2O and Fe atom is strengthened. In addition, the S/H distances become shorter, implying that the S/H bonds are also strengthened after adsorbing multilayer water. Compared to the monolayer water adsorption, the average ˚ , and the bond population value of FeeO bond length shortens from 2.21 to 2.14 A

134 Chapter 4

Figure 4.14 Optimized structures for the adsorption of multilayer water molecules on (A) PbS and (B) FeS2 surfaces.

increases from 0.16 to 0.19. It is indicated that the additional water molecules enhance the covalent characteristic of FeeO bond. On the PbS surface, as the adsorption of water molecules is mainly via the hydrogen bonds between the H and surface S atoms, the partial density of states (PDOS) of S and H atoms with different S/H bond length are investigated (Fig. 4.15) to give insight into the

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135

Figure 4.15 PDOS of S and H atoms with different S/H bond length on PbS surface (Gaussian smearing parameter of 0.05 eV).

nature of the bonding mechanism. From the PDOS of S/H bond with the length of ˚ , it is clearly seen that H 1s‒S 3s bonding DOS peak is located at 11.3 eV, and 2.097 A antibonding DOS peak is at 8.7 eV, meanwhile the H 1s‒S 3p bonding DOS peak appears between 4.5 and 0 eV, and the anti‒bonding DOS peak resonances at 1.3e4.8 eV. The considerably decreases of bonding and the antibonding DOS peaks are ˚ long, implying that the longer the length of observed when the S/H bond is 3.097 A S/H bond is, the weaker is the hydrogen bond between the S and H atoms. In the case of FeS2 surface, the adsorption of water molecules is mainly via the interaction of O atom and surface Fe atom, so we show the PDOS of FeeO bonding before and after multilayer water adsorption in Fig. 4.16. It is clearly shown that the DOS of Fe and O atoms are changed dramatically after water adsorption. Three DOS peaks of O 2p orbital decrease greatly and shift greatly to the lower energy direction, indicating the O 2p orbital losing electrons. The DOS of Fe 3d t2g near the Fermi level becomes localized, and two peaks of Fe 3d eg appearing around 0.3e2.8 eV merge into one great peak. The bands from 1.7 to 7.6 eV are the bonding DOS of Fe 3d eg and O 2p orbitals, and hybridization DOS peaks are observed around ‒6.5, 5.8, and 3.9 eV, implying a relatively strong interaction between Fe 3d eg and O 2p orbitals. The bands from 0.4 to 2.8 eV are the antibonding DOS of Fe 3d eg and O 2p orbitals. The preceding results suggest that the additional water enhances the FeeO interaction. To further investigate the influence of hydrogen bonding effect, we discuss the DOS of O atom of free, two-dimensional (2D), and three-dimensional (3D) water molecules (Fig. 4.17).

136 Chapter 4

Figure 4.16 PDOS of FeeO bonding before and after water adsorption (Gaussian smearing parameter of 0.05 eV).

Figure 4.17 DOS of O atom of free, two-dimensional (2D), and three-dimensional (3D) water molecules.

It is interesting to note that considerable changes of the DOS of O atom are observed for 2D and 3D water structures, which may be ascribed to the effect of hydrogen bonding. The bands of O 2p states in the presence of 2D hydrogen bond become broadened and shift to lower energy direction. When hydrogen bond appears at the z direction, O 2p states move much lower from 0.7 w 6.4 to 1.2 w 9.3 eV, which is nearer to the Fe

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3d eg orbital located from ‒1.7 to 7.6 eV. It is suggested that the hydrogen bonding between additional water molecules can enhance the interaction between O 2p orbital and Fe 3d eg orbital. Perhaps, this phenomenon may be applied for other systems, in which surfaces contain 3d transition metals.

4.2.4 Structure and electronic properties of galena and pyrite surfaces Compared with the bare surfaces, the adsorptions of water molecules have an apparent effect on the surface structure of both PbS and FeS2 surfaces, so they may influence the interaction between mineral surfaces and other coadsorbed molecules. To investigate the effects of water adsorption on the surface characteristics of galena and pyrite, the optimized geometric configurations of bare and water adsorption are shown in Figs. 4.18 and 4.19, respectively. In the case of monolayer water adsorption, it is found that on the galena surface the ˚ (see Table 4.14). In average value of PbeS bond length increases from 2.813 to 2.864 A addition, the formation of H‒bonds between surface S and H atoms results in the axial S1ePb, S3ePb, and S4ePb bonds becomes longer (from 2.835 to 2.975, 2.879, and ˚ ). 2.994 A Compared with the monolayer water adsorption, it is interesting to notice that PbeS bond ˚ (see Table 4.14). As we discussed before, the length decreases from 2.864 to 2.836 A hydrogen bonding at the z direction is stronger than SeH bonding and weakens the interaction of water and the surface, which results in the smaller relaxation of galena surface covered by multilayer water. In the case of FeS2 surface, the adsorption of monolayer water causes the surface axial FeeS bond to lengthen greatly, especially the Fe1, Fe2, and Fe3 atoms that interacted with O atoms are significantly moved upward, and the average value of these FeeS ˚ (Table 4.14). For the multilayer water bond lengths increases from 2.120 to 2.188 A adsorption, the FeeS bond length becomes longer than that of monolayer adsorption ˚ ), which is ascribed to hydrogen bonding at the z direction, (from 2.188 to 2.191 A mentioned earlier. The effect of water adsorption on the electronic properties of PbS and FeS2 surfaces is also investigated by analyzing the DOS of the first layer of PbS and the adsorbed Fe atoms at FeS2 (100) surfaces (Fig. 4.20). The adsorptions of both monolayer and multilayer water lead to the change of Pb 6p, Pb 6s, and S 3p states. The three DOS peaks of S 3p states around 0 w 5 eV are merged into two peaks. A DOS peak of Pb 6p located around 4.3 eV increases noticeably. Meanwhile, Pb 6s states become localized, and the two weak DOS peaks around 3.4 and

138 Chapter 4

Figure 4.18 The geometry configurations of (A) bare PbS surface, (B) monolayer, and (C) multilayer water adsorption on PbS surface.

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Figure 4.19 The geometry configurations of (A) bare FeS2 surface, (B) monolayer, and (C) multilayer water adsorption on FeS2 surface. Table 4.14: Comparison of the relaxation for the PbS and FeS2 (100) surfaces. Bare surface PbS (100) surface FeS2 (100) surface

Pb‒Saax Fe‒Saax

2.813 2.120

Monolayer water adsorption 2.864 2.188

Multilayer water adsorption 2.836 2.191

˚ ); Pb‒Saax: average value of the three interacted axial Fe‒Saax: average value of the three interacted axial FeeS bond lengths (A ˚ ). PbeS bond lengths (A

4.3 eV are merged into one strong DOS peak appearing at 4.1 eV. In addition, the peak value of monolayer water adsorption is higher than that of multilayer water, indicating that the effect of multilayer water adsorption on the electronic properties of PbS seems weaker.

140 Chapter 4

Figure 4.20 DOS of (100) surfaces before and after water adsorption (A) PbS and (B) FeS2 (Gaussian smearing parameter of 0.05 eV).

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For FeS2 surface, the adsorption of water leads the decrease of Fe 3d eg states around 4 to ‒1 eV, and Fe 3d eg states broaden, while two separated DOS peaks of Fe 3d eg appearing around 0e3 eV merge into one strong DOS peak at 1.7 eV. An intensified DOS peak is observed around 7 eV due to the adsorption of multilayer water.

4.3 Interaction of water and oxygen on the pyrite surface Pyrite (FeS2) is the most common and widely distributed sulfide mineral on the earth. It has been pointed out that AMD from coal mines and metal sulfide mines largely results from pyrite oxidation, which is very hazardous and causes serious environmental problems. In addition, it has been suggested that pneumoconiosis is related to the presence of FeS2 in the coals because the oxidative decomposition processes of pyrite could damage lung tissue [100,101]. The oxidation of pyrite is also very important and desired for its flotation separation from useful metal sulfide minerals (Cu, Pb, Zn, and so on), and for the leaching process of precious metals such as gold because pyrite is the main gold-bearing mineral. Recently, over 3 decades, pyrite has gotten lots of attention because of its suitable band gap and high light absorption coefficient for applications as an optoelectronic and for photovoltaic materials [102e106]. However, the oxidation of pyrite is a problem that limits its application. More importantly, pyrite’s role in the origin of life has now gotten more and more attention by scientists because its reaction with water may have formed hydroxyl radicals (OH), which could have limited the stability of prebiotic biomolecules critical to the emergence and evolution of life [107]. Oxidation of pyrite is needed to be understood in terms of reaction details with oxygen and water. Many oxidation studies have been carried out experimentally using XPS [45,62,108e114], UPS [36,113,115], STM, scanning tunneling spectroscopy [36,55,113], photoemission of adsorbed xenon [60e62], and TPD [60e62]. Generally, low reactivity of the pristine pyrite surface toward water is established [36,45,62,108,111,112,115]; however, it is also pointed that nonstoichiometric or sulfur-deficient surface sites could lead to the oxidation of pyrite [115,125]. When exposing pyrite to oxygen, there is oxidation of the iron component, while coadsorption of oxygen and water can enhance the pyrite surface oxidation compared to water or oxygen alone [36,57,111,117]. O isotopic composition of sulfate has suggested that SO2 4 produced from aqueous pyrite oxidation mainly contributed from water-derived O and minorly from atmospherically derived O [37,118e124]. At the beginning, Heidel et al. mentioned that it remains uncertain if (and how) O2 is permanently incorporated into SO2 4 during pyrite oxidation [125], while Heidel and Tichomirowa later confirmed the permanent existence of O2derived O in SO2 4 [118,124]. Tichomirowa and Junghans [126] calculated the bulk contribution of atmospheric O2 in the dissolved SO2 4 and found a value reaching up to 50% during initial oxidation stages (first 5 days, pH 2, fine-grained pyrite fraction) that

142 Chapter 4 decreased to less than 20% after about 100 days. After about 10 days, they found that the O of all newly formed sulfates originated only from water. They proposed that the greater proportion of molecular oxygen in the early formed sulfate was caused by being initially adsorbed on S sites, in addition to chemisorption on Fe sites. While for the later stages, they suggested that it was only occurred at Fe sites because the attack of water-derived hydroxyl groups at S site was more favorable, and molecular O2 acted as electron acceptor only at the Fe site for oxidation of Fe (II) to Fe (III). However, in their experiments, they did not observe the time trends for dissolved oxygen concentration. Hubbard et al. [127] also suggested the direct incorporation of O2 via pyriteeS sites, but they mentioned that such a mechanism is not favored within the literature. Kendelewicz et al. [128] using synchrotron-based PES showed the exposure to O2 alone led to S oxidation; however, they explained this was associated in part with the oxidation of the monosulfide component because surface Sedimer has much greater stability than the monosulfide component in the presence of the O2 reactant. Rosso and Becker et al. [36,57] proposed a proximity effect theory suggesting that O2 pulled electron density from underlying and surrounding Fe and S surface atoms adjacent to the O2-adsorbed Fe sites, causing an increase in the affinity of these surrounding Fe atoms for the lone pair electrons on H2O molecules. Then H2O was strongly adsorbed and dissociated at these surrounding Fe sites forming eOH groups due to the proximity effect, and finally, eOH would attack the S sites, forming the SeO groups with O from H2O. Sulfate formed by this process contains only O derived from water. By theoretical modeling, Patrick et al. [35] also gave a model that O2 dissociated at Fe sites and H2O dissociated at S sites forming SeO species, and the O in sulfate was only derived from water. It is worth mentioning that stepwise oxidation of S has been proposed by Luther [129,130] and Rimstidt and Daughan [131]; however, they suggested that S interacted with water, so the O resource of sulfite was only from water, similar to the results by Rosso and Sit et al. [35,36,57]. Based on the preceding statements, it is suggested that H2O would dissociate into OH and Hþ, and then OH attacks the S sites, forming SeO species. In fact, pyrite has been detected to spontaneously form reactive oxygen species (ROS), i.e., hydrogen peroxide (H2O2) and hydroxyl radicals (OH) [101,107,117,132e138], which are strong oxidative regents. Especially, OH is extraordinary reactive. The first experimental verification of the presence of OH in the pyriteewater system was done by Borda et al. [116]. They proposed that accompanied by the conversion of Fe (III) to Fe (II), H2O dissociated at defective pyrite surfaces producing OH and then the combination of two OH produced H2O2. However, they suggested that the dissociation of H2O to OH may be energetically unfavorable. In contrast, Cohn et al. proposed that O2 can be catalyzed by surface-bonded Fe or dissolved Fe into H2O2 and then into OH [134,138]. All these researches have pointed out the important role of Fe2þ/Fe3þ ions in producing H2O2 and OH. However, the generation details of these ROS are still unclear and not well established.

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Theoretically simulating studies on the oxidation process of pyrite are also performed based on MD method and DFT [11,35,36,57,91,139,140]. It is shown that dissociative adsorption of water molecule alone is energetically unfavorable, while coadsorption of oxygen and water molecules causes the dissociation of water. Stirling et al. [11] reported ab initio simulations of the reaction of water with pyrite (100); however, they did not considered the role of O2. Rosso and Becker et al. [36,57], using small cluster sizes, predicated theoretically a strong dissociative reaction of molecular oxygen at Fe sites and H2O molecularly adsorbing at Fe sites, while for the mixtures, they suggested that chemisorption of O2 on Fe sites promoted the adsorption and dissociation of water molecules to nearby pyrite Fe sites. So far, the most detailed study has been carried by Patrick et al. by DFT calculations [35]. They gave a model of successive surface oxidation reactions with molecular oxygen and water, where finally the complete oxidation of surface sulfur to SO2 4 occurs. They proposed that oxygen dissociated at Fe sites and water dissociated at S sites, which is different from Rosso and Becker et al., where water molecule dissociated at nearby Fe sites due to proximity effect [36,57]. In addition, they suggested that O in sulfate was only derived from water. This cannot explain well the O isotopic experimental results that there exists a small part of O in sulfate derived from molecular O2. Just like these authors stated, “it should be noted that the mechanism we have investigated in this work is not the only possible pathway in the reaction of pyrite with oxygen and water,” so it may have another pathway for pyrite oxidation. It is noted that the surface structure of pyrite for the complex reaction of water and oxygen is not fully considered. Not only their research, but all the other works have not paid attention to the surface structure of pyrite and its influence on the interaction of water and oxygen on it. For the present work, we found different ring structures consisting of Fe and S atoms, different Fe sites for O2 adsorption, and even S sites for O2 adsorption, which will be discussed in detail in the text. The subject of this work focuses on the initial stage of oxidation of pyrite surface with H2O and O2 by DFT calculations, and it aims to explore all the possible pathways for the reaction of pyrite with water and oxygen. In addition, the generating process and mechanism of hydroxyl radical were studied.

4.3.1 Computational methods The calculations were performed based on DFT using CASTEP, GGAePW91 [19,20,26]. Only the valence electrons (Fe 3 d6 4s2 and S 3s2 3p4) were considered using ultrasoft pseudopotentials [25]. A PW cutoff energy of 350 eV was determined by tests. The SCF convergence tolerance was set to 2.0  106 eV/atom. The slab model was cleaved from the optimized bulk crystal. The slab thickness was tested to determine the slab size that produced a convergence of the surface energy to within 0.005 J/m2, and slab sizes with 15 ˚ thickness of vacuum were placed between two surfaces to avoid atomic layers and 20 A the minor effect.

144 Chapter 4 Four types of sites, hollow FeeFe sites, hollow FeeS sites, hollow SeS sites, and FeeS bond sites, were tested for the adsorptions of O2 molecule on pyrite (100) surface, which is terminated with FeeS bonds and perfect SeS bonds. Fe atom is five-coordinated with S atoms, and one top S atom (S1, S2, S3, or S4) is three-coordinated with one bottom S atom (S5, S6, S7, or S8) and two Fe atoms. The surface is found to have four hollow FeeFe sites (Fe1eFe2, Fe1eFe3, Fe1eFe4, and Fe1eFe5), two hollow FeeS sites (Fe1eS1 and Fe1eS2), two hollow SeS sites (S3eS2 and S3eS4), and one FeeS bond site (Fe1eS3) existing, as shown in Fig. 4.21. It is shown that the distances between hollow FeeFe atoms are different (including two kinds of distances, lower or higher than ˚ ), while the distances between hollow SeS or FeeS atoms are the same. In 3.80 A addition, two different ring structures are found, Fe1eS6eFe5eS1eS5 and Fe1eS6eS2eFe2eS3. The former consists of one top S (S1), two bottom S (S5 and S6), and two Fe (Fe1 and Fe5), and the latter consists of two top S (S2 and S3), one bottom S (S6), and two Fe (Fe1 and Fe2). All these surface sites are likely to be the adsorption sites for O2. However, it is clear that they are located in different environments, which may affect the adsorption of oxygen and/ or water molecule. The adsorbents, H2O and O2 were placed inside a cubic cell with lengths of ˚ to optimize before adsorption on the mineral surface. The adsorption 10  10  10 A energy of adsorbates on the mineral surface was calculated as follows: Eads ¼ Eadsorbate=slab  ðEadsorbate þ Eslab Þ

Figure 4.21 Top view of pyrite (100) surface, O2, and H2O molecules.

(4.1)

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where Eads is the adsorption energy, Eadsorbate is the energy of the H2O or O2, Eslab is the energy of the pyrite slab, and Eadsorbate=slab is the energy of the H2O- and/or O2-adsorbed pyrite slab. A larger negative value of Eads indicates stronger adsorption of molecule on the surface. The electrochemical behavior of pyrite electrode was studied by cyclic voltammetry using a Chi660e electrochemical workstation in the solution of tertebutanol with pH 7.0 at room temperature of 25 C. The current with respect to potential in the potential ranged from 1 to 1 V with a scan rate of 0.05 V/s. Saturated calomel electrode and platinum electrode were used as reference electrode and counter electrode, respectively.

4.3.2 Isolated H2O/O2 molecule adsorption Experimental and theoretical studies have shown that dissociative adsorption of H2O is not thermodynamically favored, and molecular adsorption is the dominant binding mode [11,36,111,115,126], and our previous study also showed an unenergetically dissociated adsorption with an adsorption energy of þ82.4 kJ/mol [139]. Because the calculation parameters set for the present study are different from Ref. 50, here we reexamined the nondissociative adsorption of H2O. Optimized configuration is shown in Fig. 4.22. The total Mulliken charge of H2O molecule is calculated as þ0.08 e, compared to þ0.03 e obtained by Rosso et al. [36], indicating a physical adsorption of H2O. Adsorption energy is calculated as 61.8 kJ/mol, very close to 65.6 kJ/mol calculated by Patrick et al. [35]. ˚ and two S/H bonds of 2.57 Water molecularly adsorbs with FeeO distance of 2.16 A ˚ , close to 2.12 A ˚ of FeeO distance but slightly different for S/H distance and 2.58 A ˚ (2.36 and 2.70 A) as calculated by Stirling et al. [11]. Additionally, the OeFeeS angle (this S is located in the inner surface; see it in Fig. 4.21 where it is connected with Fe by blue dotted line) is 172.2 degrees, very close 180 degrees in bulk pyrite. This suggests that the binding of O restores the distorted octahedron of Fe atom.

Figure 4.22 H2O molecule adsorption on the surface: eg, t2g, and eg represent the bonding state, nonbonding state, and antibonding state of Fe 3d, respectively.

146 Chapter 4 For further investigation of interaction of H2O molecule with a surface, PDOS of atoms is plotted, as shown in Fig. 4.22. XPS study by Knipe et al. has shown the water species detected on pyrite interact with the Fe 3d eg molecular orbital. Our calculation is consistent with the experiment. It is clear from the DOS pattern that hybridization between O 2p state and Fe 3d eg bonding state occurs at the energy range of 7.5 to 1.5 eV. Although many studies have been done on the O2 adsorption on pyrite, including experimental and theoretical, we found they are still incomplete and more needed to be learned. On the pyrite surface, we have found two types of hollow FeeFe sites (see Fig. 4.21), which have different distances, i.e., the type Fe1eFe2 and Fe1eFe3 with ˚ and the other type Fe1eFe4 and Fe1eFe5 with distance 3.89 and distance 3.72 and 3.77 A ˚ . In addition, one type of hollow FeeS (Fe1eS1 and Fe1eS2 with distance of 3.56 3.86 A ˚ , respectively) and one type of hollow SeS (S3eS2 and S3eS4 with distance and 3.55 A ˚ ) site were also found. These FeeFe sites, SeS sites, and FeeS sites are likely to of 3.01 A become oxygen adsorption sites. However, previous publications have not noted these situations, and only one type of FeeFe site was considered. To test the impact of these sites on the adsorption of oxygen molecule, oxygen was placed on these sites, and the corresponding adsorption energy was calculated, as shown in Table 4.15, and the corresponding adsorption configurations are shown in Fig. 4.23. It is found that the adsorption energies of O2 on Fe1eFe2 and Fe1eFe3 sites are close, and they are also close to those on Fe1eS1 and Fe1eS2 sites, with adsorption energy about 200 kJ/mol, while the adsorption energies on Fe1eFe4 and Fe1eFe5 are much lower and are only about 110 kJ/mol. It is well worth noting that the adsorption energies of O2 on SeS (S3eS2 and S3eS4) sites have the maximum negative value down to 280 kJ/mol. The FeeS bond site was also considered, and the adsorption energy is only 61.8 kJ/mol. These results suggest that O2 molecule can strongly and chemically adsorb on one type of hollow FeeFe (Fe1eFe2 and Fe1eFe3) site, hollow FeeS sites, and hollow SeS sites on pyrite, whereas will weakly adsorb on the other hollow type of FeeFe (Fe1eFe4 and Fe1eFe5) site and FeeS bond sites. These are new findings that have not been published Table 4.15: Adsorption energies of O2 molecule on different surface sites. Adsorption types Hollow FeeFe sites

Hollow FeeS sites Hollow SeS sites FeeS bond site

Configuration a b c d e f g h i

Adsorption sites Fe1eFe2 Fe1eFe3 Fe1eFe4 Fe1eFe5 Fe1eS1 Fe1eS2 S3eS2 S3eS4 Fe1eS3

Adsorption energy/kJ/mol 202.6 173.7 115.8 111.9 194.9 213.2 284.6 283.7 61.8

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Figure 4.23 Configurations of O2 adsorbing on pyrite surface: (A)e(F) are numbered the same as numbered in Table 4.15; (A)e(D) correspond to the adsorption patterns on hollow FeeFe sites; (E)e(F) correspond to the patterns on hollow FeeS sites; (G)e(H) correspond to the patterns on hollow SeS sites; and (I) corresponds to the patterns on FeeS bond. The nonbold number next to the dotted line is the bond length and the bold number on the arcuate line is the angle formed by three atoms.

previously. First, it is generally considered that O2 molecule would adsorb on FeeFe sites, while no other sites were considered. Second, it has not been reported previously that there exist two types of FeeFe sites; i.e., one (Fe1eFe2 and Fe1eFe3) is the active site for O2 molecule adsorption but the other (Fe1eFe4 and Fe1eFe5) is not. Combined with the adsorption energies results, it is found that when O2 is strongly adsorbed, it is dissociated on the surface (configurations a, b, e, f, g, and h in Fig. 4.23), while when weakly adsorbed, it is not dissociated (configurations c, d, and i). In the ˚ , respectively, much former, the FeeO and SeO bond lengths are about 1.69 and 1.50 A

148 Chapter 4 shorter than those in the latter with FeeO and SeO bond lengths of about 2.00 and ˚ , respectively. In addition, in the latter, except configuration i, the OeO bond length 1.68 A ˚ , a typical superoxide bond. Patrick et al. [35] also gave a modeling result is about 1.38 A for the O2 adsorption; however, their work is not intact because they have not done many tests on the adsorption sites of O2 molecule on the surface. Only two models were considered in their work, i.e., the end-on configuration and the side-on configuration (hollow FeeFe site), with adsorption energies of 58.9 and 69.4 kJ/mol, respectively. They thought the latter was more stable. In the side-on configuration, they gave a FeeO ˚ , respectively. This configuration distance and the OeO distance of about 1.99 and 1.38 A is the same as the weak adsorption configuration of O2 on Fe1eFe4 and Fe1eFe5 in our study. They thought this OeO binding configuration was a key reaction intermediate in pyrite surface oxidation and could readily break exothermically by 109.5 kJ/mol. This suggests that the dissociative adsorption of O2 on pyrite surface went through two steps, and the total adsorption energy was 178.9 kJ/mol (sum of 69.4 and 109.5 kJ/mol), close to our calculation on configurations a and b. However, our calculation shows that O2 can directly and dissociatively adsorb on pyrite surface at FeeFe sites, FeeS sites, and even SeS sites. By observing the dissociative adsorption configurations of O2, it is found that the angles formed by OeFeeS and OeSeS (the bold number labeled on the arcuate line shown in Fig. 4.23) closely approximate those in bulk pyrite of 180 and 102 degrees, respectively, whereas in the undissociated configurations a part of these angles is greatly deviated from the bulk values. These suggest that the dissociative adsorption of O2 can well restore the distorted octahedron of Fe and the tetrahedron of S as found in bulk; however, the undissociated adsorption cannot well restore the shapes of all the distorted surface atoms. Moreover, electron density difference can give clear information on the electrons transfer on atoms. By plotting the electron density difference of surface Fe and S atoms cleaved from a same plane without O2 adsorption (Fig. 4.24A,B) and with O2 adsorption (Fig. 4.24C,D), it is clearly shown that charge is uniformly distributed around fullcoordinated Fe atom in bulk pyrite (Fig. 4.24A), while the charge distributed around pure surface Fe atom is diffused into the vacuum due to the lack of one sulfur ligand (Fig. 4.24B). On the undissociated O2 adsorption surface (Fig. 4.24C), part of the charges on Fe atom are still diffused into vacuum because adsorbed O atom deviates from the plane and cannot well restore the distorted octahedron of Fe atom. On the dissociated O2 adsorption surface (Fig. 4.24D), the bonding of O atom enables complete coordination of Fe atom where the distorted octahedron is well restored, so the positive charge is gathered around Fe atom, similar to that in the bulk phase (Fig. 4.24A). Based on the calculation results, this is the first confirmation that O2 molecule can be directly chemisorbed on S site by DFT simulation. Generally, it is thought that O2 is

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Figure 4.24 Electron density difference on atoms cleaved from the same plane. In bulk pyrite (A), without O2 adsorption surface (B), on undissociated O2 adsorption surface (C), and on dissociated O2 adsorption surface (D). Blue(black in print version) represents electrons loss, red(gray in print version) represents electrons enrichment, and white represents zero electron density.

dissociated at Fe sites, but not at S sites because of the electrostatic repulsion between negatively charged O and S atoms. As suggested in the introduction, both water-derived and atmospheric oxygen could be incorporated into sulfate [37,118e123]; however, such a mechanism as the direct incorporation of O2 via pyriteeS sites is not favored within the literature [125]. Our study first shows that at the initial oxidation stage, O2 can be easily dissociatively adsorbed at FeeS and SeS sites, in addition to chemisorption on FeeFe sites. Chemisorption on FeeS and SeS sites is one of the schemes of the initial oxidation of pyrite surface by O2, causing part of O in sulfate derived from O2.

4.3.3 Coadsorption of H2OeO2 on pyrite surface H2O molecule was put on the surface preferentially adsorbed O2 to investigate the interactions of H2OeO2 on the surface (O2 then H2O sequence adsorption). All nine kinds of oxygen adsorption models were considered, and the final adsorption configurations are shown in Fig. 4.25. It is shown that H2O molecule is dissociated completely on the surface after O2 molecule adsorbing on all four FeeFe sites (Fig. 4.25AeD). It is noted that the undissociated O2 molecule on pure surface (see Fig. 4.23C,D) is dissociated due to the adsorption of H2O molecule (Fig. 4.25C,D). The two dissociated H atoms are bonded to the two dissociated O atoms in O2, forming two FeeOH species with FeeO distance ˚ , and the dissociated O in H2O is bonded to top S atom, forming SeO specie about 1.83 A ˚ . When O2 is adsorbed at FeeS sites (Fig. 4.25E,F), H2O with distance about 1.52 A molecule is dissociated into one eH and one eOH. eH is bonded to the O of O2 molecule preferentially adsorbed at Fe site, forming FeeOH specie with FeeO distance of

150 Chapter 4

Figure 4.25 Configurations of H2O adsorbing on pyrite surface preferentially adsorbed O2: (A)e(D) correspond to the adsorption patterns of O2 at hollow FeeFe sites; (E)e(F) correspond to the patterns of O2 at hollow FeeS sites; (G)e(H) correspond to the patterns of O2 at hollow SeS sites; and (I) corresponds to the patterns of O2 at FeeS bond. The number next to the dotted ˚. line is the bond length in A

˚ , and eOH is adsorbed at Fe site (Fig. 4.25E) or S site (Fig. 4.25F), forming 1.82 A ˚ (Fig. 4.24E) and SeOH specie with SeO FeeOH specie with FeeO distance of 1.85 A ˚ (Fig. 4.25F). When O2 is adsorbed at SeS sites (Fig. 4.25G,H), H2O distance of 1.65 A molecule cannot be dissociated on the surface; however, the FeeO distance (2.10 and ˚ ) decreases compared to that on pure H2O adsorption surface (2.16 A ˚ ), suggesting 2.06 A the adsorption of H2O is enhanced due to the presence of O2. This is caused by the formation of hydrogen bonding between H and O of O2 molecule. When O2 is adsorbed on FeeS bond site (Fig. 4.25I), O2 is dissociated (undissociated when no H2O is present, see Fig. 4.23I) and H2O is dissociated into one eH and one eOH, forming FeeOH specie ˚ ; however, no SeOH specie is formed. with FeeO distance of 1.93 A For the coadsorption of O2 and H2O, besides the model of H2O adsorbing on the surface preferentially adsorbed O2 (O2 then H2O sequence adsorption) was considered, the models of O2 adsorbing on the surface preferentially adsorbed (H2O then O2 sequence adsorption) and simultaneous adsorption of H2O and O2 were also investigated.

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Figure 4.26 Configurations of O2 adsorbing on pyrite surface preferentially adsorbed H2O: (A) two H2O adsorption at two Fe sites, (B) corresponds to the patterns of O2 adsorption at hollow FeeFe site, and (C) corresponds to the patterns of O2 adsorption at hollow SeS site. The number next ˚. to the dotted line is the bond length in A

O2 was placed on the H2O-adsorbed surface to obtain the influences of H2O molecule on the adsorption of O2. Two H2O molecules were preferentially adsorbed at two Fe sites (Fig. 4.26), and O2 was then placed on the optimized H2O-adsorbed surface at FeeFe site and SeS site. It is found that when O2 adsorbs at FeeFe site Fig. 4.26B), one H2O molecule is repelled from the surface Fe site due to the adsorption of O2 (FeeO distance ˚ ), and this repelled H2O molecule is then adsorbed at the interface forming HeO of 1.94 A and HeS hydrogen bonds. The other H2O molecule is still adsorbed at the other Fe site ˚ , typically without any affect. It is noted that the OeO bond length is increased to 1.49 A peroxide. The O2 placed at SeS site (Fig. 4.26C) is dissociated, forming two SeO bonds, and the two adsorbed H2O molecules are still adsorbed at Fe sites. Moreover, hydrogen bond is formed between H and dissociated O in O2. We then investigated the simultaneous adsorption of H2O and O2 on the H2O-adsorbed surface, and the final adsorption configuration is shown in Fig. 4.27. It is found that both the two preferentially adsorbed H2O molecules are repelled from the surface. Moreover, the later adsorbed H2O molecule is dissociated thoroughly with O bonded to surface S forming SeO specie and the two H bonded to O2 molecule forming hydrogen peroxide.

152 Chapter 4

Figure 4.27 Simultaneous adsorption of H2OeO2 on H2O preferentially adsorbed surface.

Figure 4.28 Configurations of simultaneous adsorption of H2O and O2 on pyrite surface.

H2O and O2 molecules were placed on pyrite surface simultaneously to obtain their adsorption behaviors, and the final adsorption configurations are shown in Fig. 4.28. It is found that the simultaneous adsorption configurations of H2O and O2 on pyrite surface are the same as the configurations for the O2-then-H2O sequence adsorption.

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153

It is found that O2 adsorbing on the surface preferentially adsorbed H2O may lead to the formation of H2O2 (see Figs. 4.26 and 4.27), while the simultaneous adsorption configurations of H2O and O2 on pyrite surface (see Fig. 4.28) are the same as the configurations for the O2etheneH2O sequence adsorption. Here the cases of O2etheneH2O sequence adsorption (O2eH2O simultaneous adsorption has the same result) will be discussed. Our calculations have suggested that coadsorption of O2 and H2O can enhance the oxidization of pyrite. This result is consistent with the other theoretical calculations and experimental studies [36,112]. Table 4.16 lists the surface species and numbers derived from Fig. 4.25. Configurations a, b, c, d, and e have the same surface species and specie numbers, one of SeO and two of FeeOH, and the coadsorption energy of H2OeO2 for these configurations are close, ranging from 328.1 to 346.4 kJ/mol. Configurations f and i have the same surface species and numbers, one of SeO, one of FeeOH, and one of SeOH, and also have close adsorption energy for O2eH2O (about 270 kJ/mol). Configurations g and h have the same surface species and numbers, two of SeO, and have close adsorption energy for O2eH2O low to 390 kJ/mol. These results reflect that if the surface productions are the same after adsorbates adsorption, the adsorption energy, i.e., the adsorption strength of adsorbates, is nearly the same. In addition, based on the adsorption energy of adsorbates on the surface, it is found that the production of SeOH species on the surface is not energetically favorable, while the production of FeeOH and SeO species is favorable. Consequently, configurations F and I, where O2 locates on hollow FeeS site and FeeS bond site, are not favorable, although O2 molecule can dissociate on the surface in the presence of H2O molecule for these two configurations. It is noted that for configurations g and h, where O2 dissociatively adsorbs at hollow SeS sites and H2O adsorbs at Fe site, although H2O molecule is not dissociated and no FeeOH Table 4.16: Surface species, numbers, and adsorption energies at different adsorption sites.

Adsorption types Hollow FeeFe sites Hollow FeeS sites Hollow SeS sites FeeS bond site

Configuration a b c d e f g h i

Surface species and numbers

Adsorption sites

SeO FeeOH SeOH

Fe1eFe2 Fe1eFe3 Fe1eFe4 Fe1eFe5 Fe1eS1 Fe1eS2 S3eS2 S3eS4 Fe1eS3

1 1 1 1 1 1 2 2 1

2 2 2 2 2 1 0 0 1

0 0 0 0 0 1 0 0 1

Adsorption energy of O2 þ H2O/kJ/mol 346.4 334.8 328.1 341.6 344.5 269.2 395.6 391.7 274.0

154 Chapter 4 specie is produced, the coadsorption energies of O2 and H2O are the lowest to 390 kJ/ mol, compared to the adsorption energy of isolated H2O and isolated O2 of about 60 and 280 kJ/mol, respectively. This suggests that the adsorption of H2O molecule in the presence of O2 is enhanced, and this can be ascribed to the formation of hydrogen bonds between H derived from H2O and O derived from dissociated O2 molecule. However, this coadsorption model cannot cause any H2O molecules to be dissociated. Based on the preceding results, for these two coadsorption cases of O2 and H2O (simultaneous adsorption and O2etheneH2O sequence adsorption), it can be concluded that O2 can be dissociated at FeeFe sites, FeeS sites, and even SeS sites, and correspondingly, H2O can thoroughly, partially, and completely not be dissociated on pyrite surface. Consequently, SeO and FeeOH species are produced and energetically favored. When O2 adsorbs at FeeFe sites, two H are thoroughly dissociated from H2O molecule and bonded to two O of dissociated O2 molecule, forming two FeeOH species, leaving O bonded to surface S atom. Hence, for this adsorption scheme, the O of sulfate is derived from H2O molecule. When O2 adsorbs at FeeS sites, only one H is dissociated from H2O molecule and then bonded to one O dissociated from O2 molecule, forming one FeeOH specie, leaving eOH bonded to surface Fe atom, forming one FeeOH, and another dissociated O from O2 molecule is bonded to surface S atom. Consequently, for this adsorption scheme, the O of sulfate is derived from O2 molecule. When O2 adsorbs at SeS sites, H2O molecule is not dissociated, and the O of sulfate is derived from O2 molecule. The atomic Mulliken charge was calculated and labeled in Fig. 4.29. It is found that on pure O2 molecule adsorption surface (processes a, b, and c in Fig. 4.29), O atoms capture electrons from the surface and are negatively charged. Moreover, O atoms adsorbing at SeS site are the most negatively charged, followed by FeeS site, and then FeeFe site. When H2O molecule is adsorbed (processes d, e, and f), O2 molecule continues to capture electrons and is more negatively charged. However, the captured electrons numbers at the FeeFe site are the most, followed by FeeS site and then SeS site. It is shown that from process a to d, the charge of O2 is changed from 0.92 to 1.49 e (capturing the most electrons), and from process b to e, the charge of O2 is changed from 1.16 to 1.48 e, and from process c to f, the charge of O2 is changed from 1.52 to 1.61 e (nearly not changed). These results suggest that the O2 adsorbed at Fe site has greater activity than at S site for the dissociation of H2O molecule because it is very conducive to form FeeOH specie, which is a more energetically favored surface specie than SeOH specie. Moreover, observing from process a to d (Fig. 4.29), it is shown that the charge on Fe atom is not changed obviously after H2O adsorption, while the total charge of H2O is close to zero, and the S bonded to O in H2O loses large numbers of electrons and is positively charged. Hence, it is clear that O2 captures electrons from this S atom. This is consistent with the result by Rimstidt and Vaughan [131] that the electrons were

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Figure 4.29 Atomic Mulliken charge: aec correspond to dissociative adsorption of pure O2 molecule on FeeFe site, FeeS site, and SeS site, respectively; d, e and f correspond to addition of H2O into the O2eadsorbed surface.

transferred from sulfur atoms at an anodic site through the crystal to cathodic Fe sites and were acquired by the oxidant species (O2). We compared the bond strength between O (both from O2 molecule and H2O molecule) and surface Fe and S by calculating the Mulliken bond populations including bond length and covalent strength (see Table 4.17). The larger the bond population value is, the stronger is the covalent property of the bond. It is shown that the FeeOO bond length increases and the bond population decreases after H2O molecule adsorption, while the bond lengths and populations of SeOO are not changed after H2O molecule adsorption. This result suggests that the covalent strength of FeeOO weakens due to the adsorption of H2O molecule, while the covalent strength of SeOO is not changed. Moreover, it is found that the bond lengths and populations of SeOO and SeOW are the same, suggesting that the bond properties of SeO are the same regardless of the resource of O (from H2O molecule or O2 molecule). Similarly, the HeO properties are also the same regardless of the resource of O.

156 Chapter 4 Table 4.17: Mulliken bond populations including bond length and covalent strength. FeeFe site Adsorption configuration O2/surface O2þH2O/surface

Bond FeeOO SeOO OOeOO FeeOO SeOO FeeOW SeOW HeOO HeOW OOeOO

Len. 1.69 e 4.69 1.83 e e 1.52 0.98 e 4.78

Pop. 0.58 e e 0.42 e e 0.44 0.60 e e

FeeS site Len. 1.68 1.50 2.71 1.82 1.51 1.85 e 1.00 0.99 3.05

Pop. 0.58 0.47 e 0.42 0.47 0.41 e 0.58 0.59 e

SeS site Len. e 1.50 3.10 e 1.52 2.10 e e 0.99 3.66

Pop. e 0.46 e e 0.43 0.19 e e 0.57 e

Additionally, we compared the results of isolated H2O adsorption on Fe site with the results of H2O adsorption on Fe site after O2 adsorption on SeS sites (i.e., O2etheneH2O sequence adsorption) and found that the adsorption energy of the latter (110.9 kJ/mol) is lower than the former (61.8 kJ/mol), suggesting the latter behaved with a chemisorption property. We further compared the FeeOW bonds and found that the FeeOW bond length forming on O2etheneH2O sequence adsorption is shorter than that forming on isolated H2O adsorption. The former also has a larger bond population value. These results suggest that the adsorption of O2 on SeS site can greatly enhance the adsorption of H2O molecule, even causing chemisorbed H2O. Becker et al. proposed a proximity effect theory to explain the enhancing oxidation rate of pyrite by H2O and O2 compared with O2 alone [57]. They predicted that O2 pulls electron density from underlying and surrounding Fe and S surface atoms adjacent to the O2eadsorbed Fe sites, causing an increase in the affinity of these surrounding Fe atoms for the lone pair electrons on H2O molecules; hence, H2O interacts more strongly with available Fe sites adjacent to FeeO groups and finally dissociates, forming FeeOH species. For the dissociation reason, however, we found that it is not ascribed to the electron loss of the proximity atoms. We found that the adsorption of O2 on Fe sites has small influence on the charge number of surrounding Fe and S atoms near the O2eadsorbed Fe sites (see processes a, b, and c in Fig. 4.29); however, the density of states (DOS) of the surrounding S atom is changed significantly. We investigated the changes of DOS of surrounding S atom and O atoms from process a to d in Fig. 4.29, as shown in Fig. 4.30. It is found that on pure O2eadsorbed surface (Fig. 4.30B), the surrounding S 3p state increases near energy 1.5 eV compared to that on pure surface (Fig. 4.30A), suggesting that the electronic state of S atom is changed and the electronic activity of S 3p increases. And then observing the DOS of the S and O atoms (derived from H2O) in SeO specie formed on the surface after coadsorption of H2O and O2 (Fig. 4.30C,D), it is found that there is a strong hybridization peak near energy 1.5 eV.

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Figure 4.30 Density of states of S and O atoms changes from process a e d in Fig. 4.29.

These results suggest that it is the change of electronic density state but not the electronic density loss of surrounding S atom that leads to the affinity of the surrounding S atom for the lone pair electrons on H2O molecule. The change of DOS of S atom can be ascribed to the structural change of the atom. Fig. 4.31 shows the structure of surface atoms before and after O2 adsorption. It is found that Fe2eS1, Fe1eS2, and Fe2eS2 bond distances are increased significantly from 2.23, ˚ to 2.30, 2.30, and 2.24 A ˚ after the adsorption of O2 molecule, 2.21, and 2.16 A ˚ and 2.20 respectively, while S1eS3 and S2eS4 bonds distances are decreased from 2.21 A ˚ and 2.14 A ˚ , respectively. This means that FeeS bonds are weakened, while SeS to 2.15 A

Figure 4.31 ˚ marked next to Influences of O2 adsorption on the surrounding atomic distances. Distance in A the bond.

158 Chapter 4 bonds are strengthened due to the adsorption of O2 on Fe sites. Hence, it is predicted that further oxidation will first lead to the rupture of FeeS bonds. In fact, FeeS bond is believed to be weaker than SeS bond. In addition, for the dissociation sites of H2O on pyrite surface in the presence of O2, Becker et al. [57]. proposed that due to the proximity effect H2O molecule was first strongly adsorbed at the Fe site adjacent to the FeeO group (formed after O2 adsorption), and then H2O dissociated at this Fe site producing eOH at Fe site forming FeeOH, and this eOH then would attack the S site common to FeeOH and FeeO groups (i.e., HOeFeeSeFeeO linkages), finally forming SeO groups with O derived from H2O. However, we found that H2O is dissociated directly at the S sites adjacent to the FeeO group (formed after O2 adsorption) but not at the nearby Fe sites. This is consistent with the result of Patrick et al. [35]. In addition, we also found the formation of SeOH specie is not energetically favored. For the coadsorption behaviors of H2O and O2, our result is agreement with Patrick et al. [35]. When O2 is adsorbed at Fe sites, i.e., O2 dissociated at Fe sites forming FeeO specie, and H2O dissociated at S site forming SeO specie, leaving the dissociated H bonding to FeeO, forming FeeOH. However, they only considered one adsorption site for O2 adsorption, i.e., adsorption at Fe site. We found S site can also be an active site for O2 adsorption, which may explain the O isotopic composition of sulfate, indicating that both water-derived and atmospheric oxygen could be incorporated into sulfate, especially explaining the high percentage of O from O2 at the initial oxidation of pyrite. In summary, it can be concluded that for the interaction of O2eH2O on pyrite surface, including simultaneous adsorption, O2etheneH2O sequence adsorption and H2OetheneO2 sequence adsorption, the O of sulfate can be only derived from H2O or both from H2O and O2 at the initial oxidation stage of pyrite. This result is consistent with O isotope experiments on pyrite oxidation that both the O derived from molecular oxygen and water could be incorporated into sulfate, with most derived from water. Exactly, Usher et al. [121] showed that by exposing pyrite to gaseous O2 prior to pure H2O vapor, both SO2 4 and iron oxyhydroxide became significant products, and isotopic labeling experiments showed that the O in the SO2 4 product was derived from both H2O and O2. However, if pyrite was exposed to pure H2O vapor prior to gaseous O2, it led to the formation of sulfur oxyanions that included SO2 4 , and isotopic labeling experiments showed that the O in the sulfate product was primarily derived from the H2O reactant. Formation of hydroxyl radical. We are now concerned with the dissociation process of H2O and O2 on pyrite and the surface oxidation mechanism. Here, we discuss the cases of complete dissociation of H2O and O2 (in cases of O2etheneH2O sequence adsorption and simultaneous adsorption of H2O and O2, corresponding to process aed in Fig. 4.29) and generation of hydrogen peroxide (in case of H2OetheneO2 sequence adsorption,

Interaction of water and oxygen with sulfide mineral surface

159

Figure 4.32 Atomic Mulliken charge when H2OetheneO2 sequence adsorbing on pyrite surface.

corresponding to process aeb in Fig. 4.32) on the surface due to interaction of H2OeO2. Figs. 4.32 and 4.33 show these two cases, respectively. The case of H2OetheneO2 sequence adsorption is discussed. It has been shown that the preferentially adsorbed H2O molecule at Fe sites would be repelled from the surface due to the newly coadsorbed H2OeO2, while the interaction of newly coadsorbed H2OeO2 leads to dissociation of H2O molecule, forming hydrogen peroxide on the surface, leaving

Figure 4.33 Complete dissociation process of H2O and O2 on pyrite surface. Corresponding to the process aed in Fig. 4.29.

160 Chapter 4 the O in H2O bonded to the surface S (Fig. 4.32). Hence, the O in sulfate species generated by this interaction mode is derived from H2O molecule. It is the same as other cases of H2OeO2 interactions proposed in this work that O2 captures electrons from the surface S atom. Finally, the hydrogen peroxide molecule has almost zero charge. In Fig. 4.33, the atomic distances are plotted as a function of optimization step (reflecting the calculation process), from which the changes in distances between atoms can be clearly observed during the interaction process between molecules with pyrite surface and interaction process between molecules themselves. The complete dissociation process of H2OeO2 can be divided into three regions, I, II, and III zones. Correspondingly, three representative adsorption configurations are plotted to illustrate the reactions taking place in these three regions, as indicated by the arrows. In region I, SeO1 (in H2O) distance increases dramatically, indicating that H2O molecule is repelled from the surface. The distance of O2eO3 (in O2) is also increased. In region II, H1 dissociates from H2O molecule accompanying with O2 dissociating when H2O molecule is far away from the surface (large SeO1 distance), forming the first FeeOH (O3H1) specie and leaving eOH (O1H2) far away from the surface S. In region III, eO1H2 is down toward surface S with short SeO1 distance, and H2 dissociates from eO1H2, forming the second FeeOH (O2H2) specie. The atomic distance changes corresponding to process aeb in Fig. 4.32 are shown in Fig. 4.34. It is found that the generation process of hydrogen peroxide (H2O2) is the same as the preceding process shown in Fig. 4.33; i.e., H2O is first repelled from the surface, and one H dissociates, forming one eOH, and then eOH goes down toward the surface S and finally also dissociates. The two dissociated H interact with O2 forming H2O2. It is noted that the dissociation of H from H2O is a stepwise process. One H is dissociated when H2O molecule is far away from the surface (with SeO1 distance even larger than ˚ ), while the other H is dissociated when the leaving eOH is down toward the surface 2.0 A S. The question is why the leaving eOH that is far away from the surface can be down toward the surface S and finally form a strong SeO bond (with a final distance below ˚ ). We speculate the hydroxide radical (OH) mechanism could give an explanation 1.6 A for this result. The dissociation of H2O molecule may go through the following reactions on the surface: H2 O / OH þ Hþ

(4.3)

(4.4) (4.5) py  SOH / py  SO þ Hþ

(4.6)

Interaction of water and oxygen with sulfide mineral surface

161

Figure 4.34 Formation of H2O2 on pyrite surface, corresponding to the process aeb in Fig. 4.32.

where py represents pyrite. Eq. (4.3) indicates that H2O molecule dissociates into OH and Hþ due to interaction with dissociated oxygen, although the molecule is away from the surface. For Eq. (4.4), OH captures surface hole (hþ ), causing the production of hydroxyl radical OH. We know that OH has great activity leading to it down toward the surface and then interacting with the surface S. Finally, under the effect of the dissociated O atom, the H in OH is dissociated. Consequently, it is the hydroxyl radical, OH, that makes the reaction continue on the surface. The reaction of O2 molecule can be expressed as follows: py  2FeII þ O2 þ 2Hþ / py  2FeIII  2OH

(4.7)

(4.8)

162 Chapter 4 In fact, the first experimental verification of the presence of OH in the pyriteewater system was done by Borda et al. [116]. To verify the presence of OH, tertebutanol was used as the reactant with OH in our study. Electrochemical behavior of pyrite electrode was studied by cyclic voltammetry at different pH values by addition of different concentrations of tertebutanol. Fig. 4.35 shows the scanned cyclic voltammetric curves. Here only the oxidation of S is considered. The oxidation for S is believed to occur around potential of 0.2 V. It is found that the oxidation peak of S is very obvious under all pH conditions when there is no addition of tertebutanol (0% tertebutanol), while addition of tertebutanol (5% or 10%) leads to significant decrease (even disappearance at pH 7) of oxidation peak. The corrosion current (Icorr) of pyrite scanned around 0.2 V under different pH conditions and tertebutanol concentrations listed in Table 4.18 shows that the Icorr is lowered due to the addition of tertebutanol. These results suggest that the oxidation of S is weakened due to the decrease of OH that is reacted with tertebutanol. This result confirms the presence of OH when pyrite is oxidized under H2OeO2 circumstance.

Figure 4.35 Cyclic voltammetric curves in the potential ranging from 1 to 1 V with a scan rate of 0.05 V/s under different pH conditions.

Interaction of water and oxygen with sulfide mineral surface

163

Table 4.18: Corrosion current (Icorr, in 10¡6 A/m2) of pyrite scanned around 0.2 V under different pH conditions and tertebutanol concentrations. pH value 4 7 10

0% tertebutanol 3.963 1.349 19.810

5% tertebutanol 3.368 1.127 4.774

10% tertebutanol 3.174 0.722 e

e represents no detection.

This is the first time that directive dissociative chemisorption of O2 on the S site on pyrite surface has been confirmed, besides dissociative chemisorption on the Fe sites. This gives explanation for the small amount of O in sulfate derived from O2 besides from water. However, H2O cannot be dissociated when O2 is adsorbed on SeS sites, while it can be partially dissociated when O2 is adsorbed on FeeS sites and completely dissociated when O2 is adsorbed on FeeFe sites accompanied by the dissociation of O2. Consequently, O in sulfate can be derived from O2 when O2 is adsorbed on SeS sites and FeeS sites, while derived from H2O when O2 is adsorbed on FeeFe sites. We believed that all these cases can occur during the pyrite surface oxidation. Differences in adsorption sequence of H2O and O2 cause different surface productions. It is found that simultaneous adsorption of H2O and O2 and O2etheneH2O sequence adsorption make the same results on the adsorption behaviors of H2O and O2 on the surface, while H2OetheneO2 sequence adsorption causes different results from the former two. SeO, FeeOH, and SeOH species are formed when simultaneous adsorption of H2O and O2 and O2etheneH2O sequence adsorption occur, while H2O2 may be formed on the surface when H2OetheneO2 sequence adsorption occurs. However, SeOH specie is found energetically unfavorable on the surface. Finally, H2O is found going through a stepwise dissociation process when interacting with O2 on pyrite surface, and hydroxyl radical OH is the main reactive oxygen species (ROS) that can oxidize the surface S to sulfate. Experimental results confirm the presence of radicals.

4.4 Coadsorption of water and oxygen on the galena surface Galena (PbS) is one of the most common sulfide minerals that extensively exists in all kinds of ore deposits. Oxidation of galena is of crucial importance in environmental and geochemical processes [141e145] due to the release of sulfate, lead, and other potentially toxic trace metals, such as Ge, As, Hg, and Tl. Reaction products are largely fixed in secondary minerals, for example, in anglesite (PbSO4), cerussite (PbCO3), and lead-bearing jarosite ((Pb,K)Fe3(SO4)2(OH)6) [146]. But minor amounts of dissolved sulfate, lead, and trace metals may enter the soils, surface runoff and groundwater, rivers, and oceans [147e149]. The mobility and potential toxicity associated with galena dissolution increase

164 Chapter 4 in scenarios undergoing acid rock drainage [150,151]. Therefore, knowledge of galena oxidation mechanisms is important for the interpretation of environmental pollution. Additionally, galena is the primary mineral of lead and the major carrier of silver. It is generally recovered through froth flotation process, which takes advantage of the differences in wettability at particle surfaces to separate different minerals. Usually, a suitable organic collector reagent is necessary to enhance the hydrophobicity of mineral surface to ensure the adhesion of mineral particles to the froth. It has been observed that oxidation of galena is necessary for the froth flotation of galena mineral using xanthate (dithiophosphoric carbonate, ROCSSe) as collector [152]. The reactions are as follows: 2 PbS þ 2 O2 þ H2O / PbS2O3 þ Pb(OH)2

ð4:9Þ

2 PbS2 O3 þ 2ROCS 2 /PbðROCS2 Þ2þS2 O3

(4.10)

Moreover, the extraction of metal from galena via hydrometallurgical operations [153e155], such as leaching and bioleaching [156e163], consists of oxidation. Hence, investigation of galena oxidation is very important for the recovery of galena and hydrometallurgical extraction of lead. Experimental methods, for instance, cyclic voltammetry [164,165] and chronoamperometry [152,166], are used to study the oxidation of galena. In addition, surface species found on galena from oxidation and dissolution have been studied using several analytical techniques, including STM [42,56,167,168], X-ray photoelectron spectroscopy [42,51,169,170], Fourier transform infrared spectroscopy [169,171e174], Raman spectroscopy [175e178], and atomic force microscopy [179e181]. Such techniques are useful to observe the chemical and physical changes during galena oxidation. However, the details of the oxidation on galena surface still remain unclear. Studies have been focused on examining the oxidation mechanism of galena, which resulted in various modes of galena oxidation [3,167,170,180,182e188]. Disagreement over the exact composition of the sulfur-rich phase has ensued over years [147,181,189,190]. In addition, there is no agreement regarding the oxygen sources of sulfate in the oxidation process. Hsieh and Huang [147] suggested that oxygen in the produced sulfate should completely be derived from molecular oxygen. Fornasiero et al. [171] proposed that only water-derived oxygen is incorporated into the produced sulfate. Heidel and Tichomirowa [34], using the isotopic examination of the produced sulfate, indicated that oxygen in sulfate is largely derived from water molecules. Accordingly, the adsorption of water molecules participates in the galena oxidation process and determines the final oxidation products. DFT performs very well in the simulation of configuration and electronic structure of galena surface to gain insight into the fundamental aspects of oxidation at the atomic level

Interaction of water and oxygen with sulfide mineral surface

165

[81,191,192]. Sit et al. [35] reported DFT study results on the adsorption and reactions of oxygen and water with (100) surface of pyrite and proposed the crucial recurring process of pyrite oxidation, which is consistent with the isotopic labeling observations. However, the mechanism of galena oxidation has not yet been established. In this research, we studied the role of water in the oxidation of galena surface and conducted DFT calculations of the adsorption of O2 and H2O on the galena (100) surface.

4.4.1 Computational models and methods All our calculations were performed in the framework of CASTEP, developed by Payne et al. [92]. DFT calculations within the GGA using the Perdew-Wang [26] were carried out to study the adsorption of O2, H2O, and H2O/O2 on the galena surface. The interactions between valence electrons and ionic core are represented using ultrasoft pseudopotentials [25]. The kinetic energy cutoff (390 eV) of the PW basis was used throughout the study, and the Brillouin zone was sampled with Monkhorst and Pack special k-points of a 1  2  1 grid for all electronic structure calculations [27]. It indicates that the cutoff energy and the k-points mesh are sufficient for the present system. For self-consistent electronic minimization, the Pulay density mixing method was employed with the convergence tolerance of 2.0  106 eV/atom. The convergence criteria for structure optimization and energy calculation were set to the following: (a) energy ˚ , and tolerance of 2.0  105 eV/atom, (b) maximum force tolerance of 0.05 eV/A ˚ (c) maximum displacement tolerance of 0.002 A. The PbS (100) surface was chosen to study, as it is the most stable surface [79]. After examinations of the slab thickness and vacuum slab thickness, we constructed a ˚ vacuum slab. The three (4  2  1) PbS (100) surface with 8 atomic layers and 15A outermost atomic layers of the substrate were allowed to relax, while the five bottom-most atomic layers of the substrate were fixed to the bulk coordinates in the adsorption calculations. The optimization calculations for O2 and H2O molecules were conducted in a ˚ cubic cell. 10  10  10 A

4.4.2 Adsorption of a single oxygen molecule Several adsorption sites for O2 adsorption have been tested, and the results suggest that the adsorption of O2 molecule parallel to the hollow site between S atoms is the most energetically favorable, with the adsorption energy of 194.67 kJ/mol. The optimized configurations are shown in Fig. 4.36A. As shown in Fig. 4.36A, when O2 molecule is placed parallel to the hollow site between S atoms, the two O atoms of O2 molecule interact with the two surface S atoms, forming two SeO bonds with lengths of 1.661 and ˚ . Moreover, the distance of OeO bond is 3.133 A ˚ , which is far greater than the 1.643 A ˚ bond length of O2 molecule (1.241 A), suggesting that a complete dissociation of oxygen molecule occurs on the PbS (100) surface.

166 Chapter 4

Figure 4.36 Optimized configurations for a single O2 molecule adsorbing on the hollow site on PbS (100) surface: (A) O2 parallel to the hollow site (between S atoms) and (B) O2 parallel to the hollow site ˚ ). (between Pb atoms). The map is shown in top view. Numbers are bond lengths in angstroms (A

We also found that when O2 molecule is placed parallel to the hollow site between Pb atoms (as shown in Fig. 4.36B), the calculated adsorption energy is 65.11 kJ/mol, indicating that chemisorption occurs on the PbS surface. As shown in Fig. 4.36B, the two oxygen O atoms interact with the two surface Pb atoms with two PbeO bond lengths of ˚ . The OeO bond length of adsorbed O2 molecule is 1.346 A ˚ , suggesting 2.459 and 2.669 A that oxygen molecule becomes superoxo form, which may beneficial to the subsequent surface reaction.

4.4.3 Adsorption of a single water molecule The most stable adsorption site of water molecule on the PbS (100) surface is the hollow site with the adsorption energy of 32.25 kJ/mol, indicating a physical interaction between water and the surface. As shown in Fig. 4.37, the weak hydrogen bonds between surface S atoms and water H atoms are observed with the S/H bonds lengths of 2.386 ˚ . In addition, the bond length of PbeO is 3.118 A ˚ , which is longer than the and 2.237 A ˚ sum of atomic radius of Pb and O (2.410 A), indicating that the water O atom hardly interacts with the surface Pb atom. Hence, a single water molecule weakly interacts with the hydrophobic PbS (100) surface. The results of isotopic labeling examinations suggest that the oxidation products of galena surface are mainly derived from water molecules [34], though the galena surface is hydrophobic. Then an important question that can be raised here is how is a water molecule involved in the process of oxidation on the hydrophobic galena surface. Simulation results indicate that hydroxyl species can strongly interact with the surface Pb and S sites with the adsorption energies of 148.46 and 106.69 kJ/mol, respectively.

Interaction of water and oxygen with sulfide mineral surface

167

Figure 4.37 Optimized configuration for adsorption of a single water molecule on the PbS (100) surface. The ˚ ). map is shown in top view. Numbers are bond lengths in angstroms (A

Hence, it is speculated that H2O molecule might participate in the oxidation reaction via the other form of reaction, probably the hydroxyl species.

4.4.4 Sequential coadsorption of water and oxygen on the PbS (100) surface Two sequential coadsorption modes have been considered. First, the adsorption of oxygen on the hydrated PbS (100) surface has been simulated by placing a O2 molecule on the PbS surface with two water molecules previously adsorbed on the hollow site. Two types of hollow sites for oxygen adsorption (O2 parallel to the hollow site (between S atoms) or (between Pb atoms)) have been tested, and the calculated adsorption energies are 46.91 and 13. 94 kJ/mol, respectively, indicating that preadsorbed water molecules are energetically unfavorable for the adsorption of O2. The second mode adsorption of water molecule on the PbS surface with preadsorbed O2 has also been tested. First, different sites for water adsorption on the surface with preadsorbed O2 parallel to the hollow site (between S atoms) have been simulated, and the results (shown in Fig. 4.38) suggest that the dissociation of water molecule does not occur. Then, water adsorption on the surface with preadsorbed O2 parallel to the hollow site (between Pb atoms) has been tested. The optimized configuration is shown in Fig. 4.39, and the calculated adsorption energy is 92.81 kJ/mol. It is noted that the water molecule has been dissociated and the water O atom (labeled as OW) is bonded with the surface S ˚ and PbeOW bond length of and Pb atoms with the S＝OW bond length of 1.694 A ˚ ; meanwhile, the two dissociated water H atoms (labeled as HI and HII) are bonded 2.565 A

168 Chapter 4

Figure 4.38 Geometric configurations of water adsorption on the PbS surface with preadsorbed O2 on the S ˚ )). site (numbers are bond lengths in angstroms (A

Figure 4.39 The geometric configuration of water adsorption on the PbS surface with preadsorbed O2 on the ˚ ).) site parallel to hollow (between Pb atoms). (Numbers are bond lengths in angstroms (A

with two oxygen O atoms to form two OeH species (with bond lengths of 0.992 and ˚ ), which then interact with two surface Pb atoms to form 2 PbeOH species (with 1.078 A ˚ ). bond lengths of 2.630 and 2.646 A To investigate the mechanism of how water is involved with the surface oxidation, we give the distance variation between S＝OW, OWeHI, and OWeHII in the optimization process, as shown in Fig. 4.40. In the beginning of the interaction, water O atom is repelled by the surface S atom and water OeH bonds begin to elongate, and then with the dissociation of water molecule, the dissociative water O atom is attracted by the surface S atom to form an S＝OW bond. Simultaneously, the dissociative water H atoms interact with the oxygen O atoms to form hydroxyl species and finally react with surface Pb atoms to form PbeOH ˚. species with PbeO distances of 2.630 and 2.646 A

Distance/ Å

Interaction of water and oxygen with sulfide mineral surface 2.4 2.3 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9

169

S=O Ow–HI Ow–HII

0

5

10

15

20

25

30

35

40

45

50

55

60

65

Optimization step

Figure 4.40 Distance variation between S＝OW, OWeHI, and OWeHII as the function of the optimization step.

It is interesting to find that the dissociation of water molecule only occurs when the oxygen molecule preadsorbed on the site is parallel to the hollow between Pb atoms but not between S atoms. As we discussed before, water molecule only has a weak hydrogen bonding between surface S and water H atoms, and oxygen molecule has a very strong chemical interaction between surface S and oxygen O atoms, as shown in Fig. 4.36A. Therefore, the preadsorption of O2 on the site parallel to the hollow between S atoms will hinder the water to interact with the surface S atoms. However, when O2 molecule preadsorbed on the site is parallel to the hollow between Pb atoms, the oxygen O atoms interact mainly with surface Pb atoms and do not interact with surface S atoms. Furthermore, the adsorbed oxygen molecule becomes superoxo form, which has a certain chemical reactivity. The preceding two factors lead to the dissociation of water molecule into OW, HI, and HIIradicals. These radicals then interact with surface S and preadsorbed O atoms to involve into the oxidation process on PbS surface. Patrick et al. [35] reported similar phenomenon on the pyrite (FeS2) surface, that water molecule dissociated on the oxidized pyrite surface (preadsorbed O2), causing the water molecule to participate in the oxidation of pyrite surface.

4.4.5 Simultaneous coadsorption of water and oxygen on the PbS (100) surface Different initial structures of H2O and O2 simultaneous coadsorption on the clean galena surface were examined. Fig. 4.41 shows the optimized configuration of H2O and O2 coadsorption with the lowest adsorption energy of 70.90 kJ/mol. After simultaneous coadsorption, the water molecule dissociated, and an S＝OW double bond was observed on ˚ . Meanwhile, the dissociated water H ions are the surface with the length of 1.641 A bonded to the two oxygen O ions to form a H2O2 specie with bond lengths of 1.029 and

170 Chapter 4

Figure 4.41 H2O and O2 molecules coadsorption on the PbS (100) surface. DE is the adsorption energy. ˚ ). Numbers are bond lengths in angstroms (A

˚ . The formation of H2O2 is in agreement with the research of Nooshabadi et al. 1.025 A who found the generation of hydrogen peroxide on galena surface by experimental method [193]. The generated H2O2 specie can then react with two surface Pb ions to form lead hydroxyl radicals, which is consistent with the isotope results conducted by Heidel et al. It was reported that oxygen in sulfate produced from galena oxidation derived from water molecule and the lead-hydroxide (PbeOH) was observed as the intermediate product of galena oxidation [34]. Adsorptions of oxygen and water molecule on the PbS (100) surface were simulated by DFT to obtain microscopic information about the oxidation mechanism of galena. It is observed that the isolated O2 molecule dissociated and interact strongly with the surface S atoms, whereas the isolated H2O molecule had a weak interaction with the hydrophobic galena surface. DFT simulations for both sequential and simultaneous coadsorption of O2 and H2O on the galena surface were performed. It is found that H2O molecule could dissociate into Ow and H ions when coadsorption occurs. The dissociated Ow ion interacts with the surface S ion to form an S＝Ow radical, and the dissociated H ions interact with adsorbed O2 molecule to produce a hydrogen peroxide, which then reacts with surface Pb ions to form two lead hydroxyl (PbeOH) species. Therefore, water molecule was involved in the oxidation process of galena surface and the oxygen of sulfate on the surface derived from water.

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CHAPTER 5

Structure and reactivity of flotation reagents 5.1 Density states of collector molecules The performance of a flotation reagent is related to its molecular structure, and more attention has been paid to the relationship between the structure and performance of flotation reagents. With the development of quantum chemistry theory, especially the application of density functional theory (DFT) method [1,2], more quantum chemical parameters can be obtained to accurately judge the properties of compounds, which provides a quantitative explanation for the structureeactivity relationship of collectors [3e9]. It was difficult to solve this problem only by experiment and surface testing technology, and the quantum chemical method had the ability to explain the flotation mechanism from a micro perspective. Lots of researches used semiempirical molecular orbital theory, hard and soft acids and bases theory, and frontier orbital theory [10,11] to study, while there were few reports using the density of states (DOS) to study the relationship between structure and flotation performance of sulfide minerals flotation collectors. DOS is one of the most important parameters for the description of electron movement, and it is widely used in solid physics, surface science, and interfacial adsorption. DOS describes the number of states per interval of energy at each energy level available to be occupied. DOS can obtain detailed electronic properties such as partial density of states, orbital hybridization, localization and delocalization of electrons, and orbital bonding and antibonding effects. These properties are very important for the analysis of chemical properties and adsorption activity of flotation reagents. The sulfide minerals generally contain transition metal or heavy metal atoms, which are easy to coordinate with ligands. DOS of common collectors in the flotation of sulfide ore, such as xanthate, aerofloat, and thiocarbamate were calculated, and the relationship between structure and performance of collector was explored.

5.1.1 Methods To perform the optimizations of collector molecules, DMol3 software was used in the framework of DFT [13,14]. After geometric optimization, the DOS of collector molecules Electronic Structure and Surfaces of Sulfide Minerals. https://doi.org/10.1016/B978-0-12-817974-1.00005-3 Copyright © 2020 Central South University Press. Published by Elsevier Inc. All rights reserved.

181

182 Chapter 5 Table 5.1: Geometric parameters of ethyl xanthate using different functions and basis sets. ˚ Bond length/A Basis set

Functional

R(CeS1)

:S1eCeS2

DNP 3.5

LDA VWN LDA PWC GGA PW91 GGA PBE GGA BLYP GGA RPBE B3LYP

1.329 1.329 1.344 1.345 1.353 1.352 1.355

1.636 1.636 1.648 1.648 1.657 1.655 1.665

1.754 1.754 1.781 1.78 1.8 1.792 1.762

126.259 126.259 126.147 126.241 126.428 126.165 126.485

DND 3.5

LDA VWN LDA PWC GGA PW91 GGA PBE GGA BLYP GGA RPBE B3LYP

1.329 1.329 1.344 1.346 1.353 1.352 1.329

1.636 1.636 1.648 1.648 1.656 1.655 1.643

1.754 1.754 1.78 1.78 1.799 1.792 1.771

126.351 126.351 126.233 126.322 126.484 126.205 127.027

DNPþ

LDA VWN LDA PWC GGA PW91 GGA PBE GGA BLYP GGA RPBE

1.328 1.328 1.345 1.345 1.353 1.352

1.63 1.63 1.641 1.642 1.649 1.648

1.747 1.747 1.772 1.773 1.792 1.785

126.01 126.011 126.108 126.127 126.281 126.042

1.35

1.67

1.70

124

Experimental data [12]

R(CeO)

R(C[S2)

Bond angle/

was calculated (Fig. 5.1). Spin polarization was used in the calculations. The convergence criteria for structure optimization and energy calculation were set to (a) energy tolerance ˚ , (c) maximum of 2.7
104 eV/atom, (b) maximum force tolerance of 0.05 eV/A ˚ , and (d) convergence tolerance of 1.0
106 eV/atom. In displacement tolerance of 0.005A the geometry optimization of ethyl xanthate, different functional and basis groups were tested, and the results are listed in Table 5.1. The calculated geometric parameters conducted by GGA-RPBE functional with basis set of DNP 3.5 were closest to the experimental data [24], and thus GGA-RPBE functional with basis set of DNP 3.5 was

Figure 5.1 Molecule structure of ethyl xanthate.

Structure and reactivity of flotation reagents 183 chosen to conduct the optimization and DOS calculations. Molecule structure of ethyl xanthate is shown in Fig. 5.1.

5.1.2 Xanthate-type collector Xanthate is one of the most widely used and important sulfide collectors. Its molecular formula is ROCSSM, which is extremely unstable in acidic solution but relatively stable under alkaline medium. At present, the xanthate collectors are mainly ethyl xanthate, butyl xanthate, and isobutyl xanthate, as well as (iso) propyl xanthate and (iso) pentyl xanthate, etc. [15].

(A)

(B)

Figure 5.2 The DOS of polar groups in ethyl xanthate molecule and ethyl xanthate ion.

184 Chapter 5

5.1.3 Bonded atoms of xanthate-type collector The polar group of the xanthate molecule contains O, C, and S atoms. To determine the bonding atoms in the xanthate molecule, the DOS of the xanthate molecules and ions are calculated separately. The calculation results are shown in Fig. 5.2. The DOS reflects the distribution of electrons at specific energy levels. In general, the DOS at lower energy levels indicates that electrons are relatively stable, and the DOS at higher energy levels indicates that electrons are unstable and have strong activity. It is found from Fig. 5.2 that the DOS of oxygen atoms and carbon atoms in the xanthate molecule and xanthate ion are more negative than that of the sulfur atom, and the DOS distribution of oxygen atoms and carbon atoms is very small near the Fermi level (EF), almost closing to zero. The DOS of the sulfur atom near the Fermi level is relatively large. The DOS near the Fermi level represents the activity of the electrons. Therefore, the reactivity of sulfur atoms in the xanthate molecules and ions is the strongest, and sulfur atoms are the bonding atoms when xanthate reacts with sulfide minerals, which is consistent with the results of the frontier orbital study. For xanthate molecule, the DOS of single bond sulfur (S1) and double bond sulfur (S2) is different at 2 to 0.5 eV near the Fermi level (Fig. 5.2A), which is due to the connection of the single bond sulfur atom with hydrogen atom. The DOS of S2 at the Fermi level is greater than that of the single bond sulfur (S1), indicating that the electron activity of S2 is stronger than that of the S1atom. The DOS of single bond sulfur (S1) and double bond sulfur (S2) of xanthate molecule is also different between 8 and 2 eV. Among them, the double bond sulfur atom has strong s, p orbital hybridization near 6 eV, while the orbital hybridization of single-bond sulfur atoms is weak. According to the research results [2], the bonding between the sulfur atom and the transition metal mainly occurs between 8 and 2 eV, so the hybridization of the double bond sulfur atom can improve the interaction between xanthate and sulfide mineral. The literature results [11] show that the bonding atom of the xanthate molecule is double bond sulfur atom, which is consistent with the above analysis of the density of states. For xanthate ions, the DOS is different from that of xanthate molecule. The DOS of single bond sulfur (S1) and double bond sulfur (S2) of xanthate ion between 2.5 and 0.5 eV is almost the same (Fig. 5.2B), which is due to a resonance state of CeS single bond and C¼S double bond. It indicates that the two sulfur atoms of the xanthate ion have similar electrochemical activities. The results show that the two sulfur atoms of the xanthate ion have adsorption activity [2]. In addition, the delocalization of the S1 atom between 6 and 3 eV is stronger than that of the S2 atom, which is beneficial to the bonding of the S1 atom to the sulfide mineral surface. The simulation results also indicate that the S1 atom and the sulfide mineral surface has a smaller bond distance [2].

Structure and reactivity of flotation reagents 185 Compared with Fig. 5.2A and B, it is found that the activity of xanthate ion is obviously stronger than that of xanthate molecule according to the DOS of sulfur atom at the Fermi level, and the delocalization of xanthate ion was enhanced. Therefore, the reactivity of xanthate ion was greater than the corresponding xanthate molecule, which was consistent with literature results [11]. The carbon chain length of xanthate had a significant influence on its flotation performance. To investigate the relationship between the carbon chain length and the collecting performance, the DOS of the n-xanthate ions with different carbon chain lengths was calculated. The results are shown in Fig. 5.3. (A)

(B)

Figure 5.3 DOS of S atom in the xanthate ions with different carbon chain lengths.

186 Chapter 5 As shown in Fig. 5.3B, the change in DOS of S2 atoms in xanthate molecules with different carbon chain lengths is small, indicating that the carbon chain length has little effect on the S2 atom. It can be seen from Fig. 5.3A that there is a significant difference in the DOS of S1 atom in xanthate with different carbon chain lengths between 7.5 and 2.5 eV. With the increase of carbon chain length, the s and p orbital hybridization of S1 atom is gradually enhanced, which may be the reason why the long carbon chain xanthate is more likely to interact with metal ions. It is known from the preceding analysis that the effect of carbon chain length on the collector performance of xanthate is mainly to influence S1 atom. The longer the carbon chain, the stronger the orbital hybridization of S1 and the more beneficial to the chelating interaction of xanthate and metal ions. The calculation of DOS of the normal and isomers of propyl xanthate, butyl xanthate, and amyl xanthate showed that the influence of spatial structure of xanthate was similar to the length of carbon chain on xanthate; that is, the DOS of S2 atoms of normal and isomers of xanthate were similar but that of S1 atoms were different. Fig. 5.4AeC showed the DOS of S1 atoms in normal and isomers of xanthate with different carbon chain lengths. It can be seen from Fig. 5.4 that at the Fermi level (2.5 to 0.5 eV), the DOS of S1 of xanthate in different structures is the same, and the effect of xanthate structure on the DOS of S1 atom is mainly at 7 to 3 eV. It is shown in Fig. 5.4A that the overlap of s and p orbital of S1 atom in isopropyl xanthate is larger than that of n-propyl xanthate, and the hybridization effect is stronger, and the isopropyl xanthate has a stronger hybrid peak near 5.5 eV. At 4 eV, the DOS of S1 atom of isopropyl xanthate was significantly greater than that of n-propyl xanthate, indicating that the reactivity of S1 atom of isopropyl xanthate was stronger than that of n-propyl xanthate. In Fig. 5.4B, there are three distinct hybrid peaks of s and p orbitals of S1 atom of isobutyl xanthate. Compared with butyl xanthate, the hybridization of s, p orbital is stronger between 8 and 2 eV, indicating that activity of S1atom of isobutyl xanthate is stronger than that of n-butyl xanthate. Therefore, the collecting performance of isomers of propyl xanthate and butyl xanthate were stronger than the corresponding normal ones. However, the effect of the hydrocarbyl structure on amyl xanthate is weaker than that of propyl xanthate and butyl xanthate. In Fig. 5.4C, the DOS difference of the S1 atom in n-amyl xanthate and isoamyl xanthate is small, but the hybridization of s and p orbital of S1 atom in n-amyl xanthate at 5.5 eV can still be found. It indicates that the activity of S1 atom in n-amyl xanthate is stronger than that of isoamyl xanthate. Flotation test results [16] also showed that the collecting performance of n-pentyl xanthate was stronger than isopentyl xanthate.

Structure and reactivity of flotation reagents 187

Figure 5.4 DOS of S1 atoms in normal and isomers of xanthate with different carbon chain lengths.

188 Chapter 5 Table 5.2: Relationship between activity product L0 of zinc and silver xanthate and alkyl structure and length [17]. L0 Xanthate

Zn

Ag 10

2.1
1019 1.2
1019 4.2
1020 1.6
109 1.8
1020 6
1021

3.4
10 2.1
1010 3.7
1011 2.75
109 1.55
1012 3.1
1012

n-Propyl Isopropyl n-Butyl Iso butyl n-Pentyl Iso pentyl

In general, the stronger the orbital hybridization of a bonding atom, the easier to interact with metal ions. Based on the preceding discussion of DOS, it is found out that the s, p orbital hybridization effect of S1 atom in isopropyl and isobutyl xanthate was stronger than the corresponding normal structure of xanthate, while that in isopentyl xanthate was weaker than n-pentyl xanthate. The relationship between activity product L0 of zinc and silver xanthate and alkyl structure and length is shown in Table 5.2. It is suggested that the activity products of isopropyl and isobutyl xanthate with metal ions were smaller than corresponding normal structure of xanthate, while that of isobutyl xanthate was larger than n-pentyl xanthate. On the basis of the ethyl xanthate, three kinds of alkylthiocarbonic acid, namely monothiocarbonic acid, dithiocarbonic acid, and trithiocarbonic acid, were obtained, and the DOS of the S1 atoms of these three alkylthiocarbonic acids were calculated, respectively (shown in Fig. 5.5).

Density of States(electrons/eV)

3 2

-

s p

EF

C2H5OCOS

1 3

C2H5OCSS

2

-

1 3 2

-

C2H5SCSS

1 0 -10

-8

-6

-4

-2

0

2

4

Energy(eV)

Figure 5.5 The DOS of bonding sulfur atoms in different thiocarbonates.

Structure and reactivity of flotation reagents 189 Fig. 5.5 shows that the overlap of s and p orbitals of S1 atoms in monocarbonic acid, dithiocarbonic acid, and trithiocarbonic acid increases gradually between 8 and 2 eV in the bonding region, indicating that s and p orbital hybridization is gradually strengthened. In addition, the broadening of their DOS peak suggests that the delocalization is increasing; that is, the atomic activity is increasing. At the same time, the s and p orbital hybridization peaks of S1 atoms in three kinds of thiocarbonate gradually increase in this energy range, which further suggests increasing atomic activity. The enhancement of atomic activity in the flotation is the enhanced collecting ability for sulfide ore. That is, the collecting performance of trithiocarbonate is stronger than dithiocarbonate and that of dithiocarbonate is stronger than monothiocarbonate.

5.1.4 Aerofloat collector Although the collecting performance of aerofloat is slightly weaker than that of xanthate, its selectivity and stability are better than xanthate, and aerofloat has a good foaming performance [15]. Cresol aerofloat is the most widely used reagent among various aerofloat type collectors, and it has strong collecting ability to chalcopyrite, galena, and sphalerite. However, cresol aerofloat is corrosive and toxic and causes certain types of pollution, so it should be used as little as possible. Butylammonium aerofloat is currently the most widely used aerofloat reagent in China as it has good selectivity and convenience. Aniline aerofloat has the characteristics of good selectivity and strong collecting ability, which is more effective for collecting fine galena than cresol aerofloat and ethyl xanthate. Moreover, aniline aerofloat could achieve the separation of lead-zinc-sulfur and copper-sulfur at relatively low pH. Aniline aerofloat and cyclohexylamine aerofloat have good collecting ability for lead oxide. When used for flotation of mixed lead-zinc ore and oxide lead-zinc ore, the flotation index is better than that of 25# aerofloat and butyl xanthate [15]. Sodium diisobutyl dithiophosphinate (3418A), developed by Cytec, is a new type of aerofloat collector. It is mainly used for separation of lead, copper, and precious metals from the ore containing a high content of pyrite [18]. The results of DOS of S1 atoms and S2 atoms in different structures of aerofloat suggest that the polar groups in aerofloat collector have strong conjugation effect, and there is almost no difference in the DOS of S1 atoms and S2 atoms. The DOS of S1 atoms in butyl aerofloat ((C4H9O)2PSS), cresol aerofloat ((CH3eC6H4eO)2PSS), aniline aerofloat ((C6H11eNH)2PSS), cyclohexyl amine aerofloat ((C6H5eNH)2PSS), and 3418A (((CH3)2C2H3)2PSS) are shown in Fig. 5.6. It is found in Fig. 5.6 that the DOS splitting degree of cresol aerofloat is less than butyl aerofloat near the Fermi level (2 to 0.5 eV), and the DOS peak of cresol aerofloat is larger than that of butyl aerofloat at 2 eV. In addition, in the range of 7 to about 5 eV,

Density of States(electrons/eV)

190 Chapter 5 3 2 (C4H9O)2PSS 1 3 2 (CH3-C6H4-O)2PSS 1 3 2 (C6H11-NH)2PSS 1 3 2 (C6H5-NH)2PSS 1 3 2 ((CH3)2C2H3)2PSS 1 0 -10 -8 -6 -4

EF

-2

0

s p

2

4

Energy(eV)

Figure 5.6 DOS of S1 atoms in different aerofloat type collectors.

the hybridization of s and p orbitals of cresol aerofloat is also stronger than butyl aerofloat. It is indicated that the activity of S1 atom in cresol aerofloat is stronger than that in butyl aerofloat, and cresol aerofloat shows better collecting ability and selectivity. It is also noted from the comparison of the DOS of S1 atoms in cyclohexylamine aerofloat and aniline aerofloat that the delocalization of cyclohexylamine aerofloat is stronger than that of aniline aerofloat, especially near the Fermi level (2 to 0.5 eV) and 6 to about 4 eV interval, indicating that the collecting and selectivity of aniline aerofloat is relative better than cyclohexanol aerofloat. For 3418A, near the Fermi level, the DOS is significantly different from that of the other four kinds of reagents. The DOS of 3418A is flat and shows a strong delocalization. What is more, in the range of 4 to about 2 eV, the DOS of 3418A relative reaches the maximum, suggesting a stronger electronic activity. All the aforementioned indicate that the collecting ability and selectivity of 3418A is better than the other four kinds of aerofloats.

5.1.5 Thiocarbamate collector Thiocarbamate is a kind of nonionic polar collector exhibiting excellent collecting performance for sulfide mineral flotation. It is characterized by good selectivity as well as low dosage, and it is stable in acidic medium and has a strong foamability. Under weak alkaline conditions, it exhibits better selectivity than the xanthate collector and aerofloat collector [15]. Ethylthionocarbamate (Z-200) is one of the most representative thionocarbamate collectors, whose scientific name is O-isopropyl-N-ethyl thiocarbamate. Considering the significant effect of the substituted hydrocarbyl group at the nitrogen atom on the

Structure and reactivity of flotation reagents 191

Density of States(electrons/eV)

(A)

5 4 (CH3)2CHOCSNHC2H5 (Z-200) 3 2 1 5 4 C4H9OCSNHC3H6OC2H5 (1) 3 2 1 5 C4H9OCSNHCH2CH=CH2 (2) 4 3 2 1 5 C4H9OCSNH-COOC2H5 (3) 4 3 2 1 0 -10 -8 -6 -4 -2

s p

EF

0

2

4

Energy(eV)

DOS of S atoms in thiocarbamate

(B) 3

Density of States(electrons/eV)

2

(CH3)2CHOCSNHC2H5 (Z-200)

s p

EF

1 3 2

C4H9OCSNHC3H6OC2H5 (1)

1 3 2

C4H9OCSNHCH2CH=CH2 (2)

1 3 2

C4H9OCSNH-COOC2H5 (3)

1 0 -10

-8

-6

-4

-2

0

2

4

Energy(eV)

DOS of N atoms in thiocarbamate

Figure 5.7 DOS of S and N atoms in thiocarbamate collector.

performance of the thionocarbamate collector, some special structures of thionocarbamates have been developed by researchers, such as O-butyl-N-glycol propyl thiocarbamate (thionocarbamate 1), O-alkyl-N-allylic thiocarbamate (thionocarbamate 2), and O-alkyl-N-alkyl alkoxy carbonyl thiocarbamate (thionocarbamate 3) [15]. Both the sulfur atom and nitrogen atom in thionocarbamate collector molecule are active, and the DOS of sulfur atoms and nitrogen atoms in ethylthionocarbamate and three kinds of thionocarbamates with special structures were calculated, as shown in Fig. 5.7.

192 Chapter 5 Comparing Fig. 5.7A and B, the DOS of sulfur atoms in thionocarbamate collectors are obviously larger than that of nitrogen atoms at the Fermi level, and the s, p orbital hybridization of sulfur atoms is stronger than nitrogen atoms in the range of 7 to about 2 eV, suggesting that the activity of sulfur atom is stronger than that of nitrogen atom in thionocarbamate collector. As can be seen from Fig. 5.7A, the DOS of sulfur atom in thionocarbamate 3 is significant different from the other three thionocarbamates: its delocalization is weak, which is because the alkyl connected with nitrogen atom becomes a carbonyl. In addition, Fig. 5.7B also suggests that the DOS of nitrogen atom in thionocarbamate 3 is different from the other three thionocarbamates, as the DOS decreases near the Fermi level and moves to a negative direction, It is indicated that the presence of carbonyl group reduces the activity of thionocarbamate collector. In terms of ethylthionocarbamate, O-butyl-N-glycol propyl thiocarbamate (thiocarbamates 1), and OeN-alkyl allylic thiocarbamate (thiocarbamate 2), the DOS of their nitrogen atoms and sulfur atoms are almost the same near the Fermi level, and their differences are mainly shown in the range of 8 to about 2 eV, which is mainly due to the difference in the alkyl groups of fatty amine in thiocarbamate structure. The DOS of nitrogen atom changes greater than that of sulfur atom, which is beneficial to improve the chelating ability of thiocarbamate collector, because the nitrogen atom has stronger coordination ability than the sulfur atom.

5.2 Structureeactivity of chelating collectors Chelating reagents can be used to remove heavy metals from wastewater due to their chelating performance on metal ions forming insoluble materials, and they can also be used as flotation collectors of metallic minerals due to the high selectivity. Xanthate was found to be an effective collector for sulfide minerals flotation in 1925, and now it is one of the most used chelating collectors for sulfide minerals flotation. Researches on chelating collectors were then developed, such as cupferron [19], dimethylglyoxime [20], salicylaldoxime [21], and 8-hydroxy quinolone [22,23], etc. The relationship between the collecting performance of the collector on minerals and its chelating performance had been a concern at that time, although this relationship was not clear. With the development of detection methods, such as infrared spectroscopy [24e28] and electron paramagnetic resonance spectroscopy and XPS spectra [29] the interacting mechanism between chelating collectors and mineral surfaces and the relationship between collecting performance and chelating performance were investigated and understood gradually. It is found that metal-collector salt would be formed on the mineral surfaces. It has been suggested that the collecting performance of the collector for mineral is related

Structure and reactivity of flotation reagents 193 to its chelating performance. It is known that in the flotation, the collector would first interact with the metals on the mineral surface but not with the metal ions in the pulp; however, large amounts of experiments have suggested that the selective collection of chelating collectors on minerals is consistent with its selectivity to metal ions in solution. For example, the selectivity of xanthate to sulfide minerals to some extent is reflected by its chelating performance to the metal of this mineral. Pb-xanthate is a chelating compound that is insoluble (Ksp of 6.7
1018) in water solution, whereas Zn-xanthate is a normal salt with a certain solubility (Ksp of 5.3
108). This suggests that the xanthate has greater selectivity to Pb2þ than Zn2þ. Flotation practice suggests that xanthate has good collecting ability to galena (PbS), whereas it has weak collecting ability to sphalerite (ZnS) without activation by other metals. Large amounts chelating reagents have been found being as effective collectors both for oxide and sulfide minerals [30], such as cupferron for the flotation of hematite [31] and cassiterite [19], dimethylglyoxime for the flotation of niccolite [32] and for the flotation of copper ores [21,31], salicylaldehyde for the flotation of cassiterite, N-benzoyl-N-phenylhydroxylamine for the flotation of rutile [33], 8-hydroxyquinoline for the flotation of smithsonite and cerussite [23], etc. Most chelating collectors are bidentate chelating reagents, and they can be classified into six different types according to the type of atoms that bond the metal cation and participate in the closure of the chelate ring: NeO, OeO, SeN, SeS, and NeN [31]. Chemical equilibriums in solution are often used to predict the possibility of a reagent selected as flotation collector. However, the theoretical study based on chemical equilibriums may be limitation to select reagents as collectors because of the complex system for flotation. In the present work, the frontier orbitals of four minerals and six types of chelating collectors were studied based on density functional method (DFT) calculations. The interactions of Cu, Pb, Zn, and Fe cations with these six types of chelating collectors were also investigated.

5.2.1 Computational details DMol3 mode [34,35] based on DFT to was used to perform the calculations of frontier orbital of four minerals, including chalcopyrite (CuFeS2), pyrite (FeS2), galena (PbS), and sphalerite (ZnS), and six types of flotation chelating collectors, including SeS (mercaptobenzothiazole, ethyl xanthate, diethyldithiophosphate and diethyldithiocarbamate), SeN (dithizone (keto form and enol form)), NeN (dimethylglyoxime), SeO (thiocarboxylic acid), NeO (8-hydroxyquinoline and salicylaldoxime), and OeO (salicylhydroxamic acid, oleic acid, and cupferron) types. GGA-RPBE functional was selected to be the DFT exchange-correlation potential in the calculations. Convergence thresholds for energy change, max force, max displacement, ˚, max step size, and self-consistent field were set to 1.0
105 Ha, 2.0
103 Ha/A

194 Chapter 5 ˚ , 0.3 A ˚ , and 1.0
106 eV/atom, respectively. DNP atomic orbital basis set 5.0
103 A was chosen. All electrons were included in the calculation. The value, in Ha, of the smearing parameter was set to 5.0
103. GGA-RPBE exchange-correlation functional ˚ of CeO, 1.704 A ˚ of CeS1 A ˚ and 1.712 A ˚ of CeS2 and 128.60 of gives 1.416 A ˚ , 1.67 A ˚, :S1eCeS2 of ethyl xanthate, compared to the experimental values of 1.35 A  ˚ , and 124 , respectively [36]. 1.70 A

5.2.2 Frontier orbital results The frontier molecular orbital theory is proposed by Fukui Kenichi. It is suggested that the reactivity of a molecule is determined by the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Generally, the smaller the energy difference between the HOMO of one molecule and the LUMO of another molecule, the greater the interaction between these two molecules. Fig. 5.8 shows the HOMO and LUMO energies of the four minerals (CuFeS2, FeS2, PbS, ZnS) and the six types of collectors. It is found that most of the LUMO orbitals of the six types of collectors, except that of dithizone-keto form in SeN type and dimethylglyoxime in NeN type, are very close to the HOMO orbital of PbS, suggesting that strong interaction would occur between these chelating collectors with PbS. In this case, most of these types of chelating collectors would have collecting ability to PbS.

Figure 5.8 Energies of HOMO and LUMO of the four minerals and the six types of collectors.

Structure and reactivity of flotation reagents 195 Similar to PbS, the HOMO orbital of ZnS is also close to the LUMO orbital of these collectors, including keto form of dithizone in SeN type. However, it is known that ZnS is often needed to be activated by copper ions to float. This is because the ZnS is hydrophilic. The calculation by Long et al. suggests that xanthate, dithiocarbomate, and dithiophosphate could not adsorb on the sphalerite surface in the presence of water [7]. Both for PbS and ZnS, the LUMO orbitals are far from the HOMO orbitals of the collectors. The HOMO orbitals of CuFeS2 and FeS2 are very close, and they are close to the LUMO orbitals of keto form of dithizone in SeN type and dimethylglyoxime in NeN type. In addition, the LUMO orbitals of these two minerals are also close to HOMO orbital of keto form of dithizone in SeN type, especially close between CuFeS2 and keto form of dithizone. It can be predicted that keto form of dithizone would have great chelating effect to CuFeS2 and FeS2, especially to CuFeS2. However, there is no literature available, and only its chelating effect on copper, zinc, and nickle (and other ions) has been reported [37e39]. For further analysis of the frontier orbitals, the orbital configurations and coefficients of chelating molecules were calculated, as shown in Table 5.3 The larger the coefficient, the greater the contribution of the atom to the frontier orbital and the greater the activity of the atom.

Table 5.3: Frontier orbital configurations and coefficients of chelating molecules. Types SeS type

Molecules

HOMO

LUMO

Mercaptobenzothiazole

Ethyl xanthate

Continued

196 Chapter 5 Table 5.3: Frontier orbital configurations and coefficients of chelating molecules.dcont’d Types

Molecules

HOMO

LUMO

Diethyldithiophosphate

Diethyldithiocarbamate

SeN type

Dithizone-keto form

Dithizone-enol form

NeN type

Dimethylglyoxime

SeO type

Thiocarboxylic acid

Continued

Structure and reactivity of flotation reagents 197 Table 5.3: Frontier orbital configurations and coefficients of chelating molecules.dcont’d Types NeO types

Molecules

HOMO

LUMO

8-Hydroxyquinoline

Salicylaldoxime

OeO types

Salicylhydroxamic acid

Oleic acid

Cupferron

For SeS type, it is clear that the contribution of S atoms to the HOMO is greater than the other atoms, especially for the single-coordinated (single bond) S in mercaptobenzothiazole and double bond of S atom in ethyl xanthate, diethyldithiophosphate, and diethyldithiocarbamate. C, N, P, and S atoms have a significant contribution to LUMO. In addition, it is noted that the benzene ring of mercaptobenzothiazole contributes to both HOMO and LUMO. Keto form and enol form dithizone have been chosen as SeN type chelating collectors. The single-coordinated S atom in keto form is double bond, whereas that S atom in enol

198 Chapter 5 form is single bond. It is indicated that the HOMO and LUMO patterns of keto and enol forms are almost the same, and the contributions of atoms to the orbitals are also similar. In HOMO, the most contribution comes from the single-coordinated S atom, followed by the two of the four N atoms, and the remaining two N atoms contribute very little. In LUMO, the single-coordinated S atom has small contribution, and the largest contribution comes from the two of the four N atoms. Compared the HOMO with the LUMO, it is found that only one (not the same benzene ring) of the two benzene rings contributes to the frontier orbital, and its contribution to LUMO is larger than to HOMO. Dimethylglyoxime is an NeN type chelating collector. Both C and N atoms have large contributions to the HOMO and LUMO. In addition, the contribution of the two O atoms to the HOMO is larger than that of to the LUMO. Moreover, the contribution of the O in eOH is smaller than the double bond O. Thiocarboxylic acid, which is an SeO type chelating collector, has a double bond of S substitution of one O in COO. It is shown that S atom has great contribution to the HOMO orbital, while the contributions of O and C atoms are very small, and there is no contribution from the carbon chain. The situation in LUMO is opposite to that in HOMO. It is shown that the thiocarboxylic group eCSOe has no contribution, while the end of the carbon chain has great contribution. For NeO type, O atom and the benzene ring attached to the O atom in 8hydroxyquinoline contribute to the HOMO, and the same situation for salicylaldoxime. The situation for the N atom, however, in these two chelating reagents is different. It is shown that in 8-hydroxyquinoline, the N atom, which substitutes a C atom in one of the two benzene rings, has no contribution to the HOMO orbital, whereas in salicylaldoxime the N atom attached to eOH has a certain contribution (with coefficient of 0.32). This suggests that the activity of N atom in a benzene ring (maybe any other type of rings) would be weaker than in a strain chain. Compared to the HOMO orbital, in the LUMO orbital, the contribution from the singlecoordinated O atom decreases, whereas the contribution of N atom increases both for 8hydroxyquinoline and salicylaldoxime. In addition, the contribution of the benzene ring containing N atom in 8-hydroxyquinoline also increases. OeO type includes salicylhydroxamic acid, oleic acid, and cupferron, and the former two both have one benzene ring and a group ONNO and a group ONCO, respectively, and the later has a long carbon chain and one carboxyl COO. It is shown that ONNO, ONCO, and COO groups have contributed to the HOMO, whereas their contributions to

Structure and reactivity of flotation reagents 199 the LUMO are decreased and the contributions of benzene ring are increased. For more details, it is suggested that the contribution of single-coordinated O in ONNO and ONCO is greater than the two-coordinated O, whereas the situation of O in COO is opposite.

5.2.3 Interactions of metals with chelating collectors It has been suggested that after interacting with the metal ions the chelation could produce a chemisorbed surface film that is favorable for flotation [23]. Figs. 5.9e5.12 show the interaction configurations of Cu2þ, Fe2þ, Pb2þ, and Zn2þ with the six types of chelating collectors. One metal ion is bonded with two collector molecules. For SeS type of collectors, it is found that mercaptobenzothiazole can chelate metal ions by means of SeS and SeN, and other three reagents form a four-coordinated structure with metal in SeS mode. Moreover, mercaptobenzothiazole can only bond with Pb2þ by the one-coordinated S atom, whereas the two-coordinated S atom or N atom can no longer bond with Pb2þ. This is not consistent with Nowak et al. that mercaptobenzothiazole can form a four-membered ring with Pb2þ linked to S and N atoms [40]. Similarly, the two-coordinated S atom can no longer bond with Cu2þ and Zn2þ, and its interaction with Fe2þ is also very weak (long FeeS distance). This two-coordinated S atom is in the five-membered ring. Frontier orbital calculation has suggested that the activity of this two-coordinated S atom is much lower than the one-coordinated S atom. Hence, it can be concluded that mercaptobenzothiazole is more likely to chelate metal ions by means of SeN but not SeS. For ethyl xanthate, diethyldithiophosphate, and diethyldithiocarbamate, the distance between the double bond of S atom and metal ions is shorter than that between the single bond of S atom and metal ions. This is consistent with the frontier orbital results that the activity of the double bond of S atom is greater than the single bond of S atom. For the SeN type of collectors, including keto and enol forms of dithizone, it is indicated the interaction of metals with N atom is weaker than with S atom. It can be ascribed to the unfavorable spatial structure of N in dithizone. For NeN type, frontier orbital results suggest that the N bonding with the double bond of O is slightly larger than the N bonding with O in eOH; hence, it is clear that the distance between the metal with the former is slightly shorter than with the latter. The representatives of SeO type thiocarboxylic acid and the representatives of NeO type, 8-hydroxyquinoline, and salicylaldoxime are shown in Fig. 5.11A and B. It is

200 Chapter 5

Figure 5.9 Interaction configurations of Cu2þ, Fe2þ, Pb2þ, and Zn2þ with SeS type of collectors.

Structure and reactivity of flotation reagents 201

Figure 5.10 Interaction configurations of Cu2þ, Fe2þ, Pb2þ, and Zn2þ with SeN and NeN types of collectors.

202 Chapter 5

Figure 5.11 Interaction configurations of Cu2þ, Fe2þ, Pb2þ, and Zn2þ with SeO and NeO types of collectors.

Figure 5.12 Interaction configurations of Cu2þ, Fe2þ, Pb2þ, and Zn2þ with OeO type of collectors.

Structure and reactivity of flotation reagents 203 suggested that the interactions of metals with the O in SeO type of collectors are weaker than with the O in NeO type of collectors because the latter have a shorter metal-O distance. Furthermore, salicylaldoxime has the greatest metal-O interactions. In addition, the metal-N distance in salicylaldoxime is also slightly shorter than in 8hydroxyquinoline. This is also related to the spatial structure difference of N atom in salicylaldoxime and 8-hydroxyquinoline, where the former is located in a chain and the latter is located in a ring. For OeO type of collectors, the differences in the interactions of metals with the two O atoms in salicylhydroxamic acid are greater than in oleic acid and cupferron. This is because that the two O atoms in salicylhydroxamic acid are bonded with two different atoms, with one bonding with N and another bonding with C, whereas the two O atoms in oleic acid are bonded both with C and bonded both with N in cupferron.

5.3 Azo compound depressants In the flotation separation of sulfide ore, it is difficult to develop new reagents due to the limited types of inorganic depressants, and some of the depressants have serious pollution to the environment. Compared with inorganic depressants, organic depressants have a wide range of sources, less pollution, and can flexibly design the molecular structure and functional groups of chemicals according to the nature and actual needs of minerals. In recent years, this has received extensive attention from researchers worldwide [41e43], and the development of highly efficient and selective organic depressants to improve the flotation separation of sulfide minerals has become one of the key and difficult points in flotation research. The azo compounds [44,45], a class of compounds containing an azo group (eN¼Ne) in molecular structure, have been widely used in many industries, such as textile, paints, coatings, foods, printing, and so on. According to the number of azo groups contained, it can be classified into monoazo, disazo, and polyazo compounds. In addition to the azo group (N¼N), the azo compound also contains a number of benzene rings or naphthalene rings having large molecular polarizability and relatively high electrochemical activity. The previous studies [46,47] indicated that the p bond of benzene ring in the molecular structure could overlap with the empty orbital of a mineral surface, changing the electronic energy level of a mineral surface and reducing the stability of the collector film. In addition, the azo compound molecule also contains polar groups (such as eSO3Na, eNH2, eCOONa, eOH, and so on) which could meet the hydrophilic requirements of organic depressants.

Depressant

Structure

Type

Acid orange 7 (AO7)

1

OH

NaO3S

N

Acid brown 4 (AB4)

N

1

OH NH2

N=N

SO3Na

Basic orange 2 (BO2)

1

H2N

NHCl

N=N

Acid yellow 36 (AY36)

1

SO3Na

N

Direct red 28 (DR28)

N

NH

NH2

NH2 N N

SO3Na

N N

SO3Na

2

204 Chapter 5

Table 5.4: The molecular structures of azo reagents.

Direct blue 6 (DB6)

NH2

OH

OH N=N

N=N NaO3S

NaO3S

2

NH2

SO3Na

SO3Na

Direct blue 15 (DB15)

OCH3

NH2 OH

OCH3

N=N

2 OH

NH2

N=N NaO3S

SO3Na

SO3Na

SO3Na

Basic brown 1 (BB1)

NH2 N N

N N

Direct green 6 (DG6)

NH2

3

NH2 OH HO

N N

N N NaO3S

N N

NO2

SO3Na

Continued

Structure and reactivity of flotation reagents 205

H2N

2

NH2

Depressant

Structure

Type 3

Acid black 234 (AB234)

Acid black 210 (AB210)

NH2

N=N

SO2NH

N=N

N=N

SO3Na Direct brown 95 (DB95)

NO2

SO3Na 3

HO

NaOOC

HO

3

NH2 OH

NH2

N=N

N=N HO

HO N=N SO3Na

1, single azo; 2, double azo; 3, triple azo.

206 Chapter 5

Table 5.4: The molecular structures of azo reagents.dcont’d

Structure and reactivity of flotation reagents 207

5.3.1 Computational methods The depression effects of 12 kinds of azo reagents with different structures on five kinds of sulfide minerals were investigated. The molecular structures of these azo reagents are shown in Table 5.4. The names of the following reagents are shown in forms of English initials if there is no other special instruction. The frontier orbital energy calculation for azo reagents is performed using the DMol3 module. Geometric optimization and analysis of azo reagents are processed using the functional GGA-PW91 [48], and the self-consistent field (SCF) convergence is set at 1.06
106 eV/atom. The frontier molecular orbitals of azo compounds are calculated by basis set of DNP based on the optimized geometric configurations.

5.3.2 Effect of azo reagents on sulfide minerals flotation The effects of 12 kinds of azo reagents dosage on flotation recovery of the five sulfide minerals are investigated at natural pH with given addition of collector and frother (butyl xanthate: 5
105 mol/L and terpenic oil:16 mg/L). Results of flotation tests are shown in Fig. 5.13 to Fig. 5.17. It can be seen from Fig. 5.13 that, at a large dosage, the monoazo and bisazo reagents have no depressing effect on galena, and the recoveries are above 90%. With the increase of the dosage, in addition to DB95 in the trisazo group, the depressing effect of the other reagents on the galena is gradually enhanced. With the increase of dosage, the depressing effect of DG6 is gradually enhanced. When the dosage is more than 120 mg/L, the

100

AO7

Recovery/%

AB4

80

BO2

60

DR28

AY36 DB6 DB15

40

BB1 DG6

20

AB234 AB210

0

DB1

0

50

100

150

200

250

Dosage (mg/L)

Figure 5.13 Effect of azo reagents dosage on galena recovery.

208 Chapter 5 100

AO7 AB4

80

BO2

Recovery/%

AY36 DR28

60

DB6 DB15

40

BB1 DG6

20

AB234 AB210

0

DB95

0

50

100

150

200

Dosage/(mg . L-1)

Figure 5.14 Effect of azo reagents dosage on jamesonite recovery. 100

AO7 AB4

Recovery/%

80

BO2 AY36 DR28

60

DB6 DB15

40

BB1 DG6

20

AB234 AB210

0

DB95

0

50

100

150

200

Dosage/(mg . L-1)

Figure 5.15 Effect of azo reagents dosage on marmatite recovery. 100

AO7 AB4

80

BO2

Recovery/%

AY36 DR28

60

DB6 DB15

40

BB1 DG6

20

AB234 AB210

0

DB95

0

50

100

150

200

Dosage/(mg . L-1)

Figure 5.16 Effect of azo reagents dosage on pyrite recovery.

Structure and reactivity of flotation reagents 209 100

AO7

Recovery/%

AB4

80

BO2

60

DR28

AY36 DB6 DB15

40

BB1 DG6

20

AB234 AB210

0

DB95

0

50

100

150

200

250

Dosage/(mg . L-1)

Figure 5.17 Effect of azo reagents dosage on chalcopyrite recovery.

recovery of galena reduces to 12.97%. When the amounts of AB234 and AB210 are less than 20 mg/L, the recovery of galena decreases sharply with the increase of dosage. When the dosage is more than 20 mg/L, the recovery does not change much, and the two reagents exhibit a similar depression on galena; while the DB95 could not depress galena. As shown in Fig. 5.14, the monoazo reagents have no depression effect on jamesonite, and diazo reagents only have weak depression effect with the increasing dosage. For example, when the amount of DR28 is large, that is, greater than 140 mg/L, the recovery of jamesonite is still about 60%. When the amount of DB6 is 200 mg/L, the recovery is still about 50%, and BB1 and DB15 have no depression effect. Among the trisazo reagents, except for the DB95 reagent not being able to depress the jamesonite, the DG6, AB234, and AB210 have strong depression effects. With the increase of the dosage, the recovery of the jamesonite rapidly decreases. AB210 has the strongest depression ability. When the dosage is 10 mg/L, the recovery reduces to less than 5%, and the depression ability of AB234 is the second. When the dosage is 50 mg/L, the recovery also reduces to 5.77%. The depression ability of DG6 is weaker than the former two, but when the dosage is more than 120 mg/L, the recovery can also reduce to 11.85%. It is noted from Fig. 5.15 that both monoazo and diazo reagents have no depression effects on marmatite. Among the trisazo reagents, DG6 and DB95 also have no depression effect on marmatite, while AB234 and AB210 both exhibit a strong depression as the recovery decreased sharply with the increasing dosage, and the recovery is less than 10% when the dosage is over 60 mg/L. Fig. 5.16 suggests that monoazo reagents have no depression effect on pyrite. Among diazo reagents, BB1 shows no depression while DR28, DB6, and DB15 both show weak

210 Chapter 5 depression and the recovery decreased slightly with the increasing dosage, and the recovery could still stay at about 50% even when the dosage went up to 200 mg/L. For the trisazo reagents, DB95 has no depression on pyrite, while DG6, AB234, and AB210 have strong depression on the pyrite. With the increase of dosage, the recovery of pyrite decreases rapidly, and the depression behavior of these three reagents on pyrite is similar. Fig. 5.17 indicates that the monoazo reagents have no depression on chalcopyrite. Among the diazo reagents, DR28 has a weak depression effect when it is used in a large amount; that is, when the dosage reaches 200 mg/L, the recovery is still 48.15%. And the DB6, DB15, and BB1 have no depression effect on chalcopyrite. For the trisazo reagents, DG6 and DB95 have no depression on chalcopyrite, while both AB234 and AB210 show strong depression. With the increase of dosage, the recovery of chalcopyrite decreases rapidly. When the dosage reaches 50 mg/L, the recovery drops to about 10%. It is known from Figs. 5.13e5.17 that monoazo reagents have no depression effect on sulfide minerals. Among the diazo reagents, DR28 has a weak depression on jamesonite, pyrite, and chalcopyrite, DB6 has a weak depression on jamesonite and pyrite, and DB15 has a weak depression on pyrite, while BB1 has no depression effect on sulfide minerals. For the trisazo reagents, DB95 has no depression on sulfide minerals, DG6 has a strong depression on galena, jamesonite, and pyrite, and AB234 and AB210 have a strong depression on the aforementioned five kinds of sulfide minerals in a small amount.

5.3.3 Relationship between molecular structure and depression properties of azo agents The activity of organic depressants depends on their molecular structure. The depression performance varied greatly when the functional groups are the same but the molecular skeleton is different (such as benzene ring or linear chain), or when the molecular skeleton is the same but the functional groups are connected in different ways on the ring [47,49e51]. In addition, the frontier molecular orbital theory suggests that the most active electrons participating in the reaction are the electrons in the highest occupied orbit (HOMO). The higher the density of the HOMO electron cloud, the greater the probability of donating electrons and the easier reaction occurs at these atoms. The HOMO shape intuitively reflects the distribution of electrons on each atom in the highest occupied orbital [52e54], revealing the reactive center of the molecule. The molecular structures shown in Table 5.4 suggest that these 12 azo reagents all contain a benzene ring in the molecular structure, and some of the reagents also contain a naphthalene ring, or in the same molecular skeleton, the type and number of functional groups on the ring are also different. To further study the relationship between the

Structure and reactivity of flotation reagents 211

Figure 5.18 Front molecular orbital of azo dye reagents.

212 Chapter 5 molecular structure of azo reagents and their depression properties, the molecular structure and HOMO of 12 azo reagents are analyzed. The HOMO of the 12 azo reagent molecules are shown in Fig. 5.18. As can be seen from Fig. 5.18, the HOMO of the azo reagent is mainly distributed on the azo group (eN¼Ne) and the benzene ring or naphthalene ring connected with it. In addition, the N atom in the eNH2 group and the N and O atoms in the eSO2NH group in the AB2 and AB210 reagent molecules contribute to the HOMO of the molecule, and the N and O atoms in the group contain lone pairs of electrons, which can form coordination bonds with metal ions on the mineral surface [55,56]. In addition, the polar groups connected with benzene ring or naphthalene ring, such aseOH, eSO3H, eNO2, and eCOOH, do not contribute to the HOMO of the molecule. Therefore, it is considered that these functional groups do not undergo electron transfer or reaction with metal ions on the surface of the mineral and only play a hydrophilic role. From the results of the flotation test and Table 5.5, it is known that for the monoazo type reagent, when the molecular skeleton contains only a benzene ring and no naphthalene

Table 5.5: Molecular structures and HOMO composition of azo reagents. Depressant Single Azos

Double Azos

Triple Azos

Molecular framework

AO7

Phenyl, Naphthyl

AB4

Phenyl, Naphthyl

BO2 AY36 DR28

Phenyl Phenyl Phenyl, Naphthyl

DB6

Phenyl, Naphthyl

DB15

Phenyl, Naphthyl

BB1 DG6

Phenyl Phenyl, Naphthyl

AB234

Phenyl, Naphthyl

AB210

Phenyl, Naphthyl

DB95

Phenyl

s, strong depressing action; w, weak depressing action.

HOMO composition Azo group, phenyl, Naphthyl Azo group, phenyl Naphthyl Azo group, phenyl Azo group, phenyl Azo group, Phenyl Naphthyl Azo group, phenyl Naphthyl Azo group, phenyl, Naphthyl Azo group, phenyl Azo group, Phenyl Naphthyl Azo group, phenyl, Naphthyl Azo group, phenyl, Naphthyl Azo group, phenyl

Depression No No No No Jamesonite (w), Pyrite (w), Chalcopyrite (w) Jamesonite (w), Pyrite (w) Pyrite (w) No Galena (s), Jamesonite (s), Pyrite (s) All (s) All (s) No

Structure and reactivity of flotation reagents 213 ring (such as BO2 or AY36) or both a benzene ring and a naphthalene ring (such as AO7, AB4), regardless of whether the contribution of the benzene ring or naphthalene ring of the molecule to HOMO is strong or not, it has no depression effect on sulfide ore. Therefore, monoazo reagents are not suitable as depressants for sulfide ore flotation. For the bisazo type reagent, when the molecular skeleton contains only the benzene ring and does not contain a naphthalene ring (such as BB1), it has no depression effect on the sulfide ore; when the molecular skeleton contains both a benzene ring and a naphthalene ring (such as DR28, DB6, and DB15), it can depress the sulfide ore. If both the benzene ring and the naphthalene ring contribute to the HOMO of the molecule, the greater the contribution is, the stronger is the depression effect. It is noted from Fig. 5.18 that the contribution of the benzene ring and the naphthalene ring in the DR28 molecule to HOMO is greater than that of DB6 and DB15. Therefore, DR28 not only has a certain depression on jamesonite and pyrite but also has a weak depression on chalcopyrite, while DB6 and DB15 could not depress chalcopyrite. For trisazo reagents, the relationship between molecular structure and depression performance is similar to that of biazo reagents. When the molecular skeleton contains only benzene rings (such as DB95), trisazo reagents have no depression effect on sulfide ore; When both a benzene ring and a naphthalene ring are present (such as DG6, AB234, and AB210), the trisazo reagents can strongly depress some or all of the sulfide ore, and the more the HOMO contribution of the benzene ring and naphthalene ring to the molecule is, the stronger is the depression performance. It can be seen from Fig. 5.18 that the contribution of the benzene ring and the naphthalene ring in DG6 is less than that of AB234 and AB210, so the depression effect of DG6 is smaller than AB234 and AB210. Based on the preceding analysis, the depression performance of azo reagents on sulfide minerals depended on the molecular skeleton and the number of azo groups. The simultaneous presence of a benzene ring and a naphthalene ring in the molecular structure is an essential condition for an azo agent as a sulfide ore depressant. Monoazo agents have no depression effect on sulfide minerals and are not suitable as a sulfide ore depressant. For the bisazo and trisazo reagents, when the molecular skeleton contains only the benzene ring and no naphthalene ring, the azo reagent has no depression effect on the sulfide ore; when the molecular structure contains both the benzene ring and the naphthalene ring, the azo reagent could depress the sulfide ore, and the greater the HOMO contribution of the benzene ring and the naphthalene ring to the molecule, the stronger the depression effect of the reagent.

214 Chapter 5 Table 5.6: The frontier orbital energy differences between reagents and minerals. jDEj [ jEreagent Reagents Xanthate DR28 DB6 DB15 DG6 AB234 AB210

Pyrite 0.485 0.405 (w) 0.439 (w) 0.168 (w) 0.288 (s) 0.252 (s) 0.310 (s)

HOMO

¡ Emineral LUMOj/eV

Jamesonite

Marmatite

1.520 1.375 (w) 1.341 (w) 1.612 (n) 1.492 (s) 1.528 (s) 1.470 (s)

1.900 1.755 (n) 1.721 (n) 1.992 (n) 1.872 (n) 1.908 (s) 1.850 (s)

Galena 1.64 1.495 (n) 1.461 (n) 1.732 (n) 1.612 (s) 1.648 (s) 1.590 (s)

Chalcopyrite 0.540 0.395 (w) 0.361 (n) 0.632 (n) 0.512 (n) 0.548 (s) 0.490 (s)

n, no depressing action; s, strong depressing action; w, weak depressing action.

5.3.4 Frontier orbital energy of azo agents and minerals Frontier orbital theory suggests that the energy difference (DE) between the HOMO and the LUMO between molecules should be small enough to facilitate interaction between molecules. The chemical reaction occurs at a position and direction in which the HOMO of one reactant and the LUMO of the other reactant are capable of maximally overlapping. As can be seen from Fig. 5.18, the main reactive groups of the azo reagent are azo (eN¼Ne) and polar group amino (eNH2), and the azo and amino groups in the molecular structure can be chelated to the metal ions on the mineral surface and consequently depress the minerals. Table 5.6 lists the frontier orbitals of six azo reagents (DR28, DB6, DB15; DG6, AB234, AB210 in trisazo) and five sulfide minerals that have depression effects on sulfide ore. It is reported that when the difference between the organic depressant (Y) and the sulfide mineral (MS) frontier orbital energy (jDE(Y-MS)j) is close to or less than that of between the xanthate (X) and sulfide mineral (MS) (jDE(X-MS)j), the organic depressant can depress the sulfide ore [57]. It is noted from Table 5.6 that all values of jDE(Y-MS)j between the six azo reagents and pyrite are less than jDE(X-MS)j between the xanthate and pyrite. This suggests that the six azo reagents can depress the flotation of pyrite. DR28, DB6, DG6, AB234, and B210 have a certain depression on jamesonite as the jDE (Y- jamesonite)j (Y- DR28, DB6, DG6, AB234, and B210) are close to or less than jDE (X- jamesonite)j, while DB15 has no depression on jamesonite as the jDE (DB15- jamesonite)j is larger than jDE (X-jamesonite)j. AB324 and AB210 have depression effect on marmatite as the jDE (Y- marmatite)j (Y- AB324 and AB210) are close to or less than jDE (X-marmatite)j, and DB15 has no depression on marmatite as the jDE (DB15- marmatite)j is larger than jDE (X-

Structure and reactivity of flotation reagents 215 marmatite)j, while DR28, DB6, and DG6 do not meet the aforementioned rules. From the molecular structure analysis, the azo and amino groups contributing to HOMO in AB324 and AB210 reagents are connected to the benzene ring, while the azo and amino groups in DR28, DB6, and DG6 contributing to HOMO are attached to the naphthalene ring. In the process of forming chelate, the naphthalene ring has a larger steric-hindrance effect than the benzene ring, which is not favorable to the reaction. Therefore, although the jDEj between DR28, DB6, and DG6 and minerals is lower than that of xanthate and minerals, these three reagents have no depression effect on marmatite. Therefore, when an interaction occurs between a depressant and a sulfide mineral, in addition to the need to match the frontier orbital energy between the two, the influence of the molecular structure is also considered. The three reagents (DG6, AB324, and AB210) have depression on galena as the jDE (Y- galena)j (Y- DG6, AB234, and AB210) are close to or less than jDE (X-galena)j. DB15 has no depression on galena as the jDE (DB15- galena)j is larger than jDE (X-galena)j. Although the jDE (Y- galena)j (Y- DR28 and DB6) are less than jDE (X-galena)j, the two reagents could not depress galena. In addition to considering the steric-hindrance effect of DR28 and DB6 molecular structures, the lead ion radius in galena is relatively large and the polarizability is small, which also has a certain effect on the reaction. The three reagents (DR28, AB324, and AB210) have depression on chalcopyrite as the jDE (Y- chalcopyrite)j (Y- DR28, AB324, and AB210) are close to or less than jDE (X-chalcopyrite)j. DB15 cannot depress chalcopyrite as the jDE (DB15- chalcopyrite)j is larger than jDE (X-chalcopyrite)j. DB6 and DG6 do not meet the aforementioned rules, and that may due to the steric hindrance effect caused by the long distance between azo group (eN¼Ne) and amino group (eNH2) in structures. Another possible reason may be that the naphthalene ring connected to the amino group in the molecular of DB6 and DG6 also contains some sulfonic acid groups, and the asymmetric distribution with the amino group affects the electron density distribution of the naphthalene ring to some extent. Fig. 5.18 suggests that the benzene ring and naphthalene ring in DB6 and DG6 contribute less to the HOMO of the molecule. Therefore, the jDEj value of DB6 and DG6 and chalcopyrite is less than the jDEj value of xanthate and chalcopyrite, but DB6 and DG6 have no depression effect to chalcopyrite. It is concluded from the preceding analysis that if the azo reagent interacts with the sulfide mineral, in addition to the frontier orbital energy between the two needing to be matched, the influence of the molecular structure of the reagent should also be considered. From this perspective, the difference between the frontier orbital energy of the reagent and the mineral jDEj can be used as a preliminary quantitative criterion, and the molecular

216 Chapter 5 structure is the main determinant: that is, the depression performance of the azo reagent depends on its molecular structure.

5.4 Frothers adsorption at wateregas interface Surfactant compounds, which are amphiphilic with a polar head group and a hydrophobic hydrocarbon chain structure, have been widely used in industry for a long time [58,59]. Because of its special amphiphilic structure, surfactant shows distinct characteristics including surface activity, wetting ability, foaming, and solubilization [59], which facilitate its important role in many industrial processes, such as oil extraction, deterging, and foaming processes [60]. In addition, the adsorption of surfactants at the wateregas interface can significantly alter the interfacial properties, consequently influencing the efficiency of industrial processes, such as flotation and steam condensation [61]. Froth flotation is a separation process that exploits the wettability differences between minerals. It generally makes the hydrophobic mineral concentrated at the gaseliquid interface or on the oilewater interface, while the hydrophilic minerals remain in the water. Now, froth flotation is widely used in metallurgy, medicine, chemical, agricultural, biologic, and environmental protection. Frothers, an important member of surfactants, make full use of the foaming performance of surfactants. Generally, like the other surfactant molecules, frothers are also heteropolar surface-active compounds containing polar head groups (OH, COOH, C¼O, OSO2, and SO2OH) and hydrocarbon radical compounds, capable of adsorbing at the gaseliquid interface. Frothers can reduce the surface tension of the water. It is the force created around the air bubble in the presence of a frother that prevents the bubble from collapsing. Additionally, frother molecules concentrate on the interface of water and air bubbles, forming one adsorption layer of frother molecules around the bubbles, which prevents them from colliding or touching. When the frother molecules absorb at the gaseliquid interface, they will leave the hydrophilic or polar head groups faced to the water phase, with the hydrophobic or nonpolar hydrocarbon chain in the air phase [62e66]. It is found that frothers can enhance the generation of fine bubbles and stabilize the foam [63,66,67], which will enhance the efficiency of froth flotation in practice. The microscopic mechanism of frother property is not clearly established, and the selection of the frother in industry is usually by trial and error [68]. It has been proved that the foaming power depends on the chain length and the arrangement of the functional groups at the gaseliquid interface [69]. A great variety of modern experimental techniques, including fluorescence, resonance Raman scattering, neutron reflection, second harmonic generation, vibrational sum frequency spectroscopy, and time-resolved quasielastic laser scattering, are used to study the structures and dynamics of these systems [70e79]. However, neither the changes of the molecule structure of

Structure and reactivity of flotation reagents 217 surfactants adsorbed at the interface nor the essential interaction between surfactants and solvents have been specifically described at the molecule level by the aforementioned techniques [80]. Molecular simulation can reveal the microscopic interaction mechanism and a large number of researches have been performed based on this method. Tuma predicted the binding energies of H-bonded complexes with a comparative DFT study [81]. Shishkin calculated the molecule geometry of complex of cytosine with 14 water molecules within the DFT and made the conclusion that the structure of the hydrated nucleobase could not be described by canonical chemical formula, and it was best approximated as a superposition of the oxoamino and zwitterionic hydroxyimino resonance structures [82]. Chen discussed the surfactant complex of CH3(CH2)7OSO3(H2O)n (n ¼ 0e6). The binding free energy suggested that the hydrophilic group of sodium dodecyl sulfate molecule surrounded by six water molecules was stable. In addition, the length of the alkyl chain as well as the bond angle of the hydrophilic group change varied with the number of the water molecules [80]. However, there were few reports on the correlation between the adsorption structures of frothers and their foaming. We use DFT combined with molecule dynamics (MD) to study the adsorption structures of frothers at the gaseliquid interface. The results will contribute to further understanding of the structure and property of the frothers. All the simulations in this study are carried out by using DFTBþ, DMol3, and Forcite package.

5.4.1 Computational method Frother a-terpineol, MIBC, and DowFroth200 (DF200) together contribute to more than 90% of frother usage in froth flotation industry in the world. Fig. 5.19 displays the structure of these three frothers. DFTBþ module, which is based on the tight-binding method, is used to obtain the initial structures of the interactions between frother molecules and water molecules. For this module, the geometry optimization is built with an algorithm of conjugate gradient. Mio

Figure 5.19 Molecule structures: (A) a-terpineol-C10H18O, (B) MIBC-C6H14O, and (C) DF200-C10H22O4.

218 Chapter 5 (CeHeOeNeSeP) and divide-conquer are selected as the Slater-Koster library and eigensolver, respectively. The convergence criteria for structure optimization are set to ˚ , and (a) energy tolerance of 0.05 kcal/mol, (b) max. force tolerance of 0.5 kcal/mol/A (c) max. iterations of 9999. The smearing is set at 0.005 Ha and all the qualities are under the medium level. Based on the DFTBþ calculation results, the adsorption of the frother molecule at gaseliquid interface is simulated. The interactions between the polar head group of the frother with different numbers of water molecules are performed by Dmol3 module. This module is widely used for its accuracy for not only the molecule structure but also the molecule properties. In this module, no special treatment of core electrons are considered, and all electrons are included. More specifically, spin-unrestricted is performed and the symmetry is also used. The SCF convergence is fixed to 106 Ha, and the convergence criteria for structure optimization are set to (a) energy tolerance of 1.0
105 Ha, ˚ , and (c) max. displacement tolerance of 0.005 A ˚. (b) max. force tolerance of 0.002 Ha/A The smearing is set at 0.005 Ha, and all kinds of qualities are under the fine level. For the reason that the exchange-correlation functional and the basis set are the core parameters in DMol3 module, the dOeH and :HeOeH of H2O molecule are calculated under different functionals (all with the DNPþ basis set), and the result is shown in Table 5.7. It is clearly shown in Table 5.7 that the calculated dOeH, :HeOeH, and hydrogen bond energy of the optimized H2O under the functionals of GGA-BP and GGA-VWN-BP are Table 5.7: The dOeH and :HeOeH of H2O molecule under different functionals. Functional Experimental value (298K) LDA-PWC LDA-VWN GGA-PW91 GGA-BP GGA-PBE GGA-BLYP GGA-BOP GGA-VWN-BP GGA-RPBE GGA-HCTH GGA-PBEsol B3LYP mGGA-M06L mGGA-M11L

˚) dOeH (A 0.958 0.971 0.971 0.970 0.970 0.971 0.973 0.972 0.969 0.971 0.960 0.972 0.961 0.959 0.953

:HeOeH ( ) 104.500 104.434 104.440 104.245 103.775 103.694 104.375 103.892 103.780 103.382 103.867 103.777 104.563 103.604 102.989

Hydrogen bond energy (KJ/ mol) 18.80 41.59 41.62 27.76 18.87 26.33 30.10 16.61 18.87 19.83 21.15 29.51 44.08 23.90 22.35

Structure and reactivity of flotation reagents 219 Table 5.8: The dOeH and :HeOeH of H2O molecule under different basis sets. Basis set Experimental value (298K) MIN DN DND DNP TNP DNPþ

˚) dOeH (A 0.958 1.117 0.986 0.977 0.960 0.967 0.970

:HeOeH ( ) 104.500 98.919 108.518 103.454 103.689 104.452 103.775

Hydrogen bond energy (KJ/ mol) 18.80 36.78 33.06 21.84 19.90 16.40 18.87

quite close to the experimental values, which are tested at 298K. So in this study, GGABP is selected as the exchange-correlation functional. To find out the optimal basis set, different kinds of basis sets are compared under the functional of GGA-BP, and the results are listed in Table 5.8. Obviously, the result under the basis set of DNPþ is much close to the experimental value as shown in Table 5.8, and DNPþ is determined to be the best basis set. To find out how the layer of frother molecules absorbs at the gaseliquid interface, the molecular dynamics method is used. In the study, the Forcite module is selected, and its temperature, the pressure, and the forcefield are all adjustable. The smart module is chosen as the algorithm, and the convergence criteria are set to (a) energy tolerance of 2.0
105 ˚ , (c) max. displacement tolerance of kcal/mol, (b) max. force tolerance of 0.001 kcal/mol/A ˚ 0.005 A, and (d) max. iterations of 5000. The forcefield of cvff_nocross_nomorse is suitable. In addition, atom-based electrostatic and atom-based van der Waals are selected in simulation method. All the qualities are under the ultrafine level. The binding energy can be expressed by following equation: DE ¼ EfrothernH2 O  Efrother  nEH2 O

(5.1)

where DE here is the binding energy; EfrothernH2 O is the total energy of the frother with the water molecules; Efrother is the total energy of the frother molecule; and EH2 O is the energy of one water molecule that is calculated under the same condition.

5.4.2 Frother molecule in water phase In the DFTBþ module, the structures of each frother molecule and water molecule must be optimized first, then the frother molecule should be placed inside the water molecule cluster, leaving the frother molecule just surrounded by water molecules. The result of the interaction between frother molecule and water molecule clusters is shown in Fig. 5.20.

220 Chapter 5

Figure 5.20 Slices of the structures of frother molecules in water phase: (A) a-terpineol, (B) MIBC, and (C) DF200 (green: the polar head group, blue: the nonpolar group, orange: the water molecule connected directly with the polar head group).

As shown in Fig. 5.20AeC, it is found that the interactions of the three frothers with their surrounding water molecules are not the same. The polar head group in the frother molecule, eOH in a-terpineol, eOH in MIBC, eOH and eOe in DF200, forms hydrogen bonding with water molecules. This suggests that the polar head groups of these three frothers are hydrophilic. Nevertheless, the nonpolar head groups (hydrocarbon) in frothers are repelled from water molecules, suggesting the hydrophobic properties of frothers. As a consequence of the hydrogen bonding between the polar head group with water molecule, a hydration shell with a certain structure is formed near the polar head group. Correspondingly, around the nonpolar group, the water molecules are excluded, forming a space sandwiched between the frother molecule and water molecule cluster.

Structure and reactivity of flotation reagents 221

5.4.3 Frother molecule adsorbing at the gaseliquid interface The interaction interface between frother molecules and water molecules can be regarded as a gaseliquid interface. In DMol3 module, a frother-nH2O structure is simulated to represent the interaction between one single frother molecule with water molecules. Firstly, one single water molecule is released around the polar head group of the frother molecule. Then the number of water molecules is gradually increased until the most stable structure is obtained. The most stable structure should meet the following conditions. Firstly, the polar head group must be saturated by the hydrogen bonds with water molecules. Secondly, the formed hydration shell structure should neither have excess water molecules nor lack the necessary water molecules. Sufficient free valence bonds should be left to make the polar head group continually connected with the surrounding water molecules. Thirdly, the formed hydration shell structure should also be consistent with the conclusion of the previous section. Lastly, the binding energy should reach the lowest. 5.4.3.1 a-terpineol Twenty-one kinds of optimized structures of a-terpineol-nH2O are found, as shown in Fig. 5.21 with both the structures and the binding energies (DE). These structures can be classified into three kinds: chain-like structures; ring-like structures, and spatial structures. Under the same level of water molecule number, the binding energies (DE) of frother molecule and water molecules vary with the binding structures. It is shown that the DE of spatial structures is the lowest, followed by ring-like structures and then the chain-like structures. This suggests that the spatial structures are the most stable, while the linear structures are the most unstable. The structural stability of frother-water system is mainly determined by the coordination number of eOH group of frother with water molecules. It is found that three coordinated eOH by water molecules is the most stable, with O coordinated with two water molecules and H coordinated one water molecule, such as the structures IV-4, V-4, V-5, VI-2, VII-2, and VII-3. In addition, the closure degree of water molecules around the eOH group is also very important for the structural stability. For instance, when eOH group is interacted with four water molecules, although structures IV-2, IV-3, and IV-4 have the same coordination number with water molecules, structure IV-4 has the lowest DE due to the completely closed water molecules, followed by structure IV-3 with half-closed water molecules and then the structure IV-2 with nonclosed water molecules. It is also noted that the DE of the dense structures (V-5 and VII-2) are lower than the relatively loose structures, and the eOH group is three coordinated with water molecules and water molecules are fully completed. However, the dense structure cannot be regarded

222 Chapter 5

Figure 5.21 Optimized structures of a-terpineol-nH2O.

Structure and reactivity of flotation reagents 223

Figure 5.22 The most stable structure of a-terpineol-7H2O (W, water molecule).

Table 5.9: Changes of the bond lengths of a-terpineol-7H2O. Items R(OH) R(OeC8) R(C8eC10) R(C8eC9) R(C8eC7) R(C7eC2) R(C1eC8) R(C1eC2)

˚) Distance in frother (A 0.972 1.457 1.534 1.527 1.553 2.893 5.922 1.503

˚) Distance in complex (A 1.013 1.469 1.534 1.527 1.553 2.894 5.92 1.502

˚) Change value (A þ0.041 þ0.012 0 0 0 þ0.001 0.002 0.001

Table 5.10: Changes of the angles of the polar head group of a-terpineol-7H2O. Items :HOC8 :OC8C10 :OC8C7 :OC8C9

Angle in frother ( ) 107.157 108.294 108.916 112.504

Angle in complex ( ) 109.709 107.816 109.007 112.681

Change value ( ) þ2.552 0.478 þ0.091 þ0.177

224 Chapter 5 as a reasonable structure for its difficulty to be spontaneously formed under natural conditions. Taking all these aspects into consideration, it is convincing that the complex of a-terpineol-7H2O, which is VII-3 in Fig. 5.21, can be selected as the most stable structure, just like a spindle-like structure. The parameters of the structure are displayed in Fig. 5.22. From Fig. 5.22, Tables 5.9 and 5.10, the lengths of the hydrogen bonds that are shown in Fig. 5.22 indicate that the hydrogen bonds belong to moderate-intensity hydrogen bond. The optimized hydration shell changes the polar head group most, while the nonpolar group is affected relatively less. The polar head group related R(OH), R(OeC8), :HOC8 change most, and without any exception, they are stretched or wider. The changes in bonds and angles reveal the fact that the hydration shell makes the polar head group move closer to the water phase, while it makes the nonpolar group repelled by the water phase and closer to the air phase. There is an interesting point that the ring-like a-terpene structure inside the a-terpineol molecule shows some special properties. The changes of the angle can be seen in Fig. 5.23. This space six-member ring-like structure has an excellent cushioning characteristic. To a certain extent, it can offset the hydration shell effect on a nonpolar group. Specifically speaking, the bond angle of the ring by adjusting the size of their own, some increase and some decrease, to maintain the stability of the whole ring, which makes R(C2eC7) barely changed.

Figure 5.23 Changes of the angles of the ring-like a-terpene structure: (A) angle in frother ( ) and (B) angle in complex ( ) ([ represents rise; Y represents decrease).

Figure 5.24 The most stable structure of MIBC-7H2O (W, water molecule). Table 5.11: Changes of the bond lengths of MIBC-7H2O. Items R(OH) R(OeC5) R(C1eC2) R(C2eC3) R(C2eC4) R(C4eC5) R(C5eC6) R(C1eC5)

˚) Distance in frother (A 0.971 1.449 1.535 1.534 1.541 1.530 1.528 3.920

˚) Distance in complex (A

˚) Change value (A

1.014 1.460 1.534 1.530 1.537 1.537 1.528 3.938

þ0.043 þ0.011 0.001 0.004 0.004 þ0.007 þ0.000 þ0.018

Table 5.12: Changes of the angles of MIBC-7H2O. Items :HOC5 :OC5C6 :OC5C4 :C4C5H :C4C5C6 :HC5C6 :C1C2H :C3C2C4 :C4C3H :C1C2C3 :C1C2C4 :C3C2C4

Angle in frother ( ) 107.328 110.664 108.132 108.411 111.978 108.853 107.465 107.849 106.877 110.723 110.150 113.499

Angle in complex ( ) 107.573 110.261 109.514 109.291 111.615 108.721 107.627 107.542 107.296 110.101 111.100 112.929

Change value ( ) þ0.245 0.403 þ1.382 þ0.88 0.363 0.132 þ0.162 0.307 þ0.419 0.622 þ0.950 0.570

226 Chapter 5 5.4.3.2 MIBC The research method of MIBC is in line with that of a-terpineol. The results suggest that the MIBC with 7H2O structure shown in Fig. 5.24 is the most stable structure, which is also the similar spindle-like structure. Since the research process is so similar with that of a-terpineol in Fig. 5.21, it will not be mentioned here again. From Tables 5.11 and 5.12, it can be concluded that the major changes of the bond length and angle mainly focus on the polar head group, and the changes on the nonpolar group are less obvious. However, if we compare the two frothers together, a-terpineol and MIBC, there are some differences between them. The a-terpineol has a ring-like a-terpene in it, while the MIBC is strictly part of the aliphatic alcohol chemical compound. The ring-like a-terpene structure offsets the hydration shell effects on the nonpolar group that the nonpolar group in a-terpineol changes much less than that in ˚ of R(C1eC8) in a-terpineol, MIBC. Specifically speaking, the change is about 0.002A ˚ of R(C1eC5) in MIBC. It indicates the stability of the while respectively 0.018A structure of a-terpineol. 5.4.3.3 DF200 The molecule structure of DF200 is quite different from the preceding two. It has one eOH group on the end, three eOe groups distribute within the chain, with a long chain branched chain structure. So the research method is quite different. In step 1, for the three eOe groups, two water molecules are placed around each eOe group, and there are some different kinds of structures that can be obtained from this step. Among them, the structure with the lowest binding energy is selected to display in Fig. 5.25. From the preceding discussion, it can be inferred that the eOH group should combine with the spindle-like hydration shell to form the most stable structure and in fact it is. Then in step 2, the structure shown in Fig. 5.25 is optimized with the spindle-like hydration shell

Figure 5.25 The most stable structure of the three eOe groups with 6H2O.

Structure and reactivity of flotation reagents 227

Figure 5.26 The most stable structure of DF200-13H2O (W, water molecule).

together. The final structure is a DF200-13H2O structure that is exhibited in Fig. 5.26 in detail. It can be seen from Fig. 5.25 that there is only one water molecule interacting with O3. This phenomenon is caused by the position of the O3. It can be concluded from here that the interaction between water molecule and polar head group is affected by the position of the nonpolar group in chain and the structure of the nonpolar group. The two parts are optimized well in Fig. 5.26, and also some hydrogen bonds are built between them. Comparing DF200 with the two frothers investigated before, the obviously different point in Fig. 5.26 is that DF200 has a much more powerful ability to catch water molecules for the extra three eOe groups. The changes in bond length and bond angle are basically the same. From Tables 5.13 and 5.14, it can be seen that the polar head group changes more; nevertheless, the nonpolar group changes less. There are six more water molecules getting into reaction around the nonpolar group, so the nonpolar group-based bond length and angle alteration is a little more significant compared with that of in a-terpineol and MIBC. The more

228 Chapter 5 Table 5.13: Changes of the bond lengths of DF200-13H2O. Items R(O1H) R(O1eC9) R(C9eC10) R(C9eC8) R(C9eH) R(O2eC8) R(O2eC6) R(C6eC7) R(O3eC5) R(O3eC3) R(C3eC4) R(C2eC3) R(O4eC2) R(O4eC1) R(C1eC9)

˚) Distance in frother (A 0.970 1.444 1.524 1.525 1.104 1.423 1.438 1.531 1.423 1.437 1.531 1.520 1.424 1.420 6.277

˚) Distance in complex (A 1.025 1.448 1.521 1.527 1.100 1.437 1.460 1.525 1.434 1.454 1.526 1.518 1.440 1.438 6.607

˚) Change value (A þ0.055 þ0.004 0.003 þ0.002 0.004 þ0.014 þ0.022 0.006 þ0.011 þ0.017 0.005 0.002 þ0.016 þ0.018 þ0.330

Table 5.14: Changes of the angles of DF200-13H2O. Items :HO1C9 :O1C9C10 :HC9O1 :O1C9C8 :C8C9C10 :C8C9H :C10C9H :O2C8C9 :C6O2C8 :O2C6C5 :O3C5C6 :C3O3C5 :C2C3O3 :O4C2C3 :C1O4C2

Angle in frother ( ) 107.358 112.144 109.763 104.941 112.879 107.615 109.324 108.409 113.517 107.500 109.327 113.792 107.099 109.561 112.025

Angle in complex ( ) 108.592 111.991 108.221 104.919 113.849 108.046 109.553 109.981 112.189 108.050 109.241 113.538 106.506 109.496 112.019

Change value ( ) þ1.234 0.153 1.542 0.022 þ0.97 þ0.431 þ0.229 þ1.572 1.328 þ0.550 0.086 0.254 0.593 0.065 0.006

water molecules that get into reaction, the more changes occur on the chain. The R ˚ , getting a growth of 0.33A ˚ , which can (C1eC9) varies obviously from 6.277 to 6.607A be attributed to the increase of water molecules. The partial density of states (PDOS) of O atoms before and after H2O adsorption are investigated to give insight into the abilities of these three frother molecules bonding with water molecules. Fig. 5.27 shows that the changes of PDOS are mainly concentrated in the range between 7.5 and 0 eV. The PDOS of O 2s orbital is at a significantly low level

Structure and reactivity of flotation reagents 229

Figure 5.27 PDOS of O atom in frother molecule before and after H2O adsorption.

230 Chapter 5

Figure 5.28 PDOS of O atom in DF200 before and after H2O adsorption.

Structure and reactivity of flotation reagents 231 compared with the PDOS of O 2p orbital. More specifically, the O 2s orbital changes less, while the 2p orbital changes more. As far as the changes of PDOS before and after H2O adsorption, for a-terpineol, the PDOS of O 2p orbital in the range between 7.5 and 0 eV becomes more localized. For DF200, the PDOS of O1 2p orbital turns more delocalized. For MIBC, the PDOS of O 2p orbital is barely changed. The changes of PDOS indicate that among these three frother molecules, the bonding ability of DF200 is the best, followed by a-terpineol and MIBC. Meanwhile, there are three eOe in DF200 (O2, O3, O4), and the PDOS of these three O atoms before and after H2O adsorption is displayed in Fig. 5.28. It is found that the PDOS of O2 2p orbital and O4 2p orbital are obviously changed, while the PDOS of O3 2p orbital changes slightly.

5.4.4 Frother adsorption layer at the gaseliquid interface The disintegration of the foam is mainly affected by two aspects: liquid film drainage effect and the diffusion of gas through the liquid film. The surface viscosity directly determines the speed of the liquid film drainage, and it is mainly determined by the interaction between hydrophilic group (that is the polar head group in a frother molecule) and water molecules. The higher the surface viscosity is, the lower the liquid film drainage rate will be. And the decrease of the liquid film drainage rate will make the foam more stable. Respectively, the structure of the frother molecule and the arrangement of the frother molecules on liquid film have an impact on the strength of the diffusion effect [83,85]. As far as the liquid film drainage effect, the single a-terpineol molecule and MIBC molecule are similar in structure for they both contain just one eOH group. So the binding ability of these two is nearly the same (both bind with 7 H2O to form the stable complex; see Sections 5.4.3.1 and 5.4.3.2). On the contrary, there are three eOe groups as the hydrophilic (polar head) groups in the DF200 molecule; especially, they are distributed within the chain and not in one end. Generally speaking, the hydrophilic ability of the hydrophilic group that exists in the middle of the molecule (as eOe group in DF200) is stronger than that at the end (aseOH group in DF200). Additionally, from Section 5.4.3.3 it can be seen that there are 13 H2O binding with one DF200 molecule to compose the stable structure. The number of the water molecules connected with the frother molecule can represent the surface viscosity. In summary, among the three frothers, the surface viscosity of the liquid film of the DF200 is the strongest, while the a-terpineol and MIBC are almost at the same level. That is also to say, the liquid film drainage rate of DF200 is the lowest, while a-terpineol and MIBC are almost the same [83]. In terms of the diffusion of gas through the liquid film: for the structure of the frother molecule, the hydrophobic group (that is the nonpolar group in frother molecule)

232 Chapter 5

Figure 5.29 The layer of a-terpineol molecules adsorbing at the gaseliquid interface.

Figure 5.30 The layer of MIBC molecules adsorbing at the gaseliquid interface.

Figure 5.31 The layer of DF200 molecules adsorbing at the gaseliquid interface.

Structure and reactivity of flotation reagents 233 decided the diffusion velocity. The greater the hydrophobic group is, the smaller diffusion velocity will be, and thus the stability of the foam will get much greater. The hydrophobic group (nonpolar group) of MIBC is the smallest among the three. And the hydrophobic group is greater in a-terpineol than that in DF200 for the reason that the hydrophobic group (nonpolar group) in a-terpineol is a space six-member ringlike structure, but a single chain in DF200 under the circumstance of the same number of carbon atoms. Hence, under the hydrophobic group level, the diffusion velocity of a-terpineol is the lowest, and the velocity of DF200 is lower than a-terpineol. For the arrangement of the frother on liquid film, as is demonstrated in Figs. 5.29e5.31, the a-terpineol molecules are more neatly arranged and greater distributed, which make the frother interface thicker and higher on the intensity. All of these characteristics show that the layer of a-terpineol molecules blocks the diffusion of gas through the liquid film better than MIBC and DF200. As for DF200 and MIBC, it is obvious that MIBC is arranged much more loosely than DF200. For the stronger ability of binding with more water molecules, DF200 molecules are more deeply inset into the liquid film. So DF200 is more capable of blocking the gas diffused through the liquid film than MIBC in terms of the arrangement on liquid film [83]. The structure of a-terpineol molecule has a great influence on its foam stability. DF200 and MIBC are both liner chain structures. However, a-terpineol has a six-member ring structure with a carbonecarbon double bond, which can lower the flexibility of the generated bubble wall compared with linear chain structure. In addition, the branched structure on the ring can reduce its polarity, making the structure being certainly curved and consequently the ring structures being closely ranked. These strengthen the stability of foam [83,84]. Based on preceding discussion, it can be concluded that the foam stability of a-terpineol is the best, followed by DF200 and MIBC, which is consistent with the experimental results [62,83,85e87]. The adsorption of a-terpineol, MIBC, DF200 frothers at the gaseliquid interface is investigated by DFT simulations and MD method. The adsorption of frother at the gaseliquid interface is related to the structure of the polar head group and the nonpolar group of the frother molecule. Both a-terpineol molecule and MIBC molecule, which have a single eOH group, have almost the same spindle-like structure of hydration shell. The DF200 molecule includes a single eOH group and three eOe groups, resulting in the hydration shell containing more water molecules. It is found that the liquid film drainage rate of DF200 is the lowest, while a-terpineol and MIBC are almost the same. MD simulation results suggest that because of the ring-like structure, the a-terpineol molecules are more neatly arranged and better distributed, which makes the frother interface thicker and of higher intensity. It is obvious that MIBC is arranged much more

234 Chapter 5 loosely than DF200. However, for the stronger ability of binding with water molecules, DF200 molecules are more deeply inset into the liquid film than MIBC. These results suggest that at the gaseliquid interface, the diffusion performance of MIBC is the best, while a-terpineol is the worst. This can be ascribed to the structure of the different nonpolar group in the frother molecule. Based on the preceding results, in terms of foam stability, it is revealed that a-terpineol is the best, followed by DF200 and MIBC.

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CHAPTER 6

Interaction of flotation reagents with mineral surface 6.1 Interaction of xanthate on galena and pyrite surfaces Since the electrochemistry of flotation was proposed to explain the behaviors of sulfide mineral flotation in 1954 by Salamy and Nixon [1], the study on the interaction of xanthate with sulfide minerals has attracted extensive attention [2e5]. It has been confirmed that various xanthate products would be formed on different sulfide mineral surfaces. Allison et al. [6] correlated the reaction products extracted from the xanthate solutions to the rest potential of various sulfide minerals in the solution and found that dixanthogen and metal-xanthate were two active species responsible for the flotation of sulfide minerals, depending on the relationship between the rest potential of the mineral in xanthate solution and the reversible potential for the formation of dixanthogen. Pyrite and galena are two typical sulfide minerals. With xanthate collector, dixanthogen and Pb-xanthate are respectively used for the flotation of pyrite and galena. The kinetics and thermochemistry studies of xanthate adsorption on minerals showed that the formation of dixanthogen on sulfide mineral surface takes place through a two-step process: the chemisorptions of the xanthate ion (Xe) on the surface and the interaction of chemisorbed xanthate (Xads) with xanthate ion (Xe) forming dixanthogen [7,8]. Using experimental methods, however, Wang and Forssberg showed that Fe(III)-xanthate compounds form and directly bind to the pyrite surface through an ion-exchange mechanism [9,10]. In addition to Fe(III)-xanthate compounds, dixanthogen and xanthate ions were also adsorbed above the Fe(III)-xanthate compounds layer. The ion-exchange mechanism between xanthate ions and surface oxidation products of galena is also used to explain the flotation of galena. The study by Greenler showed that galena samples with more oxidation of the sulfide ions adsorb more xanthate than less-oxidized samples [11]. These studies give a macroscopical concept of the xanthate flotation of pyrite and galena. However, the details of the adsorption of xanthate and the formation of dixanthogen on the surface of the minerals and the role of their oxidation still remain unclear. The atomic-scale phenomena can be observed through simulation methods. Experimental and theoretical methods were used to study the mineral flotation [12,13]. Using density functional theory (DFT) method, Hung et al. simulated the structure and Electronic Structure and Surfaces of Sulfide Minerals. https://doi.org/10.1016/B978-0-12-817974-1.00006-5 Copyright © 2020 Central South University Press. Published by Elsevier Inc. All rights reserved.

237

238 Chapter 6 properties of hydrogen xanthate molecule (HOCSe 2 ) and its adsorption characteristics on pyrite (100), (110), and (111) surfaces [14,15]. The authors found that HOCSe 2 is not readily adsorbed on the (100) surface, while it is likely to be dissociated at the fourfold coordinated surface of Fe on the (110) surface and on the bridging S of the (111) surface. Further reports on the interactions of xanthate with pyrite and galena, however, have not been published. In this study, using DFT method, the adsorption of xanthate on pyrite and galena surfaces was simulated, and the influence of oxidation of surfaces was studied. Moreover, the interaction of xanthate at the mineral surfaces was explained on the basis of the differences of solid physics properties and electronic structures of pyrite and galena crystals.

6.1.1 Computational details All the calculations were performed using CASTEP (Cambridge Serial Total Energy Package) program module and GGA-PW91 (generalized gradient approximation) density function based on the DFT method [16]. Only valence electrons Fe 3d6 4S2, S 3s2 3p4, Pb 5d10 6s2 6p3, C 2s2 2p2, O 2s2 2p4, and H 1s1 were considered explicitly through the use of ultrasoft pseudopotentials [17]. Based on the test results, a plane wave cutoff energy of 280 eV was used for all calculations. The surfaces were obtained from the relaxed bulk structure. Adsorption studies were performed using surface supercells that correspond to (2
2) pyrite surface unit cells and (4
2) galena surface unit cells [18,19]. The k-point sampling densities of 2
2
1 and 1
2
1, respectively, were used for the calculations ˚ was placed between the on pyrite and galena. In addition, a vacuum thickness of 15 A slabs. The slab thickness was tested to determine the slab size that produced a convergence of the surface energy to within 0.005 J/m2, and slab sizes with 15 atomic layers for pyrite and eight atomic layers for galena were determined (Fig. 6.1). Geometric constraint was placed on the bottom nine atomic layers of pyrite slab and bottom five atomic layers of galena slab. Before adsorption, the hydrogen xanthate molecule (HOCSe 2) ˚ was placed inside a 15
15
15 A cubic cell for the optimization calculation, and the gamma point was used. The convergence tolerances for the geometry optimization ˚ , a maximum calculations were set to the following: a maximum displacement of 0.002 A 1 5 1 ˚ , a maximum energy change of 2.0
10 eV atom , and a force of 0.08 eV A maximum stress of 0.1 GP. The SCF (self-consistent field) convergence tolerance was set to 2.0
106 eV atom1. In addition, the spin polarization was used in all calculations. The adsorption energy of HOCSe 2 on the mineral surface was calculated as follows:
 Eads ¼ EHOCS2 =slab  EHOCS2 þ Eslab

(6.1)

Interaction of flotation reagents with mineral surface

239

Figure 6.1 Slab models of (A) (2
2) pyrite (100) surface and (B) (4
2) galena (100) surface.

where Eads is the adsorption energy, EHOCS2 is the energy of the HOCSe 2 calculated in a cubic cell, Eslab is the energy of the pyrite or galena slab, and EHOCS =slab is the energy of 2

the HOCSe 2 -adsorbed pyrite or galena slab. A larger negative value of Eads indicates stronger adsorption of molecule on the surface.

The slab models of (2
2) pyrite (100) surface with 15 atomic layers and (4
2) galena ˚ are shown in (100) surface with eight atomic layers with vacuum thicknesses of 15 A Fig. 6.1. On pyrite (100) surface, each Fe atom is coordinated to five S atoms, and each S atom is coordinated to two Fe atoms and one S atom, thereby retaining a perfect S2 2 dimer on the pyrite (100) surface. On galena (100) surface, each Pb atom is coordinated to five S atoms, and each S atom is coordinated to five Pb atoms.

6.1.2 Adsorption of xanthate on minerals surfaces in the absence of oxygen Different adsorption sites were examined to find the most stable adsorption configuration of xanthate molecule (HOCSe 2 ) on pyrite and galena surfaces. It was found that the Fe sites on pyrite surface and the Pb sites on galena surface were the most possible adsorption sites of xanthate. The adsorption energies of xanthate on pyrite and galena surfaces were 233.35 and 82.71 kJ/mol, respectively, suggesting that xanthate strongly chemically adsorbed on the pyrite surface, while it weakly adsorbed on the galena

240 Chapter 6 surface. The heat of adsorption in the reaction of xanthate with pyrite was measured between 235.2 and 256.2 kJ/mol [8]. The heat of adsorption reaction of xanthate with galena was found to be 83 kJ/mol, close to the calculated result (82.71 kJ/mol) [20]. Comparing the calculated value with the experimental value, it was found that the strong chemical adsorption of xanthate occured on the pyrite surface. In addition, the effects of water molecules (H2O) on the interaction of xanthate with galena surface were also investigated. It was found that the hydration of xanthate by H2O molecules could be ignored. The adsorption energies of H2O on pyrite and galena surfaces were 63.68 and þ 14.46 kJ/mol, respectively. Hence, the pyrite surface is hydrophilic, and the galena surface is hydrophobic, and the influence of H2O on the interaction of xanthate with galena surface could be neglected. The adsorption of H2O on pyrite surface had an effect to a certain extent on the interaction of xanthate with pyrite surface. Compared with the calculated values, strong chemical adsorption of xanthate remained dominant on pyrite surface. Fig. 6.2 shows the adsorption configuration of xanthate on pyrite and galena surfaces, where the values indicate the atomic distance in angstroms. It clearly shows that the two xanthate S atoms are closely bonded with two surface Fe atoms, forming two FeeS bonds ˚ on pyrite surface (Fig. 6.2A), and the electron density map with atomic distance of 2.28 A clearly shows the FeeS covalent interaction. For galena surface, however, the interaction between xanthate S atoms and surface Pb atoms is very weak with long atomic distances ˚ ), and the electron density map indicates almost between PbeS (Fig. 6.2B, 2.89 and 2.96 A no electron density between Pb and S atoms. The stability constants of chemical interaction of Fe(II)-xanthate and Fe(III)-xanthate were 1.58
107 [21] and 6.31
1024 [22], respectively, and that of Pb-xanthate was 1016.7.

Figure 6.2 Adsorption configuration of xanthate on pyrite surface and electron density map (A), and adsorption configuration of xanthate on galena surface and electron density map (B). The values shown in the figure indicate the atomic distance in angstroms.

Interaction of flotation reagents with mineral surface

241

This observation suggests that the formation of Pb-xanthate would be easier than that of Fe(II)-xanthate but more difficult than that of Fe(III)-xanthate, and the stability of Pb-xanthate would be greater than that of Fe(II)-xanthate but weaker than that of Fe(III)-xanthate. However, Fe(II) and Fe(III) are completely free in the solution, while the Fe atom on pyrite (100) surface is coordinated to five S atoms. Hence, the Fe on the pyrite surface is extremely different from the Fe ions in the solution. In fact, the Fe of pyrite (FeS2) is ferrous; therefore, the reactivity of pyrite with xanthate depends on the properties of the Fe atoms in the pyrite crystal field. The Pb atoms on the galena (100) surface are also coordinated to five S atoms and different from the Pb ions in the solution. The calculation results show that the interaction of xanthate with the pyrite surface Fe atoms is greater than that of the galena surface Pb atoms. The extent of xanthate interacting with the pyrite and galena surfaces depends on their solid surface states and electronic structures. The density of states (DOS) of S and Fe atoms on pyrite surface and of S and Pb atoms on galena surface are shown in Fig. 6.3. This suggests that the surface states of pyrite near Fermi energy level (EF) are mainly derived from Fe 3d states (Fig. 6.3A), indicating that the interaction of pyrite surface with xanthate molecules likely occurs preferentially at the Fe sites with large reactivity. The surface states of galena near EF, however, are mainly contributed from S 3p states and partially contributed from Pb 6s and 6p states (Fig. 6.3B), suggesting that the surface Pb atoms exhibit very small reactivity. In addition, the Pb 5d states located at deep valence, suggest that the 5d state of Pb would not take part in any reaction between galena and xanthate. Consequently, the interaction of xanthate S atoms with Fe on pyrite surface is strong, while that with Pb on galena surface is weak.

6.1.3 Adsorption of xanthate on minerals surfaces in the presence of oxygen The oxidation of sulfide minerals by O2 is very important in the flotation process. In this research, the oxidized mineral surface by O2 was used to study the adsorption behavior of xanthate on the pyrite and galena surfaces, which could well reflect the effects of oxidation of mineral surfaces on the xanthate adsorption. Fig. 6.4 shows the adsorption configuration of xanthate on pyrite and galena surfaces in the presence of O2. The details of oxidation of pyrite and galena surfaces by O2 in our previous study showed that O2 is chemically adsorbed on the pyrite and galena surfaces and is completely dissociated [23]. The calculations showed that the adsorption energy of xanthate on the pyrite surface changes from 233.35 kJ/mol in the absence of O2 to 215.19 kJ/mol in the presence of O2, while on the galena surface it changes from 82.71 kJ/mol in the absence of O2 to 102.00 kJ/mol in the presence of O2. These results indicate that the adsorption of xanthate on the pyrite surface is weakened, while on the galena surface, it is enhanced in the presence of O2. This is consistent with the

242 Chapter 6 (A)

50

EF

Density of states (electrons/eV)

40

Surface S

30 20

S 3p

S 3s

10 0 -18 50

-15

-12

-9

-6

40

-3

0

Surface Fe

Fe 3d

30

3

20 10 0

-18

-15

-12

(B) 50

-9

-6

Eenrgy/eV

-3

0 EF

40

Density of states (electrons/eV)

3

Surface S

30 20

S 3s

S 3p

10 0 -18 50

-15

-12

-9

-6

-3

0

40

Surface Pb

Pb 5d

30 20

Pb 6s

10 0

3

Pb 6p -18

-15

-12

-9

-6

Eenrgy/eV

-3

0

3

Figure 6.3 DOS of pyrite surface atoms (A) and galena surface atoms (B). The zero of energy has been set at the Fermi level (EF).

Figure 6.4 Adsorption configurations of xanthate on oxidized pyrite surface (A) and galena surface (B). The ˚. values shown in the figure indicate the atomic distance in A

Interaction of flotation reagents with mineral surface

243

results obtained by Klymowsky [24]. The author’s study about the role of oxygen on the xanthate flotation of galena and pyrite showed that galena reaches its maximum floatability in oxygen-saturated solutions, while pyrite is depressed in oxygen-saturated solutions. The different adsorption behaviors of xanthate on the oxidized pyrite and galena surfaces could be explained from the changes of the mineral surface states before and after oxidation by O2. The DOS of S and Fe atoms on the pyrite surface and those of S and Pb atoms on the galena surface before and after oxidation by O2 are shown in Fig. 6.5. The 3d state peak of oxidized Fe at energy level of 0.35 eV sharply decreases, which

Density of states (electrons/eV)

(A) 15

EF

4s 4p 3d

Perfect Fe

10 5 0 15

-6

10

-4

-2

0

2

-2

0

2

Oxidized Fe

5 0

-6

-4

Eenrgy/eV

EF

(B)

6s 6p 5d

Density of states (electrons/eV)

4

Perfect Pb 2

0

-18

-15

-12

-9

-6

-3

0

3

-9

-6

-3

0

3

4

Oxidized Pb 2

0

-18

-15

-12

Eenrgy/eV

Figure 6.5 DOS of pyrite surface Fe atoms (A) and galena surface Pb atoms (B) before and after oxidation by oxygen molecule.

244 Chapter 6 suggests that the activity of Fe 3d electrons near Fermi level decreases in the presence of O2, so the interaction of oxidized Fe with xanthate molecule slightly weakens. However, the 6s and 6p states of oxidized Pb clearly crossed the Fermi level, and the range of upper valence obviously broadened, which suggests that the activity of Pb 6s and 6p electrons near Fermi level after oxidation increases, so the interaction of xanthate with oxidized galena enhances.

6.1.4 Formation of dixanthogen The final products of the reactions of xanthate on the pyrite and galena surfaces are dixanthogen and Pb-xanthate, respectively. The calculations for dixanthogen formations on the pyrite and galena surfaces were performed using DFT methods to explore the formation of dixanthogen on the mineral surfaces. Fig. 6.6 shows the initial and final adsorption configurations of two HOCSe 2 on the pyrite and galena surfaces. We found that the two xanthate S atoms were covalently bonded, ˚ . The two xanthate forming dixanthogen on the pyrite surface with SeS distance of 2.10 A

Figure 6.6 Formation of dixanthogen on pyrite and galena surfaces. Two HOCS 2 molecules on pyrite surface (initial state (A) and final state (B)) and on galena surface (initial state (C) and final ˚. state (D)). The values near the dotted line indicate the atomic distance in A

Interaction of flotation reagents with mineral surface

245

H atoms were completely dissociated and then interacted with each other, forming H2 on the surface. The production of H2 on the pyrite surface could be attributed to the small xanthate model (HOCSe 2 ), which is easily catalyzed by pyrite, and this would have no effect on the analysis of HOCSe 2 adsorption on the pyrite surface. Dixanthogen is weakly and chemically adsorbed on the pyrite surface with adsorption energy of 61.75 kJ/mol, and a dixanthogen S atom (S3) was weakly bonded to a surface Fe atom with FeeS ˚ . In the case of galena surface, the two xanthate molecules are mutually distance of 2.42 A exclusive, so no dixanthogen is formed on the surface. These results suggest that dixanthogen could form on the pyrite surface without interaction with oxygen. Similar results were reported by Fuerstenau et al. [3] and Wang [10], which showed that xanthate could be oxidized to dixanthogen by ferric ions. The formation of dixanthogen on the sulfide mineral surfaces involves the following two reactions: Anodic reaction 2X / X2 þ 2e Cathodic reaction O2 þ 2H2 O þ 4e/4OH

(6.2) (6.3)

However, where the formation of the dixanthogen is taking place and what oxidizes xanthate to dixanthogen are still unclear. Haung and Miller showed that xanthate is oxidized by adsorbed oxygen at the pyrite surface [8]. However, this observation cannot interpret the fact that xanthate could not be oxidized to dixanthogen by adsorbed oxygen on the galena surface. Fuerstenau et al. [3] and Wang [10] suggested that ferric ions may oxidize the xanthate to dixanthogen, and Eq. (6.3) could be ignored. However, the electrochemical studies indicated that dixanthogen is formed directly at the surface of the pyrite by the action of oxygen in air [2]. Electrochemical measurements suggested that the formation of dixanthogen occurs according to Eq. (6.2) accompanied by Eq. (6.3). However, this electrochemical process is not related to the mineral, which plays an important role in the process of the formation of dixanthogen. Our calculation results show that the formation of dixanthogen spontaneously occurs on the pyrite surface, while it cannot occur on the galena surface in the absence of oxygen, suggesting that the formation of xanthate product on the mineral surface depends on the mineral properties. Based on the geochemistry of mineral crystalline structures, it can be concluded that pyrite and galena have totally different properties. Pyrite crystal is actually disulfide of iron, which is formed based on the following reactions: ) S2 /S þ e /½S2 2 (6.4) S2 /S þ e ½S2 2 þ Fe2þ /FeS2

(6.5)

246 Chapter 6 From Eq. (6.4) it is indicated that in the process of pyrite mineralization, S2 loses one electron and is oxidized to S ; two S in oxidation state bond together to produce one
 sulfur dimer ½S2 2 . Hence, the pyrite (FeS2) crystal is formed under the oxidative atmosphere and can be considered an oxidant. This accounts for the high electrode rest potentials and the high electrocatalytic properties [25e27]. Pyrite has been found as the most active among the sulfide minerals: its activity approaches that of gold [28]. The formation of dixanthogen and dissociation of xanthate H forming H2 on pyrite surface could be well explained by the high electrocatalytic properties of pyrite. However, it is not enough to produce large amounts of dixanthogen, and the presence of oxygen is necessary for maintaining the anodic reaction (Eq. (6.2)). The formation of galena crystal is in accordance with the following equation: S2 þ Pb2þ /PbS

(6.6)

It indicates that galena is formed under the reductive atmosphere and possesses reductive properties. This accounts for the low electrode rest potentials and electron exclusion properties of galena. Hence, dixanthate cannot be formed on the galena surface. In addition, the electrochemical flotation process shows that the interaction of xanthate with sulfide mineral surface occurs during the electron transfer between xanthate and mineral surface. The flow direction of electrons depends on the mean chemical potential of each reactant (xanthate or mineral). The mean chemical potential can be well represented by the Fermi energy level ðEF Þ:   vF EF ¼ m ¼ (6.7) vN T;V where m is the chemical potential, F is the free energy of the system, N is the total number of electrons, T is the temperature, and V is the pressure. The flow of electrons complies with the rules from high potential to low potential. The quantum chemical calculations show that the EF of ethyl xanthate equals 3.958 eV, which is greater than 5.936 eV of pyrite, while smaller than 3.742 eV of galena. Hence, the electrons of xanthate would transfer to the pyrite but not to the galena. This observation suggests that because of a thermodynamic probability, xanthate could be catalyzed to dixanthogen on the pyrite surface in the absence of oxygen. As shown in Eqs. (6.4) and (6.5), the role of oxygen in the formation of dixanthogen is only similar as a cathodic reaction to form an electrochemical circuit with the anodic oxidation reaction of xanthate. The final adsorption structure of dixanthogen on the pyrite surface suggests that the adsorption of dixanthogen occurs through the bonding of one S atom of dixanthogen with one Fe atom on the surface. It was speculated that one xanthate ion is initially adsorbed on the surface and then another xanthate ion interacts with the adsorbed xanthate to form dixanthogen.

Interaction of flotation reagents with mineral surface

247

6.2 Adsorption of xanthate, dithiophosphate, and dithiocarbamate on galena and pyrite surfaces The selectivity of a collector is an essential prerequisite to achieve high-quality concentrate and great recovery in the separation of complex sulfide ores [29]. Thiol collectors such as xanthate, dithiophosphate (DTP), and dithiocarbamate (DTC) are widely employed in sulfide minerals flotation. Xanthate is generally used in bulk flotation due to its powerful collecting property, but it would increase the subsequent separation difficulty due to a lack of selectivity. In contrast, DTP and DTC are usually used in selective flotation due to their good selectivity, especially in lead and copper sulfide mineral flotation. Although, several mechanisms for the adsorption of these three collectors on sulfide minerals have been reported [30e35]. However, the micro mechanisms of the selectivity of these three thiol collectors on different sulfide mineral surfaces are not fully understood. In the adsorption process, the heat of adsorption could characterize the intensity of adsorption between the reagent and mineral [36]. The kinetics and thermochemistry of the xanthate adsorption reaction on pyrite and marcasite were evaluated by Haung and Miller [8], and the rate of the adsorption reaction was found to be approximately one-half order with respect to the xanthate concentration. Mellgren [37] investigated the heat of adsorption of ethyl xanthate on galena samples “as ground” or previously treated with potassium carbonate, sulfate, or thiosulfate solutions and concluded that an ion exchange mechanism might be involved in the adsorption process. Sutherland and Wark [38] reported that the adsorption of diethyl dithiocarbamate (DDTC) onto sulfide minerals is faster than that of ethyl xanthate, and they attributed this phenomenon to the lower solubility of the DTC salt. A computational method such as the DFT method is an effective tool to acquire the microscopic details of configuration and electronic structure of the reagent adsorption on mineral surface, and to illuminate the fundamental aspects of adsorption at the atomic level. Hung et al. [14] employed the DFT method to study the xanthate adsorption on pyrite (110) and (111) surfaces. Yekeler et al. [39] presented the DFT results from the investigation of the structural properties and the frontier orbital energies of some thiol collectors and their interactions with the Ag (þ1) ion. Yekeler et al. [40] calculated the relevant molecular properties of 2-mercaptobenzothiazole and its 6-methyl and 6-methoxy derivatives as collector using the DFT. Moreover, our previous work on the application of the DFT approach to the study of pyrite, galena, and sphalerite surfaces [41e43] has provided a foundation for the current investigation of collector adsorption. In this paper, simulations of three thiol collectors including xanthate, DTP, and DTC adsorptions on PbS (100) and FeS2 (100) surfaces were modeled by DFT. Meanwhile, the

248 Chapter 6 kinetics and thermochemistry of these three thiol collectors on galena and pyrite were measured by the microcalorimetry method. The computational simulation and thermodynamic results can provide useful information for a better understanding of the interactions between different collectors and different minerals and give insights into the essential distinction of the selectivity of different collectors.

6.2.1 Experimental and computational methods Single crystal galena and pyrite samples obtained from Fankou Mine, Guangdong province, China, were used in this experiment. Multielement analysis shows that the galena and pyrite samples were of high purity only with a trace of the element Sb and Co. The X-ray diffraction (XRD) data also confirmed the results. The DDTC in analytical grade was purchased from Sinopharm Chemical Reagent Co., Ltd., and ammonium dibutyl dithiophosphate (ADDTP) in industrial grade was purchased from Zhuzhou Flotation Reagents Factory. Sodium butyl xanthate (SBX) was synthesized by reacting butyl alcohol with sodium hydroxide and carbon disulfide. The microcalorimetric measurements were accomplished with an RD496-III type microcalorimeter. The detailed description about the structure and the technical parameters of this calorimeter have been given elsewhere [44]. The operation temperature was kept constant at 298.15 K. Heat of the adsorption reaction was measured in an isothermal reactor. First, 1.0 g mineral samples and 20 mL of distilled water were put into the erlenmeyer flask (50 mL). The mixture was vibrated ultrasonically for 5 min, then allowed to stand for a few minutes until the liquid was divided into two layers. The supernatant was replaced with 20 mL of distilled water to prepare the mineral solution sample. The concentrations of collector solution (SBX, ADDTP, and DDTC) were 2
104 mol/L. Second, 1 mL of collector solution and 1 mL of mineral solution samples were injected, respectively, in a small cell (3 mL) and a big cell (6 mL) by a microinjector. Then the small cell was put into the big cell, which were all put into a 15-mL stainless-steel sleeve together. The sealed stainless-steel sleeve was put into the calorimeter. Then the reaction parameters were set. When the baseline was stable, the small cell was pierced, and distilled water flowed into the big cell. So the distilled water was mixed with mineral sample in the big cell. The thermal effect was then recorded automatically by a computer. The simulations of collector adsorption have been done using the CASTEP developed by Payne et al. [45], which is a first-principle pseudopotential method based on DFT. The DFT calculation employed plane wave (PW) basis sets and ultrasoft pseudopotentials. The exchange correlation functional applied was the generalized gradient approximation (GGA) of Perdew and Wang (PW91) [17,46]. The interactions between valence electrons and ionic core were represented by ultrasoft pseudopotentials. Valence electron configurations considered in the study included Pb 5d106s26p2, S 3s23p4, Fe 3d6 4s2, P 3s2

Interaction of flotation reagents with mineral surface

249

3p3, N 2s2 2p3, C 2s2 2p2, O 2s22p4, and H 1s1 states. The PW cutoff energies of 280 and 270 eV were used for galena and pyrite calculations, respectively. The surface Brillouin zone was sampled with a 1
2
1 k-point grid for PbS surface calculation and a 2
2
1 grid for FeS2 surface calculation [18], which shows that the cutoff energy and the k-point meshes are sufficient for the system. For self-consistent electronic minimization, the Pulay density mixing method was employed with the convergence tolerance of 2.0
106 eV/atom. The energy tolerance was 2.0
105 eV/atom, the force ˚ , and the displacement tolerance was 0.002 A ˚ . The models tolerance was 0.08 eV/A xanthate (HOCS2), DTP (H2O2PS2), and DTC (H2NCS2) were used in place of butyl xanthate, ammonium dibutyl dithiophosphate, and DDTC for efficient computation as the pretested results showed that the head groups gave little effect to property. The optimizations of xanthate (HOCS2), DTP (H2O2PS2), and DTC (H2NCS2) were calculated ˚ cubic cell, and the optimizations were performed at the gamma point in a 15
15
15 A in the Brillouin zone. After testing the slab thickness and vacuum slab thickness, we constructed a (4
2) PbS ˚ vacuum slab and a (2
2) FeS2 (100) (100) surface with eight atomic layers and 10 A ˚ vacuum slab (Fig. 6.7). For the FeS2 surface, surface with 15 atomic layers and 10 A

vacumm layer vacumm layer Pb

S layer 1 layer 2 layer 3

S

Fe

layer 1 layer 2 layer 3 layer 4 layer 5 layer 6 layer 7 layer 8 layer 9

Figure 6.7 The slab models of a (4
2) galena (100) surface (A) and a (2
2) pyrite (100) surface (B).

250 Chapter 6 the six outermost atomic layers of the substrate were allowed to relax, while the nine bottom-most atomic layers of the substrate were fixed to the bulk coordinates, and for the PbS surface the three outermost atomic layers of the substrate were allowed to relax, while the five bottom-most atomic layers of the substrate were fixed to the bulk coordinates in the adsorption calculations.

6.2.2 The electronic structure and properties of galena (100) and pyrite (100) surfaces In froth flotation, the mineral surface plays an important role in the process of reagent adsorption, which determines the geometry and strength of adsorption, and the difference in properties of mineral surfaces is the premise of mineral separation by flotation. We employed the quantum method to model the galena (100) and the pyrite (100) surfaces and investigate the electronic structure and property of the surfaces. The results show that the dissociation of a galena surface results in the breakage of PbeS bonds, and the Pb and S atoms are changed from six-coordinated as in the bulk to five-coordinated in the surface. The pyrite Fe and S atoms are five-coordinated and three-coordinated respectively at the surface instead of six in the bulk. The decrease in the coordination number of surface atoms may lead to the variation of their reactivity. Surface relaxation of galena (100) and pyrite (100) surfaces had been discussed in our previous study [47], and the results showed that the top three layers of both galena and pyrite surfaces underwent the surface relaxation; however, pyrite underwent greater relaxation than galena. The Mulliken electron of each layer of PbS (100) and FeS2 (100) surfaces are shown in Fig. 6.8. The electron distributions for galena and pyrite are quite different. The outermost layer of both PbS and FeS2 surfaces is electronegative, but PbS carries more negative charge than FeS2 surface. The DOS of the galena Pb and S atoms and the pyrite Fe and S atoms are shown in Figs. 6.9 and 6.10, where the numeral beside the symbol of element represents the layer number. For example, S1 represents S atom in the first layer. Compared with the deep layers (Pb5 and Pb7), the DOS of the surface Pb3 6p state is slightly stronger. It is clearly noted that the DOS of S1 and S3 atoms are quite different from those of S5 and S7 atoms, indicating that electronic properties of surface atoms are different from the deep layer atoms. Moreover, the PbS surface S1 and S3 states dominate around the Fermi level, while the S5 and S7 states have few contributions to the Fermi energy, suggesting that surface S atoms show greater reactivity than the bulk S atoms. For the pyrite surface, by comparison with the bulk Fe12 layer, the DOS peak of the outermost Fe3 states is obviously enhanced around 2.0 eV, and Fe 3d state in the conduction band increases from one peak to two peaks. Compared to the deep layer

Interaction of flotation reagents with mineral surface

251

Figure 6.8 Mulliken electron of each layer of galena (100) and pyrite (100) surfaces. 1.0

Pb7

Pb 6s

0.0 Pb5

Pb 6s

Pb 6p

0.5

0.0

Pb3

0.5

0.0

Pb 6p

Pb 6s

Pb1 Pb 6p

Pb 6s 0.5

0.0 -10

EF

S7

1

Density of states (electrons/eV)

Density of states (electrons/eV)

0.5

3p

3s

2

Pb 6p

0 2

3s

3p

S5

1 0 2

3p

3s

S3 1 0 2

3p

3s

S1

1

-8

-6

-4

Energy/eV

-2

0

2

0 -14

-12

-10

-8

-6

-4

-2

0

Energy/eV

Figure 6.9 DOS of galena Pb and S atoms in different layers.

S atoms (S5, S7, and S9), the surface S 3p states (S1 and S4) around 2.5 to 0 eV increase obviously, especially at  2.0 eV. By comparison to PbS, the Fe atom shows a larger sharp DOS peak at the Fermi level, indicating that the FeS2 Fe atom is more reactive than the PbS Pb atom.

7 6 5 4 3 2 1 0 6 5 4 3 2 1 0 6 5 4 3 2 1 0

2

Ef

1

Fe 3d

Bulk Fe

Density of states (electrons/eV)

Density of states (electrons/eV)

252 Chapter 6

Fe7

Fe3

0 1

-2

Energy/eV

0

2

S7

0 1

S5

0 1

S4

0 1

-4

EF

s p

S9

0

S1

-15

-10

Energy/eV

-5

0

Figure 6.10 DOS of pyrite Fe and S atoms in different layers.

6.2.3 The geometry and electron density of collector adsorption To further investigate the differences of xanthate, DTP, and DTC reacting with galena or pyrite, the adsorption of three thiol collectors on galena or pyrite surface has been simulated by the DFT method. Fig. 6.11 demonstrates the electron density of xanthate adsorption on galena or pyrite surface, in which the S1 and S2 refer to the sulfur atom with single bond and double bond, respectively. On the galena surface, the distance between the xanthate S1 and the surface ˚ , which is close to the radius between PbeS of 2.840 A ˚ , while that of the Pb1 is 2.863 A ˚ ˚ . It indicates that xanthate S2 and the surface Pb2 is 2.935 A, which is larger than 2.840 A the adsorption of xanthate on the PbS surface is mainly via bond formation between the xanthate S1 and the surface Pb1 atom. In addition, a strong electron overlap across S1ePb and a weak electron overlap of S2ePb2 are clearly visible in Fig. 6.6A. On the pyrite ˚ , respectively, surface, distances between the S1eFe1 and S2eFe2 are 2.284 and 2.281 A ˚ ), indicating that the interaction which are smaller than the atomic radius of SeFe (2.31 A between xanthate and pyrite is via the bonding of the two xanthate S atoms with the surface Fe atoms. Furthermore, charge overlaps between S1eFe1 and S2eFe2 are observed in Fig. 6.6B. It may explain the reason for the greater affinity of xanthate for the pyrite. Electron density maps of DTP adsorption on the PbS and FeS2 surface are shown in ˚, Fig. 6.12. On the PbS surface, the lengths of S1ePb1 and S2ePb2 are 2.860 and 2.881 A

Interaction of flotation reagents with mineral surface

253

Figure 6.11 Electron density maps of xanthate adsorption on (A) PbS surface and (B) FeS2 surface.

Figure 6.12 Electron density maps of DTP adsorption on (A) PbS surface and (B) FeS2 surface.

suggesting that the interaction between DTP and PbS is via the two S atoms in the DTP group bonding with the surface Pb atoms. The electron density suggests that the bonding of S1ePb1 is little stronger than S2ePb2, as shown in Fig. 6.12A. On the FeS2 surface ˚ , which are a little (Fig. 6.12B), the lengths of S1eFe1 and S2eFe2 are 2.324 and 2.376 A ˚ longer than the radius of SeFe (2.310 A), indicating that the reactivity of DTP on the FeS2 surface is relatively weaker than xanthate. Electron density maps of DTC adsorption on the PbS and the FeS2 surfaces are given in ˚, Fig. 6.13. On the PbS surface, the lengths of S1ePb1 and S2ePb2 are 2.863 and 2.862 A suggesting that the interaction between DTC and PbS is via the two S atoms in the DTC group bonding with the surface Pb atoms. Compared with electron density maps of xanthate (Fig. 6.11A) and DTP (Fig. 6.12A), it is noted that the adsorption of DTC on galena is the strongest, which may lead to the greatest value of heat of adsorption. On the ˚ , which FeS2 surface, the lengths of S1Fe1 and S2Fe2 are 2.271 and 2.285 A ˚ are smaller than the radius of S Fe (2.310 A), indicating strong bond formation between S1Fe1 and S2Fe2, which is also observed in the electron density map (Fig. 6.13B).

254 Chapter 6

Figure 6.13 Electron density maps of DTC adsorption on (A) PbS surface and (B) FeS2 surface.

6.2.4 The analysis of density of states The analysis from density of states (DOS) could give an insight into the interaction between different collectors and different minerals at the electronic level. The DOSs of the three reagents on the PbS and FeS2 surfaces before and after adsorption have been calculated by the CASTEP module and the Fermi energy is set to 0 eV (EF ¼ 0) in the DOS curve. In this section, we will discuss the DOS from two aspects: one is the collector and the other is the mineral surface. The DOS of xanthate, DTP, and DTC on the PbS and FeS2 surfaces before and after adsorption are shown in Fig. 6.14AeC, respectively. Before adsorption, it is shown that the partial DOS of xanthate, DTP, and DTC functional groups are similar near the Fermi level, which are composed of the S 3p orbital, indicating that the S 3p orbital is very active. In addition, the DOS of an S atom with a single bond is the same as the S atom with a double bond, indicating that the two S atoms in the thiol group have similar chemical reactivity, which may be ascribed to the conjugation effect of a pi bond. The main differences of DOS for the three reagents are caused by the O, C, P, and N atoms in the functional group. As the P 6p and P 6s orbital are located in the deep site of the conduction and valence band, the influence of the P atom on the adsorption is small. After adsorption on mineral surfaces, DOS of the three collectors change obviously. For xanthate adsorption, the DOS of xanthate changes more notably on the FeS2 surface than on the PbS surface, and especially the S 3p state depletes largely near the Fermi level. It is indicated that the reaction of xanthate on the FeS2 surface is stronger than that on the PbS surface. For DTP adsorbed on the PbS surface, the two peaks of DTP S 3p state combine into one peak, and a dramatic change near the Fermi level (EF ¼ 0) occurs where the DOS peak of

Interaction of flotation reagents with mineral surface (A)

(B)

EF

S 3p

0 -8

-6

6 S 2s

3

-4 O 2p C 2p

-2 0 S 3p S 3p O 2p S 3p C 2p

2 Free xanthate

4

C 2p

0 -8

-6

-4

-2

0

6

2 4 Xanthate on FeS2

S 3p

3

DTP on PbS

O 2p

C 2p

3

EF

S 3p O 2p

6 Xanthate on PbS

Density of states(eletrons/eV)

Density of states(eletrons/eV)

6

0

255

3 0 6 3

-8 -7 -6 -5 -4 -3 -2 -1 0 O 2p O 2p S 3p S 3p P 6s

1 2 3 Free DTP

P 6s

S 3p

O 2s

4

5

6

7

P 6p

0 -8 -7 -6 -5 -4 -3 -2 -1 6

O 2p

O 2p

0

1

2

3

4

5

6

7

5

6

7

DTP on FeS2

S 3p

3 0

-8

-6

-4

-2

0

2

-8 -7 -6 -5 -4 -3 -2 -1

4

Energy/eV

Density of states(eletrons/eV)a

(C)

0

1

2

3

4

Energy/eV EF

S 3p

6

DTC on PbS

3 0 -6

-4 N 2p

6

-2

0

2 Free DTC

S 3p

C 2p S 3p 3

C 2p

S 3p

C 2p S 3p

C 2p S 3s C 2s

4

0 -6

-4

-2

6

0

S 3p

2 DTC on FeS2

4

3 0 -6

-4

-2

0

2

4

Energy/eV

Figure 6.14 DOS of xanthate (A), DTP (B), and DTC (C) on PbS and FeS2 surface before and after adsorption.

S 3p reduces to almost zero. On the FeS2 surface, although the S 3p state at the Fermi level decreases largely, the change of S 3p state is not as dramatic as that on the PbS surface. It is suggested that the adsorption of DTP on the PbS surface is stronger than that on the FeS2 surface. After adsorption on the FeS2 surface, the DTC S 3p state shifted to a lower energy level, and the DOS peak reduced largely at the Fermi level; meanwhile, the three DOS peaks of C 2p and N 2p located at 3 to 6 eV merge into one DOS peak. On the PbS surface, the DTC S 3p state moves to the valence band, and the two DOS peaks of S 3p merge into one peak; meanwhile, the two DOS peaks of C 2p and N 2p located at  3 to 5 eV

256 Chapter 6 merge into one peak. The DOS of DTC on the PbS surface changes more obviously than that on the FeS2 surface, indicating that the adsorption of DTC on galena is stronger. DOSs of the PbS surface Pb atom and the FeS2 surface Fe atom before and after adsorption are demonstrated in Fig. 6.15. For the PbS surface, the Pb 6p and 6s states have changed after interaction with the collector, suggesting that the Pb atom participated in the bonding interaction. After interacting with DTC, the Pb 6s state has the highest DOS peak value at the Fermi level and shows the largest movement to the conduction band. In addition, a new DOS peak of the Pb 6p state appears at  4.2 eV. It is suggested that the interaction between DTC and PbS is the strongest. Due to the similar structure for xanthate (OCSS) and DTP functional groups (O2PSS), the DOS of the Pb atom interacting with xanthate and DTP are similar, and there are only little differences in the Pb 6s state. After interacting with xanthate, the peak value of Pb 6s at the Fermi level is higher than that of Pb 6s interacting with DTP, indicating that the interaction of xanthate with the PbS is stronger than DTP. For the pyrite surface, the DOS of the Fe 3d orbital changes after interaction with the reagent, indicating that the Fe atom participates in the bonding interaction. Before adsorption, Fe 3d orbital splits into two peaks (named p1 and p2, respectively) at the top of valence band. After adsorption, a significant change of p1 and p2 occurs. After interaction with the DTC, the change of Fe DOS is the largest, then xanthate and DTP. It can be found that the p1 and p2 of Fe DOS almost completely disappeared after the DTC interaction, while the change in p1 and p2 is relatively small for xanthate and DTP.

6.2.5 The heat of adsorption of collectors on galena and pyrite surfaces For an adsorption process, the Gibbs free energy can be defined (Eq. 6.8): DG ¼ DHdTDS

(6.8)

in which DH is the enthalpy, T is the temperature, and DS is the entropy, a measure of disorder. For an adsorption process, since it proceeds from disorder into an orderly process, DS is less than zero; consequently, dTDS, the second item in Eq. (6.8), is greater than zero. Therefore, DS makes a negative contribution to DG. The numeric value of the Gibbs free energy depends mainly on enthalpy DH, and the greater the value of the DH term is, the more negative the value of DG becomes, and the more easily the adsorption reaction occurs. The heats of butyl xanthate (BX), DTP, and DTC adsorption on galena and pyrite surfaces are listed in Table 6.1. For the pyrite, BX shows the strongest collecting capacity, followed by DTC, while that for DTP is the weakest. For the galena, DTC exhibits the strongest collecting capacity, then the BX and DTP. The DOS results show that the interaction

Interaction of flotation reagents with mineral surface (A)

EF

Pb adsorbed DTC 2

Pb 6s

Pb 6p

0.4 0.2 0.0 0.0

0.1

0.2

0.3

0.4

0.3

0.4

0.3

0.4

0.3

0.4

0

Density of states(eletrons/eV)

-4 2

-2

0

0.2

Pb 6s

Pb 6p

2

0.4

Pb adsorbed DTP

0.0 0.0

0.1

0.2

0 -4 2

-2

0

Pb adsorbed xanthate

2

0.4 0.2

Pb 6s

Pb 6p

0.0 0.0

0.1

0.2

0 -4 2

-2

0

2

0.4

Pb before adsorption

0.2

Pb 6p

Pb 6s

0.0 0.0

0.1

0.2

0 -4

-2

0

2

Energy/eV

(B)

15

EF

Fe adsorbed DTC

p2 p1

10

Fe 3d

Density of states(eletrons/eV)

5 15 0 -5 10

-4

-3

Fe adsorbed DTP

-2

-1

0 p2 p1

1

2

0

1

2

p1 0

1

2

0

1

2

Fe 3d

5 0 15 -5 10

-4

-3

Fe adsorbed xanthate

-2

-1

p2 p1

Fe 3d 5 0 15 -5 10

-4

-3

-2

Fe before adsorption

-1

p2

Fe 3d

5 0 -5

-4

-3

-2

-1

Energy/eV

Figure 6.15 DOS of PbS and FeS2 surface before and after adsorption.

257

258 Chapter 6 Table 6.1: The heat of adsorption values of butyl xanthate (BX), DTP, and DTC adsorption on galena and pyrite surfaces. DH (J/m2) BX PbS FeS2 Difference of DH between PbS and FeS2

2.976 1.985 0.991

DTP 2.122 1.089 1.033

DTC 3.219 1.681 1.538

between xanthate S 3p and pyrite Fe 3d is stronger than that with galena Pb 6sp, while for DTP and DTC, the interaction between their S 3p and the galena Pb 6sp is stronger than that with the pyrite Fe 3d. The activity differences in the S 3p in the three function groups may be caused by the atoms bonding to the S atom, as analyzed before. The difference of DH between PbS and FeS2 could represent the selectivity of the collector, and the greater the absolute value of the difference of DH, the selectivity of the collector is stronger. It is found that the absolute value of the difference of DH for DTC is the greatest (1.538 J/m2), then DTP (1.033 J/m2) and xanthate (0.991 J/m2), indicating that DTC and DTP will show a better selectivity than xanthate in the separation of galena and pyrite.

6.2.6 Kinetics of collector adsorption on galena and pyrite surface The reaction rate constant and the reaction order of the adsorption reaction could be calculated by the following equation, according to reference [48].     1 dHi Hi (6.9) , ln ¼ ln k þ n ln 1 H0 dt H0     dHi Hi 1 ln H0 , dt was plotted as a function of ln 1  H0 , and the intercept of the curve is lnk, and then the values of reaction rate constant k and reaction order n are obtained and are listed in Table 6.2. As we all know, the reaction rate constant quantifies the speed of a chemical reaction, and the reaction order can tell the relationship between the concentrations of species and the rate of a reaction. It is noted that the reaction order for BX on the pyrite surface is 0.58, which is very close to that of 0.60 measured by Refs. [8], indicating that the results are reliable. As shown in Table 6.2, the value of k for BX on the PbS is larger than that on the FeS2, indicating that the adsorption rate for BX on PbS is faster. In addition, the order of both reactions is approximately one-half, suggesting that the influences of xanthate

Interaction of flotation reagents with mineral surface

259

Table 6.2: Kinetic parameters of BX, DTP, and DTC adsorption on PbS and FeS2 surface. Collector

Mineral

Butyl xanthate (BX)

Galena Pyrite Galena Pyrite Galena Pyrite

Dithiophosphate (DTP) Dithiocarbamate (DTC)

 k 3103 s 2.27 1.30 3.17 2.64 0.55 2.56

n

R2

0.26 0.58 1.03 0.42 1.34 0.53

0.9938 0.9792 0.9901 0.9858 0.9911 0.9390

concentration on the two adsorption processes are similar. The reaction order of DTP on PbS is unity (1.03), while that on FeS2 is one-half order (0.42), and the reaction rate constant of DTP on PbS is also greater than that on FeS2, suggesting that chemical kinetics of DTP favors PbS surface adsorption. For DTC, the reaction rate constant on PbS is smaller than that on FeS2, indicating that the adsorption reaction of DTC on the FeS2 surface is faster than that on the PbS surface. In addition, the reaction order of DTC on PbS is unity (1.34), while that on FeS2 is one-half (0.53). It is suggested that the DTC adsorption on galena is more likely be affected by the concentration than that on pyrite. The flotation practice also shows that galena could be collected by adding a small amount of DTC and the selectivity of DTC will drop in the presence of a large concentration.

6.3 Copper activation of sphalerite and pyrite surfaces In the practice of sulfide flotation, sphalerite is poor in natural floatability, so it requires copper activation to achieve flotation. There have been many studies on the activation of sphalerite, but there is still controversy in the process of copper activation, the interaction mechanism, and surface reaction products. In addition, the presence of various impurity defects in the crystal makes this process more complex [49]. For example, marmatite is a common zinc sulfide mineral bearing high iron content, and the presence of iron impurity has an obvious influence on the copper activation of sphalerite and the subsequent flotation behavior. Solecki et al. [50] demonstrated that adsorption of Cu2þ decreased with increasing content of Fe in sphalerite. Szczype et al. further confirmed that for the synthetic sphalerite, the increase in iron content leads to the decrease of adsorption of xanthate on the copper-activated sphalerite surface, mainly due to the reduction of copper on the surface [51]. Recently, Boulton et al. [52] reported that the presence of iron in the sphalerite lattice reduces the exchange sites (zinc) for Cu2þ. However, X-ray photoelectron spectroscopy (XPS) analysis showed that the amount of Cu2þ adsorbing onto the sphalerite surface increased as the iron content of sphalerite increased [53]. Harmer et al. considered that the high iron content of the sphalerite increased the number of surface defect sites and allowed more Cu2þ to be adsorbed onto the sphalerite surface

260 Chapter 6 compared to samples with low iron content (fewer defect sites). The adsorption of Cu (II) ions on the sphalerite surface will release same amount of Zn2þ into the solution; see Eq. 6.10 [54]. 2þ ZnSðsÞ þ Cu2þ ðaqÞ /Cux Zn1x SðsÞ þ ZnðaqÞ

(6.10)

The results of SIMS and XPS [55] analysis show that at low pH, Cu (II) ions reaching at the sphalerite surface are immediately reduced to Cu (I) ions and incorporated into any Zn site on the surface with release of the zinc (II) ion to the solution. At higher copper concentration, further reaction to the second layers and subsequent layers of the ZnS lattice takes place with similar substitution of Cu (I) for zinc (II) in the lattice. It is speculated that this diffusion may take place either by site exchange between the Cu (I) in the surface layer and zinc (II) in the second layer or by interstitial movement of the smaller Cu (II) ion through the lattice. Copper ion is also an effective activator of pyrite, but its activation mechanism is completely different from sphalerite. For pyrite, it was proposed by Bushell and Krauss [56] that pyrite can be activated by copper because iron is replaced by copper to produce CuS. The research conducted by Weisener and Gerson suggested that copper uptake during pyrite activation does not result in a related 1:1 (or any) iron release from pyrite, thus ruling out an ion exchange activation mechanism. Pyrite activation follows a single, fast step involving Cu(II) adsorption onto the reactive sulfur sites only on the surface [57e59]. Therefore, this section focuses on the structure and electron transfer of copper adsorption on the surface of sphalerite and pyrite.

6.3.1 Activation model of sphalerite and its electronic properties The optimization calculations of zinc and copper exchange at different sites on the top layer, second layer, and third layer of ZnS surface have been performed. The exchange reaction of copper and surface zinc could be expressed by Eq. 6.11. Zn40 S40 þ Cu/CuZn39 S40 þ Zn

(6.11)

The model of copper activation of ZnS (110) surface is shown in Fig. 6.16. Copper atoms can replace zinc atoms with two coordination numbers: three-coordinated Zn (Zn3f) and four-coordinated Zn (Zn4f). The calculated substitution energies for copper replacing zinc atom with different coordination number are 82.09 kJ/mol for Zn3f and 66.81 kJ/mol for Zn4f. It is indicated that copper atom is preferentially exchanged with Zn3f atom. The energy band of copper-activated ZnS surface is shown in Fig. 6.17. Compared with the ideal ZnS surface, after copper activation, the energy band of ZnS is not changed greatly, and only one impurity level appears in the band gap.

Interaction of flotation reagents with mineral surface

261

Figure 6.16 The model of copper activation of ZnS (110) surface. 6 5 4

Energy/eV

3 2 1 0 -1 -2 -3 -4 -5

G

F

Q

Z

G

Figure 6.17 The energy band of copper-activated ZnS surface.

The DOS of the top three layers of copper-activated ZnS surface are shown in Fig. 6.18. It is found that the effect of copper activation on the surface DOS is mainly near the Fermi level due to the split of Cu 3d orbital. The new surface energy level appearing at the Fermi level is composed of Cu 3d and S 3p orbital. Compared to the ideal ZnS surface,

262 Chapter 6 EF

Cu 3d 4

Cu

2

Cu 4s

Cu 4s

Density of states/eletrons. eV–1

0 60 -15 3rd layer 30 S 3s

-10

-5

0

5

Zn 3d S 3p

Zn 4s

0 60 -15

-10

2nd layer 30

-5

0

5

Zn 3d

S 3s

S 3p

Zn 4s

0 40 -15 1st layer 20 S 3s

-10

-5

0 S 3p

Zn 3d

5

Cu 3d Zn 4s

0 -15

-10

-5

Energy/eV

0

5

Figure 6.18 Density of states (DOS) of top three layers of copper-activated ZnS surface.

Figure 6.19 (A) Mulliken charge and (B) differential electron density of atoms on the first layer of copperactivated ZnS surface.

after copper activation, the DOS of surface Zn 3d orbital shifts from 5.82 to 6.17 eV, and the S 3p orbital moves toward the higher energy level. The Mulliken charge and differential electron density of the first layer of copper-activated ZnS surface is shown in Fig. 6.19. After replacing surface Zn atom, the Mulliken charge of Cu atom is 0.16 e, and the charge of S atom bonded with the Cu atom reduces, indicating that electrons transfer from S atom to Cu atom, and the surface Cu atom is in a

Interaction of flotation reagents with mineral surface

263

low valence state, which is consistent with the mechanism of the adsorption of copper ions on the ZnS surface suggested in Ref. [55]. It is also found that there is an obvious electron transfer between CueS bond, as shown in the differential electron density.

6.3.2 Activation model of pyrite and its electronic properties Two possible ways of copper activation on the FeS2 (100) surface are considered: one is copper substituting iron atom, as shown in Fig. 6.20A, and the other is copper adsorbing on the surface S atom, as shown in Fig. 6.20B. The calculated substitution energy for Cu to replace Fe atom is positive, and up to 665.42 kJ/mol, which indicates that it is difficult for Cu to replace surface Fe atom, so the substitution activation way is not working. The calculated adsorption energy for Cu adsorbing on the surface S atom is 119.61 kJ/mol, indicating that a chemical adsorption occurred, and Cu atom is bonding with the S atom. Therefore, the copper activation of pyrite surface is via the chemisorption between Cu and surface S atoms. Mulliken charges of atoms on the clean surface and copper-activated surface are shown in Fig. 6.21A and B, respectively. Electron density between Cu and surface S atoms is shown in Fig. 6.21C. In the figure, the number in the parentheses is the charge of the atom in e, ˚ . It is observed from Fig. 6.21B that and the number on the bond is the bond length in A ˚ . It is Cu atom adsorbing on the surface S atom with the CueS has bond length of 2.109 A also found from Fig. 6.21C that the electron density between Cu and S1 atom is large, indicating a covalent bonding. In the pyrite, the sulfur dimer formed by two sulfur atoms is bonded to the iron atom, so the interaction between the sulfur dimer and copper should be analyzed when discussing copper adsorption. After copper adsorption, the Mulliken charge of surface sulfur dimer labeled as S1eS2 decreased from 0.12 to 0.09 e, which is in agreement with the observation of SXPS S 2p spectra by von Oertzen et al. [60].

Figure 6.20 Two possible activating ways of copper activation on the FeS2 (100) surface: (A) copper substituting iron atom and (B) copper adsorbing on the surface S atom.

264 Chapter 6

Figure 6.21 Mulliken charge of atoms on the (A) clean surface, (B) copper-activated surface, and (C) electron density between Cu and surface S atoms.

That is, after copper adsorption, the binding energy of the surface sulfur dimer increases, and the negative charge density decreases, which is also consistent with their calculation results. In addition, the copper atom is positively charged, while the positive charge value of the surface iron atom decreased, indicating that the surface has obtained electrons from copper. Fig. 6.22 shows the DOS of pyrite surface and copper atom before and after adsorption. Before adsorption, the DOS of free Cu atom is mainly composed by Cu 3d orbital, which has a sharp DOS peak near the Fermi level. In addition, Cu 4s orbital also has a small contribution near the Fermi level. After copper adsorption on the pyrite surface, the DOS of Cu 3d and 4s, which are near the Fermi level, decrease obviously, indicating that Cu 3d and 4s orbitals lose electrons. Moreover, the Cu 3d states significantly move toward to the low energy level, and the DOS peak shifts from 0.2 to 2.5 eV. The DOS of pyrite surface moves to the low energy level after adsorption. Mulliken charge population of Cu atom before and after adsorption is listed in Table 6.3. It is noted that Cu atom is positively charged after adsorption, and pyrite surface receives electrons from Cu 3d and 4s orbitals.

Interaction of flotation reagents with mineral surface 30 20

free Cu

EF

Cu 3d

10

Cu 4s

DOS /electrons.eV–1

0 20

Cu after adsorption

3

surface before adsorption

1.0

Fe 3d

S 3p

-6

0.5

Fe 3d

S 3p

-8

Cu 4p

1 0

surface after adsorption

Cu 4s

2

Cu 3d

10 0 40 30 20 10 0 40 30 20 10 0

265

-4

-2

Energy/eV

0

2

Figure 6.22 DOS of pyrite surface and copper atom before and after adsorption. Table 6.3: Mulliken charge population of Cu atom before and after adsorption.

Free Cu atom Adsorbed Cu atom

s

p

d

Charge/e

1.00 0.88

0.00 0.10

10.00 9.83

0.00 0.19

6.4 Interaction of lime with pyrite surface Pyrite is one of the most common sulfide minerals encountered in nature. Pyrite often exists in sulfide mining and coal mines, where it is usually undesired and is often removed by the flotation method. The flotation behavior of pyrite is greatly influenced by the pH of the pulp. Sodium hydroxide (NaOH) and lime (CaO) are the most common pH modifiers for pulp and are also effective depressants of pyrite. The depressing effects of NaOH and CaO on pyrite are different, and CaO is more effective. It is shown that pyrite would be effectively depressed at lower pH levels regulated by CaO. Suggested reasons for NaOH depressing pyrite include the hydrophilic compounds of iron hydroxyl forming on the pyrite surface hindering the adsorption of xanthate anion. Another view suggests that OH could exchange with xanthate anion, which then desorbs from the pyrite surface. Wang and Forssberg [61] have shown that OH would first chemically adsorb on the pyrite surface: FeS2 þ OH /FeS2  OHads þ e

(6.12)

266 Chapter 6 The main components after the dissolution of lime (CaO) in water are calcium ion (Ca2þ) and hydroxyl ion (OH). At a pH below 12.5, calcium hydroxyl ion (CaOHþ) is the main component in lime solution. Chen et al. [62] have shown that when CaO was used to adjust the pH of pulp, the zeta potential of pyrite was more positive than when NaOH was used; furthermore, at a pH range of 9e12, the zeta potential of pyrite in CaO solution increased as the pH value was increased. This result suggests that the interaction of CaOHþ with the pyrite surface is stronger than the interaction of OH with the pyrite surface at high pH levels. Different views exist with respect to the roles of calcium on the depression of pyrite. The adsorption of calcium on surface has been suggested to inhibit the oxidation of pyrite and thus reduce the formation of dixanthogen on the surface. Szargan et al. [63] have suggested that the adsorption sites of dixanthogen on a pyrite surface were reduced due to the adsorption of calcium, which resulted in the depression of pyrite. Based on evidence gathered using the XPS method, Hu et al. [64] have suggested that the surface CaSO4 species on pyrite accounted for the depression of pyrite by CaO. The adsorption of hydroxyl and calcium hydroxyl ions (OH and CaOHþ), respectively, on a pyrite (100) surface were conducted to investigate the depression of pyrite by NaOH and CaO. The copper (Cu) activation of pyrite depressed by NaOH and CaO was predicted based on the calculation results. Flotation tests were performed, and the prediction was confirmed.

6.4.1 Methods All the calculations were performed using CASTEP, GGA-PW91 [16] based on DFT. Only valence electrons were considered explicitly through the use of ultrasoft pseudopotentials [17]. Based on the test results, a PW cutoff energy of 270 eV was used for all calculations. The surfaces were obtained from the relaxed bulk structure. Adsorption studies were performed using surface supercells that corresponded to (2
2) surface unit cells, and a Monkhorst-Pack [18,19] k-point sampling density of 2
2
1 was used for all adsorption ˚ was placed between the slabs. The calculations. In addition, a vacuum thickness of 15 A slab thickness was tested to determine the slab size that produced a convergence of the surface energy to within 0.005 J/m2, and a slab size with 15 atomic layers was determined (see Fig. 6.23). Geometric constraints were placed on the bottom nine atomic layers of slab. Before adsorption, the hydroxyl and calcium hydroxyl molecules (OH and CaOHþ) ˚ cubic cell for the optimization calculation, and the were placed inside a 15
15
15 A gamma point was used. The convergence tolerances for the geometry optimization ˚ , a maximum force of calculations were set to a maximum displacement of 0.002 A 1 5 ˚ , a maximum energy change of 2.0
10 eV atom1, and a maximum stress 0.08 eV A

Interaction of flotation reagents with mineral surface

267

Figure 6.23 ˚. Slab model of (2
2) pyrite (100) surface with 15 atomic layers and vacuum thickness of 15 A The atoms on the same level occupy one layer.

of 0.1 GP; the SCF convergence tolerance was set to 2.0
106 eV atom1. In addition, the spin polarization was used for all calculations. The adsorption energy of each adsorbate (OH or CaOHþ) on a pyrite surface was calculated as shown: Eads ¼ Eadsorbate=slab  ðEadsorbate þ Eslab Þ;

(6.13)

where Eads is the adsorption energy, Eadsorbate is the energy of the OH or CaOHþ calculated in a cubic cell, Eslab is the energy of the FeS2 slab, and Eadsorbate=slab is the energy of the OH-adsorbed or CaOHþ-adsorbed FeS2 slab. A more negative value of Eads indicates a stronger adsorption of molecule on surface. The slab model of a (2
2) pyrite (100) surface with 15 atomic layers and a vacuum ˚ is shown in Fig. 6.23. Each Fe atom is coordinated to five S atoms, and thickness of 15 A each S atom is coordinated to two Fe atoms and one S atom, thereby retaining a perfect S2 2 dimer on the pyrite (100) surface. Samples of pyrite were obtained from the Dachang Tongkeng Mine in Nandan, China. High-purity samples were hand-picked from the mine, and a chemical analysis revealed

268 Chapter 6 that the pyrite content was 95.7%. The samples were dry-ground in a porcelain ball mill and dry-screened to obtain 0.09 þ 0.06 mm particles. In each test, 2.0 g of the material was added to an XFGC-80 single-trough flotation cell. Prior to the test, the sample was cleaned with supersonic waves. The reagents were added in the following order: (a) NaOH with 3 min of conditioning; (b) 1
104 mol/L CuSO4 with 5 min of conditioning; and (c) 5
105 mol/L xanthate with 5 min of conditioning. The flotation time was set to 3 min in all of the single-mineral experiments.

6.4.2 Adsorption of OHe and CaOHþ on pyrite surface The adsorption sites of hydroxyl and calcium hydroxyl molecules (OH and CaOHþ) were tested to determine the stable adsorption configuration of the molecules on pyrite surfaces. Fig. 6.24 shows the possible adsorption sites of OH and CaOHþ on pyrite surfaces, and the values shown in the figure indicate the atomic distance in angstroms. The calculation results shown in Table 6.4 suggest that the adsorption energy of a hydroxyl O atom on the surface Fe site (264.99 kJ mol1) was far less than that on a surface S site (163.65 kJ mol1), which indicates that the surface Fe atom was the active site for OH adsorption. The adsorption energy of CaOHþ on Hollow 1 (the configuration shown in Fig. 6.24C) was 191.60 kJ mol1, which was higher than that on Hollow 2 (configuration shown

Figure 6.24 Adsorption configurations of OH and CaOHþ on pyrite surface. OHe O atom on surface S site (A) and surface Fe site (B), and CaOHþ on Hollow 1 (A) and Hollow 2 (B).

Interaction of flotation reagents with mineral surface

269

Table 6.4: Adsorption energies of OH¡ and CaOHþ on different surface sites. Adsorption site OH



O on S site O on Fe site Hollow 1 Hollow 2

CaOHþ

Adsorption energy/(kJ/mol) 163.65 264.99 191.60 276.62

in Fig. 6.24D, with an O atom adsorbed on a surface Fe atom and a Ca adsorbed on surface S atoms) at 276.62 kJ mol1. This result suggests that the latter site (Hollow 2) would be the stable configuration for CaOHþ adsorption on the pyrite surface. Based on the calculated adsorption energies, the depression of pyrite by lime (CaO) was expected to be stronger than the depression by sodium hydroxide (NaOH). In addition, we have found that the adsorption energy of H2O molecule on pyrite surface was only 63.68 kJ/mol. This suggested that although water molecule may have influence on the pyrite surface properties, the strong chemical adsorption of OH and CaOHþ still plays a dominant role on the pyrite surface. ˚ ) was shorter than that The FeeO atomic distance on the OH adsorption surface (1.843 A þ ˚ on the CaOH adsorption surface (2.092 A). In addition, the Mulliken population of the FeeO bond shown in Table 6.5 suggests that the population of FeeO bond on the OH adsorption surface (0.42) was greater than that on the CaOHþ adsorption surface (0.25). Furthermore, the electron density map shown in Fig. 6.25 indicates that the FeeO interaction on the OH adsorption surface was apparently more covalent (i.e., exhibited greater electron density in the interatomic region) than that on the CaOHþ adsorption surface. However, a comparison of the adsorption energies of OH and CaOHþ on the pyrite surface indicated that the adsorption of CaOHþ was stronger than that of OH. This result suggested that the presence of Ca would greatly enhance the adsorption of CaOHþ on the pyrite surface, although the adsorption of the eOH group in CaOHþ was weaker than the adsorption of OH. In addition, the adsorption of Ca on the pyrite surface enhanced the hydrophilicity of the pyrite surface, which also contributed to the depressing effect of CaO on the pyrite. The surface Fe atoms have been confirmed to be the active sites for the interaction of xanthate with pyrite. However, our calculation showed that the active Fe sites were reduced, due to the adsorption of OH and CaOHþ, and this finding would not be Table 6.5: Mulliken population of bond forming on OH¡ and CaOHþ adsorbed surface. Bond 

OH CaOHþ

OeFe OeFe1

Higher population value indicates stronger covalent interaction between atoms.

Population 0.42 0.25

270 Chapter 6

Figure 6.25 Electron density maps of bonded FeeO atoms. After adsorption of OH (A) and CaOHþ (B). Greater degree of electron overlaps indicates stronger covalent interaction.

conducive to the interaction of xanthate with pyrite. In addition, the partial surface S atoms were shown to be covered, due to the adsorption of CaOHþ, and we predict that to recover the floatability of pyrite, the Ca adsorbed on the pyrite surface should be removed by Na2CO3, NaHCO3, H2SO4, etc. Figs. 6.26 and 6.27, respectively, show the DOS of bonding FeeO atoms before and after OH and CaOHþ adsorption. For the (100) surface, the upper parts of the valence band and conduction band had significant contributions from the surface Fe 3d states, and a significant band gap existed between the valence band and conduction band. The hydroxyl 4

O before adsorption

Density of states(eletrons/eV)

2

EF

O 2p

O 2s

0 2

O after adsorption

O 2p

0 4

Fe before adsorption

Fe 3d

2 0 4

Fe after adsorption

Fe 3d

2 0

-8

-6

-4

-2

Energy/eV

0

2

Figure 6.26 Bonding FeeO atoms before and after OH adsorption. The zero of energy has been set at the Fermi level EF.

Interaction of flotation reagents with mineral surface 6 4

O before adsorption

EF

O 2p

O 2s

2

Density of states(eletrons/eV)

271

0 4

O after adsorption

2

O 2p

0 4

Fe1 before adsorption

Fe 3d

2 0 4

Fe1 after adsorption

Fe 3d

2 0

-8

-6

-4

-2

Energy/eV

0

2

Figure 6.27 Bonding FeeO atoms before and after CaOHþ adsorption. The zero of energy has been set at the Fermi level EF.

O 2p state was occupied in the vicinity of the Fermi level (EF), thereby forming six apparent DOS peaks. After OH adsorption, the DOS peak of O 2p was lowered, and the nonlocality of the 2p electrons was enhanced. The Fe 3d states at the upper valence band, however, were decreased, and the two DOS peaks were split into three peaks. In addition, the band gap between valence band and conduction band was significantly lowered, and significant hybridization occurred between the O 2p and Fe 3d states at an energy of 0.3 eV. Compared to OH, the O 2p states of CaOHþ were located at a lower energy level (about 2 eV), and the change in the Fe (Fe1) 3d states after CaOHþ adsorption was less obvious than after OH adsorption (see Fig. 6.27). In addition, weak interactions occurred between the Fe 3d and O 2p states. The differences in the spin DOS of FeeO atoms on the OH- and CaOHþ-adsorbed surfaces shown in Fig. 6.28 could also reflect differences in the adsorption behaviors of OH and CaOHþ on the pyrite surface. Based on Fig. 6.28, the Fe and O atoms on the OH-adsorbed surface are known to be in spin-polarized states, whereas they were in low-spin states on the CaOHþ-adsorbed surface. Based on the spin calculations, we speculate that the adsorption of OH may promote the oxidation of pyrite. The adsorption of OH and CaOHþ on the pyrite surface resulted in changes in the atomic charge, and the details of the charge transfer between the ions and the pyrite surface could be determined by analysis of the changes in the atomic charges and orbital populations, as shown in Table 6.6. For OH adsorption, the O 2p state obtained electrons from the surface Fe 3d state, which resulted in increase in the negative charge of the O atom and an

272 Chapter 6 O 2p

O atom

Fe atom

-8

-6

EF

O atom

Fe atom

Fe 3d

-4 -2 Energy/eV alpha

0

2

-8

EF

O 2p

Fe 3d

-6

-4 -2 Energy/eV alpha

beta

0

2

beta

Figure 6.28 Spin DOS of FeeO atoms on OH and CaOHþ adsorption surfaces. Table 6.6: Mulliken atomic charge and population before and after OH¡ and CaOHþ adsorption. Adsorbate e

OH

Atom O Fe

CaOHþ

Ca S1 Fe1 Fe2 O

Adsorption status Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption

s

p

d

1.95 1.89 0.34 0.35 3.02 2.15 1.86 1.84 0.34 0.32 0.34 0.37 1.86 1.86

4.62 4.88 0.43 0.45 5.99 5.99 4.25 4.34 0.43 0.51 0.43 0.77 5.22 5.01

0.00 0.00 7.15 6.88 0.44 0.64 0.00 0.00 7.15 7.10 7.15 7.19 0.00 0.00

Charge (unit charge) 0.57 0.77 0.08 0.32 0.55 1.22 0.10 0.18 0.08 0.07 0.08 0.33 1.08 0.87

increase in the positive charge of the Fe atom. For CaOHþ adsorption, however, the O 2p state lost electrons to the surface Fe1 4p state, which resulted in a decrease in the negative charge of the O atom and almost unchanged Fe charge. The Ca atom lost a large amount of charge to the surface and was more positively charged, whereas the surface S1 and Fe2 atoms, which were near the Ca atom, obtained electrons from Ca and were more negatively charged. Our calculation results showed that the calcium hydroxyl molecule lost charges to the pyrite surface, which resulted in electron accumulation on the pyrite surface. This result suggested that the oxidation of pyrite would be hindered with the adsorption of calcium

Interaction of flotation reagents with mineral surface

273

hydroxyl, and consequently, the formation of dixanthogen on the pyrite surface would be inhibited. This result was consistent with those of Zhang et al. [65]. Using alternating current impedance measurements on pyrite surfaces, they have shown that the surface resistance (Rs) of pyrite increased from 48.2 U cm2 at pH 12.1 adjusted with NaOH, and to 232.6 U cm2 at pH 12.1 adjusted with CaO. The authors have suggested that the presence of CaO may greatly hinder the oxidation of the pyrite surface.

6.4.3 Copper activation of pyrite depressed by NaOH and CaO Using experimental methods, Wang et al. have shown that no iron is liberated from pyrite during the adsorption of copper (Cu(II)) by pyrite [59]. Weisener and Gerson [57,58] and Voigt et al. [63,66e69] have found that copper would coordinate to sulfur on the surface of pyrite to form CueS surface species, which accounted for the Cu activation flotation of pyrite. The formation of copper on pyrite was calculated in this research, and the calculation results shown in Table 6.7 suggested that the substitution energy of Cu substituting for surface Fe was þ665.42 kJ mol1. This result suggested that Cu could not exist on the pyrite surface by substituting for surface Fe. The adsorption energy of Cu on a surface S site was 119.61 kJ mol1, which suggested that Cu would be chemically adsorbed on the pyrite surface; this result was consistent with the experimental results. Hence, the surface S sites would be the active sites for Cu adsorption, and the adsorption configuration of Cu ˚ , which on an S site is shown in Fig. 6.29. The atomic distance of CueS was 2.109 A suggests covalent bonding between the atoms (see Fig. 6.29A), and Fig. 6.29B clearly shows the substantial electron density in the interatomic region. However, our calculations on the adsorption of CaOHþ on the pyrite surface have shown that partial surface S sites would be covered by Ca. As a result, we speculate that the Cu activation of pyrite after depressing by CaO would be more difficult than by NaOH. Comparison tests were performed on Cu activation of pyrite after depression by CaO and after depression by NaOH. As shown in Fig. 6.30, with BX being used as a collector and CuSO4 as an activator, the recovery of pyrite was investigated as a function of the pH adjusted with NaOH and CaO. The pyrite flotation with the pH adjusted with CaO was worse than with the pH adjusted with NaOH. At pH < 11, when NaOH was used as a depressant, the recovery of pyrite after Cu activation was greater than 80%. When CaO Table 6.7: Formation energy of copper on pyrite surface in different forms. Existence form of Cu

Formation energy (kJ/mol)

Cu substituting for Fe Cu adsorption on S

þ665.42 119.61

274 Chapter 6

Figure 6.29 (A) Adsorption configuration of Cu on pyrite surface and (B) electron density maps of bonding CueS atoms. 100

Recovery (%)

80

pH adjusted with NaOH

60

pH adjusted with CaO

40 20 0

9

10

pH

11

12

Figure 6.30 Recovery of pyrite as a function of the pH adjusted with NaOH and CaO. Conditions were CuSO4 of 1
104 mol/L; butyl xanthate of 5
105 mol/L.

was used as a depressant, the recovery of pyrite after Cu activation was less than 40%. In addition, the recovery of pyrite decreased to 60% when the pH value increased to 11.5 and NaOH was used as a depressant, whereas the recovery of pyrite remained constant at an increased pH value when CaO was used as a depressant. In a low-alkali medium adjusted with NaOH (without addition of CuSO4), competitive adsorption occurred between OH and xanthate on the pyrite surface Fe sites, and the pyrite was, therefore, depressed. When CuSO4 was added to the pulp, copper ions were adsorbed onto the surface S sites, and the Cu‒xanthate, which accounted for the pyrite flotation, formed on the pyrite surface after the addition of xanthate. Hence, the pyrite depressed by NaOH had good floatability after activation by Cu. However, the pyrite depressed by CaO had poor floatability. This was due to the fact that the partial surface S sites were firmly adsorbed by CaOHþ, which hindered the adsorption of Cu.

Interaction of flotation reagents with mineral surface

275

6.5 The adsorption of cyanide on pyrite, marcasite, and pyrrhotite Cyanide, mainly as sodium cyanide (NaCN) and potassium cyanide (KCN), is an effective depressant of nonferrous metal sulfide minerals during flotation. The hydrolyzates of cyanide are HCN and CN. NaCN ¼ Naþ þ CN CN þ H2 O ¼ HCN þ OH ½HCN½OH  ¼ Khydrolysis ¼ 2.1
105 ½CN 

(6.14) (6.15) (6.16)

The hydrolyzate product hydrogen cyanide (HCN) is extremely dangerous, so cyanides must always be used in an alkaline medium, because the free alkali in solution will force the hydrolysis reaction (6.15) to the left. Cyanide is the most commonly used reagent for increasing the separation efficiency of metal sulfide minerals by flotation. Pretty early on, Sutherland and Wark [70,71]studied the depression of sulfide minerals by cyanide in the presence of several xanthate collectors. Their work illustrates the effectiveness of cyanide in cyanide mineral separation by flotation and has been regarded as a standard reference for industry application of in flotation for many years. Since then, expanded studies have been carried out by many researchers [72e77]. For example, Kostovic Milena [72] studied the depressing effect of the cyanide salts (NaCN, K3[Fe(CN)6] and K4[Fe(CN)6]), as well as ferrous/ferric salts (FeSO4 and Fe2(SO4)3) on the floatability of pyrite in the presence of xanthates as collector. The results showed that all tested depressants reduce the collection ability of pyrite with K-butyl xanthate. Different combinations of reagents FeSO4 and/or Fe2(SO4)3 with NaCN have the greatest depressing effect on pyrite, while the complex cyanide salts have much less depressing effect. Despite a number of studies on the depression effect of cyanide, the mechanism on iron sulfide minerals is not entirely understood. In general, there are two explanations for the depression effect for cyanide on the flotation of iron sulfide minerals with xanthate as collector. Some researchers [61,78]thought that free cyanide preferentially adsorbs on iron sulfide mineral surfaces as iron cyanide compounds, hence inhibiting the chemisorption and oxidation of xanthate, hampering flotation recovery. Other researchers believed that free cyanide inhibits the electrochemical activities and decreases the mixed potential on mineral surfaces, preventing the chemisorption and oxidation of xanthate [79]. The two explanations were analyzed further by the thermodynamic calculations and spectrophotometric studies by Guo et al. [80]. However, Guo draw a conclusion that the depression effect of free cyanide on iron sulfide minerals on the basis of thermodynamic calculations and spectrophotometric studies may be questionable. According to their

276 Chapter 6 analysis, the existence of insoluble iron cyanide surface species remains uncertain, and it is difficult to correlate the spectrophotometric studies to flotation behavior since much higher cyanide concentrations have to be used in the spectrophotometric studies due to their detection limit. Common iron sulfides include pyrite (FeS2), marcasite (FeS2), and pyrrhotite (FexS1-x), which often coexist with other metal sulfides such as copper, lead, and zinc sulfide ore. The depression of iron sulfides is very important for the recovery of other useful metal sulfides. Of all the iron sulfides, the depression of pyrite by free cyanide has been studied the most [79,81]. However, there are not many researches on the depressing effect of cyanide on marcasite and pyrrhotite. Although pyrite, marcasite, and pyrrhotite consist of iron atoms and sulfur atoms, their crystal structures and properties are very different, which leads to their different flotation behavior. As a result, it is significant to study the depression effect of cyanide on pyrite, marcasite, and pyrrhotite. In this paper, the interactions of cyanide ions with pyrite (100), marcasite (010), and pyrrhotite (001) surfaces were studied using DFT method, including adsorption models, adsorption energy, surface charge transfer, and DOS. Flotation separation testing of lead-zinc sulfide minerals was carried out using different dosages of sodium cyanide with the depressing effect of cyanide on pyrite, marcasite, and pyrrhotite. This study provides the theoretical explanations for different interactions between cyanide and pyrite, marcasite, and pyrrhotite surfaces.

6.5.1 Computational methods and models DFT calculations were carried out using the CASTEP program module developed by Payne et al. [45]. The GGA developed by Perdew and Wang (PW91) [46] was used to describe the exchange correlation effects. A Monkhorst-Pack k-point sampling density of 2
2
1 was used for all adsorption calculations [18]. In all calculations, a PW cutoff energy of 270 eV was used based on the test results. The convergence tolerances for geometry optimization calculations are shown in Table 6.8. Table 6.8: The convergence tolerances for geometry optimization calculations. Convergence tolerance parameters

Tolerances

Maximum displacement Maximum force Maximum energy change Maximum stress Self-consistent field (SCF)

˚ 0.002 A ˚ 0.08 eV A1 2.0
105 eV atom1 0.1 Gpa 2.0
106 eV atom1

Interaction of flotation reagents with mineral surface

277

The crystal structures and models of pyrite, marcasite, and pyrrhotite have been described in detail elsewhere [82]. Different crystal faces of pyrite, marcasite, and pyrrhotite were studied to obtain the most stable faces, including (100), (001), (010), (101), (110), (011), and (111). The most stable faces of pyrite, marcasite, and pyrrhotite through optimization test of various faces are (100), (101), and (001), respectively. All surfaces were obtained from the optimum unit cell volume of the bulk sulfides. The pyrite (100), marcasite (101), and pyrrhotite (001) surfaces were modeled using (2
2
1), (2
2
1), and (1
2
1) supercell geometries, respectively, where the ˚ vacuum gap above and below the central cell contains a slab with two surfaces and a 15 A surfaces separating adjacent mirror images of the slab. The surface energies of a range of surfaces with varying slab thicknesses were calculated to determine the slab size. The most stable surface models resulted from DFT calculations are shown in Fig. 6.31AdC. The bottom several atomic layers of the slab were kept fixed during all geometry optimization calculations. The surface atomic layers were relaxed. According to these three models (Fig. 6.31), the adsorption energies of CN on the pyrite, marcasite, and pyrrhotite surfaces, Mulliken populations, and DOS of the interaction between CN and pyrite, marcasite, and pyrrhotite surfaces were calculated using the first principles density functional calculation package CASTEP.

Figure 6.31 Slab models of (2
2) pyrite (100) (A), (2
2) marcasite (101) (B), and (1
2) pyrrhotite (001) (C) surfaces.

278 Chapter 6 The adsorption energies of cyanide ions on sulfide surfaces were calculated as follows: Eads ¼ ECN  =surface  ECN   Esurface

(6.17)

where Eads is the adsorption energy, ECN  =surface is the energy of the pyrite, marcasite, or pyrrhotite slab with adsorbed CN, ECN  is the energy of the CN calculated in a cubic cell, and Esurface is the energy of the pyrite, marcasite, or pyrrhotite slab. Ore samples were obtained from Dachang of Guangxi, China. The assays of multiple elements for ore are shown in Table 6.9. The main minerals in the ore are cassiterite, jamesonite, galena, pyrite, marmatite, pyrrhotite, and marcasite. The Pb and Sn exist mainly in the form of jamesonite with very little galena. The Zn and Sn exist in the form of marmatite and cassiterite, respectively. The gangue minerals include mainly quartz, mica, feldspar, and carbonates. The proportion of the minerals in the feed is shown in Table 6.10. The test ore is ground to 55% passing 0.074 mm 400 g/t BX and 400 g/t copper sulfate. From this concentrate, cassiterite was separated by gravity concentration. After cassiterite removal the bulk concentrate was ground to 85% passing 0.074 mm, and this material was used as the feed for separating the lead minerals and marmatite. In the bulk concentrate, the assays of iron, lead, antimony, zinc, and sulfur are 23.4%, 0.81%, 0.72%, 5.2%, and 30.1%, respectively. Hence the large amount of iron sulfides (pyrite, marmatite, pyrrhotite) need to be depressed in the separation of lead-zinc minerals. It should be noticed that the flotation behaviors of jamesonite are different from galena. Jamesonite is sensitive to the pulp pH, especially lime [83]. The pulp pH of flotation for jamesonite is lower than 9.5. However, iron sulfides could not be depressed in low alkaline condition. As a result, a certain amount of sodium cyanide was added in flotation operation. The flotation flowsheet of the ore feed is shown in Fig. 6.32. To understand the effect of NaCN dosage on pyrite, marcasite, and pyrrhotite, the grade and recovery of iron in concentrate were chemically analyzed. The low content of iron Table 6.9: Assays of multiple elements for ore. Elements

Fe

Sn

Pb

Sb

Zn

S

SiO2

CaO

Assays (%)

6.54

0.30

0.23

0.18

1.20

7.35

43.00

12.80

Table 6.10: The proportion of the minerals in the feed. Minerals Cassiterite Content (%)

0.40

Jamesonite

Galena

Pyrite (marcasite)

Pyrrhotite

Marmatite

0.50

0.08

6.84

1.94

1.22

Gangue Total 89.02

100

Interaction of flotation reagents with mineral surface

279

Feed Primary grinding -0.074 mm: 55% CuSO4: 400g/t Butylxanthate: 400 g/t Pine oil: 60 g/t Pb, Sb, Zn, S Bulk Flotation Regrinding -0.074 mm: 85% NaCN Sn gravity concentration

Pb, Sb Concentrate (Jamesonite)

Zn-S separation

Figure 6.32 Flotation flowsheet of the ore feed.

means a strong depressing effect of sodium cyanide on iron sulfide minerals. In addition, the effects of NaCN on the pyrite, marcasite, and pyrrhotite in concentrate with increasing NaCN dosage were analyzed by XRD (Cu Ka radiation) using a Rigaku D/MAX-2500 V diffractometer.

6.5.2 Adsorption of CNe on pyrite, marcasite, and pyrrhotite surfaces The adsorptions of cyanide ions on the pyrite (100), marcasite (010), and pyrrhotite (001) surfaces were studied on different adsorption sites, including that its molecular was parallel or perpendicular to the surface as well as located at top S and Fe atoms, bridge (parallel to FeeS, SeS bonds), and hollow sites (N on top Fe atom, C on top S atom; or N on top S atom, C on top Fe atom). Fig. 6.33 shows the most stable configurations of CN adsorption on pyrite, marcasite, and pyrrhotite surfaces through optimization testing. The adsorption energies of CN on the pyrite, marcasite, and pyrrhotite surfaces are displayed in Table 6.11, which shows that the adsorption energy of CN on the marcasite surface is the largest at 374.91 kJ/mol, followed by pyrrhotite at 364.34 kJ/mol and pyrite at 327.94 kJ/mol. According to Fig. 6.33, after cyanide ions adsorption, carbon is bonded to one iron atom of the pyrite surface. For marcasite, carbon is bonded to one sulfur atom, while nitrogen is bonded to one iron atom of the surface. As for pyrrhotite, only nitrogen is attached to one iron atom of the surface. These different configurations lead to different adsorption energies for cyanide ions on pyrite, marcasite, and pyrrhotite surfaces.

280 Chapter 6

Figure 6.33 Adsorption configurations of CN on pyrite (100) (A), marcasite (010) (B), and pyrrhotite (001) (C) surfaces. Table 6.11: Adsorption energies of CN¡ on sulfides surfaces (negative sign represents exothermic reaction). Sulfide Pyrite Marcasite Pyrrhotite

Crystal face (100) (010) (001)

Adsorption energy/(kJ mol

¡1

)

327.94 374.91 364.34

Table 6.12 shows the Mulliken bond populations between cyanide ions and pyrite, marcasite, and pyrrhotite surfaces. It is obvious that the CeFe bond population (0.35) of pyrite surface is smaller than NeFe population (0.91) of pyrrhotite surface. Greater bond populations indicate stronger covalent interactions. Therefore, the covalent interaction between CN and pyrrhotite surface is larger than that between CN and pyrite. Although the NeFe population of marcasite surface is smaller (0.27) than that of pyrrhotite surface, the existence of CeS bond increases the interaction between CN and marcasite. As a result, the interaction of CN and marcasite is stronger than that of CN and pyrrhotite.

Interaction of flotation reagents with mineral surface

281

Table 6.12: Mulliken bond populations of the interaction between CN¡ and sulfides surfaces. Bond type Pyrite Marcasite Pyrrhotite

˚) Length (A

Population

CeFe CeS NeFe NeFe

0.35 0.75 0.27 0.91

1.891 1.656 1.943 1.848

Tables 6.13e6.15 show Mulliken charge populations of CN atoms before and after adsorption on the pyrite, marcasite, and pyrrhotite surfaces. The calculated data indicate that carbon and/or nitrogen atoms of the CN gain electrons, while iron and/or sulfur atoms lose electrons in all systems. The gain of electrons for carbon and/or nitrogen atoms mainly is from C 2p/N 2p orbitals in the sulfides with a few contributions of C 2 s/N 2s orbitals. The appearance of Fe 4p orbitals may be due to the hybridization of Fe 3d, Fe 4s, and Fe 4p orbitals [84]. The loss of electrons from an iron atom on the pyrite surface mainly is from Fe 3d orbital, while for pyrrhotite surface the loss of electrons is from the common contribution of Fe 4s and Fe 4p orbitals. One more difference is that iron atom of pyrite surface interacts with carbon atom of cyanide ions, while iron atom of pyrrhotite surface interacts with Table 6.13: Mulliken charge populations of CN¡ adsorption on pyrite surface (s, p, and d represent s orbital, p orbital, and d orbital, respectively). Atomic label C N Fe

Adsorption status Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption

s

p

d

1.29 1.27 1.72 1.72 0.34 0.32

2.40 2.83 3.59 3.69 0.43 0.51

0.00 0.00 0.00 0.00 7.15 7.05

Charge/e 0.31 0.10 0.31 0.41 0.08 0.12

Table 6.14: Mulliken charge populations of CN¡ adsorption on marcasite surface (s, p, and d represent s orbital, p orbital, and d orbital, respectively). Atomic label C N S Fe

Adsorption status Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption

s

p

1.29 1.10 1.72 1.63 1.88 1.81 0.36 0.34

2.40 2.95 3.59 3.74 4.29 4.08 0.48 0.42

d

7.05 6.98

Charge/e 0.31 0.05 0.31 0.37 0.16 0.11 0.11 0.26

282 Chapter 6 Table 6.15: Mulliken charge populations of CN¡ adsorption on pyrrhotite surface (s, p, and d represent s orbital, p orbital, and d orbital, respectively). Atomic label C N Fe

Adsorption status Before adsorption After adsorption Before adsorption After adsorption Before adsorption After adsorption

s

p

1.29 1.31 1.72 1.73 0.48 0.40

2.40 2.84 3.59 3.63 0.46 0.36

d

6.73 6.75

Charge/e 0.31 0.15 0.31 0.36 0.33 0.50

nitrogen atom. The loss of electrons of marcasite surface mainly is from Fe 3d, Fe 4p, and S 2p orbitals with a few contribution of Fe 4s and S 3s orbitals. The DOS is often used for quick visual analysis of the electronic structure, and DOS analysis can help to understand the changes in electronic states of atoms in molecules and mineral crystals caused by the interactions between reagent molecules and mineral surfaces. Fig. 6.34 shows DOS results of interaction between the carbon atom of cyanide ions and the iron atom of the pyrite surface. It is observed that there exist some hybridizations of atom orbitals in DOS curve for CeFe. For metal and narrow gap semiconductors, significant physical processes occur in the vicinity of Fermi level. In the near Fermi level (2.3e0 eV), the electrons in hybrid p-d orbitals of the iron atom on pyrite surface interact with carbon 2p electrons. The electrons transfer from hybrid p-d

Figure 6.34 DOS of interactions between CN and pyrite surface.

Interaction of flotation reagents with mineral surface

283

orbitals of Fe to C 2p (Table 6.13). The gain of electrons for carbon mainly is from C 2p, and the loss of electrons for iron atom is from Fe 3d and 4p orbitals. The bonding of C 2p and Fe p-d hybrid orbitals (-3 to 1.3 eV) is very strong, while antibonding (1.3 to 0 eV) is weak, which results in the strong interaction between C and Fe. In the range of 8 to 4 eV, there exist the hybridizations of C 2s, C 2p, and Fe 3d orbitals (about 5.2 eV), C2s, C2p, and Fe 4s orbitals (about 6.5 eV). However, these hybridizations occur away from the Fermi level, so the effect is minimal. Fig. 6.35 shows DOS results of interactions between carbon and nitrogen atoms of cyanide ions and surface atoms of marcasite. In DOS curve of NeFe, there also exists the Fe p-d hybrid orbitals at about 3.5 eV, providing evidence for the Fe 4p orbital population in Mulliken charge distribution (Table 6.14). The bonding of N 2s, N 2p, and Fe p-d orbitals in the range of 9 to 4.6 eV is very weak, while antibonding of 4.6e0 eV is very strong, which results in the weak interaction between N and Fe. According to Table 6.2, the NeFe population is only 0.27. However, the bonding of C 2p and S 3p in the range of 7.7 to 4.4 eV is very strong, while antibonding of 4.4 to 0 eV is very weak. These results show that there is a strong interaction between C and S, which enhances the interaction between CN and marcasite surface. Fig. 6.36 shows DOS results of interactions between nitrogen atoms of cyanide ions and surface atoms of pyrrhotite. It is observed that there also exist the Fe p-d hybrid orbitals at

Figure 6.35 DOS of interactions between CN and marcasite surface.

284 Chapter 6

Figure 6.36 DOS of interactions between CN and pyrrhotite surface.

about 5.8, 2.5, and 1 eV. The bonding of the N 2s, N 2p, and the Fe p-d orbitals in the range of 3 to 2 eV is very strong, while antibonding of 2e0 eV is very weak, which results in the strong interaction between N and Fe on the pyrrhotite surface. The NeFe bond population of the pyrrhotite surface (0.91) is far larger than that of the marcasite surface (0.27). However, for pyrrhotite the combined strong interaction between CeS along with the weak NeFe interaction enhances the interaction between CN and marcasite, which leads to the bigger adsorption energy of CN on marcasite surface relative to the pyrrhotite surface.

6.5.3 Effect of sodium cyanide dosage on the grade and recovery of iron Fig. 6.37 shows the effect of sodium cyanide dosages on the grade and recovery of Fe in concentrate. It was found that the flotation recovery and grades of Fe decreased gradually with an increase of NaCN dosages, indicating that NaCN has a strong depressing effect on iron-bearing minerals. Fig. 6.38 shows the effect of sodium cyanide dosages on the recovery of Zn and Pb in concentrate. It is very clear that the flotation recovery of Pb increased, while that of Zn decreased with increasing NaCN dosages. The Pb exists mainly in the form of jamesonite, while the Zn exists in the form of marmatite, so the decreased recovery of Zn and increased recovery of Pb show that NaCN has the depressing effect on marmatite, while there is no depressing effect on jamesonite.

Interaction of flotation reagents with mineral surface

285

Figure 6.37 Effect of NaCN dosage on the grade and recovery of Fe.

Figure 6.38 Effect of NaCN dosage on the recovery of Zn and Pb.

In contrast to the concentrate, the recovery of Fe and Zn increased, while that of Pb decreased with increasing NaCN dosages in the tail, which further confirms that the depressing effect of NaCN on iron sulfides and marmatite. To study the depressing behavior of sodium cyanide on pyrite, marcasite, and pyrrhotite, XRD analysis was performed on concentrates from the testing with various doses of NaCN. Fig. 6.39 shows the XRD spectra of iron sulfides with different NaCN dosages. The diffraction peaks of pyrite, marcasite, and pyrrhotite of iron sulfide minerals are

286 Chapter 6

Figure 6.39 XRD spectra of iron sulfides with different NaCN dosage in PbeZn concentrate.

observed at 33.08, 52.00, and 33.99 degrees, 44.02 and 53.30 degrees, respectively. These relative intensities of the diffraction peaks for all three minerals decreases with increasing NaCN dosages from 400 to 600 g/t, indicating the depressing effect of NaCN on pyrite, marcasite, and pyrrhotite, and the depression effect is enhanced with the increase of NaCN dosages. It is observed from Fig. 6.39 that the value of XRD peak for pyrite decreases from 700 to 600, that of marcasite from 171 to 49, while that of pyrrhotite at 53.30 from 274 to 163. Obviously, the highest decrease in the peak intensity is marcasite, then pyrrhotite and pyrite in order, suggesting that the depressing effect of NaCN on marcasite is the strongest followed by pyrrhotite and pyrite. Prestidge et al. [81] also found that the depression action of cyanide was stronger on pyrrhotite than on pyrite. These results are in agreement with the theoretical calculation results that show that the adsorption energy of CN on the marcasite surface is the largest, followed by pyrrhotite, then pyrite.

6.6 Effect of water molecules on the thiol collector interaction on galena and sphalerite surfaces Lead sulfide (galena) and zinc sulfide (sphalerite) are the primary sources of lead and zinc and are commonly associated together in ore deposits. The separation of galena and sphalerite is generally carried out by flotation, which is used to separate a target mineral from complex ores. Flotation is a surface chemistry that takes advantage of the differences

Interaction of flotation reagents with mineral surface

287

in wettability at solid particle surfaces. Flotation separation is heavily dependent on the addition of collector molecules designed to selectively adsorb onto minerals and induce a hydrophobic surface for bubbleeparticle attachment [85,86]. The most common collectors used in sulfide mineral flotation are thiol reagents including xanthate, DTC, and DTP. Generally, DTC and DTP exhibit better selectivity than xanthate in the separation of lead-zinc. Experimentally, the adsorption of xanthate, DTC, and DTP at sulfide mineral surfaces has been studied using infrared and UV spectroscopies [8,14,87,88], X-ray adsorption spectroscopy [89], and thermochemical measurement [30,31,35,37]. EtX adsorption and its effect on wettability of galena were reported by Janczuk et al. [90]. Grano et al. [91] studied the interaction of EtX and sulfite in solution and its effect on galena flotation and xanthate adsorption by UV spectroscopy. Dusica et al. [87] investigated the effect of Pb(II) on the galena and sphalerite surface properties (hydrophobicity and charge of the surface), ethyl xanthate adsorption, and ethyl xanthate adsorption kinetics in alkaline medium. Besides experimental studies, computational techniques can greatly contribute to the knowledge of the surface properties and adsorption mechanism at the atomic scale. For example, Hung et al. [14] studied xanthate adsorption on pyrite FeS2 (110), (111) surfaces using DFT. Li et al. [43] studied the adsorption of O2 on As-, Co-, Ni-bearing, and perfect pyrite surfaces using DFT. Chen et al. [92] conducted computer modeling and microcalorimetry measuring to investigate the adsorption of xanthate, DTP, and DTC on galena and pyrite surfaces. The interaction between adsorbed ethyl xanthate on a clean Ge (111) surface and a hydroxylated surface was studied, using DFT [93]. Liu et al. [94] conducted a DFT study on the adsorption of thiophosphorous compounds on a sulfide mineral surface. The adsorption of the flotation reagent does not occur at the pristine mineral surface but at the water preadsorbed surface, so the presence of water molecule would certainly affect the surface reagent adsorption. It has been reported that the adsorption of water on the sulfide mineral surface could result in the surface relaxation and the change of the density of states of the surface atoms [95e97]. Becker et al. [98] observed surface proximity effects on semiconducting mineral surfaces such as galena (PbS) and pyrite (FeS2), which means the chemical reaction on one surface site influences the electronic structure and reactivity of neighboring sites on semiconducting mineral surfaces. The chemisorption or physical sorption on the mineral surface will affect the electron transfer and the reactivity of nearby surface sites. To ascertain the influence of water molecules on thiol collector adsorption at PbS and ZnS surfaces, the computational simulations of three thiol collectors including xanthate, DTC, and DTP adsorb at PbS and ZnS surfaces in the presence and absence of water were performed. The results can provide a micro mechanism of the selectivity of thiol collectors at the solidewater interface.

288 Chapter 6

6.6.1 Computational methods All calculations were performed in the framework of CASTEP [45]. The exchange correlation functional applied was the generalized gradient approximation (GGA) of PBE and PW91 [16,99,100]. The interactions between valence electrons and ionic core were represented by ultrasoft pseudopotentials [17]. Valence electron configurations considered in the study included Zn 3d104s2, Pb5d106s26p2, S 3s23p4, O 2s22p4, and H 1s1 states. Based on the test results, the PW cutoff energies of 390 and 300 eV were used for ZnS (110) and PbS (100) surfaces, respectively, and the Brillouin zone was sampled with Monkhorst [18] and Pack special of a 1
2
1 grid for surface calculations. For self-consistent electronic minimization, the Pulay density mixing method was employed with the convergence tolerance of 2.0
106 eV/atom. The convergence criteria for structure optimization and energy calculation were set to (a) energy tolerance of 2.0
105 eV/atom, (b) maximum ˚ , and (c) maximum displacement tolerance of 0.002 A ˚. force tolerance of 0.05 eV/A The ZnS (110) and PbS (100) surfaces were chosen as they are the most stable surfaces [101,102]. Surfaces were cleaved on the basis of the optimized bulk structure. The ˚, computed lattice parameters for the bulk ZnS and PbS were 5.471 and 6.015 A ˚ [103]. respectively, which are closed to the experimental values of 5.409 [101]and 5.935 A After testing the slab thickness, we constructed a (2
2) ZnS (110) surface with 10 ˚ atomic layers and a (4
2) PbS (100) surface with eight atomic layers separated by 15 A of vacuum, as shown in Fig. 6.40A and B.

Figure 6.40 The slab model of surfaces: (A) ZnS (110) surface and (B) PbS (100) surface.

Interaction of flotation reagents with mineral surface

289

For the ZnS surface, the four outermost atomic layers of the substrate were allowed to relax, while the six bottom-most atomic layers of the substrate were fixed to the bulk coordinates, and for the PbS surface the three outermost atomic layers of the substrate were allowed to relax, while the five bottom-most atomic layers of the substrate were fixed to the bulk coordinates in the adsorption calculations. The models of ethyl xanthate (C2H5OCS2), DTC (C2H6NCS2), and DTP (C2H6O2PS2) were optimized in the same cell with the sphalerite and galena surfaces, and the optimizations were performed at the gamma point in the Brillouin zone.

6.6.2 Effect of water molecule on the surface properties of ZnS (110) and PbS (100) Before the reagent adsorption, one water molecule was placed on the ZnS (110) and PbS (100) surfaces to investigate the effect of water on the surface properties. The optimized geometry configurations are shown in Fig. 6.41. For ZnS (110) surface, water prefers to ˚. adsorb on the surface Zn atom via its O atom with the ZneO length of 2.161 A The calculated adsorption energy is 69.23 kJ/mol, which suggests that the interaction between water molecule and ZnS surface is strong. On the PbS (100) surface, it was found that the adsorption of a single water molecule is ˚. mainly via its H atoms and surface S atoms with the SeH distances of 2.386 and 2.237 A The calculated adsorption energy was 28.32 kJ/mol, indicating that the interaction of water and PbS surface is relatively weak. It is noted that the adsorption energy of water on the ZnS (110) surface is greater than that of PbS (100) surface, suggesting that ZnS (110) surface exhibits a greater hydrophilic character than PbS (100) surface.

Figure 6.41 Interaction of water molecule with surfaces: (A) ZnS (110) surface and (B) PbS (100) surface.

290 Chapter 6 To discuss the influence of water adsorption on the surface properties of ZnS and PbS, the Mulliken charge and Fukui indices of surface atoms and the bond population of ZneS and PbeS are listed in Tables 6.16e6.18. For ZnS (110) surface, the surface Zn and S atoms charge more electrons after the adsorption of water molecule. However, Pb and S atoms on the PbS (100) surface have little change in Mulliken charge. It is suggested that the effect of water molecule on the electron distribution of ZnS (110) surface is greater than that of PbS (100) surface and may consequently influence adsorption occurring on the surface. It is well accepted that the interaction between xanthate and sulfide mineral is an electrochemical reaction that involves electron transfer reaction [104]. According to the principle of “hard and soft acids and bases” (The Pearson principle) [105], xanthate as a Table 6.16: Mulliken charge of ZnS (110) and PbS (100) surface atoms in the absence and presence of water molecule.

ZnS (110) surface

Atom label

s

p

d

Total

Charge/e

Zn S1 S2 Zn S1 S2 Pb1 Pb2 S1 S2 Pb1 Pb2 S1 S2

0.89 1.85 1.85 0.82 1.85 1.85 1.99 1.99 1.93 1.93 1.95 1.98 1.92 1.92

0.79 4.64 4.64 0.77 4.69 4.69 1.41 1.41 4.75 4.75 1.42 1.38 4.77 4.78

9.98 0.00 0.00 9.98 0.00 0.00 10.00 10.00 0.00 0.00 10.00 10.00 0.00 0.00

11.66 6.50 6.50 11.57 6.54 6.54 13.39 13.39 6.68 6.68 13.38 13.36 6.70 6.70

0.34 0.50 0.50 0.43 0.54 0.54 0.61 0.61 0.68 0.68 0.62 0.64 0.70 0.70

In the absence of water molecule In the presence of water molecule

PbS (100) surface

In the absence of water molecule In the presence of water molecule

Table 6.17: The Fukui indices values of surface atoms on the ZnS (110) and PbS (100) surfaces in the absence and presence of water molecule. Atom label ZnS (110) surface

PbS (100) surface

In the absence of H2O In the presence of H2O In the absence of H2O In the presence of H2O In the absence of H2O In the presence of H2O In the absence of H2O In the presence of H2O

Zn

fþ 0.020 0.008

S Pb S

f¡

0.056 0.035 0.128 0.144 0.002 0.007

Interaction of flotation reagents with mineral surface

291

Table 6.18: Mulliken ZneS and PbeS bond populations of ZnS (110) and PbS (100) surfaces in the absence and presence of water molecule. Bond label ZnS (110) surface

In the absence of water molecule In the presence of water molecule

PbS (100) surface

In the absence of water molecule In the presence of water molecule

ZneS3 ZneS4 ZneS5 ZneS3 ZneS4 ZneS5 Pb1eS1 Pb1eS2 Pb2eS1 Pb2eS2 Pb1eS1 Pb1eS2 Pb2eS1 Pb2eS2

Population 0.67 0.67 0.56 0.63 0.63 0.46 0.21 0.09 0.09 0.21 0.19 0.08 0.07 0.17

Lewis base exhibits a nucleophilic character that is easy to react with the mineral that has a large electrophilic character. The Fukui functions [106e109] developed defined by Parr and Yang et al. provide a qualitative way of measuring and displaying the reactivity of regions of a molecule. The reactivity of a mineral surface atom can be characterized by the Fukui functions [110]. Ke et al. [111] studied reactivity of Pb, S, and Fe atoms in the galvanic interaction between galena and pyrite using Fukui indices, f þ(r) and f (r), which are obtained via Eqs. (6.18) and (6.19). 1 ðrÞ  rN ðrÞÞ (6.18) ðr DN NþD 1 ðr ðrÞ  rND ðrÞÞ (6.19) f  ðrÞ ¼ DN N Where the f þ(r) function measures the reactivity with respect to nucleophilic attack at the site r. The larger value of f þ(r) indicates that it can accept more electrons during a nucleophilic attack. Conversely, the f (r) function measures the reactivity with respect to electrophilic attack at the site r [112]. f þ ðrÞ ¼

The calculated Fukui indices of surface atoms on the ZnS (110) and PbS (100) surfaces in the absence and presence of water molecule are listed in Table 6.17. It is noted from Table 6.17 that the f þ(Zn) decreases from 0.02 to 0.008 in the presence of water molecule, suggesting that the Zn site could accept fewer electrons during a nucleophilic attack from the xanthate. For ZnS S atom, the value of f (S) decreases from 0.056 to 0.035, which means the presence of water molecule will reduce the reactivity of S atom with respect to electrophilic attack.

292 Chapter 6 While for the PbS (100) surface Pb atom, the f þ(Pb) increases from 0.128 to 0.144, indicating an improved nucleophilic attack ability, which will favor the reaction with xanthate. Moreover, the f (S) of PbS S atom increases from 0.002 to 0.007, suggesting an enhanced reactivity during electrophilic attack. Comparing the two minerals, it is found that the presence of water improves the reactivity of PbS (100) surface atoms but reduces the reactivity of ZnS (110) surface atoms during the reaction with xanthate. In the report of our previous study [95], the electronic structures and properties of the sulfide mineral surfaces were influenced by H2O molecule. The DOS of PbS surface activate evidently after adsorbing H2O. Therefore, it could predict that the interaction of xanthate with PbS is stronger than ZnS, especially in the presence of water molecule. The Mulliken bond population represents the covalent property of the bond. The greater the population value is, the greater is the covalency of the bond. It is found from Table 6.18 that the population of ZneS bond is around 0.67 and that of PbeS bond is less than 0.2, suggesting that ZneS bond exhibits covalent character and PbeS bond shows ionic character. After water adsorption, the populations of ZneS bonds decrease more than that of PbeS bonds, indicating that water adsorption could reduce the covalent binding between Zn and S atoms but have little influence on PbeS bond. The partial density of states (PDOS) of interactions between ZneO and HeS on ZnS surface are shown in Fig. 6.42A and B, respectively. From Fig. 6.42A, it is clearly seen that the DOS of Zn dsp hybridization located around e5 to 0 eV and the Zn spd-O sp bonding DOS peak appear in this interval, suggesting a relatively strong interaction between Zn and O atoms. Fig. 6.42B shows that the interaction of water H atom with surface S atom mainly involves the S 3p and H 1s orbitals. The PDOS of interactions between Pb-O and HeS are shown in Fig. 6.43A and B, respectively. For the galena surface, the interaction of water molecule with the surface is mainly between S and H atoms. It is shown in Fig. 6.43B that the interaction between SeH atoms is via the S 3p-H 1s states located around 8.2we7.3 eV and 4.7we4.2 eV.

6.6.3 Effect of water molecule on the sphalerite surface reagent adsorption The adsorption configurations and energies of xanthate, DTP, and DTC on sphalerite surfaces in the absence of water are presented in Fig. 6.44. It is found from Fig. 6.44 that the distances between xanthate/DTP/DTCS atom and the sphalerite Zn atom are around ˚ , which are close to the sum of atomic radius of Zn and S of 2.37 A ˚. 2.36e2.45 A This implies that there is a relative strong interaction between these three reagents and sphalerite surface. The calculated adsorption energies are 87.63, 100.3, and 60.49 kJ/mol, respectively, which are supposed as the chemisorption. It could be concluded from the calculated results that xanthate, DTP, and DTC could float sphalerite,

Interaction of flotation reagents with mineral surface

293

(A) Density of States(electrons/eV)

5

Zn 4s Zn 4p Zn 3d

EF

Zn 3d

4

O 2s O 2p

O 2p

3 Zn 4s

2

Zn 4p O 2s

1

Zn 4p

Zn 4s

0 -6

-4

-2

0

2

Energy /eV

4

(B) Density of States(electrons/eV)

1.00

EF

S 3p

H 1s S 3s S 3p

0.75

0.50

S 3p H 1s

0.25

S 3s

S 3s

H 1s

0.00 -6

-4

-2

0

2

4

Energy /eV

Figure 6.42 DOS of interaction of water molecule with ZnS (110) surface. (A) Interaction of O atom with surface Zn atom, (B) Interaction of H atom with surface S atom.

which does not corresponded with the flotation result. It is well known that unactivated sphalerite responds very poorly to the short chain alkyl xanthate. In addition, DTP and DTC are usually used for the preferential flotation of lead in lead-zinc separation, and they show weak collecting ability for sphalerite. Theoretically speaking, xanthate, DTC, and DTP could not float unactivated sphalerite. First, the collector could hardly electrochemically adsorb on the sphalerite surface because pure sphalerite is an insulator and lacks conductivity. Second, the solubility products (Ksp) of these three collectors with Zn2þ are relatively high, which could not produce a stable product in the aqueous environment. Third, sphalerite shows a relatively strong hydrophilic characteristic, and the natural floatability is weak, which is not in favor of thiol collector adsorption. Therefore, the model of adsorption of collector molecule on the sphalerite surface in the absence of water molecule is not suitable to simulate the real flotation process. The results indicate that the effect of water should be considered.

294 Chapter 6 (A) Density of States(electrons/eV)

5

EF

Pb 6s Pb 6p

O 2p

4

O 2s O 2p

O 2p

3

Pb 6s 2

Pb 6p

O 2s Pb 6p

1

Pb 6p

Pb 6s

Pb 6s 0 -8

-6

-4

-2

Energy /eV

0

2

4

(B) Density of States(electrons/eV)

1.5

EF

H 1s S 3s S 3p

H 1s

1.0

S 3p H 1s

S 3p

0.5

S 3s S 3p

S 3s

0.0 -8

-6

-4

-2

0

2

4

Energy /eV

Figure 6.43 DOS of interaction of water molecule with PbS (100) surface. (A) Interaction of O atom with surface Pb atom, (B) Interaction of H atom with surface S atom.

It is found from the flotation practice that galena exhibits certain natural floatability but sphalerite does not show natural floatability. It is reported [113] that the contact angles of galena and sphalerite are of 82 and 44 degrees, respectively. These experimental values agree well with the microcalorimetry results that the heat of wetting for galena and sphalerite are 2.0 and 4.04 J/m2, respectively. The results discussed in Section 6.6.2 confirm that sphalerite is more hydrophilic than galena. The adsorption configurations and energies of xanthate, DTP, and DTC on the sphalerite surface in the presence of water are shown in Fig. 6.45. It is notable that after water adsorption on the sphalerite, the adsorption energies of xanthate, DTP, and DTC decrease dramatically (5.83, 37.79, and 7.33 kJ/mol), suggesting that no chemisorption occurs on the water preadsorbed sphalerite surface, and the presence of water molecule will

Interaction of flotation reagents with mineral surface (A)

295

(B)

Ethyl xanthate

DTP

(C)

DTC

Figure 6.44 The adsorption configurations and energies of xanthate, DTP, and DTC on sphalerite surfaces in the absence of water.

hinder the adsorption of the collector. This is in accordance with the prediction of Fukui indices results (discussed in Section 6.6.2), which suggests the adsorption of water could decrease the electrochemical reactivity of sphalerite Zn and S atoms, and consequently not in favor of the interaction with the xanthate.

296 Chapter 6 (A)

(B)

Ethyl xanthate

DTP

(C)

DTC

Figure 6.45 The adsorption configurations and energies of xanthate, DTP, and DTC on the sphalerite surfaces in the presence of water.

Interaction of flotation reagents with mineral surface

297

In addition, the adsorption energy cannot represent the interaction between the reagent and the surface but include the combined adsorption of the reagent, water, and the surface. Comparing the distance between water O and the surface Zn atom for the three reagents in ˚ for DTP, which is shorter than Fig. 6.45, it is found that the distance of ZneO is 2.158 A that of xanthate and DTC. Therefore, a large value of adsorption energy for DTP may ascribe to the adsorption of water but not DTP on the sphalerite surface. Furthermore, we could discuss the interaction according to the bond length. It is noticed that the bond lengths between xanthate S and sphalerite Zn atoms (S1eZn1 and S2eZn2) ˚ , which exceed the sum of the S and Zn atomic radii, suggesting are 3.778 and 4.206 A that no chemisorption occurs on the water preadsorbed sphalerite surface. For DTP and DTC, the distances between reagent S atoms and surface Zn atoms are as long as ˚ , which are much longer than the interacting distance. It could be concluded that 4.5e4.8 A xanthate, DTP, and DTC cannot adsorb on the water preadsorbed sphalerite surface, which is in accordance with the flotation result.

6.6.4 Effect of water molecule on galena surface adsorption The adsorption configurations and energies of xanthate, DTP, and DTC on the galena surfaces in the absence of water are shown in Fig. 6.46. Concerning the adsorption energy, the interacting order is DTP (96.67 kJ/mol), xanthate (80.93 kJ/mol), and DTC (55.21 kJ/mol). Considering the interacting distance, the distances between DTP and ˚ , S2ePb2: 2.853 A ˚ ) are the shortest, while for xanthate galena surface (S1ePb1: 2.957 A and DTC, they are exactly the same, suggesting that the interaction of xanthate and DTC with the galena surface is the same. The adsorption energy order for xanthate and DTC does not agree well with the interacting distance result. The reason may be ascribed to the structural distortion during the adsorption that would consume the energy. The adsorption configurations and energies of xanthate, DTP, and DTC on the galena surfaces in the presence of water are shown in Fig. 6.47. According to the adsorption energy, the three reagents could adsorb on the water preadsorbed PbS (100) surface. The adsorption of water molecules strengthens the interaction of DTC and weakens the interaction of xanthate, and it has little influence on the DTP adsorption. Comparing Figs. 6.46 and 6.47, the distance between the reagent S and surface Pb atoms becomes shorter after water adsorption, suggesting that the presence of water will improve the adsorption of the reagent. For the DTP, xanthate, and DTC, the interacting distance ˚ , respectively, which indicates that the effect of water reduces 0.05, 0.07, and 0.10 A molecules on the DTC adsorption is the greatest.

298 Chapter 6 (A)

(B)

Ethyl xanthate

DTP

(C)

DTC

Figure 6.46 The adsorption configurations and energies of xanthate, DTP, and DTC on the galena (100) surfaces in the absence of water.

6.6.5 Effect of water molecule on the selectivity of collector in the separation of lead and zinc sulfide In the presence of water, the adsorption energy could not represent the interaction between the single collector molecule and the mineral surface. We need to find another parameter

Interaction of flotation reagents with mineral surface (A)

299

(B)

Ethyl xanthate

DTP

(C)

DTC

Figure 6.47 The adsorption configurations and energies of xanthate, DTP, and DTC on the galena (100) surfaces in the presence of water.

to define the strength of the interaction. Generally speaking, to form a covalent bonding, the interacting distance of two atoms (d1) should close to the sum of atomic radii between two atoms (d2) to cause the overlap of the electrons. Therefore, the value of Dd (Dd ¼ d1d2) could represent the strength of the interaction. When the interaction distance (d1) exceeds the sum of atomic radii between the two atoms (d2), it could be considered that there is no chemical adsorption between the collector and the mineral surface. In our case, d1 is the average distance between collector S atoms and the surface Zn/Pb atoms, and d2 is the sum of atomic radii of Zn and S or Pb and S. The smaller value of Dd indicates the larger electron overlap between two atoms and the stronger chemical interaction of the collector and the mineral surface. The values of d1, d2, and Dd for three collectors on the ZnS (110) and PbS (100) surfaces in the absence and presence of water are listed in Table 6.19.

300 Chapter 6 Table 6.19: Average interacting distance between the collector and the galena/sphalerite surface in the presence and absence of water molecule.

Collector In the absence of water

Xanthate

DTP

DTC

In the presence of water

Xanthate

DTP

DTC

Mineral surface PbS (100) ZnS (110) PbS (100) ZnS (110) PbS (100) ZnS (110) PbS (100) ZnS (110) PbS (100) ZnS (110) PbS (100) ZnS (110)

Average interacting ˚) distance d1 (A

Sum of atomic ˚) radius d2 (A

Strength of interaction ˚) Dd [ d1¡d2 (A

2.932

2.79

0.142

2.374

2.37

0.004

2.855

2.79

0.065

2.384

2.37

0.104

2.932

2.79

0.142

2.450

2.37

0.08

2.863

2.79

0.073

4.708

2.37

2.338

2.808

2.79

0.0018

3.992

2.37

1.622

2.834

2.79

0.044

4.757

2.37

2.387

In the absence of water, values of Dd for the sphalerite are all smaller than galena, indicating that the interaction between three collectors and sphalerite surface are stronger, which is not in correspondence with the flotation practice. In the presence of water, the value of Dd for sphalerite is much larger than the sum of atomic radii of ZneS (d2), indicating that these three collectors could not adsorb on the sphalerite surface in the solution, which corresponds well with the observation of flotation experiment. For the galena, the order of Dd is DTP ＜DTC＜ xanthate, indicating that the interaction of DTP is the strongest, then the DTC, and the interaction of xanthate is the weakest. It is well known that in the flotation of sulfide lead and zinc ores, DTP and DTC show better selectivity than xanthate. DTP exhibits a good selectivity used in the weak alkaline pulp, and DTC is usually used in the high-alkaline pulp [114].

Interaction of flotation reagents with mineral surface

301

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CHAPTER 7

Electronic structures and surface adsorption of impurity-bearing sulfide minerals In the flotation of sulfide minerals, it is often found that the same mineral from different deposits or the same mineral from the same deposit but from different sections of the deposit has great differences in flotation behavior. For example, for pyrite, Taneomi Harada has studied the difference in floatability of nine pyrites in Japan [1]. Chen et al. studied the difference in floatability of pyrite from eight different ore deposits in China [2]. Tsunemasa Imaizumi studied the difference in floatability of 10 pyrite samples from different parts of the Kuroko deposit in Japan [3], and found that even the pyrites in different parts of the same deposit have large differences in flotation behavior. For sphalerite, it has been found in industrial practice that sphalerite from a different deposit or different parts in the same deposit has different colors due to different impurities, from light green, brown, and dark brown to steel gray. The sphalerite of various colors has a large difference in floatability. The cadmium-containing sphalerite has better floatability, while the iron-containing sphalerite has worse floatability. Galena, silver, antimony, and copper impurities can improve the floatability, while zinc, manganese, and antimony impurities can reduce the floatability [4,5]. The flotation of sulfide ore is an electrochemical process, and the electrochemical properties of the sulfide minerals determine the flotation behavior of the mineral. Most sulfide minerals have a band gap value of 0e2 eV, such as galena with a band gap of 0.4 eV, pyrite with a band gap of 0.9 eV, and chalcopyrite with a band gap of 0.6 eV. According to the band theory, the bandwidth of semiconductors is between 0 and 3.0 eV, therefore sulfide minerals are typical semiconductors, and the conductivity of sulfide minerals is the basis of flotation electrochemistry of sulfide minerals. There are more or less defects in the actual minerals. The presence of lattice defects has a significant effect on the properties of the semiconductor. For example, the resistivity of silicon is 214
1000 U/cm2, but if one millionth of boron is incorporated, the resistivity is reduced to 0.4 U/cm2. The perfect sphalerite has a band gap of 3.6 eV and is an insulator, but when the zinc in the sphalerite crystal lattice is replaced by iron, forms marmatite (iron-containing sphalerite). When the iron content is up to 12.4%, the band gap reduces to 0.49 eV, which has good conductivity. Therefore, the presence of lattice defects can Electronic Structure and Surfaces of Sulfide Minerals. https://doi.org/10.1016/B978-0-12-817974-1.00007-7 Copyright © 2020 Central South University Press. Published by Elsevier Inc. All rights reserved.

307

308 Chapter 7 significantly change the semiconducting properties of sulfide minerals, thereby changing the interfacial adsorption behavior and flotation behavior of sulfide minerals. In this chapter, the effects of lattice defects on the structure, semiconductor properties, and surface adsorption behavior of sulfide minerals are investigated.

7.1 Effect of impurities on the floatability of sulfide minerals The floatability of sphalerite from different deposits is different, even from the same deposit. In general, sphalerite containing impurities will show different color, such as white, light green, yellow, brown, dark brown, and steel gray, as shown in Fig. 7.1. Fig. 7.2 shows the flotation behavior of sphalerite with different impurity contents [6]. It is found that copper and cadmium impurities enhance the recovery of sphalerite, while iron impurity greatly reduces sphalerite recovery. Chanturiya et al. [7] found that pyrite with high content of copper, arsenic, and gold impurities shows good floatability even under strong alkaline conditions (pH ¼ 12). However, the recovery of pyrite containing less copper impurities or a large concentration of sulfur vacancies under pH ¼ 12 does not exceed 25%, and the floatability is very poor. The flotation results of pyrite and gold-bearing pyrite at different pH are shown in Fig. 7.3. It is noted that the floatability of the gold-bearing pyrite is significantly better than that of pyrite, and the gold-bearing pyrite presents very good floatability in the range of pH 2e9; the floatability of the gold-bearing pyrite is reduced only when the pH exceeds 9.5. The floatability of pyrite is best at around pH 6. When the pH exceeds 7, the recovery of pyrite begins to decrease. At pH 9, the flotation of pyrite is strongly depressed. Fig. 7.4 shows the flotation behaviors of gold-bearing pyrite by different collectors. It is found that xanthate and dithiocarbamate have better collecting performance for goldbearing pyrite than pyrite, while dithiophosphate has worse collecting performance for

Figure 7.1 Sphalerite with different colors.

Electronic structures and surface adsorption 309 100

Cu-doping ZnS 80

Recovery (%)

Cd-doping ZnS 60

40

Fe-doping ZnS 20

0

0

2

4

6

8

10

Impurity doping content (%)

Figure 7.2 Effect of different impurities content on the floatability of sphalerite. 100 90 80

Recovery/%

70 60 50 40 30 20 10 0

1

2

3

4

5

6

7

pH

8

9 10 11 12 13 14

Figure 7.3 Flotation behaviors of pyrite and gold-bearing pyrite under different pH [8] (1) pyrite (without Au); (2) gold-bearing pyrite(Au 30 g/t).

gold-bearing pyrite than pyrite. The selectivity of xanthate, dithiocarbamate, and dithiophosphate has been discussed in Chapter 6. It is found that dithiocarbamate has strong collecting ability, and dithiophosphate has strong collecting ability. Pyrite has poor floatability and requires a collector with a strong collecting ability, and the presence of gold impurities reinforces this interaction, making xanthate and dithiocarbamate show better collecting ability for gold-bearing pyrite.

310 Chapter 7 100 80

40

Pyrite Au-bearing

Xanthate

60

0

5

10

15

20

10

15

20

10

15

20

Recovery/%

100 80

Dithiocarbamate 60 40 100

0

5

80 60

Dithiophosphate 0

5

Concentration (×10–5mol/L)

Figure 7.4 The flotation behaviors of gold-bearing pyrite and pyrite by three collectors.

In lattice defects, the mineral composition deviates from the stoichiometric number due to the absence of anions and cations, and this defect is called a vacancy defect. Vacancy defects also change the properties and reactivity of the semiconductor. Fig. 7.5 is a schematic diagram of the reaction of galena containing vacancy defects with xanthate ions [4]. The cation vacancy in galena causes the valence and charge unbalanced. The charge near the vacancy makes the sulfur ion have a strong attraction to electrons, while the cation vacancy is in a higher state of charge. When the lattice defect makes the galena into

Pb

S

Pb

S

Pb

S

Pb

S

Pb

S

Pb

S

Pb

S

S

S

Pb

S X

Figure 7.5 Schematic diagram of the reaction of galena containing vacancy defects with xanthate ions.

Electronic structures and surface adsorption 311 a p-type semiconductor, and a strong adsorption center for xanthate ions can be generated. Conversely, when the lattice defects make the galena into an n-type semiconductor (anion vacancy or cation gap), it is not favorable to xanthate ion adsorption. Most of the chemical bonds in the perfect galena crystal are covalent bonds, and only a small number of ionic bonds. Since the internal valence charge is balanced, the adsorption ability of galena to external ions is not strong. In natural galena, due to the presence of lattice defects, the internal valence charge is unbalanced, resulting in surface activity. Ishihara analyzed the relationship between the S/Fe ratio of pyrite in different deposits and its floatability [9], shown in Fig. 7.6. It can be seen that the S/Fe ratio of pyrite is in the range of 1.93e2.06. The closer the S/Fe ratio is to the theoretical value of 2.0, the better is the floatability of pyrite, the larger the S/Fe ratio deviates from the value of 2.0, and the worse the floatability of pyrite. It is also reported that the pyrite whose S/Fe ratio is less than 2 is difficult to be depressed by lime, and it is also difficult to be activated.

7.2 Effect of impurities and defects on the lattice constants of sulfide minerals The presence of impurity atoms in the mineral lattice will rebalance the crystal lattice, causing the lattice volume to expand or contract and subsequently causing the lattice constant to deviate from the ideal value to form so-called lattice distortion. Ferrer et al. found that the lattice constant of pyrite increases with increasing concentration of nickel impurity [10], as shown in Fig. 7.7. It is mainly because the crystal radius of Ni2þ in the ˚ ), and a larger ˚ , which is greater than the radius of Fe2þ (0.75 A hexacoordinate is 0.83 A

80

Recovery/%

70 60 50 40 30

100-150 mesh 1.90

1.94

1.98

S/Fe

2.02

2.06

Figure 7.6 The floatability of pyrite with different S/Fe ratios.

312 Chapter 7 5.44

Lattice constant/Å

5.43 5.42 5.41 5.40 5.39 0.00

0.10

0.30 0.20 x(NixFe1-xS2)

0.40

Figure 7.7 Relationship between unit cell constant of pyrite and nickel content.

volume of nickel atoms replace a smaller volume of iron atoms in the pyrite crystal, causing the increased lattice volume. Fig. 7.8 shows the relationship between the content of silver impurities and the unit cell constant of galena [11]. It can be seen that the unit cell constant of galena decreases with ˚, the increase of silver content because the radius of Agþ in the six-coordinated is 1.29 A 2þ ˚ which is smaller than the Pb radius (1.33 A). In the galena unit cell, the smaller volume of silver ions replaces the larger volume of lead ions, resulting in a decrease in the volume of the galena unit cell.

Lattice constant/Å

As can be seen from Fig. 7.9, the unit cell constant of sphalerite increases with increasing ˚ in the tetracoordinate iron concentration [12]. This is because Fe2þ has a radius of 0.78 A ˚ ), and consequently increases crystal, which is larger than the radius of zinc ions (0.74 A the unit cell volume of sphalerite.

5.940 5.935 5.930 0

200

400

600

800 1000 1200 1400 1600

Ag (g/t)

Figure 7.8 Relationship between unit cell constants and silver content in galena.

Lattice constant/Å

Electronic structures and surface adsorption 313

5.430 5.420 5.410 5.400 5.390 0

2

4

6

8

Fe(%)

10

12

14

Figure 7.9 Relationship between unit cell constants and iron content in sphalerite. Table 7.1: The unit cell constants of the synthetic doped galena samples. Cell constant/nm Mineral Pure galena Silver-containing galena Zinc-containing galena Copper-containing galena Stibium-containing galena Bismuth-containing galena Manganese-containing galena

Experimental value 0.5926 0.5923 0.5918 0.5920 0.5931 0.5929 0.5923

Calculated value 0.6018 0.6008 0.5958 0.5858 0.6130 0.6250 0.5760

Errors/% 1.55 1.44 0.67 1.04 3.35 5.41 2.75

Table 7.1 lists the unit cell parameters for synthetic impurity-doped galena using XRD to test. It is found that the density functional theory (DFT) calculation results are very close to the measured results. Except for the impurity of bismuth, the calculated value error of the other impurities is very small. Ag, Cu, Zn, and Mn impurities reduce the unit cell parameters of galena, while the presence of Bi and Sb increases the unit cell parameters. The calculated results are in good agreement with the measured results, indicating that DFT method is reliable to study the effect of lattice defects on mineral unit cell constants. Fig. 7.10 shows the calculated lattice constant of galena containing impurity defects by DFT [13]. It is found that the transition metal elements such as copper, zinc, silver, cadmium, and manganese reduce the lattice constant of galena. The main group elements such as indium, thallium, and arsenic impurities reduce the lattice constant of galena, while the antimony and bismuth impurities make the lattice constant of galena become larger, causing lattice expansion. Fig. 7.11 shows the lattice constant [14,15] for perfect, vacancy, and impurity-bearing sphalerite [14,15]. The presence of zinc vacancies and sulfur vacancies leads to a decrease in the lattice parameters of sphalerite, which is due to the disappearance of atoms.

314 Chapter 7 0.63 0.62

Lattice constant/nm

0.61 0.6 0.59 0.58 0.57 0.56 0.55

Per.

Cu

Zn

Ag

Cd

Mn

In

Sb

Tl

Bi

As

Lattice defect

Figure 7.10 Effect of lattice defects on the lattice constants of galena.

Lattice constant/m

0.552 0.549 0.546 0.543 0.54 0.537 0.534

Lattice defect

Figure 7.11 Effect of lattice defects on lattice constant of sphalerite.

The presence of sulfur vacancy in sphalerite causes the atoms around the vacancy to shift toward the center of the vacancy; especially the four zinc atoms adjacent to the sulfur vacancy are more obvious. However, there is no significant change in the geometry of the sphalerite containing zinc vacancy, and the atoms only relax around the vacancy. This is because the sulfur vacancy is larger than the zinc vacancy, causing the atoms around the sulfur vacancy to deform more easily. The first transition metal impurities of manganese, iron, cobalt, nickel, and copper all cause a slight decrease in the lattice constant of the sphalerite because the atomic radii of these five impurities are slightly smaller than the radius of the zinc atom. The presence of other metal impurities such as cadmium, mercury, germanium, indium, tin, lead, and antimony impurities makes the lattice constant of sphalerite larger, which is due to the relatively large atomic radius of these impurities, resulting in a cell expansion of sphalerite crystals.

Electronic structures and surface adsorption 315

Figure 7.12 Effect of lattice defects on lattice constant of pyrite.

Fig. 7.12 shows the lattice constant of pyrite with vacancies and impurities [16,17]. The sulfur vacancy causes the lattice constant of the pyrite to be slightly reduced and the cell volume is reduced, while the iron vacancy causes the constant to increase slightly and the volume to expand. Among the 20 kinds of impurities, all impurities other than cobalt increase the lattice constant to a different extent. For the first transition metal impurities (Co, Ni, Cu, Zn), the lattice constant of pyrite increases with the increase of the atomic number of elements. Platinum group elements (Ru, Pd, Pt) slightly increase the lattice constant of pyrite. Mo, Ag, Cd, Au, and Hg in the second and third transition metal elements and the metal elements of Sn, Tl, Pb, and Bi in the main group cause a large expansion of the pyrite lattice. The influence of As, Sb, Se, and Te impurities on the lattice constant is relatively small. The reason for the lattice expansion of pyrite is related to the atomic or covalent radius of the atom, the electronegativity, and the spin state of the ˚ , respectively, atom. For example, cobalt and copper have atomic radii of 1.67 and 1.57 A ˚ which are smaller than the iron atom radius of 1.72 A, but cobalt is spin-neutral in pyrite, while copper atom undergoes spin polarization, and cobalt impurity make the pyrite lattice reduced, and copper impurity causes the expansion of pyrite lattice.

7.3 Effect of impurities and defects on the band gap Table 7.2 shows the semiconductor type and band gap of galena bearing Pb-vacancy, S-vacancy, and impurity, respectively. The perfect galena is a direct band gap p-type semiconductor. The lead vacancy slightly reduces the band gap and does not change the semiconductor type of galena. The sulfur vacancy causes the band gap to increase slightly and change the galena to an indirect band gap n-type semiconductor. Among the transition metal impurities, copper, zinc, and silver impurities have little effect on the band gap, and

316 Chapter 7 Table 7.2: Effect of lattice defects on band gap and semiconductor type of galena. Defect type Perfect PbS S-vacancy Cu impurity Zn impurity Ag impurity Cd impurity Mn impurity Pb-vacancy In impurity Sb impurity Tl impurity Bi impurity As impurity

Bandgap/eV 0.54 0.56 0.54 0.57 0.53 0.55 0.71 0.52 0.55 0.48 0.25 0.49 0.45

Semiconductor type Direct p-type Indirect n-type Direct p-type Direct p-type Direct p-type Direct p-type Direct n-type Direct p-type Indirect n-type Direct n-type Direct n-type Direct n-type Direct n-type

manganese impurities increase the band gap and make the galena into an n-type semiconductor. Among the impurities of the main group, except for the indium impurity, the band gap is not greatly affected, and other impurities reduce the band gap of the galena; the thallium impurity does not change the semiconductor type of galena, and the other impurities change the semiconductor type. Table 7.3 lists the semiconductor type and band gap of sphalerite bearing Zn-vacancy, S-vacancy, and impurity, respectively. Vacancy defects do not change the semiconductor type of sphalerite; both are direct band gap p-type semiconductors. S-vacancy narrows the Table 7.3: The effect of lattice defects on band gap and semiconductor type of sphalerite. Defect type

Band gap/eV

Semiconductor type

Perfect ZnS Zn-vacancy Mn impurity Fe impurity Co impurity Ni impurity Cu impurity Cd impurity Hg impurity S-vacancy Ga impurity Ge impurity In impurity Ag impurity Sn impurity Pb impurity Sb impurity

2.18 2.20 2.32 2.35 2.36 2.36 2.39 1.99 1.90 2.06 2.64 2.29 2.55 1.96 2.10 2.05 2.07

Direct p-type Direct p-type Direct n-type Direct n-type Direct p-type Direct p-type Direct p-type Direct p-type Direct p-type Direct p-type Direct n-type Direct p-type Direct n-type Direct p-type Direct n-type Direct p-type Direct n-type

Electronic structures and surface adsorption 317 band gap of sphalerite, while Zn-vacancy broadens the band gap. The first transition element impurity manganese, iron, cobalt, nickel, and copper impurities broaden the band gap of sphalerite, wherein the band gap of the Cu-bearing sphalerite is the largest, and the band gap of Mn-bearing sphalerite is the smallest. Manganese and iron impurities make sphalerite become a direct band gap n-type semiconductor, copper impurity makes sphalerite an indirect band gap p-type semiconductor, and cobalt and nickel impurities do not change the semiconductor type of sphalerite. Cadmium and mercury are elements of the same group as zinc. Although they do not change the semiconductor type of sphalerite, they narrow the band gap of the sphalerite. The gallium and indium impurities change the semiconductor type into a direct band gap n-type semiconductor, and the gallium, germanium, and indium impurities broaden the band gap of the sphalerite, while the silver impurity narrows the band gap. The tin and antimony impurities not only narrow the band gap of the sphalerite, but also cause the sphalerite to become a direct band gap n-type semiconductor. Although the lead impurity does not change the semiconductor type of sphalerite, it also reduces the band gap of sphalerite. Table 7.4 shows the semiconductor type and band gap of pyrite bearing Fe-vacancy, S-vacancy, and impurity, respectively. Among the vacancy defects, the Fe-vacancy reduces Table 7.4: The effect of lattice defects on band gap and semiconductor type of pyrite. Defect type

Bandgap/eV

Semiconductor type

Perfect FeS2 Fe-vacancy S-vacancy Co impurity Ni impurity Cu impurity Zn impurity Mo impurity Ru impurity Pd impurity Ag impurity Cd impurity Pt impurity Au impurity Hg impurity Sn impurity Ti impurity Pb impurity Bi impurity As impurity Sb impurity Se impurity Te impurity

0.60 0.52 0.77 0.55 0.57 0.64 0.63 0.45 0.58 0.50 0.68 0.61 0.45 0.91 0.60 0.45 0.63 0.49 0.73 0.56 0.51 0.56 0.51

Direct p-type Direct p-type Direct p-type Direct n-type Direct n-type Direct n-type Direct n-type Direct p-type Direct p-type Direct n-type Direct n-type Direct n-type Direct n-type Direct n-type Direct n-type Direct n-type Direct n-type Direct n-type Direct n-type Direct p-type Direct p-type Direct p-type Direct p-type

318 Chapter 7 the band gap of pyrite, while the S-vacancy increases the band gap. Among the first transition metal impurities, cobalt and nickel impurities reduce the band gap, and copper and zinc impurities increase the band gap. The platinum group elements (ruthenium, palladium, platinum) reduce the band gap, especially the platinum-bearing pyrite with the smallest band gap. The Mo impurity in the second transition metal element reduces the band gap of the pyrite, while Ag increases the band gap, and the Cd impurity has little effect on the band gap. The Au impurity in the third transition metal element greatly increases the band gap of the pyrite, and the Hg impurity has no effect on the band gap. The metal elements Sn and Pb in the main group lower the band gap, and Tl and Bi increase the band gap. Among the 20 impurities, As, Sb, Se, and Te all reduce the band gap of pyrite. In addition, Sn and Bi impurities change the pyrite from direct band gap to indirect band gap, while Co, Ni, Cu, Zn, Pd, Pt, Ag, Cd, Au, Hg, Sn, Tl, and Pb impurities change the pyrite from a p-type semiconductor to an n-type semiconductor.

7.4 Impurities contribution on the properties of sulfide mineral: the frontier orbital coefficient studies The frontier orbital compositions of galena with different impurities are shown in Table 7.5 [13]. It is noted that the contribution of different impurity atoms to the LUMO of Pb atom is different. The influences of impurities such as lanthanum, manganese, and cerium are relatively large, while the effects of copper, cadmium, zinc, silver, and indium are relatively small. It is found from Table 7.5 that the atomic coefficients of Pb (0.231) and of Sb (0.24) in the LUMO orbital are similar, indicating that the Pb and Sb atoms have similar reactivity, and the nature of the Sb-containing galena is determined by both lead and antimony. The floatability of the Sb-containing galena is between galena and stibnite. At pH 5e6, the floatability of stibnite is the best, and it does not float under alkaline conditions. Table 7.5: The atomic orbital coefficient of LUMO of the impurity-bearing galena. Mineral name

LUMO orbital coefficient

Perfect galena Sb-containing galena Mn-containing galena Bi-containing galena Cd-containing galena Zn-containing galena In-containing galena Ag-containing galena Tl-containing galena Cu-containing galena

0.125 Pb 0.192 S 0.24 Sb þ0.231 Pb þ0.278 S 0.46 Mn þ0.181 Pb þ0.152 S 0.16 Bi 0.16 Pbv þ0.206 S 0.01 Cd 0.177 Pb 0.269 S 0.01 Zn 0.178 Pb 0.27 S 0.0 In 0.177 Pb 0.269 S 0.01 Ag 0.178 Pb 0.269 S 0.01 Tl 0.175 Pb 0.274 S 0.01 Cu 0.179 Pb 0.269 S

Electronic structures and surface adsorption 319 Galena still has good floatability under alkaline conditions. When galena contains Sb impurity, its floatability decreases under alkaline conditions. For Mn-containing galena, the coefficient of Mn (0.46) is much larger than that of Pb (0.181), indicating that the nature of Mn-containing galena is mainly determined by manganese atom, so the Mn-containing galena is easy to be oxidized and has poor floatability. The atomic orbital coefficients of LUMO of the impurity-bearing sphalerite are presented in Table 7.6. It is shown in Table 7.6 that the coefficients of Fe, Cu, Co, Ni, and Ga in LUMO are great, implying that those impurities have great effect on the interaction of sphalerite with xanthate. The coefficients of Sb, Zn, Sn, Ag, In, Ga, and Hg in LUMO are small. For Cu-bearing sphalerite the LUMO coefficient of zinc atoms is only 0.06 compared with the perfect sphalerite, while that of Cu atom reaches 0.58, indicating that the properties of Cu-bearing sphalerite depend on copper atom. Therefore, the flotation behavior of Cu-bearing sphalerite is more like copper sulfide. It also found from the flotation practice that when the sphalerite contains copper impurities, the sphalerite will have self-activation phenomenon, and the Cu-containing sphalerite is easier to be floated, and the separation of copper and zinc are difficult. When the sphalerite contains iron impurity, the LUMO coefficient of the zinc atom is only 0.11, and that of the iron atom reaches 0.59. The properties of the sphalerite mainly depend on the iron atom, and the iron-bearing sphalerite will exhibit a similar flotation behavior to pyrite. The flotation practice indicates that the iron-bearing sphalerite is easily Table 7.6: The atomic orbital coefficient of LUMO of the impurity-bearing sphalerite. Mineral

LUMO orbital coefficient

Perfect sphalerite Cu-containing sphalerite Fe-containing sphalerite Co-containing sphalerite Ni-containing sphalerite Cd-containing sphalerite Mn-containing sphalerite Mn-containing sphalerite Ga-containing sphalerite Ge-containing sphalerite In-containing sphalerite Ag-containing sphalerite Sn-containing sphalerite Pb-containing sphalerite Sb-containing sphalerite

þ0.20 S  0.19 Zn 0.58 Cu 0.27 S 0.06 Zn þ0.59 Fe þ0.21 S þ0.11 Zn þ0.70 Co þ0.20 S 0.12Zn 0.65 Ni þ0.24 S 0.07 Zn 0.41 Cd þ0.34 Zn þ0.13 S þ0.21 S 0.20 Zn 0.12 Mn 0.27 Hg þ0.21 S 0.19 Zn 0.51 Ga þ0.24 Zn 0.19 S þ0.24 Zn 0.22 S 0.13 Ge þ0.26 Zn þ0.25 S þ0.17 In þ0.21 Zn 0.20 S þ0.13 Ag þ0.24 Zn 0.22 S 0.17 Sn þ0.23 Zn 0.22 S 0.11Pb 0.22 Zn þ0.21 S þ0.07 Sb

320 Chapter 7 depressed by lime. The higher the iron content is, the worse is the floatability of sphalerite and the more sensitive it is to lime. The LUMO coefficients of cobalt and nickel impurities are large, which could enhance the interaction of sphalerite and oxygen. When sphalerite mineral contains cobalt and nickel impurities, it is easily oxidized and the floatability is worse. For cadmium-bearing sphalerite, it is noted from the LUMO coefficient that the cadmium atom provides a great contribution to the sphalerite property. Since the solubility product of cadmium ion and xanthate is small (Ksp ¼ 1013.59), the floatability of cadmium-bearing sphalerite becomes better. Table 7.7 lists the frontier orbital coefficients of perfect and impurity-bearing pyrite [16]. It can be seen from Table 7.7 that for perfect pyrite, the coefficient of iron atom plays a major role in the HOMO orbit, and the coefficient of sulfur atom plays a major role in the LUMO orbit. It is indicated that the HOMO orbit of pyrite is mainly affected by iron atoms, and the LUMO orbital is mainly affected by sulfur atoms. Cobalt and nickel impurities have a great influence on the LUMO orbital of pyrite. They greatly increase the coefficient of iron and sulfur atoms in the LUMO orbit. The LUMO orbital coefficients of cobalt and nickel impurities are also large, and the values are much larger than that of iron, which indicates that they not only have a greater impact on the LUMO orbital reactivity, but the impurities themselves will play a very important role in the reaction between the LUMO orbitals and other reactants.

Table 7.7: The atomic orbital coefficient of HOMO and LUMO of the impuritybearing pyrite. Mineral name

Frontier orbital

Orbit coefficient

Perfect pyrite

HOMO LUMO HOMO LUMO HOMO LUMO HOMO LUMO HOMO LUMO HOMO LUMO

þ0.238 Fe 0.068 S1 0.067 S2 0.004 Fe 0.124 S1 þ0.123 S2 0.011 Fe 0.007 Co 0.128 S1 0.128 S2 þ0.202 Fe 0.421 Co þ0.329 S1 0.329 S2 þ0.010 Fe 0.008 Ni þ0.131 S1 þ0.131 S2 þ0.191 Fe 0.447 Ni þ0.342 S1 0.342 S2 þ0.478 Fe þ0.315 As 0.180 S2 0.049 Fe 0.125 As 0.140 S2 0.247 Fe þ0.119 Se þ0.082 S2 þ0.015 Fe 0.153 Se þ0.132 S2 þ0.360 Fe þ0.135 Te þ0.123 S2 þ0.005 Fe  0.161 Te þ 0.153 S2

Co-containing pyrite Ni-containing pyrite As-containing pyrite Se-containing pyrite Te-containing pyrite

Remark: S1 is one sulfur atom in the sulfur dimer; S2 is another sulfur.

Electronic structures and surface adsorption 321

7.5 Occurrences and correlation of Au and As in pyrite Gold (Au) and arsenic (As) are two common heterogeneous atoms that often appear together in natural pyrite. It was suggested that a strong association exists between As and Au in pyrite and that a large amount of invisible gold is present in arsenic pyrite. In addition, gold was found to occur more in arsenic-rich pyrite than in arsenic-poor pyrite. Moreover, strong positive correlations between the As and Au content of pyrite were proposed [18e22]. Reich et al. [23,24] studied the solubility of gold in arsenic pyrite and suggested a maximum Au/As molar ratio of approximately 0.02. It was suggested that arsenic could be present at the sulfur site in pyrite, resulting in the formation of the AsS3dianions within the lattice [22,25], and our study has shown that Au would most likely exist in pyrite incorporated into interstitial lattice sites and substituted for S atoms. Using XANES measurements on gold-bearing arsenic pyrite, Simon et al. [26] suggested that the gold present as Au1þ was located in the arsenic pyrite lattice. In addition, fourfold-coordinated Au1þ was more abundant than twofold-coordinated forms. However, the nature of fourfold-coordinated Au1þ is not well understood. Simon et al. suggested that Au might be present as an AueAseS compound, where gold would be bonded in fourfold coordination compared to sulfur and arsenic atoms or in vacancy positions on a cation site in arsenic pyrite. In addition, they suggested that Au1þ was most likely incorporated into arsenic pyrite by adsorption onto pyrite surfaces during crystal growth. The coupled substitution mechanism was proposed to explain the strong positive correlation between Au and As in pyrite [20,21]. Their studies have clearly shown extensive oscillatory zonation in both the Au and As contents of single pyrite grains. It was suggested that the AsS3dianion may be charge compensated by Au3þ in the mineral lattice, i.e., Au3þ substitutes for Fe2þ and AsS3 substitutes for the S2 2 dianion. Simon et al. [26] suggested that the correlation between gold and arsenic might be related to the role of arsenic in enhancing the adsorption of gold on the pyrite surface, possibly through semiconductor effects. Some studies on the mode of occurrence of gold and arsenic in pyrite have been conducted; however, the crystal structure of pyrite-bearing gold and arsenic and whether there is a positive correlation between them are still not very clear. Moreover, the detailed properties of Au- and As-bearing pyrite are not very well studied or understood. In this study, using DFT calculations, the occurrences and correlation of Au and As in pyrite were studied; additionally, the effect of As on the structural stability of Au in pyrite was investigated.

7.5.1 Computational details Based on DFT, all calculations were performed using CASTEP, GGA-PW91 [27]. Only the valence electrons Fe 3d6 4S2, S 3s2 3p4, As 4s2 4p3, and Au 5d10 6s1 were considered explicitly through the use of ultrasoft pseudopotentials [28]. The effects of the supercell

322 Chapter 7 size on the defect properties were investigated, and a 2
2
2 pyrite supercell size (Fe32S64) is sufficient to guarantee reliable calculation results. When a plane wave cut-off ˚ energy of 270 eV was used, the calculated lattice parameter and band gap were 5.418 A ˚ [29] and and 0.60 eV, respectively, compared to the experimental values of 5.417 A 0.95 eV [30]. A Monkhorst-Pack [31,32] k-point sampling density of 2
2
2 was used. The convergence tolerances for the geometry optimization calculations were set to a ˚ , a maximum force of 0.08 eV/A ˚ , a maximum energy maximum displacement of 0.002 A 5 change of 2.0
10 eV/atom, and a maximum stress of 0.1 GPa, and the self-consistent field convergence tolerance was set to 2.0
106 eV/atom. In addition, the spin calculation was performed during the simulation. It was indicated that the calculation will be performed using different wavefunctions for different spins [33e37]. The formation energy refers to the energy required for an Au/As atom to incorporate into the crystal. Here, the formation energy of a site-defect element in the pyrite lattice DE is defined as follows [38]: total total þ Ex  Ereactant  EAuðAsÞ DE ¼ Eproduct total total where Eproduct and Ereactant are the total energies of those pyrites bearing As and/or Au and perfect pyrites, respectively. Ex and EAu=As are defined as the calculated total energies of the substituted matrix atom (x ¼ Fe or S) and the Au or As atom, i.e., the pseudo atomic energy, which is calculated during the optimized cell process. The smaller the value of DE, the more likely the existence of the element in pyrite.

7.5.2 Correlation of Au and As in pyrite Our studies have shown that gold (Au) would most likely exist in the pyrite crystal at the interstitial lattice sites and through substitution for S atoms, and As substituting for S was the most energetically favored mechanism [25,39]. In this study, Au substituting for Fe in pyrite under the effect of As was investigated. This reaction is shown as follows: One Au substituting for one Fe and one As substituting for one S: Fe32 S64 þ Au þ As/Fe31 S63 AuAs þ Fe þ S

(7.1)

Eqs. (7.2)e(7.4) describe the substitution of Au for S in pyrite with increasing As concentration, and Eqs. (7.5)e(7.9) describe the Au at interstitial sites in pyrite under the As mass concentrations of 0.0%, 1.93%, 3.82%, 5.67%, and 7.48%, respectively. One As and one Au substituting for one S2 unit at the same time: Fe32 S64 þ As þ Au/Fe32 S62 AsAu

(7.2)

Electronic structures and surface adsorption 323 One Au substituting for the S of the AsS unit: Fe32 S63 As þ Au/Fe32 S62 AsAu þ S

(7.3)

One Au substituting for 1 As of the As2 unit: Fe32 S62 As2 þ Au/Fe32 S62 AsAu þ As

(7.4)

One Au incorporating into the interstitial site of Fe32S64: Fe32 S64 þ Au/Fe32 S64 Au

(7.5)

One Au incorporating into the interstitial site of Fe32S64 substituted by one As atom: Fe32 S63 As þ Au/Fe32 S63 AsAu

(7.6)

One Au incorporating into the interstitial site of Fe32S64 substituted by two As atoms: Fe32 S62 As2 þ Au/Fe32 S62 As2 Au

(7.7)

One Au incorporating into the interstitial site of Fe32S64 substituted by three As atoms: Fe32 S61 As3 þ Au/Fe32 S61 As3 Au

(7.8)

One Au incorporating into the interstitial site of Fe32S64 substituted by four As atoms: Fe32 S60 As4 þ Au/Fe32 S60 As4 Au

(7.9)

The calculated formation energies for Eqs. (7.1)e(7.9) are shown in Table 7.8. The formation energies of Au substituting for Fe (Eq. (7.1)), Au substituting for S (Eq. (7.2)), and Au incorporating into the interstitial site (Eq. (7.5)) are 10.97, 4.62, and 5.89 eV, respectively. This result suggests that Eq. (7.1) is difficult to undergo, indicating that it is almost impossible for Fe to be substituted simply by Au under normal circumstances. For Eqs. (7.2)e(7.4), the formation energies of Au substituting for S decrease with increasing As concentration. This result indicates that the reactions are promoted due to the presence Table 7.8: Formation energies for Eqs. (7.1)e(7.9). Reactions

Formation energy/eV

(7.1) (7.2) (7.3) (7.4) (7.5) (7.6) (7.7) (7.8) (7.9)

þ10.97 þ4.62 þ3.96 þ2.86 þ5.89 þ4.67 þ2.00 þ1.33 þ0.67

The standard deviation value is 0.005 eV.

324 Chapter 7 of As. In addition, comparing Eqs. (7.3) and (7.4) shows that the reaction of Au substituting for As (Eq. (7.4)) is more likely to occur than the reaction of Au substituting for S (Eq. (7.3)), which suggests that the presence of As was conducive to the incorporation of Au. When Au is incorporated at interstitial sites (Eqs. (7.5)e(7.9)), it is shown that the formation energy is significantly lowered from þ5.89 eV to þ0.67 eV, with an increasing As concentration of 0%e7.48%, suggesting that the reactions are promoted as the As concentration increased. Relationship between arsenic content of pyrite and gold formation energy is shown in Fig. 7.13. The formation energy calculation results show that the presence of As is very conducive to the incorporation of Au into pyrite, regardless of whether the Au is in the S site or interstitial site, and it can be concluded that a positive correlation exists between Au and As in pyrite. In addition, it is noted that the formation energies of Eqs. (7.8) and (7.9) are obviously low compared to other reactions, which suggests that such highly concentrated As-bearing structures are very favorable for the incorporation of Au into pyrite.

7.5.3 Crystal structure of pyrite containing Au and As Figs. 7.14 and 7.15 show the reacting processes of Eqs. (7.2)e(7.9). It can be observed from Fig. 7.14 that the incorporation of Au and As into the S site has a small influence on the internal structure of the pyrite crystal, and the structures of their surrounding Fe and S atoms are not influenced. This result suggests that the pyrite structure would be stable when Au and As are introduced into S sites.

Figure 7.13 Relationship between arsenic content of pyrite and gold formation energy.

Electronic structures and surface adsorption 325

Figure 7.14 Reacting processes of Eqs. (7.2)e(7.4). Au is incorporated into the S site under different As mass concentrations.

The pyrite crystal structure with Au at an interstitial site is shown in Fig. 7.15. It is shown that the structure of pyrite with an interstitial Au at an As concentration of 1.93% (Fe32S63AsAu) was similar to that of pyrite at an As concentration of 0% (Fe32S64Au). However, the pyrite structure is significantly changed with a further increase in the As concentration. It is clearly shown that the Fe1 atom (in the vicinity of Au) in Fe32S62As2Au, Fe32S61As3Au, and Fe32S60As4Au is repelled into the hole due to the incorporation of Au, and its original position is occupied by Au. These results suggest that Au may exist in pyrite by substituting for Fe at a high As content. The cell lengths and angles of pyrite containing Au and As were investigated, as shown in Table 7.9. The incorporation of Au and As into S sites (Fe32S62AuAs) results in a small pyrite lattice expansion, and the expansion rate is only of 0.34%, while the incorporation of interstitial Au leads to a great deformation of the lattice, and the expansion rate is greater than 1%. In addition, the degree of changes in angles of pyrite cell is different due to the different incorporation behavior of Au. The interstitial Au results in a greater degree of changes in crystal angles than the substituting Au. Moreover, the degree of deformation

326 Chapter 7

Figure 7.15 Reacting processes of Eqs. (7.5)e(7.9). Au is incorporated at interstitial site in pyrite under different As mass concentrations.

Electronic structures and surface adsorption 327 Table 7.9: Lattice structure of pyrite containing Au and As. ˚ Cell lengths/A

Angles/degree

Species

a

b

c

a

b

g

Fe32S64 Fe32S62AsAu Fe32S63AsAu Fe32S62As2Au Fe32S61As3Au Fe32S60As4Au

10.836 10.873 10.958 10.979 10.984 10.975

10.836 10.873 10.949 10.947 10.945 10.975

10.836 10.873 10.955 10.950 10.962 10.972

90.00 89.84 89.72 89.73 89.69 89.65

90.00 90.22 89.68 89.76 89.83 89.64

90.00 89.80 89.86 89.70 89.64 89.67

˚ and for angle is 0.01 degree. The standard deviation value for cell length is 0.002 A

increases with the increase in As content. This result is related to the covalent radii of the ˚ ), As (1.21 A ˚ ), Fe (1.17 A ˚ ), and S (1.02 A ˚ )). atoms (Au (1.34 A The Mulliken overlap population of bonds may be used to assess the bonding and antibonding states between atoms and positive and negative values indicate bonding and antibonding states, respectively [40]. The calculated results listed in Table 7.10 show that the Au atoms are bonded to Fe and As atoms and are present in an antibonding state in the pyrite. The bond populations between AseAu and FeeAu bonds are stronger in Fe32S62AsAu and Fe32S63AsAu than in Fe32S62As2Au, Fe32S61As3Au, and Fe32S60As4Au, suggesting that the antibonding interactions between atoms in the former are greater than in the latter. In addition, for the case of interstitial Au, the antibonding interaction between the Fe and Au atoms is weakened with increases in the As content, while the antibonding interaction between As and Au is not changed significantly. By analyzing the atomic charge using the charge equilibration (QEq) method, it is shown that As is positively charged in the pyrite. The positive charges on the Fe atoms are lowered due to the incorporation of As. In addition, the positive charges on the Fe and As Table 7.10: Mulliken population of bond in pyrite. Species Substituting Au

Fe32S62AsAu

Interstitial Au

Fe32S63AsAu Fe32S62As2Au Fe32S61As3Au Fe32S60As4Au

Bond As1eAu (Fe4, Fe5, Fe6)eAu As1eAu (Fe1, Fe2, Fe3, Fe4)eAu (As1, As2)eAu Fe1eAu (As1, As2)eAu Fe1eAu (As1, As2, As4)eAu Fe1eAu

˚. The standard deviation value of bond length is 0.002 A

˚ Length/A 2.426 2.425 2.381 2.380e2.666 2.408 2.419 2.428 2.408 2.455 2.393

Population 0.12 0.40 1.08 0.82e1.26 0.05 0.30 0.03 0.22 0.05 0.05

328 Chapter 7 atoms decrease with increases in the As concentration. These results suggest that the presence of As could enhance the reducibility of the pyrite. After incorporating Au into the crystal, the positive charges on Fe and As are further reduced as the As concentration increases, and the positive charge on the Au atom itself also decreases. The reducibility of pyrite is apparently greatly enhanced due to the presence of Au and As.

7.5.4 Electronic structures of Au- and As-bearing pyrite The electronic structures of pyrite would be significantly influenced due to the incorporation of Au and As. The band structures of perfect and Au- and As-bearing pyrites are shown in Fig. 7.16 (the zero point of the energy was set at the Fermi level, EF). The substitution of Au and As for S atoms (Fe32S62AsAu) does not change the p-type property of the pyrite, and defect energy levels are present in the conduction band. However, with increasing As concentration, the incorporation of Au at an interstitial site changes the

Energy/eV

Energy/eV

2

2

Fe32S64

Fe32S62AsAu

2

Fe32S63AsAu

1

1

1

0

0

0

-1

-1

-1

-2

-2

-2

2

2

2

Fe32S60As4Au

Fe32S61As3Au

Fe32S62As2Au 1

1

1

0

0

0

-1

-1

-1

-2

-2

-2

alpha

beta

EF

EF

alpha

beta

Figure 7.16 Band structures of perfect and Au- and As-bearing pyrites. The solid line indicates the spin-up (alpha) state, and the dashed line indicates the spin-down (beta) state. The zero of the energy has been set at the Fermi level, EF.

Electronic structures and surface adsorption 329 p-type pyrite to an n-type pyrite, and defect energy levels are mainly located in the energy band gap. In addition, Fig. 7.16 shows that Au at the interstitial site causes the pyrite to be spin-polarized (the solid line indicates the spin-up state (alpha), and the dashed line indicates the spin-down state (beta)) at a certain As content. The spin density of states (DOS) is mainly derived from the Fe 3d state, and the magnetic moments are 0.33 hbar. The changes in the electronic structures can be clearly observed from the DOS of the pyrite, as shown in Fig. 7.17. It is shown that the DOS of Fe32S62AsAu (Au and As substituting for S atoms) are very similar to that of Fe32S64, whereas the DOS of Fe32S64-x AsxAu (x ¼ 1e4) are significantly shifted to a low-energy value, and there are apparent DOS between the valence band and conduction band. It is noted that there are DOS at the Fermi energy level for pure pyrite (Fe32S64), which is an insulating material. One of the reasons for this result is that the Fermi energy level is underestimated in the DOS

Density of states/(eV· cell)

200

160

160

120

120

120

80

80

80

40

40

40

-2

200

-1

0

Fe32S62As2Au

1

2

0

-2

200

EF

-1

0

Fe32S61As3Au

1

2

0

-2

200

EF

160

160

120

120

120

80

80

80

40

40

40

160

0

-2

-1

0

Energy/eV

1

2

0

-2

-1

0

1

Energy/eV s

EF

200 Fe S AsAu 32 63

Fe32S62AsAu EF

160

0

Density of states/(eV· cell)

200

EF

Fe32S64

p

2

0

-1

0

Fe32S60As4Au

-2

-1

0

1

2

1

2

EF

Energy/eV

d

Figure 7.17 Density of states (DOS) of the perfect pyrite and that of Au- and As-bearing pyrite. The zero of the energy has been set at the Fermi level, EF.

330 Chapter 7 calculation. In addition, the setting of the Gaussian broadening of the eigenvalues (smearing width) is also very important for the calculation. By analyzing the Mulliken bond population, it has been shown that antibonding interactions existed between the AueFe atoms and AueAs atoms. This interaction can be further analyzed by plotting the DOS of the atoms, where the antibonding interactions of the s, p, and d orbitals between atoms can be clearly shown. Fig. 7.18 presents the s, p,

Figure 7.18 DOS of Fe, Au, and As atoms in pyrite. The zero of the energy has been set at the Fermi level, EF.

Electronic structures and surface adsorption 331 and d orbitals of Au, As, and Fe at energies ranging from 2 to 2 eV. It can be clearly seen that strong hybridizations occur between the 6p and 5d orbitals of the Au atoms. In addition, strong interactions are found between the Fe 3d and Au 6p orbitals and between the Au 5d and As 4p orbitals.

7.6 Effect of impurities on the band structure and oxidation of galena Galena is a primary source of Pb metal and a narrow band gap semiconductor. Generally, galena cannot be collected by xanthate in the absence of oxygen [41,42], and galena reaches its maximum floatability in oxygen-saturated solutions [43]. Oxygen is an essential reagent in the flotation of sulfides in which the reduction of oxygen acts as cathode (Eqs. 7.10) and the oxidation of xanthate acts as anode (Eqs. 7.11) [44e47]. O2 þ 2e /2O 

(7.10) 

PbS þ 2X /PbX2 þ S þ 2e 0

(7.11)

It is indicated that the oxygen chemisorption favors the oxidation of xanthate anions to produce an adsorbed hydrophobic species [48]. The oxidation of galena has been extensively studied using electrochemical methods [49,50], Raman spectroscopy [51], thermodynamic methods [52e54], and synchrotron radiation (SR-XPS) [55]. Some more recent studies of galena oxidation have also used vibrational spectroscopies to identify oxidation products. Shapter et al. (2000) used Raman spectroscopy to identify oxysulfates produced by laser heating in air. Remarkably, Chernyshova [56] used in situ FTIR spectroscopy to study the products of electrochemical oxidation of galena formed at the electrode/electrolyte interface in solution at pH 9.2 and found that the first step of the oxidation of galena needs holes. The semiconductor types play important roles in the oxidation and xanthate interaction with galena. Generally, p-type semiconductor has dominant holes concentration, and ntype semiconductor has dominant electrons concentration, which would enhance or weaken the electrochemical adsorption on the surface. It is suggested that p-type galena oxidizes faster than n-type [57], and the oxygen chemisorption could convert the semiconductor types of galena surface [48]. It is also found that xanthate favors adsorption on p-type galena surface than on n-type [58], and the flotation results carried out by Glembotskii [71] confirmed that the p-type galena has higher flotation recovery than that of n-type galena. Moreover, the greater the holes concentration is, the higher is the flotation recovery. Natural galena is commonly nonstoichiometric and contains impurity elements, such as Ag, Cu, Bi, or Mn, which are substituted for Pb atoms that widely exist in the lattice of

332 Chapter 7 galena. In the flotation practice of galena, it is found that Ag, Cu, and Bi impurities could improve the floatability of galena, and Mn impurity weakens the floatability [59,60]. Hu [59] reported that the cationic vacancy favors the adsorption of xanthate. However, there are few reports about the effects of lattice impurities on the oxygen adsorption on the galena surface. The DFT can now be easily used to calculate the equilibrium crystal structures of solids and surfaces from first principles and to provide insights into their electronic structure. Moreover, it has been proven that the DFT calculation can now produce results in remarkably good agreement with experiments [61]. Andrew Hung et al. [62] using DFT studied the xanthate adsorption on pyrite FeS2(110) and (111) surfaces, which suggests that xanthate may undergo chemisorption at defect sites on real FeS2 surfaces, which contain low-coordinate Fe sites and sites in proximity to cleaved SeS bonds. Chen et al. [13] and Chen Y. et al. [14] investigated the influence of typical impurities on the lattice parameter and electronic properties of bulk galena and sphalerite. Chen et al. [72] conducted a simulation by DFT method and observed that the activities of Pb 6s and 6p orbital near Fermi level increase after oxidation, which enhances the interaction of xanthate with oxidized galena. To investigate the influence of impurities on the adsorption of oxygen on galena surface, the surface models (100) of galena bearing Cu, Mn, Ag, and Bi impurity have been constructed, and the electronic structure and adsorption of oxygen molecules on the impurity-galena surface have been calculated, which could be helpful for further understanding of the mechanism of galena oxidation and provide useful suggestions for the galena flotation optimization.

7.6.1 Computational methods Based on the DFT method, all the calculations were performed using CASTEP [63,64], GGA-PW91 [28]. The surfaces were obtained from the relaxed bulk structure. A (4
2
1) supercell was constructed to model bulk PbS. Based on the test results, a plane wave cut-off energy of 280 eV was used for all calculations. The interactions between valence electrons and the ionic core were represented by ultrasoft pseudopotentials, and a MonkhorstePack k-point sampling density of 2
2
1 [31,32] ˚ was was used for all adsorption calculations. In addition, a vacuum thickness of 15 A 6 placed between the surface slabs. The energy tolerance was 2.0
10 eV/atom, the force ˚ , and the displacement tolerance was 0.002 A ˚ . The maximum tolerance was 0.05 eV/A 5 energy change was 2.0
10 eV/atom, and the maximum stress was 0.1 GPa. Valence electron configurations considered in the study were the following: Pb 5d106s26p2, S 3s23p4, Ag 4d105s1, Bi 4f145d106s26p3, Cu 3d104s1, Mn 3d54s2, O2s22p4 states. All calculations adopted the spin polarization and were carried out in the reciprocal space.

Electronic structures and surface adsorption 333 ˚ unit cell. Then, the structure of the oxygen molecule was optimized in a 15
15
15 A Gamma point was used as the MonkhorstePack k-point. It was reported that the oxidation of galena included a series of reactions, and electrochemical reaction (7.12) is the first stage and rate-determining reaction at rO ¼ 7e10, accompanying the cathodic reduction of oxygen; Eq. (7.13). Hydroxide and carbonate ions participate the subsequent stages forming Pb(OH)2 or PbCO3 without electron transfer [65,66]. 0  PbS / Pb2þ ads þ Sads þ 2e O2 þ 2e /2O

(7.12) (7.13)

Based on this assumption, the electrochemical oxidation of galena surface mainly depends on the semiconducting properties of galena. Consequently, the effects of water and pH were not considered in the DFT simulation. The present work focused on the effect of impurity on adsorption of oxygen based on the first stage (Eq. (7.12)). Impurity can mainly influence the properties of galena surface, such as band structure, electronic level, and electrochemical reactivity, which obviously influence the electrochemical reaction (7.12) and (7.13). The DFT calculations on the oxygen adsorption on galena surface bearing different impurities are performed in vacuum. The common cleavage of galena is (100) and the Pb atoms in the surface are all pentacoordinated. Reported results suggest that eight-layer galena surface is enough to make it stable [67]. The galena surface bearing impurity was built via the replacement of one lead atom with an impurity atom, and the chemical composition was Pb63S64M (M is Ag, Cu, Bi, and Mn impurity atoms). To obtain the stable adsorption configuration, the different adsorption structures were examined. The results are shown in Fig. 7.19. The data presented in Table 7.11 indicate that oxygen paralleled to hollow site (between S atoms) gets the lowest adsorption energy, suggesting that this adsorption structure for oxygen on the galena surface is the most stable one. It is shown in Fig. 7.19F that the distance between the two O atoms is 0.2698 nm, which is greater than the length of oxygen molecules (0.121 nm), indicating that the oxygen molecule is dissociated. The adsorption energy of oxygen molecule on galena surface can be calculated as shown: Eads ¼ EO2 =surface  EO2  Esurface

(7.14)

where Eads is the adsorption energy, EO2 is the energy of the O2 molecule calculated in a cubic cell, Esurface is the energy of PbS slab, and EO2 =surface is the energy of the PbS slab with adsorbed O2. In this test, saturated calomel electrode, platinum electrode, and glassy carbon electrode are used as reference electrode, counter electrode, and working electrode, respectively.

334 Chapter 7

Figure 7.19 Equilibrium adsorption of O2 on different sites of galena (100) surface: (A) top S site, (B) top Pb site, (C) parallel to PbeS bond, (D) parallel to hollow (between Pb atoms), (E) vertical to hollow, and (F) parallel to hollow (between S atoms). The numbers shown near the bond indicate the bond length in nanometer. Arrows are the indicators of x, y, and z axes. Table 7.11: Adsorption energy of O2 on different sites on galena (100) surface. Adsorption site

Adsorption energy (eV)

Top S site Top Pb site Parallel to PbeS bond Parallel to hollow (between Pb atoms) Vertical to hollow Parallel to hollow (between S atoms)

0.407 0.107 0.067 0.306 0.084 1.191

7.6.2 Effects of impurity on electronic band structure of galena The semiconductor type of galena could be changed in the presence of impurities. The electronic structures of perfect galena and galena bearing impurity atoms (Cu, Ag, Mn, and Bi) are shown in Fig. 7.20. Compared with the perfect galena, the impurity levels are observed for the Ag-, Cu-, Bi- and Mn-PbS. The impurity levels of Ag- and Mn-PbS overlap with the Fermi level. The impurity levels of Cu- and Bi-PbS appear around 0.5 and 12 to 9 eV, respectively. The band structures of Ag- and Cu-PbS are similar to that of perfect PbS. The Mn and Bi impurities change the galena surface from p-type to n-type,

Electronic structures and surface adsorption 335

Figure 7.20 Electronic structures of the perfect galena and impurity-bearing galena.

336 Chapter 7 and the Fermi energy level enters in the conduction band, which suggests that galena bearing Mn and Bi impurities is degenerated. The influence of impurities on the semiconductor type is dependent upon the valence electron configuration of impurity atom. Ag and Cu atoms have the same valence electron configurations: Ag 4d105s1 and Cu 3d104s1. They act as the acceptor of electrons in the doping of galena, which results in galena exhibiting p-type. The valence electron configurations of Mn and Bi atoms are Mn 3d54s2 and Bi 6s26p3, respectively. They act as the donor of electrons in the doping of galena, resulting in galena exhibiting n-type. The total DOS of perfect galena and galena containing Ag, Cu, Bi, and Mn impurities is shown in Fig. 7.21. It can be seen that the total DOS of n-type surfaces (Bi-doped and Mn-doped surface) shifts to negative energy, compared with the p-type surface (Ag-doped, Cu-doped, and perfect surface), indicating that the electronic energy level of the n-type surfaces is lower than that of the p-type surface. In other words, the electronic activity of p-type surface is stronger than n-type. The O atom has great electronegativity (3.5), suggesting that oxygen has strong electrophilicity. Hence, p-type galena surface is favorable to the adsorption of oxygen.

7.6.3 Adsorption energy and structure The adsorption structures of oxygen molecule on the galena surface bearing impurities are shown in Fig. 7.22. The numbers in the figure indicate the distance between two atoms (bond length). As shown in Fig. 7.22, the distances between two O atoms on the galena

Figure 7.21 The total density of states of perfect and impurity-galena surface before O2 adsorption.

Electronic structures and surface adsorption 337

Figure 7.22 Adsorption configurations of O2 on perfect surface (A), Ag-doped (B), Bi-doped (C), Cu-doped (D), and Mn-doped (E).

surface bearing impurities are greatly larger than that of oxygen molecule (0.121 nm), suggesting the oxygen molecules adsorbed are completely dissociated. The length of OeS bond on the perfect galena surface is 0.1644 nm, and the bond lengths on the galena surfaces bearing Ag, Cu, Bi, and Mn impurities are 0.1586, 0.1616, 0.1651, and 0.1691 nm, respectively. The sum of the covalent radiuses of O and S atom is 0.175 nm, suggesting that the oxygen atoms are bonded to S atoms on all of the galena surfaces. In addition, the length of OeS bond on galena surface bearing Ag and Cu impurities is smaller than that on perfect galena surface (0.1644 nm), whereas those on the galena surface bearing Mn and Bi are larger. To investigate the effect of the impurity atom on the adjacent S atom that reacted with the oxygen atom, the Mulliken charge of surfaces Pb and S and the impurity atoms are shown in Fig. 7.23. It is shown in Fig. 7.23 that the substitutions of the impurities for the Pb atoms result in the decrease of Mulliken charge of the adjacent S atoms (S1eS4). Among the four impurities, the influence of Bi impurity on the neighboring S atoms is relatively small. It is indicated that the surface property of Bi-PbS surface may be similar to the perfect PbS surface. The Mulliken bond populations of pure and impurity-PbS after O2 adsorption are shown in Table 7.12. It is found that the Mulliken bond population of OeS bond on the Mn-PbS surface decreases from 0.17 to 0.11 compared with the pure PbS, indicating that the Mn impurity weakens the covalent characteristics of OeS bond. For the Cu- and Ag-PbS, the OeS bond population values increase to 0.23 and 0.24, respectively, suggesting that the

338 Chapter 7

Figure 7.23 Mulliken charge of perfect galena surface (A), and surface bearing Mn impurity (B), Ag impurity (C), Cu impurity (D), and Bi impurity (E).

Table 7.12: Mulliken bond population of OeS bond on the pure and impurity-galena surface. Adsorption model O2/Pb64S64 O2/Pb63(Mn)S64 O2/Pb63(Ag)S64 O2/Pb63(Bi)S64 O2/Pb63(Cu)S64

Bond O1eS1 O2eS2 O1eS1 O2eS2 O1eS1 O2eS2 O1eS1 O2eS2 O1eS1 O2eS2

Population 0.17 0.17 0.11 0.10 0.25 0.24 0.19 0.19 0.21 0.23

Electronic structures and surface adsorption 339 Cu and Ag impurities benefit for the interaction between O and S atoms. For the Bi-PbS, the OeS bond population is 0.19, which is similar to that of pure PbS (0.17). The adsorption energies of perfect galena surface, Cu-doped, Ag-doped, Bi-doped, and Mn-doped galena surfaces are 114.82, 175.60, 129.29, 158.24, and 80.08 kJ/mol, respectively. These suggest that Mn impurity weakens the adsorption of oxygen, but Cu, Ag, and Bi impurities enhance the adsorption of oxygen. Electronic structure calculations suggest that oxygen molecule favors adsorbing on p-type galena surface compared to n-type galena surface. So Ag-doped, Cu-doped, and perfect galena surface (p-type) have more negative adsorption energy than the Mn-doped galena surface (n-type). However, Bi-doped galena surface (n-type) is an exception, which also has relatively low adsorption energy, which will be discussed later.

7.6.4 DOS analysis of oxygen with galena surface bearing impurities The impurity atom could influence adjacent S atoms that reacted with oxygen atom. Fig. 7.24 shows the DOS of the OeS bond on the galena surface bearing impurities. 3 2 1 0

Perfect PbS

Density of States electrons/eV

-25

3 2 1 0

-20

Mn-doped

-25

3 2 1 0

-15

Bi-doped

O 2p

-15

-5 O 2p

0

5

0

5

0

5

0

5

0

5

S 3p

-10 S 3s

O 2s

S 3p

-10 S 3s

O 2s

-20

-5 O 2p S 3p

-25

3 2 1 0 3 2 1 0

S 3s

O 2s

-20

Cu-doped

O 2s

-10 S 3s

-5 O 2p S 3p

-25

-25

-15

-20

Ag-doped

-15

-10 S 3s

O 2s

-5 O 2p S 3p

-20

-15

-10

-5

Energy/eV

Figure 7.24 Effects of impurities on DOS of OeS bond.

340 Chapter 7 Generally, the most important bonding reaction occurs in the vicinity of Fermi level, so the DOS in the range of 7.5 to 2.5 eV are important to be considered. For the perfect galena surface, the 2p orbital of O atom and the 3p orbital of S atom are bonded in the range of 5.57 to 0.63 eV, and the 2p orbital of O atom and the 3p orbital of S atom are antibonding in the range of 0.63 to 0.48 eV. The bonding and antibonding between O and S atoms for the Ag-, Cu-, and Bi-galena surfaces are similar to the perfect surface. However, for the galena surface bearing Bi impurity, the DOS peak near the Fermi level shifts to negative energy. For the galena surface bearing Cu and Ag impurities, the 2p orbital of O atom and 3p orbital of S atom near the Fermi level are overlapped. For the galena surface bearing Mn impurity, the DOS peaks near the Fermi level disappear and appear in the range of 7.286 to 6.384 and 2.004 to 0 eV. Fig. 7.25 shows the DOS of Bi-O (a), AgeO (b), MneO (c), and CueO (d) on impuritygalena surface. The DOS of Bi and O atoms before and after adsorption were shown in Fig. 7.25 (a). After adsorption, the DOS peaks of Bi 6p and O 2p obviously broaden. It is found that a bonding DOS of Bi 6p- O2p orbital appears around 6 to about e0.5 eV and an antibonding DOS near the 0.5 to 1.8 eV, and the bonding effect is obviously stronger than the antibonding effect, indicating that the interaction between Bi and O atoms is relatively strong. It may suggest that the Bi atom could make contributions to the adsorption of oxygen molecule by interacting with O atom. The results in Fig. 7.25B,C,D also indicate that for the Ag-, Cu-, and Mn-PbS surface the antibonding is obviously stronger than their bonding, indicating that the interaction of the O atom with Ag, Cu, and Mn atoms is very weak. It may suggest that the Ag, Cu, and Mn impurity atoms do not directly react with oxygen atom.

7.6.5 Electron density map The electron density map (EDM) shows the electron distribution due to the formation of the bonds. It is useful for illustrating bonding interaction. The EDMs of oxygen molecules in Ag-, Cu-, Bi-, and Mn-doped galena surfaces are shown in Fig. 7.26. The orbitals used to calculate EDM are as follows: O 2s22p4, S 3s23p4, Pb 5d106s26p2, Ag 4d105s1, Bi 4f145d106s26p3, Cu 3d104s1, and Mn 3d54s2. Each of the colors represents a specific range of the charge density, shown in slice1. The electron density is increasing with the EDM color changing from blue to red. A deeper red color in the region between two bonding atoms suggests the greater overlap of their electron cloud and the stronger covalent interaction between the two atoms. Fig. 7.26 reveals that the electron clouds of O1 and O2 atoms overlap with the electron cloud of S1 and S2 atoms for surfaces bearing Ag, Cu, Bi, and Mn impurities, suggesting

Electronic structures and surface adsorption 341

Figure 7.25 Density of states of Bi-O (A), AgeO (B), CueO (C), and MneO (D) on impurity-galena surface.

342 Chapter 7 (A) Slice1 1.585 1.157 7.290e-1 3.011e-1 -1.268e-1

(B) Slice1 1.585 1.157 7.290e-1 3.011e-1 -1.268e-1

(C) Slice1 1.585 1.157 7.290e-1 3.011e-1 -1.268e-1

(D) Slice1 1.585 1.157 7.290e-1 3.011e-1 -1.268e-1

scale: electrons/Å3

Figure 7.26 Electron density map of O2 on (A) Ag-, (B) Cu-, (C) Bi-, and (D) Mn-bearing galena surfaces.

that covalent interaction existed in the OeS bond. In addition, a deeper red color can be observed in the regions between OeS atoms in Fig.7.26 (A), (B), (C) than that of Fig.7.26 (D), suggesting that the covalent interaction between O and S atom in Ag-, Cu-, and Bi-doped galena surface is stronger than that of Mn-doped galena.

Electronic structures and surface adsorption 343

7.6.6 Cyclic voltammetry examination Cyclic voltammetry examinations were performed on PbS electrodes bearing various impurities in a buffer solution with pH of 9.18, and the results are shown in Fig. 7.27. The CV curve of Mnegalena does not exhibit any oxidation peak, which suggests the presence of Mn impurity strongly depresses the oxidation of galena surface. The CV curve of Bigalena is similar to that of the perfect galena, suggesting the oxidation of Bi-PbS is close to the perfect PbS. There are two peaks appearing in the CV curves of Cu-, Ag-, and BiPbS. The oxidation peaks of Cu- and Ag-PbS are strengthened compared to the perfect PbS, indicating that the Cu and Ag impurities favor the oxidation of galena. It is reported by Chernyshova [56] that oxidation of galena starts with the following reaction: PbS þ 2 xhþ / Pb1xS þ xPb2þ, which is followed by the reaction: PbS þ 2 hþ / Pb2þ þ S0, where hþ denotes a hole. Hence the change of hole concentration would influence the oxidation of galena. Generally, a p-type semiconductor has dominant holes concentration, and an n-type semiconductor has electrons concentration. In addition, the DOS results (Fig. 7.21) also indicate that p-type surfaces have higher electronic activity than those of n-type. Therefore, the electronic structure of a p-type surface favors the oxidation of galena and n-type surface is unfavorable.

-0.2

PbS

-0.2 0.0

peak 0.0

0.2

0.4

0.6

0.8

0.0

0.2

0.4

0.6

0.8

Pb(Mn)S

Current/1e-5A

-0.2 -0.4 -0.2 0.0

Pb(Bi)S

peak I peak II

-0.2 -0.2 0.0

0.0 Pb(Cu)S

-0.2 -0.2

0.4

0.6

0.8

peak II

-0.2 -0.2 0.0

0.2 peak I

0.0 Pb(Ag)S

0.2

0.4

peak I

0.0

0.6

0.8

peak II

0.2

0.4

0.6

0.8

Potential/V

Figure 7.27 Cyclic voltammetry curves of PbS electrode with various impurities in sodium borate buffer solution with pH of 9.18 (scan rate v ¼ 0.1v/s).

344 Chapter 7 DFT calculations indicated that Cu- and Ag-galena surfaces are p-type, and the calculated adsorption energies of oxygen on their surface are more negative, and obvious oxidation peaks are observed in CV curves. However, Mn- and Bi-galena surfaces with the same semiconductor type, n-type, showed different oxidation behaviors. The Bi-bearing galena surface is favorable to oxygen of adsorption, but the Mn-bearing is not. That may be ascribed to their difference of valence electron configurations between Mn (3d54s2) and Bi (6s26p3). The DOS results (Fig. 7.25) indicated that there is little interaction between Mn 3d and O2p orbital, and there is a strong interaction between Bi 6p and O 2p orbital, which could improve the adsorption of oxygen on Bi-galena surfaces.

7.7 Activation and collecting of impurity-bearing sphalerite Impurities have a significant effect on the semiconducting properties and flotation behavior of sphalerite. The band gap of perfect sphalerite is 3.6 eV, which is an insulator that cannot interact with oxygen and xanthate, and its floatability is very poor. Impurities in the sphalerite lattice could change the energy band structure and enhance the conductivity of sphalerite, improving the electrochemical activity of sphalerite. Meanwhile, impurities atoms can be considered as active centers for the adsorption of reagents, which improves the reactivity of sphalerite surface. In this section, the effects of several common impurity atoms include iron, copper, and cadmium on the floatability and adsorption activity of sphalerite are investigated.

7.7.1 Effect of impurities on the band structure of sphalerite surface The band structures of perfect and impurity-bearing sphalerite surface are shown in Fig. 7.28. The semiconductor type of perfect sphalerite surface is p-type, which is hole-conducting. The presence of iron impurity changes the semiconductor type into n-type, which is electron-conducting. In addition, the iron impurity energy level appears near the Fermi energy level, which is close to the conduction band and serves as a hole-trapping center, excites electrons for conduction band, and improves the conductivity of the sphalerite. Fig. 7.29 shows the model of impurity level as a hole-trapping center and to excite electrons. In Fig. 7.29, the impurity level is represented by a short line, from EC (the bottom of the conduction band) to ED., and each short line corresponds to one donor. A black dot at an impurity level ED indicates an electron bound by an impurity, and a black dot in the conduction band indicates an electron transition into the conduction band. 4 indicates that the impurity show a positive charge after the electron transition, which is equivalent to the impurity trapping the hole. Since the impurity level near the conduction band becomes the trapping center of hole, the electron concentration of the conduction band increase, and

Energy/eV

Electronic structures and surface adsorption 345 6

6

6

6

4

4

4

4

2

2

2

2

0

0

0

0

-2

-2

-2

-2

-4

-4

-4

-4

-6

-6

-6

-6

-8

-8

-8

-8

G

F Q

Z G

Perfect ZnS

-10

-10

-10

-10

G

F Q

Z G

Fe-bearing ZnS

EF

G

FQ

Z G

Cd-bearing ZnS

G

F Q

Z G

Cu-bearing ZnS

Figure 7.28 Band structures of perfect and impurity-bearing sphalerite surface.

Figure 7.29 Model of impurity level as a hole-trapping center and to excite electrons.

the electronic conductivity of the semiconductor is improved. The relationship between the content of iron and the conductivity of sphalerite is shown in Fig. 7.30. It is noted that the higher the content of iron impurity, the greater the conductivity of sphalerite [68]. The copper impurity does not change the band structure of sphalerite surface, but there is an impurity level at the Fermi level, which is close to the valence band and can serve as a capture center for the electron transition. This is beneficial to increase the valence band hole concentration and to enhance the p-type conductivity of sphalerite. The model of impurity as electron capture centers and exciting electrons to valence is shown in Fig. 7.31. A circle at the impurity level represents a hole bound by an impurity, and a

346 Chapter 7

Figure 7.30 Effect of iron content in sphalerite on its conductivity.

Figure 7.31 The model of impurity energy levels as electron capture centers and to excite electrons to valence.

circle in the valence band represents a hole that transitions into a valence band. symbol indicates that the impurity is negatively charged after the hole is excited, or the impurity level captures the electron from the valence band. Since the impurity at the valence band becomes an electron-trapping center, the number of holes in the valence band increases, and the conductivity of the p-type semiconductor is improved. Due to the same valence electron configurations of cadmium and zinc, cadmium impurity doesn’t affect the band structure of sphalerite, and a new DOS peak at the valence band of 7.38 eV is noted, which is composed of Cd 4d orbital. Since the impurity peak is located at a relatively deep energy level, it is not easily excited, and the electron activity is relatively poor. Therefore, the cadmium impurity has little effect on the conductivity of the sphalerite. It is known from the preceding discussion that iron impurity enhances the n-type conductivity of the sphalerite surface, which is not favorable to the oxygen adsorption.

Electronic structures and surface adsorption 347 The copper impurity improves the p-type conductivity of the sphalerite surface and facilitates the adsorption of oxygen. The cadmium impurity does not change the band structure of the sphalerite, and its effect on flotation may depend on the reactivity of the surface cadmium atom and xanthate.

7.7.2 Effect of impurities on flotation behavior of sphalerite Fig. 7.32 shows the effect of different doping concentrations of iron, copper, and cadmium impurities on the flotation recovery of sphalerite with and without Cu activation. It is found from Fig. 7.32A that the floatability of copper-bearing sphalerite and cadmiumbearing sphalerite increases with the increase of impurity content without copper activation, and the floatability of manganese-bearing sphalerite is poor. From the chemical point of view, the ksp of butyl xanthate and copper, cadmium and iron ions is 4.7
1020, 2.08
1016, and 8.0
108, respectively, while the ksp of butyl xanthate and zinc ion is 3.7
1011. The flotation results are basically consistent with the ksp data; that is, copper and cadmium impurities enhance the reaction of xanthate and sphalerite, and iron impurity does not favor the reaction of sphalerite and xanthate. From the electrochemical point of view, the iron-bearing sphalerite is an n-type semiconductor, which is not favorable to the oxygen adsorption, thereby depressing the electrochemical adsorption reaction of xanthate on the sphalerite surface; copper-bearing sphalerite is a p-type semiconductor, which is beneficial to the oxygen adsorption and promotes the electrochemical adsorption of xanthate on the sphalerite surface. When sphalerite is activated by copper sulfate, the floatability of the impurity-containing sphalerite is improved, especially when the doping content is relatively low, and the

Figure 7.32 Effect of impurities on flotation recovery of sphalerite using butyl xanthate as collector. (A) without Cu activation, (B) with Cu activation.

348 Chapter 7 improvement effect is remarkable. This is because at the low doping concentration, the surface of the sphalerite is mainly zinc ions, and the copper ions replace the zinc ions and a small amount of impurity ions on the surface. The activation effect of the sphalerite surface is mainly determined by the zinc ions. When the impurity concentration is high, the copper and cadmium impurities are not affected, but the recovery of iron-bearing sphalerite is significantly reduced. When the impurity concentration is relatively high, the impurity atoms dominate on the sphalerite surface, and the copper activation effect depends on the reaction between the impurity and copper ions. The DFT simulations of copper activation of impurity-bearing sphalerite have been conducted [69]. The results suggest that the energy of the copper atom replacing the cadmium atom on the sphalerite surface is 217.82 kJ/mol, indicating that the replacing reaction is energetically favorable. That is, the presence of cadmium impurity does not hinder the copper activation of sphalerite surface. However, the energy of the copper replacing the iron atom is 391.21 kJ/mol. It is suggested that the iron atom on the surface of the sphalerite cannot be replaced with copper. That is, the presence of iron impurity may hinder the copper activation, and the higher the iron impurity content, the worse the copper activation on the sphalerite surface. Fig. 7.33 shows the results of copper adsorption on sphalerite surface doped with different iron contents. It is found that the copper adsorption on sphalerite surface decreases with the increase of iron doping concentration. The effect of iron and cadmium impurities on the copper activation of sphalerite can also be explained by the stability of the DOS. The effect of impurities on the DOS of sphalerite

Figure 7.33 Relationship between iron content of sphalerite and the adsorption amount of copper irons adsorbed by sphalerite.

Electronic structures and surface adsorption 349 50

EF

Fe-doped ZnS Cd-doped ZnS Cu-doped ZnS

DOS/electrons. eV

-1

40

30

20

10

0 -15

-10

-5

0

5

Energy/eV

Figure 7.34 Effect of impurities on the DOS of copper-activated sphalerite surface.

surface is shown in Fig. 7.34. It is found that the iron-bearing sphalerite has the lowest electron density energy, followed by the copper-activated sphalerite surface, and the highest energy is the cadmium-bearing sphalerite. The lower the electron energy, the more stable the surface electron configuration. From this result, the surface electronic configuration of the iron-bearing sphalerite is more stable than that of the copper-activated sphalerite surface. Therefore, the sphalerite surface tends to form the iron-bearing sphalerite surface, and the copper atom cannot replace the iron atom to form the copperactivated surface. The surface electronic configuration of cadmium-bearing sphalerite is unstable compared with the copper-activated sphalerite surface. Therefore, the cadmiumbearing sphalerite surface tends to form copper-activated sphalerite, and the cadmium atom on the surface is easily replaced by copper atom to form a copper-activated sphalerite surface.

7.8 Effect of impurities on the interaction between galena and xanthate Table 7.13 shows the adsorption heat of butyl xanthate on the surface of impurity-doped galena measured by microcalorimeter. The results show that the adsorption of xanthate on galena surface is an exothermic reaction, indicating that there is a strong chemical interaction between xanthate and galena surface, which is a spontaneous process. It is found that the adsorption heat of xanthate on the surface of pure galena is 0.28 J/m2. After doping silver and antimony, the adsorption heat of xanthate obviously increases to 0.82 J/m2 and 0.61 J/m2, respectively, indicating silver and antimony impurities can improve the adsorption of xanthate on the galena surface. After doping manganese, antimony, and zinc, the adsorption heat of xanthate decreases, which indicates that these impurities are not favorable to the adsorption of xanthate on galena surface.

350 Chapter 7 Table 7.13: The heat of xanthate on the surface of impurity-doped galena. Specific surface area (m2/g)

Mineral Pure galena Ag-doped galena Bi-doped galena Mn-doped galena Sb-doped galena Zn-doped galena

Heat of adsorption OH(J/m2)

9.35 7.23 5.24 5.81 9.01 3.56

0.28 0.82 0.61 0.19 0.17 0.15

The relationship between adsorption heat of xanthate on the impurity-doped galena surface and the flotation recovery is shown in Fig. 7.35. It is noted the adsorption heat of xanthate on the impurity-doped galena surface is proportional to the recovery; that is, the higher the adsorption heat, the higher the recovery of the impurity-doped galena. The silver-doped galena has the greatest adsorption heat, and the recovery of silver-doped galena reaches 100%, while the zinc-doped galena has the lowest adsorption heat, and its recovery is the smallest, only 46%. These results indicate that the adsorption heat can better reflect the interaction of minerals and reagents, and there is a positive correlation between the adsorption heat of the collector and the flotation recovery. From the point of view of chemistry, the interaction between xanthate and mineral surface metal ions is related to their solubility product Ksp. Table 7.14 lists the solubility product data for ethyl xanthate and lead, silver, strontium, barium, and zinc ions (data for butyl 100 90

Recovery (%)

80 70

PbS

60

Ag-doped PbS

50

Bi-doped PbS

40

Mn-doped PbS Sb-doped PbS

30

Zn-doped PbS

20 10 0

0

0.2

0.4

0.6

0.8

1

1.2

Δ H (J/m2)

Figure 7.35 The relationship between adsorption heat of xanthate on the impurity-doped galena surface and the flotation recovery.

Electronic structures and surface adsorption 351 Table 7.14: Solubility product (Ksp) of ethyl xanthate metal salt in water at 25 C. Metal Mnþ Pb2þ Agþ Bi3þ Zn2þ Sb3þ

pKsp 16.1, 16.77 18.1, 18.6 w30.9 8.2, 8.31 w24

Literature 33, 34 34, 33 34 33, 34 34

xanthate and ethyl xanthate are similar). It is found that the larger the value of pKsp, the greater the heat of adsorption of xanthate, the smaller the pKsp, and the smaller the heat of adsorption of xanthate. The values of pKsp of silver-xanthate and bismuth-xanthate are relatively large, and the adsorption heats of xanthate on the surface of silver-doped galena and bismuth-doped galena are also relatively large, while the pKsp of zinc-xanthate is the smallest, and the heat of xanthate on the surface of the zinc-doped galena is also minimal. However, there are still two questions that cannot be explained here: (1) The pKsp of bismuth-xanthate is larger than that of silver-xanthate, but the adsorption heat of xanthate on bismuth-doped galena is less than that of silver-doped galena; (2) The pKsp of stibiumxanthate is larger than that of silver-xanthate and lead-xanthate, but the adsorption heat of the stadium-doped galena is smaller than that of the pure galena and silver-doped galena. Therefore, the analysis from the chemistry aspect cannot fully explain the effect of the impurity on the interaction between galena and xanthate, and it is necessary to give a more comprehensive and reasonable explanation from the semiconductor electrochemical aspect. The reaction of xanthate and galena is an electrochemical process in which xanthate undergoes oxidation at the anode [70]: PbS þ 2X ¼ PbX2 þ S0 þ 2e

(7.15)

Oxygen reduction at the cathode: 1 O2 þ H2 O þ 2e ¼ 2OH 2

(7.16)

These two reactions form an electrochemical conjugation reaction, and if the oxygen adsorption reaction (7.16) is inhibited, the anodic reaction of the xanthate is also inhibited. The effect of band structure of galena semiconductor on oxygen adsorption has been discussed in Section 7.6. It is found that the n-type semiconductor galena surface is unfavorable to oxygen adsorption, and the p-type galena semiconductor surface is favorable for oxygen adsorption. According to the electrochemical conjugation relationship between xanthate and oxygen on the galena surface, it is also possible to obtain a general conclusion that the n-type semiconductor galena surface is not favorable to the xanthate adsorption, and the p-type semiconductor galena surface is in favor of the adsorption of xanthate.

352 Chapter 7

Energy/eV

As it is shown in Fig. 7.36, the pure galena is an n-type semiconductor, and there is no energy level in the forbidden band. After containing impurities, the semiconductor band structure and semiconductor type of galena have changed. Ag-doped and Zn-doped galena are still p-type semiconductors. The difference between the two is that the Ag-doped galena has an impurity level at the Fermi level, while the Zn-doped galena has no impurity 3

3

3

0

EF0

EF0

-3

-3

-3

-6

-6

-6

-9

-9

-9

G

FQ

ZG

G

ZG

G

3

3

0

0

0

EF

-3

-3

-3

-6

-6

-6

-9

-9

-9

FQ

ZG

Bi-doped PbS

ZG

3

EF

G

FQ

Zn-doped PbS

Ag-doped PbS

Pure PbS

Energy/eV

FQ

EF

G

FQ

Sb-doped PbS

ZG

EF

G

FQ

Mn-doped PbS

Figure 7.36 Band structure of impurity-doped galena surface.

ZG

Electronic structures and surface adsorption 353 Table 7.15: Semiconductor type of impurity-doped galena surface. Mineral Perfect galena surface Ag-doped galena Bi-doped galena Zn-doped galena Sb-doped galena Mn-doped galena

Semiconductor type p-type p-type n-type p-type n-type n-type

Impurity level No Yes Yes No Yes Yes

Adsorption heat (J/m2) 0.28 0.82 0.61 0.15 0.17 0.19

in the forbidden band. Sb-doped, Zn-doped, and Bi-doped galena have become n-type semiconductors, and impurity levels have appeared at the Fermi level. The semiconductor types of impurity-doped galena surfaces are listed in Table 7.15. According to the semiconductor type of impurity-doped galena, the contradiction between the solubility product and the adsorption heat of xanthate proposed in the previous section can be explained. Although the pKsp of bismuth-xanthate (30.9) is larger than that of silver-xanthate (18.1), the Ag-doped galena surface is p-type semiconductor, which is beneficial to oxygen adsorption and enhances the anodizing reaction of xanthate; while the Bi-doped galena surface is n-type, which is unfavorable to the adsorption of oxygen, which weakens the anodizing reaction of xanthate. Therefore, the adsorption heat of xanthate on Ag-doped galena surface is greater than Bi-doped galena. The pKsp of stibium-xanthate is 24, which is larger than that of lead-xanthate and silver-xanthate. However, perfect galena and Ag-doped galena are p-type semiconductors, which are favorable to the electrochemical action of xanthate, while the Sb-doped galena is an n-type semiconductor, which is not favorable to the electrochemical action of xanthate. In addition to thermodynamic parameters affecting mineral flotation behavior, the kinetic parameter is also an important factor. Thermodynamics theoretically gives the spontaneous magnitude of a reaction, but it does not give the speed of the reaction. The kinetics is mainly to study the elements and reaction mechanisms that affect the reaction rate and describe the actual progress of the reaction. The floatability of minerals depends on many factors, and the adsorption rate of the reagent on the mineral surface has an important influence on the flotation of the mineral. The nature of the mineral, the particle size, and the alkalinity of the pulp all affect the adsorption rate of the reagent. Lattice impurities significantly change the mineral properties and would have an effect on the adsorption kinetic parameters of the reagent on the mineral surface. Fig. 7.37 is a thermodynamic curve of the adsorption of butyl xanthate on impurity-doped galena surface. It is noted that the adsorption curves of xanthate on the galena surface with different impurities are different. The adsorption rates of xanthate on the Ag-doped and Bi-doped galena surface are the fastest, and that of on the Zn-doped galena is the slowest. It is suggested that impurities can influence the adsorption kinetics of xanthate on the

354 Chapter 7 0.005

0.005 Pb(Ag)S

0.003

Heat flow/mv

Heat flow/mv

0.004

PbS

0.002

Pb(Zn)S

0.001

0.004

Pb(Bi)S

0.003

Pb(Mn)S Pb(Sb)S

0.002

0.001

0.000 2000

4000

Time/s

6000

8000

0.000

2000

4000

6000

8000

Time/s

Figure 7.37 Thermodynamic curve of adsorption reaction of butyl xanthate on impurity-doped galena surface.

galena surface. By processing the adsorption curve, the corresponding adsorption rate constant and adsorption order can be obtained. Table 7.16 lists the adsorption rate constants of xanthate on the impurity-doped galena surface, and the corresponding recovery is also given in the table. It is found from Table 7.16 that the impurity has a significant effect on the kinetic constant of xanthate adsorption on impurity-doped galena surface. The adsorption reaction order is between 0.2 and 1.3, which is close to the first-order reaction; that is, the adsorption of xanthate on galena surface is proportional to its concentration. The reaction order of xanthate on the impurity-doped galena is larger than that of on the perfect galena, indicating that the impurity can improve the reaction order of xanthate. The adsorption rate constants of xanthate on pure galena, Ag-doped, and Bi-doped galena are large, and the reaction orders are small, while adsorption rate constants of xanthate on Mg-doped, Sb-doped, and Zn-doped galena surface are small and the reaction orders are large. The relationship between the adsorption rate constant and reaction order and mineral floatability is shown in Fig. 7.38. It is noted from Fig. 7.38 that there is no linear relationship between the reaction order of xanthate adsorption on the impurity-doped galena and the flotation recovery. It can be considered that the adsorption of xanthate on the surface of the galena is a first-order reaction. The effect of the impurity on the floatability of galena is mainly to change the adsorption constant of xanthate. Under the constant temperature and the same reaction order, the magnitude of the constant directly reflects the speed of the adsorption rate. It is found from Table 7.16 that the reaction rate constant of xanthate on the surface of Ag-doped and Bi-doped galena is relatively large. The experimental results show that the floating rates of galena with Ag and Bi impurities are relatively fast, and their recoveries are also relatively high; while the adsorption rate coefficients of xanthate on the Sb-doped

Electronic structures and surface adsorption 355 Table 7.16: Adsorption kinetic parameters and flotation recovery of butyl xanthate on the impurity-doped galena surface. Mineral samples

Recovery (%) 65.3 100 72.4 64.7 52.9 46.6

0.278 0.93 0.75 1.11 1.24 1.30

100

100

80

80

60 40 20 0

Semiconductor type

Reaction order/n

5.22 5.87 5.36 2.92 0.583 0.019

Revovery (%)

Recovery (%)

Pure galena Ag-doped galena Bi-doped galena Mn-doped galena Sb-doped galena Zn-doped galena

Reaction rate constant/k (10¡3/s)

p p n n n p

60 40 20

0

0.4

0.8

1.2

1.6

Reaction order/n

2

0

0

1

2

3

4

5

Rate constant (10-3.s-1)

6

Figure 7.38 Relationship between kinetic constant of xanthate adsorption on impurity-doped galena surface and flotation recovery.

and Zn-doped galena are relatively small, and the corresponding recoveries are also small. It indicates that the adsorption rate of xanthate on the galena surface directly determines the floating rate of mineral per unit time. The higher the adsorption rate of xanthate on the galena surface, the more the adsorption of xanthate on the surface and the greater the hydrophobicity of galena surface. The highly hydrophobic galena is more likely to adhere to the foam, resulting in greater recovery. Table 7.16 also lists the semiconductor type of impurity-doped galena. It is interesting to note that in addition to Bi-doped and Zn-doped galena, the adsorption rate of xanthate on the surface of galena of p-type semiconductor is greater than that of n-type semiconductor. The reaction order on the surface of galena of n-type semiconductor is larger than that of the p-type semiconductor. According to the theory of semiconductor catalysis, p-type

356 Chapter 7 semiconductor is beneficial to oxygen adsorption and is favorable to deep oxidation reaction; n-type semiconductor is unfavorable to oxygen adsorption and is beneficial to partial oxidation reaction, i.e., selective oxidation reaction. The anodizing of xanthate on galena and the reduction of oxygen on the galena cathode are a pair of conjugated electrochemical reactions. Galena in p-type is beneficial to the oxygen adsorption and promotes the electrochemical oxidation reaction of xanthate. Therefore, xanthate is easily adsorbed on the p-type galena surface and has a large adsorption rate. In addition, p-type semiconductor is beneficial to the deep oxidation reaction. The oxidation reaction of xanthate depends on the electron energy level and has little relationship with the concentration. Therefore, the adsorption of xanthate on the p-type galena surface is not sensitive to the reaction order and has a small reaction order. The n-type galena surface is not favor to the adsorption of oxygen and has an inhibiting effect on the electrochemical oxidation reaction of xanthate. Therefore, xanthate has a small adsorption rate constant on the n-type galena surface, and n-type semiconductor is beneficial to selective oxidation reaction. The selective oxidation reaction is sensitive to the concentration, so the xanthate adsorption on the n-type galena surface has a large reaction order. For bismuth impurity, although the Bi-doped galena is an n-type semiconductor, it is known from the analysis in Section 7.6 that there is a strong interaction between the Bi impurity and the oxygen atom, which weakens the adverse effect of the n-type semiconductor on oxygen adsorption and is beneficial to the electrochemical adsorption of xanthate. Therefore, xanthate on the Bi-doped galena has a large adsorption rate constant. Although the Zn-doped galena is a p-type semiconductor, there is no impurity level in the forbidden band, and the contribution of Zn impurity to the electrochemical activity of galena is very small. In addition, considering the full electron structure of the outer layer of the zinc atom and that the interaction with xanthate and oxygen is relatively weak, the adsorption rate constant and reaction order of zinc-doped galena are very small.

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Electronic structures and surface adsorption 359 [57] Eadington P, Prosser AP. Oxidation of lead sulphide in aqueous suspensions. Trans Inst Min Metall 1969;78:74e82. [58] Richardson PE, O’Dell CS. Semiconducting characteristics of galena electrodes relationship to mineral flotation. J Electrochem Soc 1985;132(6):1350e6. [59] Hu XG. Mineral processing of nonferrous sulphide ores. Beijing, China: Metallurgical Industry Press; 1987. [60] Chen JH. Principles of the flotation of sulphide minerals bearing lattice defects. Changsha, China: Central south university press; 2012. [61] Rosso KM, Vaughan DJ. Sulfide mineral surfaces. Rev Mineral Geochem 2006;61:505e56. [62] Hung A, Yarovsky I, Russo SP. Density-functional theory studies of xanthate adsorption on the pyrite FeS2(110) and (111) surfaces. J Chem Phys 2003:6022e9. [63] Clark SJ, Segcall MD, Pickard CJ, Hasnip PJ, Probert MIJ, Refson K, Payne MC. First principles methods using CASTEP. Zeitschrift fur Krist 2005;220(5e6):567e70. [64] Segall MD, Lindan PJD, Probert MJ, Pickard CJ, Hasnip PJ, Clark SJ, Payne MC. First-principles simulation: ideas, illustrations and the CASTEP code. J Phys Condens Matter 2002;14(11):2717e44. [65] Goryachev BE, Nikolaev AA. Galena oxidation mechanism. J Min Sci 2012;48(2):354e62. [66] Strizhko VS, Goryachev BE, Ulasyuk SM. Main kinetic parameters of electrochemical galena oxidation in alkaline solutions. Izv Vuzov Tsv Metall 1986;6. [67] Li YQ, Chen JH, Lan LH, Guo J. Adsorption of O2 on pyrite and galena surfaces. Chin J Nonferrous Met 2012;22(4):1184e94. [68] Xiong X. Effect of iron composition on semiconductor properties and chemical reactivity of zinc sulfide concentrate. Nonferrous Met 1989;41(4):55e66. [69] Chen JH, Chen Y, Li YQ. Quantummechanical study of effect of lattice defects on surface properties and copper activation of sphalerite surface. Trans Nonferrous Metals Soc China 2010;20(8):1121e30. [70] Feng Q, Chen J. Flotation electrochemistry of sulfide minerals. Changsha: Central South University Press; 2014. [71] Glembotskii BA. Foundation of physical chemistry in the process of flotation. Beijing, China: Metallurgical Industry Press; 1981. [72] Chen JH, Lan LH, Chen Y. Computational simulation of adsorption and thermodynamic study of xanthate,dithiophosphate and dithiocarbamate on galena and pyrite surfaces. Miner Eng 2013;46e47:136e43.

Subject index Note: ‘Page numbers followed by “f” indicate figures and “t” indicate tables’.

A AB210. See Acid black 210 (AB210) AB234. See Acid black 234 (AB234) AB4. See Acid brown 4 (AB4) Acid black 210 (AB210), 204te206t, 207e210, 212e215, 212t Acid black 234 (AB234), 204te206t, 207e210, 212t, 213e215 Acid brown 4 (AB4), 204te206t, 212e213, 212t Acid mine drainage (AMD), 127 Acid orange 7 (AO7), 204te206t, 212e213, 212t Acid yellow 36 (AY36), 204te206t, 212e213, 212t ADDTP. See Ammonium dibutyl dithiophosphate (ADDTP) Adsorption energy, 129e130 of oxygen molecule, 333, 336e339 Adsorption of isolated water molecule, 130e132, 131f Aerofloat collector, 189e190 AES. See Auger electron spectroscopy (AES) Alkylthiocarbonic acid, 188 AMD. See Acid mine drainage (AMD) Amino group (eNH2), 215 Ammonium dibutyl dithiophosphate (ADDTP), 248 Antibonding effect, 340 AO7. See Acid orange 7 (AO7) Arsenic (As), 321 occurrences and correlation in pyrite, 321e331

computational details, 321e322 correlation, 322e324 crystal structure of pyrite, 324e328 electronic structures, 328e331 Arsenopyrite (FeAsS), 43 atomic coordination structures, 48f band structures and density of states, 50f bond lengths and Mulliken population of, 47t electronic and chemical structures, 43e56 computational methods, 45 crystal structure, 44e45 crystal structure differences, 46e49 electronic structures, 49e53 energy bands, 51f Fermi level, 53 flotation behaviors, 54f frontier molecular orbital, 54e56 unit cells, 46f parameters and bond angles, 47t Atomic atomic-scale phenomena, 237 energy, 4 orbital coefficients, 23e24 Auger electron spectroscopy (AES), 84 AY36. See Acid yellow 36 (AY36) Azo compound depressants, 203e216 azo reagents effect on sulfide minerals flotation, 207e210, 208f

361

chalcopyrite recovery, 209f dosage on pyrite recovery, 208f molecular structures, 204te206t computational methods, 207 frontier orbital energy of azo agents and minerals, 214e216 interaction configurations, 202f molecular structure and depression properties of azo agents, 210e213 front molecular orbital of azo dye reagents, 211f molecular structures and HOMO composition, 212t Azo group (eN¼Ne), 215

B Band gap, effect of impurities and defects on, 315e318 Band structures, 16 Band structure of iron sulfides, 30e32 impurities effect of galena, 331e344 Basic brown 1 (BB1), 204te206t, 209e210, 212t, 213 Basic orange 2 (BO2), 204te206t, 212e213, 212t BB1. See Basic brown 1 (BB1) N-Benzoyl-N-phenylhydroxylamine, 193 Bi-doped galena, 356 surface, 339 Binding energies (DE), 221 Bioleaching of metal sulfides, 13e14 Bloch’s theorem, 8e9, 90 BLYP. See Hybrid density functional (BLYP)

Subject index BO2. See Basic orange 2 (BO2) Bond Mulliken population, 34e35 Bonding analysis of copper sulfide minerals, 19e23 Bornite (Cu5FeS4), 13, 14f, 15 band structure and DOS, 17f DOS of CueS and FeeS bonding for, 22f Brillouin area, 9 Brillouin zone (BZ), 9 Butyl xanthate (BX), 256e258, 258t

C Cambridge Serial Total Energy Package (CASTEP), 15, 38, 57, 114, 165, 238, 248e249, 276 Car-Parrinelloab initio molecular dynamics method (CPMD method), 127e128 Carboxyl COOe, 198e199 Cassiterite, 193 CASTEP. See Cambridge Serial Total Energy Package (CASTEP) Cation vacancy in galena, 310e311 CECILIA method, 127e128 Chalcocite (Cu2S), 13, 14f, 15, 115e116 band structure and DOS, 18f DOS of, 120f DOS of CueS bonding with different coordination number of Cu atoms, 23f Chalcopyrite (CuFeS2), 13, 14f, 15e16, 193e194 band structure and DOS, 16f DOS of bonding atoms in, 20f sulfur atoms, 27 Charge equilibration method, 327e328 Chemical potential of Fermi level, 53 Chronoamperometry, 164 Collector adsorption heat of collectors, 256e258

geometry and electron density of collector adsorption, 252e253 kinetics adsorption, 258e259 Conjugation effect, 189, 254 Contact distance effect on galvanic interaction, 68e70 Copper activation of pyrite depressed by NaOH and CaO, 273e274 of sphalerite and pyrite surfaces, 259e264 model of pyrite and electronic properties, 263e264 model of sphalerite and electronic properties, 260e263 Copper sulfate, 56e57 minerals bonding analysis, 19e23 computational methods, 15 crystal structure, 13e15 electronic properties, 16e19, 25e27 Fermi level, 27t floatability for, 25e27 frontier orbitals, 23e25, 24t lattice parameters, 16t Copper xanthate, 27 Copper-bearing sphalerite, 347 Covellite (CuS), 13, 14f, 15 band structure, 17f DOS of, 17f, 18 DOS of CueS bonding with different coordination for, 21f sulfur atoms, 27 CPMD method. See CarParrinelloab initio molecular dynamics method (CPMD method) Crystal, 9 Crystal structure for copper sulfide minerals, 13e15 differences between pyrite and arsenopyrite, 46e49 effects of leadeantimony sulfide minerals, 38e40

362

of iron sulphides, 28e30 of pyrite containing Au and As, 324e328 Cu 3d state of bornite, 18, 26 Cupferron, 192, 198e199 Cyanide (CNe), 275 adsorption on pyrite, marcasite, and pyrrhotite surfaces, 279e284 compound adsorption on pyrite, marcasite, and pyrrhotite, 275e286 computational methods and models, 276e279 sodium cyanide dosage effect on grade and recovery of iron, 284e286 Cyclic voltammetry, 164 examination observations, 343e344 Cytec, 189

D Dangling bonds, 117 DB6. See Direct blue 6 (DB6) DB15. See Direct blue 15 (DB15) DB95. See Direct brown 95 (DB95) DDTC. See Diethyldithiocarbamate (DDTC) Density functional theory (DFT), 2e3, 15, 57, 113e114, 127, 181, 193, 237e238, 247, 313 energy band theory, 8e11 exchange-related energy functional, 6e8 HohenbergeKohn theorem, 5e6 KohneSham equation, 6 ThomaseFermi model, 4 Density of states (DOS), 16, 97e99, 101, 117, 156e157, 181, 241, 282e283, 328e329 analysis of, 254e256 of jamesonite, galena, and stibnite, 40e41 of oxygen with galena surface bearing impurities, 339e340

Subject index of bonding sulfur atoms, 188f of copper-activated ZnS surface, 261e262, 262f effect on sulfide minerals surfaces, 119e121 of monoclinic and hexagonal pyrrhotite, 58e61 of S and N atoms in thiocarbamate collector, 191f of S atom in xanthate ions, 185f of S1 atoms in different aerofloat type collectors, 190f of surface atoms, 74e75 Depression effects, 207, 210, 213 properties of azo agents, 210e213 DF200. See DowFroth200 (DF200) DFT. See Density functional theory (DFT) DFTB+ module, 217e219 DG6. See Direct green 6 (DG6) Di-xanthate, 66 Diethyldithiocarbamate (DDTC), 199, 247 Diethyldithiophosphate, 199 Dimethylglyoxime, 192e193, 198 Direct blue 6 (DB6), 204te206t, 209e210, 212t, 213e215 Direct blue 15 (DB15), 204te206t, 209e210, 212t, 213e215 Direct brown 95 (DB95), 204te206t, 207e210, 212t, 213 Direct green 6 (DG6), 204te206t, 207e210, 212t, 213e215 Direct red 28 (DR28), 204te206t, 209e210, 212t, 213e215 Disulfide, 33 Dithiocarbamate (DTC), 247, 308e309 adsorption on galena and pyrite surfaces, 247e259 Dithiophosphate (DTP), 247, 308e309 adsorption on galena and pyrite surfaces, 247e259

Dixanthogen, 27, 36, 237, 244e246 DMol, 15, 38, 45, 193e194 module, 218, 221 software, 181e183 DOS. See Density of states (DOS) Double xanthate, 53 DowFroth200 (DF200), 217, 226e231, 226fe227f, 228t bond lengths of, 228t PDOS of O atom before and after H2O adsorption, 230f of O atom in frother molecule, 229f DR28. See Direct red 28 (DR28) DTC. See Dithiocarbamate (DTC) DTP. See Dithiophosphate (DTP) Dual descriptor of surface atoms, 73

E Earliest electronic spectrometer, 84 EDM. See Electron density map (EDM) EDTA, 55e56 Electrochemical flotation process, 246 Electrochemical process, 245 Electrochemistry of flotation, 237 Electron delocalization, 44e45 Electron density of collector adsorption, 252e253 function, 6 of monoclinic and hexagonal pyrrhotite, 61, 62f Electron density map (EDM), 340e342 Electronic properties for copper sulfide minerals, 16e19, 25e27 structures of pyrite-bearing Au and As, 328e331 Electrophilicity of surfaces, 71e74

363

Element sulfur, 24 Energy band of monoclinic and hexagonal pyrrhotite, 58e61 theory, 8e11 Bloch’s theorem, 8e9 first Brillouin zone, 9e11 Ethyl xanthate, 188, 199, 289 Ethylenediamine bipyridine, 55e56 Ethylthionocarbamate, 190e191 EulereLagrange equation, 5 Exchange-associated functional, 7 Exchange-related energy functional, 6e8 generalized gradient approximation, 7e8 local density approximation, 7

F Fe 3d orbitals, 33e34 Fe-containing copper sulfide, 24 Feather mine, 36 Fermi energy level, 246 Fermi level (EF), 16, 19, 27, 32, 184 of copper sulfide, 27t of pyrite and arsenopyrite, 53 FFs. See Fukui functions (FFs) First Brillouin zone, 8e11, 11f two-dimensional square lattice Brillouin zone, 10f First Brillouin zone. See Simple Brillouin zone First principle method, 3 First-principle pseudopotential method, 57 Floatability for copper sulfide minerals, 25e27 of gold-bearing pyrite, 308 of iron sulphides, 28e30 of leadeantimony minerals, 37 Flotation, 13, 286e287 behavior, 113 of monoclinic and hexagonal pyrrhotite, 63e64 of metal sulfides, 13e14 of sulfide ore, 307e308

Subject index Flotation reagents, 181 aerofloat collector, 189e190 azo compound depressants, 203e216 bonded atoms of xanthate-type collector, 184e189 frothers adsorption at wateregas interface, 216e234, 218te219t computational methods, 217e219 frother molecule adsorbing at gaseliquid interface, 221e231 frother molecule in water phase, 219e220 molecule structures, 217f geometric parameters, 182f interaction with mineral surface adsorption of xanthate, DTP, and DTC on galena and pyrite surfaces, 247e259 copper activation of sphalerite and pyrite surfaces, 259e264 cyanide compound adsorption on pyrite, marcasite, and pyrrhotite, 275e286 lime interaction with pyrite surface, 265e274 water molecules effect on thiol collector interaction, 286e300 xanthate interaction on galena and pyrite surfaces, 237e246 methods, 181e183 structureeactivity of chelating collectors, 192e203 computational details, 193e194 frontier orbital results, 194e199 metals with chelating collectors, 199e203 thiocarbamate collector, 190e192 FMO theory. See Frontier molecular orbital theory (FMO theory) Forbidden bandwidth, 95e96 Formation energy, 322e324, 323t Frontier molecular orbital theory (FMO theory), 25

of iron sulfide, 35e36 of pyrite and arsenopyrite, 54e56 Frontier orbital coefficient studies, 318e320 of copper sulfide minerals, 23e25, 24t energy of azo agents and minerals, 214e216 reagents and minerals, 214t results, 194e199 energies of HOMO and LUMO, 194f frontier orbital configurations and coefficients, 195te197t Frother molecule in water phase, 219e220 adsorbing at gaseliquid interface, 221e231 a-terpineol, 221e224 DF200, 226e231 MIBC, 226 slices of structures of, 220f Fukui functions (FFs), 108e110, 290e291 Fukui indices, 71e72, 72f

G Galena, 36, 115e116, 163e164, 193e194, 286e287 atomic orbital coefficient of LUMO of impurity-bearing galena, 318t coordination structures of Pb atoms in, 39f DOS, 120f analysis, 40e41 of surfaces before and after water adsorption, 140f flotation behaviors, 43f recoveries, 37f frontier orbital coefficients, 42t galvanic interaction between pyrite and, 65e76 effect of H2O and N2 molecules at interface of pyrite and, 76 effect of impurities on band structure and oxidation, 331e344 adsorption energy and structure, 336e339

364

computational methods, 332e333 cyclic voltammetry examination observations, 343e344 DOS analysis of oxygen with galena surface bearing impurities, 339e340 EDM, 340e342 effects of impurity on electronic band structure of galena, 334e336 effect of impurities on interaction between galena and, 349e356 effect of lattice defects on band gap and semiconductor type, 316t on lattice constants, 314f models, 38f multilayer water molecules adsorption on surfaces, 126e141 adsorption of isolated water molecule, 130e132, 131f computational methods, 128e130 excess water molecules adsorption, 132e137 slab model, 129f structure and electronic properties, 137e141 water and oxygen coadsorption on galena surface, 163e170 adsorption of single oxygen molecule, 165e166 adsorption of single water molecule, 166e167 computational models and methods, 165 sequential coadsorption of water and oxygen on surface, 167e169 simultaneous coadsorption of water and oxygen on surface, 169e170 Galena surface adsorption of xanthate, dithiophosphate, and dithiocarbamate, 247e259

Subject index adsorption heat of collectors, 256e258 analysis of DOS, 254e256 electronic structure and properties, 250e251 experimental and computational methods, 248e250 geometry and electron density of collector adsorption, 252e253 kinetics of collector adsorption, 258e259 surface atoms, 95e96 water molecule effect on galena surface adsorption, 297 on thiol collector interaction on sphalerite surface and, 286e300 xanthate interaction, 237e246 Galvanic corrosion, 66 Galvanic effect, 66 Galvanic interaction between pyrite and galena, 65e76 DOS of surface atoms, 74e75 effect of contact distance, 68e70 of Galvanian action on mineral flotation, 67e68 of H2O and N2 molecules at interface of pyrite and galena, 76 electronic transferred between mineral surface atoms, 70e71 Mulliken charge population of surface atoms, 71t nucleophilicity and electrophilicity of surfaces, 71e74 orbital coefficients of surface atoms, 74 principle of galvanism, 15 Gangue minerals, 278 Gaussian broadening, 49e50 Generalized gradient approximation (GGA), 6e8, 57, 114, 238, 248e249, 288

GGA. See Generalized gradient approximation (GGA) GGA-PW91, 38, 45, 207, 238, 266e267, 321e322, 332e333 Gibbs free energy, 256 Glassy carbon electrode, 333 Glauconite (Sb2S3), 36 frontier orbital coefficients, 42t models, 38f Gold (Au), 321 occurrences and correlation in pyrite, 321e331 computational details, 321e322 correlation, 322e324 crystal structure of pyrite, 324e328 electronic structures, 328e331 Gold-bearing pyrite floatability, 308, 309fe310f Grinding process, 34 Guangxi Dachang in China, 36

H H2OeO2 coadsorption on pyrite surface, 149e163. See also Water molecules (H2O) atomic Mulliken charge, 155f, 159f corrosion current of pyrite, 124t cyclic voltammetric curves, 162f DOS of S and O atoms changes, 157f H2O adsorbing on pyrite surface, 150f H2O2 formation on pyrite surface, 161f O2 adsorbing on pyrite surface, 151f simultaneous adsorption of H2O and O2 on pyrite surface, 152f of H2OeO2 on H2O preferentially adsorbed surface, 152f surface species, numbers, and adsorption energies, 123t

365

Hardness formula of pure covalent bond, 59e61 Hartree equation, 2 Hartree-Fock method (HF method), 2e3, 127 HF equation, 2 Hexagonal pyrrhotite, 13 computational methods and models, 57e58 electronic structure and flotation behavior, 56e64 electrons density, 61, 62f energy band and density of states, 58e61 flotation behavior, 63e64 frontier orbital calculations, 62e63 unit cells, 58f Hexyl thioethylamine, 55e56 HF method. See Hartree-Fock method (HF method) High chalcocite, 15 Highest occupied molecular orbital (HOMO), 23e25, 35e36, 107e108, 194, 198, 210 HohenbergeKohn’s theorem, 4e6 HOMO. See Highest occupied molecular orbital (HOMO) Hybrid density functional (BLYP), 6 Hydrocarbon radical compounds, 216 Hydrogen cyanide (HCN), 275 Hydrogen molecular model, 1 Hydrogen peroxide (H2O2), 160 Hydrogen xanthate molecule (HOCSe 2 ), 238 Hydrometallurgy of metal sulfides, 13e14 8-Hydroxy quinolone, 192 Hydroxyl radical formation, 158e159 8-Hydroxyquinoline, 199e203

I Ideal galena, 315e316 Impurity-bearing sulfide minerals

Subject index Impurity-bearing sulfide minerals (Continued) activation and collector adsorption on sphalerite surface bearing impurities, 307 impurities contribution on properties of sulfide mineral, 318e320 effect of impurities on band structure and oxidation of galena, 331e344 and defects on band gap, 315e318 and defects on lattice constants of sulfide minerals, 311e315 on floatability of sulfide minerals, 308e311 on interaction between galena and xanthate, 349e356 occurrences and correlation of Au and As in pyrite, 321e331 In situ FTIR spectroscopy, 331 Iron sulfide (FeS2), 28, 276 band structure, 30e32 bond Mulliken population, 34e35 bonding between S and Fe atoms, 33e34 crystal structure and floatability, 28e30 frontier molecular orbital, 35e36 minerals, 27 spin polarization, 33 Iron-bearing sphalerite, 347 Isobutyl xanthate, 186 Isolated H2O/O2 molecule adsorption, 145e149 Isolated water molecule adsorption on PbS and FeS2 surfaces, 130e132, 131f O-Isopropyl-N-ethyl thiocarbamate, 190e191

J Jamesonite (Pb4FeSb6S14), 36, 278 coordinated modes of Sb atoms for, 40f

coordination structures of Pb atoms in, 39f DOS analysis of, 40e41 flotation behaviors, 43f flotation recoveries, 37f frontier orbital coefficients, 42t models, 38f

K Kinetic energy, 4 KohneSham equation, 6

L Lattice constants of sulfide minerals, effect of impurities and defects on, 311e315 Lattice defects, 307e308 LDA. See Local density approximation (LDA) Lead sulfide (PbS). See Galena Lead xanthate, 66 Leadeantimony sulfide minerals, 36e43 computational methods, 37e38 DOS analysis of jamesonite, galena, and stibnite, 40e41 effects of crystal structures, 38e40 frontier orbital analysis, 42e43 LEED. See Low-energy electron diffraction (LEED) LEPD. See Low-energy positron emission spectroscopy (LEPD) Ligand field theory, 1 Lime (CaO), 64, 265 interaction with pyrite surface, 265e274 adsorption of OHeand CaOH+ on pyrite surface, 268e273, 269t copper activation of pyrite depressed by NaOH and CaO, 273e274 methods, 266e268 Local density approximation (LDA), 3, 7 Local spin density approximation (LSDA), 6

366

Low chalcocite, 15 Low-energy electron diffraction (LEED), 84, 92, 127 Low-energy positron emission spectroscopy (LEPD), 85 Lowest unoccupied molecular orbital (LUMO), 23e25, 35e36, 107e108, 194e195 LSDA. See Local spin density approximation (LSDA) LUMO. See Lowest unoccupied molecular orbital (LUMO)

M Magnetic Phoenix pyrrhotite, 56e57 Magnetic pyrite. See Pyrrhotite Magnetized water, 113 Marcasite, 27e28, 32 band structure and DOS, 31f bond overlap populations, 35t cyanide compound adsorption, 275e286 density of states between FeeS bond, 34f effect of oxidation on recovery, 30f relationship between oxidation time and oxygen consumption, 29f spin density of states, 33f unit cell structures, 29f Marmatite, 259e260 MD. See Molecule dynamics (MD) Mercaptobenzothiazole, 199 Metal sulfides, 276 minerals, 141 Metal-xanthate, 237 Metals with chelating collectors, 199e203 interaction configurations, 202f MIBC, 217, 225f, 225t, 226 a-terpene structure, 224f Microcalorimetry method, 247e248 Mineral crystals, 38 flotation, 106, 113

Subject index effect of Galvanian action, 67e68 surface, 250 MO. See Molecular orbital (MO) Modern solid physics theory, 8 Mohs hardness, 34 Molecular orbital (MO), 44e45 theory, 1e2 Molecule dynamics (MD), 216e217 Molybdenite (MoS2), 115e116 DOS of, 120f Monkhorst-Pack k-point sampling density, 45, 276 Monocarbonic acid, 189 Monoclinic arsenopyrite, 46 Monoclinic pyrrhotite, 78 computational methods and models, 57e58 electronic structure and flotation behavior, 56e64 electrons density, 61, 62f energy band and density of states, 58e61 flotation behavior, 63e64 frontier orbital calculations, 62e63 Mulliken bond population, 62t spin DOS, 61, 61f unit cells, 58f Mulliken bond population, 292 overlap population of bonds in pyrite, 327, 327t populations effect on sulfide minerals surfaces, 121e126, 122t Multilayer water molecules adsorption on PbS and FeS2 surfaces, 126e141 adsorption of isolated water molecule, 130e132, 131f computational methods, 128e130 excess water molecules adsorption, 132e137 structure and electronic properties of galena and pyrite surfaces, 137e141 Multielement analysis, 248

N n-type semiconductor, 331 Naphthalene ring, 213 Natural galena, 331e332 Nonmagnetic Sudbury pyrrhotite, 56e57 Nucleophilic index reflects, 108 Nucleophilicity of surfaces, 71e74

O Oleic acid, 198e199 Orbital coefficients of surface atoms, 74 Oxidation impurities effect of galena, 331e344 of pyrite, 141 Oxygen, 331, 333 and water coadsorption on galena surface, 163e170 and water interaction on pyrite surface, 141e163

P p-type semiconductor, 331 Partial density of states (PDOS), 134e135, 228e231, 292 of O atom in DF200 before and after H2O adsorption, 230f of O atom in frother molecule, 229f Pb-xanthate, 237 PBE, 8 PDOS. See Partial density of states (PDOS) Pearson principle, 290e291 Perdew-Wang (PW91), 8, 29, 114, 128, 248e249, 276, 290 Plane wave (PW), 57, 114 Platinum electrode, 333 Potassium cyanide (KCN), 275 Proximity effect theory, 141e142, 156e157 Pseudo atomic energy, 322 Pulay density mixing method, 128, 165, 248e249, 288 PW. See Plane wave (PW) PW91. See Perdew-Wang (PW91)

367

Pyrite (FeS2), 27e29, 37, 43, 115e116, 193e194, 307 atomic coordination structures, 48f atomic orbital coefficient of HOMO and LUMO of impurity-bearing pyrite, 320t band structure and DOS, 31f, 50f bond lengths and Mulliken population, 47t bond overlap populations, 35t crystal, 245 cyanide compound adsorption on, 275e286 density of states between FeeS bond, 34f DOS of, 119f of surfaces before and after water adsorption, 140f electronic and chemical structures, 43e56 computational methods, 45 crystal structure, 44e45 crystal structure differences, 46e49 electronic structures, 49e53 energy bands, 51f Fermi level, 53 flotation behaviors, 43f, 54f, 309fe310f frontier molecular orbital, 54e56 galvanic interaction between galena and, 65e76 H2O and N2 molecule effect at interface of galena and, 76 interaction of water and oxygen on pyrite surface, 141e163 computational methods, 143e145 H2OeO2 coadsorption on pyrite surface, 149e163 isolated H2O/O2 molecule adsorption, 145e149 lattice defects effect on band gap and semiconductor type, 317t on lattice constants, 315f

Subject index Pyrite (FeS2) (Continued) Mulliken overlap population of bonds, 327, 327t multilayer water molecules adsorption on surfaces, 126e141 adsorption of isolated water molecule, 130e132, 131f computational methods, 128e130 excess water molecules adsorption, 132e137 slab model, 130f structure and electronic properties, 137e141 occurrences and correlation of Au and As, 321e331 oxidation effect on recovery, 30f relationship between oxidation time and oxygen consumption, 29f spin density of states, 33f unit cells, 46f constant of pyrite and nickel content, 312f parameters and bond angles, 47t structures, 29f Pyrite surface, 97e99 activation model and electronic properties, 263e264 adsorption of xanthate, dithiophosphate, and dithiocarbamate, 247e259 adsorption heat of collectors, 256e258 analysis of DOS, 254e256 electronic structure and properties, 250e251 experimental and computational methods, 248e250 geometry and electron density of collector adsorption, 252e253 kinetics of collector adsorption, 258e259 copper activation, 259e264 lime interaction with, 265e274 mulliken charge of atoms, 100t, 102t

xanthate interaction, 237e246 Pyrometallurgic process, 13 Pyrrhotite, 27e28 band structure and DOS of, 32f bond overlap populations, 35t cyanide compound adsorption on, 275e286 density of states between FeeS bond of, 34f effect of oxidation on recovery of, 30f relationship between oxidation time and oxygen consumption for, 29f spin density of states, 33f unit cell structures, 29f

Q Quadrupole splitting, 44e45 Quantum chemistry model, 113e114 Quantum mechanics theory, 1 Quantum theory, 2, 113e114

R Raman spectroscopy, 127, 331 RD496-III type microcalorimeter, 248 Reactive oxygen species (ROS), 141e142 Reagent adsorption, 113 RHF equation. See RoothaanHartree-Fock equation (RHF equation) Rigaku D/MAX-2500 V diffractometer, 278e279 ROCSSM, 181 Roothaan-Hartree-Fock equation (RHF equation), 2 ROS. See Reactive oxygen species (ROS) RPBE, 8

S Salicylaldoxime, 192, 199e203 Salicylhydroxamic acid, 198e199 Saturated calomel electrode, 333 SBX. See Sodium butyl xanthate (SBX)

368

Scanning tunneling microscope (STM), 85, 127 Scanning tunneling spectroscopy (STS), 85 SCF. See Self-consistent field (SCF) Schrodinger differential equation, 8 Schrodinger equation, 1e3, 87e88 Second Brillouin zone, 10 Self-consistent field (SCF), 38, 114, 207, 238 Semiconductor valence band, 95e96 Single oxygen molecule adsorption on galena surface, 165e166 Single water molecule adsorption on galena surface, 166e167 Slab model, 89e90, 91f Sodium butyl xanthate (SBX), 248 Sodium carbonate (Na2CO3), 53 Sodium cyanide (NaCN), 275 dosage effect on grade and recovery of iron, 284e286 Sodium hydroxide (NaOH), 265, 268e269 copper activation of pyrite depressed by, 273e274 Sodium sulfate (Na2SO4), 53 Solid crystal structure, 86 Solid materials, 3 Solideliquid interface, 113 Sphalerite, 3e4, 115e116, 193e194, 286e287, 307 activation and collector adsorption on sphalerite surface bearing impurities, 309 activation and collection of impurity-bearing sphalerite, 344e349 effect of impurities on energy band structure of sphalerite surface, 344e347 effect of impurities on flotation behavior, 347e349 atomic orbital coefficient of LUMO of impurity-bearing sphalerite, 319t

Subject index copper activation of, 259e264 with different colors, 308f DOS of, 119f effect of different impurities content on floatability, 309f of lattice defects on band gap and semiconductor type, 316t of lattice defects on lattice constants, 314f flotation behavior, 308 unit cell constants and iron content in, 313f water molecules effect on sphalerite surface reagent adsorption, 292e297 on thiol collector interaction on galena surface and, 286e300 Spin DOS of monoclinic pyrrhotite, 60, 61f Spin polarization of iron sulfide, 33 Split of d orbital, 22e23 Ssbauer effect, 44e45 Stibnite (Sb2S3), 37, 115e116 coordinated modes of Sb atoms for, 40f DOS analysis of, 40e41 flotation behaviors, 43f flotation recoveries, 37f STM. See Scanning tunneling microscope (STM) Structure cell distortion, 311e312 STS. See Scanning tunneling spectroscopy (STS) Sulfide minerals, 13, 307e308 charge distribution of surface atoms, 100e104 model of sphalerite, 103f sketch map of changes, 101f crystal structure and electronic properties of copper sulfide minerals, 13e27 of iron sulfide minerals, 27e36 leadeantimony sulfide minerals, 36e43 DOS effect, 119e121

DOS of surface, 96e104, 98f, 105f Fe atoms at different layers of pyrite, 98f surface model of pyrite, 97f total density of states of pyrite (100) surface electronic and chemical structures of pyrite and arsenopyrite, 43e56 electronic properties, 13 electronic structure and flotation behavior of monoclinic and hexagonal pyrrhotite, 56e64 galvanic interaction between pyrite and galena, 65e76 effect of impurities and defects on lattice constants, 311e315 surface atomic reactivity, 106e110 FFs, 108e110 frontier orbital coefficient, 106e108 nucleophilic and electrophilic indices, 109t surface relaxation, 90e96 surface state, 90e96 coordination number and atomic displacement of galena, 91t coordination number and atomic displacement of pyrite, 92t reconstruction of chalcopyrite (001), 93f reconstruction of pyrrhotite (001), 93f sphalerite (110) surface unit cell, 93f structural parameters, 92t surface state energy level, 93e96 band structure of bulk and galena, 94f band structures of bulk pyrite and pyrite, 95f energy band models of galena and pyrite, 96f surface structure on electronic properties, 104e106

369

Sulfide ore flotation, 65 Sulfur atoms, 106 of chalcopyrite and covellite, 27 Sulfur vacancies, 313e314 Supercell approach, 116 Surface atomic coordination, 83 Surface electron density distribution, 89 Surface electronic states, 83e86 comprehensive development period, 84e85 mature period, 85e86 startup period, 84 Surface layer environment, 93e94 Surface relaxation, 86e90 slab model, 89e90 of sulfide minerals, 90e96 surface electronic states, 83e86 total energy of each surface, 86f surface states, 86e90 water molecule effect, 113e126 atomic displacement and coordination of sulfide mineral surfaces, 122t computational method, 114e116 DOS effect on sulfide minerals surfaces, 119e121 minerals surfaces relaxation after adsorption of H2O molecule, 116e117 Mulliken populations effect on sulfide minerals surfaces, 121e126 optimized geometries for single water molecule adsorption, 117f slab models of sulfide minerals surfaces, 115f Surface states, 86e90 electronic density curves near surface, 89f of sulfide minerals, 90e96 Surface structure, 89e90, 106f model of galena, 107f Synchrotron-based PES, 141e142 Synthetic “hexagonal” pyrrhotite, 56e57

Subject index T Temperature-programmed desorption (TPD), 127 a-Terpineol, 217, 221e224, 231e233 bond lengths of a-terpineol7H2O, 223t optimized structures of aterpineol-nH2O, 222fe223f polar head group of a-terpineol7H2O, 223t Thiocarbamate collector, 190e192 DOS of S and N atoms in thiocarbamate collector, 191f Thiocarboxylic acid, 198e203 Thiol collectors, 247e248 Third Brillouin zone, 10 ThomaseFermi model, 4 theory, 6 Three-dimensional water molecules (3D water molecules), 135 Toxic trace metals, 163e164 TPD. See Temperatureprogrammed desorption (TPD) Triclinic arsenopyrite, 46 Truncated octahedrons, 11 Two-dimension (2D) square lattice, 10 water molecules, 135

U Ultra-high vacuum technology, 84e85 Ultrasoft pseudopotentials, 57 Ultraviolet photoelectron spectroscopy (UPS), 84, 127 Uncertainty principle, 1

V

Valence band maximum (VBM), 49e50 Valence bond theory, 1 Valence electron configuration, 104

W Water molecules (H2O), 221, 226e227, 240. See also H2OeO2 coadsorption on pyrite surface density of states effect on sulfide minerals surfaces, 119e121 effect computational methods, 288e289 on galena surface adsorption, 297 on sphalerite surface reagent adsorption, 292e297 on surface properties of ZnS and PbS, 289e292 on surface relaxation, 113e126 on thiol collector, 286e300 Mulliken populations effect on sulfide minerals surfaces, 121e126 and oxygen coadsorption on galena surface, 163e170 interaction on pyrite surface, 141e163 Wave equation, 6, 89e90 White iron pyrite. See Marcasite

X X-ray absorption near-edge structure (XANES), 24 X-ray diffraction (XRD), 248 X-ray photoelectron spectroscopy (XPS), 84, 100e101, 127, 259e260 X-ray standing wave technique (XSW), 127

Vacancy defect, 310e311

370

XANES. See X-ray absorption near-edge structure (XANES) Xanthate, 27, 29e30, 290e291, 308e309, 331 adsorption on minerals surfaces in absence of oxygen, 239e241 in presence of oxygen, 241e244 frontier orbital energy of minerals and, 35t heat on surface of impuritydoped galena, 350t effect of impurities on interaction between galena and, 349e356 interaction on galena and pyrite surfaces, 237e246 adsorption on galena and pyrite surfaces, 247e259 computational details, 238e239 dixanthogen formation, 244e246, 244f Xanthate-type collector, bonded atoms of, 183f, 184e189 atoms in normal and isomers, 187f zinc and silver xanthate and alkyl structure and length, 188t XPS. See X-ray photoelectron spectroscopy (XPS) XRD. See X-ray diffraction (XRD) XSW. See X-ray standing wave technique (XSW)

Z Zinc (Zn) vacancies, 313e314 Zn-doped galena, 356 Zinc sulfide (ZnS). See Sphalerite

Author index Note: ‘Page numbers followed by “f ” indicate figures and “t” indicate tables’.

A

B

Abraitis PK, 45, 321 Abreu H A de, 92, 129e130 Abreu HAD, 13e14, 56 Abreu IA, 127, 131e132 Acharya HN, 331 Achimovicova´ M, 164 Ackerman PK, 207, 210 Adams GE, 210 Adriano DC, 163e164 Ahmadi E, 13e14, 19, 45, 141e142, 164, 246 Ala´cova´. A, 164 Alfonso DR, 127 Alfredsson M, 45, 321e322 Alizadeh S, 13e14, 19, 45 Alla G, 45 Allan DC, 15, 16t, 38, 45, 57, 128, 165, 248e249, 276, 288 Allison SA, 53, 237 Alonso-Vante N, 141 Altermatt PP, 141 Amarantidis J, 286e287 Amma EL, 44e45 Andersson K, 127, 129 Andiaa JPM, 275 Andreev SI, 127, 164 Anedda A, 164 Aplan FF, 207, 210 Appelbaum JA, 89e90 Arau´joc FVF, 275 Arce EM, 13e14 Arehart GB, 321 Arias TA, 15, 16t, 38, 45, 57, 128, 165, 248e249, 276, 288 Ayers PW, 108, 290e291

Bae SJ, 237e238 Bala´z P, 164 Balci N, 141e142, 148e149 Bancroft GM, 100e101, 127, 141 Bancroft MG, 54e55 Barbaro M, 193, 199 Bardeen J, 83 Barkowski S, 44, 321e322 Barres O, 192e193 Bartlett R, 164 Bartolotti LJ, 108 Batchelder FV, 192e193 Batonneau Y, 164 Bauer D, 164 Bayliss P, 44 Beattie DA, 259e260 Beattie JK, 127, 141e142, 148e149 Bebie J, 141, 145, 153 Becker M, 56e57 Becker U, 56e58, 61, 99e100, 127, 131e132, 141e143, 145, 153, 156e158, 287, 321 Benner RE, 331 Bernasconi M, 113e114, 127e128, 131e132, 143, 145 Bertrand V, 74 Bethe H, 1 Bigham JM, 164 Bindi L, 44, 46 Bird DK, 322 Biswas AK, 13 Black S, 141e142

371

Blanchard M, 45, 321e322 Bodily DM, 331 Boehme C, 127, 131e132 Boese HCN, 216e217 Bolin NJ, 260, 273 Borda MJ, 141e142, 162 Borode JO, 164 Bostick BC, 141e142 Boulton A, 259e260 Boylu F, 216 Bradshaw D, 56e57 Bradshaw DJ, 247, 287 Bre´mard C, 164 Brodholt J, 45, 321e322 Bronold M, 131e132, 141, 145 Broo AE, 141e142, 164, 246 Brooker MH, 164 Brown GE, 127 Brown JGE, 141e142 Brown Jr GE, 127, 129 Bruggen CF, 127 Bryce RA, 127e128 Buckley AN, 13e14, 164, 263e264, 290e291 Budden JR, 164 Buerger MJ, 44, 47e48 Buker K, 141 Bulatovi CS, 203 Bulatovic S, 286e287 Bulatovic SM, 216 Burdett JK, 44e45, 48e49 Burke K, 8, 288 Burrows MJ, 56e57 Bushell CHG, 260 Butler IS, 192e193 Butsman MP, 24

Author index C Cai J, 127 Cai YF, 127 Calis GHM, 24e25 Callaway J, 45 Candra N, 163e164 Cao F, 181 Car R, 127, 131e132 Cardona M, 164 Carroll SA, 163e164 Carter EA, 45, 321e322 Cases JM, 164, 192e193 Castro S, 216 Catalano JG, 113 Cathey L, 44e45 Catlow CRA, 45, 321e322 Chander S, 247, 287 Chanturiya VA, 45, 308 Charnock JM, 287 Chaturvedi S, 127 Chaudhary D, 216 Chen BC, 113 Chen FW, 181 Chen J, 113, 143, 145, 259e260, 315, 331, 351 Chen JH, 26e27, 44f, 53, 106e107, 113e114, 126e129, 164e165, 181, 184, 186, 203, 210, 241e243, 247, 250, 266, 277e278, 287, 290e292, 308, 313e315, 318, 320, 331e333, 348 Chen ML, 216e217 Chen SP, 258 Chen Y, 106e107, 113e114, 126e127, 143, 145, 181, 184, 231e233, 247, 250, 266, 287, 290e291, 308, 313e315, 318, 320, 332 Chen YJ, 56e57 Chernyshova IV, 127, 164, 331, 343 Chevary JA, 8, 114, 143, 165, 210, 238, 266e267, 288, 321e322 Chiuzbaian SG, 44, 321e322 Cho BU, 237e238 Choi P, 181, 287 Chryssoulis SL, 321

Ciriachi M, 193 Clark LA, 44 Clark RJH, 164 Clark SJ, 114, 143, 332e333 Cocula V, 45, 321e322 Cohen MH, 127, 131e132, 141e143, 145, 147e148, 158, 164e165, 169 Cohen RE, 8, 16t Cohn CA, 141e142 Coleman ML, 141e142 Cook NJ, 321 Cooper WC, 275 Cord-Ruwisch R, 13e14 Corkhill CL, 45, 54e55 Corn RM, 216e217 Cortecci G, 141e142, 148e149 Cotterill GF, 164 Craig JR, 56e58 Critchley JK, 240e241 Crozier RD, 247 Cruywagen JJ, 247, 287 Cruz R, 74 Cui YQ, 43

D Dadfarnia S, 195 Dahanayake M, 216e217 Dai Z, 56e57 Dai ZL, 181 Dang LX, 294 Davenport WG, 13 Davidson R, 321 De Donato P, 192e193 De F, 73 De Giudici G, 163e164 de Leeuw NH, 127e128, 131e132, 143 Delley B. J, 193e194 Demirel H, 65e66 Deng LJ, 233 Devey AJ, 127 Devi S, 195 Devries AJ, 233 Dewitt CC, 192e193 Diggle JW, 164 Ding Y, 15 Dodonay I, 56 Donato PD, 164 Dong FL, 216

372

Doyle CS, 127, 129, 141e142 Dreisinger DB, 275 Dreizler RM, 181 Du H, 275 Du Z, 181, 184 Duarte HA, 13e14, 56, 92, 129e130 Dudka S, 163e164 Duke CB, 92, 92t Dumonceau J, 273 Dutrizac JE, 164

E Eadington P, 331 Edelro R, 45, 49e50 Eggleston CM, 127, 141 Egiebor NO, 163e164 Ehrhardt JJ, 141 Ekmekci Z, 65e66 Eldridge CS, 321 Elgillani DA, 237, 244e245, 275e276 Ellmer K, 141 Elsetinow AR, 141e142, 145, 153, 162 Emekci Z, 247, 287 Emezerhof M, 8 Engel E, 181 England KER, 287 Ennaoui A, 141 Erlenmeyer H, 192 Ernzerhof M, 288 Eschrig H, 45 Espinosa-Gomez R, 275e276 Esteva JM, 45 Evan JN, 210 Evans HT, 14e15, 19, 24e25 Ewing RC, 321 Eyert V, 44e45, 49e50

F Fanfani L, 163e164 Farrokhpay S, 216 Fedorov AA, 45, 308 Feng Q, 351 Feng QM, 26e27, 53, 113, 203, 210, 331

Author index Fermi E, 4 Fernandez PG, 53 Ferrer IJ, 311e312 Ficeriova´ J, 164 Fiechter S, 44e45, 49e50, 141 Finch JA, 65e66, 68e70, 192e193, 275 Finkelman RB, 141 Finkelstein NP, 331 Finklea SL, 44e45 Fiolhais C, 8, 114, 143, 165, 210, 238, 266e267, 288, 321e322 Flavell WR, 127 Fleet ME, 321 Fletcher S, 164 Flotation AM, 68 Fock V, 2 Folmer JCW, 24e25 Fornasiero D, 164, 259e260, 287, 331 Forsling W, 113, 164, 247 Forssberg E, 260, 273 Forssberg KSE, 237, 265, 275e276 Freeman AJ, 86f Friedeberg H, 195 Fu CL, 86f Fuerstenau DW, 193, 247, 287 Fuerstenau MC, 237, 244e245, 247, 275e276, 300 Fuess H, 44 Fujimori A, 16 Fujisawa M, 16 Fukui K, 2

G Gadre SR, 216 Gale JD, 127 Gao FM, 59e61 Gao SL, 248, 258 Gao SW, 132 Gao YD, 181 Garcia Jr O, 164 Gardner JR, 164 Gaudin AM, 331 Geerlings P, 73 Gehrke T, 164 Gerson A, 260, 273

Gerson AR, 44e45, 49e50, 56e57, 75, 127, 260, 262e263, 281 Giudici GD, 164 GlembotskII BA, 188t, 247 Godoc´ıkova´ E, 164 Gokagac G, 247, 287 Goliney IY, 127e128, 143 Gomes CL, 127 Goncharova LV, 288 Gonza´lez I, 13e14, 74, 164 Gonza´lez IC, 164 Gonzalezcaballero F, 331 Goodenough JB, 44, 48e49 Goold LA, 53, 237 Gorb L, 216e217 Goryachev BE, 333 Grano S, 26e27 Grano SR, 286e287 Granville A, 53, 237 Grau-Crespo R, 127 Graua RA, 216, 233 Greatbanks SP, 127 Greenler RG, 237 Gu YL, 233 Guevremont J, 127 Guevremont JM, 127, 131e132, 141, 145, 153 Guillon E, 273 Guler T, 247, 287 Gunnarsson O, 114, 181e183 Guo B, 275e276 Guo J, 44f, 106e107, 113e114, 127e129, 164e165, 241e243, 247, 250, 287, 292, 313e315, 318, 320, 332e333 Guzma´n MTO, 164 Gyftopoulos EP, 108

H Hall RJ, 127e128 Hall SR, 15, 55f Hamilton IC, 13e14 Hammer B, 8, 15, 16t, 38, 288 Hampton MA, 164 Hansen LB, 8, 15, 16t, 38, 288 Harada J, 307 Harada T, 29fe30f

373

Harmer SL, 259e260, 288 Harris GH, 207, 210 Harrison NM, 127 Hartree DR, 2 Hasegawa M, 322 Hasnip PJ, 114, 143, 332e333 Hatsopoulos GN, 108 Haubrich F, 163e164 Hauman DR, 89e90 Haung HH, 237, 239e240, 245, 247, 258e259, 287 Hayes RA, 127, 164 Hckhella Jr MF, 127 He GY, 181, 185, 210, 272e273 He J, 43 He JL, 59e61 He MF, 56e57 He Q, 278 Hedin LA, 45, 321e322 Heide H van der, 127 Heidel C, 127, 141e142, 148e149, 164, 166e167, 169e170 Heidel CM, 141e142 Heinonen M, 141 Heiskanena K, 216, 233 Heitler W, 1 Hellstro¨m P, 287 Hemmel R, 127 Henderson MA, 287 Heras CDL, 311e312 Herrera-Urbina R, 193 Hicyilmaz C, 247, 287 Hideki S, 163e164 Higgins DA, 216e217 Hill IR, 127 Hiller IH, 113e114, 127e131, 165, 288 Hirsch D, 164 Hochella Jr MF, 99e100, 127, 131e132, 141e143, 145, 153, 156e158, 287 Ho¨ck KH, 44e45, 49e50 Hoechst H, 54e55 Hoffman I, 331 Hohenberg P, 3, 5, 321e322 Holman BW, 192 Holmgren A, 287 Hong QY, 56e57 Hopfner C, 141

Author index Horne MD, 164 Hromadova M, 216e217 Hsieh YH, 163e164 Hu RZ, 258 Hu XG, 25, 47t, 307, 331e332 Hu XL, 132 Hu YH, 164e165, 181, 185, 203, 210, 266 Huang CP, 163e164 Huang DW, 277 Huang GH, 26e27 Huang H, 321 Huang JP, 181 Huang X, 141 Huang YG, 181 Hubbard CG, 141e142 Hu¨ckel E, 1 Huggins ML, 44 Hughes AE, 164 Hulliger F, 44e45, 48e49 Hung A, 97e99, 127, 129, 237e238, 247, 287, 332 Hunter CJ, 240e241 Hunz AW, 56e58, 61

I Ignatkina VA, 290e291 Imanuel M, 163e164 Israelachvili JN, 210

J Jackson KA, 8, 114, 143, 165, 210, 238, 266e267, 288, 321e322 Jaegermann W, 131e132, 141, 145 Jameson G, 300 Ja nczuk B, 287, 331 Janzen MP, 56 Jasieniak M, 56e57 Jellinek F, 24e25 Ji M, 248 Jia CY, 212 Jin G, 315 Jin JCZ, 307 Jin JQ, 294 Joannopoulos JD, 15, 16t, 38, 45, 57, 128, 165, 248e249, 276, 288 Jones RO, 114, 181e183

Jones RT, 44e45, 49e50, 75, 281 Jozsa P-G, 164 Jumas JC, 45 Junghans M, 141e142, 145, 148e149, 163e164

K Kakovsky IA, 240e241 Kalahdoozan M, 56e57 Kanazawa Y, 19 Kang D, 44f, 287, 292 Kao LS, 321 Karnatak RC, 45 Karthe S, 266, 273 Kartio I, 127, 141, 164, 273, 331 Kartio L, 273 Katz R, 127 Ke BL, 181, 290e291 Kelebek S, 56e57 Kendelewicz T, 127, 129, 141e142 Kerr AN, 56e57 Kesler SE, 321 Kevin P, 141 Khalid S, 141 Khan Y, 141 Kiesewetter T, 141 Kikuo M, 163e164 Kim BS, 127, 164 King M, 13 Kinzler K, 164 Kitamori T, 216e217 Klauber C, 127, 288 Klimpel RR, 207, 210 Klymowsky IB, 241e243, 331 Knipe SW, 141 Koepernik K, 45 Kohn W, 3, 5e6, 45, 88e89, 114, 321e322 Kolarova R, 288 Kolobova KM, 24 Komosa A, 259e260 Konnert JA, 14e15, 24e25 Konno H, 141e142 Kostovic M, 275 Koto K, 15, 19 Kratz T, 44

374

Krauss CJ, 260 Kravets IM, 164 Kresse G, 127e131 Krestan AL, 58e59 Kubicki JD, 141e142, 148e149, 158 Kuepper K, 44, 321e322 Kuhn MC, 237, 244e245 Kunze S, 164 Kydros KA, 55e56

L Laajalehto K, 30, 127, 141, 164, 192e193, 273, 331 Laffers R, 141e142 Lai CH, 56e57 Laiho T, 164, 273 Lam-Thi PO, 164 Lamache M, 164 Lan LH, 126e127, 129, 164e165, 181, 241e243, 287, 308, 333 Lang ND, 88e89 Lange AG, 260, 262e263 Laskowski J, 68 Laskowski JS, 216, 233 Lastra MR, 164 Lattanzi P, 163e164 Lauck R, 164 Laureyns J, 164 Lawson V, 56e57 Lazic PM, 287 Lee WJ, 237e238 Lefebvre I, 45 Leiro JA, 127, 141 Leja J, 331 Lennard WN, 288 Lennie AW, 56e58, 61 Leone P, 44, 46 Leppinen J, 192e193, 273 Leszczynski J, 216e217 Levy M, 290e291 Lewis DJ, 141 Li CG, 189 Li DC, 59e61 Li F, 164 Li FS, 331 Li HY, 258 Li J, 331 Li WZ, 277

Author index Li Li Li Li

X, 127 XA, 113 Y, 210, 216, 315 YQ, 44f, 106e107, 113e114, 127, 129, 164e165, 181, 203, 241e243, 247, 250, 266, 277e278, 287, 290e291, 315, 320, 333, 348 Liang DY, 56e57 Liang W, 19 Lima G F de, 129e130 Lima GF, 92 Lima GFD, 13e14, 56 Lin QW, 272e273 Lin TT, 127e128 Lindan PJD, 114, 143, 332e333 Linge HG, 53 Lins FF, 126e127 Liu FX, 186 Liu GY, 181, 287 Liu J, 181 Liu MY, 248 Liu P, 127 Liu QX, 181, 184 Liu SB, 71e73, 290e291 Liu SM, 59e61 Liu WG, 212 Liu WL, 181, 185, 210 Liz WZ, 56e57 London F, 1 Long QR, 203 Long X, 143, 145 Long XH, 127e128, 164e165, 181, 184, 287, 292 Lorimer JW, 127 Lowson RT, 127, 141e142, 148e149 Lu D, 114 Lu JM, 275 Lu JR, 216e217 Lu YP, 113, 203, 210 Luther III GW, 141e142 Lyttle DJ, 216e217

M Ma LQ, 181 Maclean PJ, 321 Majima H, 237 Malik MA, 141

Mandernack KW, 141e142, 148e149 Mannan MB, 237e238 Marabini AM, 192e193, 199 Marrocco A, 216e217 Martı´n-Izard A, 127 Marx D, 127, 131e132 Marzari N, 114, 181e183 Masatomo I, 163e164 Matis KA, 55e56 Matteucci M, 44, 321e322 Mattila SS, 127, 141 Matveeva TN, 45, 308 Mavros P, 55e56 Mayer B, 141e142, 148e149 McGlashan DW, 193 McIntyre NS, 127 Mellgren O, 239e240, 247, 287 Melo F, 216 Meng S, 132 Merlin JC, 164 Mian M, 127 Michaelides A, 132 Miehe G, 44 Mielczarski JA, 192e193 Mierczynska Vasilev A, 259e260 Mikhlin Y, 50 Miller JD, 237, 239e240, 245, 247, 258e259, 266, 275, 287, 294 Mir N, 13e14, 19, 45 Mizokawa T, 16 Moelo Y, 44, 46 Moloshag VP, 24 Monkhorst HJ, 45, 114, 238, 248e249, 266e267, 276, 288, 321e322, 332e333 Monkhorst J, 114, 128, 165 Monroy M, 74 Montalti M, 287 Monte MBM, 126e127 Monteil-rivera F, 273 Mooser E, 44e45, 48e49 Morimoto N, 15, 19, 44 Moroi Y, 216 Mosselmans JFW, 287 Mousavi-Kamazani M, 13e14, 19, 45

375

Muir IJ, 127, 141 Mullens TE, 321 Mullike RS, 1 Muscat J, 97e99, 127, 129, 288 Mycroft JR, 127, 141

N Nair NN, 127 Nakahara H, 216 Nakamura S, 141 Narayansamy J, 141e142, 148e149, 158 Nasirizadeh N, 195 Nathaniel A, 331 Naujok RR, 216e217 Nava-Alonso F, 65e66, 68e70 Naveau A, 273 Ndlovu S, 164 Ndzebet E, 164 Nelson EJ, 127 Nesbitt HW, 30, 45, 49e50, 54e55, 100e101, 127, 141, 263e264 Nesset JE, 275 Neumann M, 44, 321e322 Ngoepe PE, 127e128, 131e132, 143 Nguyen AV, 164 Nguyen CV, 216 Nicholson RV, 56 Nickel EH, 44e45, 48e49 Nicol MJ, 53, 164, 237 Nikolaev AA, 333 Nishidate K, 322 Niu XX, 181 Nixon JC, 237 Nonferr T, 241e243 Nooshabadi AJ, 169e170 Nordlund D, 127, 129 Nordstrom DK, 141e142, 148e149 Norskov JK, 8, 15, 16t, 38, 288 Nowak P, 127, 164, 192e193, 199 Nusair M, 45, 321e322 Nyberg M, 127, 129

Author index O ¨ berg S., 287 O O’Brien P, 141 O’Connor CT, 247, 287 O’Day PA, 163e164, 322 O’Dea AR, 127 O’Dell CS, 331 O’Riordan T, 141e142 Odell CS, 331 Oertzen GUV, 44e45, 49e50, 75 Ogasawara H, 127, 129 Ohtsuka T, 141e142 Oliveira C, 92 Oliveira C de, 129e130 Oliveira JF, 126e127 Oliveria CD, 13e14, 56 Olivier-fourcade J, 45 Olubambi PA, 164 Oni B, 163e164 Opahle I, 45 Opara A, 275 Oriova TA, 58e59

P Pack JD, 45, 114, 128, 165, 238, 248e249, 266e267, 276, 288, 321e322, 332e333 Pak A, 141e142 Palenik CS, 321 Palero-Ferna´ndez FJ, 127 Pan YG, 127 Papadoyannis IN, 55e56 Paquin I, 192e193 Parker RJ, 164 Parker SC, 127e128, 131e132, 143 Parr RG, 108, 290e291 Parrinello M, 113e114, 127e128, 131e132, 143, 145 Pasina-Trevellao ET, 189 Patrick H-LS, 127, 131e132, 141e143, 145, 147e148, 158, 164e165, 169 Pattrick RAD, 45, 287, 321 Paugh PJ, 203 Paul A, 331 Paul J, 45, 49e50 Paul KW, 141e142, 148e149, 158 Paul RL, 164

Pauling L, 1 Pauporte´ T, 164 Payne MC, 15, 16t, 38, 45, 57, 114, 128, 143, 165, 181e183, 248e249, 276, 288, 327, 332e333 Pcak JD, 114 Pearson RG, 108 Pecina-Trevin˜o ET, 65e66, 68e70 Pederson MR, 8, 114, 143, 165, 210, 238, 266e267, 288, 321e322 Peggy MKG, 163e164 Pelkner S, 163e164 Penfold J., 216e217 Peng YJ, 275e276 Penner-Hahn JE, 321 Perdew JP, 7e8, 16t, 38, 45, 57, 114, 128, 143, 165, 238, 248e249, 266e267, 276, 288, 321e322 Perry DL, 24e25 Peters E, 237 Pettenkofer C, 131e132, 141, 145 Phan CM, 216 Philpott MR, 127e128, 143 Piasecki DA, 216e217 Pickard CJ, 114, 143, 327, 332e333 Piechowski M, 163e164 Pingale SS, 216 Pistorius PC, 275e276 Plackowski C, 164 Plaskin IN, 331 Plescia P, 193 Poling GW, 331 Pollet R, 131e132 Pomianowski A, 127 Potgieter JH, 164 Potter RW, 15 Pratt AR, 100e101, 141, 263e264 Prestidge CA, 126e127, 164, 276, 286e287 Prewitt CT, 15 Prince KC, 44, 321e322 Prince KE, 260, 262e263

376

Probert MIJ, 332e333 Pronbert MJ, 114, 143 Prosfai M, 56 Prosser AP, 331 Provert MIJ, 114, 143 Pucci R, 290e291

Q Qin WQ, 56e57, 164e165, 203 Qiu GZ, 164e165, 266 Qiu XY, 181

R Raikar GN, 141e142 Rajagopal AK, 45 Raju BG, 247 Ralston J, 126e127, 164, 259e260, 276, 286e287, 331 Ralston S, 164 Ramos O, 216 Ramsdell LS, 44 Rand DAJ, 246 Rao KH, 169e170 Rao SR, 65e66, 68e70, 275 Reedy BJ, 127, 141e142, 148e149 Refson K, 114, 143, 332e333 Reich M, 321 Ren SY, 19, 25 Rezaei O, 13e14, 19, 45 Ricci P, 164 Richardson PE, 331 Riley AM, 331 Rimstidt JD, 141e142, 154e155 Rinelli G, 192e193, 199 Robert BF, 163e164 Rodriguez JA, 127, 131e132 Rohwerder T, 164 Ro¨nngren L, 113, 164 Roothaan CCJ, 2 Rosen MJ, 216e217 Rosic AA., 287 Rossi A, 163e164 Rosso KM, 99e100, 127, 131e132, 141e143, 145, 153, 156e158, 287, 332 Ruan BF, 203

Author index Russo SP, 97e99, 127, 129, 237e238, 247, 287, 332 Ryu JY, 237e238

S Salamy SG, 237 Salavati-Niasari M, 13e14, 19, 45 Sanchez C, 311e312 Sand W, 164 Sandenbergh RF, 275e276 ˚ , 45, 49e50 Sandstro¨m A Sarmientod CM, 275 Sasaki K, 141e142 Sato K, 16, 127 Saunders AP, 164 Saunders VR, 127 Savage KS, 322 Sawada T, 216e217 Scaini MJ, 54e55, 100e101 Scharer JM, 56 Schaufuss AG, 54e55, 141 Schindler PW, 113 Schippers A, 164 Schlegel A, 30, 47t, 51, 321e322 Schlesinger M, 13 Schoonen MAA, 127, 131e132, 141e142, 145, 148e149, 153, 158, 162 Schreiner E, 127 Schuhmann D, 164 Schwarcz HP, 141e142, 148e149 Segall MD, 114, 143, 327, 332e333 Seke MD, 275 Sekia M, 127 Selloni A, 127, 131e132, 141e143, 145, 147e148, 158, 164e165, 169 Sexton BA, 164 Shabani AMH, 195 Shabanova IP, 24 Shafeev R, 331 Shah R, 195, 327 Sham LJ, 6, 45, 114, 321e322 Shanks Iii WC, 141e142, 148e149 Shapter JG, 164 Shchukarev AV, 164

Sherwin R, 164 Shi QZ, 248, 258 Shi YT, 311 Shibata O, 216 Shibuya S, 127 Shields Y, 56e57 Shina S, 127 Shingu H, 2 Shishehbore MR, 195 Shishkin OV, 216e217 Shockley W, 83 Shuwen C, 307 Silva GD, 164 Simister EA, 216e217 Simola J, 164 Simon G, 321 Simon SR, 141e142 Singh DJ, 8, 114, 143, 165, 210, 238, 266e267, 288, 321e322 Sirkeci AA, 55e56 Sithole HM, 127e128, 131e132, 143 Sjo¨berg S, 113, 164 Skinner WM, 45, 49e50, 56, 100e101, 127, 164, 263e264, 286e287 Slater JC, 2 Smart C, 164 Smart J, 164 Smart RSC, 56, 127, 164, 276, 286e287 Solecki J, 259e260 Somasundaran P, 216e217 Song BK, 237e238 Song Q, 127e128 Sparks DL, 141e142, 148e149, 158 St R, 164 Starrost F, 45, 321e322 StC R, 164 Steele HM, 113e114 Stefanovich EV, 127e128 Steiger JV, 192 Stewart JM, 15, 55f Stirling A, 113e114, 127e128, 131e132, 143, 145 Stixrude L, 321 Strens RGJ, 51 Strizhko VS, 333

377

Strongin DR, 127, 131e132, 141e142, 145, 148e149, 153, 158, 162 Stumm W, 141 Stupnikow VM, 58e59 Su GZ, 127 Su TJ, 216e217 Suarez DF, 56e57 Suchaud M, 44, 46 Suga S, 16, 127 Sun CY, 181, 183, 189e191, 212 Sun QF, 127 Sun W, 164e165, 181, 185, 210, 272e273 Sun ZX, 113, 164 Suoninen E, 127, 164, 192e193, 266, 331 Sutherland KL, 247, 259e260, 275 Szargan R, 30, 54e55, 141, 164, 266, 273 Szczypa J, 259e260

T Tabiguchia M, 127 Taggart AF, 247 Takashi S, 163e164 Takeda M, 237 Takenaka T, 216e217 Tamm IE, 83 Tang YH, 56e57 Tao FM, 216e217 Taylor BE, 127, 141e142, 148e149 Taylor JA, 24e25 Teixeira LAC, 275 Teter MP, 15, 16t, 38, 45, 57, 128, 165, 248e249, 276, 288 Theilheimer W, 192 Thi OH, 164 Third KA, 13e14 Thomas JE, 56 Thomas LH, 4 Thomas RK, 216e217 Thornton G, 56e58, 61 Thurgate SM, 141e142 Tian Y, 59e61, 203, 216e217 Tichomirowa M, 127, 141e142, 145, 148e149, 163e164, 166e167, 169e170

Author index Tingle TN, 322 Tobschall HJ, 113 Tolun R, 237, 245 Tomashevich Y, 50 Tong X, 43 Topel-Schadt J, 44 Tossell JA, 35e36, 44e45, 48e49 Trahar WJ, 164 Tributsch H, 44e45, 49e50, 141 Trofimova VA, 24 Truong TN, 127e128 Tsunekawa M, 141e142 Tsuyumoto I, 216e217 Tuma C, 216e217 Tuovinen OH, 164 Turcotte SB, 331

U Uhlig I, 30 Ulasyuk SM, 333 Umemura J, 216e217 Urch DS, 35e36 Uribe-Salas A, 65e66, 68e70 Usher CR, 141e142, 148e149, 158 Usoni L, 193 Usul AH, 237, 245 Utsunomiya S, 321

V Valente TM, 127 van Haas C, 127 Vanderbilt D, 8, 45, 114, 128, 143, 165, 181e183, 238, 248e249, 266e267, 288, 321e322, 332e333 Vanel P, 164 Vanier LL, 286e287 Vaughan DJ, 35e36, 44e45, 48e49, 54e58, 61, 127e131, 141e142, 154e155, 165, 288, 321, 332 Veblen DR, 15 Villiers JD, 56e57 Vincent MA, 127e131, 165, 288 Vivian AC, 192e193 Voigt S, 273

Von Barth U, 45, 321e322 von Oertzen GU, 100e101, 127, 263e264, 281 Vosko SH, 8, 45, 114, 143, 165, 210, 238, 266e267, 288 Vosko SHK, 321e322 Vosko SJ, 321e322 Vreugdenhil AJ, 192e193 Vucinic DR, 287

W Wachter P, 30, 47t, 51, 321e322 Wadsley MW, 53 Wadsworth ME, 331 Wang DZ, 210, 216e217 Wang EG, 132 Wang HJ, 181, 216e217 Wang JS, 203 Wang L, 106e107, 113e114, 313, 318, 332 Wang S, 181 Wang XH, 237, 244e245, 260, 265, 273, 275e276 Wang Y, 7, 16t, 38, 45, 56e57, 128, 248e249, 276 Wang YR, 92, 92t Wang ZW, 216e217 Ward JC, 57e58 Wark IW, 259e260, 275 Warren MC, 45, 54e55 Watling HR, 13e14 Watson SC, 45, 321e322 Waychunas GA, 322 Weerasooriya R, 113 Wei DZ, 212 Weinert M, 86f Weisener C, 260, 273, 321 Wells JD, 321 Wells PF, 56e57 Wen SM, 113 Wet JRD, 275e276 Whangbo MH, 19 Wheeler MC, 127, 141e142, 148e149 Wiech G, 35e36 Wilk L, 45, 321e322 Wilson N, 127 Wimmer E, 86f Wirth MJ, 216e217

378

Wittstock G, 164 Wo´jcik W, 287, 331 Womes M, 45 Wood BJ, 51 Woods R, 13e14, 164, 237, 290e291, 331 Wright K, 45, 113e114, 127e131, 165, 288, 321e322 Wu BZ, 278 Wu ED, 59e61 Wu JY, 203 Wu WG, 212 Wu Z, 8, 16t Wyslouzil DM, 203, 286e287

X Xiao JJ, 181, 287 Xiao JX, 216 Xie XD, 114 Xiong DL, 203 Xiong X., 344e345 Xu J, 210 Xu M, 56e57 Xu ZH, 181, 184, 287 Xue JY, 127

Y Yamaguchi T, 127 Yamamoto A, 141 Yan P, 216 Yan Y, 312 Yang F, 181, 185, 210 Yang LY, 181 Yang MJ, 308 Yang WT, 108, 290e291 Yang XL, 181 Yarovsdy I, 97e99, 127, 129, 237e238, 247, 287, 332 Ye S, 312 Yekeler H, 247 Yekeler M, 247 Yin X, 275 Yokoyamac L, 275 Yonezawa T, 2 Yoon RH, 300 Yoshizawa M, 322 Yu DL, 59e61 Yu LX, 56e57

Author index Z Zdziennicka A, 287, 331 Zeng K, 54f Zeng XQ, 113e114 Zhang GX, 216e217 Zhang JF, 210 Zhang LX, 127e128 Zhang P, 216 Zhang SB, 127e128 Zhang SL, 266 Zhang SY, 59e61

Zhang WB, 113 Zhang Y, 272e273 Zhang YK, 108 Zhang ZC, 163e164 Zhang ZH, 216e217 Zhao CH, 127e128, 164e165, 277e278, 287, 290e292 Zhao G, 181 Zhao LM, 233 Zhao Q, 203 Zhong H, 181, 287

379

Zhou DQ, 212 Zhou DW, 181, 287 Zhou QH, 43 Zhou TX, 189 Zhu JJ, 113 Zhu YK, 212 Zhu YM, 212 Zipoli F, 127, 131e132 Zuddas P, 163e164