Oxide Thermoelectric Materials: From Basic Principles to Applications 3527341978, 9783527341979

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Oxide Thermoelectric Materials

Oxide Thermoelectric Materials From Basic Principles to Applications

Yuan-Hua Lin Jinle Lan Cewen Nan

Authors Prof. Yuan-Hua Lin

Tsinghua University School of Materials Science and Engineering No.30 Shuangqing Road, Haidian Haidian District 100084 Beijing China

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Library of Congress Card No.:

Prof. Jinle Lan

Beijing University of Chemical Technology College of Materials Science and Engineering North Third Ring Road 15 Chaoyang District 100029 Beijing China Prof. Cewen Nan

Tsinghua University School of Materials Science and Engineering No.30 Shuangqing Road, Haidian Haidian District 100084 Beijing China Cover Image: © ThomasVogel/Getty

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The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at . © 2019 Wiley-VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Print ISBN: 978-3-527-34197-9 ePDF ISBN: 978-3-527-80752-9 ePub ISBN: 978-3-527-80754-3 oBook ISBN: 978-3-527-80755-0 Typesetting SPi Global, Chennai, India Printing and Binding

Printed on acid-free paper 10 9 8 7 6 5 4 3 2 1

v

Contents Foreword ix

Part I

Theories and Fundamentals 1

1

Electron Transport Model in Nano Bulk Thermoelectrics 3

1.1 1.2 1.3 1.4 1.5 1.6

History of Conducting Oxides 3 Structural Characteristics of Oxides 8 Band Structure of Conventional Oxides 11 Electrical Properties 11 Model for Thermoelectric Oxides 15 Effect of Interface on Electron Transport 17 References 22

2

Controlling the Thermal Conductivity of Bulk Nanomaterials 25

2.1 2.2 2.2.1 2.2.2 2.2.3 2.3 2.4 2.5 2.5.1 2.5.2 2.5.3 2.6 2.7 2.8

Bonding and Lattice Vibration 25 Lattice Distortions in Determining Thermal Properties 25 Point Defects and Dislocations 25 Peierls Distortion 27 Octahedral Distortion in Manganite Perovskites 28 Callaway Model and the Minimum Thermal Properties 30 Temperature Relationship in Thermal Properties 32 Model for Lattice Thermal Conductivity 36 Kinetic Theory 36 Boltzmann Equation 36 Phonon–Phonon Collisions 38 Interfacial Thermal Conductivity 40 Model for Nano Bulk Materials 43 Minimum Value for Oxides 48 References 49

vi

Contents

Part II 3

3.1 3.2 3.3 3.4

Materials 53

55 Bi2 Te3 -Based Materials 55 Skutterudite-Based Materials 59 Si–Ge Alloys 62 Other Alloy Materials 66 References 71

Nonoxide Materials

4.1 4.2 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 4.2.6 4.2.7 4.2.8 4.3 4.4 4.5 4.6 4.6.1 4.6.2 4.6.3 4.7 4.8 4.9

77 Introduction for ZnO 77 Property of ZnO 77 Structure 77 Lattice Parameters 77 Electronic Band Structure 77 Mechanical Properties 79 Thermal Expansion Coefficients 79 Thermal Conductivity 80 Specific Heat 80 Electrical Properties of Undoped ZnO 81 Doping for ZnO-Based Thermoelectric Materials 81 ZnO Nanostructures 84 Introduction for In2 O3 87 Property of In2 O3 88 Structure 88 Electronic Band Structure 89 Thermal Properties and Electrical Properties 89 Doping for In2 O3 -Based Thermoelectric Materials 90 In2 O3 Nanostructures 94 TiO2 and Others 98 References 101

5

Perovskite-Type Oxides 105

5.1 5.2

Introduction for Perovskite-Type Oxides 105 Crystal Structure and Electronic Structure of Perovskite-Type Oxides 106 Crystal Structure 106 Electronic Structure 107 A- and B-Sites Doping for Perovskite-Type Oxides 108 SrTiO3 108 CaMnO3 109 LaCoO3 111 Double Perovskites 112 Structure of Double Perovskites 112 Thermoelectric Properties of A′ A′′ B2 O5+ 𝛿 113 Thermoelectric Properties of A2 B′ B′′ O6 113 Doping Modulation 115

4

5.2.1 5.2.2 5.3 5.3.1 5.3.2 5.3.3 5.4 5.4.1 5.4.2 5.4.3 5.4.4

Binary Oxides

Contents

5.4.5 5.5

Composite Ceramics 118 Nanostructure Property Relationships in Perovskite-Type Oxides 120 References 124

6

6.1 6.2 6.3 6.3.1 6.3.2 6.3.3 6.3.4 6.4

133 Introduction 133 Nax CoO2 133 Ca3 Co4 O9 138 Single Dopants of Ca3 Co4 O9 139 Dual Dopants of Ca3 Co4 O9 144 Texture for Ca3 Co4 O9 147 Nanocomposites for Ca3 Co4 O9 147 New Concepts for Oxide Cobaltites 150 References 151

7

Promising Complex Oxides for High Performance 155

7.1 7.2 7.3 7.3.1 7.3.2 7.3.3 7.4 7.4.1 7.4.2 7.4.3 7.4.4 7.4.5 7.5 7.6

Crystal Structure–Property Relationships 155 History of Complex Superconductors 156 Ternary Oxyselenides 158 Donor Doping on [Bi2 O2 ]2+ Layers 158 Donor Doping on [Se]2− Layers 160 The Solid Solution of Bi2 O2 Se and Bi2 O2 Te 160 Quaternary Oxyselenides 164 Thermoelectric Properties 166 Band Gap Tuning 168 Texturing 168 Modulation Doping 169 Nanocompositing 171 Complexity Through Disorder in the Unit Cell 173 Complex Unit Cells 174 References 176

8

New Thermoelectric Materials and Nanocomposites 179

8.1 8.1.1 8.1.2 8.1.3 8.2 8.2.1 8.2.2 8.2.3 8.2.3.1 8.2.3.2 8.2.3.3 8.2.3.4 8.2.4 8.2.5

Nanocomposite Design 180 Energy-filtering Design 180 All-Scale Hierarchical Architectures 181 Quantum Nanostructured Bulk Materials 183 Organic Thermoelectric Materials 183 p-Type Organic Thermoelectric Materials 184 PEDOT 184 PANI 187 The Molecular Structure of PANI 188 Conductive Mechanism of PANI 188 Synthesis of PANI 188 Electrochemical Method 189 Doping of PANI 189 Tuning the Work Function of Polyaniline 190

Oxide Cobaltites

vii

viii

Contents

8.2.6 8.3 8.3.1 8.3.2 8.3.3

n-Type Thermoelectric Materials 192 Organic/Inorganic Thermoelectric Nanocomposites 192 0D Nanoparticles/Polymer 192 1D Nanowires or Nanotubes/Polymer 193 2D Nanosheets/Polymer 197 References 201 Part III

Devices and Application

207

9

Oxide Materials Preparation 209

9.1 9.1.1 9.1.2 9.1.2.1 9.1.2.2 9.1.2.3 9.1.3 9.2 9.2.1 9.2.2 9.2.3 9.2.4 9.2.5 9.3 9.3.1 9.3.2 9.3.3

Synthesis Method of Nanopowder 209 Solid-State Reaction 209 Solution Preparation 210 Sol–Gel Method 211 Precipitation and Coprecipitation Method 211 Hydrothermal Method 213 Gas-Phase Reaction 214 Advanced Bulk Technology 214 Spark Plasma Sintering 215 Hot-Press Sintering 215 Microwave Sintering 217 Two-Step Sintering 218 Phase-Transformation Sintering 219 Sintering Conditions on the Properties of Bulk 219 Effect of Sintering Temperature 219 Effect of Sintering Atmosphere 220 Effect of the Addition for Sintering 220 References 221

10

Modeling and Optimizing of Thermoelectric Devices 229

10.1 10.2 10.3 10.4 10.5 10.6 10.7

Introduction to Thermoelectric Devices 229 The Theoretical Analysis 230 The Model Design 232 The Interfaces in Thermoelectric Modules 236 The Simulation and the Optimization 238 The Measurement Theories and Systems 241 All-oxide Thermoelectric Device 242 References 245

11

Photovoltaic Application of Thermoelectric Materials and Devices 247

11.1 11.2 11.3

Introduction 247 Photovoltaic–Thermoelectric Integration Devices 248 Photoelectric–Thermoelectric Composite Materials 253 References 260 Index 263

ix

Foreword Materials that can convert heat into electricity or vice versa are called thermoelectric materials (TE materials). When direct current is passed through a TE material, either absorption or dissipation of heat occurs at the two ends of a material by Peltier effect so that this phenomenon can be applied to cooling or heating. Cooling the surrounding area of the one end of a TE material is specifically called Peltier cooling. In contrast, when the temperature difference is applied to the two ends of a material, electromotive force (thermoelectric power) is generated by Seebeck effect and electric power can be extracted by flowing the current to the external circuit. This is called thermoelectric power generation. Thermoelectric devices or modules for cooling or power generation are all energy converters (transducers), and their performance, namely thermoelectric energy conversion efficiency, depends largely on that of TE materials. Dimensionless figure of merit, ZT, is usually used to evaluate the performance of a TE material, and search for high ZT materials has been an enthusiastic topic in the past 30 years. Global issues of environmental disruption were recognized in the thermoelectric community and triggered searching for new TE materials in the mid-1980s. Vining’s prediction that there is no limit for ZT value (1992), Dresselhaus’s proposal of low-dimensional nanostructure (1993), and Slack’s concept of “phonon glass-electron crystal” (PGEC; 1995) were the major supporters for the following materials exploration research. Low-dimensional nanostructure concept led to the research of superlattice materials/devices and further developed to the “bulk nanostructuring” concept, which has greatly increased the ZT value. The “PGEC” concept has given rise to many new materials such as skutterudite and its related compounds and clathrates with network structure. Various other proposals of novel concepts, discovery of new physical phenomena, and development of low-cost chemical processes all enhanced TE materials research worldwide, resulting in improving the thermoelectric performance of inorganic materials reaching ZT > 2 at mid to high temperatures. On the other hand, organic and hybrid TE materials research has been widely conducted in the past 10 years aiming at its application to flexible energy harvesting that is required in the future IoT society. Based on such a background, this book was timely written by three distinguished materials scientists. It contains fundamentals and applications of TE

x

Foreword

materials and devices, and their near-future perspectives are introduced and discussed. The book consists of 11 chapters. Chapter 1 describes the fundamentals of electronic transport, Chapter 2 describes the controlling phonon transport in nano bulk solids, and Chapter 3 describes the nonoxide materials such as Bi2Te3-based materials, skutterudite-based materials, Si–Ge alloys, and other alloy materials. In Chapters 4–8, synthetic processes, structures, and properties of representative TE materials are presented. In Chapter 4, ZnO and In2 O3 ; in Chapter 5, perovskite type oxides; in Chapter 6, oxide cobaltates; and in Chapter 7, complex oxides are employed and fully described. Chapter 8 describes the novel TE materials and nanocomposites, followed by nanostructure design and organic–inorganic nanocomposites. Chapter 9 provides the detailed description of synthesis and processing of oxide TE materials. Chapter 10, modeling and optimizing of thermoelectric devices. Finally, in Chapter 11, photovoltaic–thermoelectric integration devices for the future applications are introduced. This is a well-organized guide book for graduate students. I would strongly suggest professors and teachers in physics, chemistry, or materials science to adopt it as a textbook or a reference book for their teaching classes. It is also helpful for researchers who are getting involved in TE research and development. November 30, 2018 Nagoya

Kunihito Koumoto

1

Part I Theories and Fundamentals

3

1 Electron Transport Model in Nano Bulk Thermoelectrics 1.1 History of Conducting Oxides In this book, the term “oxides” is defined as an important part of ceramics. One oxide material contains at least one oxygen atom and one other nonoxygen element in its crystal structure. The widely accepted definition of a ceramic is given by Kingery: A ceramic is an inorganic, nonmetallic, solid material comprising metal, nonmetal, or metalloid atoms primarily held in ionic and covalent bonds. Oxides possess the widest range of electrical properties. They could show good electrical insulation and the electrical resistivity, 𝜌 > 1014 Ω cm; meanwhile, they could also show extremely high electrical conduction, such as in hightemperature superconductors that have no resistance to the electrical current. The conductivity of oxides are usually found in two conditions: metal-like and semiconducting-like. Oxides with metal-like conduction such as ITO (indium tin oxides) are used as electrodes and transparent conducting oxides (TCOs) in portable electronics, displays, flexible electronics, and solar cells. Oxides in semiconductor condition such as TiO2 are important for photocatalysis and solar cells. Besides the electrical conductor, some oxides are good ion conductors, such as lithium lanthanum titanate (La 2/3−x Li3x TiO3 ), which exhibits high Li-ion conductivity. The electrical conductivities for ceramics are shown in Figure 1.1 [1]. It is difficult to simplify the history of conducting oxides due to the diversity of the oxides. As far as the application of TCOs is concerned, CdO was reported as the first TCO in 1907 by German physicist Karl Baedeker, who used thermal oxidation to yield it [2]. As far as the application of high-temperature superconductors is concerned, in the late 1980s, Ba–La–Cu–O and YBa2 Cu3 O7−x (YBCO) were the two first high-temperature superconductors discovered [3, 4]. In 1987, Bednorz and Müller were jointly awarded the Nobel Prize in Physics for discovery of the high-temperature superconductors. Recently, Hideo and coworkers discovered a new type of high-temperature superconductor, LaFeAsO, marking the new beginning of worldwide efforts to investigate high-temperature superconductor, especially in Japan and China (Figures 1.2–1.4) [5]. Thermoelectric (TE) materials can convert the temperature difference to voltage difference reversibly. As a result, TE materials have great potential application from solid-state cooling and thermal couples to power generation and waste heat recovery, as shown in Figure 1.5. The conversion efficiency is generally Oxide Thermoelectric Materials: From Basic Principles to Applications, First Edition. Yuan-Hua Lin, Jinle Lan, and Cewen Nan. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

La

Ni

2 ·I

ctr

Na βA

od

l

YSZ(1 000 °C ) Oxyg en se nsor

/S

Ba

)

tal

st

ion

Me

100 co

nd

cto

tor

ele

10–6

ctr

Na Cl sal t

oly

te

Si ivati de on vic on es

u nd

n yge

co

mi

Se

So

lid

–x

TiO 2

r

uc

10–12

Ins

sor

sen

Ox

P O3 V 2O 3– 2 ss) (gla O3 Al 2 te tra bs Su

tor

ula

SiO

2

SrTiO 3 ode electr Photo

Ins

ZnO

Varistor

ula

tor Electric

ble

Fa

O2 s Ru stor si Re

°C

ry

Ta

ss

2O 3

es

106

00

tte

KP Pri x b1– F ma x 1.2 ry b 5 atte ry La F 3E S el pec uF ec ifi 2 tro c de

Pa

2O 3 (3

Na

n

Ca

Ele

La Ca O ta lys 3 t

O SnO 3

BaPa 1–x Bix O 3 Supercondu ctor

1 Electron Transport Model in Nano Bulk Thermoelectrics

Ionic

4

10–18

Figure 1.1 Range of conductivities of ceramics. Source: Carter and Norton 2007 [1]. Reproduced with permission of Springer Nature.

characterized by the dimensionless figure of merit, ZT = S2 𝜎T/(𝜅 l + 𝜅 e ), where T, S, 𝜎, and 𝜅 l (𝜅 e ) are the absolute temperature, Seebeck coefficient, electrical conductivity, and lattice thermal conductivity (electronic thermal conductivity), respectively. To date, state-of-the-art TE materials usually contain toxic, scarce, and expensive metal elements (e.g. Pb, Te, Sb). The practical application of these materials is restricted by the high-temperature instability and high cost (Figure 1.6). After the discovery of NaCo2 O4 single crystals with high TE potential performance by Terasaki et al. [9], many oxides such as Ca3 Co4 O9 [10], ZnO [11], and SrTiO3 [12] were carefully investigated for oxide TE materials. These types of oxides have proven to be very promising for high-temperature TE application, which are thermally and chemically stable in air at high temperature. These oxides are easy to prepare, low-cost, and eco-friendly. Therefore, they have drawn considerable attention in the TE community. However, the TE performance of oxides, especially the polycrystallines, have relative low ZT values, which is ascribed to low electrical conductivity and high thermal conductivity caused by

1.1 History of Conducting Oxides

0.020

0.06

0.05 0.016

0.04 ρ (Ω cm)

ρ (Ω cm)

0.012 0.03 0.008 0.25 A cm–2 0.50 A cm–2 0.50 A cm–2

0.02

0.004

0.01

0

0

100

0 300

200 T (K)

Figure 1.2 Temperature dependence of resistivity in Bax La5−x Cu5 O5(3−y) for samples with x(Ba) = 1 (upper curves, left scale) and x(Ba) = 0.75 (lower curve, right scale). Source: Bednorz and Müller 1986 [3]. Reproduced with permission of Springer Nature.

La

150

Tanom Tmin Tonset Tc

Fe

As

Temperature (K)

O 100

50

SC

0 0.00

0.05

0.10

F – content (atomic fraction)

Figure 1.3 The transition temperature (T c ) dependence of F− doping content. Source: Kamihara et al. 2008 [5]. Reproduced with permission of ACS.

5

1 Electron Transport Model in Nano Bulk Thermoelectrics

200 1994

165 K under pressure

135 K

HgBaCaCuO TlBaCaCuO

Tc (K)

6

1993

100

YBaCuO

SmFeAsO LaBaCuO

39 K MgB2 2001 LaFeAsO 18 K 2002 PuCoGa5 2008 LaFePO

BaKBiO

Nb3Ge 1973

0 1970

23 K

1980

56 K

1986

1990 Year

2000

2010

Figure 1.4 Superconducting transition temperatures versus year of discovery for various classes of superconductors. Source: Keimer et al. 2015 [6]. Reproduced with permission of Springer Nature.

TEG cooling Heat sink

High-T TE generators in heating systems

Combustion chamber TEG module

Wood stove

Heat recovery in industry

Wireless sensors

Heat recovery in cars

Catalytic converter

Figure 1.5 Overview of potential application of thermoelectric generators. Source: Nielsch et al. 2011 [7]. Reproduced with permission of John Wiley & Sons.

1.1 History of Conducting Oxides

0

100

200

300

400

500

600

700

800

T

°C Co–Sb

Bi–Te Pb–Te Noxious

Ag–Sb–Ge–Te (TAGS)

BiCuSeO

Eco-friendly

Oxides (Ca3Co4O9, CaMnO3, ZnO) Si–Ge

Polymer

Figure 1.6 Schematic comparison of various thermoelectric (TE) materials, in terms of the temperature range of operation and environmental friendliness of constituent elements. Source: He et al. 2011 [8]. Reproduced with permission of Cambridge University Press.

the strong ionic bonding. So far, some layered structure oxides with outstanding performance have given some hope for further development. The p-type oxide TE materials, such as Co-based oxide material Ca3 Co4 O9 has been intensively investigated due to low thermal conductivity originated from its misfitted structure and high Seebeck coefficient by the plus spin entropy. The highest ZT value of Ca3 Co4 O9 ∼ 0.61 at 1118 K was achieved by heavy rare-earth doping and metallic nanoinclusion approach [13]. BiCuSeO oxyselenides have been reported to exhibit low intrinsic thermal conductivity and high ZT value [14]. Recently, high-performance TE oxyselenide BiCuSeO ceramics with ZT > 1.1 at 823 K and a high average ZT value (ZT ave ∼ 0.8) that is comparable to the currently used alloy TEs (e.g. PbTe) are made by our group (Figures 1.7 and 1.8) [16]. 3.0 2.5

Na

Ag

m Sb

ZTmax

Sd

Te

2.0

no

DO

Pb

Ban +a

18

rph

rtio

rar

onv

mo

isto

m+

Hie

dc

erg

.-B iT bTe 2 e3

1.5

Nano-Bi2Te3

1.0

Modulation-SiGe

cal

enc

nP

SnSe

chi

eP

Te

bTe

Nano-SiGe

Nanostructural PbS BiCuSeO

0.5

Cu2Se:Al

Pb

Cu2Se:l Cu2S Cu2Se Panoscopic PbSe Band align PbS Half-Heusler SnS

Cu1.8S

0.0 1960

1990 2004

2006

2008 Year

2010

2012

2014

2016

Figure 1.7 ZT of the current bulk thermoelectric materials as a function of year. Source: Zhang and Zhao 2015 [15]. Reproduced with permission of Elsevier.

7

1 Electron Transport Model in Nano Bulk Thermoelectrics

Figure 1.8 ZT of the current bulk oxide thermoelectric materials as a function of temperature.

BiCuSeO 1.2

Figure of merit ZT

8

0.8 In2O3

Ca3Co4O9

0.4

ZnO

SrTiO3 CaMnO3 Bi2O2Se

0.0 400

600

800

1000

1200

T (K)

1.2 Structural Characteristics of Oxides Most of the oxides are ionically bonded due to their large electronegativity difference (Δx) between transition metals and oxygen. When Δx > 1.7, the compound is considered to be ionic crystal, when Δx < 1.7, the covalent bonding is predominant. The fraction of ionic character (I) for binary system Ma Xb can be calculated by the following equation: I = 1 − exp(−0.25(XM − XX )2 )

(1.1)

where X M and X X represent the electronegativities of M and X, respectively. As mentioned earlier, oxide materials are ionically bonded. For most of the oxides, the volume of the oxygen anion is much larger than that of the cation in a crystal structure. The stabilization of the crystal structure is based on a balance between the attractive and repulsive forces in the crystal. Pauling’s rules are regarded as a law in the scope of ceramics on most occasions, which are discussed in materials science–related textbooks in detail. In this chapter, we will show crystal structures of some typical oxides (ZnO, SrTiO3 , and Ca3 Co4 O9 ). Zinc oxide is a very promising material for semiconductor applications. ZnO crystallizes in three main phases: hexagonal wurtzite (B4), cubic zinc blende (B3), and rocksalt (or Rochelle salt) (B1). The wurtzite structure ZnO is very stable at ambient conditions. The zinc blende ZnO is not stable in the bulk, but it can be stabilized as the film grown on the cubic lattice structure substrates. The rocksalt (NaCl) structure can only be obtained under high pressure (Figure 1.9). Strontium titanate (SrTiO3 ) has an ABO3 cubic perovskite structure like calcium titanium oxide (CaTiO3 ) at room temperature. A perovskite refers to the materials with the same type of crystal structure as CaTiO3 . The general chemical formula for perovskite compounds is ABO3 , where “A” and “B” are two cations with large size difference. “A” is larger than “B”, and O is an anion that bonds to both. The ideal cubic-symmetry structure has the B cation in sixfold coordination, surrounded by an octahedron of anions, and the A cation in 12-fold

1.2 Structural Characteristics of Oxides

(a)

(b)

(c)

Figure 1.9 Crystal structures of three forms of ZnO: (a) rocksalt (B1), (b) zinc blende (B3), and (c) wurtzite (B4). Source: Morkoç and Özgür 2009 [17]. Reproduced with permission of John Wiley & Sons. Figure 1.10 Crystal structure of perovskite structure in ABO3 form.

A B

O

cuboctahedral coordination. In SrTiO3 , the Ti4+ ions are sixfold coordinated by O2− ions, the Sr2+ ions are surrounded by four TiO6 octahedra and are coordinated by 12 O2− ions (Figure 1.10). Misfit-layered cobaltite Ca3 Co4 O9 has received a special attention because of large power factor, strong electronic correlations, and natural misfit-layered structure. Ca3 Co4 O9 has two monoclinic layers: one is the triple rock salt-type Ca2 CoO3 layer and the other is CoO2 layer. These two layers alternately stack along c direction to build the structure. Two layers have the same lattice parameters except the length of b-axis, making Ca3 Co4 O9 possess more distorted structure, as shown in Figure 1.11. Ca2 CoO3 layer is charge-resistor layer, which can scatter phonon strongly due to the distorted substructure, while the CoO2 layer is a charge-conducting layer. Therefore, Ca3 Co4 O9 can be considered as naturally materials with decoupling electronic and thermal properties.

9

1 Electron Transport Model in Nano Bulk Thermoelectrics

Co2 CoO2

Col Ca2CoO3 c

c a

b

(b)

(a) Ca:

Co:

O:

6

6

4

4

2

2

Energy (eV)

Energy (eV)

Figure 1.11 Diagram of the crystal structure of Ca3 Co4 O9 , perpendicular to the a-axis (a) and the b-axis (b). The Co1 and Co2 sites refer to Co atoms from Ca2 CoO3 and CoO2 layers, respectively.

0 –2 –4 –6

(a)

0 –2 –4

Γ A

L M

Γ

K H

A

–6 (b)

6

6

4

4

2

2

Energy (eV)

Energy (eV)

10

0 –2 –4

–6 Γ (c)

Γ

Y

VΓ A

M

L V

0 –2 –4

Y

VΓ

A

M

L

V

–6 (d)

Γ

P

N

Γ

H

P|H

N

Figure 1.12 Band structures of typical n-type oxides (a) ZnO, (b) Ga2 O3 , (c) TiO2 , and (d) In2 O3 .

1.4 Electrical Properties

1.3 Band Structure of Conventional Oxides Most semiconducting oxides (e.g. ZnO, TiO2 , In2 O3 ) are natural n-type oxides; a few oxides (e.g. Cu2 O, Nax CoO2 ) showed p-type conduction. This asymmetry can be understood based on fundamental principles of electronic structure. Furthermore, oxides always have wide band gaps due to the strong metal–oxide bond compared to the similar compounds, which are not favorable for high electrical conductivity. Figure 1.12 shows the typical band structures of ZnO, Ga2 O3 , TiO2 , and In2 O3 . A density function theory (DFT) [18–20] calculation was performed in VASP code [21] to calculate the band structure of In2 O3 . The projector-augmented wave [22, 23] technique was used and the exchange-correlation energy is in the form of Perdew–Burke–Ernzerhof [24].

1.4 Electrical Properties The electrical properties have been fully summarized in some literature [25, 26]. In this chapter, we describe the electrical properties (Seebeck coefficient (S), electrical conductivity (𝜎), and the electronic thermal conductivity (k e )) derived from the Boltzmann transport equation (BTE). The formal expression of BTE is ( ) df df dr dk = (1.2) + ∇ f + ∇r f dt sc dt dt k dt where t is time, k and r are the wave and position vectors of electrons, and f is the nonequilibrium distribution function. For electrons, the perturbations arise from the force exerted by an electric field (𝜀) or the temperature gradient (along the x-direction), e𝜀 dk =− dt ℏ

(1.3)

∇r f = (𝜕f ∕𝜕T)(dT∕dx)

(1.4)

where −e is the unit charge of electrons. The relaxation time (𝜏) approximation usually is applied to resolve the BTE for f : ( ) df = −( f − f0 )∕𝜏 (1.5) dt sc At equilibrium, electron distribution follows the Fermi–Dirac statistics through: f0 (E) =

1 exp((E − EF )∕kB T) + 1

(1.6)

where E is the electron’s energy level, EF is the “Fermi energy,” and k B is the Boltzmann constant.

11

12

1 Electron Transport Model in Nano Bulk Thermoelectrics

Then, the first-order, steady-state ((df /dt) = 0) solution to the BTE may be written as [ ( ) ] df E − EF dT f (E) − f0 (E) = −𝜏(E)v(E) 0 ∓e𝜀 − (1.7) dE T dx Subsequently, Eq. (1.7) is used to determine the magnitude of charge and heat current density (J and Q, respectively): +∞

J ≡ ∓nev = ±e

∫−∞

g(E)v(E)[ f (E) − f0 (E)]dE

(1.8)

+∞

Q ≡ n(E − EF )v =

∫−∞

g(E)(E − EF )v(E)[f (E) − f0 (E)]dE

(1.9)

where n is the carrier concentration, v is the carrier velocity, and g(E) is the density of states (DOS). From Eqs. (1.8) and (1.9), we can obtain J 𝜎 ≡ |dT∕dx=0 = e2 X0 (1.10) 𝜀 ] [ 𝜀 1 X1 S ≡ dT |J=0 = ± − EF (1.11) eT X0 dx ] [ (X )2 Q 1 𝜅e ≡ dT |J=0 = (1.12) X2 − 1 T X0 dx

where X i = − ∫ g(E)v2 (E)Ei (df 0 /dE)dE. Now, assuming a single band/sub-band with parabolic energy dispersion, and a power law relaxation time (𝜏(E) = 𝜏 0 Er ), the integral X i can be explicitly written as: ( ) ( ) 2md 3∕2 𝜏0 3 + 2(r + i) r+3∕2+i Xi = 2 (kB T) (1.13) F1∕2+r+i 2π m𝜎 ℏ2 3 +∞

Fj (𝜂) =

∫0

xj ∕ (exp(x − 𝜂) + 1)dx

𝜂 = EF ∕kB T where 𝜂 = (EF − E0 )/k B T is the reduced Fermi level. And then the parameters for TE materials can be written as: ( )3∕2 1 2kB Tmd n= 2 F1∕2 (𝜂) 2π ℏ2 F1∕2+r (𝜂) 2r + 3 e𝜏0 𝜇= (kB T)r 3 m𝜎 F1∕2 (𝜂) ) ( kB (r + 5∕2)F3∕2+r (𝜂) S=± −𝜂 e (r + 3∕2)F1∕2+r (𝜂) ( )2 [ ( )] (r + 5∕2)F3∕2+r (𝜂) 2 (r + 7∕2)F5∕2+r (𝜂) kB L= − e (r + 3∕2)F1∕2+r (𝜂) (r + 3∕2)F1∕2+r (𝜂)

(1.14) (1.15)

(1.16) (1.17) (1.18) (1.19)

Figure 1.13 The carrier concentration (a) and normalized mobility (b) as a function of 𝜂. (Assuming m𝜎 = md = m0 , and m0 is the mass of free electron.)

n (cm–3)

1.4 Electrical Properties

1022 1021 1020 1019 1018 1017 1016 1015 1014 1013

η = 1.0

–15

–10

–5

(a)

Δμ

5

10

15

r = –1/2 r=0 r = +1/2 r = +3/2

10

1

0.1

(b)

0 η

–15

–10

–5

0 η

5

10

15

Using Eqs. (1.16) and (1.17), we can calculate the n and 𝜇 for specific material with the parameter of m and r. In semiconductor technology, doping is the most common and effective method to alter the electrical conductivity. According to Figure 1.13a, the carrier concentration can be changed with 8 orders of magnitude by adjusting the 𝜂. The variation of the mobility as a function of 𝜂 is different with the scattering constant r, as shown in Figure 1.13b. It is widely accepted that the parameter r = −1/2 is for acoustic scattering process, r = 0 for neutral impurity, r = 1/2 for optical-mode scattering, and r = 3/2 is for the ionized-impurity scattering. It is interesting to note that the mobility increases with the increase of 𝜂 in the ionized-impurity scattering; in other words, high doping can lead to high mobility. However, most of the experiments show opposite results in the ionized-impurity samples. When the Seebeck coefficient is plotted against 𝜂, as shown in Figure 1.14, a linear scale can be used when 𝜂 ≪ 0. For 𝜂 ≫ 0, the Seebeck coefficient becomes very small, ∼0. At fixed 𝜂, the Seebeck coefficient exhibits larger value when r = 3/2. As seen in Figure 1.14b, for example, in order to obtain S = 200 μV K−1 , the doping concentration varies widely with different scattering mechanism. As shown in Figure 1.15, the Lorenz number is only weakly dependent on the Fermi energy when 𝜂 ≪ 0. When 𝜂 ≫ 0, the Lorenz number approaches 2.45 × 10−8 W Ω−1 K−2 for metals.

13

1 Electron Transport Model in Nano Bulk Thermoelectrics

1800 1400 1200 S (μV K–1)

Figure 1.14 The Seebeck coefficient as a function of 𝜂 (a) and carrier concentration (b). (Assuming m𝜎 = md = m0 , and m0 is the mass of free electron.)

r = –1/2 r=0 r = +1/2 r = +3/2

1600

1000 800 600 400 200 0 –15

–10

–5

(a)

0 η

5

10

250

S (μV K–1)

15

r = –1/2 r=0 r = +1/2 r = +3/2

200 150 100 50 0 1019 (b)

1020 Carrier concentration (cm–3)

1021

3.2 × 10–8 3.0 × 10–8 2.8 × 10–8 L (W ΩK–2)

14

2.6 × 10–8 2.4 × 10–8 2.2 × 10–8

r = –1/2 r=0 r = +1/2 r = +3/2

2.0 × 10–8 1.8 × 10–8 1.6 × 10–8 1.4 × 10–8 –15

–10

–5

0 η

Figure 1.15 Plot of Lorenz number against 𝜂.

5

10

15

1.5 Model for Thermoelectric Oxides

When 𝜂 ≫ 1 (𝜂 > 4), the conductor can be treated as a metal and the degenerate approximation can be reasonably adopted. In this occasion, the Fermi–Dirac integrals can be written as: 𝜂 n+1 π2 7π4 + n𝜂 n−1 + n(n − 1)(n − 2)𝜂 n−3 +··· (1.20) n+1 6 360 The first term of the expression can be used to obtain the electrical conductivity. Thus, ( ) 𝜏0 2md 3∕2 2 𝜎= 2 e (EF )r+3∕2 (1.21) 3π m𝜎 ℏ2 ( )3∕2 1 2EF md (1.22) n= 2 3π ℏ2 The Lorenz number is given by: ( )2 π2 kB (1.23) L= 3 e But it requires the first two terms to calculate Seebeck coefficient. Fn (𝜂) =

π2 kB (r + 3∕2) (1.24) 3e𝜂 For most of the semiconductors with not-so-high carrier concentration, the classical or nondegenerate approximation is acceptable. This assumption can be used when 𝜂 < −2: S=∓

∞

Fn (𝜂) = exp(𝜂)

∫0

𝜉 n exp(−𝜉)d𝜉 = exp(𝜂)Γ(n + 1)

(1.25)

where the gamma function is Γ(n + 1) = nΓ(n), Γ(1/2) = π1/2 , n is an integer, Γ(n + 1) is equal to n!. Thus, 8π2 kB2 T ∗ ( π )2∕3 S=∓ md (r + 3∕2) (1.26) 3n 3eh2 ( ) 2kB Tmd 3∕2 1 exp(𝜂) (1.27) n = 3∕2 ℏ2 2π 4 e𝜏 (1.28) 𝜇 = 1∕2 0 (kB T)r Γ(r + 5∕2) 3π m𝜎 k S = ∓ B ((r + 5∕2) − 𝜂) (1.29) e ( )2 kB L= (r + 5∕2) (1.30) e

1.5 Model for Thermoelectric Oxides Generally, metal oxides are considered not suitable for TE application. Metal oxides are ionic in nature with smaller orbital overlap (narrow band) than those found in covalent intermetallic alloys. This leads to very low carrier mobility due to the strong localization.

15

16

1 Electron Transport Model in Nano Bulk Thermoelectrics

The small polaron conduction model within 3d orbitals of transition-metal cations have been applied to investigate high-temperature Seebeck coefficient in transition-metal oxide (e.g. Ca3 Co4 O9 , CaMnO3 ). Assuming the energies of the Jahn–Teller (ΔJT ) effect and the Coulomb interaction (U) are smaller than the thermal energy k B T, the generalized Heikes formula for the Seebeck coefficient in the HT limit can be expressed as: ( ) 2 − 𝜌e kB (1.31) S = − ln e 𝜌e where 𝜌e is the ratio of charge carriers to sites (𝜌e = n/N v ; n is the number of charge carriers, and N v is the number of available sites). For fermions with large electron–electron repulsion (forbidden double occupancy) spins (k B T ≪ U), the Seebeck coefficient is expressed as: ) ( 1 − 𝜌e k (1.32) S = − B ln 2 e 𝜌e Koshibae et al. show that the spin state of the transition metallic ions (e.g. Co3+ and Co4+ ions) in the metal oxides is essential to the high Seebeck coefficient. The thermopower of the transition metal oxides at high temperature is given by: ( ) g x k S = − B ln 3 (1.33) e g4 1 − 4 where g 3 and g 4 are the numbers of the configurations (low-, intermediate-, and high-spin states) of the Co3+ and Co4+ ions, respectively, and x is the concentration of Co4+ ions. The above formula is applicable to most TE oxides, including Nax CoO2 and its derivative structures La1−x Srx CoO3 , perovskites (e.g. CaMnO3 ), and double perovskites, and misfit-layered Ca3 Co4 O9 and its derivative structure Ca2 Co2 O5 (Figure 1.16). Co3+ eg

1

t2g

(a)

18

t2g

(b)

15

t2g

(c)

LS state, S = 1/2 Co4+ eg

24

t2g

IS state, S = 1 Co3+ eg

6

t2g

LS state, S = 0 Co3+ eg

Co4+ eg

HS state, S = 2

IS state, S = 3/2 Co4+ eg

6

t2g

HS state, S = 5/2

Figure 1.16 Schematic representation of local states of cobalt ions, Co3+ and Co4+ . The lines indicate the energy levels of eg and t2g orbitals. The arrow represents a spin of an electron.

1.6 Effect of Interface on Electron Transport

1.6 Effect of Interface on Electron Transport In this section, we can combine the BTE model and the rectangular potential barriers promoted by A. Popescu et al. [27]. The model has three parameters: an average height Eb , width w, and distance between them L, as shown in Figure 1.17. In this chapter, we assumed the m𝜎 = md = m0 and power law relaxation time (𝜏(E) = 𝜏 0 Er ) is applicable. Then the total relaxation time is obtained according to the Mathiessen’s rule: ∑ 1 1 = (1.34) 𝜏(E) 𝜏i (E) i where 𝜏 i (E) is the relaxation time for each contributing mechanism. For TE bulk materials, the most carrier scattering may be due to acoustic phonons (r = −1/2), nonpolar optical phonons (r = 1/2), or ionized impurities (r = 3/2). Then the relaxation time due to the barrier scattering is given by: ⎛ ⎞ ⎛ ⎞ ( ) ⎜ ⎟ E E ⎜ √ ⎟ 1− 4 ⎜ ⎟ ⎜ ⎟ Eb Eb m ⎜ ⎟ , E < Eb ⎟ ⎜L √ ( )⎞ ⎟ 2E ⎜ ⎛ ⎜ ⎟ 2 ⎜ sinh2 ⎜ 2mEb w 1 − E ⎟ ⎟ ⎜ ⎟ ⎜ ⎜ ℏ2 Eb ⎟ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎟ 𝜏b = ⎜ ⎛ ⎞ ⎜ ⎟ ) ( ⎜ ⎟ ⎜ ⎟ E E −1 4 ⎜ √ ⎟ ⎜ ⎟ E E b b ⎜L m ⎜ ⎟ , E > Eb ⎟ √ )⎞ ⎟ ( ⎜ ⎟ 2E ⎜ ⎛ 2 E ⎜ ⎟ ⎜ sin2 ⎜ 2mEb w ⎟⎟ − 1 2 ⎜ ⎟ ⎜ ⎜ ⎟⎟ ℏ E b ⎝ ⎠ ⎝ ⎝ ⎠⎠

(1.35)

Figure 1.18 shows the calculated values of normalized electrical conductivity as a function of the length L. The electrical conductivity increases with the increasing L. In this model, the volume fraction of nanoinclusions can be roughly evaluated by 𝜑 = (w/L)3 . For the neutral scattering samples, when the 𝜑 > 1%, i.e. L > 43 nm, the electrical conductivity decreases to 80% of the pristine bulk sample. This result shows that the nanoparticle would strongly affect the electrical conductivity. In our calculation, we may overestimate the adverse effect of secondary nanoparticle on electrical conductivity due to the simplify of the scattering process. For the different scattering mechanism samples, the effect of nanoparticle on electrical conductivity is also different. Figure 1.19 normalized Seebeck coefficient as a function of the length L. One can see that the Seebeck coefficient increases obviously by adding the nanoparticle, which is called energy-filtering effect due to a strongly energy-dependent Figure 1.17 The model for the nanocomposite.

Eb L

w

17

1 Electron Transport Model in Nano Bulk Thermoelectrics

1.0 r = –1/2 r=0 r = +1/2

Eb = 60 meV

σ/σ0

0.9

w = 20 nm

0.8

0.7

0.6 20

40

60

80

100

L (nm)

Figure 1.18 The normalized electrical conductivity as the function of L. Parameters are E b = 60 meV and w = 20 nm.

1.50 r = –1/2 r=0 r = +1/2

1.45 1.40 1.35 S

18

1.30 1.25 1.20 1.15 1.10 20

40

60 L (nm)

80

100

Figure 1.19 The normalized Seebeck coefficient as the function of L. Parameters are E b = 60 meV and w = 20 nm.

electronic scattering time. For example, the 1% volume fraction nanoparticle in the acoustic scattering samples can bring up over 35% enhancement in Seebeck coefficient. An enhancement in power factor can be observed in Figure 1.20. These results show that the rational design of nanocomposites can improve the TE properties. In Figures 1.21–1.23, we discuss the influence of nanoparticle size w on the electrical properties. The electrical conductivity decreases with the increasing w because of the increasing volume fraction of nanoparticles.

1.6 Effect of Interface on Electron Transport

1.50

r = –1/2 r=0 r = +1/2

w = 20 nm Eb = 60 meV

1.45 1.40

PF/PF0

1.35 1.30 1.25 1.20 1.15 1.10 1.05 20

40

60 L (nm)

80

100

Figure 1.20 The normalized power factor as the function of L. Parameters are E b = 60 meV and w = 20 nm.

L = 100 nm Eb = 60 meV

1.00

r = –1/2 r=0 r = +1/2

0.95

σ

0.90 0.85 0.80 0.75 0.70 0

5

10 w (nm)

15

20

Figure 1.21 The normalized electrical conductivity as the function of w. Parameters are L = 100 nm and E b = 60 meV.

Figure 1.22 shows the relationship between Seebeck coefficient and w. It is interesting to note that a maximum value can be observed at around 5 nm. And the sharp increasing trend of S appears when w < 5 nm. These results demonstrate that the energy-filtering effect in nanocomposites depends on the size of nanoparticle. The smaller size of nanoparticles will cause larger enhancement in Seebeck coefficient. Figure 1.23 demonstrates the enhancement on power factor with various w. A maximum peak can be observed at around 5 nm due to the moderate decrease in electrical conductivity and larger increase of Seebeck coefficient. It is clearly seen

19

1 Electron Transport Model in Nano Bulk Thermoelectrics

L = 100 nm Eb = 60 meV

1.35

r = –1/2 r=0 r = +1/2

1.30 1.25

S

1.20 1.15 1.10 1.05 1.00 0

5

10 w (nm)

15

20

Figure 1.22 The normalized Seebeck coefficient as the function of w. Parameters are L = 100 nm and E b = 60 meV.

1.40

r = –1/2 r=0 r = +1/2

1.35 1.30

L = 100 nm Eb = 60 meV

1.25 PF

20

1.20 1.15 1.10 1.05 1.00 0.95 0

5

10 w (nm)

15

20

Figure 1.23 The normalized power factor as the function of w. Parameters are L = 100 nm and E b = 60 meV.

that the acoustic scattering matrix has the highest enhancement on power factor, while the ionized-impurity scattering matrix does not have the obvious effect. To get a more comprehensive understanding of the role of nanoinclusions in enhancing the TE properties, we plot the electrical conductivity, Seebeck coefficient, and power factor as functions of the interface potential Eb , as shown in Figures 1.24–1.26. The interface potential plays an important role in tuning the electrical conductivity, as shown in Figure 1.24. When Eb > 0.1 eV, the electrical conductivity becomes lesser than 30%, which indicates strong scattering of the

1.6 Effect of Interface on Electron Transport

r = –1/2 r=0 r = +1/2

1.0 0.8 0.6 σ

L = 100 nm w = 20 nm

0.4 0.2 0.0 0.00

0.05

0.10 Eb (eV)

0.15

0.20

Figure 1.24 The normalized electrical conductivity as the function of E b . Parameters are L = 100 nm and w = 20 nm.

9 8 7

S

6 5

r = –1/2 r=0 r = +1/2 L = 100 nm w = 20 nm

4

0.123 ∗ 0.084 ∗

3 2

0.169 ∗

0.052 ∗

1 0 0.00

0.05

0.10 Eb (eV)

0.15

0.20

Figure 1.25 The normalized Seebeck coefficient as the function of E b . Parameters are L = 100 nm and w = 20 nm.

electronic due to the high barrier. Therefore, the design of the interface is important in nanocomposites. It is interesting to observe several maximum peaks of S in Figure 1.25. In Figure 1.25, four peaks appear when the Eb < 0.2 eV. The results show that the barrier energy Eb is the most critical factor that determines a successful nanocomposite design. The barrier energy Eb is related not only to the intrinsic properties of matrix and nanofillers but also to the interface of the matrix and nanofillers.

21

1 Electron Transport Model in Nano Bulk Thermoelectrics

5

4

L = 100 nm

r = –1/2 r=0 r = +1/2

w = 20 nm

3 PF

22

2

1

0 0.00

0.05

0.10 Eb (eV)

0.15

0.20

Figure 1.26 The normalized power factor as the function of E b . Parameters are L = 100 nm and w = 20 nm.

The relationship between power factor and the function of Eb is depicted in Figure 1.26. The power factor can be greatly enhanced by more than fourfold in some specific interface potentials. For the interface potentials range from 0 to 0.2 eV, there are four maximum values and four worst peaks. So, the PF is very sensitive to the interface potential, which calls for an elaborate nanocomposite design.

References 1 Carter, C.B. and Norton, M.G. (2007). Ceramic Materials: Science and

Engineering, 546. Springer. 2 Bädeker, K. (1907). Über die elektrische Leitfähigkeit und die thermoelek-

trische Kraft einiger Schwermetallverbindungen. Annalen der Physik 327: 749–766. https://doi.org/10.1002/andp.19073270409. 3 Bednorz, J.G. and Müller, K.A. (1986). Possible high T c superconductivity in the Ba–La–Cu–O system. Zeitschrift für Physik B Condensed Matter 64: 189–193. https://doi.org/10.1007/BF01303701. 4 Wu, M.K., Ashburn, J.R., Torng, C.J. et al. (1987). Superconductivity at 93 K in a new mixed-phase Y–Ba–Cu–O compound system at ambient pressure. Physical Review Letters 58: 908–910. https://doi.org/10.1103/PhysRevLett.58 .908. 5 Kamihara, Y., Watanabe, T., Hirano, M., and Hosono, H. (2008). Iron-based layered superconductor La[O1−x Fx ]FeAs (x = 0.05−0.12) with T c = 26 K. Journal of the American Chemical Society 130: 3296–3297. https://doi.org/10 .1021/ja800073m.

References

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matter to high-temperature superconductivity in copper oxides. Nature 518: 179–186. https://doi.org/10.1038/nature14165. Nielsch, K., Bachmann, J., Kimling, J., and Böttner, H. (2011). Thermoelectric nanostructures: from physical model systems towards nanograined composites. Advanced Energy Materials 1: 713–731. He, J., Liu, Y., and Funahashi, R. (2011). Oxide thermoelectrics: the challenges, progress, and outlook. Journal of Materials Research 26: 1762–1772. Terasaki, I., Sasago, Y., and Uchinokura, K. (1997). Large thermoelectric power in NaCo2 O4 single crystals. Physical Review B 56: R12685–R12687. https://doi.org/10.1103/PhysRevB.56.R12685. Shikano, M. and Funahashi, R. (2003). Electrical and thermal properties of single-crystalline (Ca2 CoO3 )0.7 CoO2 with a Ca3 Co4 O9 structure. Applied Physics Letters 82: 1851–1853. Ohtaki, M., Tsubota, T., Eguchi, K., and Arai, H. (1996). High-temperature thermoelectric properties of (Zn1−x Alx )O. Journal of Applied Physics 79: 1816–1818. Ohta, S., Nomura, T., Ohta, H., and Koumoto, K. (2005). High-temperature carrier transport and thermoelectric properties of heavily La- or Nb-doped SrTiO3 single crystals. Journal of Applied Physics 97: 42. Van, N.N., Pryds, N., Linderoth, S., and Ohtaki, M. (2011). Enhancement of the thermoelectric performance of p-type layered oxide Ca3 Co4 O(9+𝛿) through heavy doping and metallic nanoinclusions. Advanced Materials 23: 2484–2490. Zhao, L.-D., He, J., Berardan, D. et al. (2014). BiCuSeO oxyselenides: new promising thermoelectric materials. Energy & Environmental Science 7: 2900–2924. Zhang, X. and Zhao, L.-D. (2015). Thermoelectric materials: energy conversion between heat and electricity. Journal of Materiomics 1: 92–105. Lan, J.-L., Liu, Y.-C., Zhan, B. et al. (2013). Enhanced thermoelectric properties of Pb-doped BiCuSeO ceramics. Advanced Materials 25: 5086–5090. Morkoç, H. and Özgür, Ü. (2009). Zinc Oxide: Fundamentals, Materials and Device Technology. Wiley-VCH. Kresse, G. and Hafner, J. (1993). Ab initio molecular dynamics for liquid metals. Physical Review B 47: 558. Kresse, G. and Hafner, J. (1994). Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semi-conductor transition in germanium. Physical Review B 49: 14251. Kresse, G. and Furthmüller, J. (1996). Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Computational Materials Science 6: 15. Kresse, G. and Furthmüller, J. (1996). Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Physical Review B 54: 11169. Blöchl, P.E. (1994). Projector augmented-wave method. Physical Review B 50: 17953.

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23 Kresse, G. and Joubert, D. (1999). From ultrasoft pseudopotentials to the

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25

2 Controlling the Thermal Conductivity of Bulk Nanomaterials 2.1 Bonding and Lattice Vibration Considering the propagation of sound waves for different systems, their velocity becomes faster with increasing bond strength. Therefore, the lattice vibration and the corresponding thermal conductivity 𝜅 in compounds constituted by ionic and/or covalent bonds are stronger and higher than those made by weak bonds [1]. Meanwhile, ultra-low lattice thermal transport properties could be expected in materials with soft bonds. Velocity can be calculated by the slope of k-vector versus phonon frequency or the square root of the force constants over the atomic mass. Both small forces between different atoms and heavy masses could introduce ultra-low phonon velocity and thermal conductivity.

2.2 Lattice Distortions in Determining Thermal Properties Introducing lattice distortions is a way to reduce thermal conductivity and to further enhance the thermoelectric figure-of-merit ZT. In this section, several types of distortions and their effects in weakening thermal conductivity are illustrated and analyzed. In 1955, Klemens et al. demonstrated elastic scattering due to the static imperfections of lattice waves and used it to describe the subsequent effects of impurities, vacancies, dislocations, and grain boundaries (GBs) on thermal conductivity [2]. 2.2.1

Point Defects and Dislocations

Considering the effects of mass difference, the phonon scattering rate caused by point defects can be described as follows: (𝜔) = τ−1 pd

V 0 𝛤 𝜔4 4𝜋v3

(2.1)

Oxide Thermoelectric Materials: From Basic Principles to Applications, First Edition. Yuan-Hua Lin, Jinle Lan, and Cewen Nan. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

26

2 Controlling the Thermal Conductivity of Bulk Nanomaterials −1 where 𝜏pd (𝜔) is the phonon relaxation time, 𝜔 the phonon frequency, V 0 the volume per atom, and v the single-branch polarization-averaged velocity. 𝛤 is determined by {( )} ∑ Mi 2 (2.2) fi 𝛤 = 1− M i

Here f i and Mi are the percentage and mass of atom i, respectively, and M is the average atom mass. Considering the effect of distortions, it becomes {( )]} [ ( ) ∑ Ri Mi 2 (2.3) Γ= fi + 2 6.4𝛾 1 − 1− M R i where Ri is the Pauling ionic radius of atom i and R the average atom radius. Klemens et al. used two distinctive mechanisms to illustrate phonon scattering. −1 One is the phonon scattering on dislocations [3]. The phonon scattering rate 𝜏DC is proportional to the density of dislocations: V0 (2.4) v2 where N D is the density of dislocations and 𝜂 the factor to evaluate the efficient scattering. For dislocations that are perpendicular to the temperature gradient, 𝜂 = 1, whereas for those parallel to the gradient, 𝜂 = 0. The other one is phonon scattering caused by distortions, which can be interpreted as a long-range elastic field. The phonon scattering rate calculated by the elastic field of edge 𝜏E−1 and screw 𝜏S−1 dislocations can be written as follows: −1 𝜏DC = 𝜂ND

]2 ⎫ ⎧ ( )[ √ ( v )2 ⎪ 23∕2 E 2 2 ⎪ 1 1 1 − 2v2 L = 7∕2 𝜂ND bE 𝛾 𝜔 ⎨ + 1+ 2 ⎬ (2.5) 1−v vT 3 ⎪ ⎪ 2 24 ⎭ ⎩ 3∕2 2 (2.6) 𝜏S−1 (𝜔) = 7∕2 𝜂NDS b2S 𝛾 2 𝜔 3 where v is the Poisson ratio, 𝛾 the Gruneisen parameter, bS and bE the magnitudes of Burgers vectors for the screw and edge dislocations, respectively, vL and vT the longitudinal and transverse sound velocities, respectively, and N S and N E the densities of screw and edge dislocations, respectively. In 2000, Florescu et al. measured thermal conductivities of three series of hydride vapor-phase epitaxy (HVPE) n-GaN samples at 300 K using a SThM Discoverer system [4], and in 2002, Zou et al. [5] calculated the defect-concentration dependence of lattice thermal conductivity for wurtzite GaN films based on Eq. (2.1). The results are shown in Figure 2.1; the solid line corresponds to changes in Si nSi and H doping density nH , whereas the dashed line only varies with nSi . Therefore, the calculation results are in good agreement with the experimental data. 𝜏E−1 (𝜔)

2.2 Lattice Distortions in Determining Thermal Properties

Figure 2.1 The doping concentration dependence of thermal conductivity for Si-doped GaN films. The experimental points with error bars were taken from Ref. [4].

Thermal conductivity (W cm–1 K–1)

2.4 2.2 2.0

Solid: Correlated H and Si concentrations Dashed: Fixed H concentration

1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 1017

2.2.2

1018 Doping concentration (1/cm–3)

1019

Peierls Distortion

Peierls distortion also can be used to reduce thermal conductivity. Phonon softening, called Kohn anomaly, and Peierls lattice distortion decrease phonon energy and increase phonon scattering, respectively, resulting in lower thermal conductivity [6]. Based on the mean field theory, the energy gap Δ in quasi-1D crystalline [7] is given by ( ) 1 (2.7) Δ = 4𝜀F exp − NF g where N F is the density of states at the Fermi energy and g the electron–phonon coupling constant. Charge density 𝜌(x) has the form of periodic modulation: ] [ Δ (2.8) cos(2kF x + 𝜙) 𝜌(x) = 𝜌0 1 + hvF kF 𝜆 where 𝜌0 is the electronic density in the metallic state, 𝜆 the wavelength of charge density wave (CDW), 𝜙 the phase variable, k F the Fermi wave vector, and vF the Fermi velocity. The expectation value of the lattice displacement ⟨u(x)⟩ is ⟨u(x)⟩ = Δu cos(2kF x + 𝜙) where

( Δu =

2ℏ M𝜔q

)1∕2

Δ g

(2.9)

(2.10)

here 𝜔q is the frequency of lattice vibration with momentum q. In 2009, Rhyee et al. measured the thermal conductivity of CeTe2−x Snx system using a physical property measurement system (Quantum Design) [8]. The result is shown in Figure 2.2.

27

2 Controlling the Thermal Conductivity of Bulk Nanomaterials

3.0 κtot

2.5 κ (W m–1 K–1)

28

κph

2.0 1.5 1.0

Figure 2.2 Temperature-dependent total thermal conductivity 𝜅 tot (symbols) and lattice thermal conductivity 𝜅 ph (lines) CeTe2−x Snx for x = 0.0 (black), 0.05 (red), and 0.1 (blue) in the temperature range of 2 K ≤ T ≤ 300 K [8].

x = 0.0 x = 0.05 x = 0.1

0.5 0.0 50

0

100

150

200

250

300

Temperature (K)

Figure 2.3 The crystal structure of In4 Se3 [9]. In Se

b c

a

The lattice thermal conductivities 𝜅 ph at T=300 K are estimated to be 1.20, 0.74, and 1.73 W m−1 K−1 for x = 0, 0.05, and 0.1 compounds, respectively. The low total thermal conductivities of CeTe2−x Snx may be related to CDW states. Rhyee et al. also measured the thermal conductivity of In4 Se3−𝛿 [9], which is a candidate of quasi-1D systems. The structure of In4 Se3−𝛿 is shown in Figure 2.3. The thermal conductivity of In4 Se3−𝛿 (𝛿 = 0.65) is plotted in Figure 2.4. In this study, Se vacancies are tuned to investigate the electronic and lattice structures. In this way, the electron–phonon interaction and CDWs can be modified to evaluate the impact on thermal conductivity. The thermal conductivity along the bc-plane is lower than that in the ab-plane as shown in Figure 2.4, which is acceptable due to the lower bonding strength in the bc-plane (Figure 2.4). 2.2.3

Octahedral Distortion in Manganite Perovskites

The octahedral distortion induced by the Jahn–Teller effect plays an important role in varying the physical properties of manganite perovskites. Radaelli et al. proposed that the local distortions of the MnO6 octahedra in La1−x Cax MnO3 (LCMO) and Pr0.5 Sr0.5 MnO3 (PSMO) are probably the sources of strong phonon

2.2 Lattice Distortions in Determining Thermal Properties

κ (W m–1 K–1)

Figure 2.4 The thermal conductivity of In4 Se3−𝛿 (𝛿 = 0.65) [9].

1.6

In4Se3–δ(δ = 0.65)

1.4

a–b plane b–c plane

1.2 1.0 0.8 400

300

500

600

700

Temperature (K)

1.5

κL–1 (mK W–1)

Figure 2.5 Lattice thermal resistivity at T = 35 K (open symbols) and 300 K (closed symbols) versus corresponding low- and high-T Mn—O bond distortion [10].

1.0

LCMO x=0 x = 0.15 x = 0.30 x = 0.65 PSMO

0.5

0.0 0.01

0.1

1

10

D (%)

scattering. The structural data shown in Figure 2.5 further support this proposal [10]. Here distortion D is defined by 3 1 ∑ || (ui − u) || D≡ (2.11) | | 3 i=1 || u || where √ u = 3 u1 u2 u3 (2.12) where ui is the Mn—O bond length. The fact 𝜅 L scales with D at both high and low T indicates that the thermal resistance of these materials is predominantly controlled by the static rather than the dynamic MnO6 distortions, since the latter are larger in colossal magneto resistance (CMR) compounds at T > T c ; however, they are independent of the doping level at low T. In addition, a correlation is given that D is dramatically altered by the FM and CO transitions. For instance, PSMO has the smallest D at 300 K, but at 35 K has one of the largest values, as shown in Figure 2.6.

29

2 Controlling the Thermal Conductivity of Bulk Nanomaterials

Figure 2.6 Thermal conductivity vs temperature for the LSMO crystal and PSMO polycrystal. Solid (open) symbols represent cooling (warming) data for H=0. The solid (dashed) lines are for cooling (warming) in H=9T [10].

La0.83Sr0.17MnO3

4

3 κ (W m–1 K–1)

30

H = 9T Pr0.5Sr0.5MnO3

2

TC

H=0 1

0 0

50

100

150

200

250

300

T(K)

2.3 Callaway Model and the Minimum Thermal Properties In order to analyze the thermal properties of most materials, relaxation time (𝜏 c ) approximation of phonon gas is applied using Eq. (2.13), which was provided by Debye [11]. C V represents the isochoric heat capacity and lph the average phonon mean free path (lph = 𝜏 c ⋅ vm ). The mean velocity of sound (vm ) can be calculated by combining the transverse branch (vt ) and longitudinal branch (vl ). 𝜅L =

1 C l v 3 V ph m

(2.13)

))− 1 ( ( 3 For bulk materials, vm can be directly described as vm = 13 v23 + v13 [12] t l ))− 1 ( ( 2 for two-dimensional thin films and further reduced to vm = 12 v12 + v12 t l [13]. When using first-principle calculations, the contribution of each phonon mode should be given by 1 ∑ 𝜏(⃗q)Cph (𝜔𝜆 )[v𝜆 (⃗q) ⋅ n⃗ ]2 (2.14) 𝜅𝜆 = Lx Ly Lz 𝜆,⃗q All modes would be summed up to calculate 𝜅 L . Overall, a small C V and low lph combined with inferior vm would lead to an inferior 𝜅 L in thermoelectric materials. To analyze intrinsic factors that affect 𝜅 L , Slack’s model [14] as empirical formula should be mentioned, which is given by 𝜅L = A

MΘ3D V 1∕3 𝛾 2 n2∕3 T

(2.15)

where n is the number of atoms in the primitive cell, V the volume per atom, ΘD the Debye temperature, M the average atomic mass, 𝛾 the high temperature

2.3 Callaway Model and the Minimum Thermal Properties

limit of the acoustic-phonon Gruneisen parameter, and A a collection of physical constants that depend on 𝛾. This model is accurate for simulating the lattice thermal conductivity of materials with relatively low 𝜃 D , such as NaCl, NaI, and PbTe, but for materials with higher ΘD (>973 K) is not applicable. It is noted that the Slack model is not suitable to calculate high-temperature thermal conductivity for TE materials [15]. In order to analyze 𝜅 L for high temperatures, Eucken [16] also proposed an empirical theory, which is not fit for most of the TE materials, which always have high melting point. Based on this fact, Keyes proposed a better approximation at high temperatures [17]: 3∕2

𝜅L T =

R3∕2 Tm 𝜌2∕3 1∕3

3𝛾 2 𝜀3 N0 M7∕6

(2.16)

where 𝜌 is density, 𝜀 the amplitude of thermal vibration of the atoms, and N 0 Avogadro’s number. Even though this approximation did not take anisotropy into account, it identified that 𝜅 L in the covalently bonded solids tends to be greater than that in the ionic and van der Waals solids, finally attributing the 𝜅 L variation from material to material to variation of the average mass, the interatomic forces and the crystal structure. Based on these models and relaxation time approximation (RTA), the Debye–Callaway model divided the effect of phonon scattering into several parts, which can be written as follows: ΘD ( )3 T 𝜏c x4 ex kB kB 3 𝜅L = T dx (2.17) ∫0 (ex − 1)2 2𝜋 2 𝜈 ℏ where x = ℏ𝜔/k B T is a dimensionless quantity, ℏ Planck’s constant, k B the Boltzmann constant, and 𝜔 the phonon frequency. The overall relaxation rate 𝜏c−1 in this model can be determined by combining the various scattering processes as follows: 𝜏c−1 = 𝜏N−1 + 𝜏u−1 𝜏u−1

=

𝜏b−1

+

𝜏d−1

(2.18) +

𝜏U−1

+···

(2.19)

where, 𝜏 N , 𝜏 u , 𝜏 b , 𝜏 d , and 𝜏 U are the relaxation times for normal process scattering, unnormal process scattering, grain boundary (GB) scattering, point defect scattering, and Umklapp scattering, respectively, which are defined as follows: 𝜏N−1 = 𝛿𝜏U−1

(2.20)

𝜏b−1

(2.21)

∝ vm ∕L V Γ𝜔4 4𝜋v3 ∼ 𝜔a (T∕ΘD )𝛽 exp(−ΘD ∕bT)

𝜏d−1 = B𝜔4 =

(2.22)

𝜏U−1

(2.23)

𝛿 is a dimensionless constant, which describes the relative intensity between the normal and Umklapp processes, L the grain size for polycrystalline samples, Γ the disorder scattering parameter, and B a constant that is independent of temperature and frequency, represents mass and strain–stress fluctuations. There is

31

32

2 Controlling the Thermal Conductivity of Bulk Nanomaterials

no satisfactory theoretical work for the relaxation time model to be used in the Umklapp and normal processes. However, Slack obtained an expression for the relaxation time to be used in the Umklapp model, which is given in Eq. (2.23), where 𝛼, 𝛽, and b are constants [18]. There should be many other processes included in these materials that affect the comprehensive thermal properties, such as electron–phonon interactions, dislocations, and second-phase effects. Although their impacts are so small in most systems, for the sake of simplicity, most researchers choose to ignore these functions in simulations. As the momentum of the normal process remains conservative, the rate of change of the total phonon momentum due to the normal process has to be zero; therefore, this process does not give rise to thermal resistance. As a result, the original model used for most alloys ignores the normal process and only considers unnormal processes that do not conserve momentum. However, the normal process would affect the phonon concentration for a whole range of frequencies and have the profound effect of transferring energy between different phonon modes [19]. For minimum thermal conductivity values, as shown in the Callaway model, phonons with high, medium, and low frequencies should be scattered effectively. Therefore, all-scale phonon engineering will be designed in thermoelectric materials to achieve the minimum values; considerable evidence has been shown in thermoelectric alloys such as PbTe [20] and (AgCrSe2 )0.5 (CuCrSe2 )0.5 [21]. For oxides, similar work has been done in In2 O3 -based and BiCuSeO-based ceramics via nanostructuring and point defect engineering. The lattice thermal conductivity of In2 O3 could be reduced by 60%, and extraordinary low lattice thermal conductivity below the amorphous limit was achieved in both kinds of oxides: 1.2 W m−1 K−1 at 973 K in In2 O3 and 0.25 W m−1 K−1 at 873 K in BiCuSeO [22, 23].

2.4 Temperature Relationship in Thermal Properties Normally, the total thermal conductivity 𝜅 can be written as a sum of all the components representing various excitations: ∑ 𝜅= 𝜅𝛼 (2.24) 𝛼

where 𝛼 denotes an excitation [24]. In order to utilize different defects to modulate the thermal properties, the relationship between them with varying temperature should be investigated first. As shown in Figure 2.7, electrical properties are dominated by carrier concentration and the electronic part of 𝜅. Nevertheless, whether the total 𝜅 increases with temperature or not, we need to consider the connections between 𝜅 e and 𝜅 L . For nondegenerate semiconductors, the carrier concentration normally increases with temperature, further leading to a higher 𝜅 e , yet the limit of intrinsic low carrier concentration renders that 𝜅 e cannot be compared with 𝜅 L , as lattice vibrations play a predominant role due to phonon–phonon scattering. When the dopants or other strategies are introduced to intrinsic semiconductors, the Fermi energy moves into the valence or conduction band, making the conducting behavior

2.4 Temperature Relationship in Thermal Properties

Figure 2.7 A qualitative diagram of the thermopower S, thermal conductivity 𝜅, and the resistivity 𝜌 of a material. 𝜎 is the electrical conductivity, and n denotes the carrier concentration. Total thermal conductivity 𝜅 is the sum of the carrier thermal conductivity 𝜅 e and the lattice thermal conductivity 𝜅 L .

κ κele. κlat.

S

S

σ

S2σ

n∼1019 Insulators

σ

n

Semiconductors

Metals

more like metals rather than traditional semiconductors, and the several increasing magnitudes of carrier concentration makes 𝜅 e comparable with 𝜅 L . Besides, the 𝜅 e in degenerate semiconductors is normally decreased with increasing temperature, as high temperatures render more carriers to be scattered, including ionized impurity scattering (scattering parameter r = 1.5), neutral impurity scattering (r = 0), acoustic (r = −0.5), and optical lattice scattering (r = 0.5). When the acoustic lattice scattering dominates the mechanism (𝜇 ∝ T −1.5 ), decreased carrier mobility 𝜇 combined with constant carrier concentration leads to smaller 𝜎 at higher temperatures, thereby a decrease in the 𝜅 e . Total thermal conductivity 𝜅 can be calculated by the expression 𝜅 = DC p 𝜌, where D is the thermal diffusivity, 𝜌 the mass density, and C p the specific heat. For specific heat, as shown in Figure 2.8, a constant value would be achieved after Debye temperature 𝜃 D , and the applied temperature of most TE materials available for power generation is over 𝜃 D ; thus, the D normally represents the trend of 𝜅 to temperature. As for TE oxides without bipolar conductions, the variation of D is more dependent on the contribution of 𝜅 L rather than that of 𝜅 e . Lattice thermal conduction is the dominant thermal conduction mechanism in nonmetals such as oxides. Even in some semiconductors and alloys, it still Figure 2.8 The temperature dependence of specific heat capacity.

3R Cv = constant Cv

0

R = gas constant

θD(Debye temperature)

T (K)

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2 Controlling the Thermal Conductivity of Bulk Nanomaterials

1000 Umklapp Boundary + Point-defect

100

Boundary

κL (W m−1 K−1)

34

10

1

1

10

100

1000

T (K)

Figure 2.9 The lattice thermal conductivity versus temperature of a CoSb3 sample [25, 26].

dominates the thermal transport in a wide temperature range. To indicate the relationship between 𝜅 L and T, the RTA is very useful, which is mentioned in Section 2.3. As shown in Figure 2.9, the Callaway model based on RTA qualitatively demonstrates that phonon scattering is dominated by boundary scattering at low temperatures, defect scattering at intermediate temperatures, and Umklapp processes at high temperatures. Therefore, to modify the 𝜅 L of TE oxides, effective ways in scattering phonons according to the scattering mechanism of different temperature ranges should be discovered. As researchers have found, ultra-low heat conduction of amorphous solids arises from phonons whose mean free path lph is comparable to the interatomic spacing. Introduced point defects are very useful in triggering these interatomic effects [27]. These factors would reflect in the consequent effects. For instance, irrespective of the type of dopants, different atom sizes and masses trigger strain–stress and mass fluctuations. These fluctuations would enlarge the scattering of phonons with particular wavelengths, which is indicated by the Callaway model, as given by Klemens from Eqs. (2.22), (2.25)–(2.27): Γ = ΓMF + ΓSF , ∑n

i=1 ci

(2.25)

(

)2 Mi

fi1 fi2

(

Mi1 −Mi2

)2

Mi M ∑n ci ( )2i=1 ( 1 2 )2 ∑n r −r Mi fi1 fi2 𝜀i i r i i=1 ci i M = ∑n i=1 ci

ΓMF =

(2.26)

ΓSF

(2.27)

2.4 Temperature Relationship in Thermal Properties

where the disorder scattering parameter Γ is related to both strain field ΓSF and mass fluctuation scattering ΓMF , ci the relative degeneracy of the site, f i the fractional occupation, Mi and ri the average mass and radii of that element, and M the average atom mass [28]. Therefore, by finding the impurity scattering coefficient Γ through specific calculations and fitting, it is possible to predict a comprehensive B and ultimately apply this value to analyze and further optimize the thermal conductivity of TE oxides. In practice, the dominant phonon method works quite well in predicting the effect of phonon scattering processes. The dominant phonon method assumes that at a given temperature all phonons are concentrated about a particular dominant frequency 𝜔dom ∼ k B T/ℏ. An empirical power law can then be deduced as follows. If one particular defect can be described by 1/𝜏 ∝ 𝜔a or, equivalently, by 1/𝜏 ∝ xa T a , taking C ∝ T 3 (for low 𝜃 D ) and employing the simple kinetic formula yields 𝜅 L ∝ T 3−a . Even though the dominant phonon method is not mathematically justified, the power law is usually valid at low temperatures. For example, one should have 𝜅 L ∝ T 3 at low temperatures if boundary scattering is the dominant phonon scattering mechanism. According to the Callaway model, 𝜏 d for point defect scattering should be proportional to 1/𝜔4 . This means that point defect scattering would not have a significant effect on low-frequency phonons, even diatomic doping could be simply interpreted as an overlay of two monatomic doping for enlarging doping limitation. Fortunately, a plenty of researches on alloy materials have proved that nanostructuring effects increase the scattering of low-frequency phonons. From Figure 2.10, Gd-doped CMO synthesized by a chemical coprecipitation method exhibited a much lower 𝜅 L for the whole temperature range, even could be ∼1.1 W m−1 K−1 at 973 K, which is ascribed to the higher concentration of grain boundaries caused by smaller grain sizes of 200–400 nm, compared with 3–5 μm particles fabricated by a solid-state reaction mechanism [29]. 3.6 3.2

CMO

Y0.1

Dy0.1

Yb0.1

Mn0.98Nb0.02

κL (W m–1 K–1)

Gd0.04

2.8

Chem.-Gd0.04

2.4 2.0 1.6 1.2 0.8 1.0

1.5

2.0

2.5

3.0

3.5

1/T (1000/K)

Figure 2.10 The thermal properties of CaMnO3 with substitutional point defects.

35

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2 Controlling the Thermal Conductivity of Bulk Nanomaterials

2.5 Model for Lattice Thermal Conductivity When we concentrate exclusively on electronic conduction, it has been assumed that lattice vibrations are in thermal equilibrium, which is independent of the electronic states. Nevertheless, this assumption is not valid in some circumstances. For instance, in metals the lattice conductivity is usually covered by the electronic contribution, yet the lattice section plays the key role in heat transport through insulators. In order to understand the mechanism of lattice thermal conduction, we need to first build a proper model that can well explain lattice thermal conduction phenomenon and then use it to explore the theoretical depth. 2.5.1

Kinetic Theory

Let us put the mechanism involved aside first, and enquire what can be discussed about the 𝜅 L from elementary considerations. Apparently, we would view the phonons as gas, which has an isotropic kinetic property, and the thermal conductivity is given by 1 Cvl (2.28) 3 where C, v, and l are, respectively, the specific heat, mean velocity, and free path of phonons. It is more likely to get the right order of magnitude for v rather than the exact value; therefore, it is set equal to the velocity of sound vs in the lattice, then we obtain 1 (2.29) 𝜅 = Cvs l 3 At low temperatures, the Debye cube law indicates that the lattice specific heat varies with T 3 and l becomes dependent of scattering by impurities or boundaries rather than phonon–phonon collisions, thus in Eq. (2.29) we expect 𝜅 ∝ T 3 , which has been observed. For the high-temperature regime, we know that C becomes independent of T, and if we suppose that the mean free path l varies as T −1 , then we get 𝜅 ∝ T −1 , which is roughly correct. Actually, if the conductivity is limited by phonon–phonon collisions, then a mean free path (MFP) is not meaningful; more details will be discussed below. There are circumstances where the concept does have some validity, e.g., in a magnetic system 𝜅 is partly determined by the collisions between phonons and magnons. In any case, it is better to substitute l as v𝜏, where 𝜏 is a relaxation time. With this substitution, Eq. (2.29) should be justified into a semiclassical framework. 𝜅=

2.5.2

Boltzmann Equation

We apply certain considerations to set up the Boltzmann equation, which means that we are implicitly dealing with wave packets of phonons that travel with a group velocity d𝜔/dk, with a frequency of Δ𝜔. The phonon occupation number n(k) is supposed to be a slowly varying function of position in the presence of

2.5 Model for Lattice Thermal Conductivity

thermal gradient ∇T. The rate of change caused by the motion of phonons with group velocity of vk can be defined as follows: 𝜕n 𝜕𝜔 𝜕n 𝜕n = − vk = − 𝜕t 𝜕r 𝜕r 𝜕k

(2.30)

In this formulation, we can write n = n0 + n1

(2.31)

where n1 is proportional to ∇T and n0 is the distribution in the absence of a thermal gradient ) ( 1 ℏ n0 = 𝛽𝜔 (2.32) 𝛽= kB T e −1 Then, to first order in ∇T 𝜕n ℏ𝜔 e𝛽𝜔 ℏ𝜔 𝜕n = ∇Tn0 (n0 + 1) = ∇T 0 = ∇T 𝛽𝜔 𝜕r 𝜕T kB T 2 (e − 1)2 kB T 2 𝜕n 𝜕n = − 0 vk ∇T 𝜕t 𝜕T

(2.33) (2.34)

It is noted that this is canceled by the rate of change due to collisions. If we define the relaxation time 𝜏, then n1 = 𝜏

𝜕n 𝜕n = −∇Tvk 𝜏 𝜕t 𝜕t

Therefore, the thermal current can be written as ∑ ∑ 𝜕n Q= n1 ℏ𝜔k vk = −∇T vk ℏ𝜔k vk 𝜏 𝜕t k k

(2.35)

(2.36)

since Q = −𝜅∇T

(2.37)

Then, for an isotropic medium such as a cubic crystal, the thermal conductivity can be addressed as 1 ∑ 2 𝜕n 1 ∑ || 𝜕𝜔 || 𝜕n 𝜅= vk 𝜏 (2.38) ℏ𝜔k = ℏ𝜔 l 3 k 𝜕T 3 k || 𝜕k || 𝜕T k in which l = vk 𝜏. In the Debye model, it takes the approximation that | 𝜕𝜔 | vk ≡ || || = vs | 𝜕k |

(2.39)

And if we put the specific heat under the Debye model into the derivation, then ∑ 𝜕n(k) C= (2.40) ℏ𝜔k 𝜕T k Ultimately, Eq. (2.29) could be achieved, which makes our derivation selfconsistent.

37

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2 Controlling the Thermal Conductivity of Bulk Nanomaterials

2.5.3

Phonon–Phonon Collisions

It is easy to see that normal phonon–phonon processes provide no thermal resistance. We can see from Eq. (2.37) that 𝜅 would be infinite if a heat current Q were possible with the absence of a thermal gradient. For instance, a heat current established in a ring that is subsequently thermally isolated would circulate forever, similar to the electrical current in a superconductor. To obtain a finite conductivity, it is required that the energy in the current needs to be eventually dissipated through the system with, in particular, the total crystal momentum, as shown below: ∑ P= n(k)k (2.41) returning to its equilibrium value of zero. By definition, normal processes conserve P and so Umklapp processes must be involved in order to ensure the eventual dissipation. To illustrate the role of phonon–phonon collisions in detail, the Boltzmann equation is used here as 𝜕nk || ℏ𝜔 𝜕𝜔 = ∇Tn0 (n0 + 1) 𝜕t ||coll kB T 2 𝜕k

(2.42)

In order to calculate the rate of change due to collisions, the anharmonic perturbation V is supposed to induce transitions from state i to state j according to Fermi’s golden rule 2𝜋 dP = |⟨i|V |j⟩|2 𝛿(𝜀i − 𝜀j ) dt ℏ then it follows that dnk || 2𝜋 ∑ = p |⟨i|V |j⟩|2 (nkk − nik )𝛿(𝜀i − 𝜀j ) | dt |coll ℏ ij i

(2.43)

(2.44) j

where pi is the probability of the state |i⟩ being occupied, nik and nk the numbers of phonons of wave vector k in state i and j, respectively. The lowest order in the perturbation involves the so-called three-phonon processes, which is given as ∑ 𝜎 𝜎 𝜎 V = V (k1 k2 k3 )(ak𝟏 𝜎1 + a†−k 𝜎 )(ak𝟐 𝜎2 + a†−k 𝜎 )(ak𝟑 𝜎3 + a†−k 𝜎 ) (2.45) 𝟏 𝟐 𝟑 𝟏 1 𝟐 2 𝟑 3 k𝟏 k𝟐 k𝟑 𝜎1 𝜎2 𝜎3 j

Firstly, we note that |nk − nik | = 1 (if nonzero), and secondly, since we consider the energy change in the process must be zero, so the process in which all three phonons are created or destroyed can be disregarded, then four possibilities can be deduced; the phonon k𝜎 merges with a second phonon to produce a third; a phonon split into a phonon k𝜎 and a third phonon; two phonons produce the phonon k𝜎; and the phonon k𝜎 splits into two other phonons. The first two processes carry double weight. That is, k + k′ + k′′ = K

(2.46)

2.5 Model for Lattice Thermal Conductivity

And in the last two processes: ′′

k′ + k′ + k = K

(2.47)

After necessary derivation, including contributions of each process, we obtain { ∑ dn(k𝜎) || ′ ′′ 3 ′ dk = 2 |V (𝜎k k𝜎′ 𝜎k′′ )|2 [(n + 1)(n′ + 1)n′′ − nn′ (n′′ + 1)] | ∫ dt |coll 𝜋 𝜎 ′ 𝜎 ′′ ′ ′′′ 1∑ |V (𝜎k 𝜎k′ 𝜎k′′′ )|2 × 𝛿(𝜔 + 𝜔′ − 𝜔′′ ) − 2 𝜎 ′ 𝜎 ′′′ } × [(n + 1)n′ n′′′ − n(n′ + 1)(n′′′ + 1)] × 𝛿(𝜔 − 𝜔′ − 𝜔′′′ ) (2.48) ′′

′ ′′

′

where k and k are given in terms of k and k through Eqs. (2.46) and (2.47), containing all possible values. | Besides, the dn | must vanish due to the limit of equilibrium; we shall follow dt |coll Peierls (1955) in writing n1 = n0 (n0 + 1)g(k𝜎)

(2.49)

Taking first order in g, then the Boltzmann equation (2.42) becomes ℏ𝜔 𝜕𝜔 ∇T kB T 2 𝜕k { ∑ ′ |V (𝜎k k𝜎′ dk′

n0 (n0 + 1) =

3 𝜋 2∫

𝜎 ′ 𝜎 ′′

1∑ − |V (𝜎k 2 𝜎 ′ 𝜎 ′′′

𝜎 ′′ 2 k′′ )| [(n0

+ 1)(n′0 + 1)n′0 (g ′′ − g − g ′ )𝛿(𝜔 − 𝜔′ − 𝜔′′ ) }

𝜎 ′ 𝜎 ′′′ 2 k′ k′′′ )| (n0

+

1)n′0 n′′0 (g ′

+g

′′′

− g)𝛿(𝜔 − 𝜔 − 𝜔 ) ′

′′′

(2.50)

Now we can check the temperature-dependent situation, namely, the form of this formulation at high temperatures and low temperatures. For high temperatures, the terms (n0 + 1), etc. can be replaced by n0 , etc. throughout Eq. (2.50), and bear in mind that n0 ∝ T, in this regime n1 ∝ 1/T, then ∑ 𝜕𝜔 Q= n1 ℏ𝜔k (2.51) 𝜕k It is also proportional to T −1 and hence 𝜅 ∝ T −1 , which is a result achieved very simply earlier. On the other hand, there is a similar argument that using four-phonon processes instead of three-phonon processes as the next term in the perturbation theory will give another inference 𝜅 ∝ T −2 . Actually, three-phonon processes will presumably dominate because the experiments do indicate the rough validity of 𝜅 ∝ T −1 ; however, we can judge that the decrease with increasing temperature must be more rapid than T −1 , lying between T −1 and T −2 . With decreasing temperature, most phonons become long wavelength ones; as a result, the frequency of Umklapp processes decreases much more rapidly than

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2 Controlling the Thermal Conductivity of Bulk Nanomaterials

that of normal processes. We thus expect the distribution to be pretty well in equilibrium as far as normal processes are concerned. With the absence of driving forces and Umklapp processes, Eq. (2.50) has the solution, if we deal specifically with the x-direction: g = Ck x

(2.52)

where C is a constant. Based on Eqs. (2.46) and (2.47), this should be a good approximation for lattices of cubic symmetry with ∇T in the x-direction at low temperatures. The constant C may be obtained by including Umklapp processes in the right-hand side of Eq. (2.50), and the contribution of normal processes vanishes by virtue of the solution for g adopted. Then C will be dependent on the value of k. Peierls suggests that C can be obtained by multiplying through Eq. (2.50) by k x and summing over all k; C is then found by considering the rate of change of P. This theory is doubly satisfactory in that the contribution of normal processes now vanishes due to not only our choice of g but also the exact solution. From the above discussion, it is clear that although normal processes themselves do not give a finite thermal conductivity, they are nevertheless important in maintaining equilibrium against fluctuations for which P is conserved. An effect that becomes important at low temperatures, when Umklapp processes are rare, is the scattering of crystal vibrations by isotopes and other crystal imperfections. Neglecting normal phonon–phonon processes, we find 𝜅 → ∞ because the imperfections are not very good at scattering long waves. This difficulty disappears when the normal processes are taken into account, because they limit the energy that the long waves can carry. Another example is the size effect, where the appropriate MFP for insertion into Eq. (2.38) depends on the dimension of the crystals. This also becomes noticeable at low temperatures. Since we know that normal processes are much more frequent than Umklapp processes, the former should again have the dominant effect.

2.6 Interfacial Thermal Conductivity The finding that a thermal resistance might exist at the interface between liquid helium and solids was first discovered as early as 1936. Kurti et al. [30] assumed such a thermal resistance to be small and ignored it. However, a few months later, Keesom and Keesom [31] recognized that the thermal resistance at the interface was “relatively very considerable,” but they didn’t conduct a further research. In 1941, Kapitza reported his measurements of the temperature drop at the boundary between helium and a solid when heat flows across the boundary, which is the so-called interfacial thermal resistance. Interfacial thermal resistance is a measurement of an interface’s resistance to thermal flow. In the presence of the heat flux normal to the interface, a discontinuous temperature drop ∇T develops due to the differences in electronic and vibrational properties in different materials. The interface will scatter

2.6 Interfacial Thermal Conductivity

the phonon or electron that attempts to traverse the interface. The associated interfacial resistance R𝜅 [32], also called the Kapitza resistance, or, equivalently, the interfacial thermal conductance G𝜅 = 1∕R𝜅 , is quantified by JQ = −G𝜅 ∇T

(2.53)

where J Q is the heat flux across the interface and ∇T the observed temperature drop. We all know that an interface plays a critical role in determining the overall physical properties of materials, for example, the thermal and mechanical properties of devices can be modulated when the grain boundaries [33], heterojunctions [34], or aggregates [35] are involved. Therefore, understanding the physical mechanisms at interfaces is crucial to improve the performance of structures and devices in a diverse spectrum of technologies, such as heat dissipation in electronic devices. Low thermal resistance at interfaces is technologically important for applications where very high heat dissipation is necessary. This is of particular concern to the development of microelectronic semiconductor devices as defined by the International Technology Roadmap for Semiconductors in 2004 [36, 37], where an 8-nm-feature-size device is projected to generate as high as 100 000 W cm−2 that need to be dissipated efficiently to preserve the device integrity, reliability, and performance. The heat dissipation of an anticipated die-level heat flux of 1000 W cm−2 is an order of magnitude higher than that of the present metal oxide semiconductor devices [38]. On the other hand, applications requiring good thermal isolation, such as jet engine turbines, would benefit from interfaces with high thermal resistance. This would also require material interfaces that are stable at very high temperatures, such as metal–ceramic composites, which are currently used for these applications. In addition, high thermal resistance can also be achieved with multilayer systems. As stated above, thermal boundary resistance (TBR) is the result of carrier scattering at an interface. The type of carrier scattering will depend on the materials governing the interfaces. For example, at a semiconductor interface, phonon scattering effects will dominate the TBR, because phonons are the main thermal energy carriers. In the context of phonon-dominant thermal transport, interfaces present an additional site for phonon scattering and impediment to the propagation of thermal energy [39]. The phonons behave differently at different types of interfaces such as liquid–solid and solid–solid interfaces. Two widely used predictive models are the acoustic mismatch model (AMM) [40, 41], which assumes no scattering, and the diffuse mismatch model (DMM) [32], which assumes that all phonons incident on the interface will scatter. The details of the two models are as follows. At an interface between two metals, however, we can expect that electrons will contribute significantly to heat transport. Bryan C. Gundrum provides data and employs a simple theoretical model, an electronic version of the “diffuse mismatch model,” which successfully describes the magnitude and temperature dependence of heat transport [42]. For heat transport to occur across metal–nonmetal interfaces, energy transfer must occur between electrons and phonons. There are two possible pathways: (i) coupling between electrons

41

42

2 Controlling the Thermal Conductivity of Bulk Nanomaterials

Heat flux, q Nonmetal

Metal Te

Te′ (0)

Tp

Electron y

Rep

Figure 2.11 Schematic illustrating a pathway for heat flow from a metal to a nonmetal across an interface. The electrons must transfer their energy to the phonons in the metal, which has a resistance Rep , and then the phonons transfer their energy across the interface with a resistance Rpp [43].

x T

Phonon

Phonon Rpp

of the metal and phonons of the nonmetal through anharmonic interactions at the metal–nonmetal interface and (ii) coupling between electrons and phonons within the metal, and then subsequently coupling between phonons of the metal and phonons of the nonmetal (see Figure 2.11; [43]). In the AMM, the only essential simplifying assumption is that the phonons are governed by continuum acoustics and the interface is treated as a plane. That is, phonons are treated as plane waves, and the materials in which the phonons propagate are treated as continua (no lattice). For phonons with wavelengths much greater than typical interatomic spacing, this continuum approximation might be expected to be accurate. Given this (very strong) assumption, there are only a few results possible when a phonon is incident on the interface; the phonon can specularly reflect, reflect and mode convert, refract, or refract and mode convert (Figure 2.12). The interface resistance of AMM can be written as )−1 ( kB4 𝜋 2 Γ1→2 Rint = T2−3 (2.54) 15ℏ3 c21 l

l, t1, or t2

l

t1

t1

t2

t2

Figure 2.12 Schematic of the many possibilities within the framework of the acoustic mismatch model for phonons incident on an interface. The picture simplifies if one of the sides is liquid helium; there are no transverse modes on that side [43].

2.7 Model for Nano Bulk Materials

Γ is the integrated transmissivity. 𝜃1c

Γ1→2 =

∫0

a1→2 sin 𝜃 cos 𝜃 d𝜃

(2.55)

( ) where 𝜃 is the incident angle, and 𝜃c = sin−1 c1∕c2 the critical angle, where ci is the phonon velocity in materials i and a the energy transmission probability: a1→2 =

4𝜌2 c2 cos 𝜃2 × 𝜌1 c1 cos 𝜃1 (𝜌2 c2 cos 𝜃1 + 𝜌1 c1 cos 𝜃2 )2

(2.56)

In the diffuse mismatch model, the assumption of complete specularity is replaced with the opposite extreme: all the phonons are diffusely scattered at the interface; this leads to an upper limit of the effect that diffuse scattering can have on the boundary resistance. In the diffuse mismatch model, acoustic correlations at the interfaces are assumed to be completely destroyed by diffuse scattering, so that the only determinants of the transmission probability are densities of phonon states and the principle of detailed balance. The probability of transmission is nonetheless determined by a mismatch between densities of states. The effect on the TBR of diffuse scattering at the interface can be qualitatively understood with the following arguments. We shall assume that scattering destroys the correlation between the wave vectors of the incoming and outgoing phonons. Simply put, we assume that a scattered phonon forgets where it came from. The probability that the phonon will scatter into a given side of the interface is then independent of where it came from. Instead, the probability of scattering into a given side is proportional to the density of phonon states on that side (see Fermi’s "golden rule") and is also restricted by the principle of detailed balance. The interface resistance of DMM can be written as )−1 ( kB4 𝜋 2 −2 c a T2−3 (2.57) Rint = 30ℏ3 1 1→2 where a is the energy transmission probability, a1→2 =

c−2 2 −2 c−2 1 + c2

(2.58)

Molecular dynamics (MD) simulation is a powerful tool to investigate the interfacial thermal resistance. Recent MD studies have demonstrated that the solid–liquid interfacial thermal resistance is reduced on nanostructured solid surfaces by enhancing the solid–liquid interaction energy per unit area and reducing the difference in vibrational density of states between the solid and liquid [44].

2.7 Model for Nano Bulk Materials Materials with nanostructures exhibit different properties from those of the corresponding bulk substances, single crystals, coarse-grained polycrystals,

43

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2 Controlling the Thermal Conductivity of Bulk Nanomaterials

and glasses, although they have an identical chemical composition. The two dominant concepts in the nanostructuring that affect the improvement of thermoelectric properties are quantum confinement by the introduction of nanoscale constituents and enhanced phonon scattering by the interfacial surfaces in nanostructures. The former contributes to high S with relatively reduced n by carrier filtering effect, while the latter reduces the 𝜅 through nanoscale building blocks, which causes a significant increase in the density of grain boundaries. In the nanostructured bulk materials that have been tested, decrease in thermal conductivity has proven to be a primary mode of the enhancement in the thermoelectric figure of merit. Moreover, the size dependence of physical properties in nanostructured materials becomes evident when the size of building blocks is reduced to the nanometer scale, which is comparable to the critical length of microphysical phenomena such as the MFPs of electrons or phonons. Selecting nanoscale as the target also considers the fact that the MFPs of electrons and phonons have a big discrepancy at that length, phonons are efficiently scattered, but electrons can successfully pass through. As a result, it reduced thermal conductivity and retained high carrier mobility simultaneously. As the MFP of low-frequency phonons is at a nanometer magnitude, materials fabricated with 1–100 nm grains would obviously introduce efficient boundary scattering. This phenomenon has been indicated by many early reports in thermoelectric alloys [45]. In the Debye–Callaway model, 𝜏b−1 = 𝜈∕L represents boundary scattering, and it was closely connected to the microstructure of thermoelectric materials. As mean acoustic velocity, v was one of the intrinsic properties that depended only on the composition itself, which was almost impossible to alter by varying the external environment. Nevertheless, L generally could be taken for mean grain size and negatively correlated to the whole relaxation time, further reducing the lattice contribution to heat transport. As shown in Figure 2.13a, similar to CMO, STO and its compounds are also a typical perovskite-type oxides, which have an isotropic cubic crystal c

c b

a

a

b

O Ti O In

Sr (a)

(b)

Figure 2.13 The crystal structure of (a) perovskite oxides: SrTiO3 (P m 3m) and (b) bixbyite oxides: In2 O3 (Ia3).

2.7 Model for Nano Bulk Materials

structure (a = 3.904 Å, P m 3m) above 105 K. The strong structural tolerance makes substitutional doping in STO easier and allows it to reach degenerate state and possess high electrical conductivity. Because of its high melting temperature of 2353 K, STO has the fundamental potential for application at very high temperatures, and it can even be used as a middle transformation at nuclear electricity. The conduction bands of STO are formed by Ti 3d orbitals consisting of triply degenerate orbitals (3dxy , 3dyz , and 3dxz ) and its valence bands formed by an O 2p orbital, and the bandgap Eg could be 3.2 eV. Therefore, STO simultaneously has large S and relatively high modulated n, and the power factor of doped STO (∼6.5 μW cm−1 K−2 ) is promising enough to compete with conventional TE alloys. Nevertheless, considering the heat transport, lattice vibration contribution 𝜅 L is almost one order of magnitude higher than those of conventional TE materials. Even with dopant cations as point defects, its relatively simple structure, limited doping level, and lack of effective phonon scattering centers make it impossible to exhibit the effects of point defects. Therefore, the ZT values of STO and its related compositions are still far below that of alloys, ascribed to high thermal conductivity (∼9.5–4.3 W m−1 K−1 ) in the temperature range of 300–1000 K. As shown in Figure 2.14a, though the 𝜅 L of SrTiO3 single crystal was relatively high, high concentration of GBs in STO polycrystalline ceramics, even micrometer grained, could scatter low-frequency phonons. Moreover, this result also indicated GB-phonon scattering was much stronger in samples with smaller grains, though with increasing temperature the MFP of phonons were shortened and GB-phonon scattering would be inevitably less significant at high temperatures. As a result, the lowest 𝜅 L values observed in the 55-nm-grained undoped STO were 5.3 W m−1 K−1 at 300 K and 3.4 W m−1 K−1 at 1000 K, corresponding to a 45% reduction and a 20% reduction, respectively, compared with 𝜅 L values of the bulk single crystals. Nevertheless, the reduction in 𝜅 L at 1000 K in the 55-nm-grained ceramic was only approximately 20% of that in single crystals. This indicated that even a grain size as small as 55 nm was not sufficient to reduce the 𝜅 L of a polycrystalline STO ceramic to the glassy limit (∼1 W m−1 K−1 ) because it was still far larger than the phonon MFP, which is given by the graph in Figure 2.14b, lph = 20Tm d∕𝛾 2 T

(2.59)

with melting point T m , lattice parameter d, Gruneisen constant 𝛾 (usually 1–2), and absolute temperature T. In graph Figure 2.14b, lph decreases from 25 nm at 300 K to 10 nm at 1000 K, meanwhile, the critical grain size for satisfactory reduction in 𝜅 L was estimated to have a comparison with MFP, therefore adjusting it to be 10–25nm would be much more appropriate. In order to clarify this thermal transport behavior, the effective 𝜅 L values were plotted as a function of reciprocal temperature in the inset graph of Figure 2.14a, and simulation work through the Callaway model is shown in Figure 2.14c,d. The physical parameters come from Sakhya et al. [46]. Figure 2.14a demonstrates that the 𝜅 L value for a STO single crystal has a strong linear dependency on 1000/T in the whole temperature range, which meant that characteristic phonon–phonon

45

7 6

1.0 1.5 2.0 2.5 3.0 1/T (1000/K)

5 4 3

(a)

300 400 500 600 700 800 900 1000 T (K) 10 9 8

STO-Cal. 20 μm-Cal. 10 μm-Cal. 85 nm-Cal. 55 nm-Cal.

7 6 5

110 100 90 80 70 60 50 40 30 20 10 0 0

200

400

600 T (K)

(b) 10 9

4

8 7 6

2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4

40

800

1000 1200

Oxygen vacancy

60

80

10000 15000 20000

Grain size (nm)

5 4

3

(c)

STO

Oxygen vacancy (%)

8

STO (Single crystal)10 20 μm 9 85 nm 8 10 μm 7 55 nm 6 5 4 3

κL (W m–1 K–1)

κL (W m–1 K–1)

9

κL (W m–1 K–1)

10

Iph (nm)

2 Controlling the Thermal Conductivity of Bulk Nanomaterials

κL (W m–1 K–1)

46

3 300 400 500 600 700 800 900 1000 T (K)

(d)

300 400 500 600 700 800 900 1000 T (K)

Figure 2.14 (a) Temperature dependence of lattice thermal conductivity: STO single crystal and polycrystalline ceramics with different grain sizes, and the inset graph is a function of reciprocal temperature with 𝜅 L , (b) temperature dependency of phonon mean free path for STO ceramics, (c) 𝜅 L calculated by optimized Debye–Callaway model (the content of oxygen stays the same among all samples), (d) 𝜅 L calculated by optimized Debye–Callaway model (with variable oxygen vacancies that depend on the grain size); the inset graph is grain size dependency of oxygen vacancies for STO ceramics. Source: Koumoto et al. 2010 [28]. Reproduced with permission of Annual Reviews.

scattering, and the Umklapp process was predominant in it. However, even the simulation line of a single crystal calculated by the Callaway model was good, as shown in the graph of Figure 2.14c, but when considering grain boundary scattering approximated by 𝜏b−1 = 𝜈∕L, the discrepancies exhibited there should have some compensation in oxides, both for micrometer-level and nanometer-level grain sizes. We suspected the reason for the discrepancies could come from the content of oxygen vacancies and the fact that nanograins were not easy to produce oxygen vacancies as micron-sized polycrystals. Based on this assumption, we repeated the simulation by considering various oxygen vacancy contents for different grain sizes, as shown in the graph of Figure 2.14d and its inset graph. The results were in good agreement with experimental work, which indicated the phenomenon that partial loss of oxygen vacancies in smaller grain sizes was highly possible at the same synthesis condition. Therefore, adjusting the fabrication process for samples with different grain sizes is important for retaining oxygen vacancies.

2.7 Model for Nano Bulk Materials 14

κL (W m–1 K–1)

5.5 5.0 4.5 4.0 3.5

3.1% La-69 nm 4.7% La-69 nm 7.7% La-69 nm 9.0% La-69 nm

In1.76(ZnCe)0.12O3-Nanodot (ZnCe)0.08–50 nm –150 nm 14

12 κL (W m–1 K–1)

6.0

–0.4 μm –0.6 μm –2 μm

10 8 6

12

κL (W m–1 K–1)

6.5

10 8 6 4 2 1.0 1.5 2.0 2.5 3.0 3.5 1/T (1000/K)

4

3.0 2.5

2

κmin

2.0 0 300 400 500 600 700 800 900 1000 300 400 500 600 700 800 900 1000 1100 T (K) T (K) (a) (b)

Figure 2.15 (a) Temperature dependence of effective thermal conductivity for La-doped STO with 69 nm grain size, (b) the lattice thermal property of In2 O3 with different grain sizes; the inset graph is a function of reciprocal temperature. Source: Park et al. 2014 [47]. Reproduced with permission of RSC.

Besides, when combining effect of point defects and nanograins, as shown in Figure 2.15a, the 𝜅 L of La-doped STO with 69nm grain size exhibited a regular tendency, more dopants led to lower 𝜅 L on the basis of GB effect. Ultimately, the lowest 𝜅 L was 2.3 W m−1 K−1 at 973 K in 9 at% doped sample, decreased 46.5% compared with undoped one. Therefore, with one or two decades of nanometer grain and doping work of properly heavy elements combined, ∼1 W m−1 K−1 would be possible as the next strategy for STO in the future. This strategy also works for In2 O3 and its compounds. By contrast with the fast grain growth of ZnO during synthesis, the grain size of In2 O3 and its system is much easier to control, due to its different crystal structure. As shown in Figure 2.13b, the lattice structure (space group: Ia3) of In2 O3 was much more complex than that in ZnO. Based on a relatively high PF, In2 O3 has been developed as a promising thermoelectric oxide when the cubic bixbyite structure becomes disordered with various cations substituted for indium ions, and furthermore, cosubstitution can significantly enhance the solubility of the dopant, which can simultaneously increase electrical resistivity and decrease thermal conductivity. On this basis, Lan et al. introduced Zn and Ce codoping that significantly reduced thermal conductivity by fabricating these nanograined In2 O3 -based bulks, and thus improving the thermoelectric performance. Similar to STO, as shown in Figure 2.15b, the T −1 trend indicates that the intrinsic Umklapp processes dominate the phonon transport. Moreover, the smaller the composite size is, the smaller the 𝜅 L , and even closer to the glassy limit 1.2 W m−1 K−1 . Specifically, the 𝜅 L of the 50 nm grained sample can be decreased to 7.9 W m−1 K−1 at room temperature, and is much lower compared with that of the 2 μm grained one, which is 13.2 W m−1 K−1 . At high temperatures, the 𝜅 L decreased from 2.7 W m−1 K−1 in the 2 μm grained sample to 1.5 W m−1 K−1 in 50 nm grained samples, which clearly exhibited the effect of nanograins on phonon scattering at high temperatures.

47

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2 Controlling the Thermal Conductivity of Bulk Nanomaterials

Besides, based on this nanograin work, when CeO2 came out as a second phase, nanodots were included in In2 O3 , which rendered the lattice thermal conductivity even closer to the amorphous limit, and it was finally reduced down to 1.2 W m−1 K−1 at 973 K, which was ascribed to the introduction of second-phase scattering: 𝜏sp −1 = v(𝜒s −1 + 𝜒sp −1 )−1 Vsp ,

(2.60)

where 𝜒 s represents the effects of the intrinsic superficial area, 𝜒 sp the effect of the introduced second phase, and V sp the number density of second phase. Besides, for a two-phase composite, based on the effective medium approximation (EMA), Nan et al. introduced a general equation for the thermal conductivity that is applicable in a wide variety of geometries and includes TBR [48]; however, in nanocomposites where the inclusion size is smaller than the MFP, the results from the EMA cannot agree with those from more rigorous solutions. This is because the host and particle thermal conductivities in nanocomposites are not equal to their bulk values due to increased interface scattering. Due to this reason, Chen et al. introduced a modified EMA formulation that gives a closed-form expression for the thermal conductivity of a nanocomposite [49]. The principle is to account for size effects in each phase by modifying the bulk MFP, from which modified thermal conductivities can be obtained to use in the usual EMA equations. In this work, they obtained an expression for the effective thermal conductivity of a nanocomposite as a function of the interface density Φ and the nanoparticle diameter d, 1 1 keff (Φ; d) = Ch uh 3 (1∕Λh ) + (Φ∕h) kp (d)(1 + 2𝛼(Φ, d)) + 2kh (Φ) +2(Φd∕6)[kp (d)(1 − 𝛼(Φ, d)) − kh (Φ)] × (2.61) kp (d)(1 + 2𝛼(Φ, d)) + 2kh (Φ) −(Φd∕6)[kp (d)(1 − 𝛼(Φ, d)) − kh (Φ)] The good agreement with results from MC simulations and solutions to the Boltzmann equation further indicates that the thermal conductivity in nanocomposites is governed by the interface density and that TBR plays a critical role in determining the effective thermal conductivity.

2.8 Minimum Value for Oxides Based on RTA and previous work, the minimum values for oxides can be achieved only in materials with nanograin size (5–100 nm), which is comparable to the MFP of phonons, because most phonons with these wavelengths can be scattered by enormous grain boundaries. Besides, a lot of defects and nanoinclusions should be introduced to constitute all-scale hierarchical structures, further scattering the phonons with different frequencies. Once the MFP is close to the lattice parameter of the corresponding crystal structures, the glassy limit of 𝜅 L will be achieved.

References

The glassy limit of disordered materials demonstrated by Cahill et al. is based on the assumption that the mechanism of heat transport in crystals was a random walk of the thermal energy between neighboring atoms vibrating with random phases [50]. The formula at high temperature can be simplified as follows: 𝜅min =

( ) 1 𝜋 1∕3 kB V −2∕3 (2vt + vl ), 2 6

(2.62)

where V is the average volume per atom calculated from the refined lattice parameters and vt and vl are transverse and longitudinal sound velocities, respectively. Therefore, minimum values of oxides can be calculated and provide a promising effect for strategies working on reducing 𝜅 L , e.g. 𝜅 min ∼ 1.0 W m−1 K−1 at 1050 K. Recently, many materials systems have exhibited ultra-low thermal conductivities that even lower than the glassy limit, including Cu2 Se, BiCuSeO, Cu3 SbSe4 , SnSe, etc. With the deep analysis done by many researchers, the reasons are possibly due to the effect of “liquid-like” behavior of copper ions or large anharmonicity. The development of BiCuSeO has further indicated, other than the glassy limit, more work should be done on these oxygen-containing compounds. Recently, G. J. Snyder et al. have mentioned estimating how low the thermal conductivity engineered can set practical limits for a variety of applications. Heat that is transported by the vibrational energy of atoms in a solid can be defined from different perspectives, and low thermal conductivity materials are typically full of many types of disorders and defects: from impurity atoms and solid solutions to dislocations, grain boundaries, and other interfaces. Alternatively, they consider the transport of heat by diffusons, which are atomic vibrations that carry heat by diffusion. As diffusons are present in all materials, without the structural conditions required by phonon calculations. It follows that diffusons may better describe the physics of heat transfer in low thermal conductivity materials, particularly at high temperatures. The model described in their work is formulated in a way that is both physically insightful and experimentally accessible, grounded in random walk theory, and more details can be found in the previous work [51].

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interaction on the lattice thermal conductivity of Co1−x Nix Sb3 . Physical Review B 65 (9): 094115. Tritt, T.M. (2005). Thermal conductivity: theory, properties, and applications. Springer Science & Business Media. Petersen, A., Bhattacharya, S., Tritt, T. et al. (2015). Critical analysis of lattice thermal conductivity of half-Heusler alloys using variations of Callaway model. Journal of Applied Physics 117 (3): 035706. Koumoto, K., Wang, Y., Zhang, R. et al. (2010). Oxide thermoelectric materials: a nanostructuring approach. Annual Review of Materials Research 40: 363–394. Lan, J., Lin, Y.H., Fang, H. et al. (2010). High-Temperature Thermoelectric Behaviors of Fine-Grained Gd-Doped CaMnO3 Ceramics. Journal of the American Ceramic Society 93 (8): 2121–2124. Kurti, N., Rollin, B.V., and Simon, F. (1936). Preliminary experiments on temperature equilibria at very low temperatures. Physica 3: 266–274. Keesom, W.H. and Keesom, A.P. (1936). On the heat conductivity of liquid helium. Physica 3 (5): 359–360. Swartz, E.T. and Pohl, R.O. (1989). Thermal boundary resistance. Reviews of Modern Physics 61 (3): 605. Schelling, P., Phillpot, S., and Keblinski, P. (2004). Kapitza conductance and phonon scattering at grain boundaries by simulation. Journal of Applied Physics 95 (11): 6082–6091. Chen, G. (1998). Thermal conductivity and ballistic-phonon transport in the cross-plane direction of superlattices. Physical Review B 57 (23): 14958. Prasher, R.S., Hu, X., Chalopin, Y. et al. (2009). Turning carbon nanotubes from exceptional heat conductors into insulators. Physical Review Letters 102 (10): 105901. Schaller R.R. (2004). Technological innovation in the semiconductor industry: a case study of the International Technology Roadmap for Semiconductors (ITRS). George Mason University Fairfax, VA. Prasher, R.S., Chang, J.-Y., Sauciuc, I. et al. (2005). Nano and Micro Technology-Based Next-Generation Package-Level Cooling Solutions. Intel Technology Journal 9 (4). Hu, M., Keblinski, P., Wang, J.-S. et al. (2008). Interfacial thermal conductance between silicon and a vertical carbon nanotube. Journal of Applied Physics 104 (8): 083503. Kapitza, P. (1941). The study of heat transfer in helium II. Journal of Physics 4: 181. Merabia, S. and Termentzidis, K. (2014). Thermal boundary conductance across rough interfaces probed by molecular dynamics. Physical Review B 89 (5): 054309. Liang, Z., Sasikumar, K., and Keblinski, P. (2014). Thermal Transport across a Substrate–Thin-Film Interface: Effects of Film Thickness and Surface Roughness. Physical Review Letters 113 (6): 065901.

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42 Gundrum, B.C., Cahill, D.G., and Averback, R.S. (2005). Thermal conductance

of metal-metal interfaces. Physical Review B 72 (24): 245426. 43 Majumdar, A. and Reddy, P. (2004). Role of electron–phonon coupling in

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thermal conductance of metal–nonmetal interfaces. Applied Physics Letters 84 (23): 4768–4770. Hu, H. and Sun, Y. (2012). Effect of nanopatterns on Kapitza resistance at a water-gold interface during boiling: A molecular dynamics study. Journal of Applied Physics 112 (5): 053508. Toprak, M.S., Stiewe, C., Platzek, D. et al. (2004). The impact of nanostructuring on the thermal conductivity of thermoelectric CoSb3 . Advanced Functional Materials 14 (12): 1189–1196. Sakhya, A.P., Maibam, J., Saha, S. et al. (2015). Electronic structure and elastic properties of ATiO3 (A= Ba, Sr, Ca) perovskites: A first principles study. Indian Journal of Pure and Applied Physics 53 (2): 102–109. Park, K., Son, J.S., Woo, S.I. et al. (2014). Colloidal synthesis and thermoelectric properties of La-doped SrTiO3 nanoparticles. Journal of Materials Chemistry A 2 (12): 4217–4224. Nan, C.-W., Birringer, R., Clarke, D.R. et al. (1997). Effective thermal conductivity of particulate composites with interfacial thermal resistance. Journal of Applied Physics 81 (10): 6692–6699. Minnich, A. and Chen, G. (2007). Modified effective medium formulation for the thermal conductivity of nanocomposites. Applied Physics Letters 91 (7): 073105. Cahill, D.G. and Pohl, R. (1989). Heat flow and lattice vibrations in glasses. Solid State Communications 70 (10): 927–930. Agne, M.T., Hanus, R., and Snyder, G.J. (2018). Minimum thermal conductivity in the context of diffuson-mediated thermal transport. Energy and Environmental Science 11 (3): 609–616.

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55

3 Nonoxide Materials In the 1950s, Bi2 Te3 was found to exhibit excellent thermoelectric properties. Nonoxide materials are promising thermoelectric materials owing to high ZT values at low and medium temperatures. In this chapter, recent results of thermoelectric properties of the state-of-the-art nonoxide materials including bismuth antimony telluride, skutterudite-based materials, silicon-based materials, and other emerging materials are reported.

3.1 Bi2 Te3 -Based Materials Bismuth telluride was considered a potential thermoelectric material due to its high mean atomic weight, which met the criteria by both Ioffe [1] and Keyes [2] for a suppressed k l . Bismuth telluride plays a dominant role in the thermoelectric application field until now. The melting temperature of Bi2 Te3 is merely 585 ∘ C and thus mainly functions as a thermoelectric cooler near room temperature. The first study on high thermoelectric performance of Bi2 Te3 was published in 1954 [3]. A thermocouple consisting of a p-type (Bi,Sb)2 Te3 connected to its n-type counterpart of Bi was reported to obtain a temperature difference of 26 K below room temperature due to the Peltier effect. Both n-type Bi2 (Te,Se)3 and p-type (Bi,Sb)2 Te3 have been widely used as Bi2 Te3 -based thermoelectric materials in electronic cooling devices [4, 5]. The rhombohedral structure with space group R3m of Bi2 Te3 is composed of –Te(1)– Bi–Te(2)–Bi–Te(1)– atomic layers stacked along the c-axis. The crossing angle of the two a-axes perpendicular to the c-axis is 60∘ [6]. The densified bulks exhibit the best thermoelectric (TE) performance along the direction of crystal growth. Because of the anisotropies on the crystal structure of Bi2 Te3 , thermoelectric properties of Bi2 Te3 are strongly anisotropic, and the Bi2 Te3 -based materials are usually fabricated by zone melting, Bridgman method and Czochralski method, which are known as one-direction growth methods [7, 8]. Strong covalent–ionic bonds can be formed between Bi atoms and Te atoms. However, the large grain size and the weak Van der Waals bonds linking Te(2) and Te(1) layers lead to poor mechanical properties, hindering the realization of Bi2 Te3 in practical thermoelectric applications. The cleavage of the Bi2 Te3 crystals perpendicular to the c-direction causes difficulties in fabrication (Figure 3.1). Oxide Thermoelectric Materials: From Basic Principles to Applications, First Edition. Yuan-Hua Lin, Jinle Lan, and Cewen Nan. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

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Figure 3.1 Layered crystal structure of Bi2 Se3 and Bi2 Te3 , with each quintuple layer (QL) formed by five Bi and Se (or Te) atomic sheets. Source: Reproduced with permission of Kong et al. [9]. Copyright 2010, American Chemical Society. Quintuple layer

Se (Te) Bi

To prepare Bi2 Te3 -based bulk materials with good thermoelectric and mechanical properties, various novel methods such as mechanical alloying, hot pressing (HP), spark plasma sintering (SPS), and ingot-extrusion have been widely used; however, some disadvantages exist such as time-consuming and complex process, high cost, impurities introduced from milling balls and containers [10–14]. Although mechanical properties have been greatly enhanced, the figures of merit Z of the (Bi,Sb)2 Te3 materials prepared by these methods reported before 2000 (2.6–3.2 × 10−3 K−1 ) were relatively inferior to those of the ingot by melting single crystals (3.4–3.6 × 10−3 K−1 ) at ambient temperature [15, 16]. Despite persistent efforts to improve ZT, the maximum figure of merit of commercially used Bi2 Te3 -based materials, for example, Bix Sb2−x Te3 (p-type), could not exceed 1 in the 20th century. Over the past decade, the efforts of pursuing higher ZT values have eventually made a great breakthrough. The high ZT value of 1.4 for nanostructured bulk Bix Sb2−x Te3 alloys has been achieved, which is a significant enhancement compared to ZT ≈ 1 in commercial ingots [17, 18]. These nanocrystalline bulks were densified by hot pressing of ball-milled mixtures from elemental chunks in an inert atmosphere. The process is significantly simplified compared to the traditional methods for preparing single crystals, thus lowering manufacturing costs. Compared with the dominant commercial materials, the ZT improvement can be ascribed to the intensified phonon scattering by grain boundaries and defects and consequently low thermal conductivity as shown in Figure 3.2. At the same time, low-dimensional thermoelectric materials including superlattice thin films [19, 20] and nanowire arrays [21–25] have been widely studied in an attempt to further improve thermoelectric figures of merit. The Bi2 Te3 /

3.1 Bi2 Te3 -Based Materials

Figure 3.2 Bright-field TEM image of the mechanically alloyed nanopowders from elements. Source: Reproduced with permission of Ma et al. [18]. Copyright 2008, American Chemical Society.

10 nm

3

p-TeAgGeSb [27] CeFe3.5Co0.5Sb12 [27] Bi2−xSbxTe3 [16] CsBi4Te6 [16] Bi-Sb [26] Bi2Te3/Sb2Te3SL (this work)

2.5

ZT

2 1.5 1 0.5 0 0

200

400

600

800

1 000

Temperature (K)

Figure 3.3 Temperature dependence of ZT of 10 Å/50 Å p-type Bi2 Te3 /Sb2 Te3 superlattice compared to those of several state-of the-art thermoelectric alloys. Source: Reproduced with permission of Venkatasubramanian et al. [20]. Copyright 2001, World Scientific.

Sb2 Te3 superlattice film has exhibited an ultra-high peak ZT value of around 2.4 [20], which is outstanding among many high-performance thermoelectric alloys (Figure 3.3). Thin-film thermoelectric materials offer promise for further improvement in ZT, and there exist three effective methods. One method applies 2D carrier quantum-confinement effects [28] to achieve a greatly increased density of states near the Fermi energy. The second one [29] is based on phonon-blocking/electron-transmitting superlattices. In these specially designed structures, the acoustic mismatch on the interface plays an effective role in reducing k l [30, 31], rather than the traditional alloying approach, hence possibly avoiding alloy scattering. The third one is related to thermionic effects in heterostructures [32, 33]. The comprehensive consideration of ZT, power density, and speed realized in the low-dimensional TE materials shows great

57

3 Nonoxide Materials

Melt spun Te excess Bi0.5Sb1.5Te3 (Te-MS)

S-MS Liquid (L) Te

620 °C Te-MS Bi0.5Sb1.5Te3

Temperature (°C)

58

450 °C ~420 °C 92.6 Eutectic

Bi0.5Sb1.5Te3 + Te compostion

(a)

60

Atomic % Te

Bi0.5Sb1.5Te3 Grain

Liquidified Te

100

0.5 μm

(b) Dislocation arrays

Expelled liquid Te

(c)

Figure 3.4 Generation of dislocation arrays at grain boundaries in Bi0.5 Sb1.5 Te3 . (a) Phase diagram of Bi0.5 Sb1.5 Te3 –Te system showing a eutectic composition at 92.6 at% Te. Blue and red arrows indicate the nominal composition of melt-spun stoichiometric Bi0.5 Sb1.5 Te3 (S-MS) and 25 wt% Te excess Bi0.5 Sb1.5 Te3 (Te-MS) material, respectively. (b) The scanning electron microscope (SEM) image of melt-spun ribbon of Te-MS material showing the Bi0.5 Sb1.5 Te3 platelets surrounded by the eutectic phase of Bi0.5 Sb1.5 Te3 –Te mixture, in which the Bi0.5 Sb1.5 Te3 particles (white spots) are of 10–20 nm. (c) Schematic illustration showing the generation of dislocation arrays during the liquid-phase compaction process. The Te liquid (red) between the Bi0.5 Sb1.5 Te3 grains flows out during the compacting process and facilitates the formation of dislocation arrays embedded in low-energy grain boundaries. Source: Reproduced with permission of Kim et al. [34]. Copyright 2015, the American Association for the Advancement of Science.

potential for wider technological applications, for instance, fiber-optic switches, thermochemistry-on-a-chip, DNA microarrays, and microelectrothermal systems [20]. Recently, a great number of periodic dislocations at grain boundaries of Bi0.5 Sb1.5 Te3 has been generated via a facile liquid-phase densification process (Figure 3.4a) [34]. The excess Te contributes to a eutectic microstructure between the Bi0.5 Sb1.5 Te3 platelets (Figure 3.4b). The SPS process was conducted at 480 ∘ C, which is higher than the melting point of Te (450 ∘ C). The Te in the eutectic phase became a liquid phase and flowed out from the graphite die (Figure 3.4c). The semicoherent grain boundaries formed by this sintering process would not cause strong electron scattering. Moreover, low-energy grain boundaries produce dense periodic dislocations and then add a new phonon scattering mechanism with both 𝜏 −1 ∼ 𝜔 and 𝜏 −1 ∼ 𝜔3 dependence, aiming at mid-frequency phonons (Figure 3.5a). Therefore, a much lower k l than solid-phase Bi0.5 Sb1.5 Te3 (ball milling and stoichiometric melt-spun) has been achieved (Figure 3.5b). This strategy successfully intensified full-spectrum phonon scattering and subsequently greatly enhanced the ZT to 1.86 at 320 K (Figure 3.5c).

3.2 Skutterudite-Based Materials

0.24

Umklapp (U)

0.16

BM S-MS Te-MS

1.6

Dislocation (DC+DS)

0.12

Ref. [7]

0.08 fa 0.3

(a) 1.2 0.9

BM S-MS

0.6 0.9 1.2 1.5 Frequency (THz)

1.2

1.8

0.8

Experiment model Experiment model

2.0 1.6

0.4

1.2

ZT

0.00 0.0

κlat(W m–1K–1)

Ingot

U U+B+PD U+B+PD+DC+DS

0.04

0.8

0.6

0.4

Te-MS

0.0

0.3

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350

400

T (K)

lo

s

0.0

Experiment model

ca

ti o

450

n arr a y

30 Te-MS samples

0.0 300 350

Di

Te-MS

(b)

2.0

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0.20

ZT

κs(f) (pW S m–1K–1)

0.28

300

400 450

T (K)

350

500

400

450

500

T (K)

500

(c)

Figure 3.5 Full-spectrum phonon scattering in high-performance bulk thermoelectrics. (a) The inclusion of dislocation scattering (DC + DS) is effective across the full frequency spectrum. Boundary (B) and point defect (PD) are effective only at low and high frequencies. The acoustic mode Debye frequency is f a . (b) Lattice thermal conductivity (klat ) for Bi0.5 Sb1.5 Te3 alloys produced by melt-solidification (ingot), solid-phase compaction (BM and S-MS), and liquid-phase compaction (Te-MS). The lowest klat of Te-MS can be explained by the mid-frequency phonon scattering due to dislocation arrays embedded in grain boundaries. (c) The figure of merit (ZT) as a function of temperature for Bi0.5 Sb1.5 Te3 alloys. The data points (red) give the average (TSD) of all 30 Te-MS samples, which shows excellent reproducibility. Source: Reproduced with permission of Kim et al. [34]. Copyright 2015, the American Association for the Advancement of Science.

3.2 Skutterudite-Based Materials Skutterudites get their name from a naturally occurring mineral, CoAs3 , which was first found in Skotterud, Norway. MX3 represents the general formula of skutterudites, here M stands for transition metals of group 9 such as Co, Rh, or Ir, and X denotes a pnictogen atom including P, As, and Sb. Skutterudites possess a cubic structure, belonging to the space group Im− 3 (see Figure 3.6). The corner-sharing octahedra together form a void (called Sb-icosahedron voids) at the body-centered position. Therefore, there are two voids at the corner (000) and the body center (1/2 1/2 1/2) in every cell. The coordination numbers are relatively low in the covalent structures of the skutterudites, which makes it possible to incorporate atoms into the voids [36]. Unfilled skutterudites have been investigated since the mid-1950s. Among skutterudites, CoSb3 was identified as a promising thermoelectric in the 500–900 K temperature range in the early 1990s and has attracted the greatest attention until now [37, 38]. CoSb3 exhibits fine transport properties, including small bandgap (0.2 eV), high carrier mobility [39, 40], and earth abundance as

59

60

3 Nonoxide Materials

c

a

b

Co Sb

(a)

(b)

Figure 3.6 Two model structures of the skutterudite, CoSb3 ; the void cages are filled with blue spheres for clarity. (a) The unit cell of skutterudite structure. The transition metals (Co) are at the center of the octahedra formed by pnictogen atoms (Sb). (b) The model shifted by the fractional coordinates 1/4, 1/4, 1/4 from the unit cell. The Co atoms are connected for clarity. The only chemical bonds in this model are those of the Sb squares. Source: Reproduced with permission of Sootsman et al. [35]. Copyright 2009, John Wiley & Sons.

well as low toxicity of the constituent elements Co and Sb compared to other skutterudites such as CoAs3 , all of which are highly desirable for excellent thermoelectric performance. Since the unit cell is quite complex and contains heavy atoms (average atomic mass M = 106), k of these compounds is intrinsically decreased to some extent [41, 42]. Unfortunately, it is still much greater than that of other high-performance TE materials, for example, Bi2 Te3 . La-filled [43] and Ba-filled [44] skutterudites were obtained in 1977 and 1991, respectively, but it was not until 1994 when Slack [45] introduced the concept of phonon-glass electron crystal (PGEC) of thermoelectric materials to improve the ZT as much as possible, the filled skutterudites became popular. For heat conduction, a material behaves like a glass, while for electron conduction, it functions as a crystal. CeFe4 Sb12 is a good example of the PGEC concept [46]. For filled skutterudites, a semiconductor-like behavior can contribute to both large S and high electrical conductivity. Apart from this, rattling of the filler atoms can effectively scatter phonons and largely suppresses k l . Hence, the filled skutterudites are called PGEC [47–49]. The formula RM4 X12 of the filled skutterudites was acknowledged in the late 1990s, where R is foreign filling rare-earth atoms (La, Ce, Yb, Eu, Nd, and Sm) [42, 50–54], alkaline-earth elements (Ba, Sr, and Ca) [49, 55–57], and others (Y, Sn, Tl, Ge, In, and K) [37, 58–63]. Both p- and n-type single-filled skutterudites have achieved high TE performance [42, 49, 55, 56]. Chen et al. [49] investigated n-type Ba-filled skutterudites Bay Co4 Sb12 with y up to 0.44. Figure 3.7 illustrates thermal conductivity as a function of measuring temperature. The room-temperature k l varying with the Ba content is shown in Figure 3.8. The k l of Ba-filled skutterudites Bay Co4 Sb12 can be significantly suppressed compared with unfilled Co4 Sb12 , and it continuously decreases with the increasing Ba content. The maximum ZT of 1.1 at 850 K is obtained in the

3.2 Skutterudite-Based Materials

18

Thermal conductivity, κ (W m–1 K–1)

Figure 3.7 Temperature dependence of thermal conductivity of Bay Co4 Sb12 . Source: Reproduced with permission of Chen et al. [49]. Copyright 2001, American Institute of Physics.

Ba0.04* Ba0.22* Ba0.3* Ba0.07 Ba0.16 Ba0.24 Ba0.38 Ba0.44 Co4Sb12

12

6

0 0

300

600

900

Temperature, T (K)

10.0 8.0 κL (W m–1 K–1)

Figure 3.8 Relationship between lattice thermal conductivity and Ba content for Bay Co4 Sb12 . Source: Reproduced with permission of Chen et al. [49]. Copyright 2001, American Institute of Physics.

6.0 4.0 2.0 0.0 0

0.1

0.2

0.3

0.4

0.5

0.6

Ba content (y)

Ba0.24 Co4 Sb12 . One should also note that the introduction of fillers also effectively tunes the electronic transport properties including carrier concentration, carrier mobility, and carrier effective mass. In this work, the filler Ba atoms effectively increase the electrical conductivity because Ba serves as electron donor in the semiconductor. Studies have demonstrated that the thermoelectric performance of double-filled skutterudite compounds such as CeLa [64], CaCe [65], BaYb [66, 67], and InYb [68] is higher than that of single-filled ones. The double-atom fillers can further reduce the k l of skutterudites. According to Shi et al. [69], the Ba and Yb fillers altogether enable a wide range of frequency phonon scattering, and thus a strongly suppressed k l is realized as shown in Figure 3.9. As different fillers have different resonant frequencies, multiple-filled skutterudites could even achieve a further reduction in k l , as Yang et al. [66] reported in 2008. In 2011, Shi et al. [69] synthesized CoSb3 cofilled by multiple foreign fillers Ba,

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3 Nonoxide Materials

x = 0.03, y = 0 x = 0.15, y = 0.01 x = 0.11, y = 0.03 x = 0.00, y = 0.12 x = 0.05, y = 0.09 x = 0.08, y = 0.09 x = 0.11, y = 0.08

κ (W m−1 K−1)

8 6 4 2 200

300

400

500

600

700

800

900

T (K) 6 κL (W m−1 K−1)

5 4 3 2 1 0 0.00

0.05

0.10

0.15

0.20

Figure 3.9 Temperature dependence of the thermal conductivity (c), and room-temperature lattice thermal conductivity as a function of total filling fraction (x + y) for Bax Yby Co4 Sb12 skutterudites (d). The lattice thermal conductivities of Ba0.23 Co4 Sb12 .10 (×), Ba0.07 La0.04 Co4 Sb12.08 ( ), Ba0.12 Ce0.06 Co4 Sb12.08 ( ), and Ba0.17 Sr0.08 Co4 Sb12 (⋄) from Ref. [65] are also shown. The solid line emphasizes the monotonic decrease in 𝜅 lL with increasing filling fraction (x + y). Source: Reproduced with permission of Shi et al. [67]. Copyright 2008, American Institute of Physics.

0.25

x+y 2.0

α2/ρ

Multiple-filled

1.6

ZT

Double-filled

1.2

Single-filled

ZT

62

0.8 Bi2Te3

Single- to double-, and multiple-filled

κL

PbTe

SiGe

0.4 0.0 0.0

0.1

0.2

0.3

Total filling fraction

0.4

0.5

0

200

400

600

800

1000 1200

T (K)

Figure 3.10 Performance optimization from single-filled to double-filled and multiple-filled skutterudites. Source: Reproduced with permission of Shi et al. [69]. Copyright 2011, American Chemical Society.

La, and Yb, leading to a high ZT value of 1.7 at 850 K. The optimum carrier density of the filled skutterudite system can be attained by tuning the filling fraction of fillers and thus realizing high power factors. Furthermore, k l can also be largely decreased to the amorphous limit, by integrating various fillers to cover a broader frequency of phonon scattering. Hopefully, the strategy of adding multiple fillers for improving ZT in Figure 3.10 could be applicable for other caged TE compounds.

3.3 Si–Ge Alloys Both silicon and germanium have large power factors due to their high carrier mobility. By reducing high lattice thermal conductivities, ultra-high ZT values

3.3 Si–Ge Alloys

can be achieved [70]. It has been proven to be a robust thermoelectric (SiGe alloy) material used for power generation at 600 ∘ C < T < 1000 ∘ C for radio-isotope thermoelectric generators (RTGs) to convert radioisotope heat into electricity for deep space missions [71, 72]. The bandgaps for Si and Ge are 1.15 and 0.65 eV, respectively, so excitation of minority carriers can be avoided in silicon-rich alloys when heavily doped [70]. From the 1960s, so many studies have been reported to enhance the thermoelectric performance of SiGe alloys [73–76]; the maximum ZT of n-type SiGe (phosphorous-doped) readily surpassed unity at around 900 ∘ C but the performance of p-type SiGe remained far below expectation for long, and the best p-type SiGe (boron-doped) alloy was reported to merely have a peak ZT of about 0.65 in 1990 [76, 77]. Practically, SiGe TE power generators with a ZT of 0.5 (p-type module) and 0.9 (n-type module) have been used by NASA since 1976 [72]. However, energy conversion at elevated temperatures demands higher thermoelectric performance to improve the energy conversion efficiency. In recent years, many studies have made continuous breakthroughs in ZT via nanostructuring approach in many kinds of material systems, including tellurides, silicides, skutterudites, and so on [31, 78, 79]. The common practice is nanostructuring the powders by high-energy ball milling followed by HP or SPS for rapid consolidation and densification while keeping the fine grain size. Consequently, nanostructured Si80 Ge20 alloys possess a k l lower than that in bulk crystalline materials, with their electrical transport properties remaining stable since phonons are scattered more easily than electrons at boundaries and interfaces [80, 81]. Therefore, the ZT of p-type Si80 Ge20 alloys is improved from 0.5 [77] to 0.95 [81], while for the corresponding n-type alloys, the ZT is increased from 0.93 [82] to 1.3 [80]. The medium-magnification TEM image (Figure 3.11) shows that the nanostructured powder is composed of fine particles with diameters of ∼20–200 nm. However, the individual particles are themselves multicrystalline, which is confirmed by the selected-area electron-diffraction (SAED) rings (inset) for a single particle [81]. The k of the nanostructured samples is much decreased compared with that of the sample used in RTG (Figure 3.12), and the corresponding PF is superior to the RTG sample at high temperatures, both of which result in a maximum ZT of ∼0.95 in nanostructured Figure 3.11 TEM image with medium magnifications of the ball-milled Si80 Ge20 nanopowders. The inset is the selected electron diffraction rings to show the multicrystalline nature of an individual particle. Source: Reproduced with permission of Joshi et al. [81]. Copyright 2008, American Chemical Society.

100 μm

50 nm

63

3 Nonoxide Materials

Thermal conductivity (W m−1 K−1)

64

Figure 3.12 Temperature dependence of thermal conductivity of hot-pressed nanostructured dense bulk Si80 Ge20 alloy samples (solid circles, open circles, triangles, and squares) and the 7-day annealed (at 1100 ∘ C) sample in comparison to the p-type SiGe bulk alloy used in RTGs for space power missions. Source: Reproduced with permission of Joshi et al. [81]. Copyright 2008, American Chemical Society.

6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

200

400

600

800

1000

Temperature (°C)

Si80 Ge20 bulks [81]. Therefore, decoupling of electrical and thermal properties and a synergistic optimization of thermoelectric performance have been realized in SiGe alloys via nanostructuring strategy. In 2012, Bathula et al. [83] achieved a significant improvement in ZT of n-type Si80 Ge20 to about 1.5 at 900∘ C. The samples were prepared by mechanical alloying followed by rapid densification using SPS. Similarly, the low k (2.3 W mK−1 ) has been speculated to derive from nanostructures, introduced by ball milling. And the rapid SPS process helps retain the nanostructures. Without long-time heating and pressing, the very short sintering time hinders mass transport and subsequently the grain growth [84]. The combination of high temperature and high pressure results in good densification, and the density of bulk samples is close to their theoretical one [84]. Previously, much work had also been conducted to study the kinetics of synthesis of SiGe alloy via ball milling [85–87]. The formation of SiGe by ball milling depends on the diffusion of Ge into the Si, and this diffusion process can be facilitated by the defects and strains produced by high-energy ball milling. The thermoelectric properties of the resultant SiGe alloys are also tuned by these defects. Based on this finding, Basu et al. [88] investigated the effect of ball milling time on the thermoelectric properties, and a further improvement in the ZT of ball-milled n-type SiGe alloys followed by HP was achieved. As Figure 3.13 illustrates, the highest value of ZT ∼ 1.84 at 1073 K for n-type SiGe was attained for the sample fabricated via ball milling of 72 hours, which is a 34% enhancement to the previously reported record value. This mainly results from the extremely low and almost temperature-independent k (∼0.93 W m−1 K−1 ), which outweighs the slight degradation of the power factor. The effective suppression of phonon transport is attributed to full-spectrum phonon scattering by hierarchical structures including atomic size defects, dislocations, and grain boundaries (Figure 3.14), which is closely associated with the control of the parameters of ball milling process. Hence, long-time ball milling has successfully demonstrated the concept of all-scale phonon scattering in SiGe alloys. Modulation-doping is another effective approach to enhance the ZT value of SiGe alloys. Yu et al. [89] used Si70 Ge30 as the nanoparticles and Si95 Ge5 as the

3.3 Si–Ge Alloys

2.0

1.5 ZT

Figure 3.13 Temperature dependence of thermoelectric properties of the hot-pressed SiGe alloys with different milling time. Source: Reproduced with permission of Basu et al. [88]. Copyright 2014, The Royal Society of Chemistry.

SiGe-24 SiGe-48 SiGe-72 SiGe-96 Ref. [80] Ref. [83] Ref. [80]

1.0

0.5

0.0 200

400

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T (K)

Figure 3.14 TEM images of 72-hour ball-milled n-type SiGe alloy samples. The regions within the dotted white lines show the nanoscale features within the bulk material. The arrows marked show the presence of a dislocation. Source: Reproduced with permission of Basu et al. [88]. Copyright 2014, The Royal Society of Chemistry.

72 h

5 nm

matrix to improve the electrical transport properties, while maintaining k at a relatively low level. The modulation-doping witnessed a 54% increase in electrical conductivity of the modulation-doped (Si95 Ge5 )0.65 (Si70 Ge30 P3 )0.35 compared to the sample with the same overall chemical composition (Si86.25 Ge13.75 P1.05 ). On the one hand, the 50% increase in the carrier mobility was realized via spatially separating carriers from the heavily doped phase, and the transport of the carriers inside the lightly doped phase is the key to achieving high carrier mobility considering less lattice distortion inside. On the other hand, the introduced nanoparticles retained low thermal conductivity by phonon scattering at the grain boundaries. Meanwhile, the Seebeck coefficient remained unchanged. A maximum ZT value of ∼1.3 at 900 ∘ C was eventually achieved, which is close to that of the previously reported best n-type Si80 Ge20 P2 thermoelectric bulk materials. This study is highly important since a much smaller amount of Ge was used, which is much rarer in the earth and much more expensive than Si.

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However, if Ge is totally discarded, the peak ZT of pure nano-Si would decrease to only 0.7 at ∼1000 ∘ C [90]. There is indeed a compromise between the cost and the performance of SiGe alloys.

3.4 Other Alloy Materials As mentioned earlier in this chapter, nanostructuring is an effective strategy to enhance the ZT values of Bi2 Te3 [17, 18] and SiGe [80, 81] alloys. Nanostructures in bulk thermoelectrics introduce effective wide-spectrum phonon scattering, but phonons with relatively long mean free paths remain more or less undisturbed. Qiu et al. [91] detailed the contribution of phonons with different mean free paths (MFPs) to the cumulative k l for PbTe in a theoretical way, which is shown in Figure 3.15. According to their simulation, ∼80% contribution to the k l value of PbTe is from phonons with MFPs less than 100 nm, which can be attributed to scattering by a combination of atomic-scale defects and nanoscale precipitates embedded in the PbTe matrix [91]. The remaining ∼20% of k l in PbTe is contributed by phonons with MFPs of 0.1–1 mm. Based on this result, Biswas et al. [92] adopted a panoscopic approach in the preparation of p-type PbTe, whose nanostructure is in situ SrTe precipitates. Mesostructure is simultaneously obtained by high-energy ball milling and SPS. This hierarchical architecture covers all relevant length scales by integrating the effects of mesoscale grain boundaries, endotaxial nanostructuring, and atomic-scale elemental doping in the same bulk material. The mesoscale grain structure is comparable in size to the phonon mean free path and thus scattering a great number of phonons with a comparable length scale. This results in further reduction of k l (Figure 3.16), compared with nanostructuring alone and therefore a great improvement of ZT value (Figure 3.17). An ultra-high ZT value of ∼2.2 was achieved at 915 K for the sample composed of hierarchical architecture. This significant enhancement in ZT greater than 2 emphasizes the significance of, also the need for, multiscale structures in intensifying phonon scattering as well as optimizing thermoelectric performance in bulk materials. 100

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Figure 3.15 Contributions of phonons with different mean free paths to the cumulative 𝜅 L value for PbTe. Source: Reproduced with permission from Qiu et al. [91]. Copyright 2012, Macmillan Magazines Limited.

3.4 Other Alloy Materials

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Figure 3.16 Temperature-dependent lattice thermal conductivity of SPS and ingot samples of PbTe–SrTe doped with 2 mol% Na. Inset is the comparison of 𝜅 L in SPS and ingot samples with the same composition (PbTe–SrTe [4 mol%] doped with 2 mol% Na). Source: Reproduced with permission of Biswas et al. [92]. Copyright 2012, Macmillan Publishers Limited.

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Figure 3.17 ZT as a function of temperature for an ingot of PbTe doped with 2 mol% Na (atomic scale), PbTe–SrTe (2 mol%) doped with 1 mol% Na (atomic plus nanoscale), and spark-plasma-sintered PbTe–SrTe (4 mol%) doped with 2% Na (atomic plus nano plus mesoscale). The measurement uncertainty of all experimental ZT versus T data was 10% (error bars). Inset: comparison of ZT in SPS and ingot samples with the same composition (PbTe–SrTe (4 mol%) doped with 2 mol% Na. Source: Reproduced with permission of Biswas et al. [92]. Copyright 2012, Macmillan Publishers Limited.

However, at the other extreme, exceptionally low k l (0.23 W m−1 K−1 at 973 K) has also been witnessed in SnSe single crystals along the b-axis (Figure 3.18) of the orthorhombic phase [94], which results in a unprecedented ultra-high ZT of 2.6 ± 0.3 at 923 K (Figure 3.19). The layered structure of SnSe possesses anomalously high Gruneisen parameters, reflecting the highly anharmonic and anisotropic bonding. Different from nanostructures, the ultra-low k l in SnSe single crystals is intrinsic and ascribed to strong anharmonicity. However, there exists a phase change from Pnma to Cmcm [95, 96] in SnSe, and high

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Figure 3.18 Crystal structure along the b-axis: gray, Sn atoms; red, Se atoms. Source: Reproduced with permission of Zhao et al. [94]. Copyright 2014, Macmillan Publishers Limited.

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Figure 3.19 Temperature-dependent ZT values of SnSe single crystals along different axial directions. Source: Reproduced with permission of Zhao et al. [94]. Copyright 2014, Macmillan Publishers Limited.

thermoelectric performance is achieved beyond the temperature of phase change (750 K). In crystals, the grain size ranges from a few nanometers to several centimeters. Figure 3.20 illustrates the examples of a single crystal and a polycrystalline specimen. When the grain size is of a few nanometers, the material can be recognized as a nanocrystalline bulk. The variable grain sizes definitely have a profound influence on thermoelectric properties. Both excellent electrical

3.4 Other Alloy Materials

Usual polycrystal

[0001]

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Figure 3.20 Structural characteristics of a single crystal, a usual polycrystal, and a mosaic crystal. Arrows refer to alignment of crystal grains. Source: Reproduced with permission of He et al. [97]. Copyright 2015, John Wiley & Sons.

and thermal conduction can be realized in a single crystal. In contrast, the grain boundaries and interfaces in nanocrystalline materials could hinder the transport of electrons and phonons. Therefore, it is necessary to take advantage of both single crystals and nanocrystalline materials to achieve the synergistic optimization of thermoelectric performance. The ZTs above the threshold of 2 in bulk materials are reported for both, i.e., perfect single crystals of SnSe [94] and PbTe-based all-scale nanocomposites [92], which have already been illustrated in the previous part of this chapter. In addition to nanomaterials and single crystals, a “mosaic crystal” is another special case reported by Darwin [98], which is of high degree of perfection in the lattice translations throughout the crystal. However, it consists of many “mosaic blocks,” with each one being a single crystal but rotated by a minute of arc compared to others. The “mosaic crystal” contains many small angle boundaries at the micro level due to a nearly identical orientation among the blocks [98–100]. Similar to single crystals, highly coherent grain boundaries in the mosaic crystal would not impede electrical transport, but a slight misorientation of countless small grains is highly effective in scattering heat-carrying phonons and contributes to unexpected thermoelectric properties. He et al. [97] successfully prepared the mosaic structure in Cu2 (S,Te) system where micro-scale crystals are composed of mosaic grains of 10–20 nm in size (Figure 3.21). The corresponding fast Fourier transform (FFT) of the diffractogram (top-right corner) in Figure 3.21 illustrates a typical single-crystal-type characteristic although it contains four nanocrystallites of 15–20 nm. The diffractograms derived

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Figure 3.21 HRTEM image and its FFT diffractogram of the mosaic crystal Cu2 S0.5 Te0.5 . Source: Reproduced with permission of He et al. [97]. Copyright 2015, John Wiley & Sons.

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Figure 3.22 Enhanced temperature-dependent ZT values for Cu2 (S,Te) mosaic crystals. The measurement uncertainty of ZT is about 15%. Source: Reproduced with permission of He et al. [97]. Copyright 2015, John Wiley & Sons.

from these four nanograins are almost identical. Different relative reflection intensities imply a slight misorientation among these grains but merely about tens of milliradians. In these mosaic crystals, the frameworks of quasi-single crystals provide pathways for electrons to be freely transferred along, while phonons are intensely scattered by lattice mismatch and the resultant strains or boundaries of numerous mosaic nanograins. Compared to the polycrystalline samples Cu2 S and Cu2 Te here, the ZTs of the mosaic crystals are substantially increased (Figure 3.22), and a record-high ZT value of 2.1 is achieved in the Cu-based bulk thermoelectric materials. The newly found mosaic-based strategy has been proven to be effective in suppressing k and can be combined with other proven strategies such as energy filtering effect to further improve the thermoelectric performance.

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microstructure of Si76 Ge23.95 P0.05 alloys produced by mechanical alloying. Physica Status Solidi A 146 (1): 109–118. 86 Pixius, K., Wunderlich, W., Schilz, J. et al. (1995). A microscopic model for the mechanical alloying of silicon and germanium. Scripta Metallurgica et Materialia 33 (3): 407–413. 87 Schilz, J., Pixius, K., Wunderlich, W. et al. (1995). Existence of enhanced solid state diffusion during mechanical alloying of Si and Ge. Applied Physics Letters 66 (15): 1903–1905. 88 Basu, R., Bhattacharya, S., Bhatt, R. et al. (2014). Improved thermoelectric performance of hot pressed nanostructured n-type SiGe bulk alloys. Journal of Materials Chemistry A 2 (19): 6922–6930. 89 Yu, B., Zebarjadi, M., Wang, H. et al. (2012). Enhancement of thermoelectric properties by modulation-doping in silicon germanium alloy nanocomposites. Nano Letters 12 (4): 2077–2082. 90 Bux, S.K., Blair, R.G., Gogna, P.K. et al. (2009). Nanostructured bulk silicon as an effective thermoelectric material. Advanced Functional Materials 19 (15): 2445–2452. 91 Qiu, B., Bao, H., Zhang, G. et al. (2012). Molecular dynamics simulations of lattice thermal conductivity and spectral phonon mean free path of PbTe: bulk and nanostructures. Computational Materials Science 53 (1): 278–285. 92 Biswas, K., He, J., Blum, I.D. et al. (2012). High-performance bulk thermoelectrics with all-scale hierarchical architectures. Nature 489 (7416): 414–418. 93 Biswas, K., He, J., Zhang, Q., et al. (2011). Strained endotaxial nanostructures with high thermoelectric figure of merit. Nature Chemistry 3 (2): 160. 94 Zhao, L.D., Lo, S.H., Zhang, Y. et al. (2014). Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals. Nature 508 (7496): 373–377. 95 Peters, M.J. and Mcneil, L.E. (1990). High-pressure Mössbauer study of SnSe. Physical Review B 41 (9): 5893. 96 Baumgardner, W.J., Choi, J.J., Lim, Y.F. et al. (2010). SnSe nanocrystals: synthesis, structure, optical properties, and surface chemistry. Journal of the American Chemical Society 132 (28): 9519–9521. 97 He, Y., Lu, P., Shi, X. et al. (2015). Ultrahigh thermoelectric performance in mosaic crystals. Advanced Materials 27 (24): 3639–3644. 98 Darwin, C.G. (1922). XCII. The reflexion of X-rays from imperfect crystals. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 43 (257): 800–829. 99 Geis, M.W., Smith, H.I., Argoitia, A. et al. (1991). Large-area mosaic diamond films approaching single-crystal quality. Applied Physics Letters 58 (22): 2485–2487. 100 Oguz Er, A., Chen, J., Tang, J. et al. (2012). Coherent acoustic wave oscillations and melting on Ag (111) surface by time resolved X-ray diffraction. Applied Physics Letters 100 (15): 15191.

77

4 Binary Oxides 4.1 Introduction for ZnO Metal oxides are a strong candidate for thermoelectric materials because they possess unique physical characteristics of a wide and direct bandgap. The direct bandgap of ZnO is 3.37 eV at room temperature, which makes it a representative. ZnO it has wide applications, such as optoelectronics [1, 2], sensors [2–4], pharmaceuticals. Additionally, ZnO is used as photocatalyst [5–7] in different catalytic reactions. As a candidate thermoelectric applications [8–10], n-type zinc oxide (ZnO) has received attention for its high-temperature stability, moderate electrical conductivity, and moderate Seebeck coefficient by Al doping [11]. In addition, ZnO is less costly and nontoxic compared with tellurium.

4.2 Property of ZnO 4.2.1

Structure

ZnO crystallizes in three main phases – hexagonal wurtzite (B4), cubic zinc blende (B3), and rocksalt (or Rochelle salt) (B1) (Figure 4.1). The wurtzite structure is most stable at ambient conditions and thus is the most common form. The zinc blende form can be stabilized by growing ZnO on substrates with cubic lattice structure. The rocksalt or Rochelle salt (NaCl) structure may be obtained at relatively high pressures of ∼10 GPa. 4.2.2

Lattice Parameters

For the wurtzite ZnO, the range of lattice constants is from 3.2475 to 3.2501 Å for the parameter a and from 5.2042 to 5.2075 Å for the parameter c [13]. Its lattice constant at room temperature determined by various experimental measurements is in good agreement with the theoretical calculations. 4.2.3

Electronic Band Structure

The electronic structure of the ZnO(0001) surface has been researched by angleresolved photoelectron spectroscopy. Both normal and off-normal-emission Oxide Thermoelectric Materials: From Basic Principles to Applications, First Edition. Yuan-Hua Lin, Jinle Lan, and Cewen Nan. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

4 Binary Oxides

(a)

(b)

(c)

Figure 4.1 Stick and ball representation of ZnO crystal structures. (a) Cubic rocksalt B1, (b) cubic zinc blende B3, and (c) hexagonal wurtzite B4. The shaded gray and black spheres denote Zn and O atoms, respectively. Source: Özgür et al. 2005 [12]. Reproduced with permission of AIP.

F C A hν F″ F′ 32 eV D

E

hν

2

30 eV E

F″ G

F′

Γ6

B F″F′G

28 eV

D

EF = 0

50 eV

26 eV

G

F″ D 24 eV

F″

C A 22 eV

48 eV C

46 eV

D

44 eV

G F″ D

42 eV

A 4

Binding energy (eV)

E

Intensity (a. u.)

78

C 6

12 (a)

8

E

D C 36 eV B F′ 34 eV F″

12 8 4 0 Binding energy (eV)

4

D F′ F″

Γ3

38 eV

F″

A1,3

G

8

40 eV

20 eV

A5,6

B

E

10

0 = EF

12 (b)

Γ

k⊥

A

Figure 4.2 (a) Normal-emission spectra for photon energies ranging from 20 to 50 eV. The spectra were normalized with respect to the photon flux. (b) The bulk-band structure of ZnO, A corresponding to 0.6 Å−1 . The dashed lines are the LDA calculation results. Source: Schröer et al. 1993 [15]. Reproduced with permission of APS.

spectra give valuable information about bulk and surface states as well as Zn 3d states [14]. In some measurements, we can extract some information for bulk-band structure, then make the binding energies referring to the Fermi level and make the intensities normalized to the photon flux, as shown in Figure 4.2.

4.2 Property of ZnO

4.2.4

Mechanical Properties

Mechanical properties are important parameters for evaluating the practicability of materials, such as hardness, stiffness, piezoelectric constants, Young’s and bulk moduli, yield strength. Decremps et al. [16, 17] have studied the pressure behavior of elastic moduli for the wurtzite phase of single-crystal ZnO. Figure 4.3 shows the elastic moduli at ambient temperatures using ultrasonic wave velocity measurements up to 10 GPa. All the moduli exhibit a linear dependence on pressure up to the phase-transition pressure, with positive values for the room-temperature longitudinal moduli (dC11/dP = 5.32 and dC33/dP = 3.78) and negative values for the shear moduli (dC44/dP = −0.35 and dC66/dP = −0.30). 4.2.5

Thermal Expansion Coefficients

Thermal expansion coefficients are denoted as || and ⟂ parameters for in-plane and out-of-plane cases, respectively. They can quantify the lattice parameters of semiconductors that depend on temperature. Thermal expansion coefficients || and ⟂between 300 and 800 K are tabulated in Figure 4.4 [18]. The ⟂ of ZnO is larger than ||. 260 Elastic constants Cij (GPa)

Figure 4.3 Elastic moduli of ZnO versus pressure at ambient temperature. The slope of the C11 and C33 pressure dependences is positive (dC11/dP = 5.32 and dC33/dP = 3.78), whereas that for C44 and C66 is negative (dC44/dP = −20.35 and dC66/dP = −20.30). Decremps et al. 2001 [16]. Reproduced with permission of APS.

240 220

C11 C33 C44 C66

200 44 42 40 38 0

1

2

3

4

5

6

7

8

Pressure (GPa)

α (10–7K–1)

Figure 4.4 Coefficients of thermal expansion, || and ⟂.

90

α∕∕

75

α⊥

60 45 30 15 300

400

500 600 T (K)

700

800

9

79

Thermal conductivity (W m−1 K−1)

4 Binary Oxides

Figure 4.5 Thermal conductivity of fully sintered ZnO heated from room temperature to 1000 ∘ C. Source: Olorunyolemi et al. 2002 [20]. Reproduced with permission of John Wiley & Sons.

40

30

20

10

0

0

200

400

600

800

1000

Temperature (°C)

4.2.6

Thermal Conductivity

M.W. Wolf and Martin investigated the thermal conductivities of large single crystals of zinc oxide from 3.5 to 300 K [19], which suggested that anisotropy in thermal conductivity of ZnO single crystals is very small. As the temperature increased from room temperature to 1000 ∘ C, thermal conductivity of a fully sintered polycrystalline sample decreased from 37 to 4 W m−1 K−1 , as shown in Figure 4.5. Therefore, for the ZnO, the lattice thermal conductivity is the critical factor determining the thermal conductivity. 4.2.7

Specific Heat

Lawless and Gupta investigated the specific heat for both pure and varistor types of ZnO samples of an average 10 μm grain size between the temperature ranges of 1.7–25 K [21]. The Debye temperature θD by fitting the measured temperature-dependent heat capacity to the Debye theory of specific heat. For ZnO, the Debye temperature θD = 399.5 K is labeled in Figure 4.6.

105

Figure 4.6 Specific heat data measured for pure ZnO compared to data for varistor ZnO. Source: Lawless and Gupta 1986 [21]. Reproduced with permission of AIP.

ZnO

Varistor C (erg g–1 K–1)

80

104

Pure 10

3

θD = 399.5 K 102 2

5

10 T (K)

20

30

4.3 Doping for ZnO-Based Thermoelectric Materials

4.2.8

Electrical Properties of Undoped ZnO

According to Albrecht et al., the theoretical electron mobility of ZnO is about 300 cm2 V−1 s by Monte Carlo simulations at room temperature [22]. Nominally undoped ZnO with a wurtzite structure naturally becomes an n-type semiconductor due to the presence of intrinsic or extrinsic defects. There are major native defects such as the Zn-on-O antisite ZnO , the Zn interstitial ZnI , and the O vacancy V O [22–24]. However, recently first-principles investigations based on density functional theory suggest that hydrogen in ZnO occurs exclusively in the positive charge state and is responsible for the n-type conductivity of ZnO [25].

4.3 Doping for ZnO-Based Thermoelectric Materials Doping can improve the thermoelectric properties of materials to a large extent. For example, doping a small amount of Al2 O3 in ZnO can greatly improve the power factor of the material (up to 10–15 × 10−4 W m−1 K−2 ), which is mainly due to the significantly increase in conductivity after adding Al2 O3 , while retaining moderate thermoelectric power. A large number of carrier mobility and the density of states are conducive to enhance the electrical properties of ZnO. Thus, even with a high thermal conductivity, the value of ZT can reach 0.24 by ∼(Zn0.98 Al0.02 )O at 1000 ∘ C [26]. However, the properties of a material depend not only on the doped material itself but also on its preparation conditions. For example, Al-doped ZnO samples exhibited a large difference in electrical conductivity under different sintering atmospheres [27, 28]. Compared to the samples sintered under air, ball-milled-ZnO–2% Al samples showed an order of magnitude greater electrical conductivity when sintered under nitrogen atmosphere. Samples prepared using sol–gel-synthesized powders sintered under vacuum and nitrogen showed 107 times higher electrical conductivity than the samples sintered under air. The electrical conductivity of ZnO–2% Al sintered in vacuum at 1200 ∘ C was found to reach 1000 S cm−1 , which is typical for thermoelectric alloys. The reason for this increase is that low oxygen pressure promotes Al substitution in ZnO and impedes the formation of Zn2+ vacancies, leading to an increase in the amount of interstitial Zn and in turn electrical conductivity (Figure 4.7) [27]. Highly dispersed nanosized closed pores (nanovoids) are found to be effective to substantially enhance the thermoelectric performance due to the selective phonon scattering and possible carrier energy filtering, resulting in a dimensionless figure-of-merit of ZT = 0.65 at 1250 K for Al-doped ZnO [29]. The dopant of Bi was found to increase the Seebeck coefficient greatly; a highest absolute Seebeck coefficient value of 484 μ VK−1 was obtained for Zn0.9975 Bi0.0025 O at 800 ∘ C. The thermoelectric power factor for Zn0.9975 Bi0.0025 O at 800 ∘ C was 3.06 × 10−4 W m−1 K−2 , which was about six times higher than that of Bi2 O3 -free ZnO (0.54 × 10−4 W m−1 K−2 ) at 800 ∘ C [30]. The substituted Ti led to a marked increase in electrical conductivity. This is mainly due to an increase in the electron concentration of the system. The absolute value of the Seebeck coefficient decreased with increasing TiO2 content. The power factors of the TiO2 -doped Zn1−x Tix O samples were extremely high,

81

4 Binary Oxides

105

σ (S m–1)

82

NC (N2 + CO) N (N2) A (Air)

104

103

102 300

400

500

600 700 T (K)

800

900

1000

Figure 4.7 Electrical conductivity as a function of measurement temperature for ZnO-based TE material sintered under different atmospheres. Source: Tian et al. 2016 [27]. Reproduced with permission of Elsevier.

compared to that of the Ti-free ZnO sample. Zn0.98 Ti0.02 O showed the highest value of power factor (7.6 × 10−4 W m−1 K−2 ) at 1073 K [31]. The Sb2 O3 -added Zn1−x Sbx O (0.005 ≤ x ≤ 0.05) showed a large absolute value of the Seebeck coefficient at 1073 K in comparison to the Sb2 O3 -free ZnO. The magnitude of the power factor depended strongly on the Sb2 O3 content at 1073 K. The maximum value of the power factor was 3.88 × 10−4 W m−1 K−2 for the Zn0.99 Sb0.01 O at 1073 K [32]. Kiyoshi Fuda and Sugiyama [33] investigated the effects of doping of rare-earth ions (Ce, Pr, Nd, Sm, and Eu) on the thermoelectric properties of ZnO and on the microscopic texture. Firstly, the rare-earth ions were deposited on the grain boundary, so that, in the large ZnO grains, some small structural units with a size order of 100 nm were developed. As a result, such doped samples had higher Seebeck coefficient than those of Al-doped samples. The power factor at 100 ∘ C for Pr-doped ZnO was twice or more as much as that for Al-doped one. Commercially available ZnO nanoparticles doped with 0.3 at% Ga were successfully densified at low temperature without significant grain growth by applying 500 MPa of external pressure. The advantage of nanograins was evident from the marked reduction in thermal conductivity. For 30-nm-grain ZnO, thermal conductivity is 2–3 W m−1 K−1 from room temperature to 500 ∘ C [34]. Lihong Shi et al. [35] investigated the Ga-content-dependent thermoelectric properties in Zn1−x Gax O nanowires. They found that the thermoelectric performance was strongly dependent on the Ga content. The Ga doping can reduce the thermal conductivity of ZnO NW down to less than 90% at Ga content of 0.08.

4.3 Doping for ZnO-Based Thermoelectric Materials

40

ZnAl0.02Ga0.01O ZnAl0.02Ga0.02O ZnAl0.02Ga0.03O ZnAl0.02Ga0.04O ZnAl0.02Ga0.05O ZnAl0.03Ga0.01O ZnAl0.03Ga0.02O ZnAl0.03Ga0.03O ZnAl0.04Ga0.02O ZnAl0.02O

Thermal conductivity (W m–1 K–1)

35 30 25 20 15 10 5 0

0

100

200

300

400

500

600

700

800

Temperature (°C)

Figure 4.8 Temperature dependence of the thermal conductivity of Zn1−x−y Alx Gay O (0.02 ≤x ≤ 0.04, 0 ≤ y ≤ 0.05) ceramics. Source: Ohtaki et al. 2009 [36]. Reproduced with permission of Springer Nature.

The maximum attainable ZT corresponds to an optimal Ga content of x = 0.04, which is 2.5 times that of the pure ZnO wires. In addition to the doping of one material, there is double doping. Dual doping of ZnO with Al and Ga results in a drastic decrease in thermal conductivity of the oxide, while the decrease in electrical conductivity is relatively small [36]. The thermal conductivity, k, of the dually doped samples is shown in Figure 4.8 as a function of temperature. The k values at room temperature decreased drastically from 40 W m−1 K−1 for Zn0.98 Al0.02 O down to 13 W m−1 K−1 for Zn0.96 Al0.02 Ga0.02 O and further decreased with increasing Ga content. It is remarkable that Ga doping of only 2 mol% was enough to halve the k value at room temperature. The reduction in k for the Ga-doped samples was obvious even at 800 ∘ C, demonstrating the validity of the codoping with Ga for k reduction even at high temperatures. Scanning electron microscopy (SEM) observations revealed that some samples (at y = 0.02) have a heterogeneous granular texture in the cross-section of the

83

84

4 Binary Oxides

SEM SEI

15.0 kV

× 3,000

1 μm WD 15 mm

(a)

SEM SEI

15.0 kV

× 3,000

1 μm WD 15 mm

(b)

Figure 4.9 SEM images of fracture surfaces of Zn1−x−y Alx Gay O: ((a) x = 0.02, y = 0.02; (b) x = 0.02, y = 0.05) ceramics. Source: Ohtaki et al. 2009 [36]. Reproduced with permission of Springer Nature.

densely sintered sample matrix (Figure 4.9a). And some samples containing larger amounts of Ga (namely, y ≥ 0.04) are highly porous (Figure 4.9b), which may explain the strong suppression in k thanks to the microstructure. Finally, the largest ZT values they obtained were 0.47 at 1000 K and 0.65 at 1247 K for Zn0.96 Al0.02 Ga0.02 O. Similarly, the textured n-type Zn0.98−x Al0.02 Nix O (x = 0.01, 0.02, 0.03, 0.04) bulks were synthesized by a process combining hydrothermal synthesis (HS) and spark plasma sintering (SPS) technique. Texturing contributes to the slightly enhanced mobility, and codoping Ni2+ could enhance the solution of Al3+ , which leads to a dramatic increase in carrier concentration. Consequently the power factor was boosted up to 6.16 × 10−4 W m−1 K−2 at 673 K in Zn0.97 Al0.02 Ni0.01 O and the ZT value was increased to 0.057 at 773 K in Zn0.96 Al0.02 Ni0.02 O bulks [37].

4.4 ZnO Nanostructures The preparation method and doping can successfully prepare different microstructures of ZnO. L. Han et al. [38] successfully made the nanoparticles of Al-doped ZnO grown into rod-like and platelet-like morphologies by soft chemical routes. Then these powders were consolidated using SPS technique. (1) Rod samples: The Al-doped ZnO rods were measured to be 25 mm in length and 4 mm in width by SEM images (Figure 4.10). TEM and SAED (selected-area electron-diffraction) of the rods indicate that each “rod” is single crystalline in the wurtzite structure. (2) Platelet samples: L. Han et al. [38] synthesized hexagonally shaped platelets with an average diameter of 800 nm and thickness of 100 nm (see Figure 4.11a). A TEM image and SAED of a single platelet indicate the existence of a single crystal in the wurtzite structure (see Figure 4.11b,c). Figure 4.12a shows the SEM image of a bulk consolidated fracture surface of the nanoparticle sample consolidated from the Al-doped ZnO nanoparticles. The

4.4 ZnO Nanostructures

(a)

(b)

(c)

< 210 >

(120)

(002) 20 μm

2 μm

Figure 4.10 (a) SEM images of hydrothermally grown Al-doped ZnO rods. (b) TEM image of a single rod and (c) its electron diffraction pattern along the direction, indicating the wurtzite structure. Source: Han et al. 2014 [38]. Reproduced with permission of RSC.

(a)

(b)

(c)

< 001>

(110)

(010)

(100)

(100)

(010) 1 μm

(110)

100 nm

Figure 4.11 (a) SEM images of hydrothermally grown Al-doped ZnO platelets. (b) TEM image of a single platelet and (c) its electron diffraction pattern along the direction, indicating the wurtzite structure. Source: Han et al. 2014 [38]. Reproduced with permission of RSC.

(a)

(b)

(c)

(101) 63.9°

1 μm

5 nm

(010)

50 nm

Figure 4.12 (a) SEM image of a bulk consolidated fracture surface of the nanoparticle sample consolidated from nanoparticles. (b) HRTEM image of Al-doped ZnO nanoparticles and (c) TEM image of the nanoparticles. Source: Han et al. 2014 [38]. Reproduced with permission of RSC.

HRTEM image of the Al-doped ZnO nanoparticles reveals that each nanoparticle is a single crystal (Figure 4.12b). Its average particle size is estimated to be 8 nm by using XRD Rietveld refinement, which is consistent with the TEM observation (sere Figure 4.12c). The structure of the sample causes anisotropy differences in thermoelectric properties in different directions. First, electrical conductivity of the consolidated samples including the rods and platelets decreased with increasing temperature, as shown in Figure 4.13, which exhibited a metallic conduction behavior when

85

4 Binary Oxides

Electrical conductivity (σ) (S m–1)

86

105

Ea ∼ 45.6 meV 104

103

0.5

Rod (⊥p) Rod (║p) Platelet (⊥p) Platelet (║p) Nanoparticle 1.0

1.5

2.0

2.5

3.0

3.5

1000/T (K–1)

Figure 4.13 Temperature dependence of the electrical conductivity of the samples, a clear anisotropy of the rod and platelet samples observed. Source: Han et al. 2014 [38]. Reproduced with permission of RSC.

the nanoparticles were opposite and smaller. The result was attributed to the preferred orientation of the rod and platelet samples. The temperature dependence of the Seebeck coefficients (S) of the samples showed that the absolute values of S increased with increasing temperature (−20 to −120 μV K−1 ). The S values for the rod and platelet samples showed negligible anisotropy and a little smaller than the nanoparticles (−50 to −210 μV K−1 ). The k values measured along the pressure axis (||p) and perpendicular to the pressure axis (⟂p) showed that the values for (||p) direction are relatively smaller compared with the values for (⟂p) direction over the whole temperature range for both samples, as shown in Figure 4.14. The nanoparticle sample showed significantly small k values of 8.46 W m−1 K−1 at 373 K and 3.21 W m−1 K−1 at 1223 K, which are roughly 1/5 and 1/2 as large as those for the rod (⟂p) sample at 373 and 1223 K, respectively. The ZT values thus obtained are shown in Figure 4.15. Due to the preferential orientation of the rod and platelet samples, they showed different ZT values along the different measured directions. The (⟂p) direction of both samples showed higher ZT values than the (||p) direction, reaching 0.2–0.25 at 1223 K. The platelet sample showed higher ZT values than the rod sample along either measurement direction. The nanoparticle sample was benefited from low k of 3.2 W m−1 K−1 at 1223 K, and its electrical conductivity and Seebeck coefficient increased significantly with increasing temperature, attaining a power factor of 7.97 × 10−4 W m−1 K−2 at 1223 K. Thus, the sample showed a peak ZT of 0.3 at 1223 K. Ya Yang et al. [39] have demonstrated Sb-doped ZnO micro/nanobelt nanogenerator for thermoelectric energy conversion. The single Sb-doped ZnO microbelt shows a Seebeck coefficient of about 350 μV K−1 and a power factor of about 3.2 × 10−4 W m−1 K−2 .

Thermal conductivity (κ) (W m–1 K–1)

55 50 45 40

Rod (⊥p) Rod (║p) Platelet (⊥p) Platelet (║p) Nanoparticle

35 30

Lorenz number (10–8 W Ω K–2)

4.5 Introduction for In2 O3

2.6

Degenerate limit

2.4 2.2

Rod Platelet Nanoparticle

2.0 1.8 1.6 200

25

400

600 800 1000 1200 1400 Temperature (K)

20 15 10 κmin

5 0 400

600

800

1000

1200

Temperature (K)

Figure 4.14 Temperature dependence of the thermal conductivity of the samples. The inset shows the calculated Lorenz number of the samples as a function of temperature. The lower limit of the lattice thermal conductivity, 𝜅 min , for Zn0.98 Al0.02 O was calculated using Cahill’s equation (dashed line) [38]. 0.40 Rod (⊥p) Rod (║p) Platelet (⊥p) Platelet (║p) Nanoparticle

0.35 0.30

ZT

0.25 0.20 0.15 0.10 0.05 0.00 400

600

800

1000

1200

Measurement temperature (K)

Figure 4.15 Temperature dependence of figure of merit, ZT, of the samples. Source: Han et al. 2014 [38]. Reproduced with permission of RSC.

4.5 Introduction for In2 O3 In2 O3 is a semiconducting oxide, which has been known as a transparent conducting oxide or transparent semiconducting oxide (TCO or TSO) for several decades. The Sn-doped In2 O3 (ITO) is favored as TCO due to the highest available transmissivity for visible light and the lowest electrical resistivity.

87

88

4 Binary Oxides

More recently, it has been reported that In2 O3 can become a new promising thermoelectric materials – if choose proper dopant [40]. n-Type-In2 O3 is of particular interest for use in thermoelectrics due to the following reasons [41]: (1) Tin-doped In2 O3 (ITO) can realize the maximum electron concentration and maximum conductivity among conducting metal oxides. (2) The lattice thermal conductivity in In2 O3 is much lower than in SnO2 and ZnO because the lattice structure of indium oxide in the unit cell is more complicated and the metal atom is heavier. (3) In2 O3 shows excellent thermal stability and can operate at temperatures up to 1400 ∘ C in the oxygen-containing atmospheres.

4.6 Property of In2 O3 4.6.1

Structure

The crystal structure of In2 O3 is in two phases, the cubic (bixbyite type) and rhombohedral (corundum type). The bixbyite (cubic, space group symmetry: Ia3, lattice constant: 1.0117 nm, JCPDS: 6-0416), as shown in Figure 4.16 is the stable phase. Each unit cell contains 16 formula units of In2 O3 and 90 atoms; indium atoms occupy Wyckoff positions of 8b and 24d, while oxygen atoms occupy Wyckoff positions of 48e. The indium atoms in b-sites are coordinated by six oxygen atoms at an equal distance of around 2.17 Å, while the d-sites are located in the center of distorted octahedra formed by oxygen atoms. The

O

In : 24d In8b

In8b In : 8b

In8b

In8b

b a

c

Figure 4.16 Crystal structure of cubic In2 O3 and the two nonequivalent indium sites. Source: Liu et al. 2015 [42]. Reproduced with permission of Royal Society of Chemistry.

4.6 Property of In2 O3

rhombohedral phase is formed at high temperatures and pressures or when using nonequilibrium growth methods [43]. It has a space group R3c, a = 0.5487 nm, and c = 0.57818 nm. 4.6.2

Electronic Band Structure

The direct bandgap of In2 O3 was found to be 3.75 eV from the onset of significant optical absorption. Moreover, the weaker absorption onset at 2.62 eV in experiment was attributed to indirect electronic transitions [44]. The details of the band structure and optical transitions were clarified in 2008 by a combination of first-principles calculations and X-ray spectroscopy [45]. The bandgap of single-crystalline In2 O3 is recently determined to be 2.93 ± 0.15 and 3.02 ± 0.15 eV for the cubic bixbyite and rhombohedral polymorphs, respectively [43]. Density functional theory (DFT) [46–48] calculation was performed in VASP code [49] to calculate the band structure of In2 O3 . The projector-augmented wave [50, 51] technique was used and the exchange-correlation energy was in the form of Perdew–Burke–Ernzerhof (Figure 4.17) [52]. 4.6.3

Thermal Properties and Electrical Properties

Specific heat of In2 O3 was measured from 5 to 350 K by E.H.P. Cordfunke and Westrum [53] (Figure 4.18). The Debye temperature θD can be obtained by measuring the heat capacity associated with temperature and combining the Debye expression. The Debye temperature θD = 420 ± 205 K for In2 O3 [54].

Figure 4.17 The energy band structure of In2 O3 .

6

Energy (eV)

4 2 0

–2 –4 –6

Γ

P

N

Γ

H

P H

N

89

4 Binary Oxides

120

Cp (J mol–1 K–1)

100 80 12

60

9

40

6 3

20

0

0

0

50

100

0

150

10

200

20

30

250

40

350

300

T (K)

Figure 4.18 The molar heat capacity of In2 O3 . Source: Kresse and Hafner 1993 [46]. Reproduced with permission of APS.

4.7 Doping for In2 O3 -Based Thermoelectric Materials The influence of doping elements (Ge4+ , Ce4+ , Zn2+ , Co3+ , Ti4+ , Zr4+ , Sn4+ , Ta5+ , and Nb5+ ) on the transport properties of In2 O3 has been carefully studied. Some of the most significant results of these studies are summarized in Figure 4.19 [40, 42, 55–62]. D. Bérardan et al. proposed that Ge doping could greatly improve the thermoelectric properties of In2 O3 greatly. The Rietveld refinement of a sample with

k (W m–1 K–1)

20

ZTmax (1000 K) 15

]

6,

5 .[

ef R ] 5 5

10 5

.[

] 40

ef R

ef R

.[

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2]

57

. ef

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.[

R

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1.0

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8

]

9]

5 .[

12

]

61

.[

ef

2]

. ef

R

[6

6

R

0.6 0.4 0.2

4 0

0.0 2

–5 –10

0 ) ) ) ) ) ) ) ) O3 In 2 e (8% (4–8% (10% n 2O 16 –10% (2–6% 2–6% ) (4% o (2% ( n i :C Ce) :Ga In 5+xS :Ge (1 O 3:T Sn Nb, Z O 3:C : 3 O , 3 O n 3 O ( In 2 In 2 :(Z In 2 In 2 a 3-x In 2O 3 In 2 n O 3: O3 G I 2 In 2

Metal oxide

Figure 4.19 Some of the most significant doping for In2 O3 .

–0.2 –0.4

ZTmax (1000 K)

PFmax (μW cm–1 K–2)

κ (W m–1 K–1)

25

PFmax (μW cm–1 K–2)

90

4.7 Doping for In2 O3 -Based Thermoelectric Materials

In2Ge2O7 fraction

0.20

I (a.u.)

In2O3

20

0.10 0.05 0.00 0.0

In2Ge2O7

10

0.15

30

40

50

0.1 0.2 Nominal Ge fraction

60

70

80

0.3

90

2θ

Figure 4.20 XRD pattern and Rietveld refinement for a sample with nominal composition In1.9 Ge0.1 O3 . Inset: In2 Ge2 O7 fraction determined from Rietveld refinement as a function of the nominal germanium fraction. Source: Bérardan et al. 2008 [40]. Reproduced with permission of Elsevier.

nominal composition In1.9 Ge0.1 O3 (Figure 4.20) showed that all Bragg peaks can be indexed due to a mixture of In2 O3 as main phase and In2 Ge2 O7 as secondary phase. Although the ionic radii of In(+III) and Ge(+IV) are very different, systematic evolution of the lattice parameter a does not occur when the germanium fraction is increased. And the fractions of In2 Ge2 O7 determined using Rietveld refinement of the X-ray diffraction patterns are very close to those predicted without substitution (see the inset in Figure 4.20). Therefore, either Ge cannot be replaced in In2 O3 . The electrical conductivity is strongly enhanced by Ge doping with best values exceeding 1200 S cm−1 at room temperature. The dimensionless figure of merit ZT reaches 0.1 at 1273 K in In2 O3 and exceeds 0.45 at 1273 K in the composites with nominal composition In1.8 Ge0.2 O3 [40]. Figure 4.21a shows that electrical conductivity of the sample increases abruptly for very low titanium fraction x. Importantly, beyond a certain limit value x𝓁 , the increase in conductivity is suddenly stopped and tends to decrease with increasing x. This shows that below x𝓁 , titanium substitutes for indium, increasing the carrier concentration by valency effect (Figure 4.21b). In contrast, it suggests that beyond x𝓁 , the substitution does not take place anymore, leading to the formation of a secondary phase. To further examine the lattice evolution over Ce doping, we draw the lattice constant versus doping level curve as shown in Figure 4.22. For doping level below 0.01, it shows a linear evolution following Vergard formula, a = a0 + kx, where a0 is the equilibrium lattice constant and x refers to the doping level. By contrast, the lattice constant increases slower as the doping content increases above 0.01 due to the appearance of an impurity phase. Meanwhile, the solubility of cerium

91

4 Binary Oxides

6

–20 –60

4

–80 –100 2

–120

S (μV K–1)

σ (× 103 S cm–1)

–40

–140 –160

(a) 0

–180

n (× 1020 cm–3)

4 3 2 1 0 (b)

0.00

0.05

0.10

0.15

0.20

Ti fraction (x)

Figure 4.21 Influence of the titanium fraction In2−x Tix O3 on (a) the electrical resistivity (open symbols) and the thermopower (square filled symbols) and (b) the carrier concentration measured at RT. The dotted line in the n(x) plot corresponds to the doping by one electron per Ti cation. Source: Guilmeau et al. 2009 [59]. Reproduced with permission of AIP. Figure 4.22 Lattice constant versus various doping level curves of the In2−x Cex O3 ceramic samples. Source: Liu et al. 2012 [55]. Reproduced with permission of John Wiley & Sons.

a = a0 + kX

10.128 Lattice parameter (Å)

92

10.124 Impurity phases 10.12

10.116 0.00

0.02

0.04

0.06

0.08

0.10

X value

in In2 O3 is estimated as x = 0.01, or less than 2 at% for cerium, according to the Vergard formula. The low solubility limit is also reported for many metals: about 2–6 at% for Zn, Sn, Ti, etc., [49] and 1.5 at% for Ge [59]. Figure 4.23a shows the temperature dependence of electrical conductivity. All samples show metallic conducting behavior except In1.98 Ce0.02 O3 , whose

4.7 Doping for In2 O3 -Based Thermoelectric Materials

Electrical conductivity, σ (S cm–1)

500

Seebeck coefficient, S (μV K–1)

(a)

In2O3 (SPS) In2O3 (CS)

400

In1.99Ce0.01O3 In1.98Ce0.02O3 In1.96Ce0.04O3

300

In1.92Ce0.08O3 In1.90Ce0.10O3

200

100

0 –350 –300 –250 –200 –150 –100

400 (b)

In1.995Ce0.005O3

600

800

1000

1200

Temperature, T (K)

Figure 4.23 The temperature dependence of electrical transport properties for various In2−x Cex O3 samples: (a) electrical conductivity; (b) Seebeck coefficient. Source: Liu et al. 2012 [55]. Reproduced with permission of John Wiley & Sons.

electrical conductivity increases slightly with increasing temperature above 800 K. Significant reduction of electrical conductivity observed in In1.9 Ce0.1 O3 sample can be attributed to increased scattering of charge carriers by the increased grain boundaries due to secondary phase. The electrical conductivity at 1073 K of In2−x Cex O3 (0.01 ≤ x ≤ 0.08) samples increases with doping levels up to 200 S cm−1 , much larger than the undoped In2 O3 ceramic samples. Figure 4.23b shows the temperature dependence of the Seebeck coefficient for In2−x Cex O3 samples. The dominant charge carrier of those In2 O3 -based ceramics is electron, as indicated by the negative sign of the Seebeck coefficient. For all doped samples, the absolute value of Seebeck coefficients increases linearly from −83 to −120 μV K−1 at room temperature up to −174 to −289 μV K−1 at 1173 K. The absolute values of Seebeck coefficient as a function of temperature exhibit a dome-like feature around 800 K for pure In2 O3 ; whereas the absolute values of Seebeck coefficient of doped samples is almost a linear function of temperature.

93

94

4 Binary Oxides

4.8 In2 O3 Nanostructures It has been reported that the ZT can be enhanced in nanostructured materials. The quantum confinement effects can increase the power factor S. The numerous interfaces and defects in nanostructures can significantly reduce the lattice thermal conductivity. Figure 4.24 shows the surface SEM and high-resolution TEM of a 50 nm grained sample. The SEM image (Figure 4.24b) shows that the grains range from 20 to 60 nm. The low-magnification TEM image (inset Figure 4.24b) confirms that the average grain is about 50 nm. As seen from a higher magnification TEM image of grains, Figure 4.24c, the grains are highly crystalline and the grain boundaries are clear as shown in Figure 4.24d [56]. Figure 4.25a indicates the temperature dependence of electrical conductivity for In1.92 (Ce, Zn)0.08 O3 with different grain sizes. As seen in the figure, the electrical conductivity value of nanograined samples is higher than that of the (a)

(b)

5 nm

20 nm

(c)

50 nm

100 nm (d) d400 = 2.53 Å

d220 = 3.58 Å 10 nm

2 nm

Figure 4.24 (a) TEM image of In1.92 (ZnCe)0.08 O3 nanopowder. (b) SEM image of 50 nm grained sample. (c) TEM image at medium magnification. (d) HRTEM image of the 50 nm grained sample. Source: Lan et al. 2012 [56]. Reproduced with permission of John Wiley & Sons.

4.8 In2 O3 Nanostructures

50 nm 150 nm 0.4 μm 0.6 μm 2 μm

700 600 500 400 300

50 nm 150 nm 0.4 μm 0.6 μm 2 μm

–60 Thermopower (μV K–1)

–1

Electrical conductivity (S cm )

800

–80 –100 –120 –140 –160 –180

200

400 400

(a)

600

T (K)

800

1000

50 nm 150 nm 0.4 μm 0.6 μm 2 μm

8 7

Thermal conductivity (W m−1 K−1)

Power factor (μW cm–1 K–2 )

10 9

6 5 4 3

(c)

600

800 T (K)

T (K)

800

16 14 12 10

2 400

600

(b)

(d)

50 nm 150 nm 0.4 μm 0.6 μm 2 μm

8 6 4

2

1000

1000

400

600

800

1000

T (K)

Figure 4.25 Temperature dependence of (a) electrical conductivity, (b) thermopower, (c) power factor, and (d) thermal conductivity for In1.92 (ZnCe)0.08 O3 bulks with different grain sizes. Source: Lan et al. 2012 [56]. Reproduced with permission of John Wiley & Sons.

samples of 2 μm grained. It cannot be explained by the energy filter theory since energy barrier in the interface can reduce electrical conductivity. The absolute thermoelectric power decreases with the decreasing grain size as shown in Figure 4.25b. This change is consistent with that of electrical conductivity. It is expected that the thermoelectric power can be improved due to the quantum confinement effect. However, in our experiment the 50 nm grained sample does not clearly show the quantum confinement effect. As seen in Figure 4.25c, the power factor increases in the nanostructured sample since the reduced thermoelectric power is compensated by the increased electrical conductivity. A highest power factor (>8 μW cm−1 K−2 ) has been obtained for the 50 nm grained samples at 1050 K. Thermal conductivity for the samples with different grain sizes is shown in Figure 4.25d. Thermal conductivity for all the samples decreases rapidly with increasing temperature. It indicates the intrinsic Umklapp process dominates the phonon transport at high temperatures. As noted, thermal conductivity significantly reduces with decreasing grain size. At room temperature, thermal conductivity of 50 nm grained ceramics can be decreased to 7.9 W m−1 K−1 compared with that of the 2 μm grained ceramic sample, which is 13.2 W m−1 K−1 . At high temperatures, thermal conductivity decreases from 3.0 W m−1 K−1 in 2 μm grained sample to 2.2 in 50 nm grained samples, which clearly shows that the effect of nanograins on phonon scattering also exists at high temperatures.

95

96

4 Binary Oxides

(a)

(b)

100 nm

(c)

100 nm

(d)

100 nm

100 nm

Figure 4.26 High-magnification SEM and BSE images of x = 0.08 (a, b), x = 0.12 (c, d). The Ce-rich area corresponds to the brighter region and the Zn-rich area corresponds to the darker region in (d). Source: Lan et al. 2014 [57]. Reproduced with permission of Europe PMC.

To take advantage of both point defects and nanostructuring engineering, heavy doping and SPS method are applied to fabricate nanostructured (Zn,Ce) codoped In2 O3 . Figure 4.26 shows the microstructure and phase composition of the bulk samples prepared by SPS. As observed in the high-magnification SEM (Figure 4.26a,c), the x = 0.08, 0.12 samples exhibit nanostructure. The grain size ranges from 20 to 100 nm, similar to our previous work for x = 0.04 [56]. Based on the backscattered images (Figure 4.26d), it is clear that the higher doping content presents compositional inhomogeneity. However, for lower doping levels (x = 0.08), no evident mass fluctuation is observed, indicating the doping is homogeneous. Many CeO2 nanodots (10–20 nm) are observed, which distributes homogeneously in the grain boundaries [57]. The suppressed thermal conductivity caused by the point defects and nanostructures is shown in Figure 4.27a. A low thermal conductivity of 6.9 W m−1 K−1 at room temperature is achieved in x = 0.12, which is about 25% lower than that of the sample x = 0.04 with a grain size of 50 nm. At high temperatures, the thermal conductivity is decreased from 2.8 W m−1 K−1 in x = 0.04 to 2.1 W m−1 K−1 in x = 0.12, which clearly shows that the effect of nanoinclusions and point defects on phonon scattering works at high temperatures, too. The temperature dependence of lattice thermal conductivity 𝜅 l for all the samples is shown in Figure 4.27b. The sample x = 0.12 shows the lowest 𝜅 l at high temperatures, yielding the value of 1.2 W m−1 K−1 , which is about 60% and 40% lower than that of the undoped In2 O3 and the sample x = 0.04, respectively. This implies

4.8 In2 O3 Nanostructures

Figure 4.27 Temperature dependence of (a) total thermal conductivity and (b) lattice thermal conductivity using the calculated Lorenz number of various In2−2x Znx Cex O3 . The dashed line denotes the calculated minimum lattice thermal conductivity.

k (W m–1 K–1)

8

x = 0.04 x = 0.08 x = 0.12 x = 0.16

7 6 5 4 3 2

(a)

300 400 500 600 700 800 900 1000 T (K) 8 x = 0.04 x = 0.08 x = 0.12 x = 0.16

kt (W m–1 K–1)

7 6 5 4 3 2 1 (b)

Figure 4.28 Temperature dependence of ZT for In2−2x Znx Cex O3 .

0.5 0.4

300 400 500 600 700 800 900 1000 T (K)

x=0 x = 0.04 x = 0.08 x = 0.12 x = 0.16

ZT

0.3

κmin

0.2 0.1 0.0 300 400 500 600 700 800 900 1000 T (K)

that phonon scattering from the point defects and the nanostructures (including nanograins and nanoinclusions) is an effective approach to reduce the lattice thermal conductivity of oxides at high temperatures. The ZT value is increased to 0.44 at 923 K for x = 0.12 as shown in Figure 4.28. The ZT value of In2 O3 is enhanced fourfold by Zn and Ce dual doping compared to that of the pristine sample and is about 60% higher than that of the sample x = 0.04. ZnO nanoinclusions inside the In2 O3 matrix were proposed to reduce thermal conductivity without impairing the power factor. XAFS data demonstrated the formation of ZnO nanoinclusions with a radius of ∼0.7 nm as shown in Figure 4.29. The thermal conductivity can be then assigned to the scattering of mid- and long-wavelength phonons by such nanoinclusions.

97

4 Binary Oxides

Zn

O

R = 0.6 nm; 77 atoms Zn K-edge a

b c

c′

Wurtzite:ZnO

In1.98Zn0.02O3 R ~ 1 nm: 340 atoms

Normalized absorption (a.u.)

98

R = 0.4 nm; 27 atoms

R ~ 0.8 nm: 183 atoms

R ~ 0.6 nm: 77 atoms R ~ 0.4 nm: 27 atoms

R = 0.3 nm; 18 atoms R ~ 0.3 nm: 18 atoms

R ~ 0.2 nm: 5 atoms

Cluster-size 9660

9680 9700 Energy (eV)

R = 0.2 nm; 5 atoms

9720

Figure 4.29 (Left) Comparison among simulated Zn K-edge spectra of nanoclusters with a radius ranging from 0.2 nm up to 1 nm, the as-measured Zn K-edge spectrum of the ZnO polycrystalline wurtzite and that of the In1.98 Zn0.02 O3 ; (right) the different cluster calculations: Yellow spheres are Zn atoms, while red ones are O atoms.

4.9 TiO2 and Others Titanium dioxide (TiO2 ) is one of the most widely used and intensively studied materials such as zinc oxides. In nature, TiO2 appears in three crystal structures as shown in Table 4.1: rutile, anatase, and brookite. The rutile phase is the most stable (rutile melts near 2100 K), and the other two phases convert irreversibly to the rutile phase above ∼900 and 1100 K, respectively. Large Seebeck coefficients are reported from −360 to −700 μV K−1 for rutile sample and from −240 to −500 μV K−1 for anatase samples. The highest power factor ∼14 μW (K2 cm)−1 at 350 K was reported in Ti0.94 Nb0.06 O2 thin film [56]. Despite these promising characteristics, the highest reported value ZT is 0.35 at 973 K in rutile [64], which is well below that of other oxides such as ZnO and In2 O3 . Poor electrical conductivity and high thermal conductivity are the main reasons for the low performance.

4.9 TiO2 and Others

Table 4.1 The crystal structure and parameters of the three crystal forms of TiO2 . Crystal form

Crystal system

a (Å)

b (Å)

c (Å)

Rutile

Tetragonal

4.591

4.591

2.957

Anatase

Tetragonal

3.777

3.777

9.488

Brookite

Orthorhombic

5.456

9.182

5.143

Source: Yuan et al. 2017 [63]. Reproduced with permission of Elsevier.

Table 4.2 The crystal structure and parameters of the Magnéli phase titanium oxides. Magnéli phase

Crystal system

a (Å)

b (Å)

c (Å)

𝜶 (∘ )

Ti4 O7

Triclinic

5.600

7.133

12.466

95.05

95.17

Ti5 O9

Triclinic

5.569

7.126

8.865

93.17

112.34

108.50

Ti6 O11

Triclinic

5.552

7.126

32.233

66.94

57.08

108.51

Ti7 O13

Triclinic

5.537

7.132

38.151

66.70

57.12

108.50

Ti8 O15

Triclinic

5.526

7.133

44.057

66.54

57.18

108.51

Ti9 O17

Triclinic

5.524

7.142

50.030

66.41

57.20

108.53

𝜷 (∘ )

𝜸 (∘ )

108.71

Source: Yuan et al. 2017 [63]. Reproduced with permission of Elsevier.

Therefore, numerous works on the optimization of doping and nanostructures have been carried out. When oxygen defects are introduced into the crystal lattice of TiO2 , the atoms rearrange to form an ordered Tin O2n−1 structure. The Tin O2n−1 (4 ≤ n ≤ 10) has been named Magnéli phase titanium oxides. The structures of the Magnéli phase are similar as shown in Table 4.2. Miao’s group reported the synthesis process of N- and Nb-codoped TiO2 powders by a fast combustion method using urea (CO(NH2 )2 ) as fuel [64]. The particle size of N- and Nb-codoped TiO2 powders is in the range of 15–50 nm as shown in Figure 4.30. The optimized N- and Nb-codoped TiO2 exhibits higher electrical conductivity up to 2.4 × 104 S m−1 at 700 ∘ C, while the undoped sample has 2.0 × 103 S m−1 . The Seebeck coefficient of N- and Nb-codoped TiO2 decreases somewhere in the range of about −195 to −230 μV K−1 . The power factor of N- and Nb-codoped TiO2 is 7 times greater, up to about 9.87 × 10−4 W m−1 K−2 at 700 ∘ C. The thermal conductivity of TiO2 can be greatly reduced by the codoped at room temperature, while at high temperatures the reduction is not so effective. Finally, the codoped samples reach the highest ZT value ever reported to be 0.35 at 700 K (Figure 4.31). Although CdO is the first reported TCO, there are few report as thermoelectric materials due to its high thermal conductivity. Recently, the n-type CdO has been systematically investigated by the Shufang Wang group. The highest ZT value of ∼0.5 has been achieved in the porous CdO at about 1000 K [65]. Wang’s group also adopt heavy element dopants (e.g. Ba, Ag, and Ni) and nanocomposite to reduce thermal conductivity [66–69].

99

4 Binary Oxides 25

(a)

25

(b)

20

Ratio (%)

Ratio (%)

20

15

15

10

10

5

5 0 15

20

25 30 35 40 Diameter (nm)

45

0 20

50

25

(c)

30 35 40 45 Diameter (nm)

50

55

15 20 25 30 Diameter (nm)

35

40

Ratio (%)

Ratio (%)

20

15

15 10

10

5

5 0 10

25

25

(d)

20

15

20 25 30 35 Diameter (nm)

40

0 5

45

10

–160 TNO17-12 104

TiO2-δ

Seebeck coefficient (μV K–1)

Electrical conductivity (S m–1)

Figure 4.30 SEM images of N- and Nb-codoped TiO2 nanoparticles (scale bars = 100 nm): (a) TiO2 , (b) Ti(O,N)2±𝛿 , (c) Ti0.91 Nb0.09 (O,N)2±𝛿 , and (d) Ti0.83 Nb0.17 (O,N)2±𝛿 . The insets show the corresponding estimated particle size distributions. Source: Liu et al. 2013 [64]. Reproduced with permission of ACS.

100 200 300 400 500 600 700 800 Measurement temperature (°C)

0

(a) 10

(c)

–180 –200 TNO17-12

–220 –240 –260

TiO2-δ

–280 –300 –320 –340

103

(b)

κ (Total) κ (Lattice)

9

100 200 300 400 500 600 700 800 Measurement temperature (°C)

0.30

8 7

0.25

6

0.20

5

0

0.35

ZT

Thermal conductivity (W m–1 K–1)

100

TiO2-δ

TNO17-12

0.15

4 0.10

3

TNO17-12

2

0.05

1

0.00

0

100 200 300 400 500 600 700 800 Measurement temperature (°C)

(d)

TiO2-δ 0

100

200 300 400 500 600 700 Measurement temperature (°C)

Figure 4.31 Thermoelectric properties of sintered TiO2 bulk materials: (a) electrical conductivity, (b) Seebeck coefficient, (c) thermal conductivity, and (d) ZT.

800

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Ga-doped [0001] ZnO nanowires. Physics Letters A 376 (8–9): 978–981. 36 Ohtaki, M., Araki, K., and Yamamoto, K. (2009). High thermoelectric perfor-

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53 Cordfunke, E.H.P. and Westrum, E.F. (1992). The heat capacity and derived

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63

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65

66 67

68 69

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5 Perovskite-Type Oxides 5.1 Introduction for Perovskite-Type Oxides Perovskite-type oxides possess a general formula ABO3 and are structurally similar to CaTiO3 , the mineral that gave its name to that group of compounds. In the general formula, A ions can be rare earth, alkaline earth, alkali, and other large ions such as Pb2+ and Bi3+ . The B ions can be 3d, 4d, and 5d transitional metal ions (e.g. Ti, Zr, Sc). There also exist perovskite-like materials such as Sr2 FeO4 or Sr3 Fe2 O7 , which are composed of basic perovskite cells separated by intervening layers [1]. The perovskite-type materials can tolerate by partial substitution of Aand B-sites and nonstoichiometry, while still remain with the typical perovskite structure. Due to the special oxygen octahedron structure of perovskite materials, they have attracted intense attention in solid-state chemistry, physics, photoelectronics, and catalysis. The oxygen ions in the perovskite unit cells constitute an octahedral distribution. The deformation or tilting of the special oxygen octahedron structure leads to new performances or property changes. These materials exhibit important physical properties such as ferro-, piezo-, and pyroelectricity and magnetism effects. The earliest works using perovskites as catalysts were conducted in 1952 and 1953 by Parravano, who observed that the rate of catalytic oxidation of carbon monoxides is affected by ferroelectric transitions in NaNbO3 , KNbO3 , and LaFeO3 . This may be interpreted as evidence supporting an electronic mechanism for this reaction. A similar effect in the rate of CO oxidation was observed in the neighborhood of the ferromagnetic transition in La0.65 Sr0.35 MnO3 [1]. Whittingham group [2] reported on the recombination of oxygen atoms on the surface of alkali metal tungsten bronzes Mx WO3 , where M = Li, Na, or K. The catalytic activities were found to be closely related to the electronic properties of the bronzes. Galasso et al. [3] reported on the application of A(BB′ )O3 oxides as electrodes for fuel cells; B and B′ cations were selected, respectively, for their catalytic properties and for the corrosion resistance they impart to the perovskite. Since the discovery of the good p-type material Nax CoO2 , many perovskite-type oxides such as SrTiO3 , CaMnO3 , and LaCoO3 have been investigated from the TE perspective [4, 5].

Oxide Thermoelectric Materials: From Basic Principles to Applications, First Edition. Yuan-Hua Lin, Jinle Lan, and Cewen Nan. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

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5 Perovskite-Type Oxides

5.2 Crystal Structure and Electronic Structure of Perovskite-Type Oxides 5.2.1

Crystal Structure

Generally, the typical perovskite-type structure of oxides ABO3 is cubic with the space group Pm3m-Oh . A is the larger cation (e.g. Ca, Sr, Ba) and B is the smaller one (e.g. Ti, Zr). The B cation is 6-fold coordinated and the A cation is 12-fold coordinated with the oxygen anions. As shown in Figure 5.1, the B cation is located in the center of the octahedron, and the A cation is in the center of the cube. The ReO3 -type framework can be regarded as a host structure for deriving numerous structures of metal oxides [7]. In the ideal structure, one perovskite unit cell involves six oxygen atoms, which occupy the face-centered sites of the face-centered cubic (FCC) structure, forming an oxygen octahedron, and the B-site cations infill the central vacancy. The origin of the oxygen octahedron tilting is reflected by the deviation of the B—O—B bond described by two quantitative definitions [8]. The first one is Goldschmidt tolerance factor [6]: r + rO (5.1) t=√ A 2(rB + rO ) where rA , rB , and rO are radii of A cation, B cation, and O anion, respectively. The second is the intersection angle of the two bonds: 𝜃 = ⟨B—O—B⟩

(5.2)

For a centrosymmetrical perovskite wherein the A cation matches in size with the O anion to form cubic close-packed layers and the B cation matches the size of the interstitial sites of the BO6 octahedron, the tolerance factor is 1. However, once a distortion happens, the ideal packing will be broken, and t will deviate from 1.0, with the deviation reflecting how far the ionic sizes can move and still be “tolerated” by the perovskite structure. When the deviation of t from 1.0 is small, e.g. −0.05 ≤ t − 1.0 ≤ 0.04, the crystal structures preserve the cubic symmetry. Different distortions of the perovskite structure can appear by doping A- or B-sites. z y x Cation A Oxygen anion Cation B

Figure 5.1 Crystal structure of perovskite oxides [6].

5.2 Crystal Structure and Electronic Structure of Perovskite-Type Oxides

The compound CaTiO3 was originally thought to be cubic, but its true symmetry was later shown to be orthorhombic [9]. Additionally, substitutions can be the two ions at the B-site, and the general formula of the perovskite can be A2 BB′ O6 or AB0.5 B′ 0.5 O3 , which is doubled along the three axes, regarding the primitive cell of ABO3 . If the charge of B and B′ is different, the oxygens are slightly shifted toward the more charged cation [10]. Normally, if the deviation is positive and relatively large, for example, in Ba5 Ta4 O5 , the B—O bonds are tensed, the A—O bonds are compressed, and the B—O—B bond angle 𝜃 remains 180∘ , leading to a hexagonal atomic stacking accompanied by ferroic properties. However, if the deviation is negative and relatively large, the A—O bonds are tensed and the B—O bonds are compressed, resulting in the tilting of the oxygen octahedra and bending of the B—O—B bonds. Such distortion gives rise to tetragonal stacking, rhombohedral stacking, or orthorhombic stacking, and the average bond angle 𝜃 continues to decrease as the symmetry changes from tetragonal to rhombohedral to orthorhombic. Therefore, the tolerance factor and the oxygen octahedral tilting are the criteria for the structure symmetry. The distorted structure may exist at room temperature, and the tilting of the oxygen octahedra is largely related to the tunable properties in the perovskite oxides. 5.2.2

Electronic Structure

Density of states (electrons/eV)

The electrical properties of solid-state materials are determined by their electronic structures, and the oxygen octahedral tilting can reduce the overlap between the B d and O 2p orbitals and hence affects the electric bandgap of the perovskite oxides. Many studies reported on the electronic structure of perovskite-type oxides in detail [11–16]. Figure 5.2 shows the calculated band structure (Figure 5.2a) and calculated total density of states (DOS) (Figure 5.2b) for SrTiO3 [12]. The valence band (VB) consists of O 2p, Sr 5s, and Ti 3d hybrid orbitals, and O 2p. The O 2p orbital contribute more electrons due to closer to the Fermi level. The conduction band (CB) is determined by the Ti 3d orbital. Figure 5.3a shows the calculated band structure for the G-type antiferromagnetic phase CaMnO3 system along a high symmetry direction in the Brillouin

Energy (eV)

4 2 0 –2 –4 G

(a)

F

Q

Z

G

O 2s

O 2p

Sr 5p

Sr 5s

Ti 4p, 4s

–20

(b)

Figure 5.2 The band structure (a) and DOS (b) of SrTiO3 [12].

Total O Ti 3d

Ti 3d

Sr Ti

–10 Energy (eV)

0

107

5 Perovskite-Type Oxides 2.0

30

1.5 25 DOS (states/eV)

1.0 Energy (eV)

108

0.5 0.0 –0.5 –1.0

20

total

15

p

10 d

5

–1.5

S

0

–2.0 G

F

(a)

Q

Z

–30

G

(b)

–10 –20 Energy / eV

0

Figure 5.3 The band structure (a) and total partial density of states (b) of CaMnO3 [16].

zone. The valence band maximum (VBM) and the conduction band minimum (CBM) at different points result in an indirect bandgap material. The calculated total partial DOS for CaMnO3 is shown in Figure 5.3b. The valence bands are mainly composed of the Mn 3d and O 2p orbitals with minor contributions of the other states of Ca. Since the bands near the VBM and the bands near the CBM contribute to the electrical properties, the Mn d and O p electrons can play a major role in transportation behaviors [16].

5.3 A- and B-Sites Doping for Perovskite-Type Oxides The perovskite-type strontium titanate (SrTiO3 ) [17] and CaMnO3 [18] are promising candidates for n-type oxide TE materials. These oxides can be realized as semiconducting by doping according to the following defect equations: A-site: Ln2 O3 + 2BO2 → 2Ln⋅A + 2BxB + 2e′ + 6OxO + 1∕2O2 ↑ B-site: 2AO + M2 O5 → 2MB⋅ + 2AxA + 2e′ + 6OxO + 1∕2O2 ↑ where Ln can be a rare-earth element, M denotes Nb and Ta, and the A-site cation (Sr, Ca), as well as the B-site cation (Ti, Mn). Because the valence state of Ti ions can be changeable in STO (SrTiO3 ), they become easily oxidized to Ti4+ above ∼700 K in air, which result in insulating behaviors. However, in CaMnO3 , Mn3+ is more stable than Ti3+ , so the doping reaction can occur even in air. Therefore, CaMnO3 can be a high-temperature n-type TE material, whereas STO can only have medium-temperature applications. 5.3.1

SrTiO3

The TE properties of perovskite-type STO have been intensively investigated in the form of single crystals, films, and polycrystalline ceramic bulks.

5.3 A- and B-Sites Doping for Perovskite-Type Oxides

As previously reported [19], ZT values can be 0.37 at 1000 K for single-crystals, lower for polycrystalline ceramics, and as high as 2.4 for SrTiO3 /SrTiO3 :Nb superlattices [20]. As for the TE practical applications, the performance is still insufficient, and improving their ZT values is still a challenge. STO is a typical perovskite-type oxide with a very high melting point of 2080 ∘ C, suggesting the potential of TE applications at high temperatures. High electrical conductivity 𝜎 can be obtained by substitutional doping, e.g. with lanthanides for Sr2+ or Nb5+ for Ti4+ . The thermopower |S| of STO single crystals and Sr1−x Lax TiO3 (x = 0.1–0.5) ceramics was reported by Frederikse et al. [21] and Moos et al. [22], which can be comparable to the TE properties of Nax CoO2 [23]. Both STO single crystals and polycrystalline ceramics show a rather heavy DOS effective mass, m* , due to the large DOS of the triply degenerate 3d-t2g orbitals at the bottom of the conduction band. The large effective mass results in a large S > 0.1 mV K−1 at 300 K. In Sr1−x Lax TiO3 (x = 0–0.1) and reduced single crystals, large power factors (1.2–3.6 mW m−1 K−2 at 300 K) are also observed. However, the thermal conductivity of STO crystals is very high (7–11 W m−1 K−1 ) due to strongly bonded lightweight atoms [24]. The further reduction in 𝜅 is critical to improve the ZT of STO. In STO epitaxial films, heat transport cannot be suppressed by enhanced phonon scattering with heavy doping and thus decreasing 𝜅 [19]. Kato et al. reported that Sr replaced with Eu in Sr1−x Eux Ti0.8 Nb0.2 O3 (x = 0–0.8) epitaxial films [25], Eu substitution almost did not affect the electrical properties; however, it suppressed heat transport by shortening the phonon mean free path (MFP) about 12% at room temperature. Ohta et al. [26] reported that the polycrystalline Nb-doped micrometer-grained STO ceramics maintain a high S2 𝜎 and 𝜅 values cannot be decreased at high temperatures. Dy and La codoped STO ceramics with nanosized second phases can maintain high power factor and also have a lower thermal conductivity (2.3 W m K−1 at 1074 K) by the nanophase [27]. The maximum ZT value, obtained in a La0.08 Dy0.12 Sr0.8 TiO3 ceramic, is 0.36 at 1048 K. The grain size in these ceramics is very important for phonon scattering [28]. The thermoelectric properties tuned by various La dopant concentrations are summarized in Figure 5.4 [17, 24, 29–37]. La doping can greatly change the electrical properties and also reduce thermal conductivity. Other lanthanides can also be used to improve the ZT performance. Titanium-site substitution with Nb ions is another way to improve the thermoelectric performance of STO [17, 26, 38–45]. Wang et al. [39, 43–45] investigated Nb-doped STO composites with second phase and showed that thermoelectric performance of the STO can be further enhanced than with only Nb dopant. Ta-doped strontium titanates were studied by Cui et al. [46], and their results indicated that 10% Ta-doped sample exhibits the best performance. The results of these studies are summarized in Figure 5.5. 5.3.2

CaMnO3

CaMnO3 is an orthorhombic perovskite-type structure in the Pnma space group, which is chemically stable even at temperatures as high as 1200 K. It possesses

109

102 0.05La-doped STO crystal24 La-doped STO crystal17 0.08La29 0.09La30 0.08La31 0.10La32 33 0.15La 0.12La34 0.10La35 0.08La36 0.10La37

101 100 200

400

Thermal conductivity (W m–1 K–1)

(a)

Seebeck coefficient (μV K–1)

La-doped STO

103

150 100 50 0 –50 –100 –150 –200 –250 –300 –350 200

600 800 1000 1200 1400 Temperature (K) (b)

0.05La-doped STO crystal24 La-doped STO crystal17 0.08La29 0.09La30 0.08La31 0.10La32 0.15La33 0.12La34 35 0.10La 0.08La36 0.10La37

400

600 800 1000 1200 1400 Temperature (K)

0.8

10 0.05La-doped STO crystal24 La-doped STO crystal17 0.08La29 0.09La30 0.10La32 0.08La31 0.15La33 0.12La34 35 0.10La 0.08La36 0.10La37

9 8 7 6

0.6 ZT

Electrical conductivity (S cm–1)

5 Perovskite-Type Oxides

0.4

0.05La-doped STO crystal24 La-doped STO crystal17 0.08La29 0.09La30 0.08La31 0.10La32 0.15La33 0.12La34 0.10La35 0.08La36 37 0.10La

5 0.2

4 3

0.0

2 200

400

(c)

600 800 1000 1200 1400 Temperature (K) (d)

200

400

600 800 1000 1200 1400 Temperature (K)

Figure 5.4 Thermoelectric properties of La-doped STO. 0.60 0.55

ZT

110

0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15

Nb-doped STO crystal17 0.20Nb26 0.20Nb38 0.15Nb+KTO39 0.05Nb40 0.05Nb41 0.05Nb42 0.15Nb+YSZ43 0.15Nb+MS44 0.15Nb+TNT45 0.10Ta46

0.10 0.05 0.00 200

300

400

500

600

700

800

900 1000 1100

Temperature (K)

Figure 5.5 ZT of niobium-doped STO.

correlated electrons such as manganates and cobaltates, and the spin of electrons can contribute to the additional source of entropy, which results in large thermopower [47]. The TE properties in this system can be tuned by element doping, e.g. La on the Ca-site and Nb on the Mn-site, which are summarized in Figure 5.6 [48–58].

400 Doped CaMnO3

350 300 250

0.12Y48

0.05Ce48

0.10Dy49 0.02Dy51

0.08Pr50 0.10Yb49 0.10Dy52 0.10La52 0.10Yb52 0.04Gd53 0.10Y52 0.10Yb58 0.15Pr54 0.10Yb55 0.05Yb/0.02Nb57 0.02Nb58

200 150 100 50 200

400

(a) 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 200

600 800 1000 1200 1400 Temperature (K) (b) 0.10La48 0.10Dy49 0.02Dy51

0.12Y48

0.05Ce48

0.10Yb49 0.10La52

0.08Pr50 0.10Dy52 0.04Gd53 0.10Yb56

–50 –100 –150 –200 –250 –300 –350 –400 –450 –500 200

0.10Yb52 0.10Y52 0.15Pr54 0.10Yb55 0.05Yb/0.02Nb57 0.02Nb58

ZT

Thermal conductivity (W m–1 K–1)

0.10La48

Seebeck coefficient (μV K–1)

Electrical conductivity (S cm–1)

5.3 A- and B-Sites Doping for Perovskite-Type Oxides

400

(c)

600 800 1000 1200 1400 Temperature (K) (d)

0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 200

0.10La48

0.12Y48

0.05Ce48

0.08Pr50 0.10Yb49 0.10Dy52 0.10La52 52 52 0.04Gd53 0.10Y 0.10Yb 0.10Yb56 0.10Yb55 0.15Pr54 0.02Nb58 0.05Yb/0.02Nb57 0.10Dy49 0.02Dy51

400

600 800 1000 1200 1400 Temperature (K)

0.10La48 0.10Dy49 0.02Dy51

0.12Y48

0.05Ce48

0.10Yb49 0.10La52

0.10Yb52

0.10Y52

0.08Pr50 0.10Dy52 0.04Gd53 0.10Yb56

0.15Pr54

0.10Yb55 0.02Nb58 0.05Yb/0.02Nb57

400

600 800 1000 1200 1400 Temperature (K)

Figure 5.6 Thermoelectric properties of CaMnO3 .

The earlier results indicate that Dy and Yb additions were most effective for increasing the ZT [49, 52, 59]. These dopants lead to increase in electrical conductivity and change thermal conductivity. The Nb substitutions increased electrical conductivity but increased thermal conductivity [60]. Bi doping at the Ca-site [61, 62] and W doping at the Mn-site [63, 64] can also lead to an increase in electrical conductivity, but they decrease thermal conductivity. Many codoping studies [57, 65–69] showed a potential possibility of improving the thermoelectric properties of CaMnO3 . 5.3.3

LaCoO3

LaCoO3 -related materials exhibit a high Seebeck coefficient of about 600 μV K−1 at room temperature. However, their electrical resistivity is rather high, and thus the ZT value is not high [70–72]. The cation substitutions of the La3+ ions with alkaline-earth metals or rare-earth elements and Co3+ ions with 3d or 4d transition metals (such as Ni, Fe, Mn, Cu, Rh) have been intensively studied. Substitution of La3+ by divalent ions in LaCoO3 , such as Ca2+ , Sr2+ , and Ba2+ , has a significant influence on the spin state of Co3+ /Co4+ . The oxygen vacancy concentration also affects the physical properties, i.e. electric and magnetic properties. Seebeck coefficient is significantly affected by the spin state of Co3+ /Co4+ like Ca–Co–O systems [73–75]. The electrical conductivity can be largely improved by cation substitutions; however, the Seebeck coefficient will dramatically decrease simultaneously. For this system, it is difficult to improve the ZT value. The highest ZT value of 0.18 is achieved at room temperature with 5% Sr doping [5].

111

112

5 Perovskite-Type Oxides

5.4 Double Perovskites Double perovskite-like oxides have two common formulas of A′ A′′ B2 O5+𝛿 (where A′ , A′′ , and B represent the rare-earth metal, alkaline-earth metal, and 3d transition metal, respectively) [76] and A2 B′ B′′ O6 (where A = rare-earth or alkaline-earth elements, B = two kinds of transition metals, first synthesized by Donohue and McCann) [77]. 5.4.1

Structure of Double Perovskites

The basic structure of A′ A′′ B2 O5+𝛿 is made up of [BO5 ] bilayers formed by corner-shared pyramid structures with A′′ atoms embedded in and A′ atoms staying between the bilayers and linking them [78–80]. The structure diagram of A′ A′′ B2 O5+𝛿 is shown in Figure 5.7. Recently, some types of this class such as RBaB′ B′′ O5+𝛿 (B′ B′′ = CuFe, CoFe, CoCu) [81–83], RBaCu2 O5+𝛿 [84], RBaCo2 O5+𝛿 [85], and RBaMn2 O5+𝛿 [86] have been researched. Most of these oxides have a tetragonal structure with a space group P4mm [87] or P4/mmm [88], while LaBaB′ B′′ O5+𝛿 belongs to Pm3m due to a little ionic radius difference between La3+ and Ba2+ , thus leading to a statistical distribution in A-sites [89, 90]. The crystal structure of A2 B′ B′′ O6 (Sr2 FeMoO6 ) is shown in Figure 5.8. A is a large cation capable of 12-fold coordination by oxygen, while B′ and B′′ must have a large difference on charge or size to arrange a NaCl-type ordered structure [91, 92]. Figure 5.7 The structure diagram of A′ A′′ B2 O5+𝛿 .

A″ B A′ O B

c a

b

Figure 5.8 The structure diagram of Sr2 FeMoO6 . Sr

O Fe c Mo

ab

5.4 Double Perovskites

A2 B′ B′′ O6 may have many kinds of crystal structures and different synthesis processes. For example, at room temperature, A2 B′ B′′ O6 was reported to be cubic cells for A2 = Ba2 or BaSr, tetragonal ones for A2 = Sr2 , and orthorhombic ones for A2 = Ca2 [93]. Furthermore, the crystal cells would change with increase in doping [94] or temperature [95]. Until now, the current focus on these materials is mainly about their structure and magnetic and electrical performance, but only a few systematical studies have been reported on the thermoelectric (TE) properties of layered RBaCuFeO5+𝛿 [83, 96–98]. Oxygen defects 𝛿 (0 < 𝛿 < 1) [78, 85, 99] generated in the preparation process would affect the TE properties of this type of materials. Due to their naturally layered structures and tunable electronic properties, their potential high-temperature TE properties cannot be neglected. 5.4.2

Thermoelectric Properties of A′ A′′ B2 O5+ 𝜹

RBaB′ B′′ O5+𝛿 , as a A′ A′′ B2 O5+𝛿 family member, exhibits totally different property on 𝜎 and S when B-site atoms have different collocation among Cu, Fe, and Co. As seen in Figure 5.9, RBaCuFeO5+𝛿 owns the highest average S value of 350 μV K−1 at high temperatures, while RBaCoFeO5+𝛿 owns a lower average S value of 50 μV K−1 at high temperatures compared with RBaCoCuO5+𝛿 [83, 96]. Different collocation of transition metals in the double perovskite-like oxides can bring about varying degrees on strong electron correlations and spin-orbital degeneracy, leading to a discrepancy of S. 𝜎 is opposite to S, and thus, the interplay becomes a difficult obstacle for further improvement on TE properties. It is worth mentioning that oxygen defects 𝛿 ordering play an important role in determining the physical properties of perovskite-related oxides especially for 𝜎 and S. For example, 𝜎 of LaBaCuFeO5+𝛿 decreases due to the release of weakly bonded oxygen at 670 K, even in high-content La-doped RBaCuFeO5+𝛿 compounds [100, 101]. At low temperatures, A. Taskin et al. [98] have found a remarkable divergence of S from >0 to 0.1) decreased thermal conductivity and the PF simultaneously, which resulted in a smaller ZT value. 0.35 0.32

0.32

0.28

0.26

0.28 ZT

Figure of merit (ZT)

0.22

0.21

0.21 0.19 0.000

0.14

0.075

0.150

0.225

Fe (moles)

CCO Fe0.05 Fe0.1 Fe0.1

0.07

0.00 300

(a)

0.25 0.20

0.19

ZT

Figure of merit (ZT)

146

400

500

600 700 800 Temperature (K)

900 1000

0.24 Fe

0.16

0.0

(0, 0)

(x 0.1 mo les

)

(0.1, 0.2) (0.2, 0.2) (0.1, 0.1)(0.2, 0.1) 0.2 0.1 s) ole 0.0 m (y 0.2

La

CCO La0.1 Fe0.1 La0.1 Fe0.2 La0.2 Fe0.1 La0.2 Fe0.2

0.08

0.00 300

(b)

400

500

600 700 800 Temperature (K)

900 1000

Figure 6.20 Temperature dependence of ZT for Fe-doped Ca3 Co4−x Fex O9 and Ca3 Co4−y Fey O9 (a) and (La, Fe) codoped Ca3−x Lax Co4−y Fey O9 (b), ceramic specimens, where the insets show dependence of ZT upon doping concentration. Source: Lin et al. 2009 [37]. Reproduced with permission of AIP.

6.3 Ca3 Co4 O9

6.3.3

Texture for Ca3 Co4 O9

The thermoelectric properties of Ca3 Co4 O9 are anisotropic due to its layered structure, and highly grain-aligned ceramics exhibited higher TE performance than randomly oriented Ca3 Co4 O9 ceramics. SPS technique and the dynamic forging process are very effective for fabricating highly grain-aligned, dense Ca3 Co4 O9 -based ceramics (Table 6.1) [37]. As shown in Figure 6.21, a strong preferred orientation along the (00l) plane of the Ca3 Co4 O9 appeared after the dynamic forging process, especially the CCO-4 sample. The higher orientation CCO-4 sample shows the best TE performance, and ZT can reach 0.26 at 975 K due to better electric performance along the orientation. Noudem et al. proposed the use of a mold with a diameter much larger than the desired final diameter of the sintered sample, called edge-free spark plasma sintering or spark plasma texturing (SPT). The sample behaves like in an edge-free mold (the hot-pressing configuration) as shown in Figure 6.22. The SPT method has a great influence on the degree of texture and indicates the anisotropic properties such as transportation behaviors and Seebeck coefficients. 6.3.4

Nanocomposites for Ca3 Co4 O9

In 2011, Ngo Van Nong et al. reported the highest ZT value of 0.61 at 1118 K for Ca3 Co4 O9 -based ceramics using the heavy doping and metallic nanoinclusions methods [48]. As shown in Figure 6.23, the Ag-rich region was in the range of 100 nm, which can effectively scatter phonons with various lengths of mean paths. The design of given oxide TE composites has been deduced from the idea of combining the higher electrical conductivity of La0.8 Sr0.2 CoO3 (LSCO) Table 6.1 Sample numbers and their composition [37]. Processing technology

CCO-1

Ca3 Co4 O9

SPS

CCO-2

(La0.1 Ca0.9 )3 Co4 O9

SPS

CCO-3

Ca3 Co4 O9

SPS + dynamic forging

CCO-4

(La0.1 Ca0.9 )3 Co4 O9

SPS + dynamic forging

(008)

(007)

(006)

(005)

(003)

(002) (001)

Figure 6.21 XRD patterns of various CCO samples prepared by SPS and dynamic hot forging process [37].

(004)

Samples’ composition

Relative intensity

Sample No.

CCO-4 CCO-3 CCO-2 CCO-1

0

10

20

30

40

50

2θ (deg)

60

70

80

147

148

6 Oxide Cobaltites

F

Figure 6.22 Schematic configuration of the SPS and SPT processes: (a) free deformation configuration and (b) conventional SPS. Source: Noudem 2009 [52]. Reproduced with permission of Elsevier.

(a)

F

(b)

(a)

(b) a

88.8° b

1.09 nm [110]

IFFT image

10 nm (c)

5 nm (d) Ag-rich Grain 5 Grain 1 Grain 2

Grain 4 Grain 3 200 nm

100 nm

Figure 6.23 (a) HRTEM image; the inset is an electron diffraction pattern. (b) HRTEM and simulation inverse fast Fourier transform (IFFT) (inset) images. (c, d) BF-TEM images. Source: Ngo et al. 2011 [48]. Reproduced with permission of John Wiley & Sons.

6.3 Ca3 Co4 O9

with the higher thermopower of CCO at high temperatures, while the presence of these two different phases renders increased phonon scattering at the grain boundaries [53]. Figure 6.24 indicates the typical HRSEM images taken from the freshly broken cross-sectional view of pellets obtained after SPS, demonstrating the intermixing morphology of LSCO and CCO in the composite phases [53]. The pure-phase CCO exhibits the lamellar grains such as microstructures, whereas for the composite phases, the nanosized particles ranging from 50 to 80 nm are seen. Most of the nanoparticles are residing on grain boundaries and tips of the CCO grains. The nanosized LSCO particles filled in the voids among CCO grains behave like electrical contacts among the CCO grains, which increase electrical conductivity. Moreover, the enhanced Seebeck coefficient might be associated with the strains induced by LSCO nanoparticles. The total thermal conductivity can be reduced to 1.1 W m−1 K−1 by phonon scattering caused by the dispersed LSCO nanoparticles. The synergy of increasing PF and decreasing thermal conductivity in these CCO–LSCO nanocomposites realized the highest ZT value up to 0.41 at 1000 K.

(a) CCO

1 μm

1 μm (d) LSCO-75%

Concentration (a.u.)

(c) LSCO-75%

(b) LSCO-50%

1 μm

1 μm

0.0

Ca-K La-L Curve fitting : Ca Curve fitting : La

0.2

0.4 0.6 0.8 Distance (μm)

Figure 6.24 The SEM images of the cross-sectional view of (a) pure CCO phase, (b) LSCO-50% and (c) LSCO-75% composite phase specimens; (d) the BSE image of LSCO-75% showing clear contrast of CCO and LSCO phases. The elemental distribution, as obtained through EDX technique, along the white line indicated in (d) is shown in the inset. Source: Sajid et al. 2015 [53]. Reproduced with permission of John Wiley & Sons.

149

6 Oxide Cobaltites

6.4 New Concepts for Oxide Cobaltites Except Nax CoO2 and Ca3 Co4 O9 , Bi–(Sr, Ba)–Co–O, Tl–Sr–Co–O [54], and (Gd, Nd)BaCo2O5 [55] have also attracted intensive attention due to their special structures, unusual anisotropic properties, and structural stability at high temperatures. Depending on the number of layers (m) in the rock-salt-type block, this family of cobaltites can be divided into two parts. These m = 3 and m = 4 misfit cobaltites can exhibit good thermoelectric power values. Funahashi et al. prepared Bi2 Sr2 Co2 O9 polycrystalline materials by partial melting techniques with various chemical compositions of the samples, i.e., Bi2 Sr2 Co2 Ox (BSC-222), Bi1.8 Sr2 Co2 Ox (Bi-1.8), and Bi2 Sr1.8 Co2 Ox (Sr-1.8). All samples show p-type conductor behaviors. The Seebeck coefficient and electrical resistivity of the samples are strongly correlated to the chemical composition. The S values increase with temperature and are ∼150 μV K−1 for the Sr-1.8 samples. Thermal conductivity for all samples is lower than that for ordinary conducting oxides, and the best ZT can be 0.2 at 1000 K (Figure 6.25). Figure 6.25 Figure of merit Z (=S2 /ρκ) for 2202, Bi-1.8, and Sr-1.8 samples. Source: Funahashi et al. 2000 [5]. Reproduced with permission of AIP.

Figure of merit Z (10–4 K–1)

2.0

1.5

1.0

0.5

0 400

500

600

700

800

900

1000

Temperature (K)

Figure 6.26 Variation of the figure of merit ZT versus temperature for the BSC-222 bulk materials. Source: Combe et al. 2014 [56]. Reproduced with permission of Materials Research Society.

0.30 Sintering (910 °C) Hot pressing (800 °C) Hot pressing (850 °C) Partial melting (923 °C) Partial melting (940 °C)

0.25 0.20 ZT

150

0.15 0.10 0.05 0.00 0

200

400 T (°C)

600

References

Bi2 Sr2 Co2 Ox (BSC-222) bulk materials have also been prepared by three different processing methods – conventional sintering, hot pressing, or partial melting [56]. Hot pressing and partial melting methods are very effective to improve electrical conductivity in BSC-222 bulks due to the higher density in hot-pressed samples or by the grain growth during the partial melting process. The higher ZT values have been obtained in the sample by partial melting method as shown in Figure 6.26 and reach 0.27 at 700 ∘ C for partially melted Bi2 Sr2 Co2 Ox bulks, which increased by a factor of 2.7 compared to the bulk materials by conventional sintering method.

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7 Promising Complex Oxides for High Performance Thermoelectric materials have attracted great attention because of their potential applications in the area of waste-heat recovery, power generation, and cooling. Compared with regular alloys, e.g. Bi2 Te3 , PbTe, oxide-based thermoelectric materials are treated as the possible candidates for thermoelectric applications in high temperature due to their outstanding thermal and chemical stabilities in air. The poor figure-of-merit (ZT) values of them have retained relatively low around 0.1–0.4 for more than 20 years, which limit further application. According to previous researches, the strong ionicity in the bonds between light oxide atoms with others leads to intrinsically small carrier mobility 𝜇 and electrical conductivity 𝜎. Besides, these simple but strong bonds in oxides also make the lattice distortions be suppressed, and the vibrations of atoms are rarely disturbed, which further results in relatively high lattice thermal conductivity 𝜅 L . Therefore, in order to achieve higher thermoelectric performance in oxide-based materials, the bonds between oxygen and other atoms need to be considered and modified. In this chapter, we will talk about the properties of several oxide-based materials with complex structures, more kinds of atoms, and bond types, and new concepts of scatter mechanisms for carriers and phonons would be introduced.

7.1 Crystal Structure–Property Relationships The relationship between crystal structure and properties (e.g. thermal and electrical properties) is complex for thermoelectric oxides, and based on the kind of atom, number included in a unit cell, oxide-based thermoelectric materials can be divided into simple and complex oxides. Among them, the complex oxides are defined as materials with layered structure, and there are oxygen and two or more kinds of other atoms included in the unit cell; in comparison with simple oxides (not in layered structure, with three or less kinds of atoms, e.g. ZnO, In2 O3 , and CaMnO3 ), the complexities, including crystal structures and bond types, are normally increased and lead to totally different properties. For thermal properties, dopants with different sizes and masses normally introduce the corresponding fluctuations, further lead to phonons scattering, and reduce thermal transport around room temperature, and high-temperature Oxide Thermoelectric Materials: From Basic Principles to Applications, First Edition. Yuan-Hua Lin, Jinle Lan, and Cewen Nan. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

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thermal properties based on Umklapp process or phonon–phonon scattering cannot be varied without largely disturbing the intrinsic crystal structure; for electrical properties, the carrier concentration can be modulated to the optimized peak with efficient doping on lattice site, further achieving the best power factor based on single parabolic band model (SPB) [1]. The common crystal structures in oxides are normally cubic (e.g. rock salt and perovskite structures), hexagonal, or tetragonal, as shown in Figure 7.1a–c, and for simple oxides such as ZnO, the intrinsically strong ionic and covalent bonds in Zn—O, Zn—Zn, or O—O make decoupling the electrical and thermal properties difficult. Besides, the low solubility of other dopants in simple oxides limits the optimization of carrier concentration, which is possibly led by strong bonding between adjacent atoms and the small number of available sites for dopants. However, complex oxides with layered structures assembled by atoms with different valence orbitals and other physical properties have been an efficient avenue to decouple the contradictions in oxide-based thermoelectrics. Through previous work on relaxation time approximation [2], we realize that point defects, enormous boundaries, and Umklapp process make a contribution to phonon scattering; even a normal process would affect phonon distribution, and the kinds of atoms and the crystal structure they constitute dominate the thermal conductivity. Therefore, complex structures, more kinds of atoms and big quantities in unit cell, and less bond strengths between atoms would lead to lower thermal conductivity. Besides, according to Eq. (7.1), which is described by Dulong–Petit’s law, C = 3R , R is the gas constant and M the average atom mass. M The heavier mean atom mass will result in a much lower heat capacity C. Simple oxides such as ZnO and NiO are not easy to reduce thermal property, but complex oxides that have layered structure and various atoms would have more potential, as shown in Figure 7.1d; layered BiCuSeO-based materials have ultra-low 𝜅 L . Therefore, to explore oxide-based materials with complex structure, enormous and heavy atoms can be an experimental strategy. Many researchers have found that the ultra-low heat conduction of amorphous solids arises from phonons whose mean phonon free path (lph ) is comparable to interatomic spacing. With ultra-low thermal conductivity, the comprehensive figure of merit would enhance and further be a candidate for future application. However, when it comes to electrical properties, complex oxides are not easy to transport carriers as a large number of obstacles exist among the structure, and to find proper ways to solve this problem is still a big challenge for researchers.

7.2 History of Complex Superconductors Layered rare-earth copper oxides have been known as high-temperature superconductors [3, 4]. These compounds have one or more two-dimensional CuO2 planes in a unit cell. The anisotropy of the conduction is very strong as a result of the layered structure. Yamanaka et al.’s research demonstrates that the

7.2 History of Complex Superconductors

c

c b

a

b

a

O Ca Mn

O Zn

(a)

(b) c

30 κL (W m–1 K–1)

a

40 b

O Bi Cu Se (c)

ZnO CaMnO3 BiCuSeO

20 10 4 3 2 1 0

(d)

300 400 500 600 700 800 900 1000 T (K)

Figure 7.1 The crystal structure of (a) some simple wurtzite oxide-based materials: ZnO (P63mc), (b) CaMnO3 (Pbnm), and (c) BiCuSeO (P4/nmm); (d) the lattice thermal conductivity (𝜅 L ) of ZnO, CaMnO3 , and BiCuSeO [2].

2-1-4-type layered rare-earth copper oxides, for example RE2 CuO4 , where RE is neodymium, samarium, or gadolinium, can be developed as thermoelectric materials. However, inferior electrical properties and high thermal conductivity require more strategies to be introduced to improve the thermoelectric performance. Different from RE2 CuO4 (RE: Nd, Sm, or Gd), the electrical transport properties of La2 CuO4 and La1.96 M0.04 CuO4 (M: Mg, Ca, and Sr) at high temperature have been investigated, and all of these La2 CuO4 -based materials show a high positive Seebeck coefficient (∼100–510 mV K−1 ), and the highest ZT value of the Sr-doped sample of about 0.06 can be achieved. Further work done by Liu et al. [5] utilizes dopants, including Pr, Y, and nb, to enhance the electrical properties of La2−x Rx CuO, and a large thermoelectric power ∼0.1 μW cm−1 K−2 and evaluated ZT of about 0.17 at 330 K can be achieved as a result.

157

158

7 Promising Complex Oxides for High Performance

7.3 Ternary Oxyselenides In recent years, with layered crystal structure, n-type Bi2 O2 Se has attracted much attention worldwide. To have this ternary compound with the composition of Bi2 O2 Se, we can substitute oxygen atoms for selenium atoms in Bi2 Se3 . Bi2 O2 Se is composed of alternate stack layers including the insulating [Bi2 O2 ]2+ layer and the conductive [Se]2− layer, which can be seen in Figure 7.2 [6, 7]. In this naturally formed superlattice-like structure, high Seebeck coefficient (∼500 μV K−1 ) [8] was observed [9]. Besides, the layered structure, which can weaken the bonding between atoms, is beneficial for good thermoelectric performance. The weakened bonding can hamper the transport of phonon. However, the electrical conductivity of its pristine sample is too low to be a good thermoelectric material (ZT < 0.1), which is primarily due to its intrinsically low carrier concentration (about 1015 cm−3 ) [7]. Therefore, a series of systematic research has been conducted to search for the possible mechanisms to boost the electrical conductivity of the potential Bi2 O2 Se-based thermoelectric materials. 7.3.1

Donor Doping on [Bi2 O2 ]2+ Layers

For an n-type Bi2 O2 Se, substitution of Bi3+ ions by Sn4+ ions could result in higher carrier concentration and enhancement of electrical conductivity. Hence, the results of Sn doping on the thermoelectric performance of Bi2 O2 Se have been investigated in detail. A typical spectrum of the Bi1.9 Sn0.1 O2 Se sample is shown in Figure 7.3. It can be shown that the Sn 3d5/2 and 3d3/2 are located at 486.6 and 495 eV, which suggests that Sn shows the +4 valence state [10]. For the doped samples, with increasing Sn contents, it is observed that there is an obvious increase in the electrical conductivity, which can be seen in Figure 7.4a. In the sample with 10% Sn, the highest electrical conductivity of 57.33 S cm−1 is obtained, which is about 25 times higher than the pristine Bi2 O2 Se. Meanwhile, the Seebeck coefficient is decreased with increased amount of Sn, implying the increase of carrier concentration (Figure 7.4b). The phonon Figure 7.2 The structure diagram of Bi2 O2 Se. Bi O Se

c b

a

7.3 Ternary Oxyselenides

Figure 7.3 A typical core-level XPS spectrum of Sn 3d in Bi1.9 Sn0.1 O2 Se.

Sn 3d5/2 Intensity (a.u.)

3d3/2

500

496

492

488

484

Seebeck coefficient (μV K–1)

60 50 40 30 20 10 0 300

400

1.4

Lattice thermal cond. (W m–1 K–1)

Thermal conductivity (W m–1 K–1) (c)

500

600

700

1.2 1.0

–100 –200 –300 –400 –500 300

800

T (K)

(a)

400

500

600

700

800

700

800

T (K)

(b)

1.4

0.20

1.2 1.0

Pure Sn 5% Sn 7.5% Sn 10%

0.15

0.8 0.6 300

450 600 T (K)

750

ZT

Electrical conductivity (S cm–1)

Binding energy (eV)

0.10 0.05

0.8

0.00

0.6 300

400

500

600

T (K)

700

800

300 (d)

400

500

600

T (K)

Figure 7.4 The temperature dependence of (a) electrical conductivity, (b) Seebeck coefficient, (c) thermal conductivity, and (d) ZT value for Bi2−x Snx O2 Se.

159

160

7 Promising Complex Oxides for High Performance

scattering is intensified in the sample with x = 0.05 and the lowest thermal conductivity of 0.63 W mK−1 at 773 K (Figure 7.4c). Finally, the ZT value has been enhanced with a maximum value of ∼0.20 obtained at 773 K for the Bi1.9 Sn0.1 O2 Se sample (Figure 7.4d). 7.3.2

Donor Doping on [Se]2− Layers

Since the donor doping at Bi-site has contributed to enhanced thermoelectric performance of Bi2 O2 Se, the modification on conductive Se layers has later been considered to tune its thermoelectric properties. It demonstrates that chlorine can act as an efficient electron donor [7]. The electrical conductivity at room temperature boosts from 0.019 S cm−1 for the pure sample to 101.6 S cm−1 for the 1.5% Cl-doped sample, which drops significantly as the Cl content is further increased as shown in Figure 7.5a. The carrier concentration measured at room temperature turns from 1.50 × 1015 to 1.38 × 1020 cm−3 with increasing Cl dopant content to x = 0.015. When Cl− is doped into the Se2− -site, an extra electron carrier would be introduced to the Se layers, as presented by the defect chemistry reaction: Se2−

Cl− −−−−→ Cl⋅Se + e′

(7.1)

Furthermore, when the doping level is beyond the solution limit, the Bi12 O15 Cl6 secondary phase prohibits the increasing carrier concentration and thus the electrical conductivity. According to the small polaron hopping conduction theory, the excitation of intrinsic carrier is easily achieved in the Bi2 O2 Se1.985 Cl0.015 sample due to its lowest activation energy of 0.068 eV (Figure 7.5b). Although the secondary phase could lead to increased lattice thermal conductivity, the lowest 𝜅 l value of 0.56 W m−1 K−1 at 823 K of 1.5% Cl-doped Bi2 O2 Se originates from the intense phonon scattering by the point defect and enhanced grain boundaries scattering. It is noteworthy that Young’s modulus and sound velocities of Bi2 O2 Se are evidently lower than those of other typical oxides [11, 12] ranging from Gd2 Zr2 O7 , BaDyAlO5 , and Ba2 ErAlO5 to Ba2 YbAlO5 . Therefore, the intrinsically low thermal conductivity is closely related to weak bonding between atoms. As a result, both the improvement of the power factor and suppression of the thermal conductivity contribute to the enhancement of thermoelectric performance, and the highest ZT value of 0.23 at 823 K is achieved for the sample of Bi2 O2 Se0.985 Cl0.015 , which is 188% higher than that of pristine Bi2 O2 Se (Figure 7.6). 7.3.3

The Solid Solution of Bi2 O2 Se and Bi2 O2 Te

Bi2 O2 Te, a homologue of Bi2 O2 Se, has been reported to be a kind of potential n-type thermoelectric material recently [13]. Bi2 O2 Te has the same crystal structure as tetragonal Bi2 O2 Se (space group I4/mmm). The estimated band gap of Bi2 O2 Te is only about 0.23 eV, and the carrier concentration at room temperature can achieve 1.06 × 1018 cm−3 . For narrow-gap Bi2 O2 Te, moderate electrical conductivity of ∼75 S cm−1 can be obtained at mid-temperature (665 K). Therefore, it is possible to apply the strategy of Te doping of Se to Bi2 O2 Se in order to incorporate the fine electrical properties of Bi2 O2 Te into Bi2 O2 Se.

7.3 Ternary Oxyselenides

x=0 x = 0.01 x = 0.015 x = 0.02 x = 0.04

200

σ (S cm–1)

150 100 30 20 10 0 300

400

500

600

700

800

Temperature (K)

(a) 12

Activation energy

0.25

8

4

1.6

0.20 0.15 0.10

6

2

(b)

0.30

Ea(eV)

Ln (σT) (S cm–1 K)

10

0.05

x=0 x = 0.01 x = 0.015 x = 0.02 x = 0.04

2.0

2.4

0.00 0.01 0.02 0.03 0.04 x

2.8

3.2

1000/T(K–1)

Figure 7.5 The temperature dependence of (a) electrical conductivity; the fitting plots of the small polaron model along with the activation energy (E a ) are shown in the inset (b) for Bi2 O2 Se1−x Clx ceramics.

The optical absorption spectrum of the Bi2 O2 Se1−x Tex samples is shown in Figure 7.7a in which the absorption edge obviously moves from high energy to the low energy. Accordingly, the band gap of about 1.77 eV for pristine Bi2 O2 Se is continuously narrowed to about 0.78 eV for Bi2 O2 Se0.94 Te0.06 . As a result, the electrons in the valence band can jump across the band gap much more easily due to the narrowed band gap, and the electrical conductivity is thus higher because of more electrons (Figure 7.7b) [14]. As shown in Figure 7.8a, all the samples with Te substitution at Se-site have evidently higher electrical conductivity (𝜎) than the pristine Bi2 O2 Se in the entire measured temperature range. Consequently, for the sample of Bi2 O2 Se0.96 Te0.04 , the electrical conductivity boosts from 5.38 S cm−1 at 300 K to 24.95 S cm−1 at 673 K and then drops down, which implies a typical

161

7 Promising Complex Oxides for High Performance

0.25

Figure 7.6 The temperature dependence of ZT value for Bi2 O2 Se1−x Clx ceramics.

x=0 x = 0.01 x = 0.015 x = 0.02 x = 0.04

0.20

ZT

0.15 0.10 0.05 0.00 300

400

500

600

700

800

Temperature (K)

1.8

2.0

Band gap

Conduction band

Eg (eV)

1.6 1.4 1.2

(αhv)2 (eV)2

162

1.5

0.00

0.5

0.0 0.5 (a)

1.0 0.8

1.0

Conduction band

0.02

x Bi2O2Se Bi2O2Se0.98Te0.02 Bi2O2Se0.97Te0.03 Bi2O2Se0.96Te0.04 Bi2O2Se0.94Te0.06

0.04

Narrowing band gap – induced by Te substitution

0.06

+ Valence band

1.0

1.5

hv (eV)

2.0

Valence band

2.5 (b)

Figure 7.7 The optical absorption spectra of Bi2 O2 Se1−x Tex ceramics (a) with the band gap illustrated in the inset and the schematic figure of narrowed band gap (b).

semiconductor characteristic. Since the band gap of Bi2 O2 Se has been narrowed dramatically by Te substitution, more electrons can jump across the band gap and contribute to the electronic conduction. As a result, the carrier concentration of n-type Bi2 O2 Se has been boosted from 1015 to ∼1018 cm−3 , which is better for good thermoelectric material. According to the small polaron hopping mechanism, the Ea of pristine Bi2 O2 Se is 0.33 eV, while that of Bi2 O2 Se0.96 Te0.04 and Bi2 O2 Se0.94 Te0.06 reaches 0.14 and 0.15 eV, respectively, which indicates that the intrinsic excitation of electrons can be much more easily attained after Te substitution (Figure 7.8b). The maximum value of power factor of the sample of x = 0.04 can reach up to 296.99 μW K−2 m−1 . The temperature dependence of the total thermal conductivity (𝜅) for Bi2 O2 Se1−x Tex can be seen in Figure 7.9a. The total thermal conductivity decreases monotonously with the rising temperature, which suggests that the majority of thermal conductivity is the lattice thermal conductivity (𝜅 l ). As seen in Figure 7.9b, the lattice thermal conductivity is progressively suppressed

7.3 Ternary Oxyselenides

Bi2O2Se

25

Bi2O2Se0.98Te0.02 Bi2O2Se0.97Te0.03

20 σ (S cm–1)

Figure 7.8 The temperaturedependent electrical conductivity (a); the fitting plot of the electrical conductivity by the small polaron model along with the activation energy (E a ) is shown in the inset (b).

Bi2O2Se0.96Te0.04 Bi2O2Se0.94Te0.06

15 10 5 0 400

300

500

600

700

800

Temperature (K)

(a)

8

6 Activation energy

0.35 0.30

4

Bi2O2Se Bi2O2Se0.98Te0.02 Bi2O2Se0.97Te0.03 Bi2O2Se0.96Te0.04 Bi2O2Se0.94Te0.06

Ea (eV)

Ln (σT) (S cm–1K)

10

0.25 0.20 0.15

2 1.2 (b)

0.00

0.02 x 0.04

1.6

0.06

2.0

2.4

2.8

1000/T (K–1)

by increasing Te substitution. This decrease is explicitly caused by the point defects, which is induced by Te substitution. As Te2− enters the Se2− -site, the mass and size difference causes the lattice distortion and thus intensification of the phonon scattering, which declines the 𝜅 l . It has been proved that the mean free path of phonon for pristine Bi2 O2 Se (∼12.7 Å) is almost the same with the lattice constants of Bi2 O2 Se (a = b = 3.891 Å and c = 12.213 Å) (Figure 7.9c). Therefore, the point defects in the lattice can scatter a great amount of heat-carrying phonons of similar size. Consequently, the continuous decline of lph for Bi2 O2 Se0.94 Te0.06 decreases the 𝜅 l . Both the electrical conductivity and the thermal transport properties have been optimized. And the thermoelectric performance of Bi2 O2 Se is thus enhanced. Finally, the highest ZT value reaches 0.28 at 823 K for Bi2 O2 Se0.96 Te0.04 , which is almost two times higher than that of the pristine Bi2 O2 Se (Figure 7.10a). Figure 7.10b compares the ZT values of Bi2 O2 Se0.96 Te0.04 and those of other Bi2 O2 Se-based thermoelectric materials [7, 8, 10, 14, 15], which shows that the thermoelectric performance of Bi2 O2 Se with Te substitution is very competitive in other reported works (Figures 7.7–7.10).

163

7 Promising Complex Oxides for High Performance

1.4

Bi2O2Se0.96Te0.04

1.6 κl (W m–1 K–1)

κ (W m–1 K–1)

1.6

Bi2O2Se Bi2O2Se0.98Te0.02 Bi2O2Se0.97Te0.03

L (×10–3 W Ω K–2)

1.8

1.8

Bi2O2Se0.94Te0.06

1.2 1.0 0.8

1.4 1.2

1.62 1.60 1.58 1.56 1.54 1.52 1.50 300 400 500 600 700 800 Temperature (K)

1.0 0.8

300 (a)

400 500 600 700 Temperature (K)

800

300 (b)

Phonon MFP (Å)

13.5

400 500 600 700 Temperature (K)

800

At room temperature

13.0 12.5 12.0 11.5 11.0 10.5 10.0

(c)

0.00 0.01 0.02 0.03 0.04 0.05 0.06 Te content (x)

Figure 7.9 The temperature dependence of the total thermal conductivity (a) and the lattice thermal conductivity (b); the room-temperature phonon mean free path (lph ) as a function of Te content for Bi2 O2 Se1−x Tex ceramics (c). 0.30

0.20

0.15

0.15

0.10

0.10

0.05

0.05

0.00

0.00 300

(a)

0.25 ZT

0.20

400 500 600 700 Temperature (K)

Bi2O2Se0.96Te0.04 Bi2O2Se0.985Cl0.015 Bi1.90O2Se Bi1.90Sn0.10O2Se Bi2O2Se/5 vol.% Ag

0.30

Bi2O2Se Bi2O2Se0.98Te0.02 Bi2O2Se0.97Te0.03 Bi2O2Se0.96Te0.04 Bi2O2Se0.94Te0.06

0.25 ZT

164

800

300 (b)

400

500 600 700 Temperature (K)

800

Figure 7.10 The temperature-dependent ZT values for Bi2 O2 Se1−x Tex ceramics (a); the comparison of ZT values of Bi2 O2 Se0.96 Te0.04 and those of other Bi2 O2 Se-based thermoelectric materials (b).

7.4 Quaternary Oxyselenides In recent years, quaternary oxychalcogenides MCuOCh (M = lanthanide ion or Bi; Ch = chalcogen ion) with the layered crystal structure have shown unique optoelectronic and thermoelectric properties due to their special crystal as well as electronic structures [16]. As shown in Figure 7.1c, BiCuSeO-based materials

7.4 Quaternary Oxyselenides

Table 7.1 Measured and estimated bond lengths in BiCuSeO and LaCuSeO. Bond

d (Å)

dc + da (Å)

Diff. (%)

−9.4

BiCuSeO Bi—O

2.33

2.57

Bi—Se

3.23

3.15

2.5

Cu—Se

2.51

2.58

−2.5

La—O

2.38

2.56

−7.2

La—Se

3.33

3.14

6

Cu—Se

2.52

2.58

−2.2

LaCuSeO

belong to oxychalcogenides and their crystal structure is tetragonal, and the space group is P4/nmm. Regardless of the wide band gaps, the hole concentration modulated from 1018 to 1021 cm−3 , and the possibility to synthesize numerous materials having similar ions but containing different ions makes oxychalcogenides the promising thermoelectric materials. For the band structure of this system, the p-type electrical transport properties, including positive Seebeck coefficient and Hall coefficient, combined with first-principle calculations demonstrate that CuCh layers rather than MO layers determine the electrical properties, and Cu 3d, Ch p orbitals mainly control the valence band maxima (VBM). As one of the most promising branch of oxychalcogenides for thermoelectric application, the Ch in oxyselenides is defined as selenium, and all together would be MCuOCh (M = Bi, La; Ch = Se). Previous work demonstrated by Hiramatsu et al. showed that the Cu-sites in MCuFCh (M = Sr, Eu) are less than 1.0, further indicating that both LaCuOSe and BiCuOSe contain Cu vacancies, which generate mobile holes and lead to p-type conduction. For bond types in oxyselenides, the nature of the chemical bonds can be assessed by the lengths. In an ideal situation, the measured bond length (d) of ionic bond is close to the estimated bond length (dc + da ), which is calculated by the sum of the ionic radii of a cation (dc ) and the neighbored anion (da ). As seen in Table 7.1, for Cu—Se bonds in both systems, the measured bond lengths agreed well with the estimated values and thus they were reasonably explained by the ionic radii. However, the estimated values were much longer than the measured Bi—O and La—O bond lengths, which is possibly caused by the reason that the Bi—O and La—O bonds have greater covalent character than that of the Cu—Se bonds. Besides, the long bond lengths of La—Se and Bi—Se also show that the bonds between them seem rather weak, which means that the force between the MO and CuCh layers is less when compared with these bonds inside layers. This special layered structure is similar to superlattice in 2D films to some extent, which would affect the electrical transport properties effectively. As for the electronic structures (Figure 7.11), oxyselenides have similar VBM electronic structures, but different from LaCuSeO, where CBM is mainly

165

7 Promising Complex Oxides for High Performance

p(Bi)

0

d(Cu)

EF

p(Se)

–0.5

–1.0

Energy (eV)

166

–1.5

–2.0 7 (a)

6

5

4

3

2

DOS (states/eV)

1

Γ

0

X

M

Γ Z

R

(b)

Figure 7.11 (a) Projected DOS and (b) electronic band structure of BiCuSeO (P4/nmm). Source: Zhao et al. 2014 [17]. Reproduced with permission of RSC.

composed of Cu 4s orbitals with smaller contributions from the La 5d orbitals; the effect of Bi 6p orbitals for CBM of BiCuSeO is rather significant, and the deeper CBM in BiCuSeO is the primary cause of the smaller band gaps of BiCuSeO relative to those of LaCuSeO. The relatively smaller band gap even makes BiCuSeO one of the promising thermoelectric materials. 7.4.1

Thermoelectric Properties

Most recently, BiCuSeO oxyselenide has been reported to have low intrinsic thermal conductivity with tunable electrical transport properties. The highest ZT it can achieve is 1.4 at 923 K (Figure 7.12) [17]. BiCuSeO is composed of conductive (Cu2 Se2 )2− layers and alternately stacked (Bi2 O2 )2+ along the c-axis of a tetragonal cell. In the entire temperature range of measurement, the electrical conductivity at room temperature (about 1 S cm−1 ) is much lower than those of the state-of-the-art thermoelectric materials. BiCuSeO has low thermal conductivity (∼0.40 W m−1 K−1 ) at 923 K, and it can be even further decreased by other methods such as nanocomposites. For BiCuSeO, the very low thermal conductivity and high Grüneisen parameter (𝛾) value of 1.5 contribute to the increased bond anharmonicity associated with the occurrence of trivalent Bi. Besides, because of the presence of the layered structure, phonons can be confined in the layers and scattered at the layer interfaces. And also group velocity for the phonons was limited as a result of the presence of heavy elements. Lan et al. found that doping with heavy elements can increase phonon scattering and also introduce nanocomposites simultaneously [20]. Highly efficient phonon scattering was caused by large amount of nanodots with the size of 5–10 nm. Therefore, the thermal conductivity was further decreased. High electrical conductivity combined with low thermal conductivity leads to significantly enhanced ZT value (about 1.14 at 823 K).

7.4 Quaternary Oxyselenides

1.5

140% enhancement

ZT ∼1.2 1.2

BiCuSeO -Ref. [18] Pb0.04 Pb0.04-Te0.025 Pb0.04-Te0.05 Pb0.04-Te0.075 Pb0.04-Te0.1

0.9 ZT

Figure 7.12 Recent progresses of BiCuSeO (ZT): (a) Pb/Te codoped BiCuSeO; (b) high-temperature maximum ZT comparison for BiCuSeO-based materials. Source: Ren et al. 2017 [19]. Reproduced with permission of RSC.

ZT ∼0.5

0.6

0.3

0.0 300

400

500

600

700

800

900

1000

T (K)

(a) 1.80

1.5 @ 873 K

0.00 (b)

∼1 h

24 h 24∼48 h 48 h

Bi0.875Ba0.125CuSeO-Ref. 25

Bi0.875Ba0.125CuSeO -Ref. 26

0.7 @ 773 K

BiCuSeO -Ref. 64

0.45

[19]

1.2 @ 873 K

1.2 @ 873 K 1.2 @ 873 K

1.0 @ 873 K Bi0.875Ba0.125CuSeO -Ref. 14

0.90

Bi0.94Pb0.06CuSeO -Ref. 65

ZT

1.1 @ 823 K

Bi0.88Ca0.06Pb0.06CuSeO -Ref. 11

1.35

>48 h

Time (h)

Li et al. found that BiCuSeO with Ca substitution shows great thermoelectric performance. It exhibited ultra-high electrical conductivity at room temperature. Meanwhile, stable low thermal conductivity was kept in comparison with the pristine BiCuSeO [21], which is caused by the decreased grain size. It is estimated that the effective mass of undoped BiCuSeO is about 1.1 me . After doping with K, the effective mass changes to about 0.4 me because the Fermi level moves deep into the second valence band. And thus the effective mass of K-doped BiCuSeO is composed of heavy and light hole bands. As a potential thermoelectric material, BiCuSeO plays a very important role among oxides. However, there are only a few reports based on this material. Therefore, focusing on the new strategy of developing high-performance BiCuSeO should be paid much more attention. To shed more light on the optimized properties for this material system, strategies including band gap tuning, modulation doping, texturing, and nanocompositing will be discussed in the following sections.

167

7 Promising Complex Oxides for High Performance

7.4.2

Band Gap Tuning

Recently, several works focusing on band gap tuning have been reported, and one is using Te doping on Se-site to introduce BiCuSeO–BiCuTeO compositing, as these two material systems are in the same structure [22], and another is Bi replacements by La to utilize LaCuSeO–BiCuSeO solid solution (Figure 7.13) [23]. The band gaps have been tuned with Te substitution at Se-sites, and the electronic structure within the (Bi2 O2 )2+ layer has been significantly affected by the replacements based on the first-principle calculations. A high ZT of 0.71 at 923 K is achieved by both low thermal conductivity and tunable power factor by Te substitution, further indicating that this strategy is highly efficient. Besides, Bi1−x Lax CuSeO ceramic bulks have also been synthesized, and the results have shown that the band structure of BiCuSeO has been largely changed by La doping, which can be evidenced by the absorption spectra and the electric transportation behaviors (e.g. m* and Seebeck coefficient). The offset between the primary and secondary valence bands is decreased, and thus the carrier mobility is enhanced largely. As a result, the highest ZT value of 0.74 can be obtained at 923 K for the sample of 8% La-doped BiCuSeO. In summary, tuning the band structure of BiCuSeO could be an effective method to improve the thermoelectric properties of p-type BiCuSeO. All these works together reveal that the strategy to tune band gap and structure is an effective way for the enhancements of the thermoelectric properties in BiCuSeO system. 7.4.3

Texturing

For BiCuSeO, the carrier concentration can be optimized by doping via tuning the carrier concentration; however, the intrinsically low carrier mobility induced by strong bonding between atoms, and the enhanced scattering for carrier transport,

CB

CB

x Band gap decreasing – eV

+

0.80

0.65 eV 0.72 eV

0.40 e

0 0.06 0.1 0.2 1.0

V

BiCuSe1–xTexO

α/S (a.u.)

168

VB

VB

(b) 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (a)

Energy (eV)

Figure 7.13 (a) Electronic absorption spectra of BiCuSe1−x Tex O samples and (b) the schematic figure for band gap tuning. CB, conduction band and VB, valence band.

7.4 Quaternary Oxyselenides

including scattering from lattice distortions and ionized (or neutral) impurities, makes the carrier mobility reduce more, and all together lead to vigorous limitations for further improvements. Therefore, to find a way to enhance the mobility while maintaining the optimized carrier concentration is significant for further enhancements of thermoelectric performance in this material system. Considering that oxyselenides crystallize in a layered crystal structure, it is believed that the electrical and thermal transport in the BiCuSeO-based material should be anisotropic. The fact that carrier mobility in the in-plane much higher than that in the out-of-direction plane can be expected, which could be similar to the transport phenomenon observed in layered Bi2 Te3 and CaCoO3 compounds. A promising strategy to further enhance the thermoelectric performance would be making use of anisotropy and introducing textures by applying a hot-forging process, further improving the carrier mobility. The textured microstructure, which has preferred grain orientation, has been obtained in Bi0.875 Ba0.125 CuSeO prepared by a hot-forging process (Figure 7.14) [24]. After the hot-forging process, the carrier mobility perpendicular to the pressing direction was significantly increased. As a result, the electrical conductivity was largely enhanced, and thus the power factor at 923 K was increased from 6.3 to 8.1 mW cm−1 K−2 after the process of texturing. Although the total thermal conductivity was increased after the process, this increment was compensated by the largely improved electrical conductivity, and finally a maximum ZT of 1.4 at 923 K has been achieved for Bi0.875 Ba0.125 CuSeO after texturing. 7.4.4

Modulation Doping

In addition to texturing for enhancing carrier mobility, modulation doping (MD) is widely studied and used in two-dimensional electron gas (2DEG) devices. The carrier mobility can be improved by this method. An MD device is usually composed of two layers. The doped layer provides charge carriers, and the undoped layer is usually treated as the charge transport channel. Moreover, the MD approach has been revealed to be effective not only for 2D film structures, but also for three-dimensional (3D) bulk structures (e.g. Si1−x Gex ) recently. Therefore, applying the MD approach for BiCuSeO system could be a promising strategy and has been investigated by Pei et al. recently [25]. The carrier mobility can be significantly improved and thus the thermoelectric performance (Figure 7.15). With the modulation-doping approach, the carrier concentration does not change much, but the higher carrier mobility is obtained as compared to the pristine one. The charge carriers prefer transporting in the area with low carrier concentration in the heterostructures of doped sample, which increases the carrier mobility. Benefitting from the improved electrical conductivity and retained high Seebeck coefficient, a high power factor is obtained. Together with the low thermal conductivity of about 0.25 W m−1 K−1 , the highest ZT value of 1.4 can be obtained at 923 K in this modulation-doping BiCuSeO system.

169

(a)

(b)

001

Count (%)

20

2 μm

(d)

10

30 Count (%)

(e)

30

0 0

2 μm

010

(c)

40

1 2 3 4 Grain size (μm)

5

110 (g)

(f)

010

20

001

10 0 0

1 2 3 4 Grain size (μm)

5

(h)

Count (%)

30

2 μm

110

10 0 0 15

(k)

1 2 3 4 Grain size (μm)

010

5

(m)

(l) Count (%)

5 μm

(j)

(i) 20

001

10 5 0 0

(n) 1 2 3 4 Grain size (μm)

Figure 7.14 EBSD microstructures of textured Bi0.875 Ba0.125 CuSeO.

5

110

7.4 Quaternary Oxyselenides

Pristine BiCuSeO

Modulation doping (b)

(a)

Uniformly doping (c)

Car

riers

CB

CB

CB

EF

EF

VB

VB

VB

Figure 7.15 Three-dimensional schematic showing the band structures and Fermi energy levels for the pristine BiCuSeO, modulation-doped Bi0.875 Ba0.125 CuSeO (50% BiCuSeO + 50% Bi0.75 Ba0.25 CuSeO), and uniformly doped Bi0.875 Ba0.125 CuSeO.

7.4.5

Nanocompositing

The importance of making nanostructures in oxide-based thermoelectric materials has been discussed in Chapter 2; however, to introduce nanostructures or nanograins in BiCuSeO is still a challenge. Other than the ball milling process, a new preparation process called self-propagating high-temperature synthesis (SHS) has been developed for thermoelectric materials recently. Rich multiscale microstructures can be found in thermoelectric materials by the nonequilibrium recipes. As compared with the preexisting methods for designing all-scale structures, such as melt-quenching or solid-state reaction, SHS is energy and time saving. Besides, four-element BiCuSeO possesses more sites to import point defects, and large possibilities to produce second phases than binary alloys to design nanocompositing and all-scale structures for scattering phonons of wide frequency range in this system could be easier by the SHS processes (Figure 7.16). BiCuSeO material system has been synthesized successfully by SHS in recent years [18, 27], and a lot of new microstructures have been indicated. Based on this method, further with substituting Te on Se-site and Pb for Bi-site, all-scale hierarchical structures can be created by a combination of dual point defects, Cu2 Sex nanodots, Cu7 Te4−x Sex nanoinclusions, and mesograins, which effectively reduces the lattice thermal conductivity to ∼0.3 W m−1 K−1 for Bi0.96 Pb0.04 CuSe0.95 Te0.05 O at 873 K. Meanwhile, to some extent this structuring engineering has reduced the carrier concentrations from compositing effect with multiphase in the BiCuSeO system, but Te doping obviously enhanced the carrier mobility from 4 to 11 cm2 V−1 s−1 . Therefore, high power factors of Bi0.96 Pb0.04 CuSeO are retained for the codoped samples. Ultimately, a high ZT value of ∼1.2 at 873 K could be achieved in 4% Pb to 5% Te codoped BiCuSeO.

171

500

Main phase

Phonon

T (K) 600

700

Single crystal τMesoscale

Cu7Te4-xSex inclusion

τMesoscale + τNano

Cu2Sex nanodot

τMesoscale + τNano + τPoint defects

900

Total Bi Cu Se O

0.30

10

0.25

8

0.20

Nanoinclusions + Nanodots

κL

Phonon

800

0.15

Phonon

Mesoscale

T –1

Point defects

0.10 0.05

Point defects 0 (a)

60

4 2

0.00

2 (c)

1.0

3

4

5

6 7 Te (%)

5.0

0.7 0.6

0.6

900

800

T (K)

700

600

500

400

0.4

300

0.5

0.7

Kmin

0.5 0.4

BiCuSeO -Ref.2 Pb0.04 Pb0.04-Te0.025 Pb0.04-Te0.05 Pb0.04-Te0.075

0.3 300

400

500

0.9

600 T (K)

700

κL (W m–1 K–1)

0.8

4.8 4.6 4.4 4.2

800

900

0.8 0.7

10

0.6 0.5

0.3 0

(e)

9

0.4

4.0

Pb0.04-Te0.1

8

303 K 373 K 473 K 573 K 673 K 773 K 873 K

1.0

0.8

Iph

0.9

Iph

5.2

0.9

(10–1nm)

κ (W m–1 K–1)

1.0 κL (W m–1 K–1)

50

6

5.4

1.1

(d)

40 20 30 Frequency (cm–1)

10

(b)

Theory Experimental

Te content (%)

400

DOS of phonons

300

2

4 6 Te (%)

8

10

Minimum KL PureRef.2 Pb0.04 Pb0.04Te0.025 Pb0.04Te0.05 Pb0.04Te0.075 Pb0.04Te0.01

(f)

Sample

Figure 7.16 (a) The schematic diagram of all-scale hierarchical structures in BiCuSeO. (b) The density of states (DOS) of phonons for BiCuSeO, adapted from the literature [26] and contributions of different mechanisms (𝜏) to the decrease of calculated 𝜅 L value by the Debye–Callaway model. Phonons with low, medium, and high frequencies can be scattered by mesoscale grain boundaries (red background), nanodots or nanoinclusions (green background), and point defects (blue background), respectively. (c) The theoretical and experimental Te atom content achieved from EDS. (d) The lattice thermal conductivity; the inset graph is the total thermal conductivity. (e) The mean free path (lph ) of Te/Pb codoped samples and (f ) Pb/Te-content-dependent lattice thermal conductivity at different temperatures.

7.5 Complexity Through Disorder in the Unit Cell

Besides, it is noteworthy that most of the materials with high ZTs (over 1) were synthesized by time-consuming (>1 d) and energy-intensive techniques [20, 24, 25, 28–31]. Nevertheless, considering the error range of measurement, the highest ZT value of Bi0.96 Pb0.04 CuSe0.95 Te0.05 O could also be ∼1.4 at 873 K, and the time- and energy-saving synthesis (∼1 hours) can also produce high-performance BiCuSeO ceramics, making SHSed Pb/Te codoped BiCuSeO a promising candidate for large-scale commercial applications.

7.5 Complexity Through Disorder in the Unit Cell The unit cell of ABO3 within three kinds of atoms is normally called perovskite structure; however, Ca–Co–O- or Na–Co–O-based materials are in layered structure [32, 33], as shown in Figure 7.17, and based on it, the disorder between layers as well as intralayers optimized by other elements further increases the complexity. Along the c-axis direction, Ca3 Co4 O9 is composed of alternative layers of a distorted CaO–CoO–CaO layer and CoO2 layer, and it has been widely studied [34, 35]. The lattice parameters of a, c, and 𝛽 are almost the same for these two layers; however, the lattice parameters of b are quite different. The first-principle calculations suggested that there were two-dimensionally dispersive eg bands across the Fermi energy included in the electronic structures of the misfit-layered Ca3 Co4 O9. It has been proved in the previous studies that partial substitutions by Bi3+ , Gd3+ , and Na+ in Ca3 Co4 O9 could be beneficial to the electrical conductivity and thus the thermoelectric properties. Lybeck et al. [36] reported that c-axis-oriented Ca3 Co4 O9 thin films could be prepared by atomic layer deposition (ALD) technique. The high Seebeck coefficient is as high as about 130 μV K−1 , which is even competitive with those Co2 CoO2 (a)

(b)

Co1 Ca2CoO3 c a

c a

b

Ca:

Co:

O:

Figure 7.17 Diagram of the crystal structure of Ca3 Co4 O9 perpendicular to (a) the a-axis and (b) the b-axis. The Co1 and Co2 sites indicated refer to the Co atoms from the Ca2 CoO3 layer and the CoO2 layer, respectively.

173

174

7 Promising Complex Oxides for High Performance

of the single-crystal samples. In single-crystal (Ca2 CoO3 )0.7 CoO2 , which has a Ca3 Co4 O9 structure, Seebeck coefficient is about 240 μV K−1 , and electrical resistivity of 230 μΩ cm can be obtained at 973 K. For Ca3 Co4 O9 /Ag composites, the electrical conductivity of the composite increases with the additional second phase of Ag over the entire temperature range that is measured. It can be concluded from the SEM results that Ag nanophases have been formed in the Ca3 Co4 O9 matrix, which provides more ways for carriers to transport. Even though there is no data about the thermal conductivity of Ca3 Co4 O9 /Ag composites, the thermal conductivity is believed to be decreased by more phonon scattering. Besides, a recent study showed that nanocrystalline Ca3 Co4 O9 ceramics can also be prepared by a novel technique. The ceramics are prepared by sol–gel-based electrospinning followed by SPS. The electrical transport and thermal transport properties can be optimized because of the existence of smaller grain size and texture. Compared with La-doped Ca3 Co4 O9 ceramics that are synthesized with the traditional method, even pure Ca3 Co4 O9 ceramics prepared by this novel technique have substantially lower thermal conductivity, which can lead to 55% enhancement of ZT (ZT ∼ 0.40 at 975 K).

7.6 Complex Unit Cells Unlike oxides with the single perovskite structure (e.g. CaMnO3 or SrTiO3 ), YBaCuFeO5+𝛿 was firstly reported to be synthesized and studied as a new double perovskite-like oxide by Er-Rakho et al. [37] This kind of material has a general formula of A′ A′′ B2 O5+𝛿 , where A′ is a rare-earth element, A′′ is an alkaline-earth element, and B is a transition metal element. The pyramid structure is constituted by B-site atoms and oxygen atoms to connect the basic frame, with the A-site atoms arranging into it. As seen in Figure 7.18, composed of B Figure 7.18 The structure diagram of SmBaCuFeO5+𝛿 .

c a

b Sm Ba Fe Cu O

7.6 Complex Unit Cells

(e.g. Cu, Fe) site atoms and oxygen atoms, the basic pyramid structure forms the main structure, and A (e.g. Sm) site atoms go through the frame to make up the border. The crystal structure has the structure of tetragonal with a space group P4mm or P4/mmm, while LaBaCuFeO5+𝛿 has a cubic structure with a space group Pm3m [38]. The electrical properties and thermal transport properties of A′ A′′ B2 O5+𝛿 -type materials have been studied worldwide in recent years. Roy et al. [39] have reported that oxygen vacancy 𝛿 can control the spin state of Co in RBaCo2 O5+𝛿 ; Suescun et al. [40] have pointed out that the structure is connected with the magnetic properties of LaBaCoCuO5+𝛿 . Besides, the electrical and thermoelectric properties of RBaCuFeO5+𝛿 have been studied by Klyndyuk et al. [38]. Although there are only a few systematical studies related with the high-temperature thermoelectric properties of layered A′ A′′ B2 O5+𝛿 , it should be noticed that its potential for thermoelectric applications is still huge. GdBaCuFeO5+𝛿 , a member of A′ A′′ B2 O5+𝛿 family, is shown to have a relatively high Seebeck coefficient (about 230 μV K−1 ) at high temperature, and its thermal conductivity is quite low (about 2.5 W m−1 K−1 ), but its poor electrical conductivity limits its thermoelectric properties [41]. Previous work showed that La substitution can narrow the band gap, and thus effectively enhance the electrical conductivity. The thermoelectric properties of La-substituted GdBaCuFeO5+𝛿 ceramics prepared by different methods (sol–gel method and traditional method) could be improved. Specifically, the effect of La substitution on the phase composition, morphology, electrical transport properties, and thermal transport properties has been investigated. Both enhanced electrical conductivity and low thermal conductivity contribute to enhanced ZT values through La substitution, revealing a potential candidate for high-temperature thermoelectric applications. As a member of a large double perovskite-like family, SmBaCuFeO5+𝛿 (Figure 7.18) also has a moderate Seebeck coefficient but very poor electrical conductivity, which leads to low power factor and low ZT value of 0.02 [37, 42]. La-doped SmBaCuFeO5 polycrystalline ceramics have been synthesized through sol–gel method followed by solid-state sintering reaction. Significantly enhanced ZT values of SmBaCuFeO5 have been obtained by La doping. The results suggest that the La substitution could increase the electrical conductivity remarkably. The Seebeck coefficient decreases with increased amount of La content, which is consistent with the enhanced electrical conductivity. The existence of nanosized grains leads to the decreased thermal conductivity at room temperature from 2.1 to 1.7 W m−1 K−1 . Consequently, the highest ZT of 0.042 at 1023 K is obtained for the sample Sm0.6 La0.4 BaCuFeO5 , which is 13 times higher than that of the pristine sample [43]. Further research was conducted on Ag as an additive second phase to enhance the electrical conductivity. After adding Ag, 70-nm Ag particles precipitate on the grain boundaries. The electrical conductivity increases with the addition of Ag. The Seebeck coefficient decreases because of increased hole concentration. As a result, the highest ZT value of 0.047 has been obtained at 1023 K for the sample of SmBaCuFeO5+𝛿 /Ag 20 vol%, which is about 16 times higher than that of the pristine one.

175

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References 1 Snyder, G.J. and Toberer, E.S. (2008). Complex thermoelectric materials.

Nature Materials (7): 105–114. 2 Ren, G.-K., Lan, J.-L., Ventura, K.J. et al. (2016). Contribution of point defects

3

4 5

6 7

8

9 10

11

12 13

14

15 16

and nano-grains to thermal transport behaviours of oxide-based thermoelectrics. npj Computational Materials 2: 16023. Takagi, H., Uchida, S., and Tokura, Y. (1989). Superconductivity produced by electron doping in CuO2 -layered compounds. Physical Review Letters 62: 1197. Tokura, Y., Takagi, H., and Uchida, S. (1989). A superconducting copper oxide compound with electrons as the charge carriers. Nature 337: 345–347. Liu, Y., Lin, Y.-H., Zhang, B.-P. et al. (2009). High-Temperature Thermoelectric Properties in the La2−x Rx CuO4 (R: Pr, Y, Nb) Ceramics. Journal of the American Ceramic Society 92: 934–937. Ruleova, P. et al. (2010). Thermoelectric properties of Bi2 O2 Se. Materials Chemistry and Physics 119 (1–2): 299–302. Tan, X. et al. (2017). Enhanced thermoelectric performance of n-type Bi2 O2 Se by Cl-doping at Se site. Journal of the American Ceramic Society 100 (4): 1494–1501. Zhan, B. et al. (2015). Enhanced thermoelectric properties of Bi2 O2 Se ceramics by Bi deficiencies. Journal of the American Ceramic Society 98: 8, 2465–2469. Dresselhaus, M.S. et al. (2007). New directions for low-dimensional thermoelectric materials. Advanced Materials 19: 8, 1043–1053. Zhan, B. et al. (2015). High-temperature thermoelectric behaviors of Sn-doped n-type Bi2 O2 Se ceramics. Journal of Electroceramics 34 (2–3): 175–179. Kurosaki, K. et al. (2005). Ag9 TlTe5 : a high-performance thermoelectric bulk material with extremely low thermal conductivity. Applied Physics Letters 87 (6): 061919. Chiritescu, C. et al. (2007). Ultralow thermal conductivity in disordered, layered WSe2 crystals. Science 315 (5810): 351–353. Luu, S.D.N. and Vaqueiro, P. (2015). Synthesis, characterisation and thermoelectric properties of the oxytelluride Bi2 O2 Te. Journal of Solid State Chemistry 226: 219–223. Tan, X. et al. (2018). Synergistically optimizing electrical and thermal transport properties of Bi2 O2 Se ceramics by Te-substitution. Journal of the American Ceramic Society 101 (1): 326–333. Zhan, B. et al. (2015). Enhanced thermoelectric performance of Bi2 O2 Se with Ag addition. Materials 8 (4): 1568–1576. Hiramatsu, H., Yanagi, H., Kamiya, T. et al. (2007). Crystal structures, optoelectronic properties, and electronic structures of layered oxychalcogenides MCuOCh (M = Bi, La; Ch = S, Se, Te): effects of electronic configurations of M3+ Ions. Chemistry of Materials 20: 326–334.

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17 Zhao, L.-D., He, J., Berardan, D. et al. (2014). BiCuSeO oxyselenides: new

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23

24

25

26 27

28

29

30 31

32

promising thermoelectric materials. Energy and Environmental Science 7: 2900–2924. Ren, G.-K., Butt, S., Ventura, K.J. et al. (2015). Enhanced thermoelectric properties in Pb-doped BiCuSeO oxyselenides prepared by ultrafast synthesis. RSC Advances 5: 69878–69885. Ren, G.-K., Wang, S.-Y., Zhu, Y.-C. et al. (2017). Enhancing thermoelectric performance in hierarchically structured BiCuSeO by increasing bond covalency and weakening carrier–phonon coupling. Energy & Environmental Science 10: 1590–1599. Lan, J.L., Liu, Y.C., Zhan, B. et al. (2013). Enhanced thermoelectric properties of Pb-doped BiCuSeO ceramics. Advanced Materials 25: 5086–5090. Li, F., Wei, T.-R., Kang, F., and Li, J.-F. (2013). Enhanced thermoelectric performance of Ca-doped BiCuSeO in a wide temperature range. Journal of Materials Chemistry A 1: 11942–11949. Liu, Y., Lan, J., Xu, W. et al. (2013). Enhanced thermoelectric performance of a BiCuSeO system via band gap tuning. Chemical Communications 49: 8075–8077. Liu, Y., Ding, J., Xu, B. et al. (2015). Enhanced thermoelectric performance of La-doped BiCuSeO by tuning band structure. Applied Physics Letters 106: 233903. Sui, J., Li, J., He, J. et al. (2013). Texturation boosts the thermoelectric performance of BiCuSeO oxyselenides. Energy & Environmental Science 6: 2916–2920. Pei, Y.L., Wu, H., Wu, D. et al. (2014). High thermoelectric performance realized in a BiCuSeO system by improving carrier mobility through 3D modulation doping. Journal of the American Chemical Society 136: 13902–13908. Shao, H., Tan, X., Liu, G.Q. et al. (2016). A first-principles study on the phonon transport in layered BiCuOSe. Scientific Reports 6: 21035. Yang, D., Su, X., Yan, Y. et al. (2016). Manipulating the combustion wave during self-propagating synthesis for high thermoelectric performance of layered oxychalcogenide Bi1−x Pbx CuSeO. Chemistry of Materials 28: 4628–4640. Liu, Y., Zhao, L.D., Zhu, Y. et al. (2016). Synergistically optimizing electrical and thermal transport properties of BiCuSeO via a dual-doping approach. Advanced Energy Materials 6: 1502423. Li, F., Li, J.-F., Zhao, L.-D. et al. (2012). Polycrystalline BiCuSeO oxide as a potential thermoelectric material. Energy and Environmental Science 5: 7188–7195. Phillips, J. (2012). Bonds and Bands in Semiconductors. Elsevier. Li, J., Sui, J., Pei, Y. et al. (2012). A high thermoelectric figure of merit ZT > 1 in Ba heavily doped BiCuSeO oxyselenides. Energy and Environmental Science 5: 8543–8547. Butt, S., Xu, W., He, W.Q. et al. (2014). Enhancement of thermoelectric performance in Cd-doped Ca3 Co4 O9 via spin entropy, defect chemistry and phonon scattering. Journal of Materials Chemistry A 2: 19479–19487.

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33 Terasaki, I., Sasago, Y., and Uchinokura, K. (1997). Large thermoelectric

power in NaCo2 O4 single crystals. Physical Review B 56: R12685. 34 Masset, A., Michel, C., Maignan, A. et al. (2000). Misfit-layered cobaltite with

an anisotropic giant magnetoresistance: Ca3 Co4 O9 . Physical Review B 62: 166. 35 Morita, Y., Poulsen, J., Sakai, K. et al. (2004). Oxygen nonstoichiometry and

36

37

38 39

40 41

42

43

cobalt valence in misfit-layered cobalt oxides. Journal of Solid State Chemistry 177: 3149–3155. Lybeck, J., Valkeapaa, M., Shibasaki, S. et al. (2010). Thermoelectric properties of oxygen-tuned ALD-Grown [Ca2 CoO3 ]0.62 [CoO2 ] thin films. Chemistry of Materials 22: 5900–5904. Er-Rakho, L., Michel, C., Lacorre, P., and Raveau, B. (1988). YBaCuFeO5+δ : A novel oxygen-deficient perovskite with a layer structure. Journal of Solid State Chemistry 73: 531–535. Klyndyuk, A. and Chizhova, E. (2006). Properties of RBaCuFeO5+δ (R = Y, La, Pr, Nd, Sm-Lu). Inorganic Materials 42: 550–561. Roy, S., Dubenko, I., Khan, M. et al. (2005). Magnetic properties of perovskite-derived air-synthesized RBaCo2O5+δ (R=La, Ho) compounds. Physical Review B 71: 024419. Suescun, L., Jones, C.Y., Cardoso, C.A. et al. (2005). Structural and magnetic study of LaBaCoCuO5+δ . Physical Review B 71: 144405. Gao, F., Zhang, J., Song, H. et al. (2013). Thermoelectric properties of GdBaCo2−x Fex O5+δ ceramics. Journal of Materials Science: Materials in Electronics 24: 3095–3100. Kolesnik, S., Dabrowski, B., Chmaissem, O. et al. (2012). Comparison of magnetic and thermoelectric properties of (Nd,Ca)BaCo2 O5.5 and (Nd,Ca)CoO3 . Journal of Applied Physics 111: 07D727. Zeng, C., Liu, Y., Lan, J. et al. (2015). Thermoelectric properties of Sm1−x Lax BaCuFeO5 ceramics. Materials Research Bulletin 69: 46–50.

179

8 New Thermoelectric Materials and Nanocomposites The research for new thermoelectric materials and nanocomposites is vital to the thermoelectric community to resolve two contradictions: (i) the irreconcilable conflict of high electrical conductivity and high Seebeck coefficient; (ii) the conflict of the high electrical conductivity and low thermal conductivity because of the correlation by Wiedemann–Franz law, in the framework of condensed matter physics. The new nanocomposite and organic thermoelectric materials provide a high possibility to decouple the electrical conductivity and thermal conductivity and further improve the power factor (PF). According to the Bergman’s theorem, a homogeneous composite made of components of different Seebeck coefficient, electrical conductivity, and thermal conductivity functioning independently of each other cannot have a new ZT higher than the highest ZT of any single component [1]. However, when the composites interact with each other or one phase changes the scattering or the wave functions of the carriers in the other, this conclusion is not applicable. Furthermore, a large number of experimental and theoretical studies have shown that the thermoelectric (TE) performance of the composites can get further improved when the length scale of a system is comparable to its electron mean free path or wavelength because of the significant quantum-confinement effect and energy-filtering effect. In this case, the density of state increases, which leads to the improvement of the Seebeck coefficient. Conversely, the nanostructured surfaces or interfaces can intensify the scattering of phonons and then suppress the thermal conductivity [2–4]. This strategy has been demonstrated to be valid in low-dimensional materials including superlattices, nanowires, quantum dots, and thin-film systems [5–8]. Polymer TE materials have the advantages of low thermal conductivity, low cost, nontoxicity, and large-scale fabrication as compared with the best inorganic materials. Especially, the Wiedemann–Franz law is not applicable for the organic–inorganic composite due to the larger thermal resistance at the interface between the inorganic and the polymer materials. Therefore, the organic–inorganic composite can gain high electrical conductivity (>2000 S cm−1 ) and low thermal conductivity (900 S cm−1 [22].

Table 8.1 Chemical structures of a few typical conductive polymers. Materials

Chemical structure

Polyaniline: leucoemeraldine (y = 1), emeraldine (y = 0.5), and pernigraniline (y = 0)

O

N H

y

N

N

H

H1– y

S

n

n

trans-Polyacelylene

O

S

n

n

Polypyrrole

Poly(para-phenylene) N

n n

H

Poly(2,7-carbazolylenevinylene)

Chemical structure

Polythiophene N H

Poly(3,4-ethylenedioxythiophene)

Materials

C6H13

H13C6

N C6H13 Source: Du et al. 2012 [17]. Reproduced with permission of Elsevier.

n

Poly(para-phenylene vinylene) n

186

8 New Thermoelectric Materials and Nanocomposites

O

*

O

* n

S *

n

S O

*

O

(a)

(b)

SO3–

(c)

Figure 8.6 Molecular structures of (a) poly(3,4-ethylenedioxythiophene) (PEDOT), (b) tosylate (tos), and (c) poly(styrenesulfonate) (PSS).

SO3–

Table 8.2 Thermoelectric properties of different Clevios PEDOT products. Electrical conductivity (S cm−1 )

Seebeck coefficient (𝛍V K−1 )

Clevios p (5% DMSO)

81.9

12.6

1.28

Clevios PH500 (5% DMSO)

317

22.5

16.05

Power factor (𝛍W m−1 K−2 )

Clevios PH1000 (5% DMSO)

945

22.2

46.57

Clevios FET

320

30.3

29.39

Source: Zhang et al. 2010 [22]. Reproduced with permission of ACS.

A number of works put forward the research of the high-conductive PEDOT:PSS films. The first question is why the addition of a second solvent can substantially enhance the electrical conductivity. The scientists used the X-ray diffraction and scattering to study the morphological change of PEDOT polymer after the addition of a second solvent. The results showed that PEDOT exhibits face-on packing; the π-conjugated planes of the PEDOT crystal were more vertical. Apart from this, its crystallinity improved after the addition of the EG or DMSO [23, 24]. To improve the TE performance, adjusting the properties, such as the carrier mobility and carrier concentration, is very important. The carrier mobility and carrier density will significantly increase with the addition of the second solvent, such as EG, from 0.045 cm2 V−1 s−1 , 1020 cm−3 to 1.7 cm2 V−1 s−1 , 1021 cm−3 , respectively [23]. By treating the PH1000 films in strong acid, a high 𝜎 of 4380 S cm−1 can be achieved [25, 26]. Furthermore, a tos-doped PEDOT film with ZT of 0.25 at room temperature [27] and a PSS-doped PEDOT film with ZT of 0.42 at room temperature [28] were successively reported, which is the highest TE performance achieved for the pure PEDOT:PSS film so far. The Seebeck coefficient as a function of electrical conductivity for different PEDOT derivatives is summarized in Figure 8.7 [29]. Controlling the doping level of PEDOT can effectively improve the ZT of PEDOT-based films. For example, by controlling the doping levels of PEDOT:tos films by in situ polymerized using electrochemistry method, the power factor can improved from 862.9 μW m−1 K−2 to 1290 μW m−1 K−2 [30]. Studies suggest that PEDOT:tos could become semimetallic due to the carrier having bipolarons only [28]. Due to the zero band gap and a very low density of states (DOS) near the Ef of semimetallic polymers, they usually possess a higher S and lower k than the metallic polymers, which is most suitable for thermoelectric applications. The results of some progressive research of the doped-PEDOT system are shown in Table 8.3.

8.2 Organic Thermoelectric Materials

Seebeck coefficient (μV K–1)

190

(1) PEDOT–PSS (2) PEDOT–PSS (0.05% DEG) (3) PEDOT–PSS (0.5% DEG) (4) PEDOT–PSS (5% DEG) (5) PEDOT–Tos (6) PEDOT–Tos (2,900 Mw) (7) PEDOT–Tos (DMF) (8) PEDOT–Tos (5,800 Mw + DMF) (9) PEDOT–Tos–PP [15] (10) BiSbTe alloys [16]

180 80 70 60 50

10

9

8

40

6

30

7

5

20

1

2

3

4

1

10

10 0.01

0.1

100

1,000

Electrical conductivity (S cm–1)

Figure 8.7 Seebeck coefficient versus electrical conductivity of various PEDOT derivatives including pristine PEDOT/PSS and diethylene glycol (DEG)-containing samples, chemically polymerized PEDOT/tos, and three vapor-phase polymerized PEDOT/tos samples with triblock copolymers PEG–PPG–PEG with different Mw (PEG, polyethylene glycol; PPG, polypropylene glycol). Source: Bubnova et al. 2014 [29]. Reproduced with permission of Springer Nature. Table 8.3 Thermoelectric properties of poly(3,4-ethylenedioxythiophene) (PEDOT)-based materials (tos = tosylate and PSS = poly(styrenesulfonate)). Materials

PEDOT:PSS PEDOT:tos (dedoped) PEDOT:PSS

S (𝛍V K−1 )

PF (𝛍W m−1 K−2 )

ZT

References

22

47

0.1

[22]

200

324

0.25

[27]

0.42

[28]

73

469

PEDOT:tos

∼85

1290

—

[27]

PEDOT:tos

55

453

—

[29]

PEDOT:BTFMSI

∼40

147

0.22

[31]

PEDOT:PSS (dedoped)

∼50

112

0.093

[32]

PEDOT:PSS (dedoped)

43

116

0.2

[33]

PEDOT:PSS

65

355

∼0.3

[34]

8.2.3

PANI

PANI is a classical conducting polymer due to its variety of structures, high conductivity, unique doping mechanism, excellent physical properties, and good environmental stability. The simple synthesis, easily tunable properties, and numerous applications of PANI attract many researchers [35]. PANI is an intrinsic conducting polymer with conjugated electrical structure, but the low electrical conductivity restricts its application.

187

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8 New Thermoelectric Materials and Nanocomposites

8.2.3.1

The Molecular Structure of PANI

The molecular structure of PANI is shown in Table 8.1. PANI consists of the reduction unit and the oxidation unit. When y = 1, PANI is the fully reduced leucoemeraldine state (LEB, colorless) and an electrical insulator; when y = 0, it is the fully oxidized pernigraniline state (PE), which is also an electrical insulator and called the highest oxidation state [36]; and when y = 0.5, it is the 50% intrinsically oxidized emeraldine state (EB). The intrinsic oxidation state of the polymer ranges from LEB through the EB to PE [37]. When PANI is the protonated intermediate oxidation state (doped PANI), it is conductive and green, the so-called emeraldine base. This doped PANI can be obtained by proton acid doping of the intrinsic PANI. 8.2.3.2

Conductive Mechanism of PANI

Polymer materials being conductive must have the following functions: (i) generate a sufficient number of carriers (electrons, holes or ions, etc.); (ii) form a macromolecular chain and between the chain to be able to form a conductive channel. The conductive mechanism of the conductive polymer is different from the metal or the semiconductor. The carrier of the metal is free electrons, and the carriers of the semiconductor are electrons or holes. But the carriers of the conducting polymer are “delocalized” π electrons and solitons, polarons, or bipolarons formed by a dopant. Similar to the case of inorganic semiconductors, upon the doping of the conjugated polymer, i.e. incorporated electron donor or electron acceptor, a sharp increase in the conductive polymer and a change in the nature of the conductive property from the semiconductor to the metal can occur. The mechanism of doping is thought to produce unpaired p-electrons. This p-electron nonbonding orbital energy level is in the center of the band gap, which is easy to occur as a donor or acceptor level of the electron transfer reaction between the conduction band (CB) and the valence band (VB), and the polymer carbon chain becomes a charged body. In general, emeraldine base is the insulating phase of PANI with two amine groups (—N—) and two imine groups (=N—), per unit. The doping (protonation) of PANI with a protonic acid changes some or all of the imine groups into amine groups through internal redox reaction, contributing to another conductive phase of PANI, emeraldine salt [34]. 8.2.3.3

Synthesis of PANI

By chemical or electrochemical oxidation method, PANI can be easily synthesized using aniline monomer, and with proton alkali to doping, and then doped with protonic acid. Chemical synthesis method is a very facile route for the large-scale production of PANI, without a conducting substrate, which is inexpensive. Classical Chemical Oxidation Polymerization Method Classical chemical oxidation

polymerization method is to add the oxidant into the aniline or aniline derivatives containing protonic acid–solvent system, making the aniline oxidation polymerization reaction to produce PANI [38]. Machado et al. obtained a

8.2 Organic Thermoelectric Materials

needle-like structure of PANI with dodecylbenzenesulfonic acid (DBSA) as a dopant using chemical oxidation. The classic chemical oxidation method is the most commonly used synthesis method. Emulsion Polymerization The emulsion polymerization is a method in which an

initiator is added to an acidic emulsion system containing aniline and its derivatives. A 10–20 nm PANI dispersion was synthesized in sodium dodecyl sulfonate emulsion by Byoung-Jin Kim et al. The ratio of the surfactant to PANI controls the size of the nanoparticles agglomeration [39]. Emulsion polymerization uses environmentally friendly and low cost water as a heat carrier, and the product need not undergo precipitation separation to remove the solvent. Besides, the conductivity of synthetic PANI is better due to the higher molecular weight and solubility. Microemulsion Polymerization Microemulsion polymerization method is devel-

oped on the basis of the emulsion method. The droplet size in the microemulsion method is less than that of ordinary emulsion, which is favorable for preparation of nanoscale PANI [40]. 8.2.3.4

Electrochemical Method

Electrochemical polymerization method refers that the oxidation polymerization reaction of aniline on the anode, then the PANI film form on the electrode surface. The electrochemical method possesses several advantages such as high purity and good experimental reproducibility. Furthermore, the reaction conditions are simple and easy to control. But the electrochemical method is only applicable to the synthesis of small quantities of PANI and to carry out the structural analysis of PANI and other basic research. 8.2.4

Doping of PANI

Doping is to introduce a large number of carriers into the polymer. Although intrinsic PANI is nonconducting, doped PANI can be a good conductor. PANI proton acid doping mainly has small molecular proton acid doping and macromolecular protonic acid doping. The protonic acids in the doping process play two roles: (i) providing the required pH of the reaction medium; (ii) endowing a certain conductivity by entering into the PANI skeleton in the form of a dopant. Different dopants have been employed to protonate PANI, including HCl, H2 SO4 , or camphorsulfonic acid (CSA) [41, 42]. Doping degree of PANI can be controlled by adjusting the pH because of the small inorganic molecular acid can easily spread in the PANI chain. HCl is the most commonly used small molecule protonic acid. For the macromolecular protonic acid dopant, it acts as surfactants dopant, which can improve the solubility of PANI. Besides, the macromolecular protonic acid dopant is beneficial to delocalize charge on the molecular so that it can improve electrical conductivity. They belong to macromolecular protonic acid, including benzenesulfonic acid (BSA), sulfosalicylic acid (SSA), p-toluenesulfonic acid (TSA), CSA, and DBSA.

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8 New Thermoelectric Materials and Nanocomposites

The type [43] and concentration [44] of the dopant have a decisive effect on the structural properties of PANI films. Increasing the CSA protonation level helps improve the PANI structure by enhancing the interchain stacking of PANI chains. However, further protonation could lead to poorer crystallinity of PANI since excessive CSA could cause a cross-linking effect. Solvents including chloroform, xylene, and/or m-cresol can be used to dissolve PANI [45–47]. Different solvents have different effects on the morphology and surface topography of PANI thin films [45]. For example, owing to the compact coil conformation, PANI cast out of chloroform shows localized polarons in short conjugated lengths, while for PANI cast from m-cresol, there exists a transition between the energy bands within the half-filled delocalized polaron band. Dopant together with the solvent has a great effect on the chain stacking because the solvent is useful for the dissolution or solvation of the positive and negative charges on the polymer chain and the negative charges of dopant anions, which would hinder the interaction between the positive and negative charges at the same chain triggering more expanded coil conformation. MacDiarmid and Epstein have postulated that CSA along with m-cresol affected the chain stacking [47]. According to the difference of the processes and steps of doping, proton acid doping can be classified as primary doping, doping–dedoping–redoping, secondary doping, and codoping. Primary doping: Primary doping means that the monomer polymerization and doping reactions are completed in the same process. Doping–dedoping–redoping: A corresponding dedoping and redoping is required if it is desired to change the type of the dopant acid, because the synthesis of PANI is carried out in an acidic medium. Dedoping is the process of removing the protonic acid from the PANI synthesized. During redoping, the intrinsic PANI is immersed in the acidic solution for a period of time and then filtered, washed, and dried to obtain a doped PANI. Li W et al. [48] prepared porous PANI films with high conductivity at room temperature by the “doping–dedoping–redoping” method. Secondary doping: Dedoping leads to a cancellation of the doping-related properties. A secondary dopant induces further changes in the properties, including the electronic, optical, magnetic, or structural properties. MacDiarmid et al. [47] proposed the concept of secondary doping for the first time. Codoping: Codoping refers to using two or more proton acids simultaneously with dopants. One dopant is used to improve the processing and solubility of PANI, and another dopant is used to improve the conductivity of PANI. 8.2.5

Tuning the Work Function of Polyaniline

Work function (WF) is defined as the minimum work needed to remove an electron from the surface of a solid, which belongs to the inherent properties of solid surfaces. The work function for different materials can differ with the electronic structure, the surface orientation [49], surface contamination, and roughness [50, 51]. According to the studies of the WF using different solvents, a linear relationship between the WF of PANI and the dielectric constant of the solvent has been confirmed (Table 8.4).

Table 8.4 Literature survey on work function of polyaniline. WF trend with increasing dopant

Method of determining WF

References

Increases up to 1 : 4 then decreases

Kelvin probe

[46]

DWF (no absolute value)

No trend presented

Kelvin probe

[51]

No specific conductivity

DWF (no absolute value)

Decreases with increasing dopant

Field-effect transistor

[52]

Water

Not specified

DWF (no absolute value)

Decreases with increasing dopant

Kelvin probe

[53]

1 : 0.6 to 1 : 2

m-Cresol

7.5–10.5

4.7–4.8

No trend with increasing dopant

Kelvin probe

[54]

1 : 0.25 to 1 : 1

m-Cresol

2–217

4.42 ± 0.14 to 4.78 ± 0.13

Increases with increasing dopant

XPS

[55]

Dopant type

PANI:dopant ratio

Solvent

Conductivity (S cm−1 )

Polystyrene sulfonate

1 : 1 to 1 : 8

Water, xylene, or alcohol

8 × 10−7 to 1 × 10−2

4.75–5.06

Sulfuric, trifluoroacetic, perchloric, and hydrochloric acids

Not specified

Formic acid then electrochemical

0.03–0.2

Triflic acid or tetrafluoroboric

1 : 0 to 1 : 1

DMF

Hydrochloric acid

Not specified

Camphorsulfonic acid Camphor sulfonic acid

Source: Ahmad et al. 2013 [54]. Reproduced with permission of John Wiley & Sons.

WF (eV)

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8 New Thermoelectric Materials and Nanocomposites

8.2.6

n-Type Thermoelectric Materials

Generally, to synthesize stable, solution-processable, and efficient n-type organics is very difficult, impeding the resultant performance and the corresponding application. However, a newly reported approach to tackle these problems is to use a polymer nanocomposite composed of n-type inorganic TE nanostructures embedded in a polymer matrix. For instance, both the electrical conductivity and Seebeck coefficient of organosoluble PANI doped with HCl exhibit a positive temperature dependence [56]. The electronic band structure of PEDOT is small (Eg ∼ 0.9 eV). The Seebeck coefficient of PEDOT is ∼100 and ∼140 μV K−1 for p- and n-type, respectively [17]. An n-type PEDOT exhibits a high S of ∼ −4008 μV K−1 at RT but a low 𝜎 of 0.64 × 10−3 S cm−1 [57]. The n-type TE materials are of great importance in the assembly of thermoelectric devices; thus, it is a promising work to develop n-type organic composite thermoelectric materials.

8.3 Organic/Inorganic Thermoelectric Nanocomposites Although organic polymers such as PANI, PTH, and PEDOT:PSS are electrically conducting, their TE application is still limited by low 𝜎 and small S as compared with inorganic TE materials. The PF of most polymer TE materials is in the range of 10−7 to 10−3 μW m−1 K−2 , much lower than that of the high-performance inorganic thermoelectric materials [58]. Combining the advantages of low 𝜅 of organic materials and high S or 𝜎 of inorganic materials may enhance the overall thermoelectric properties of the nanocomposites. Nowadays, more attention has been paid to organic/inorganic thermoelectric nanocomposites since the effect of “1 + 1 > 2” was found out in various organic/inorganic thermoelectric composite systems. In the following sections, organic/inorganic thermoelectric nanocomposites classified as 0D nanoparticles/polymer, 1D nanowires or nanotubes/polymer, and 2D nanosheets/polymer will be discussed. 8.3.1

0D Nanoparticles/Polymer

Inorganic materials can be roughly divided into two types when used as proper fillers for polymer matrix to achieve the enhancement of TE performance. One type is inorganic materials with high electric conductivity, and the other is with high Seebeck coefficient. Hence, if composite materials are prepared using metal particles with high 𝜎 and polymer with high S, the composites may have both advantages and achieve improved TE properties. On the other hand, low-dimensional thermoelectric materials exhibit high ZT values both theoretically and experimentally, owing to the quantum effect and phonon scattering on the interfaces. Toshima et al. [59] carried out two different methods – physical mixture and solution mixture to fabricate organic–inorganic nanohybrids of PANI and Bi2 Te3 nanoparticles and explored their TE property. It is found that both composites

8.3 Organic/Inorganic Thermoelectric Nanocomposites

showed decreased electric conductivity, while for the physical mixture, it was maintained much higher. On the contrary, their Seebeck coefficient increased as the temperature increased especially for the solution mixture. Nevertheless, compared to pure PANI, much higher PF was achieved by the physical mixture method, which probably attributed to better dispersion of Bi2 Te3 nanoparticles and better contacting between the PANI molecule and the Bi2 Te3 nanoparticles. In order to obtain the optimal thermoelectric performance of organic–inorganic nanocomposites, the agglomeration of nanoparticles should be avoided as much as possible, which will lead to a sharp decrease in conductivity and result in poor TE property. Therefore, what matters most is how to make good dispersion of nanocrystals. The introduction of functional groups to nanoparticles and in situ polymerization of conducting polymers on the nanofillers are effective methods. With the development of thermoelectric application, alloy semiconductors system including filled skutterudites alloy [60], half-Heusler alloys [61], and chalcogen compounds [62] can no longer meet the demands of the people, especially in higher temperature. The oxide-based thermoelectric materials have been considered as potential TE materials owing to their high temperature and chemical stability, low toxicity, and low cost. Zheng mixed different oxide-based thermoelectric materials (Ca3 Co4 O9 , CaMnO3 , and BiCuSeO) with PANI through the ball-milling method and a hotpressing process to fabricate bulk composites, which effectively avoided the agglomeration of inorganic particles. Compared with pure PANI, the ZT of Ca3 Co4 O9 /PANI and BiCuSeO/PANI increased 40 and 500 times as much as the content of Ca3 Co4 O9 and BiCuSeO [63, 64]. 8.3.2

1D Nanowires or Nanotubes/Polymer

Because the TE figure of merit increases with decreasing dimensions of a material, 1D nanostructures can form dense networks even at a low volume fraction, which will enhance the electrical conductivity of the composite film. 1D thermoelectric materials including nanowires, nanotubes, or nanobelts are promising candidates for the filler in TE composites. It has been more than 20 years since carbon nanotubes (CNTs) were discovered by Iijima [65]. According to the in-depth study of the scientists, CNTs have become popular for the superior electrical, thermal, and mechanical properties [66, 67], especially the development of CNT-based flexible electronics and energy conversion and storage devices has attracted the most attention [68, 69]. The CNTs have also been widely discussed as potential thermoelectric materials [70, 71]. The electrical conductivity of CNT can reach 2 × 105 S cm−1 [72] (for individual CNT) and 103 –104 S cm−1 [72] (for random CNT network). Apart from this, CNT cannot be regarded as a good TE material for its high 𝜅 [73] (>3000 W m−1 K−1 for individual CNT and 30–75 W m−1 K−1 for random CNT network film) and low Seebeck coefficient [74] (100 kPa); and (iii) completing the reactions followed by filtration, washing, and drying [43]. Figure 9.4 exhibits the oxides synthesized by the hydrothermal method with different types of shapes, such as nanoparticles, nanorods, nanotubes, and nanowires [43–48, 52–56]. Here, take the hydrothermal synthesis of ZnO nanorods, for example, Bin Liu and Hua Chun Zeng [44] firstly prepared the precursor solution by mixing the Zn(NO3 )2 ⋅6H2 O, NaOH, and C2 H5 OH in deionized water, and then transferred the mixture solution into a Teflon-lined autoclave for reaction of 20 hours at 180 ∘ C. After a careful filtration, washing treatment, the obtained ZnO nanorods are monodispersed and have an average diameter of 99% dense nanostructured titanium with an average grain size of less than 60 nm. The authors suggested that the increased atomic mobility during the phase transformation was responsible for the enhanced sintering rate.

9.3 Sintering Conditions on the Properties of Bulk 9.3.1

Effect of Sintering Temperature

Sintering temperature is widely studied in many materials; it plays an important role in the microstructure and properties of materials. The influence of sintering temperature on densification, microstructure, and electrical properties of (K,Na)NbO3 -based ceramics was studied by Zhen et al. [72] They found that the densification increases with the sintering temperature increasing from 1020 to 1080 ∘ C for Li-doped (K,Na)NbO3 ceramics, and that the piezoelectric coefficient

219

220

9 Oxide Materials Preparation

of the samples sintered at different temperatures shows significant difference. Jeon investigated the influence of different sintering temperatures on the dielectric properties of Ba1−x Srx TiO3 ceramics. From his results, it can be seen that the grain growth rate of Ba1−x Srx TiO3 increases with increasing x, which would introduce variation to the dielectric property [73]. In fact, not only the sintering temperature but also the sintering time influences the microstructure and property of materials. The effect of sintering time on properties of TiB2 ceramics was reported by Wang et al. They reported that the relative density, grain size, and the fracture toughness increase continuously with increasing sintering time, but the bending strength decreases with the extension of sintering time [74]. 9.3.2

Effect of Sintering Atmosphere

Sintering atmosphere is an important factor that affects the properties, even crystal structure and microstructure of materials, especially for oxide materials. Hence, it is widely investigated in many materials [75–79]. ZnO films grown by pulsed laser deposition (PLD) were annealed under different oxygen ambience. The crystalline quality and Seebeck anisotropy were affected by the annealing atmosphere [76]. Sr1−x Mnx TiO3 ceramics were prepared in different atmospheres (oxygen, air, and nitrogen). There is a part of Mn being tetravalent when the samples were heated in air or oxygen flow, but only divalent Mn existing when fired in nitrogen atmosphere. The dielectric relaxation temperature shifts to higher temperature for samples sintered in reducing atmosphere than those sintered in air and oxygen [78]. The structure of double-perovskite materials would change while they are prepared under different atmospheres due to the change of the oxygen stoichiometry, and the magnetic and electrical properties of those oxides would also significantly change [79–81]. 9.3.3

Effect of the Addition for Sintering

The addition with a low melting point has been widely used to improve the sinterability and optimize the microstructure of ceramics. The common addition contains oxides [82–90], nitrides [91, 92], carbides [93, 94], diboride [95, 96], and glass compositions [97–100]. Kim et al. reported that the sintering temperature decreased from 1150 ∘ C for ZnNb2 O6 ceramics without CuO additions to ∼900 ∘ C for ZnNb2 O6 ceramics with 5 wt% CuO [101]. The effect of CuO on the sintering temperature and piezoelectric property of (Na0.5 K0.5 )NbO3 (NKN) ceramics has been studied by Park and his coworkers. They found that the sintering temperature of NKN ceramics was decreased to below 1000 ∘ C, and the Curie temperature and coercive field were slightly increased with CuO aid [102]. ZnO was demonstrated as an effective sintering aid for yttrium-doped barium zirconate by Babilo et al. [82]. With ZnO addition, the sintering temperature of Y-doped BaZrO3 ceramics (BYZ) ceramics was dramatically reduced from ∼1600 to 1300 ∘ C, and the chemical stability was significantly enhanced. Besides improving sinterability and optimizing the microstructure of ceramics, addition can be used to optimize the properties. Wang et al. investigated the effect of different additions on the thermoelectric properties of Nb-doped SrTiO3

References

[103–105]. They reported that the thermal conductivity was significantly reduced and the electrical conductivity was enhanced with K2 Ti6 O13 (KTO) or mesoporous silica addition, but the electrical conductivity and thermal conductivity were simultaneously enhanced with titanate nanotube addition. Metal additions are also widely used to enhance the properties of oxide thermoelectric materials [106–110]. Nano inclusions of Ag were introduced into p-type oxide Ca3 Co4 O9+𝛿 ceramics, and a peak ZT value of 0.61, which is almost the highest value for Ca3 Co4 O9 -based ceramics, was achieved at 1118 K [111].

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precursors, intermediates and reaction mechanism. Microporous and Mesoporous Materials 82 (1): 1–78. Liu, B. and Zeng, H.C. (2003). Hydrothermal synthesis of ZnO nanorods in the diameter regime of 50 nm. Journal of the American Chemical Society 125 (15): 4430–4431. Bavykin, D.V., Parmon, V.N., Lapkin, A.A. et al. (2004). The effect of hydrothermal conditions on the mesoporous structure of TiO2 nanotubes. Journal of Materials Chemistry 14 (22): 3370–3377. Greene, L.E., Law, M., Goldberger, J. et al. (2003). Low-temperature wafer-scale production of ZnO nanowire arrays. Angewandte Chemie International Edition 42 (26): 3031–3034. Zhang, Y.X., Li, G.H., Jin, Y.X. et al. (2002). Hydrothermal synthesis and photoluminescence of TiO2 nanowires. Chemical Physics Letters 365 (3): 300–304. Wang, X. and Li, Y. (2002). Selected-control hydrothermal synthesis of 𝛼-and 𝛽-MnO2 single crystal nanowires. Journal of the American Chemical Society 124 (12): 2880–2881. Zhang, S., Liu, J., Han, Y. et al. (2004). Formation mechanisms of SrTiO3 nanoparticles under hydrothermal conditions. Materials Science and Engineering: B 110 (1): 11–17. Zhu, H., Yang, D., Yu, G. et al. (2006). A simple hydrothermal route for synthesizing SnO2 quantum dots. Nanotechnology 17 (9): 2386. Sun, X., Zheng, C., Zhang, F. et al. (2009). Size-controlled synthesis of magnetite (Fe3 O4 ) nanoparticles coated with glucose and gluconic acid from a single Fe (III) precursor by a sucrose bifunctional hydrothermal method. Journal of Physical Chemistry C 113 (36): 16002–16008. Daou, T.J., Pourroy, G., Bégin-Colin, S. et al. (2006). Hydrothermal synthesis of monodisperse magnetite nanoparticles. Chemistry of Materials 18 (18): 4399–4404. Lu, Q., Gao, F., and Zhao, D. (2002). One-step synthesis and assembly of copper sulfide nanoparticles to nanowires, nanotubes, and nanovesicles by a simple organic amine-assisted hydrothermal process. Nano Letters 2 (7): 725–728. Chiu, H.C. and Yeh, C.S. (2007). Hydrothermal synthesis of SnO2 nanoparticles and their gas-sensing of alcohol. Journal of Physical Chemistry C 111 (20): 7256–7259. Wang, J.X., Sun, X.W., Yang, Y. et al. (2006). Hydrothermally grown oriented ZnO nanorod arrays for gas sensing applications. Nanotechnology 17 (19): 4995. Tsai, C.C. and Teng, H. (2004). Regulation of the physical characteristics of titania nanotube aggregates synthesized from hydrothermal treatment. Chemistry of Materials 16 (22): 4352–4358. Kosuga, A., Wang, Y., Yubuta, K. et al. (2010). Thermoelectric properties of polycrystalline Ca0.9 Yb0.1 MnO3 prepared from nanopowder obtained by gas-phase reaction and its application to thermoelectric power devices. Japanese Journal of Applied Physics 49 (7R): 071101.

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10 Modeling and Optimizing of Thermoelectric Devices 10.1 Introduction to Thermoelectric Devices Thermoelectric (TE) devices are products that apply thermoelectric materials to convert the energy forms between heat and electricity. The TE refrigerator was fabricated in 1950 [1], which proved that the application of TE materials was realizable with an acceptable efficiency. The all solid-state TE device is totally scalable, with dimensions from millimeters to meters. Meanwhile, its reliability and flexibility are normally superb owing to its simple structure [2]. Thermoelectric cooler (TEC) and thermoelectric generator (TEG) are two common applications of TE materials that apply the Peltier effect and Seebeck effect, respectively. The first thermoelectric power generator was constructed with the efficiency of 5% [3]. The most charming application of the TE device is the generation driven by the radiative heat source for spacecraft of NASA, including Pioneer F/10, Viking-1, and Apollo-12 [4]. In such an environment, TE generators had a higher reliability than the traditional ones, and it is difficult to continuously force the mechanical generators in space for a long time. Since then, more and more ideas applying Seebeck effect were analyzed and tested, such as the TE watch powered by the heat source of the human body, energy recycling from the exhaust of motors, and the distributed generators in remote area. The generation applications have been partially realized, whereas they are presently far from the extensive installation. The TE coolers are more commercially successful as they are used in controlling the temperature of some important instruments. For example, the polymerase chain reaction amplifies DNA with repeated recycles of heating and cooling, which is a typical TEC application area where both heating and cooling are required [5]. The refrigeration has also widely applied in the limited space, like the temporary storage of the red wine or supporting a portable box-like refrigerator. The applications of thermoelectric materials in life can improve the quality of life, such as car seat cooling systems and wearable temperature control equipment in hot summer. These ideas have attracted the scientists and engineers to develop more useful TE devices to improve the quality of life.

Oxide Thermoelectric Materials: From Basic Principles to Applications, First Edition. Yuan-Hua Lin, Jinle Lan, and Cewen Nan. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

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10.2 The Theoretical Analysis The design of TE modules is based on the analysis of the heat and electricity behaviors, which commonly include the Joule heat, the Peltier heat, the Seebeck electromotive force, the Thomson heat, and the heat conduction,. For the TEC, the efficiency 𝜂 could be written as Qc (10.1) P where Qc is the heat absorbed for one second from the cold side and P the input power. As shown in Figure 10.1a, the heat is absorbed at one side of the module and dissipated at the other side, resulting in a temperature gradient ΔT = T h − T c , where T h is the temperature of the hot side and T c the temperature of the cold side. There is also heat flow from the hot side to the cold side because of heat conduction stemming from the temperature gradient. By constituting the thermal equilibrium equation of the simplest model, Qc could be represented as 𝜂=

1 Qc = ΔSTc I − I 2 R − K(Th − Tc ) 2

(10.2)

ΔS = Sp − Sn

(10.3)

lp ln 𝜌n + 𝜌 An Ap p Ap A K = n 𝜅n + 𝜅 ln lp p

(10.4)

R=

(10.5)

where I is the current in the cycle, S the Seebeck coefficient, R the total resistance, 𝜌 the resistivity of TE materials, K the thermal diffusion coefficient, 𝜅 the thermal conductivity, A the cross-sectional area, and l the length of the TE legs. Heat absorbed Ceramic plate Electrode n-type

Heat applied Ceramic plate Electrode

p-type

–

n-type

+

–

Electrode Electrode Ceramic plate Dissipated heat

(a)

+

–

+ –

p-type

+

Electrode Electrode Ceramic plate Heat rejected

(b)

Figure 10.1 A simple schema of (a) the TEC and (b) the TEG.

10.2 The Theoretical Analysis

The subscripts p and n denote the p- and n-type TE materials, respectively. The outer voltage is separated into two parts. The first part drops in the TE materials transforming to the Joule heat, and the another is canceled by the electromotive force of Seebeck. So the input power is expressed as P = I 2 R + ΔS(Th − Tc )I

(10.6)

The maximum of 𝜂 is obtained if 𝜕𝜂 = 0, and the optimal solution is simplified as 𝜕I √ T 1 + ZT − Th Tc c (10.7) 𝜂max = √ Th − Tc 1 + ZT + 1 where T is the average temperature of the hot and cold sides and Z the figure of merit of the module whose value is calculated by ΔS (10.8) Rk The efficiency of TEG is also linked to the power and the heat working, as shown in Figure 10.1b. On the contrary, the electricity is the output, so the efficiency of TEG 𝜙 is written as Z=

𝜙=

P Qh

(10.9)

where P is the output power and Qh the heat absorbed for one second from the hot side. Normally a resistor R is introduced to calculate the output power using the formula: P = I2R

(10.10)

where I is the output current. The heat absorbed results from the heat conduction, the Joule heat, and the Peltier heat, so it could be written as 1 (10.11) Qh = ΔSTh I − I 2 R + K(Th − Tc ) 2 The value of 𝜙 reaches the maximum if √ Th − Tc 1 + ZT − 1 𝜙max = √ T Th 1 + ZT + Tc

𝜕𝜙 𝜕I

= 0 and the optimal solution is (10.12)

h

The TEC and the TEG share the same definition of Z, as mentioned earlier; the figure of merit indicates the performance of the device. If the temperature of each side and the TE properties are fixed, the efficiency of the TE device is determined by the geometrical parameters of the p- and n-type TE legs, and the optimal size satisfies the formula: ( )1 𝜌 p 𝜆n 2 ln Ap = (10.13) lp An 𝜌 n 𝜆p ΔS2 Zmax = (10.14) 1∕2 [(𝜌n 𝜆p ) + (𝜌p 𝜆n )1∕2 ]2

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10 Modeling and Optimizing of Thermoelectric Devices

ΔTh

Ceramic plate Electrode Ceramic plate Electrode

ΔT

ΔT0

n-type

p-type

Solder Conduct layer Barrier layer TE materials

ΔTc

Electrode Electrode Ceramic plate

Figure 10.2 A practical schema of the TE device.

The analysis above indicates the relationship between the efficiency of a device and its figure of merit without considering the influence of the contact effect, the heat loss, etc. Besides, the condition optimizing the figure of merit is presented in the situation. The efficiency of the real device is often degenerated by the mismatch between the factors mentioned above. It is essential to analyze theoretically the efficiency on considering more practical factors. There are unavoidable interfacial thermal resistance, interfacial electrical resistance, and thermal resistance of upper and lower plates that degenerate the efficiency of both TEC and TEG. As shown in Figure 10.2, the temperature difference on the TE materials (ΔT 0 ) is lesser than the temperature difference between the two sides (ΔT) as the thermal resistance of plate and the interfacial resistance are unneglectable: ΔT = ΔT0 − (ΔTc + ΔTh )

(10.15)

where ΔT c is the temperature difference at the cold side and ΔT h that at the hot side. Obviously, better plate has a relatively high thermal conductivity that minimizes the heat loss at the two ends of the TE module.

10.3 The Model Design The TE module is a solid-state energy converter that traditionally consists of a bunch of TE unicouples wired electrically in series and thermally in parallel [6]. The basic requirements for selecting a specific module configuration are to capture the heat most efficiently and provide maximum module reliability. The most applied structure is π-shaped configuration, consisting of the columnor cube-like n- and p-type TE elements connected electrically in series and thermally in parallel. The TE elements are sandwiched between two polymer or ceramic plates that serve as electrical insulators and thermal conductors. The π-shaped module is applicable to situations where the heat flow is perpendicular to the plates. The rectangular shape makes the module easy to manufacture.

10.3 The Model Design

The heat in parallel Ceramic plate Electrode

TE materials

Electrode Ceramic plate The electricity in series

Figure 10.3 The conduction ways of electricity and heat.

Besides, the extensibility of π-shaped module is pretty good as the modification of three dimensions results in nearly no change in the structure (Figure 10.3) [7]. In applications such as capturing heat from the exhaust gas, the heat flows along a cylinder and, hence, attaching a TE power generator made from the π-shaped modules around a cylindrical heat source becomes extremely complicated. It is especially hard to connect all parts when the diameter of the cylindrical heat source is less than 1 cm. In that case, a tube-shaped module becomes a better option. The tube-shaped module is assembled with a number of n- and p-type ring-shaped TE elements in a coaxial arrangement. These tube-shaped TE elements are connected electrically in series and joined alternately at their inner and outer perimeters by interleaved ring-shaped electrodes (Figure 10.4). The gaps between the n- and p-type tube-shaped TE elements both underneath and above the tube-shaped electrodes are filled with electrically and thermally insulating materials. The inner tube surface of the tube-shaped module serves as one thermocouple junction and the outer tube surface serves as another. In principle, both the inner and the outer surface ought to possess an electrically insulating and thermally conducting liner whose functions are the same as those of the ceramic plates used in the π-shaped module. When the heat flows through the outer surface or the inner space of the TE tube, which depends on the design, a temperature difference can be established and the electrical power is generated consequently. The new design solves the big question of application in tube-like heat source. However, the tube-shaped TE modules involve tube-like TE materials, electrodes, surface plate, etc. Considering more precise work to assemble a tube-shaped multilayers device, the fabrication becomes harder than that of the traditional π-shaped TE module increasing the price of the device [8]. Not only specific application needs but also the properties of TE materials such as the coefficient of thermal expansion (CTE) play important roles in the design of TE modules. Another novel Y-shaped configuration accommodates TE elements with different thickness, area, and CTE more easily (Figure 10.5) [9]. Each column- or cube-like TE element is sandwiched between the connectors. The connectors not only provide an electrical path from one TE element to another but also facilitate a thermal path from the fluid-carrying channels to the TE elements. In the Y-shaped configuration, the electrical current runs parallel to both

233

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10 Modeling and Optimizing of Thermoelectric Devices

The outer side

The heat in parallel

The inner side The inner electrode

TE materials

(a)

The outer electrode

(b)

The electricity in series

Figure 10.4 A simple schema of (a) the side view and (b) the cut-away view of a tube-shaped TE module.

the heat and sink sources, allowing for integration of TE materials with multiple geometries. Each TE element can be optimized semi-independently, which is particularly favorable for a segmented module. Specifically, each p- and n-type leg may have a different cross-sectional area and/or thickness, where each layer could be optimized to export the highest ZT in each specific temperature range. The structure avoids negative influences of any compatibility mismatch on the optimum power output when the maximum efficiency of different element segments occurs at significantly different current densities. In addition, the Y-shaped connector provides a shorter electrical path between the adjacent TE elements and a larger area between the heat (or sink) source and the connector. Different configurations of TE modules have widened the application of TE materials. The structure of multilayer TE modules is also a useful design that obviously increases the maximum temperature difference of TEC. Taking a two-layer TE module as an example, Q denotes the heat absorbed for one second by the first layer with the efficiency of 𝜀 and the power consumption of P. The subscripts 1 and 2 refer to the first and the second layer. According to the formula (Eq. (10.1)), the two layers could be linked by the formula: ( ) 1 (10.16) Q2 = P1 + Q1 = Q1 1 + 𝜖1 The formula could describe two adjacent layers, and finally for more layers, the efficiency of a module is written as ) ( 1 1 ∏ (10.17) 1+ 1+ = 𝜖 𝜖i where 𝜖 is the efficiency of the whole module and the subscript i represents the ith layer. Multilayer modules do not always succeed in increasing the efficiency

10.3 The Model Design

The heat in partly parallel Ceramic plate Electrode TE materials

Ceramic plate The electricity in series

Figure 10.5 A simple schema of a Y-shaped TE module.

High temperature TE material for high temperature A single material

The connection of two materials TE material for low temperature Low temperature

Figure 10.6 A single TE leg and a segmented leg of two kinds of TE materials.

because the more the layers are involved, the more the electricity is consumed. Three or more layer modules are rare to fabricate, and as compared with the two-layered module, it cannot effectively improve the efficiency. Meanwhile, the additional price and the instability make them less competitive in practice. The segmented TE module is another idea to ameliorate the TE module efficiency [10]. Two or more TE materials are connected to form a segmented TE module so that each material could serve near the temperature of the peak figure of merit. No materials keep a high figure of merit in the temperature range of more than 300 ∘ C, but segmented TE module make the most of several materials, leading a better performance. For example, Figure 10.6 shows a normal single TE leg and a segmented TE leg. In the normal TE leg, the material serves under high and low temperatures. whereas, the efficiency of TE materials typically has a single peak, that is not suitable to work in two distinguish temperatures. The segmented leg consists of two TE materials that are connected by solder and the conducting layers. A TE material suitable for the high temperature and another for low temperature are chosen, leading to a higher total efficiency, despite the extra thermal and electrical resistance introduced by the connection layers.

235

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It is the TE module design principles that satisfy the practical situation. The price, the complexity of fabrication, the efficiency, and the cooperation of other parts are all important factors that should be considered during the design process. Normally, it is impossible to cover all the factors, and a balanced and optimal solution is the target of TE module design.

10.4 The Interfaces in Thermoelectric Modules An entire TE module has at least three parts: TE materials, electrodes, and the outer plates. The connection between the TE materials and the electrodes unavoidably introduces interfaces that influence TE modules in many aspects. More practically, as shown in Figure 10.2, there are solders, contact layers, and barrier layers between the electrodes and the TE materials. The interface properties are dominated by the manufacturing process and the intrinsic properties of each material, affecting the efficiency and stability during the cycling of a TE module. The degradation mainly stems from the mutual diffusion of the electrodes and the TE materials; the contact resistance, including the thermal and electrical resistance; and mismatching the CTE among the layers and the TE materials. Some principles are summarized to guide the selection of each material and to point out the developing direction. First of all, the CTE is one of the most important factors, and the CTE of the electrode should match with that of the TE materials. The CTE mismatching damages the stability of the module because there will be cracks resulting from the strains while the TE module undergoes a remarkable change in temperature. A tolerance of 20% mismatching is normally considered a ceiling for a good design [11]. The stability is also greatly influenced by the mutual diffusion between the TE materials and other parts, especially at a high temperature for a TEG device as the performance of doped TE materials may be greatly damaged by a slight diffusion. The barrier layers are designed for avoiding or decreasing the diffusion by selecting a more stable metal. For a higher efficiency, the electrodes and layers should have low thermal and electrical resistance, and the thermal and electrical properties should be excellent at the interfaces as well. Besides the three essential factors, the strength of the connection, the stability of the electrode, and the complexity of the process are the factors that should be premeditated for a practical TE module. It is impossible for any kind of material to meet all the demands listed above, but multilayer structures enable an optimal goal, and each layer plays a role to solve one or several question(s). The layers directly contacting the TE materials are named contact layers, mainly aiming to decrease the electrical resistance between the semiconductors (TE materials) and the metals. Either Schottky contact or Ohmic contact forms at the semiconductor–metal junction, and the electrical properties of the two kinds of contacts are totally different. The contact resistance is mainly derived from Schottky contact. The general theory holds that the work function of the semiconductor and the metal is an important factor affecting the contact properties. In the traditional semiconductor field, there have been

10.4 The Interfaces in Thermoelectric Modules

Metal

Metal

Conduction band Valance band

(b)

(a)

Junction interface Fermi level

Metal

Metal (c)

(d)

Figure 10.7 The junction for (a and b) n-type and (c and d) p-type TE materials with (a and c) Schottky contact and (b and d) Ohmic conduct.

more researches on Schottky contact. According to Mott–Schottky theory, the work function and electron affinity of a material are the important parameters that determine the nature of the contact. When the semiconductor material is in contact with the metal, the contact surface electrons will move due to the difference in work function, and finally the Fermi level will remain consistent near the contact surface. Since the conduction band and the valence band change due to the flow of electrons, the charge may be subjected to an additional barrier when moving at the interface, which is macroscopically represented by an increase in resistance and a decrease in thermoelectric performance. According to the work function and the type of semiconductor, the contact resistance, as shown in Figure 10.7, can be divided into four cases: (a) 𝜑m > 𝜑sn (Schottky contact); (b) 𝜑m < 𝜑sn (Ohmic contact); (c) 𝜑m > 𝜑sp (Schottky contact); and (d) Φm > 𝜑sp (Ohmic contact), where 𝜑m represents the work function of the metal, 𝜑s represents the work function of the semiconductor, and the subscripts n and p represent the case of the n- and the p-type material [12]. In practice, it is more complex to define the result by simply analyzing the work function. In the covalent compound, the work function of the metal has little effect on the contact form, but in the material composed of the ionic bond, the work function of the metal has a great influence on the actual contact property. This difference is mainly due to the Fermi energy level pinning, so the strategy will change for different materials when choosing the contact metal materials. Among the common thermoelectric materials, materials such as Bi–Te and Pb–Te based are covalently bonded, and the choice of the metal has little effect on the contact resistance; however, for the skutterudite TE materials or oxygenated TE materials, mainly based on ionic bonds, the choice of the metal has a great influence on the final contact properties. The contact properties are still unsatisfactory for oxygenated TE materials. At present, all oxygenated modules are composed of p-type TE materials of Ca3 Co4 O9 or NaCo2 O4 and n-type of CaMnO3 or LaNiO3 . The high contact resistance at interfaces has enormously degraded the performance of the module. An effective way is to mix the paint and the TE material powder that makes the conduct more strengthened. This method was introduced in a successful

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oxide TE module in 2004, where the contact resistance decreased from 56.8% to 12.5% of the total internal resistance [13]. A mixture of a silver paint and a 6 wt% oxygenated powder was investigated, which opened the doors for oxide TE modules. Several oxygenated modules are fabricated by applying the method. Ni, Fe, and Cr were tested for playing a role of the conduct layers [14, 15]. NiO, a kind of material having high electrical resistance, and Ni1−x Cox O formed at the interface after a long-time test at working temperature. The metal of Ni mixed with SrRuO3 was also investigated in NaCo2 O4 -based TE materials; the result showed that the resistance was obviously reduced to a moderate value of 6 × 105 μΩ cm2 [16]. The Fe–Cr alloy was more suitable in the aspect of the electrical resistance. However, the stability of the alloy made it less possible to become a practical option because the reaction between the TE materials and the alloy increased the internal resistance. For oxygenated TE modules, the conduct layer is still a big question, and more research is expected for improving the efficiency. Different CTEs of oxygenated and metallic materials are another challenge for TE materials. One of the useful strategies is to optimize the CTE by the modification of the composition of an alloy that consists of two materials having huge CTE difference. A reported material, Mo–Cu alloy, is a good example whose CTE increases from 6.59 to 9.87 × 10−6 K−1 , while the ratio of Mo/Cu varies from 90 : 10 to 50 : 50. The reaction between the contact layer and the TE materials will be forbidden in the application, and if there is no suitable contact material, another strategy is to add an extra layer to share the stress, improving the stability and making the module effective. Similarly, to decrease the contact resistance, the mixture of the conduct layer material and the TE material reduced the interface stress. An acceptable result is obtained in PbTe-based TE materials with the CTE of ∼23 × 10−6 K−1 and a contact layer Fe whose CTE is about 12 × 10−6 K−1 . A buffer layer, 50% Fe and 50% PbTe, is inserted to the conduct layer and the PbTe, successfully diffusing the stress [17].

10.5 The Simulation and the Optimization The TE device has feeble efficiency as the materials have a theoretically low efficiency. The optimization in the engineering process is an essential method to make the most of the properties of the thermoelectric materials. The design of the module starts with the theoretical analysis, and the simulation using a computer is the last step for the design before the manufacturing process. Each property parameter of all parts is the input, the model is selected, and then a computed optimal solution will be presented. The main method of optimization is the finite element method, a typical numerical method for structure analysis, heat transform, fluid flow, etc. The key factors in the design of a TE module are totally within the range of the method. The parameters are determined by the experimental data, such as contact resistance, thermal conductivity, electrical conductivity, and Seebeck coefficient.

1 0 –1 –2 –3 –4 –5 –6 –7 –8

ΔT (K)

COP

10.5 The Simulation and the Optimization

ΔT: 20 K ΔT: 40 K ΔT: 60 K

0.5 (a)

I/Imax

70 65 60 55 50 45 40 35 30 25 20 1

(b)

2

3

I (A)

Figure 10.8 The influence of different currents for (a) the COP and (b) the temperature difference for a commercial module.

Normally, the method gives a computational optimal solution by modifying the three dimensions, load, electrodes, and interfaces. Every TEC has its own optimal load, fixing the temperature on one side, normally the cold side, and while a series of increasing currents are input, a peak performance will be presented because the Peltier cooling dominates the heat effect at low current and the Joule heat decreases the temperature difference quickly at high current. As shown in Figure 10.8, a simulation for a simple TE module indicates that the current will affect the coefficient of performance (COP) and the temperature difference. Clearly, there are different optimal currents for maximal COP and maximal temperature difference. The cross-sectional area S and the length of the TE legs length, l, also dominate the peak efficiency, and normally the cross-sectional area of the n- and p-type legs is the same. According to formulas (10.4) and (10.5), the value of ZT does not change if S/l remains the same, which indicates that the peak efficiency also does not change. But the contact resistance greatly degenerates the efficiency as it is no longer negligible. Given a fixed cross-sectional area S, the coefficient of TEG is simulated by changing l. A typical TEG efficiency tendency is shown in Figure 10.9, where the smaller the length, the higher the efficiency. When it comes to the power output, there is an obvious arc-like peak. When the length is small, the efficiency is respectively lower. Meanwhile, a too long leg leads to huge resistance, making the power output feeble. The tendency of the power output is shown in Figure 10.10. In practice, maximal power output is the key factor other than the efficiency for a generator. So, a suitable length should be simulated before manufacture. The simulation for segmented TE modules is also an effective way to decide the length of each part. The segmented modules use more than one n- and p-type materials to increase the efficiency. As the length of each part is a key factor for the high performance of the TE module, the computing result may help the decision before the fabrication. Zhang et al. fabricated a segmented TE module of 12% conversion efficiency with the help of the simulation to get the best ratio between the length of a high-temperature TE material and that of a low-temperature one [18].

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Theoritical max efficiency: the contact resistance becomes negligible

Efficiency

2 typical lines: the efficiency versus the current

Lo

ng

er

leg

s

The length of legs tends to 0

Current

Figure 10.9 The efficiency versus the current for different lengths of legs (dashed lines). The red line describes the tendency of maximal efficiency of different leg lengths.

Maximal power output 3 typical lines: the power output versus the current

Power output

240

The length of legs tends to 0 Longer legs

Current

Figure 10.10 The efficiency versus the current for different lengths of legs (dashed lines). The red line shows the tendency of the peak power outputs with different leg lengths.

10.6 The Measurement Theories and Systems

10.6 The Measurement Theories and Systems The measurement of the TE module has three factors to consider, the error, the complexity of the system, and the cost. The performance of a module is described by either the efficiency or the figure of merit, one standard focusing on the ratio of the total output and the input and the other on the values of the electrical and thermal properties. For the TEG, the efficiency could be written as 𝜙=

P IV = Qh IV + Qc

(10.18)

where I is the output current, V the corresponding voltage, and Qc the heat released from the cold side. There is a lower level of radiation on the cold side, and the result becomes more accurate. The measurement could be realized by an instrument, as shown in Figure 10.11a; the current and the voltage are easily measured by the ammeter and the voltmeter. Meanwhile, the heat flux crossing a selected area at the cold side is calculated by the detected temperature difference and the parameters of the cooling block (Figure 10.11b). In practice, this method has a high accuracy, and there is little difficulty during the measurement, making it a common way to determine the efficiency of the TEG. A similar idea for measurement is also applied in the TEC, and the efficiency is calculated by Eq. (10.1). Besides the efficiency, the figure of merit is another factor to describe the performance of a TE module. However, the complexity of the direct measurement has blocked the way as total electrical resistance, total Seebeck coefficient, and total thermal resistance are difficult to be measured precisely. Some indirect methods are proposed to get the value of the figure of merit. According to Eq. (10.2), the maximum temperature difference could be achieved 𝜕(Th −Tc ) if = 0 when the system is in a stable condition, i.e. Q = 0, and the 𝜕I maximum temperature difference could be written as 1 2 ZT 2 c

(10.19)

The insulating TE module The electrical output

The heat side Several thermocouples

Heat source The insulating

TE module The electrical input

Cooling block

(a)

The heat flux of released heat

Several thermocouples

ΔTmax =

The cold side

(b)

The heat flux of absorbed heat

Figure 10.11 A schema of an instrument for measuring the current, voltage, and the heat flux for (a) TEG and (b) TEC.

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10 Modeling and Optimizing of Thermoelectric Devices

Figure 10.12 A typical voltage–time curve in Harman method.

Cutting the input U Voltage

242

Us

Time

The maximum temperature difference and the temperature on the cold side are easily measured by thermocouples; thus, the figure of merit, Z, could be calculated. In this method, the equilibrium state is required so that the TEC has reached exactly the maximum temperature difference. The dimensionless figure of merit is normally defined by ZT, not ZT c , for a TE module. The Harman method is an effective way to calculate the value of the figure of merit for TEC. The voltage detected consists of two parts: U = IR + ΔS(Th − Tc )

(10.20)

The Joule heat stems from the first term, denoting U R , and the Seebeck heat is generated by the second one, denoting U S . If the current is low, the Joule heat becomes negligible as it is proportional to I 2 . Thus, Eq. (10.2) is rewritten as K(Th − Tc ) = ΔSTc I = ΔSTc UR ∕R

(10.21)

Note that the definition of the Seebeck coefficient is the ratio between the temperature difference and the Seebeck electromotive force, equal to U s . Moreover, the average of the temperature is close to the cold side temperature if the input current is low. Thus, the figure of merit could be represented as ZT =

U ΔS2 T= S KR UR

(10.22)

Figure 10.12 shows a typical result in the Harman measurement; U S is obtained directly by getting the voltage when the outer power is cut off, and U R = U − U S . This method is simple, and if the current is well controlled, the result has high accuracy. The method has two limitations, one is low current, so the Joule heat is negligible, and the other is not too high temperature in order to degrade the radiation.

10.7 All-oxide Thermoelectric Device In nonoxide thermoelectric devices, the effects of air and high temperature have always limited the practical application of the device. Thermal stability, surface

10.7 All-oxide Thermoelectric Device

Thermocouple Pt wire

fin (SUS430) 150 × 100 × 1 mm3

p- leg

100 mm

Figure 10.13 Schematic illustration of the fin-type thermoelectric device. Spark plasma sintered Ca2.75 Gd0.25 Co4 O9 and conventionally sintered Ca0.92 La0.08 MnO3 are used for p and n legs, respectively. Source: Malochkin et al. 2004 [21]. Reproduced with permission of IOP.

n- leg

Al2O3 coating

30 mm 150 mm

oxidation resistance, decomposition and melting of thermoelectric materials at high temperatures, and oxide ceramics are considered due to their thermal properties. It is a promising high-temperature application material with good stability and strong oxidation resistance. The prototype oxide thermoelectric element was first manufactured by Woosuck Shin [19] for generating electricity at high temperatures in the air. Motivated by the discovery of a layer-structured Ca–Co–O system with a figure of merit of over 1.2 at high temperature reported by Funahashi [20], Ca3 Co4 O9 was widely used as p-type leg for oxide-based thermoelectric power generation. As schematically shown in Figure 10.13, Gd-doped Ca3 Co4 O9 p-type legs and La-doped CaMnO3 n-type legs are fabricated to a TE device [22]. Tomes et al. reported a four-leg thermoelectric all-oxide module where polycrystalline GdCo0.95 Ni0.05 O3 and CaMn0.98 Nb0.02 O3 serve the p- and n-type leg, respectively. Meanwhile, a test setup for the electrical and power measurements was instrumented for checking the efficiency of fabricated modules [19]. The pressure from the top side will stabilize the module to be tested, especially the one connected loosely between the legs and the electrodes. Figure 10.14 shows the schema of the instrument and its photos. There is a high-precision control unit module between the heat source and the thermoelectric oxide module (TOM), which can change the interface area between the two. The heating function achieves controlled temperature rise through the heating plate. The cooling function is realized by a large block of water-cooled copper blocks, which are, respectively, located at the top and bottom of the TOM to provide a temperature difference to the tested module. The use of thermal conductive adhesive on the contact surface enhances the heat dissipation between the interfaces and reduces the error of the results from the influence of the device. The system uses a K-type thermocouple to measure temperature changes from the cold end to the hot end. They are placed at various critical locations between

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10 Modeling and Optimizing of Thermoelectric Devices

Heating up to 873 K

Alumina plate Current

Cooling system with temperature range: 253 K–353 K

Load switch with resistors

(a)

(b)

Figure 10.14 (a) Configuration of the electrical and power measurements setup. (b) Microinfrared (IR) camera for temperature profile measurements. Source: Malochkin et al. 2004 [21]. Reproduced with permission of IOP.

the hot plate on the hot side of the module and the Al2 O3 layer, and between the Cu cooling block on the cold side of the module and the Al2 O3 layer. Since the load can significantly affect the output power, the output power can be measured under different loads by adjusting the load. The voltage measurement uses a precision digital multimeter (DMM) that is divided into two modes, open-circle mode and load-resistance mode. The internal resistance Rin is calculated using the following relationship: Rin = Rload [(Voc − Vload )∕Vload ]

(10.23)

The power output is also related to the reload, which could be expressed by a simple formula: 2 Pmax = Voc ∕[4Rload ((Voc − Vload )∕Vload )]

(10.24)

Figure 10.15 shows the measured power characteristics at different temperature differences from ΔT = 100 K to ΔT = 500 K with a maximal power output ∼0.04 W. The power curve is a distinct arch shape that achieves maximum output power with the same internal and external resistance, which is characteristic of most batteries. In this case, the output voltage is equal to half of the open circuit voltage.

References

0.040

ΔT 100 K 200 K 300 K 400 K 500 K

0.035

Power (W)

0.030 0.025 0.020 0.015 0.010 0.005 0.000 0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Voltage (V)

Figure 10.15 Power as a function of voltage for various temperature gradients. Source: Tomeš et al. 2010 [19]. Reproduced with permission of Springer Nature.

References 1 Taroni, P.J., Hoces, I., Stingelin, N. et al. (2014). Thermoelectric materials:

2 3

4

5

6

7

8

a brief historical survey from metal junctions and inorganic semiconductors to organic polymers. Israel Journal of Chemistry 54 (5–6): 534–552. Snyder, G.J. and Toberer, E.S. (2011). Complex thermoelectric materials. Nature Materials 7 (2): 105. Silva, M.F., Ribeiro, J.F., Carmo, J.P. et al. (2012). Thin Films for thermoelectric applications. In: Scanning Probe Microscopy in Nanoscience and Nanotechnology 3, 485–528. Berlin/Heidelberg: Springer. Pei, Y., LaLonde, A., Iwanaga, S., and Snyder, G.J. (2011). High thermoelectric figure of merit in heavy hole dominated PbTe. Energy and Environmental Science 4 (6): 2085–2089. Amasia, M., Cozzens, M., and Madou, M.J. (2012). Centrifugal microfluidic platform for rapid PCR amplification using integrated thermoelectric heating and ice-valving. Sensors and Actuators B: Chemical 161 (1): 1191–1197. Zhang, Q.H., Huang, X.Y., Bai, S.Q. et al. (2016). Thermoelectric devices for power generation: recent progress and future challenges. Advanced Engineering Materials 18 (2): 194–213. Park, K. and Lee, G.W. (2013). Fabrication and thermoelectric power of π-shaped Ca3 Co4 O9 /CaMnO3 modules for renewable energy conversion. Energy 60: 87–93. Ismail, B.I. and Ahmed, W.H. (2009). Thermoelectric power generation using waste-heat energy as an alternative green technology. Recent Patents on Electrical & Electronic Engineering (Formerly Recent Patents on Electrical Engineering) 2 (1): 27–39.

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9 Crane, D.T. and Bell, L.E. (2006). Progress towards maximizing the

10

11 12

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16

17

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19

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22

performance of a thermoelectric power generator. In: Thermoelectrics 25th International Conference on ICT’06, 11–16. IEEE. Crane, D.T. and Jackson, G.S. (2004). Optimization of cross flow heat exchangers for thermoelectric waste heat recovery. Energy Conversion and Management 45 (9–10): 1565–1582. Skomedal, G. (2016). Thermal durability of novel thermoelectric materials for waste heat recovery. Doctoral thesis. University of Agder. Mott, N.F. (1938). Note on the contact between a metal and an insulator or semi-conductor. Mathematical Proceedings of the Cambridge Philosophical Society 34 (4): 568–572. Funahashi, R., Urata, S., Mizuno, K. et al. (2004). Ca2.7 Bi0.3 Co4 O9 / La0.9 Bi0.1 NiO3 thermoelectric devices with high output power density. Applied Physics Letters 85 (6): 1036–1038. Holgate, T.C., Wu, N., Søndergaard, M. et al. (2013). Kinetics, stability, and thermal contact resistance of nickel–Ca3 Co4 O9 interfaces formed by spark plasma sintering. Journal of Electronic Materials 42 (7): 1661–1668. Holgate, T.C., Han, L., Wu, N. et al. (2014). Characterization of the interface between an Fe–Cr alloy and the p-type thermoelectric oxide Ca3 Co4 O9 . Journal of Alloys and Compounds 582: 827–833. Arai, K., Matsubara, M., Sawada, Y. et al. (2012). Improvement of electrical contact between TE material and Ni electrode interfaces by application of a buffer layer. Journal of Electronic Materials 41 (6): 1771–1777. Liu, W., Jie, Q., Kim, H.S., and Ren, Z. (2015). Current progress and future challenges in thermoelectric power generation: from materials to devices. Acta Materialia 87: 357–376. Zhang, Q., Liao, J., Tang, Y. et al. (2017). Realizing a thermoelectric conversion efficiency of 12% in bismuth telluride/skutterudite segmented modules through full-parameter optimization and energy-loss minimized integration. Energy and Environmental Science 10 (4): 956–963. Tomeš, P., Robert, R., Trottmann, M. et al. (2010). Synthesis and characterization of new ceramic thermoelectrics implemented in a thermoelectric oxide module. Journal of Electronic Materials 39 (9): 1696–1703. Funahashi, R., Matsubara, I., Ikuta, H. et al. (2000). An oxide single crystal with high thermoelectric performance in air. Japanese Journal of Applied Physics 39 (11B): L1127. Malochkin, O., Seo, W.S., and Koumoto, K. (2004). Thermoelectric properties of (ZnO)5 In2 O3 single crystal grown by a flux method. Japanese Journal of Applied Physics 43 (2A): L194. Yasukawa, M. and Murayama, N. (1997). High-temperature thermoelectric properties of the oxide material: Ba1-x Srx PbO3 (x = 0–0.6). Journal of Materials 16 (21): 1731–1734.

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11 Photovoltaic Application of Thermoelectric Materials and Devices 11.1 Introduction Solar energy has been considered an ideal source of energy for a long time. With the features of clean, safe, and renewable energy, solar energy has a wide range of frequency, varying from short wavelength radiation of 200 nm to spectral distribution of long-wave radiation of 3000 nm [1, 2], whose thermal efficiency is more evident in longer wavelengths [3]. The solar radiation travels to the surface of the Earth and is converted into electricity by thermoelectric conversion devices and photoelectric conversion devices [4]. Sunlight, including ultraviolet and visible light, can be directly converted into electricity by solar cells [5]. Solar water heaters are one of the common commercial devices that directly use thermal radiation. They are directly used for heating by collecting infrared light thermal radiation in the wavelength range 800–3000 nm. Solar thermal power generation is also an important way to collect heat radiation. For example, the use of thermoelectric (TE) materials to directly convert heat into electrical energy is an available solution. Although photovoltaic (PV) and TE materials have made a lot of progress, respectively, the solar energy and thermal energy of the solar radiation cannot be converted at the same time, although the two parts of energy are always closely linked and cannot be processed and separated. On the one hand, solar cells cannot directly use thermal radiation, and even most photovoltaic technologies are affected by high temperatures, and efficiency decreases with increasing temperature. This phenomenon is particularly noticeable in polycrystalline silicon solar cells [6, 7]. For example, Raga and Fabregat-Santiago [7] report that the temperature of the polycrystalline silicon solar module has risen from −20 to 70 ∘ C, and the efficiency has dropped significantly from 16.5% to about 10.5%. In contrast, dye-sensitized solar cells (DSSCs) are relatively less sensitive to changes in temperature, not only increasing the efficiency when heated at low temperatures, but almost unchanged between 20 and 40 ∘ C. Until 40 ∘ C or above, the efficiency of DSSC begins to decrease slowly [7]. On the other hand, TE materials or modules cannot directly absorb sunlight, and most thermoelectric materials are incapable of transmitting light, which causes absorption of heat radiation and also absorbs light itself. Energy causes solar energy to be further converted into electricity by solar cells. Therefore, integrating photovoltaic and thermoelectric technologies into a single Oxide Thermoelectric Materials: From Basic Principles to Applications, First Edition. Yuan-Hua Lin, Jinle Lan, and Cewen Nan. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

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device would be a viable way to take full advantage of solar energy, including solar and solar thermal radiation. So far, many efforts have been made to achieve synergistic use of solar energy. In the past few decades, PV and TE modules have been combined to develop integrated devices as an effective method for research and validation [9–13]. Recently, composite materials of optoelectronic materials and thermoelectric materials have been prepared and used in photovoltaic devices. For the synergistic use of solar energy, it has attracted more and more attention. This chapter will introduce and discuss the two aspects of solar energy synergy, integrated devices and composite materials.

11.2 Photovoltaic–Thermoelectric Integration Devices A photovoltaic cell is a photovoltaic device that utilizes the photovoltaic effect and sunlight can be directly converted into electrical energy. However, photovoltaic cells use photovoltaic semiconductors to generate electricity, but its band gap determines that photovoltaic cells can only use a fraction of the energy in sunlight. Only part of the energy and band gap matching is converted into electrical energy, and photons below the band gap energy cannot be converted and utilized, and those photons with higher energy levels than the band gap energy can be absorbed by the semiconductor, but only partially absorb photons. Energy can be converted into electrical energy, and photon energy of the part that is greater than the band gap value is also converted into heat, which cannot be converted into electrical energy. Hurst et al. studied the loss of solar cells based on this intrinsic property and found that the thermal loss was 29.8% in terms of the band gap value of 1.31 eV, and the loss of light energy below the band gap energy accounted for the entire solar spectrum and 25% of energy [14]. Therefore, photovoltaic cells can only use part of the energy of solar energy, and many spectrums of solar energy are not effectively utilized. Thermoelectric generator (TEG) is a device that directly converts thermal energy into electrical energy through the Seebeck effect. It can just use photovoltaic cells to convert unused electricity into electricity by utilizing the unused heat in the solar process [15, 16]. Weidenkaff et al. have introduced high-temperature TE oxide materials into solar energy system using a TEG [17]. Li et al. reported a system with efficiency of 10–14% by applying a concentration solar TEG system [18]. Combining the advantages of the above two devices, the PV–TE (photovoltaic–thermoelectric)-based hybrid system can more effectively utilize the energy of the solar multiband. The hybrid system combines the PV cell and the TEG into an integrated device while utilizing the sunlight and excess waste heat to generate electricity [19]. Guo et al. developed a dual-chamber hybrid tandem cell, including DSSC to absorb solar energy and thermoelectric cells as bottom cells for thermal energy conversion. Combined with two-part energy conversion, its overall photoelectric conversion efficiency (PCE) is 10% more DSSC than a single battery, but its PCE value is at a lower level [20]. Van Sark et al. [11] from a computational point of view, starting from an idealized model, implemented a tool for calculating the efficiency of a PV–TE hybrid system by connecting the TEG to the back of the PV module. With the development of solar cells and TE modules, PV–TE-integrated devices have improved

11.2 Photovoltaic–Thermoelectric Integration Devices hν Glass substrate SnO2F TiO2•dye

Dye-sensitized solar cell

Photoanode

– Electrolyte

+

–

Pt –

Solar selective aborber

(b)

+

Thermoelectric generator

Counter electrode

Glass substrate

Hot side

Cold side

Anti reflection layer

(a)

LMVF cermet absorber layer LMVF-low metal volume fraction HMVF cermet absorber layer HMVF-high metal volume fraction IR-Reflector layer Metal substrate

(c)

Silicon wafer

– (e)

(d)

+

Figure 11.1 Schematic illustration and photograph of the novel PV–TE hybrid device using DSSC and SSA-pasted TE generator as the top cell and the bottom cell: (a) hybrid device; (b) DSSC; (c) SSA; (d) TE; and (e) photograph of the hybrid device. Source: Wang et al. 2011 [10]. Reproduced with permission of Royal Society of Chemistry.

in performance. Wang et al. [10] developed a hybrid PV–TE device consisting of a transparent DSSC, a solar-selective absorber (SSA), and a series connection of TE generators, making full use of solar power for high conversion efficiency. Figure 11.1 shows the structure of a PV–TE mixing device that absorbs and converts the solar energy layer by layer. The DSSC is the top unit, and the TE generator is the bottom unit. The SSA is located between the DSSC and the TE generator. The electrical connections of the DSSC and the TE generator are in series. As shown in Figure 11.2a, the transmission spectra of the FTO glass substrate and the DSSC battery indicate that the DSSC absorbs part of the sunlight and generates electricity by the photoelectric effect. The wavelength transmittance from 600 to 1600 nm drops rapidly, indicating that the energy of this portion of the spectrum is not absorbed and absorbed by the DSSC unit. On the other hand, Figure 11.2b shows that the reflectance of the SSA is relatively low in the wavelength range 600–1600 nm, demonstrating that the transmitted sunlight passing through the DSSC is efficiently converted into heat by the SSA for power generation by the thermoelectric device. According to the Seebeck effect, this heat can be directly converted into electrical energy by the TE generator [21]. The two-part device absorbs energy in different bands, making that the device as a whole could

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11 Photovoltaic Application of Thermoelectric Materials and Devices 100

100 DSSC cell FTO

Commercial solar selective absorber Ti-Al-O-N-Si/Al substrate

80

Reflectance (%)

Transmittance (%)

80

60

40

20

60

40

20

0

0 400

(a)

600

800 1000 1200 1400 1600 1800 2000 Wavelength (nm)

(b)

400 600 800 1000 1200 1400 1600 1800 2000 Wavelength (nm)

Figure 11.2 (a) Transmittance spectra of the FTO and DSSC; (b) reflectance spectrum of the commercial SSA. Source: Wang et al. 2011 [10]. Reproduced with permission of Royal Society of Chemistry.

Current density (mA cm–2)

250

34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0

DSSC DSSC/TEs/c DSSCs/c/TE DSSC/TE DSSC/SSA/TEs/c DSSCs/c/SSA/TE DSSC/SSA/TE

Figure 11.3 The photocurrent density–voltage (J–V) characteristic curves of the DSSC/TE hybrid devices and the devices with either part short-circuited (AM1.5G, 100 mW cm2 ). Source: Wang et al. 2011 [10]. Reproduced with permission of Royal Society of Chemistry.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Voltage (V)

absorb incident sunlight in a wider wavelength range, effectively improving solar energy conversion efficiency. Measurements of DSSC/SSA/TE hybrid equipment support the notion of this evidence. The J–V characteristic curve is shown in Figure 11.3. Tables 11.1 and 11.2 summarize the photovoltaic performance of the hybrid unit. Figure 11.3, Tables 11.1, and 11.2 show that the mixing device can effectively improve the total energy conversion efficiency. The TE and DSSC components have different contributions to the total energy conversion. To compare the conversion and output efficiency of the two, the particular component is short-circuited (s/c), and the output contribution of the remainder is measured.

11.2 Photovoltaic–Thermoelectric Integration Devices

Table 11.1 The photovoltaic performance of a DSSC/TE hybrid device (AM1.5 G, 100 mW cm2 , ambient temperature).

Test device

𝜼 (%)

V oc (V)

Jsc (mA cm−2 )

Pmax (mW cm−2 )

DSSC

9.26

0.670

19.2

9.26

0.72

DSSC /TEs/c (DSSC contribution)

9.39

0.668

19.8

9.39

0.71

DSSCs/c/TE (TE contribution)

—

0.487

28.3

3.45

—

DSSC/TE

12.8

1.15

20.2

12.8

FF

0.55

Source: Wang et al. 2011 [10]. Reproduced with permission of Royal Society of Chemistry.

Table 11.2 The photovoltaic performance of DSSC/SSA/TE hybrid device (AM1.5 G, 100 mW cm2 , ambient temperature).

Test device

𝜼 (%)

V oc (V)

Jsc (mA cm−2 )

Pmax (mW cm−2 )

DSSC

9.26

0.670

19.2

DSSC/SSA/TEs/c (DSSC contribution)

9.39

0.671

19.7

9.39

0.71

DSSCs/c/SSA/TE (TE contribution)

—

0.576

33.0

4.75

—

DSSC/SSA/TE

13.8

1.21

20.3

9.26

13.8

FF

0.72

0.56

Source: Wang et al. 2011 [10]. Reproduced with permission of Royal Society of Chemistry.

In the mixing apparatus, a DSSC TE generation is connected in series, therefore DSSC/TE, the V oc values of the mixing apparatus equal to the sum of DSSC/TEs/c and DSSC/c/TE. The J sc of mixing device depends largely on the lower current density parts. The silicon substrate can also effectively reflect light, and the transmitted sunlight is reflected and captured again. Overall, the device can achieve higher light-capturing efficiency, and the J sc is enhanced from 19.2 to 19.8 mA cm−2 . As shown in Figure 11.3, thanks to the contribution of the TE module to V oc , the conversion efficiency of the DSSC/TE hybrid device reached 12.8%, which is higher than that of the DSSC. These results firmly demonstrate that the combination of DSSC and TE generators, padding forward to the target of full utilization of the solar spectrum, significantly improves the conversion efficiency. The PV–TE mixing equipment achieved an efficiency of 13.8% by using extra part of SSA. The absorbance and thermal emissivity of SSA are about 95% and 5%, respectively, according to Figure 11.2b, which involved the reflectance spectrum of SSA. By inserting the SSA into the gap between the DSSC and the TE generator, the temperature difference across the TE generator can be increased from 4.9 to 6.2 K. Table 11.2 shows that due to the increase in temperature difference, the V oc of the TE module is significantly increased, resulting in an increased efficiency in the V oc of the DSSC/SSA/TE hybrid device, leading to further improve the entire efficiency of the hybrid device. Da et al. proposed a comprehensive photon and thermal management method to improve the full-spectrum solar utilization of photovoltaic–thermoelectric (PV–TE) hybrid systems [22]. Under AM1.5 lighting, the overall efficiency of

251

252

11 Photovoltaic Application of Thermoelectric Materials and Devices

H Concentrator

p-Al0.8Ga0.2As t1

PV cell

P n

d

GaAs

Thermoelectric module

t2 t3

n-Al0.3Ga0.7As Cooling system SiO2 (a)

(b)

Λ

Λ

Figure 11.4 (a) The schematic diagram of the PV–TE hybrid system with an optical concentrator; (b) the structure of the PV cell within one period. Source: Yun et al. 2016 [22]. Reproduced with permission of Elsevier.

the hybrid system reached 18.51%. The schematic diagram of the PV–TE hybrid device is shown in Figure 11.4a. The PV–TE hybrid system consists of four parts, an optical concentrator, a PV cell, a TE module, and a cooler. The PV cell is the executor of the photoelectric effect and can generate electricity by utilizing the light energy of the incident solar energy. At the same time, part of the energy passes through natural convection and surface radiation in the form of heat. Finally, the TE module utilizes the remaining heat, including the heat generated by the PV cells and the remaining energy of the transmitted radiant power, to generate electrical energy. Owing to the Seebeck effect, the TE module can convert a portion of the energy into electrical energy, and the cooling system can eliminate excess energy. The structure of the solar cell in one cycle is shown in Figure 11.4b. p-Al0.8 Ga0.2 As in the GaAs nanostructure solar cell acts as the moth-eye structure window layer. Heavily doped p-GaAs and lightly doped n-GaAs take the roles of emitter and base, respectively. At the bottom of the structure, the module consists of a back surface field of n-Al0.3 Ga0.7 As and the SiO2 enhancement transmissive film. Figure 11.5 compares the performance of the moth-eye structure surface and the planar surface. As shown in Figure 11.5a, the reflection of the surface of the moth-eye structure is significantly lower than the emissivity of the planar surface due to enhanced optical absorption. Figure 11.5b,c shows the J–V characteristics of PV cells of different structures under AM1.5 and AM0 illumination. Figure 11.5d compares the overall efficiency of a PV–TE hybrid system under different lighting conditions. In the case of AM0 and AM1.5 illumination, the moth-eye structure surface increased the efficiency of the hybrid system from 13.79% and 12.94% to 18.51% and 16.84%, respectively. Reflection losses significantly affect the efficiency of PV cells and PV–TE hybrid systems. Experimental data indicates that designing a PV–TE hybrid system with low reflection losses is a significant way to increase efficiency. Hsueh et al. reported a hybrid system in which TEG and CuInGaSe2 (CIGS) PV cells were connected in series to obtain a green energy device with a CuInGaSe2

11.3 Photoelectric–Thermoelectric Composite Materials 0.7

30 Moth-eye structured surface Planar surface

Current density (mA cm–2)

Reflection spectrum

0.6 0.5 0.4 0.3 0.2 0.1 0.0

1000

500

(a)

20 15 10

Moth-eye structured surface Planar surface

5 0 0.0

2500

0.2

0.4

(b)

0.6

0.8

1.0

Voltage (V) 25

AM0

AM0

AM1.5

30 Efficiency, ηPV-TE (%)

–2

Current density (mA cm )

2000

Wavelength (nm) 35

25 20 15 10

Moth-eye structured surface Planar surface

0.2

0.6 0.4 Voltage (V)

20 15

18.51 13.79

16.84 12.94

10 5

5 0 0.0

(c)

1500

AM1.5

25

0.8

0

1.0

Planar

Moth-eye

Planar

Moth-eye

(d)

Figure 11.5 The performance comparison between moth-eye-structured surface and planar surface: (a) reflection spectrum; (b) J–V characteristics of PV cell under AM1.5 illumination; (c) J–V characteristics of PV cell under AM0 illumination; (d) efficiency of the PV–TE hybrid system under both AM1.5 and AM0 illumination. Source: Yun et al. 2016 [22]. Reproduced with permission of Elsevier.

(CIGS) photovoltaic cell, which was captured by ZnO nanowires (NW) and connected to a thermoelectric generator [23]. As shown in Figure 11.6, the ZnO NWs/CIGS PV device with multilayer structure effectively utilizes solar energy, and the overall efficiency reaches 16.5%. At present, when the cold junction temperature is less than 5 ∘ C, the efficiency of using CIGS PV battery reaches 22%, and the open-circuit voltage reaches 0.85 V.

11.3 Photoelectric–Thermoelectric Composite Materials Material-level solar energy is synergistically utilized by combining photoelectric materials with thermoelectric materials. The temperature difference between the two sides of solar energy due to different radiation levels can be used for thermoelectric power generation. Therefore, if thermoelectric materials are introduced into solar cells, the temperature difference that would damage the efficiency of the system will become available energy. According to the Seebeck effect, the temperature difference can be used to generate the corresponding temperature difference electromotive force, which strengthens the utilization of solar radiation heat. By effectively changing the negative effects of temperature difference

253

254

11 Photovoltaic Application of Thermoelectric Materials and Devices

ZnO nanowires

Al

Al

AZO ZnS CIGS Mo Glass Ceramic substrate

N

Metal

P

N

P

Metal

N

Metal

P

Metal

Ceramic substrate

Figure 11.6 Schematic cross-section of ZnO nanowires/CIGS solar cell connected to the thermoelectric generator. Ting-Jen et al. 2015 [23]. Reproduced with permission of John Wiley & Sons.

into positive effects, the overall utilization efficiency of the system can be effectively improved. Bi2 Te3 thermoelectric materials are excellent materials for comprehensive performance in the field of thermoelectrics. Deng et al. introduced a Bi2 Te3 thermoelectric material with nanostructures into a photovoltaic system in combination with a CdTe photovoltaic material [8]. Synergistic use in a single photoelectrode is achieved by the integral composite (Figure 11.7). The power conversion efficiency, short-circuit photocurrent, and open-circuit photovoltage of the photoelectrode are higher than that of the isolated CdTe nanowire array. However, the photovoltaic performance of the CdTe/Bi2 Te3 /FTO photoelectrode is relatively weak, and its power conversion efficiency (Eff ) is 0.02%, the short-circuit current (J sc ) is 0.21 mA cm−2 , the open-circuit voltage (V oc ) is 0.35 V, and the FF is 0.22. Chen et al. prepared a novel thermoelectric material Bi2 Te3 /TiO2 composite photoanode for DSSC [24]. The nanostructure Bi2 Te3 directly converts thermal energy into electrical energy through the Seebeck effect, thereby converting “waste heat” into electrical energy, which significantly improves the system. The overall PCE process are shown in (Figure 11.8). On the other hand, the cooling effect of the thermoelectric Bi2 Te3 power generation process has been proved by experiments to extend the working life of the DSSC. In addition, the Bi2 Te3 material can significantly increase the charge transfer rate of the photoreaction, which ultimately reduces the charge recombination process during the reduction process. These synergies improved the overall PCE by 28%, from 6.08% to 7.33%.

11.3 Photoelectric–Thermoelectric Composite Materials

Figure 11.7 The schematic diagram of charge transfer model of CdTe/Bi2 Te3 nanorod arrays/nanolayer photoelectrode. Source: Yuan et al. 2013 [8]. Reproduced with permission of World Scientific.

Pt Na2S e

e

CdTe Cold e

Bi2Te3

Hot

SnO2 Glass

Light

Thermoelectric effect

Photovoltaic effect Pt electrode

FTO (2)

Bi

TiO2

2 Te 3

EF,Bi2Te3 (1) S* e

e

CB

Electrolyte I–/I3–

TiO2 e TiO2

hv

Bi2 Te

3

Bi2Te3 S/S* TiO2/Bi2Te3 e

TiO2

Dye e

Figure 11.8 Schematic illustration of the structure and electron generation/transfer process of the DSSC. There are two routes for energy conversion. Route (1) is the photovoltaic effect: from the excited dye to the conduction band (CB) of TiO2; route (2) is the thermoelectric effect: charge transport from the Fermi level of Bi2 Te3 nanoplate to TiO2 upon heating by sunlight irradiation [24].

255

11 Photovoltaic Application of Thermoelectric Materials and Devices

TiO2 nanoparticles Dye molecules

NaCo2O4-TiO2 composite coaxial nanocables FTO glass

Figure 11.9 Schematic illustration of the composite photoanode with thermoelectricphotoelectric CNCs randomly scattered in the TiO2 nanocrystals [25].

He et al. designed a new composite photoanode based on the thermoelectric– photoelectric composite nanocable (CNC), as shown in Figure 11.9. p-Type NaCo2 O4 was selected as the thermoelectric cell, and it was assumed that its resistivity was about 1 mΩ cm and the Seebeck coefficient was 110 μV K−1 at room temperature [26]. NaCo2 O4 nanocrystals uniformly coated with a thin TiO2 layer were prepared by coaxial electrospinning [27]. In this structure, the TiO2 shell of the nanocable receives the injected electrons from the photo excited dye molecules and TiO2 nanocrystals, and the NaCo2 O4 core of the nanocable that not only generates hot electrons but also facilitates the separation of charges. The driving force generated by the temperature difference promotes the separation of charges according to the Seebeck effect and also provides a means for directly and rapidly transmitting electrons. The photovoltaic properties of DSSCs with different content of TiO2 –NaCo2 O4 CNCs are shown in Figure 11.10. Short-circuit current density (J sc ), open-circuit potential (V oc ), fill factor (FF), and power results are summarized in Table 11.3. DSSC conversion efficiency (PCE) of different addition amounts of TiO2 –NaCo2 O4 CNCs is also different. Devices with pure TiO2 nanocrystalline photoanodes showed common photovoltaic performance with J sc of 15.16 mA cm−2 , V oc of 0.747 V, FF of 67.01%, and PCE of 7.47%. When TiO2 –NaCo2 O4 CsCs was added to TiO2 nanocrystals by 10% by weight, J sc was observed to be 16.92 A cm−2 , V oc was 0.758 V, FF was 70.76%, and PCE was 9.05%. The performance was enhanced, which means that the TiO2 was passed. Adding 10wt% TiO2 –NaCo2 O4 Cs to the photoanode increased PCE by more Figure 11.10 The photovoltaic J–V characteristics of DSSCs with various contents of TiO2 –NaCo2 O4 composite nanocables [25].

20 Current density (mA cm–2)

256

16 12 TiO2 TiO2 + 10% CNC

8

TiO2 + 20% CNC

4 0 0.0

TiO2 + 40% CNC

0.1

0.2

0.3

0.4

0.5

Voltage (V)

0.6

0.7

0.8

11.3 Photoelectric–Thermoelectric Composite Materials

Table 11.3 The photovoltaic parameters and Rs of the DSSCs with various contents of TiO2 –NaCo2 O4 composite nanocables. TiO2 –NaCo2 O4 CNCs (wt%)

Dye loading (10−8 mol cm−2 )

Jsc (mA cm−2 )

V oc (V)

FF (%)

PCE (%)

Rs (𝛀)

0

13.52

15.16

0.747

67.01

7.47

21.1

10

13.08

16.92

0.758

70.76

9.05

18.9

20

11.75

14.72

0.753

71.96

7.96

18.3

40

7.54

13.31

0.759

71.79

7.25

16.6

Source: Hongcai et al. 2016 [25]. Reproduced with permission of RSC.

than 21%. However, as the CNCs content further increased to 20% and 40%, the photovoltaic parameters such as J sc and PCE of DSSC decreased as shown in Table 11.3, while their V oc and FF remained at a higher level than the device. There are no CNCs. In order to further clarify the role of titanium dioxide-NaCo2 O4 CNCs thermoelectric core and prove the effect of thermoelectric Seebeck effect on the photovoltaic performance of DSSCs, controlled temperature gradient (T) was applied on both sides of the solar cell through slight cooling or heating. If the temperature at the electrode side is higher than that at the photoelectric anode side, a positive temperature gradient will occur, whereas a negative temperature gradient is assumed in the opposite case. For comparison, a fixed temperature difference of +5 K or −5 K is reserved between the two sides of each DSSC to measure photovoltaic performance. The effect of temperature gradient on photovoltaic performance of DSSC with 10 wt% titanium dioxide-NaCo2 O4 CNC and without any CNCs was studied. As shown in Figure 11.11, the related photovoltaic parameters are shown in Table 11.4. For DSSC containing 10 wt% titanium dioxide-NaCo2 O4 CNC, negative T at −5 K significantly enhanced its photovoltaic performance. As shown in Figure 11.11a, J sc , V oc , FF, and PCE increased to 18.55 mA cm−2 , 0.763 V, 72.24%, and 10.07%, respectively. When T was +5 K, the photovoltaic performance was significantly decreased. J sc was 15.09 mA cm−2 , V oc was 0.737 V, FF was 69.80%, and PCE was 7.76%. For comparison, the PV performance of DSSC without any CNC was investigated using different T, as shown in Figure 11.11b and Table 11.4. However, the same change in temperature gradient does not produce similar results. The temperature difference between −5 K and +5 K is shown in Figure 11.11b. The results show that the photoelectric properties of the pure TiO2 photoanode sample do not change significantly. This indicates that the temperature change on the electrode side of the device has no significant effect on the performance. The effect on the photovoltaic performance of DSC containing 10 wt% TiO2 –NaCo2 O4 nanocrystals was mainly due to the addition of thermoelectric nanocrystals. According to the physical mechanism of the thermoelectric Seebeck effect, under the action of the thermoelectromotive force, the carriers on the high-temperature side of the thermoelectric material obtain higher kinetic energy and then diffuse toward the low-temperature side, causing the carrier diffusion to be affected by the additional electric field [28]. Finally, a

257

11 Photovoltaic Application of Thermoelectric Materials and Devices

Figure 11.11 The photovoltaic J–V characteristics of the DSSCs (a) with 10 wt% TiO2 –NaCo2 O4 CNCs and (b) without any CNCs under different temperature gradients [25].

Current density (mA cm–2)

20 16 12 8

TiO2 + 10% CNC

4

ΔT = 0 ΔT = +5K ΔT = –5K

0 0.0

0.2

0.4

0.6

0.8

0.6

0.8

Voltage (V)

(a) 20 Current density (mA cm–2)

258

16 12 8

Pure TiO2

4 0 0.0

(b)

ΔT = 0 ΔT = +5K ΔT = –5K

0.2

0.4 Voltage (V)

Table 11.4 The photovoltaic parameters of the DSSCs with 10 wt% TiO2 –NaCo2 O4 CNCs and without any CNCs under different temperature gradients. TiO2 –NaCo2 O4 CNCs (wt%)

𝚫T (K)

Jsc (mA cm−2 )

V oc (V)

FF (%)

PCE (%)

10

−5

18.55

0.763

72.24

10.07

10

0

16.92

0.758

70.76

9.05

10

+5

15.09

0.737

69.80

7.76

0

−5

15.06

0.748

61.32

6.90

0

0

15.16

0.747

67.01

7.47

0

+5

15.21

0.753

66.42

7.61

Source: Hongcai et al. 2016 [25]. Reproduced with permission of RSC.

stable potential difference, the Seebeck voltage, is created by the formation of a dynamic equilibrium, the final equilibrium being determined by the temperature difference and the Seebeck coefficient. For a DSSC consisting of TiO2 –NaCo2 O4 CNC, the temperature difference between −5 K and +5 K between the two sides of the device produces a thermoelectromotive force in the opposite direction inside the thermoelectric cell.

11.3 Photoelectric–Thermoelectric Composite Materials FTO glass

T–ΔT –

–

–

–

–

–

T+ΔT

Pt counter electrode

–

–

– –

Electrolyte

+ + + +

– –

– – – – –

–

– –

+ + + P type TiO2 – NaCo2O4 – – – –

Electron

TiO2

–

–

Hole N719 dye

– T

–

– –

– – –

–

TiO2 nanocrystals

– FTO glass

–

–

–

– – –

–

T Anode

Anode (a)

+ + + +

–

–

–

– – – – P type – NaCo2O4 TiO 2 + + +

– – – – –

–

– – – –

TiO2

–

–

–

(b)

Figure 11.12 Schematic illustration of charge transport in a composite nanocable of TiO2 –NaCo2 O4 under (a) a negative temperature gradient and (b) a positive temperature gradient [25].

Figure 11.12 shows a schematic diagram of charge transfer in a titania-AlCo2 O4 CNC under different temperature gradients. The side illustrates the working mode of the thermoelectric effect. NaCo2 O4 is a p-type thermoelectric oxide, which is an n-type semiconductor having a wide band gap and a high resistivity [26]. Owing to its lower conductivity, n-type titanium dioxide exhibits overall poor thermoelectric properties. In the p-type thermoelectric semiconductor, the low-temperature side is rich in holes, and the high-temperature side concentrates on electrons, and in the n-type semiconductor, electrons are concentrated on the high-temperature side. Therefore, different thermoelectric potentials having opposite directions are generated in the p-type NaCo2 O4 core and the n-type titanium oxide shell under the same temperature gradient. When the temperature gradient is negative, as shown in Figure 11.12a, the low-temperature side is the opposite electrode. Thermoelectromotive force in NaCo2 O4 drives the hole to the lower temperature side, i.e. to the opposite electrode, and electrons accumulate to the photoelectric anode. As a result, the cryogenic end of NaCo2 O4 core is rich in holes. Within n-type titanium dioxide, electrons should be driven to the opposite electrode. However, owing to the high resistivity of titanium dioxide and the existence of NaCo2 O4 with low resistivity and strong thermoelectric Seebeck effect, the influence of thermoelectric EMF in titanium dioxide will be weakened [29]. Considering that there are many nanocrystalline titanium dioxide and titanium dioxide shells around the low-temperature end of thermoelectric NaCo2 O4 core, when photogenerated electrons are injected into titanium dioxide from dye molecules under solar radiation, an obvious electron concentration gradient will be generated to drive the electron diffusion to the low-temperature end of the NaCo2 O4 core. Then, the thermoelectric balance is destroyed. However, because the temperature

259

260

11 Photovoltaic Application of Thermoelectric Materials and Devices

between the two ends of NaCo2 O4 core remains unchanged, the Seebeck potential should remain unchanged. As a result, more holes move to lower temperatures, while higher temperatures collect more electrons. Similarly, the aggregated electrons can be further driven by the concentration gradient and diffused to the direction of the photoanode. The above process is equivalent to the transmission of electrons from the low-temperature end of NaCo2 O4 core to the high-temperature end, i.e. from the reverse electrode side to the photoanode side. It not only promotes the photoinduced charge separation and reduces the recombination probability, but also improves the electron transmission, so that the enhanced charge transfer efficiency of DSSC can be obtained using titanium dioxide-NaCo2 O4 CNCs at a negative temperature gradient. On the contrary, when the temperature gradient is positive, as shown in Figure 11.12b, the lower temperature side is the photoelectric anode. When the thermoelectric potential in NaCo2 O4 drives the hole to the lower temperature side, the electrons gather in the direction of the opposite electrode, which increases the possibility of electron–hole recombination and reduces the charge collection efficiency. As shown in Figure 11.11 and Table 11.4, the temperature gradient of −5 K significantly improves the photovoltaic performance, including J sc , V oc , FF, and PCE of DSSC, and 10 wt% titanium dioxide-NaCo2 O4 CNC, while the temperature gradient of +5 K decreases the photovoltaic performance. This result means that the DSSC with thermoelectric CNC can be further adjusted by controlling the temperature gradient in DSSC. Thermoelectric–photoelectric CNCs can also be used in perovskite solar cells. Liu et al. prepared a perovskite solar cell using NaCo2 O4 /TiO2 coaxial nanofibers [30]. Under illumination, p-type NaCo2 O4 can convert unwanted heat into a thermal voltage, thereby promoting the extraction and transport of electrons under the action of electrostatic forces. Together, these advantages contribute to an overall power conversion efficiency increase of −20%. Thermoelectric–photoelectric composites not only provide ideas for the development of highly efficient photovoltaic devices, but also provide an alternative to the use of a variety of new energy technologies, including photovoltaics and thermoelectrics, for higher energy use.

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Index a A′ A′′ B2 O5+δ 112, 113 A2 B′ B′′ O6 (Sr2 FeMoO6 ) 112–115 acoustic mismatch model (AMM) 41 advanced bulk technology 214–217 hot–press sintering 215–216 microwave sintering 217–218 phase transformation sintering 219 spark plasma sintering 215 two-step sintering technique 218–219 Al-doped ZnO bulk material (AZO) 216 Al doped ZnO rods 84, 85 Al-doped ZnO samples 81 alkali and alkali-earth metal ions 141 all-oxide thermoelectric devices 242–245 Apollo-12 229 as-prepared SnSe nanosheet/ PEDOT:PSS composites 200

b Ba-filled skutterudites 60 ball-milled n-type SiGe alloys 64 band gap tuning 167, 168 barrier energy 21 benzenesulfonic acid (BSA) 189 Bergman’s theorem 179 Bi0.875 Ba0.125 CuSeO 169 BiCuSeO-based materials 164 BiCuSeO-BiCuTeO compositing 168 BiCuSeO oxyselenides 7, 166 bi-doping 139 [Bi2 O2 ]2+ layers 158

Bi2 O2 Se1-x Clx ceramics 162 Bi2 O2 Se1-x Tex samples 161 Bi0.5 Sb1.5 Te3 58 Bi1.9 Sn0.1 O2 Se sample 158 Bi2 Sr2 Co2 O9 polycrystalline materials 150 Bi2 Sr2 Co2 Ox (BSC-222) bulk materials 151 Bi2 Sr2 Co2 Oy 133 Bi2 Te3 155 Bi2 Te3 -based materials 55–59 Bi2 Te3 /Sb2 Te3 superlattices film 57 Bi2 Te3 thermoelectric materials 254 Bi2 Te3 /TiO2 composite photoanode 254 Bi1-x Lax CuSeO ceramic bulks 168 Boltzmann constant 11, 31 Boltzmann equation 36–37 Boltzmann transport equation (BTE) 11 bonding and lattice vibration 25 brick-and-mortar-type nanoscale ceramic 183 Bridgman and Czochralsky method 55

c Ca3 Co4 O9 (CCO) 138 charge and spin-state of Co ion 139 dual-dopants 144–146 single dopant of 139–144 spin-entropy contribution 139 texture 147 Ca3 Co4 O9 133 Ca3 Co4-x TMx O9+δ 139

Oxide Thermoelectric Materials: From Basic Principles to Applications, First Edition. Yuan-Hua Lin, Jinle Lan, and Cewen Nan. © 2019 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2019 by Wiley-VCH Verlag GmbH & Co. KGaA.

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Index

Ca3 Co4-y Fey O9 144–146 Ca2 FeMoO6 115 CaMn0.98 Nb0.02 O3 243 CaMnO3 109 camphorsulfonic acid (CSA) 189 Ca3-x Tbx Co4 O9 142 Ca0.9 Yb0.1 MnO3 122, 214 CdI2 -type [CoO2 ] sheet 133 CdO 3, 99 CdTe/Bi2 Te3 /FTO photoelectrode 254 centrosymmetrical pervoskite 106 CeO2 nanodots 96 ceramics 3, 4, 7, 8, 95, 109, 122, 146, 147, 168, 173–175, 183, 212–215, 217–221 Clevios PEDOT products 186 Co-based oxide material Ca3 Co4 O9 7 co-doping 190 coefficient of thermal expansion (CTE) 233 cold isostatic pressing (CIP) 214 column or cube-like n-type and p-type TE elements 232 commercially available ZnO nanoparticles 82 complex oxides 155–175 complexity through disorder in the unit cell 173–174 complex superconductors 156–157 complex unit cells 174–175 crystal structure and propery relationship 155–156 quaternary oxyselenides 164–166 ternary oxyselenides 158–164 complex superconductors 156–157 complex unit cells 174–175 composite ceramics 118–120 conducting oxides 3–8, 11, 87, 150 conduction band (CB) 32, 45, 107–109, 162, 168, 183, 188, 237 conduction band minimum (CBM) 108, 183 Cu-based bulk thermoelectric materials 70 cubic zinc blende (B3) 77

Cu2 Gax Sn1-x Se3 bulks 216 CuInGaSe2 (CIGS) PV cells 252 Cu2 Sex nanodots 171, 181 Cu7 Te4-x Sex nanoinclusions 171, 181

d Debye–Callaway model 31, 44, 46, 182 de-doping 190 density function theory (DFT) 11, 89 density of dislocation 26 diffuse mismatch model (DMM) 41, 43 digital multimeter (DMM) 244 dodecylbenzenesulfonic acid (DBSA) 189 dominant phonon method 35 donor doping on [Bi2 O2 ]2+ layers 158–160 on [Se]2- layers 160 doped-PEDOT system 186 double perovskites composite ceramics 118–120 doping modulation 115–118 structure of 112–113 thermoelectric properties of A2 B′ B′′ O6 113–115 DSSC/SSA/TE hybrid equipment 250, 251 dual doping of ZnO 83 Dulong–Petit’s law 156 dye-sensitized solar cells (DSSCs) 247

e edge-free spark plasma sintering 147 electrical properties 3, 11–15, 18, 32, 81, 89–90, 107, 109, 120, 155–157, 160, 165, 175, 219, 220, 236 energy-filtering effect 179, 180, 196

f Fe-Cr alloy 238 Fe-doped Ca3 Co4-y Fey O9 144, 146 Fermi–Dirac integrals 15 Fermi energy 11, 13, 27, 32, 57, 173, 237 Fermi’s golden rule 38

Index

four-element BiCuSeO 171 four-leg thermoelectric all oxide module 243

g gas phase reaction (GPR) 122, 214 GdBaCuFeO5+δ 116, 175 Gd-doped Ca3 Co4 O9 p-type legs 243 Gd-doped CMO 35 Gd1-x Lax BaCuFeO5+δ 116 Goldschmidt tolerance Factor 106 grain-aligned dense Ca3 Co4 O9 -based ceramics 147 grain boundaries (GBs) 25, 35, 44, 48, 49, 56, 58, 59, 65, 66, 69, 93, 94, 96, 116, 118, 120, 122, 160, 175, 183 Gruneisen constant 45 Grüneisen parameter 26, 31, 67, 166 G-type anti-ferromagnetic phase CaMnO3 system 107

i indium tin oxide (ITO) 3 In1.92 (Ce, Zn)0.08 O3 94 In2 O3 87 crystal structure 88–89 doping 90–93 electronic band structure 89 nanostructures 94–98 thermal properties and electrical properties 89–90 In2 O3 -based and BiCuSeO-based ceramics 32 In2 O3 -based thermoelectric ceramics 217 in-situ polymerized PEDOT+tos films 186 in-situ SrTe precipitate 66 interface potential 20, 22 interfacial thermal conductivity 40–43 intrinsic Umklapp process 47, 95

j h Harman method 242 heat conduction 34, 60, 156, 230, 231 heavily doped bulk n-type SiGe alloys 180 heavily doped p-GaAs 252 hexagonal wurtzite (B4) 8, 77, 78 hierarchically microstructured Bi0.96 Pb0.04 CuSe1-x Tex O 181 highly dispersed nanosized closed pores 81 highly efficient phonon scattering 166 high performance thermoelectric oxyselenide BiCuSeO ceramics 7 high-temperature Seebeck coefficient 16 high temperature superconductors 3, 156 homogeneous composite 179 hot–press sintering 215–217 hydride vapor phase epitaxy (HVPE) 26 hydrothermal synthesis 84, 213

Joule heat 230, 231, 239, 242 J-V characteristic curve 250

k Kapitza resistance 41 kinetic theory 36 (K,Na)NbO3 -based ceramics Kohn anomaly 27

219

l LaBaCu0.9 Co0.1 FeO5+δ 117 LaBaCuFeO5+δ 113, 117 LaCoO3 111 La2 CuO4 157 LaCuSeO-BiCuSeO solid solution 168 La-doped CaMnO3 n-type legs 243 La-doped SmBaCuFeO5 polycrystalline ceramics 175 LaFeAsO 3 (La, Fe) co-doped Ca3-x Lax Co4-y Fey O9 144–146 LaFeO3 nanocrystals 209 La-filled skutterudites 60 La1.96 M0.04 CuO4 157

265

266

Index

lanthanide elements doped Ca3 Co4 O9 141 La-substituted GdBaCuFeO5+δ ceramics 175 lattice distortions octahedral distortion 28–30 Peierls distortion 27–28 point defects and dislocations 25–27 lattice thermal conductivity Boltzmann equation 36–37 kinetic theory 36 phonon-phonon collisions 38–40 Li-doped (K,Na)NbO3 ceramics 219 lightly doped n-GaAs 252 lithium lanthanum titanates 3 Lorenz number 13–15 low-energy grain boundaries 58

m macromolecular protonic acid doping 189 Magnéli phase titanium oxides 99 manganite perovskites 28–30 material-level solar energy 253 Mathiessen’s rule 17 microwave sintering 217–218 minimum values for oxides 48 misfit-layered cobaltites (Ca3 Co4 O9 ) 9, 133, 138 modulation-doped (Si95 Ge5 )0.65 (Si70 Ge30 P3 )0.35 65 modulation doping (MD) 64, 65, 169–171 molecular dynamics simulation 43 mosaic blocks 69 mosaic crystal 69, 70 Mott–Schottky theory 237

n NaCo2 O4 -based TE materials 238 NaCo2 O4 nanocrystals 256 NaCo2 O4 /TiO2 coaxial nanofibers 260 N and Nb codoped TiO2 powders 99 nano bulk materials 43–48 nanocomposites 17, 18, 147 design

all-scale hierarchical architecture 181–183 energy filtering 180 quantum nanostructured bulk materials 183 nano compositing 171 nanocrystallites 69 nano-grained In2 O3 -based bulks 47 nanograins 47, 48, 70, 95, 97, 120, 121, 171 nanoinclusions 17, 20 ZnO 97 nano-powder gas phase reaction 214 hydrothermal synthesis 213–214 precipitation or coprecipitation method 211–213 sol-gel (solution-gelation) method 211 solid-state reaction 209–210 nanosized LSCO particles 149 nanostructured bulk Bix Sb2-x Te3 alloys 56 nanovoids 81 nanowire arrays 56, 213 narrow-gap Bi2 O2 Te 160 Nax CoO2 105, 109, 133–138 Nb-doped STO 109 (Na0.5 K0.5 )NbO3 (NKN) ceramics 220 NiO 238 nominally undoped ZnO 81 non-oxides materials Bi2 Te3 -based materials 55–59 other alloy materials 66–70 Si-Ge alloys 62–66 skutterudite-based material 59–62 non-oxide thermoelectric devices 242 n-type Ba-filled skutterudites Bay Co4 Sb12 60 n-type Bi2 (Te,Se)3 55 n-type CdO 99 n-type-In2 O3 88 n-type SiGe 64 n-type thermoelectric materials 192 n-type titanium dioxide 259 n-type zinc oxide 77

Index

o octahedral distortion 28–30 Ohmic contact 236, 237 1D nanowires/nanotubes/polymer 193–197 organic-inorganic thermoelectric nanocomposites 1D nanowires/nanotubes/polymer 193–197 2D nanosheets/polymer 197–200 0D nanoparticles/polymer 192–193 organic thermoelectric materials n-type 192 PANI 187–189 PEDOT 184–187 p-type 184 O vacancy V O 81 oxide-based thermoelectric materials 155, 171, 193 oxide cobaltates Ca3 Co4 O9 138–149 Nax CoO2 133–138 new concepts for oxide cobaltites 150–151 effect of the addition for sintering 220–221 gas phase reaction 214 hot-press sintering 215–217 hydrothermal synthesis 213–214 microwave sintering 217–218 phase transformation sintering 219 precipitation or coprecipitation method 211–213 sintering atmosphere 220 sintering temperature effect 219–220 sol-gel (solution-gelation) method 211 solid-state reaction 209–210 spark plasma sintering 215 two-step sintering technique 218–219 oxides 3 band structure 11 effect of interface on electron transport 17–22 electrical properties 11–15

history of 3–8 minimum values for 48–49 structural characters of 8–11 thermoelectric 15–16 oxygenated TE materials 237

p PANi/graphene 198 PANI/Te hybrid film 196, 198 Pauling ionic radius of atom 26 PbTe 66, 67, 155 PbTe-based all-scale nanocomposites 69 Pb/Te co-doping 181 Peierls distortion 27–28 Peltier cooling 239 Peltier heat 230, 231 Perovskite type oxides CaMnO3 109–111 crystal structure 106–107 double 112–120 electronic structure 107–108 LaCoO3 111 nanostructure property relationships 120–124 special oxygen octahedron structure 105 SrTiO3 108–109 phase transformation sintering 219 phonon frequency 25, 26, 31 phonon-glass electron crystal (PGEC) 60 phonon occupation number 36 phonon-phonon collisions 36, 38–40 phonon relaxation time 26 phonon scattering rate 25, 26 photoelectric conversion efficiency (PCE) 248 photoelectric-thermoelectric composite materials 253–260 photovoltaic-thermoelectric integration devices 248 P3HT–Bi2 Te3 interfacial potential barrier diagram 196 Pioneer F/10 229 π-shaped module 232 π-shaped TE module 233

267

268

Index

Planck’s constant 31 point defects and dislocations 25–27 Poisson ratio 26 poly(2,7-carbazole) 184 poly(3,4-ethylenedioxythiophene) (PEDOT) 184 polyactylene (PA) 184 polyaniline (PANI) 184 classical chemical oxidation polymerization method 188–189 conductive mechanism 188 doping 189–190 electrochemical polymerization method 189 emulsion polymerization method 189 microemulsion polymerization 189 molecular structure 188 polycrystalline Ca3 Co4 O9 bulks 142 polycrystalline GdCo0.95 Ni0.05 O3 243 polymer/graphene nanocomposites 197 polymer TE materials 179, 192 poly(3,4-ethylenedioxythiophene): poly(styrenesulfonate) and/or polyvinyl acetate composites 194 polypyrrole (PPY) 184 poly(3,4-ethylenedioxythiophene)– reduced graphene oxide (PEDOT-rGO)nanocomposite 198 polythiophene (PTH) 184 Pr-doped ZnO 82 precipitation or coprecipitation method 211 pristine Bi2 O2 Se 160 projector-augmented wave technique 11, 89 PSS doped PEDOT film 186 p-toluenesulfonic acid (TSA) 189 p-type NaCo2 O4 256, 259, 260 p-type organic thermoelectric materials 184 p-type oxide TE materials 7, 108 p-type PbTe 66

p-type SiGe (boron doped) alloy 63 p-type (Bi,Sb)2 Te3 55 p-type thermoelectric semiconductor 259 pulsed laser deposition (PLD) 173, 220 pure TiO2 nanocrystalline photoanodes 256 PV-TE (photovoltaic-thermoelectric) based hybrid system 248 PV-TE mixing device 249 PV-TE mixing equipment 251

q quantum confinement effect 57, 94, 95, 179 quantum nanostructured bulk materials 183 quaternary oxyselenides 164 band gap tuning 168 electronic structures 165 Hall coefficient 165 modulation doping 169–171 nanocompositing 171–173 Seebeck coefficient 165 texturing 168–169 thermoelectric properties 166–167

r radio-isotope thermoelectric generators (RTGs) 63 RBaCuFeO5+δ 113 RE2 CuO4 157 reduced Fermi level 12 Rietveld refinement 85, 90, 91 rocksalt (or Rochelle salt) (B1) 8, 77

s Sb-doped ZnO micro/nanobelt nanogenerator 86 Sb-icosahedron voids 59 Schottky contact 236, 237 Seebeck coefficient 4, 7, 11, 13–21, 65, 77, 93, 98, 111, 122, 133, 135, 138, 139, 141, 142, 145, 146, 150, 158, 173, 175, 179, 180, 186, 187, 192, 242, 248

Index

Seebeck electromotive force 230, 242 segmented TE modules 239 [Se]2- layers 160 self-propagating high temperature synthesis (SHS) 171, 210 semicoherent grain boundaries 58 short-circuit current density 256 short-wavelength phonons 120–121 Si-Ge alloys 62–66 silicides 63 single-branch polarization-averaged velocity 26 single-layer MoS2 and MoS2 nanoribbons 198 single parabolic band model (SPB) 156 single Sb-doped ZnO microbelt 86 single-walled carbon nanotubes 194 sintered polycrystalline sample 80 sintering atmosphere 81, 220 sintering temperature effect 219 skutterudite-based material 55, 59–62 skutterudites 59, 60, 63, 193 skutterudite TE materials 237 small molecular proton acid doping 189 small polaron conduction model 16 small polaron hopping conduction theory 160 mechanism 162 SmBaCuFeO5+δ 117, 175 SmBaCuFe1-x CoxO5+δ 119 SmBaCu1-x Cox FeO5+δ 119 Sm1-x Lax BaCuFeO5+δ 115 Sn doped In2 O3 (ITO) 87 SnSe 67 nanosheets 200 solar selective absorber (SSA) 249 sol-gel (solution-gelation) method 211 solid solution of Bi2 O2 Se and Bi2 O2 Te 160 solid-state reaction 35, 122, 142, 171, 209–210 spark plasma sintering 56, 84, 141, 147, 215 spark plasma texturing (SPT) 147 specific heat 33, 36, 37, 80 Sr2 FeMoO6 112

SrTiO3 108, 109 Sr1-x Mnx TiO3 ceramics 220 STO epitaxial films 109 strontium titanate (SrTiO3 ) 8, 108 sulfosalicylic acid (SSA) 189 superlattice thin films 56 SWNTs/PANI composite TE materials 194

t Ta-doped strontium titanates 109 TE cooler (TEC) 229 TE generator (TEG) 229, 251 tellurides 63, 196 TE module efficiency 235 ternary oxyselenides donor doping on [Bi2 O2 ]2+ layers 158–160 donor doping on [Se]2- layers 160 solid solution of Bi2 O2 Se and Bi2 O2 Te 160–164 textured n-type Zn0.98-x Al0.02 Nix O bulks 84 thermal boundary resistance (TBR) 41, 48, 120 thermal conductivities 26, 28, 48, 49, 62, 80, 216 thermal conductivity of nano bulk materials lattice 36 lattice distortions 25–30 temperature relationship 32–35 thermal expansion coefficients 79 thermoelectric Bi2 Te3 power generation process 254 thermoelectric (TE) devices 229 all-oxide thermoelectric devices 242–245 interfaces 236–238 measurement theories and systems 241–242 model design 232–236 simulation and optimization 238 theoretical analysis 230–232 thermoelectric generator (TEG) 229, 248, 253, 254

269

270

Index

thermoelectric oxide module (TOM) 243 thermoelectric oxides 15, 47, 243, 259 thermoelectric-photoelectric composite nanocable (CNC) 256 thermoelectric Seebeck effect 257 Thermo Microscope’s SThM Discoverer system 26 thin-film thermoelectric materials 57 Thomson heat 230 three-phonon processes 38, 39 Ti0.94 Nb0.06 O2 thin film 98 tin-doped In2 O3 88 TiO2 -NaCo2 O4 composite nanocables 256 TiO2 -NaCo2 O4 nanocrystals 257, 258 titania-AlCo2 O4 composite nanocable 259 titanium dioxide (TiO2 ) 98–100 titanium dioxide-NaCo2 O4 CNCs 260 tosylate doped PEDOT film 186 transition-metal-oxide 16 transition metals (TM) 8, 59, 60, 111–113, 139, 141 transparent conducting oxide 3, 87 triple rock-salt-type [Ca2 CoO3 ]RS 133 2D carrier quantum-confinement effects 57 2D nanosheets/polymer 197–200 two-step sintering technique 218–219 2-1-4 type layered rare earth copper oxides 157

u Umklapp process 31, 34, 38–40, 46, 95, 156 undoped BiCuSeO 167 undoped In2 O3 93, 96 unfilled skutterudites 59 urea (CO(NH2 )2 ) 99

v valence band (VB) 45, 107, 108, 161, 162, 165, 167, 168, 188, 237 valence band maximum (VBM) 108, 165 Vergard formula 91, 92 Viking-1 229

w waste heat 3, 155, 248, 254 Wiedemann–Franz law 179 work function (WF) 190–191, 196, 236, 237 wurtzite GaN films 26 wurtzite structure ZnO 8

y YBaCuFeO5+δ

117

z 0D nanoparticles/polymer 192–193 zinc blende ZnO 8 zinc oxide (ZnO) 8, 77, 80, 98, 211 applications 77 doping 81–84 electrical properties 81 electronic band structure 77–78 lattice parmaters 77 mechanical properties 79 nanostructures 84–87 specific heat 80 structure 77 thermal conductivities 80 thermal-expansion coefficients 79–80 Zn0.9975 Bi0.0025 O 81 Znic oxides 98 Zn interstitial ZnI 81 ZnO nanorods 209, 210, 213 ZnO nanowires (NW) 253 Zn-on-O antisite ZnO 81 ZnO NWs/CIGS PV device 253 zone melting 55