Introduction to the material science. (Введение в материаловедение) Изд. 9965791120

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Kazakh National University named al-Farabi

N. Korobova Sh. Sarsembinov

INTRODUCTION TO THE MATERIAL SCIENCE

Almaty «Kazak univercity» 2011 475

УДК 539.2 : 537.3 ББК 22.37+30.03я7 К 68 Рекомендовано к изданию Ученым советом физического факультета и РИСО КазНУ имени аль-Фараби Р е ц е н з е н т ы: доктор физико-математических наук, профессор А.М. Ильин; доктор физико-математических наук, профессор, академик НАН РК Н.Ж. Такибаев; доктор технических наук, профессор Deawha Soh (Южная Корея)

Коробова Н.Е., Сарсембинов Ш.Ш. Introduction to the material science (Введение в материаловедение)/ N. Korobova, Sh. Sarsembinov. – Изд. 2, дополненное. – Алматы: Қазақ университеті, 2011. – 472 с.

8812 КМЖ 68

ISBN 9965-791-12-0 В первых главах книги рассмотрены фундаментальные физические и химические положения, непосредственно относящиеся к материалам; структура твердых тел. где особое внимание уделено кристаллам, несовершенству структуры и твердым растворам. Последние главы имеют инженерную направленность и образуют единое целое с теоретическими вопросами материаловедения. Учебное пособие на английском языке позволяет расширить знания студентов не только по материаловедению, но и увеличить словарный запас специальных терминов. Рассчитанная на бакалавров старших курсов, магистрантов и докторантов Ph.D, эта книга окажется полезной всем инженерам, физикам и химикам. интересующимся вопросами современного материаловедения. Библиогр. 9 назв. Ил. 385. Табл. 19

УДК 539.2 : 537.3 ББК 22.37+30.03я7

К 4310020000-071 015-10 460(05)-11

ISBN 9965-791-12-0

© Коробова Н.Е, Сарсембинов Ш.Ш., 2011. © КазНУ им. аль-Фараби, 2011.

476

Introduction to the Material Science

Korobova N.E.& Sarsembinov Sh.Sh.

Department of Physics Kazakh National University

PREFACE Material Science – the study of engineering materials – has become a notable addition to engineering education during the past decade. It has gained its position in the curriculum part because of increased level of sophistication required of engineers in a rapidly changing technological society. The properties and characteristics of materials figure prominently in almost every modern engineering design, providing problems as well as opportunities for new invention, and setting limits for many technological advances. The study of solids and relationship between structure and physical properties is therefore an important component of modern engineering education. It is our belief that an introductory course on materials should emphasize principles rather than empirical facts; consequently, this book does not give the student extensive knowledge about the myriad engineering materials now in existence; it does provide a conceptual framework for understanding the behavior of engineering materials by emphasizing important relationships between internal structure and properties. It attempts to present a general picture of the nature of materials and the mechanisms that act upon, modify, and control their properties. The subject matter in this book is meant to provide prospective engineers with sufficient background and understanding for them to appreciate existing materials and to exploit new materials development effectively. The Introduction to the Material Science is designed for a third- or forth-year undergraduate course and therefore draws upon the student’s knowledge of introductory physics, chemistry, and elementary calculus. The book has three main parts. The first part treats the internal structure of materials, both perfect in imperfect. It also deals with kinetic problems of diffusion, phase transformations, and structure control. The second and third parts treat the mechanical and electronic properties of materials showing the relation to structure. The authors wish to acknowledge the assistance and able advice of many colleagues at Kazakh National University. This book is an outgrowth of the introductory materials science course offered at KNU, to which many people have contributed substantially. 4

CHAPTER 1 Materials for Engineering

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CHAPTER 1 MATERIALS FOR ENGINEERING 1.1 Material world We live in the world of materials that influence on our life. In the ancient time the material define tools and weapons. In the early human civilization there is a popular way to name the era: Stone Age – form weapons for hunting; Bronze Age – the foundation of metallurgy (alloys of copper and tin used for tools and weapons); Iron Age – iron alloys replaced bronze for tool and weapons. There are no “pottery age” or “glass age”, but we know about importance of the clay in the human cultures. Present days we can name: 1) “plastic age”. This is compliment to the economical polymeric materials from which so many products are made. 2) or “silicon age” – because of modern electronics largely based on silicon technology. So Material science and Engineering is very important branch in the fundamental, scientific studies and practical engineering. It made great contribution to many traditional fields, including:  metallurgy,  ceramic engineering,  polymer chemistry,  condensed matter physics,  physical chemistry. Today you begin to investigate this subject. Before we continue, I would like to explain our joint work. For better understanding you must do your homework. If you don’t understand something, ask me question. My idea is to know how you 1) understand the new material about the key aspects of selection material by yourself without me; 2) how you try to analyze it; 3) how you can explain something to another person. Do you have some questions for me? Let’s continue. 6

1.2 Types of Materials We consider 5 categories for practical engineers: 1. metals; 2. ceramics and glasses; 3. polymers; 4. composites; 5. semiconductors. Metals If I ask you what typical metal do you know? You answer me – steel! Metallic properties: (1)strong and be formed into practical shapes; (2) permanent deformability or ductility; (3) characteristic metallic luster; (4)good conductor of electrical current Fig. 1.1 shows how many chemical elements in the periodic table are metallic.

Fig.1.1 Periodic table of the elements with those elements that are inherently metallic in color

This is a large family indeed. But so many compounds based on the various alloys, including the iron and steels (from Fe); aluminum alloys (Al); magnesium alloys (Mg); titanium alloys (Ti); copper alloys (Cu) and etc. Ceramics and glasses Aluminum is a common metal, but aluminum oxide Al2O3 is 7

typical of a fundamentally different family – ceramics. Advantages ceramics over metallic compound: 1) chemically stable in a wide variety of severe environment; 2) has a significantly higher melting point (2020 0C for Al2O3 and for Al only 660 0C). Conclusion: this makes oxides a popular refractory and a high-temperature resistant material of wide use in industrial furnace construction. Disadvantages: Brittleness (so ceramics are eliminated from many structural application because they are brittle). SiO2 Is typical example of the traditional ceramics and SiO2 is another good example. SiO2 is the basis of a large and complex family of silicates, which includes clays and claylike minerals. Si3N4 is an important nonoxide ceramic used in a variety of structural applications Fig.1.2.

Fig.1.2 Periodic table with ceramic compounds indicated by a combination of one or more metallic elements ( in light color) with one or more nonmetallic elements ( in dark color)

You can see in the Periodic table only 5 nonmetallic elements (C, N, O, P, S). 8

Remember: Many commercial ceramics include compounds and solutions of many than 2 elements.

Fig.1.3. Some common ceramics for traditional engineering applications

Properties: 1) metals and ceramics may be crystalline structure (atoms are stacked together in a regular and repeating pattern); 2) many ceramics can be made in noncrystalline form (atoms are stacked in irregular and random pattern). Example of noncrystalline form is glass. Most common glasses are silicates. Ordinary window glass is approximately 72 % silica (SiO2 ) by weight + sodium oxide (Na2O) and calcium oxide (CaO). Glasses are important engineering materials because of other properties, such as  their ability to transmit visible light (ultraviolet and infrared radiation); chemical inertness. So we consider: Ceramics, then Glass. Now we have 3-d category: 9

Glass-ceramics (Fig.1.4).

Fig.1.4.Some common silicate glasses for engineering applications

Certain glass composition (lithium aluminosilicates) can be fully devitrified (that is from vitreous or glassy state transformed to the crystalline state) by special thermal treatment.  Polymers Polymers are the representatives of the materials of the modern engineering technology Fig.1.5. The alternative name for this category is plastics. These synthetic or human-made materials are the special branches of organic chemistry. The main part of the 10

polymer is a single hydrocarbon molecule such as ethylene (C2H4). Polymers are long-chain molecules composed of many mers bonded together. The most common commercial polymer is polyethylene (C2H4-)n, where n can range from approximately 100 to 1000.

Fig.1.5. Miscellaneous internal parts of a contemporary parking meter are made of an acetyl polymer

Fig.1.6 shows the limited portion of the Periodic table that is associated with commercial polymers.

Fig.1.6. Periodic table with the elements associated with commercial polymers in color 11

Remember: 1) Many important polymers including polyethylene are simply compounds of hydrogen and carbon. 2)Others contain oxygen (e.g., acrylics), nitrogen (nylons), fluorine (fluoroplastics), and silicon (silicones). Properties: (1) ductility; (2) lightweight; (3) low cost alternatives to metals in structural design applications; (4) lower strength compared with metals; (5) lower melting point and higher chemical reactivity compared with ceramics and glasses.  Composites Composites – combinations of individual materials from the previous categories. The best example is fiberglass. This is composite of glass fibers embedded in a polymer matrix.

(a)

(b)

Fig.1.7. (a) SEM picture as a good example of a fiberglass composite composed of microscopic scale reinforcing glass fibers in a polymer matrix, (b) application of fiberglass

Properties (the best properties of each component): 1) high strength of the small-diameter glass fibers is combined with 2) ductility of the polymer matrix = result is 12

3) the strong material capable of withstanding the normal loading required of a structural material. In the Lecture 14 we will discuss in detail 3 main types of composites. Remember: Fiberglass is typical synthetic fiberreinforced materials ( Fig.1.7). 1) Wood – excellent example of a natural material with useful mechanical properties because of a fiber-reinforced structure. 2) Concrete is a common example of an aggregate composite. 3) Rock and sand reinforce a complex silicate cement matrix. 1.3 Semiconductors Polymer materials we can see every day and everywhere. But semiconductors are relatively invisible for us.

Fig.1.8 Preparation of semiconductor silicon wafers

A relatively small group of elements and compounds has an important electrical property – semiconduction – in which they are neither good electrical conductor (as metals) nor good electrical insulators (as polymers or ceramics). Their ability to conduct electricity is intermediate and we call them semiconductors. Three important compounds Si, Ge (germanium) – widely used compounds, Sn – serve as a kind of boundary between metallic and nonmetallic elements. Remember: 13

1) Precise control of chemical purity allows precise control of electronic properties. 2) The elements can form compounds. (e.g., GaAs – gallium arsenide) – it used as a high-temperature rectifier and a laser material, or (CdS – cadmium sulfide) – as a relatively low-cost solar cell for conversion of solar energy to useful electrical energy. 1.4 “Compound – structure – properties” Question: What is the difference between graphite and diamond? They consist of the same compoundCARBON! To understand the difference it is necessary to understand their structure on an atomic or microscopic scale. Remember: Every major property of the 5 materials’ categories is a result of atomic and microscopic mechanisms. Any engineer responsible for selecting various metals for design applications must be aware that some alloys are relatively ductile, whereas others are relatively brittle. Example: Aluminum alloys are characteristically ductile, while magnesium alloys are typically brittle. Question: Why? Answer: This fundamental difference relates directly to their different crystal structures. See Fig.1.8.

Fig.1.8. Comparison of crystal structure for (a) aluminum and (b) magnesium Later in Lecture 3 we consider the nature of this crystal structure, but now note, that Al structure follows a cubic packing and Mg – a hexagonal one. 14

On Fig. 1.9 you can see the contrast in mechanical behavior of Al (it relatively ductile) and Mg (relatively brittle). Each sample was pulled in tension until it fractured. This is result of atomic scale structure.

Fig.1.9. Contrast in mechanical behavior of (a) of aluminum (relative ductile) and (b) magnesium ( relative brittle) resulting from the atomic-scale structure shown in Fig. 1-8. Each sample was pulled in tension until it fractured.

A significant achievement in materials technology in recent decades is the development of transparent ceramics, which has been made possible new products and substantial improvements in others (such as commercial lighting). To make traditionally opaque ceramics, such as Al2O3 into optically transparent materials required a fundamental change in microscopic-scale architecture. Question: How to eliminate the porosity? In 1962 in USA proposed simple invention – to add a small amount of impurity (0,1 % MgO), which caused the high temperature densification process for the Al2O3 powder to go to completion. The resulting pore-free microstructure produced a nearly transparent material (Fig.1.10c and 1.10d) with an important additional property – excellent resistance to chemical attack high-temperature sodium vapor. 15

Cylinders of translucent Al2O3 became the heart of the design of high-temperature (1000 0C) sodium vapor lamps, which provide substantially higher illumination than do conventional light bulbs. Compare: 100 lumens/W and 15 lumens/W!!!!

Fig.1.10. Porous microstructure in polycrystalline Al2O3 (a) leads to an opaque material (b). Nearly pore-free microstructure in polycrystalline Al2O3 (c) leads to a translucent material (d).

Look Fig.1.11. Note that the Al2O3 cylinder is inside the exterior glass envelope.

Fig.1.11. High-temperature sodium vapor lamp made possible by use of a translucent Al2O3 cylinder for contain the sodium vapor.

1.5 Processing materials Our use of modern materials ultimately depends on our ability to make those materials. 16

I try to explain how each of 5 types of materials are produced. Now I want to discuss with you: 1) do you understand the different nature of each type of material? 2) you must remember, that effects of processing history influenced on the properties. 3) Example:  Al2O3 - from oxidation Al; 4Al + 3O2 = 2Al2O3  Al2O3- from thermal treatment Al(OH)3; 2Al(OH)3 = Al2O3+ 3H2O So it is very difficult and very important to know: “How do you produce a material with optimal properties?”

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1.6 Selection of materials Before we try to understand “What material are available for you?” and then you must to know “which material do you select for a practical application?” Materials selection is the final, practical decision in the engineering design process and can determine that design’s ultimate success or failure. Important points for Quiz #1 You must make 2 separate decisions: Which general type of material is appropriate (metal, ceramic, etc.). The best specific material within that category must be found (e.g., is a magnesium alloy preferable to aluminum or steel?) The choice of the appropriate type of material is sometimes simple and obvious. Example N1 You must select semiconductor component for a solid-state electronic device. So conductors or insulators are entirely inappropriate in this place. But most choices are less obvious. Example N2: You must select material for construction of a commercial gas cylinder. Let’s see the sequence of choices leading to selection of metal as the appropriate type of material for construction of a commercial gas cylinder on Fig.1.12. Explanation: You must remember that the appropriate type of material for construction of a commercial gas cylinder must be capable of storing gases at pressures as high as 14 MPa for indefinite periods. So it must be: 1) Strength; 2) Ductile; 3) Low cost 18

Fig.1.12. (a) Sequence of choices leading to selection of metal as the appropriate type of material for construction of a commercial gas cylinder. (b) Commercial gas cylinder.

Your decision: 3 common structural materials: metals, ceramics, polymers. Polymers – rejected because of typically low strengths. (1) property – “strength” had metals, ceramics, composites; Some structural ceramics generally fail to provide the necessary ductility to survive practical handling. So the use of such a brittle material in a pressure-containing design can be extremely dangerous. (2) property – “ductile” had metals, composites; Several common metals provide sufficient strength and ductility to serve as excellent candidates. It must also be noted that many fiber-reinforced composites can satisfy the design requirements. However, the 3-d criterion – COST – eliminates them from competition. (3) property – “low cost” had only metals We try to use composites with high price and as we said with “added cost” only if a special advantage results, (it may be 19

reducing weight. It is one such advantage that frequently does justify the cost) – cosmic application. Final selection: Metals But there are so many candidates for this. Remember: 1) You must consider:  commercially available,  moderately priced alloys with  acceptable mechanical properties 1) In making the final alloy selection, property comparisons must be made at each step in the path. 2) Superior mechanical properties can dominate the selection of material. But really and more often cost dominates. 3) Mechanical performance typically focuses on a trade-off between the strength of the material and its deformability.

4) 5) 6) 7) 8)

Conclusion 1) The wide range of materials available to engineers can be divided into 5 categories: metals, ceramics and glasses, polymers, composites, semiconductors. 2) The first 3 categories can be associated with distinct types of atomic bonding. 3) Composites involve combinations of 2 or more materials from previous 3 categories. The first 4 categories comprise – Structural materials Semiconductors comprise a separate category of electronic materials that is distinguished by its unique, intermediate electrical conductivity. Structure at the microscopic or atomic scale influenced on the properties of these materials. If you understand the necessary properties the processing and selection of the appropriate material for a given application can be done. The selection of materials is done at 2 levels: 1) competition among the various categories of materials; 2) competition within the most appropriate category for the optimum material. 20

CHAPTER 2 Atomic Bonding

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CHAPTER 2 ATOMIC BONDING Atomic bonding falls into 2 general categories. 1) Primary bonding involves transfer or sharing of electrons and produces a relatively strong joining of adjacent atoms. Remember: ionic, covalent and metallic bonds are in this category. 2) Secondary bonding involves a relatively weak attraction between atoms in which no electron transfer or sharing occurs. Remember: Van-der-Waals bonds are in this category. Conclusion: each of the 4 fundamental types of engineering materials (metals, ceramics and glasses, polymers, and semiconductors) is associated with a certain type of atomic bonding. 2.1 Atomic structure Lets remember the simple planetary model of atomic structure: electrons (as the planets) orbit about a nucleus ( the sun). We need consider the number of protons and neutrons in the nucleus as the basis of the chemical identification of a given atom. See Fig. 2-1. It is a planetary model of a carbon atom. Nucleus is very small and contains all the mass of the atom. Remember: 1) Each proton and neutron has the mass of 1.66  10–24 g. This value is referred to as an atomic mass unit (amu). Carbon C12 contains in its nucleus 6 protons and 6 neutrons, for an atomic mass of 12 amu. 2) Avogadro’s number (NA) – the number of protons or neutrons necessary to produce a mass of 1 g. NA =0.6023  1024 amu/g. 3) For a compound, the corresponding term is mole. Example N1: 1 mole NaCl contains Avogadro’s number of Na atoms and Avogadro’s number of Cl atoms. Example N2: Avogadro’s number of atoms would have a mass of 12.00 g. 4) Some elements contain not the same number of neutron as protons and we call such element isotope. Carbon can contain 7 neutrons 22

and we have isotope C13. But the nuclei of all carbon atoms contain six protons.

(a)

(b)

Fig.2.1 (a) Schematic of the planetary model of 12C atom, and (b) helium

5) The number of protons is knows as the atomic number of the element. 6) Neutron – electrically neutral 7) Proton has positive charge 8) Electron has a negative charge ( 0.16 10-18 C – coulomb). 9) Electron is a goof example of the wave- particle duality ( has wavelike and particle like behavior). 10) Electrons are grouped at fixed orbital positions about a nucleus. Each orbital radius is characterized by an energy level. Fig. 2.2 shows the energy-level diagram for the orbital electrons 12C atom. An attractive energy is negative. The 1s electrons are closer to the nucleus and more strongly bond (binding energy = - 283.9 eV). The outer orbital electrons have a binding energy of only –6.5 eV. The zero level of binding energy corresponds to an electron completely removed from the attractive potential of the nucleus.

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Fig.2.2 Energy-level diagram for the orbital electrons 12C atom

6 electrons in the C12 atom are described as 1s22s22p2 distribution. It means 2 electrons in the 1s orbital; 2 electrons in the 2s orbital, 2 electrons in the 2p orbital . In fact electrons described as 1s22s12p3 . Hybridization – called the sp3 configuration in the second energy level. 2.2 The ionic bond Ionic bond – is the result of electron transfer from one atom to another. Fig.2.3 shows an ionic bond between sodium and chlorine. Ionic bonding between Na and Cl presents electron transfer from Na to Cl creates a cation (Na+) and an anion (Cl -). Question: Why electron easy transfers from Na to Cl? Explanation: Electron transfers from Na (sodium) because it is favored and produces a more stable electron configuration and chlorine readily accepts the electron.

24

Fig.2.3 Ionic bonding between sodium and chlorine atoms.

Remember: 1) As a result Na has positive charge and full outer orbital shell = Na+ = cation. Cl has negative charge and also full outer orbital shell = Cl - = anion. 2) Charged atoms are termed ions. 3) Ionic bond is non-directional. Na+ will attract Cl– equally in all directions. 4) The ionic bond is the result of the coulomb attraction between the oppositely charged species. 5) Well-known relationship Fc = -K/a2 (1) Where Fc is the coulomb force of attraction between 2 oppositely charged ions; 1) separation distance between the centers of the ions; K = ko (Z1q)  (Z2q), 25

(2)

where Z is the valence of the charged ion (e.g., +1) for Na+ and –1 for Cl -. Q – is the charge of a single electron (0.16 10-18 C); ko – constant = 9 109 V m/C. Remember: 2) Coulomb force of attraction increases dramatically as the separation distance between ions centers decreases. 3) The attempt to move 2 oppositely charged ions closer together to increase coulomb attraction is counteracted by an opposing repulsive force FR. 4) Repulsive force FR is due to the attempt to move 2 positively charged nuclei closer together. FR =  e –a/ (3) where  and  are constant for a given ion pair. Repulsive force as a function of a. 5) Bonding force is the net force of attraction (or repulsion) as a function of the separation distance between 2 atoms or ions. Fig. 2.4 shows the bonding force curve in which net bonding force F=FA + FR is plotted against a.

Fig. 2.4 Plot of the Coulomb force (Eq.1) for a Na+ - Cl- pair. 26

6) 7) 8) 9)

The equilibrium bond length a0 occurs at the point where the forces of FA and FR are balanced, FA + FR = 0. Coulomb force of attraction dominates for large values of a; Repulsive force dominates for small values of a. Bonding energy E is related to bonding force through the differential expression F = dE/da ,

(4)

when F=0, then a = a0; bonding energy =0 (minimum in the energy curve). Fig. 2.5 shows comparison of the bonding force curve and the bonding energy curve for Na +  Cl- pair.

Fig.2.5 Net bonding force curve for a Na+ - Cl- pair showing an equilibrium bond length of ao = 0,28 nm. 27

F =0 = (dE/da) a=ao

(5)

Important concept in material science: The stable ion position corresponds to an energy minimum. To move the ions from their equilibrium spacing, energy must be supplied to this system. Equilibrium bond length a0 = rNa+ + r Cl- = 2 ionic radii. (6) 2.3 Coordination number Coordination number (CN) is the number of ions (or atoms) surrounding a reference ion (or atom). Look at Fig 2.6. Structure of NaCl in which 6 Na + surround each Cl – and vice versa. So CN for NaCl = 6 (explanation: each has 6 nearest neighbors).

Fig.2.6 The largest number of ions of radius К that can coordinate an atoms of radius к is 3 when radius ratio, r/R=0.2

Fig.2.7 The minimum radius ratio, r/R that can produce three-fold coordination is 0.155.

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2.4 The covalent bond I am sure, that you remember 1) Ionic bond – is nondirectional; 2) Covalent bond – is highly directional; 3) The name covalent derives from cooperative sharing of valence electrons between 2 adjacent atoms. 4) Valence electrons are those outer orbital electrons that take part in bonding. Example N1: :Cl : Cl: Cl  Cl Figure illustrates the covalent bond in a molecule of chlorine gas (Cl2) and electron density, concentrated along a straight line between the 2 Cl nuclei. (electron dots and bond line).

Fig.2.8 The covalent bond in a molecule of chlorine gas, Cl2 is illustrated with (a) planetary model compared with (b) the actual electron density.

Example N2: You see bond-line representation of covalent molecule ethylene (C2H4). The double line between the 2 carbons signifies a double bond or covalent sharing of 2 pairs of valence electrons. 29

Fig.2.9. (a) An ethylene molecule (C2H4) is compared with (b) a polyethylene molecule -(C2H4)-n that result from the conversion of the C=C double bond into two C-C single bond.

By converting the double bond to 2 single bonds, adjacent ethylene molecules can be covalently bonded together, leading to a long – chain molecule of polyethylene. On Fig. 2.10 you can see 2-dimensional schematic representation of the “spaghetti-like” structure of solid polyethylene. The straight lines between C and C, and between C and H represent strong, covalent bonds. The bonding force and bonding energy curves for covalent bonding look similar to those as shown for ionic bonding. Remember: Important characteristic of covalent solids is the bond angle, determined by the directional nature of valence electron sharing. 30

Fig. 2.10 Two-dimensional schematic representation of the “spaghetti-like” structure of solid polyethylene.

Fig.2.11 Three-dimensional schematic structure of bonding in the covalent solid, carbon (diamond).

Fig. 2.12 illustrates the bond angle for a typical carbon atom, which tends to form 4 equally spaced bonds. This tetrahedral configuration gives a bond angle of 109.50. 31

Fig. 2.12 Tetrahedral configuration of covalent bond with carbon.

2.5 The metallic bond Remember again: 1) ionic bond involves electron transfer and is non-directional; 2) covalent bond involves electron sharing and is directional; 3) metallic bond involves electron sharing and is non-directional. Explanation: In this case, the valence electrons are said to be delocalized, that is they have an equal probability of being associated with any of a large number of adjacent atoms. In typical metals this delocalization 32

is associated with the electron cloud or electron gas. This “gas” is the basis for the high electrical conductivity in metals.

Fig.2.13. Metallic bond consisting of an electron cloud or gas. An imaginary slice is shown through the front face of the crystal structure of copper, revealing Cu2+ ion cores bonded by the delocalized valence electrons.

2.6 The secondary bond ( Van der Waals) Remember: 1) The mechanism of secondary bonding is somewhat similar to ionic bonding , that is the attraction of opposite charges. 2) The key difference is that no electrons are transferred. Attraction depends on asymmetrical distributions of positive and negative charge within each atom. Such charge asymmetry is referred to as a dipole. 3) Secondary bonding can be of 2 types depending on whether the dipoles are:  Temporary  Permanent. 33

Fig.2.14. Development of induces dipoles in adjacent argon atoms leading to a weak, secondary bond. The degree of charge distortion shown here is greatly exaggerated.

Fig.2.14 illustrates how 2 neutral atoms can develop a weak bonding force between them by a slight distortion of their charge distribution. Example – is argon (noble gas). It does not tend to form primary bonds because it has a stable and filled outer orbital shell. A) Isolated argon atom has a spherical distribution of negative electrical charge surrounding its positive nucleus. B) When another argon atom is nearby, the negative charge is drawn slightly toward the positive nucleus of the adjacent atom. Remember: 1) This slight distortion of charge distribution occurs simultaneously in both atoms. 2) The result is an induced dipole. 3) Secondary bonding energies are greater when molecular units containing permanent dipoles are involved. Best example is hydrogen bridge, which connects adjacent molecules of water H2O (Fig.2.15). Because of the directional nature of electron sharing in the covalent O – H bonds, the H atom s become positive centers and O atoms become negative centers for the for the H2O molecules. We call them polar molecules (molecule with a permanent separation of charge, gives a larger dipole moment M =ql (product of charge and separation distance between centers of positive and negative charge). So, water properties derives from the regular and repeating alignment of adjacent H2O molecules.

34

Fig.2.15 “Hydrogen bridge”. This secondary bond is formed between two permanent dipoles in adjacent water molecules.

2.7 Materials – the bonding classification We can se relative bond energies of the various bond types by comparison of melting point. Melting point of a solid indicates the temperature to which the material must be subjected to provide sufficient thermal energy to break its cohesive bonds. Let’s consider Table 2.1 35

Table 2.1 Comparison of melting points for some of the representative materials Material NaCl C (diamond) (-C2H4-)n Cu Ar H2O

Bonding type Melting point (oC) Ionic 801 Covalent  3550 Covalent and secondary  120 Metallic 1084.87 Secondary (induced dip - 189 Secondary (permanent d 0

Remember: 1) Note that polyethylene has mixed-bond character. 2) The secondary bonding is a weak link that causes the material to lose structural rigidity above approximately 120 0 C. This is not a precise melting point but a temperature above which the material softens rapidly with increasing temperature. 3) The irregularity of the polymeric structure produces variable secondary bond lengths and, variable bond energies. 4) Variation in bond energy is the average magnitude, which is relatively small. 5) Polyethylene and diamond have similar C – C covalent bonds!!, but the absence of secondary bond weak links allows diamond to retain its structure rigidity more than 3000 0C beyond polyethylene. 6) Mixed-bond character for ceramics referred to both ionic and covalent nature for a given bond (e.g., Si-O); 7) Mixed-bond character for polymers referred to different bonds being covalent (e.g., C-H) and secondary (e.g., between chains). Secondary bonding act as a weak link in the structure, giving characteristically low strengths and melting points. Let’s consider Table 2.2 and Fig.2.16.

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Table 2.2. Bonding Character of the 4 Fundamental Types of Engineering Materials Material type Metal

Bonding character Metallic

Ceramics & glass Ionic/covalent Polymers Semiconductors

Covalent and secondary Covalent or covalent/ionic

Example Iron (Fe) and the ferrous alloys Silica (SiO2): cryst, and noncryst. Polyethylene –(C2H4)nSilicon (Si) or cadmiu (CdS)

Fig.2.16. Tetrahedron representing the relative contribution of different bond types to the four fundamental categories of engineering materials ( the three structural types plus semiconductors).

37

Conclusion 1) One basis of the classification of engineering materials is atomic bonding. 2) Nature of atomic bonding is determined by the behavior of the electrons that orbit the nucleus. 3) Ionic bond involves electron transfer and is non-directional. The electron transfer creates a pair of ions with opposite charge. The attractive force between ions is coulomb in nature. 4) The covalent bond involves electron sharing and is highly directional. 5) The metallic bond involves sharing of delocalized electrons, producing a non-directional bond. The resulting electron cloud or gas results in high electrical conductivity. 6) Secondary bonding is a result of attraction between either temporary or permanent electrical dipoles.

CHAPTER 3 Crystalline Structure. Perfection

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CHAPTER 3 CRYSTALLINE STRUCTURE – PERFECTION Crystalline structure that is atoms of the material is arranged in a regular and repeating manner. 3.1 Seven Systems and Fourteen Lattices We must determine which structural unit is being repeated. The main idea – to have structural unit or we may say “unit cell”. The geometry of a general unit cell is shown in Figure 3.1.

Fig.3.1. Geometry of a general unit cell.

The length of unit cell edges and the angles between crystallographic axes are referred to as lattice constants or lattice parameters: a, b, c; , , . Remember:  The key feature of the unit cell is that it contains a full description of the structure as a whole because the repeated stacking of the adjacent unit cells face to face throughout three-dimensional space can generate the complete structure.  There are only 7 unique unit cell shapes that can be stacked together to fill 3-dimensional space. 40



Periodic stacking of unit cell generates point lattices, arrays of points with identical surroundings in 3-dimensional space. These lattices are skeletons upon which crystal structures are built by placing atoms or groups of atoms on or near the lattice points. Some of the simple metal structures are of this type (Fig.3.2).

Fig.3.2. The simple cubic lattice becomes the simple cubic crystal structure when an atom is placed on each lattice point. 41

3.2 Metal structures Look on Fig. 3.3. This is body-centered cubic (bcc) structure. This is cubic Bravais lattice with one atom centered on each point. There is 1 atom at the center of the unit cell and one-eighth atom at each of eight-unit cell corner. In each unit cell we have 1 +8 1/8 = 2 atoms. Typical metal for bcc structures: -Fe (stable form at room temperature), V, Cr, Mo, W. Look at Fig. 3.4. This is face-centered cubic (fcc) structure. This is cubic Bravais lattice with one atom shared between 2 unit cell =6 1/2 and one-eighth atom at each of eight-unit cell corner. In each unit cell we have 6 1/2 +8 1/8 = 4 atoms. Typical metals for fcc: -Fe (stable form at 912-1394 0C ), Al, Ni, Cu, Ag, Pt, Au. Hexagonal close packed (hcp) structure (Fig. 3.5) – more complicated structure. There are 2 atoms associated with each Bravais lattice point. There is 1 atom centered within the unit cell and various fractional atoms at the unit cell corners (4 by 1/6 atoms and 4 by 1/12 atoms), for a total we have 1 +4 1/6 +4 1/12 = 2 atoms. Typical metals for hcp: -Ti, Be, Mg, Zn, Zr. Remember: 1) Difference between fcc and hcp structure: The difference lies in the sequence of packing of these layers. (Fig. 3.6).  The fcc arrangement is such that the 4-th close-packed layer lies precisely above the first one and fcc stacking is referred to as an ABCABC…..  In the hcp structure, the 3-d close-packed layer lies precisely above the first. And hcp stacking is referred to as an ABAB….. 2) Useful relationships between unit cell size and atomic radius given in Table 3.1.

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Table 3.1 Relationship between unit cell size and atomic radius Crystal structure Body-centered cubic (bcc) Face-centered cubic (fcc) Hexagonal close packed (hcp)

Relationship between edge length, a and atomic radius, r a = 4r/3 a = 4r/2 A = 2r

Fig.3.3. Body-centered cubic (bcc) structure for metals showing (a) the arrangement of lattice points for a unit cell; (b) the actual packing of atoms (represented as hard spheres) within the unit cell; and (c) the repeating bcc structure, equivalent to many adjacent unit cells. 43

Fig.3.4. Face-centered cubic (fcc) structure for metals showing (a) the arrangement of lattice points for a unit cell; (b) the actual packing of atoms within the unit cell; and (c) the repeating fcc structure, equivalent to many adjacent unit cells.

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Fig.3.5. Hexagonal close packed (hcp) structure for metals showing (a) the arrangement of atom centers relative to lattice points for a unit cell; (b) the actual packing of atoms within the unit cell; and (c) the repeating hcp structure, equivalent to many adjacent unit cells.

3.3 Ceramic structures We consider only some of the most important and representative of ceramics. APF – atomic packing factor – represents the fraction of the unit cell volume occupied by various atoms. IPF – ionic packing factor – represents the fraction of the unit cell volume occupied by various cations and anions.  Simplest chemical formula: MX We begin with the simplest chemical formula: MX ( M- metal, Xnonmetallic element). 45

Example N1 – CsCl (cesium chloride). Fig. 3.7. this is simple cubic. You see Cesium (Cs+) in the center and 8 ions of chlorine (Cl) associated with each point: 1+ 81/8 = 2 ions.

Fig.3.6.Comparison of the fcc and hcp structures

Fig.3.7. Cesium chloride (СsСl) unit cell showing (a) ion position and the 2 ions per lattice point, and (b) full-size ions.

Example N2 – NaCl ( sodium chloride). Fig. 3.8. NaCl structure can be described as having an fcc Bravais lattice with 2 ions (one Na+ and one Cl-) associated with each lattice point. There are 8 ions ( 4 Na+ + 4 Cl-) per unit cell. Typical ceramics with this structure: MgO, CaO, FeO, NiO.

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Fig.3.8. Sodium chloride (NaСl) unit cell showing (a) ion position and the 2 ions per lattice point, and (b) full-size ions; (c) many adjacent unit cells.

 Chemical formula: MX2 Example N1: CaF2 (fluorite structure) Fig. 3.9 shows CaF2 (fluorite structure). CaF2 structure can be described as having an fcc Bravais lattice with 3 ions (one Ca2+ and 2 F-) associated with each lattice point. There are 12 ions ( 4 Ca2+ + 8 Cl-) per unit cell. Typical ceramics with this structure uranium dioxide) UO2, ThO2, TeO2. 47

Example N2: SiO2 (silica) Fig. 3.10 shows the cristobalite SiO2 structure. SiO2 structure can be described as having an fcc Bravais lattice with 6 ions (2Si4+ and 4O2-) associated with each lattice point. There are 24 ions ( 8 Si4+ + 16 O2-) per unit cell. The general feature of all SiO2 structures is the same – a continuously connected network of SiO4 4- tetrahedral. The starting of O2- ions by adjacent tetrahedral gives the overall chemical formula SiO2.

Fig.3.9. Fluorite (CaF2) unit cell showing (a) ion position and the 2 ions per lattice point, and (b) full-size ions.

Fig.3.10. The cristobalite (SiO2) unit cell showing (a) ion position, and (b) full-size ions; (c) the connectivity of SiO4-4 tetrahedra. In the schematic, each tetrahedron has a Si4+ at its center. In addition, an O2- would be at each corner of each tetrahedron and is shared with adjacent tetrahedron.

Remember: 1) Fe had different crystal structure stable in different temperature ranges. 2) The same is true for silica, SiO2. You can see equilibrium structures of SiO2 from room temperature (Low quartz – as crystallographic form and hexagonal structure) to its melting point (1732oC) and high crystobalite as crystallographic form and fcc structure ). 3) You see we have “Low quartz” – as crystallographic form and hexagonal structure at room temperature and higher than 573 0C (High quartz) we have just the same crystallographic form and hexagonal structure, but at this temperature (heated or cooled through the vicinity of 573 0C ) there is catastrophic structural damage.  Chemical formula: M2X3 Example N1: Al2O3 (corundum structure) Fig. 3.11 shows Al2O3 (corundum structure). Al2O3 structure can be 49

described as rhombohedra Bravais lattice but closely approximates a hexagonal lattice.

Fig.3.11. The corundum (Al2O3) unit cell shown superimposed on the repeated stacking of layers of close-packed O2- ions. The Al3+ ions full two-thirds of the small (octahedral) interstices between adjacent layers.

There are 30 ions (12 Al3+ + 18 O2-) per unit cell. Typical ceramics with this structure: Cr2O3, -Fe2O3.  Chemical formula: M’M’’X3 Example N1: Important family of ferroelectric and piezoelectric ceramics CaTiO3 (perovskite structure)

Fig.3.12.Perovskite (CaTiO3) unit cell showing (a) ion position, and (b) full-size ions.

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Fig. 3.12 shows CaTiO3 (perovskite structure). At first glance, it is the combination of simple cubic + bcc + fcc structure. But!!! You see that different atoms occupy the corner ( Ca2+), bodycentered (Ti4+), and face-centered (O2-) positions. There are 5 ions (1Ca2+ + 1Ti4+ + 3O2-) per unit cell.  Chemical formula: M’M’’2X4 Example N1: Important family of magnetic ceramics MgAl2O4 (spinel structure). Fig. 3.13 shows MgAl2O4 (spinel structure).

Fig.3.13. Ion position in the spinel (MgAl2O4) unit cell. The circles in color represented Mg2+ ions (in tetrahedral or four-coordinated position), and black represent Al3+ ions ( in octahedral or six-coordinated position).

Spinel structure can be described as having an fcc Bravais lattice with 14 ions (2 Mg2+ +4 Al3+ + 8O2-) associated with each lattice point. There are 56 ions (8 Mg2+ +16 Al3+ + 32O2-). Typical ceramics with this structure: NiAl2O4 , ZnAl2O4, ZnFe2O4 51

Fig. 3.14 shows the layered crystal structure of graphite, the stable room-temperature form of carbon.

Fig.3.14. (a) An exploded view of the graphite (C) unit cell; (b) a schematic of the nature of graphite’s layered structure.

Although monoatomic, graphite is much more ceramic-like than metallic. The hexagonal rings of carbon atoms are strongly bonded by covalent bonds. The bonds between layers are however of the Van-der-Waals type, accounting for graphite’s friable nature and application as a useful “dry” lubricant. It is interesting to contrast the graphite structure with the high-pressure stabilized form, diamond cubic, which plays such an important role in solid-state technology because semiconductor silicon has this structure (Fig. 3.15). This is nickname for the structure of uniform distribution of 12 pentagons among 20 hexagons is precisely the form of a soccer ball. In this case we have positive curvature to the surface of the backyball in contrast to the flat sheet like structure of graphite rings. “Structure –Properties- Applications” 1) Individual Cn buckyballs are unique, passive surfaces on an nmscale. Bucky-tubes hold the theoretical promise of being the highest strength reinforcing fibers available for the advanced composites

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Fig.3.15. It is interesting to contrast the graphite structure with the high-pressure stabilized form, diamond cubic, which plays such an important role in solid-state technology because semiconductor silicon has this structure (Fig. 3.15).

3.4 Polymeric structures We defined the polymers category of materials by the chainlike structure of long polymeric molecules. Compared to the stacking of individual atoms and ions in metals and ceramics, the arrangement 53

of these long molecules into a regular and repeating pattern is difficult. Recently was discovered another alternative form of carbon – fullerene – C60 molecule. Fig. 3.16 shows C60 molecule or buckyball and then you can see bucky-tube.

Fig. 3.16 (a) C60 molecule or buckyball; (b) Cylindrical array of hexagonal rings of carbon atoms, or buckytube.

As a result, most commercial plastics are to a large degree noncrystalline. In those regions of the microstructure that are crystalline, the structure tends to be quite complex.  Polyethylene, -(C2H4)-n is chemically quite simple. However, the relatively elaborate way in which the long =chain molecule folds back and forth on itself is illustrated in Fig. 3.17. You see orthorhombic unit cell – common crystal system for polymeric crystals. For metals and ceramics, knowledge of the unit cell structure implies knowledge of the crystal structure over a large volume. For polymers, we must be more cautious. Single crystals of

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polyethylene are difficult to grow. They tend be thin platelets, about 10 nm thick.

Fig.3.17. Arrangement of polymeric chains un the unit cell of polyethylene. The dark spheres are carbon atoms, and the light spheres are hydrogen atoms. The unit cell dimensions are 0.255 nm x 0.494 nm x 0.741 nm.

 Fig. 3.18 shows the triclinic unit cell for polyhexamethylene adipamide or nylon-66. Up to approximately 50 % of the volume of these materials would be if this crystalline form, with the balance noncrystalline. 3.5 Semiconductor structures A single structure dominates the semiconductor industry. The elemental semiconductors (Si, Ge, and gray Sn) share the diamond cubic structure (Fig.3.15). This is built on an fcc Bravais lattice with 2 atoms associated with each lattice point and 8 atoms per unit cell.

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MX type compounds with combinations of atoms having an average valence of 4+. For example, GaAs combines the 3+ valence of gallium with the 5+ valence of arsenic, and CdS combines the 2+ valence of cadmium with 6+ valence of sulfur.

Fig.3.18. Unit cell of the α-form of polyhexamethylene adipamide or nylon-66.

GaAs is example of III-V compound, and CdS – of II-IV compound. Many of these simple MX compounds crystallize in a structure closely related to the diamond cubic. Fig. 3.19 shows the zinc blend structure (ZnS), which is essentially the diamond cubic structure with Zn2+ and S2- ions alternating in the atom positions. 56

Fig.3.19. Zinc blend (ZnS) unit cell showing (a ) ion positions. There are two per lattice point. Compare this with the diamond cubic structure (Fig.3.18a); (b) – The actual packing of full-size ions associated with the unit cell.

This is again the fcc Bravais lattice but with 2 oppositely charged ions associated with each lattice site rather than 2 like atoms. There are 8 ions (4 Zn2+ and 4 S2- ) ions per unit cell. This structure is shared by both III-V compounds (e.g., GaAs, AlP, InSb) and II-VI compounds (e.g., ZnSe, CdS and HgTe). 57

Fig. 3.20 shows wurtzite structure (ZnS) – built on a hexagonal Bravais lattice with 4 ions (2 Zn2+ and 2 S2- ions) per lattice and per unit cell. As ZnS and CdS can be found with this structure. This is characteristic structure of ZnO.

Fig.3.20. Wurtzite (ZnS) unit cell showing (a ) ion positions; (b) - full-size ions.

3.6 Lattice positions, directions, and planes Who must deal with crystalline structure of materials must know a few basic rules for describing geometry in and around a unit cell. Notations for describing lattice positions The body- centered position in the unit cell projects midway along each of the 3 unit cell edges and is designated the ½ ½ ½ position. 58

Fig.3.21.Notation for lattice positions

Remember: a given lattice position in a given unit cell is structurally equivalent to the same position in any other unit cell of the same structure. These equivalent positions are connected by lattice translations, consisting of integral multiples of lattice constants along directions parallel to crystallographic axes (Fig.3.21). Notations for describing lattice directions These directions are always expressed as sets of integers, which are obtained by identifying the smallest integer positions intercepted by the line from the origin of the crystallographic axes (Fig. 3.22). How to distinguish the notation for a direction from that of a positions? The direction integers are enclosed in square brackets. The use of square brackets is important and is the standard designation for specific lattice directions. 59

Fig.3.22. Lattice translations connect structurally equivalent positions (e.g., the body center) in various unit cell.

Other symbols are used to designate other geometrical features. Look on Fig. 3.23. Note, that the line from the origin of the crystallographic axes through the ½ ½ ½ bcc position can be extended to intercept the 111 unit cell corner position. Further extension of the line will lead to interception of other integer sets (222, 333, etc.), the 111 set is the smallest. As a result, that direction is referred to as the [111]. When a direction moves along a negative axis, the notation must indicate this. For example, the bar above the final integer in the [111] direction in Fig. 3.23 designates that the line from the origin has penetrated the 11-1 position. Note that directions [111] and [111] are structurally very similar. Both are body diagonals through identical unit cells. In fact, if you look at all body diagonals associated with the cubic crystal system, it is apparent that they are structurally identical, differing only in their orientation in space (Fig. 3.24). In other words, the [111] direction would become the [111] direction if we made a different choice of crystallographic axes orientations. 60

Fig.3.23. Notation for lattice directions. Note that parallel [uvw] directions (e.g. [111]) share the same notation because only the origin is shifted.

Such a set of directions, which are structurally equivalent, is called a family of directions and is designated by angular brackets, An example of body diagonals in the cubic system is. < 111 > = [111], [111], [111], [111], [111], [111], [111], [111]

(1)

Angles In the frequently encountered cubic system, the angle can be determined from the relatively simple calculation of a dot product of 2 vectors. Taking directions [uvw] and [u’v’w’] as vector D =ua +vb +wc, and D’ =u’a +v’b +w’c, you can determine the angle, , between these 2 directions by 61

D * D  D D cos  or D * D cos    D * D

(2)

u * u   v * v  w * w 2

2

2

u v w

Remember!!! system only.

(u )

2

 (v)

2

 ( w)

2

(3)

Eqs (2) and (3) apply to the cubic

Fig.3.24. Family of directions , representing all body diagonals for adjacent unit cells in the cubic system.

Notation for describing lattice planes Lattice planes - are planes in a crystallographic lattice (Fig.3.25). As for directions, these planes are expressed as a set of integers, known as Miller indices. Obtaining these integers is a more 62

elaborate process than was required for directions. The integers represent the inverse of axial intercepts. For example, consider the plane (210) in Fig 3.25a. The (210) plane intercepts the a-axis at 1/2a, the b-axis at b, and is parallel to the c-axis (in effect, intercepting it at ). The inverses of the axial intercepts are ½, 1/1, 1/, respectively. These inverse intercepts give the 2, 1, and 0 integers leading to the (210) notation.

Fig.3.25.Notation for lattice planes. (a) The (210) plane illustrates Miller indices (hkl); (b) Additional examples.

Remember: 1) the use of these Miller indices seems like extra work. They play an important role in equations dealing with diffraction measurements. 2) The general notation for Miller indices is (hkl), and it can be used for any of the 7 crystal systems. 3) Hexagonal system can be conveniently represented by 4 axes, a 4-digit set of Miller - Bravais indices (hkil) can be defined as shown in Fig. 3.26. 4) We can group structurally equivalent planes as a family of planes with Miller or Miller-Bravais indices enclosed in braces, {hkl} or {hkil}. 5) Fig. 3.27 shows that the faces of a unit cell in the cubic system are of the {100} family with: 63

Fig.3.26. Miller-Bravais indices, (hkil), for the hexagonal system. {100} = (100), (010), (001), (100), (010), (001)

(4)

3.7 X-ray diffraction X-ray diffraction is used:  to measure the crystal structure of engineering materials;  to determine the structure of a new material,  or the known structure of a common material can be used as a source of chemical identification.

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Fig.3.27. Family of planes, {100}, representing all faces of unit cells in the cubic system.

Diffraction – is the result of radiation’s being scattered by a regular array of scattering centers whose spacing is about the same as the wavelength of the radiation. For example, parallel scratch lines spaced repeatedly about 1m apart cause diffraction of visible light (electromagnetic radiation with a wavelength just under 1 m). This diffraction grating causes the light to be scattered with a strong intensity in a few directions (Fig.3.28). The precise direction of observed scattering is a function of the exact spacing between scratch lines in the diffraction grating, relative to the wavelength of the incident light. Remember: 1) For X-rays, atoms are the scattering centers. 2) The specific mechanism of scattering is the interaction of a photon of electromagnetic radiation with an orbital electron in the atom. 3) A crystal acts as 3-dimensional diffraction grating. 4) For a simple crystal lattice, the condition for diffraction is shown in Fig. 3.29. 65

Fig.3.28. Diffraction grating for visible light. Scratch lines in the glass plate serve as light-scattering centers.

At the precise geometry, the difference in the path length between the adjacent X-ray beams is some integral number (n) of radiation wavelengths (). The relationship that demonstrates this condition is the Bragg equation. n = 2 d sin 

(5)

where d is the spacing between adjacent crystal planes and  is the angle of scattering as defined in Fig. 3.29. The angle  is usually referred to as the Bragg angle and the angle 2 is referred to as the diffraction angle because that is the angle measured experimentally. (Fig. 3.30).

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Fig.3.29. Geometry for diffraction of X-ray. The crystal structure is a 3-dimensional diffraction grating.

Fig.3.30. Relationship of the Bragg angle (θ ) and the experimentally measured diffraction angle (2 θ).

The magnitude of interplanar spacing ( d) is a direct function of the 67

Miller indices for the plane. For a cubic system, the relationship is fairly simple. The spacing between adjacent hkl planes is a d hkl = (6)  h2 + k2 + l2 where a is the lattice parameter (edge length of the unit cell). Remember: 1) Eq. (5) – defines diffraction condition for primitive unit cells. 2) Crystal structure with non primitive unit cells have atoms at additional lattice sites located along a unit cell edge, within a unit cell face, or in the interior of the unit cell. The result is that some of the diffraction predicted by Eq. (5) does not occur. An example of this effect is given in Table 3.2 for common metal structures. Table 3.2 Reflection rules of X-ray diffraction for the common metal structures Crystal structure Bodycentered cubic (bcc) facecentered cubic (fcc) Hexagonal close packed (hcp)

Diffraction does not occur when h + k + l = odd number

Diffraction occurs when

h,k, l mixed (i.e. both even and odd numbers) (h +2 k) =3n, l odd ( n is an integer)

h,k,l unmixed (i.e., are all even numbers or all odd numbers) All other cases

h + k + l= even number

You see from the Table 3.2, which sets of Miller indices do not produce diffraction as predicted by Bragg’s law. Example of Diffraction pattern (Fig.3.31) (each spot on the film represents diffraction of the X-ray beam from a crystal plane (hkl) and another diffraction pattern (Fig.3.33), where each peak represents diffraction 68

of the X-ray beam by a set of parallel crystal planes (hkl) in various powder particles.

Fig.3.31 Diffraction pattern of a single crystal of MgO ( with the NaCl structure). Each spot on the film represents diffraction of the X-ray beam from a crystal plane (hkl).

Fig.3.32 (a) Single-crystal diffraction camera (or Laue camera); (b) Schematic of the experiment.

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Fig.3.33. Diffraction pattern of Al powder. Each peak ( in the plot of x-ray intensity versus diffraction angle, 2θ) represents diffraction of the X-ray beam by a set of parallel crystal planes (hkl) in various powder particles.

Fig.3.34 (a) An x-ray diffractometer; (b) schematic of the experiment 70

Conclusion 1. Most materials are crystalline in nature; that is their atomic-scale structure is regular and repeating. 2. There are 7 crystal systems which correspond to the possible unit cell shapes. 3. There are 14 Bravais lattices that represent the possible arrangements of points through 3-dimensional space. 4. There are 3 primary crystal structures observed for common metals: Body-centered cubic (bcc), Face-centered cubic (fcc), Hexagonal close packed (hcp) 5. fcc and hcp structures differ only in the pattern of stacking of close-packed atomic planes.

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CHAPTER 4 Crystal Defects and Noncrystalline Structure. Imperfection

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CHAPTER 4 CRYSTAL DEFECTS AND NONCRYSTALLINE STRUCTURE – IMPERFECTION We discussed about perfectly repetitive crystalline structures. But we understand that nothing in our world is quite perfect. Now we are ready to discuss about imperfections. Remember: 1. That is no material can be prepared without some degree of chemical impurity. The impurity atoms or ions in the resulting solid solution serve to alter the structural regularity of the ideally pure material. 2. The simplest type of flaw is the point defect, for example, a missing atom (vacancy). This type of flaw is the inevitable result of the normal thermal vibration of atoms in any solid at a temperature above absolute zero. 3. Linear defects, or dislocations, follow an extended and sometimes complex path through the crystal structure. 4. Planar defects represent the boundary between a nearly perfect crystalline region and its surroundings. 4.1 The solid solution – chemical imperfection It is not possible to avoid some contamination of practical materials. Even high-purity semiconductor products have some measurable level of impurity atoms. Many engineering materials contain significant amounts of several different components (commercial metal alloys are examples). As a result, all materials that the engineer deals with on a daily basis are actually solid solutions. 1. The concept of a solid solution may be difficult to grasp, (it is essentially equivalent to the more familiar liquid solution, such as the water- alcohol system (Fig.4.1). The complete solubility of alcohol in water is the result of complete molecular mixing. 2. Similar result is seen in Fig.4.2, which shows a solid solution of copper and nickel atoms sharing the fcc crystal structure. Nickel acts 74

as a solute dissolving in the copper solvent. This configuration is referred to as a substitution solid solution because the nickel atoms are substituting for copper atoms on fcc atom sites. Remember:  This configuration will tend to occur when the atoms do not differ greatly in size.

Fig.4.1. Forming a liquid solution of water and alcohol. Mixing occurs on the molecular scale.

 

The water-alcohol system represents 2 liquids completely soluble in each other in all proportions. For complete miscibility in metallic solid solutions, 2 metals must be quite similar. 75

Fig.4.2. Solid solution of copper in nickel shown along a (100) plane. This is a substitution solid solution with nickel atoms substituting for copper atoms on fcc atom sites.

4.2 Hume-Rothery rules 1. Less than about 15 % difference in atomic radii 2. The same crystal structure 3. Similar electronegativities ( the ability of the atom to attract an electron) 4. The same valence Question: If 1 or more of the Hume-Rothery rules are violated, only partial solubility is possible. (Example: less than 2 at % (atomic percent) silicon is soluble in Al. Why? 76

Explanation: Because Al and Si violate rules 1,2,4. As regarding rule 3, electron negatives of Al and Si are quite different, despite their adjacent positions on the periodic table. Fig. 4-2 shows a random solid solution. By contrast, some systems form ordered solid solutions (alloy AuCu3 – Fig. 4.3).

Fig.4.3. Ordering of the solid solution in the AuCu3 alloy system. (a) Above 390 0C there is a random distribution of the Au and Cu atoms among the fcc sites.(b) Below 390 0C, the Au atoms preferentially occupy the corner positions in the unit cell, giving a simple cubic Bravais lattice.

At high temperatures (above 390 0C), thermal agitation keeps a random distribution of the Au and Cu atoms among the fcc sites. Below 390 0C, the Cu atoms preferentially occupy the face-centered positions, and the Au atoms preferentially occupy corner positions in the unit cell. Ordering may produce a new crystal structure similar to some of the ceramic compound structures. For AuCu3 at low temperatures, the structure is based on the simple cubic Bravais lattice. When atom sizes differ greatly, substitution of the smaller atom on a crystal structure site may be energetically unstable. In this case, it is more stable for the smaller atom simply to fit into one of the spaces, or interstices, among adjacent atoms in the crystal structure. Fig 4.4 shows such interstitial solid solution, which carbon dissolved interstitially in –Fe. This interstitial solution is a dominant phase in steels. Although more stable than a substitutional configuration of C atoms on Fe lattice sites, the interstitial structure of Fig. 4.4 produces considerable strain locally to the –Fe crystal structure, and less than 0,1 at % C is soluble in –Fe. 77

Fig.4.4. Interstitial solid solution of carbon in –iron. The carbon atom is small enough to fit with the some strain in the interstice (or opening) among adjacent Fe atoms in the structure of importance to steel industry.

To this point, we have looked at solid-solution formation in which a pure metal or semiconductor solvent dissolve some solute atoms either substitutionally or interstitially. The principles of substitutional solid-solution formation in these elemental systems also apply to compounds. Example: Fig. 4.5 shows a random, substitutional solid solution of NiO in MgO.

Fig.4.5. Random, substitutional solid solution of NiO in MgO. The O2- arrangement is unaffected. The substitution occurs among Ni2+ and Mg 2+ ions.

Here the O2- arrangement is unaffected. The substitution occurs between Ni2+ and Mg 2+. Fig. 4.5 example is very simple. In general, 78

the charged state for ions in a compound affects the nature of the substitution. In other words, one could not indiscriminately replace all of the Ni2+ ions in Fig. 4.5 with Al3+ ions. This would be equivalent to forming a solid solution of Al2O3 in MgO, each having distinctly different formulas and crystal structures. The higher valence of Al3+ would give a net positive charge to the oxide compound, creating a highly unstable condition. As a result, an additional ground rule in forming compound solid solutions is the maintenance of charge neutrality. Fig. 4.6 shows how charge neutrality is maintained in a dilute solution of Al3+ in MgO by having only 2 Al3+ ions fill every 3 Mg2+ sites.

Fig.4.6. Substitutional solid solution of Al2O3 in MgO is not simple as the case of NiO in MgO (Fig.4-5). The requirement of charge neutrality in the overall compound permits only two Al+ ions to fill every three Mg2+ vacant sites, leaving one Mg 2+ vacancy.

This leaves 1 Mg2+ site vacancy for each 2 Al3+ substitutions. This type of vacancy and several other point defects will be discussed further. This example of a defect compound suggests the possibility of an even more subtle type of solid solution. Fig. 4.7 shows a nonstoichiometric compound, Fe1-xO, in which x is ~ 0.05.An ideally stoichiometric FeO would be identical to MgO with a NaCl- type crystal structure consisting of equal numbers of Fe2+ and O2- ions. 79

Fig. 4.7 Iron oxide, Fe1-xO with x ~ 0.05 is an example of a nonstoichiometric compound. Similar to the case of Fig.4-6, both Fe2+ and Fe3+ ions occupy the carbon sites with one Fe2+ vacancy occurring for every two Fe3+ ions present.

Remember: ideal FeO is never found in nature due to the multivalent nature of iron. Some Fe3+ ions are always present. As a result, these Fe3+ ions play the same role in the Fe1-xO structure as Al3+ in the Al2O3 in the MgO solid solution of Fig. 4.6. One Fe2+ site vacancy is required to compensate for the presence of every 2 Fe3+ ions in order to maintain charge neutrality. 4.3 Point defects – zero- dimensional imperfections Structural defects exist in real materials independently of chemical impurities. Imperfections associated with the crystalline point lattice are called point defects. Fig. 4.8 illustrates the 2 common types of point defects associated with elemental solids: (1) The vacancy is simply an unoccupied atom site in the crystal structure. (2) The interstitial, or interstitialcy, is an atom occupying an interstitial site not normally occupied by an atom in the perfect crystal structure or an extra atom inserted into the perfect crystal structure such that 2 atoms occupy positions close to a singly occupied atomic site in the perfect structure. 80

In the preceding section we saw how vacancies can be produced in compounds as a response to chemical impurities and nonstoichiometric compositions.

Fig.4.8 Two common point defects in metal or elemental semiconductor structures are the vacancy and the interstitial.

Such vacancies can also occur independently of these chemical factors (e.g., by the thermal vibration of atoms in a solid above a temperature of absolute zero). Fig. 4.9 illustrates 2 analogs of the vacancy and interstitialcy for compounds. The Schottky defect is a pair of oppositely charged ion vacancies. This pairing is required in order to maintain local charge neutrality in the compound’s crystal structure. The Frenkel defect is a vacancy – interstitialcy combination. Most of the compound crystal structures were too “tight” to allow Frenkel defect formation. Remember: CaF2 – type structure can accommodate cation interstitials without excessively lattice strain. Charging due to “electron trapping “or” electron hole trapping” at these lattice imperfections can further complicate defect structures in compounds.

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4.4 Linear defects, or dislocations – one-dimensional imperfection We have seen that point (zero-dimensional) defects are structural imperfections resulting from thermal agitation.

Fig.4.9. Two common point defect structures in compound structures are the Schottky defect and the Frenkel defect. Note their similarity to the structures of Fig.4.8.

Linear defects, which are one-dimensional, are associated primarily with mechanical deformation. Linear defects are also known as dislocations. An especially simple example is shown in Fig. 4.10. The linear defect is commonly designated by the “inverted T” symbol (), which represents the edge of an extra half-plane of atoms. Such a configuration lends itself to a simple quantitative designation, Burgers vector, b. This parameter is simply the displacement vector necessary to close a stepwise loop around the defect. In the perfect crystal Fig. 4.11a, an m x n atomic step loop closes at the starting point. In the region of a dislocation (Fig.4.11b), the same loop fails to close. The closure vector (b) represents the magnitude of the structural defect. Fig. 4.10 represents a specific type of linear defect, the edge dislocation, so named because the defect, or dislocation line, runs along the edge of the extra row of atoms.

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Fig.4.10. Edge dislocation. The linear defect is represented by the edge of an extra half-plane of atoms.

(a)

(b)

Fig.4.11 Definition of the Burgers vector, b, relative to an edge dislocation. (a) In the perfect crystal, an m x n atomic step loop closes at the starting point. In the region of a dislocation, the same loop does not close, and the closure vector (b) represents the magnitude of the structural defect. For the edge dislocation, the Burgers vector is perpendicular to the dislocation line. 83

Remember N1: For the edge dislocation, the Burgers vector is perpendicular to the dislocation line. Fig. 4.12 shows a fundamentally different type of linear defect, the screw

Fig.4.12. Screw dislocation. The spiral stacking of crystal planes leads to the Burgers vector being parallel to the dislocation line.

dislocation, which derives its name from the spiral stacking of crystal planes around the dislocation line. Remember N2: For the screw dislocation, the Burgers vector is parallel to the dislocation line. Remember N3: The edge and screw dislocations can be considered the pure extremes of the linear defect structure. Remember N4: Most linear defects in actual materials will be mixed. Mixed dislocations has both edge and screw character. The Burgers 84

vector for the mixed dislocation is neither perpendicular nor parallel to the dislocation line but retains a fixed orientation in space consistent with the previous definitions for the pure edge and pure screw regions. The local atomic structure around a mixed dislocation is difficult to visualize, but the Burgers vector provides a convenient and simple description. In compound structures, even the basic Burgers vector designation can be relatively complicated. Fig. 4.13 shows the Burgers vector for Al2O3 structure.

Fig. 4.13 Burgers vector for Al2O3 structure. The large repeat distance in this relatively complex structure causes the burgers vector to be broken up into two (for O2-) or four ( for Al3+) partial dislocations, each representing a smaller slip step. This complexity is associated with the brittleness of ceramics compared to metals.

The large repeat distance in this relatively complex structure causes the Burgers vector to be broken up into 2 (for O2-) or 4 (Al3+) partial dislocations, each representing a smaller slip step. This complexity is associated with the brittleness of ceramics compared to metals. 85

4.5 Planar defects – two-dimensional imperfections What you must remember: 1) point defects and linear defects are acknowledgements that crystalline materials cannot be made flaw-free. 2) These imperfections exists in the interior of each of these materials. 3) There are various forms of planar defects. Fig.4.14 shows a twin boundary which separates 2 crystalline regions that are, structurally, mirror images of each other.

Fig.4.14 A twin boundary separates 2 crystalline regions that are, structurally, mirror images of each other.

This highly symmetrical discontinuity in structure can be produced by deformation (e.g., in bcc and hcp metals) and by annealing (e.g., in fcc metals). A more detailed picture of atomicscale surface geometry is shown in Fig. 4.16. This Hirth-Pound model of a crystal surface has elaborate ledge systems rather than atomically smooth planes. The most important planar defect for our consideration in this introductory course occurs at the grain boundary, the region between 2 adjacent single crystals, or grains. 86

Fig. 4.15. Simple view of the surface of a crystalline material

Fig. 4.16. More detailed model of the elaborate ledge like structure of the surface of a crystalline material. Each cube represents a single atom.

In the most common planar defect, the grains meeting at the boundary have different orientations. Aside from the electronic industry, most practical engineering materials are polycrystalline rather than in the form of single crystals. 87

Fig. 4.17 Typical optical micrograph of a grain structure, 100x.

The grain boundaries (Fig.4.17) have been lightly etched with chemical solutions so, that they reflect light differently from the polished grains, thereby giving a distinctive contrast. Fig. 4.18 shows a usually simple grain boundary produced when 2 adjacent grains are tilted only a few degrees relative to each other. This tilt boundary is accommodated by a few isolated edge dislocations. Most grain boundaries involve adjacent grains at some arbitrary and rather large disorientation angle. The grain boundary structure in this general case is considerably more complex than that shown in Fig. 4.18. Now we have improved understanding for the nature of the structure of high-angle grain boundary (by electron microscopy and computer modeling). Explanation N1: 1. A central component in the analysis of grain boundary structure is the concept of the coincident site lattice (CSL). Fig. 4.19. 2. A high-angle tilt boundary ( = 36.90) between 2 simple square lattices is shown in Fig. 4.19a. This specific tilt angle has been found to occur frequently in grain boundary structure in real materials. The 88

reason for its stability is an especially high degree of registry between the 2 adjacent crystal lattices in the vicinity of the boundary region. (Remember: that a number of atoms along the boundary are common to each adjacent lattice).

Fig. 4.18. Simple grain boundary structure. This is termed a tilt boundary because it is formed when two adjacent crystalline grains are tilted relative to each other by a few degrees (θ ). The resulting structure is equivalent to isolated edge dislocations separated by the distance b/ θ, where b is the length of the Burgers vector, b.

3. This correspondence at the boundary has been quantified in terms of the CSL.

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(a)

(b)

Fig.4.19. (a) A high-angle ( = 36.90) grain boundary between 2 square lattice grains can be represented by a coincidence site lattice, as shown in (b).

4. Fig.4.19b shows that, by extending the lattice grid of the crystalline grain on the left, one in five of the atoms of the grain on the right is coincident with that lattice . 5. The fraction of coincident sites in the adjacent grain can be represented by the symbol -1 = 1/5 or  = 5, leading to the label for the structure in Fig. 4.19a as a “5 boundary”. 6. The geometry of the overlap of the 2 lattices also indicates why the particular angle of ( = 36.90) arises. One can demonstrate that  = 2 tan-1 (1/3). Explanation N2: Another indication of the regularity of certain high-angle grain boundary structures is given in Fig. 4.21, which illustrates a 5 boundary in an fcc metal. This is a three-dimensional projection with the open circles and closed circles representing atoms on two different, adjacent planes (each parallel to the plane of this page. The crystalline grains can be considered to be composed completely of tetrahedra and octahedra. 1. Polyhedra formed by drawing straight lines between adjacent atoms in the grain boundary region are irregular in shape due to the misorientation angle but reappear at regular intervals due to the crystallinity of each grain. 90

Fig.4.20. A 5 boundary in an fcc metal, in which the [100] directions of two adjacent fcc grains are oriented at 36.9o to each other.

2. Low-angle model (Fig. 4.18) serves as a useful analogy for the high-angle case. Specifically a grain boundary between 2 grains at some arbitrary, high angle will tend to consist of regions of good correspondence (with local boundary rotation to form a n structure, where n is a relatively low number) separated by grain boundary dislocations (GBD), linear defects within the boundary plane. 3. The GBD associated with high-angle boundaries tend to be secondary in that they have Burgers vectors different from those found in the bulk material (primary dislocations). With atomic-scale structure in mind, we can return to the microstructure view of grain structures (e.g., Fig.4.17). In describing microstructures, it is useful to have a simple index of grain size. A frequently used parameter standardized by American Society for Testing and Materials (ASTM) is the grain-size number, G, defined by N = 2 G-1

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(1)

where N is the number of grains observed in an area of 1 in.2 (=645 mm2) on a photomicrograph taken at a magnification of 100 times (100 x), as shown in Fig. 4.21.

Fig.4.21. Specimen for the calculation of the grain size number, G, 100x. The material is a low-carbon steel similar to that shown in Figure 4-17.

The calculation of G follows. There are 21 grains within the field of view and 22 grains cut by the circumference, giving 21 + 22/2 = 32 grains in a circular area with diameter = 2.25 in. The area density of grains is N = 32 grains / [ (2.25/2)2 ]in.2 = 8.04 grains / in.2 From equation (1) N = 2 G-1 or G = ln N / ln 2 + 1 = ln (8.04)/ln 2 + 1 = 4.01 Although the grain- size number is a useful indicator of average grain size, it has the disadvantage of being somewhat indirect. It 92

would be useful to obtain an average value of grain diameter from a microstructural section. A simple indicator is to count the number of grains intersected per unit length nL, of a random line drawn across a micrograph. The average grain size is roughly indicated by the inverse of nL, corrected for the magnification, M, of the micrograph. Remember: 1) You must consider that the random line cutting across the micrograph (in itself, a random plane cutting through the microstructure) will not tend, on average, to go along the maximum diameter of a given grain. 2) Even for a microstructure of uniform size grains, a given planar slice (micrograph) will show various size grain sections (e.g., Fig. 4.22), and a random line would indicate a range of segment lengths defined by grain boundary intersections. 3) In general, then, the true average grain diameter, d, is given by d = C/ nLM

(2)

where C is some constant greater than 1. Extensive analysis of the statistics of grain structures has led to various theoretical values for the constant, C. For typical microstructures, a value of C =1.5 is adequate. 4.6 Noncrystalline solids – three-dimensional imperfections Some engineering materials lack the repetitive, crystalline structure. These noncrystalline, or amorphous, solids are imperfect in 3 dimensions. The 2-dimentional schematic of Fig. 4.22a shows the repetitive structure of a hypothetical crystalline oxide. Fig. 4.22b shows a noncrystalline version of this material. The latter structure is referred to as the Zachariasen model and, in a simple way, it illustrates the important features of oxide glass structures. Remember: 1) The building block of the crystal (the AO3-3 “triangle”) is retained in the glass; that is, short-range order (SRO) is retained. 93

2) Long-range order (LRO) – that is, crystallinity – is lost in the glass. 3) The Zachariasen model is the visual definition of the random network theory of glass structure. This is the analog of the point lattice associated with crystal structure.

Fig.4.22. Two-dimensional schematics give a comparison of (a) a crystalline oxide and (b) a noncrystalline oxide. The noncrystalline material retains short-range order (the triangularly coordinated building block) but loses long-range order (crystallinity).

Our first example of a noncrystalline solid was the traditional oxide glass because many oxides (especially the silicates) are easy to form in a noncrystalline state. This is the direct result of the complexity of the oxide crystal structures. Rapidly cooling a liquid silicate or allowing a silicate vapor to condense on a cool substrate effectively “freezes in” the random stacking of silicate building blocks (SiO4-4 tetrahedra). Since many silicate glasses are made by rapidly cooling liquids, the term-supercooled liquid is often used synonymously with glass. Remember: In fact, there is a distinction. 1) The supercooled liquid is the material cooled just below the melting point, where it still behaves like a liquid (e.g., deforming by a viscous flow mechanism).

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2) The glass is the same material cooled to a sufficiently low temperature that it has become a truly rigid solid (deforming by an elastic mechanism). The atomic mobility of the material at these low temperatures is insufficient for the theoretically more stable crystalline structures to form. Those semiconductors with structures similar to some ceramics can be made in amorphous forms also. Remember: 1)

There is an economic advantage to amorphous semiconductors compared to preparing high-quality single crystals. 2) A disadvantage is the greater complexity of the electronic properties. 3) The complex polymeric structure of plastics causes a substantial fraction of their volume to be noncrystalline. 4) Very popular the newest member of the class amorphous metals, also known as metallic glasses. Because metallic crystal structures are typically simple in nature, they can be formed quite easily. It is necessary for liquid metals to be cooled very rapidly to prevent crystallization. Cooling rates of 10C per microsecond are required in typical cases. This is an expensive process but potentially worthwhile due to the unique properties of these materials. Example: The uniformity of the noncrystalline structure eliminates the grain boundary structures associated with typical polycrystalline metals. This results in unusually high strengths and excellent corrosion resistance. Fig. 4.23 illustrates a useful method for visualizing an amorphous metal structure: Bernal model, which is produced by drawing lines between the centers of adjacent atoms. The resulting polyhedra are comparable to those illustrating grain boundary structure in Fig. 4.20. In the totally noncrystalline solid, the polyhedra are again irregular in shape but, of course, lack any repetitive stacking arrangement.

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Fig.4.23. Bernal model of an amorphous metal structure. The irregular stacking of atoms is represented as a connected set of polyhedra. Each polyhedron is produced by drawing lines between the centers of adjacent atoms

At this point it may be unfair to continue to use the term imperfect as a general description of noncrystalline solids. The Zachariasen structure (Fig. 4.22b) is uniformly and “perfectly” random. Imperfections such as chemical impurities, however, can be defined relative to the uniformly noncrystalline structure as shown in Fig. 4.24. Addition of Na+ ions to silicate glass substantially increases formability of the material in the supercooled liquid state (i.e., viscosity is reduced). Finally, the state-of-the-art in our understanding of the structure of noncrystalline solids is represented by Fig. 4.25, which shows the nonrandom arrangement of Ca2+ modifier ions in a CaO-SiO2 glass.

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Fig.4.24. A chemical impurity such as Na+ is a glass modifier, breaking up the random network and leaving non-bridging oxygen ions.

What we see in Fig. 4.25 is, in fact, adjacent octahedral rather than Ca2+ ions. Each Ca2+ ion is coordinated by 6 O2- ions in a perfect octahedral pattern. In turn, the octahedral tend to be arranged in a regular, edge-sharing fashion. This is in sharp contrast to the random distribution of Na+ ions implied in Fig. 4.24. The evidence for medium-range order in the study represented by Fig. 4.25 confirms 97

long-standing theories of a tendency for some structural order to occur in the medium range of a few nanometers,

Fig.4.25. Schematic illustration of medium-range ordering in a CaO-SiO2 glass. Edge sharing CaO6 octahedra have been identified by neutron diffraction experiments.

between the well-known short-range order of the silica tetrahedral and the long-range randomness of the irregular linkage of those 98

tetrahedral. As a practical matter, the random network model of Fig.4.22b is an adequate description of vitreous SiO2 Medium-range order such as that in Fig. 4.25 is, however, likely to be present in common glasses containing significant amounts of modifiers, such as Na2O and CaO. 4.7 Quasicrystals Intermediate structural state now referred to as a quasicrystal. The novel structural concepts generated to describe quasicrystals have improved our understanding of the nature of traditional crystals and glasses.

Fig.4.26. Electron diffraction pattern of a rapidly cooled Al6Mn alloy showing fivefold symmetry; that is, the pattern is identical with each rotation of 360o/5, or 72o, about its center. Such symmetry is impossible in traditional crystallography.

The Schechtman discovery that led to the idea of quasicrystals was an electron diffraction pattern of a micrometer-size crystallite of a rapidly cooled Al6Mn alloy exhibiting five-fold symmetry (Fig.4.26).

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(a)

(b)

Fig.4.27 (a) Skinny and fat rhombuses can be repeated in (b) a two-dimensional stacking to produce a space-filled pattern with fivefold symmetry. This Penrose tiling provides a schematic explanation for the diffraction pattern of Figure 4.26.

(a)

(b)

Fig.4.28. (a) The relation of the skinny rhombus of Figure 4.27 to the geometry of a regular pentagon. (b) The acute angle in the skinny rhombus is (1/5) π and, in the fat rhombus, is (2/5)π. These angles assure the fivefold symmetry of the Penrose tiling. 100

1)

The skinny rhombus is directly related to the key dimensions of the pentagon, namely, the edge and the diagonal.

Fig.4.29. The Penrose tiling of Figure 4.27b decorated with pentagons to illustrate the fivefold symmetry of the overall pattern. Note that there is orientational order (all pentagon bases are parallel), but the lack of regular spacing of pentagons corresponds to a noncrystalline structure.

2)

3) 4) 5)

Note that the ratio of the length of the pentagon’s diagonal to its edge is Φ, an important irrational number equal to (√5 +1)/2 = 1.618. The number Φ is sometimes called the golden ratio because of its fundamental role in numerous shapes in the natural world, as well as in the proportions of much of the architecture of the ancient world. The main role of the golden ratio in Fig. 4.28 is also shown by the fact that the ratio of the number of fat rhombuses to the number of skinny rhombuses is Φ. The direct relation of the rhombuses to fivefold symmetry indicates that the acute angle in the skinny rhombus is (1/5)π and in the fat rhombus is (2/5) π. The 3-dimensional Penrose tiling produces the fivefold symmetry of the 3-dimensional icosahedrons. 101

Fig.4.30. A theoretical diffraction pattern for a three-dimensional Penrose tiling directly matching the experimental pattern of Figure 4.26.

The icosahedron composed of 20 identical equilateral triangular faces, has a fivefold symmetry, where 5 triangles join at a vertex, as well as threefold symmetry and twofold symmetry.

Fig. 4.31. Three views of an icosahedron showing (a) fivefold symmetry, (b) threefold symmetry, and (c) twofold symmetry.

All 3 symmetries have been seen in the diffraction patterns of Al6Mn and other quasicrystalline materials. They referred to as 102

icosahedra phases. To date, numerous alloy systems have exhibited quasicrystalline structure: Al – Li-Cu; Al-Co-Cu; Al-CoNi. 4.8 Microscopy We can see grains photo (grain structure, taken with an optical microscope) – as an example of a common and important experimental inspection of an engineering material. The first such inspection was made in 1863 by H.C. Sorby. Optical microscope is familiar to you. Less familiar is the electron microscope. We discussed with you about X-ray diffraction as a tool for measuring ideal crystalline structure. Electron microscope is a standard tool for characterizing the microstructural features. Electron microscope Transmission electron microscope: (TEM) is similar to design to a conventional optical microscope except that instead of a beam of light focused by glass lenses, there is a beam of electrons focused by electromagnets (Fig. 4.32).

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(b) Fig.4.32. Design of a transmission electron microscope (a). The electron microscope uses solenoid coils to produce a magnetic lens in place of the glass lens in the optical microscope, (b) A commercial TEM.

Remember:  

This is possible due to the wavelike nature of the electron. For a typical TEM operating at a constant voltage of 100 keV, electron beam has a monochromatic wavelength λ = 3.7 x 10 –3 nm. (this is 5 orders of magnitude smaller than the wavelength of visible light = 400-700 nm) in optical microscopy.  Result = substantially smaller structural details can be resolved by the TEM compared with the optical microscope.  Practical magnifications in optical microscope = 2000 x (corresponding to a resolution of structural dimensions as small as about 0.25 μm); for TEM – magnifications = 100000 x ( resolution about 1 nm)

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Fig.4.33. The basis of image formation in the TEM is diffraction contrast. Structural variations in the sample cause different fractions (I) of the incident beam to be diffracted out, giving variations in image darkness at a final viewing screen.

Explanation for basis image in the TEM The image in TEM is the result of diffraction contrast.  The sample is oriented so that some of the beam is transmitted and some is diffracted.  Any local variation in crystalline regularity will cause a different fraction of the incident beam intensity to be “diffracted out”, leading to a variation in image darkness on a viewing screen at the base of the microscope (Fig.4.34).

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(a)

(b)

(c) Fig.4.34. (a) TEM image of the strain field around small dislocation loops in a zirconium alloy. These loops result from a condensation of point defects (either interstitial atoms or vacancies) after neutron irradiation. (b) Forest of dislocations in a stainless steel as seen by a TEM. (c)TEM image of a grain boundary. The parallel lines identify the boundary. A dislocation intersecting the boundary is labeled D.

Scanning electron microscope (SEM) SEM obtains structural images by an entirely different method than that used by the TEM. Explanation for basis image in the SEM 

An electron beam spot ~ 1 μm in diameter is scanned repeatedly over the surface of the sample. Slight variation in surface topography produce marked variations in the strength of the beam of secondary electrons – electrons ejected from the 106

surface of the sample by the force of collision with primary electrons from the electron beam.

Fig. 4.35 A commercial SEM. (Courtesy of Hitachi Scientific Instruments.)

 

 

The secondary electron beam signal is displayed on a TV screen in a scanning pattern synchronized with the electron beam scan of the sample surface. The magnification possible with the SEM is limited by the beam spot size and is considerably better than that possible with the optical microscope with the optical microscope but less than that possible with the TEM. Important feature of an SEM image is that it looks like a visual image of a large-scale piece. SEM is especially useful for convenient inspections of grain structure. 107

Fig.4.36. SEM image of a 23-μm-diameter lunar rock from the Apollo 11 mission. The SEM gives an image with “depth” in contrast to optical micrographs. The spherical shape indicates a prior melting process.

Fig.4.37. SEM image of a metal (type 304 stainless steel) fracture surface, 180x. 108

(a) (b) (c) Fig.4.38. (a) SEM image of the topography of a lead-tin solder alloy with lead-rich and tin rich regions. (b) A map of the same area shown in (a) indicating the lead distribution (light area) in the microstructure. The light area corresponds to regions emitting characteristic lead x-rays when struck by the scanning electron beam. (c) A similar map of the tin distribution (light area) in the microstructure.

2) Atomic resolution electron microscope Resolution for this instrument is about 0.1 nm. 3) Scanning tunneling microscope (STM) The first is in a new instrument capable of providing direct images of individual atomic packing patterns.

Fig.4.39. Scanning tunneling micrograph of an interstitial atom defect on the surface of graphite. 109

Explanation for basis image in the STM The name of STM comes from the x-y raster (scanning) by a sharp metal tip near the surface of a conducting sample, leading to a measurable electrical current due to the quantum – mechanical tunneling of electrons near the surface. For gap distance around 0.5 nm, an applied bias of tens of mV leads to nanoampere current flow. The needle’s vertical distance (z-direction) above the surface is continually adjusted to maintain a constant tunnel current. The surface topography is the record of the trajectory of the tip. Atomic force microscope (AFM) Explanation for basis image in the AFM AFM is based on the concept that the atomic surface should be resolvable, using a force as well as a current. This hypothesis was confirmed by demonstrating that a small cantilever can be constructed to have a spring constant weaker than the equivalent spring between adjacent atoms.

Fig.4.40. Schematic of the principle by which the probe tip of either a scanning tunneling microscope (STM) or an atomic force microscope (AFM) operates. The sharp tip follows the contour A-A as it maintains either a constant tunneling current (in the STM) or a constant force (in the AFM). The STM requires a conductive sample while the AFM can also inspect insulators. 110

Example: The interatomic force constant is typically 1 N/m, similar in value to that for a piece of common Al foil 4 mm long and 1 mm wide. This mechanical equivalence permits a sharp tip to image both conducting and nonconducting materials. Remember: STM – for conductive sample; AFM – for conducting and nonconducting materials. Conclusion 1.

3.

4.

5.

When the impurity, or solute, atoms are similar to the solvent atoms, substitutional solution takes place in which impurity atoms rest on crystal lattice sites. 2. Interstitial solution takes place when a solute atom is small enough to occupy open spaces among adjacent atoms in the crystal structure. Solid solution in ionic compounds must account for charge neutrality of the material as a whole. Point defects can be missing atoms or ions (vacancies) or extra atoms or ions (interstitialcies). Charge neutrality must be maintained locally for point defect structures in ionic compounds. Linear defects or dislocations, correspond to an extra halfplane of atoms in an otherwise perfect crystal. Although dislocation structures can be complex, they can also be characterized with simple parameters, the Burgers vector. Planar defects include any boundary surface surroundings a crystalline structure. Twin boundaries divide 2 mirrorimage regions. The exterior surface has a characteristic structure involving an elaborate ledge system.

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6. 7.

8.

9.

10. 11. 12. 13. 14.

The predominant microstructural feature for many engineering materials is grain structure, where each grain is a region with a characteristic crystal structure orientation. A grain-size number (G) is used to quantify this microstructure. The structure of the region of mismatch between adjacent grains (i.e., the grain boundary) depends on the relative orientation of the grains. Noncrystalline solids, on the atomic scale, are lacking in any long-range order (LRO) but may exhibit short-range order (SRO) associated with structural building blocks such as SiO4-4 tetrahedra. Quasicrystals represent an intermediate state between crystals and glasses. Their fivefold symmetry diffraction patterns are the result of orientation order on the absence of translation periodicity. The icosahedral phases have been described as 3dimensional Penrose tilings. Optical and electron microscopy are powerful tools for observing structural order and disorder. TEM uses diffraction contrast to obtain high-magnification (e.g., 100000 x) images of defects such as dislocations. SEM produces 3-dimensional- appearing images of microstructural features such as fracture surface. STM and AFM provide direct images of individual atomic stacking patterns.

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CHAPTER 5 Diffusion

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CHAPTER 5 DIFFUSION Solid-state diffusion – atoms movement. 1) In some cases, are redistributed within the microstructure of the material. 2) In other cases, atoms are added from the materials environment, or atoms from the material may be discharged into the environment. Understanding the nature of the movement of atoms within the material can be critically important both in producing the material and in applying it successfully within an engineering design. 5.1 Thermally activated processes A large number of processes in material science share the common feature – the process rate rises exponentially with temperature. The diffusivity of elements in metal alloys, the rate creep deformation in structural materials, and the electrical conductivity of semiconductors are a few examples that will be covered in this course. The general equation that describes these various processes is of the form rate = Ce –Q/RT

(1)

where C – is a preexponential constant (independent of temperature), Q – the activation energy, R – the universal gas constant, T – the absolute temperature. It should be noted that the universal gas constant is as important for the solid state as for the gaseous state. The term gas constant derives from its role in the perfect gas low (pV = nRT) and related gas-phase equations. In fact, R is a fundamental constant that appears frequently in this book devoted to the solid state. Eq. (1) is generally referred to as the Arrhenius equation. Taking the logarithm to each side of Eq. (1) gives 114

ln rate   ln C 

Q *1 R *T

(2)

By making a semi-log plot of ln (rate) versus the reciprocal of absolute temperature (1/T) , one obtains a straight-line plot of rate data (Fig. 5.1). The slope of the resulting Arrhenius plot is -Q/R. Extrapolation of the Arrhenius plot to 1/T=0 (or T = ∞) gives an intercept equal to lnC.

Fig. 5.1. Typical Arrhenius plot of data compared to Eq.2. The slope equals –Q/R and the intercept (at 1/T=0) is ln C.

The experimental result of Fig. 5.1 is a very powerful one. WHY? 1) Knowing the magnitudes of process rate at any 2 temperatures allows the rate at a third temperature (in the linear plot range) to be determined. 115

2) Similarly, knowledge of a process rate at any temperature and of the activation energy, Q, allows the rate at any other temperature to be determined. 3) A common use of the Arrhenius plot is to obtain a value of Q from measurement of the slope of the plot. 4) This value of activation energy Q can indicate the mechanism of the process. 5) Eq. (2) contains 2 constants. Therefore. Only 2 experimental observations are required to determine them. To appreciate why rate data show the characteristic behavior of Fig. 5.1, we must explore the concept of the activation energy, Q. As used in Eq. (1), Q has units of energy per mole. It is possible to rewrite this equation by dividing both Q and R by Avogadro’s number (NA), giving rate = C · e –q/kT

(3)

where (q = Q/ NA ) is the activation energy per atomic scale init (atom, electron, ion, etc.) and (k = R/ NA) is Boltzmann’s constant (13.8 x 10-24 J/K). Eq. (3) provides for an interesting comparison with the high-energy end of the Maxwell-Boltzmann distribution of molecular energies in gases: P = ∞ e - ∆E/kT

(4)

where P is the probability of finding a molecule at an energy- ∆E greater than the average energy characteristic of a particular temperature, T. Herein lies the clue to the nature of the activation energy. It is the energy barrier that must be overcome by thermal activation. Although Eq. (4) was originally developed for gases, it applies to solids as well. As temperature increases, a larger number of atoms (or any other species involved in a given process, e.g., electrons or ions) are available to overcome a given energy barrier, q. Fig. 5.2 shows a process path in which a single atom overcomes an energy barrier, q. 116

Fig.5.2. Process path showing how an atom must overcome an activation energy, q, to move from 1 stable position to a similar adjacent position.

Fig. 5.3 shows a simple mechanical model of activation energy in which a box is moved from 1 position to another by going through an increase in potential energy, ∆E, analogous to the q in Fig. 5.2. In the many processes described in the text where an Arrhenius equation applies, particular values of activation energy will be found to be characteristic of process mechanisms. In each case, it is useful to remember that various possible mechanisms may be occurring simultaneously within the material, and each mechanism has characteristic activation energy. The fact that one activation energy is representative of the experimental data means simply that a single mechanism is dominant. If the process involves several sequential steps, the slowest step will be the rate-limiting step. The activation energy of the rate-limiting step will, then, be the activation energy for the overall process. 5.2 Thermal production of point defects Point defects occur as a direct result of the periodic oscillation, or thermal vibration, of atoms in the crystal structure. As temperature increases, the intensity of this vibration increases and, thereby, the 117

likelihood of structural disruption and the development of point defect increase.

Fig. 5.3. Simple mechanical analog of the process path of Fig. 5.2. The box must overcome an increase in potential energy, ∆E, in order to move from 1 stable position to another.

At a given temperature, the thermal energy of a given material is fixed, but this is an average value. The thermal energy of individual atoms varies over a wide range, as indicated by the Maxwell-Boltzmann distribution. At a given temperature, a certain fraction of the atoms in the solid have sufficient thermal energy to produce point defects. An important consequence of the MaxwellBoltzmann distribution is that this fraction increases exponentially with absolute temperature. As a result, the concentration of points defects increases exponentially with temperature; that is ndefects / n sites = C e –(E defect)/kT

(5)

where ndefects / n sites is the ratio of point defects to ideal crystal lattice sites, C is a preexponential constant; E defects is the energy needed to create a single-point defect in the crystal structure, k - is Boltzmann’s constant, T – is the absolute temperature.

118

The temperature sensitivity of point defect production depends on the type of defect being considered; that is, E defects for producing a vacancy in a given crystal structure is different from E defects for producing an interstitialcy. Fig. 5.4 illustrates the thermal production of vacancies in aluminum. The slight difference between the thermal expansion measured by overall sample dimensions (∆ L/L) and by X-ray diffraction (∆ a/a) is the result of vacancies.

(a)

119

(b) Fig.5.4. (a) The overall thermal expansion (∆ L/L) of Al is measurably greater than the lattice parameter expansion (∆ a/a) at high temperatures because vacancies are produced by thermal agitation. (b) A semi-log (Arrhenius –type) plot of ln (vacancy concentration) versus 1/T based on the data of part (a). The slope of the plot (E v/k) indicates that 0.76 eV of energy is required to create a single vacancy in the Al crystal structure.

The X-ray value is based on unit cell dimensions measured by X-ray diffraction. The increasing concentration of empty lattice sites (vacancies) in the material at temperatures approaching the melting point produces a measurably greater thermal expansion as measured by overall dimensions. The concentration of vacancies (n v/ n sites ) follows the Arrhenius expression of Eq. (5),

n v/ n sites = C e –(E v)/kT 120

(6)

where C is a preexponential constant; E v is the energy of formation of a single vacancy. As discussed previously, this expression leads to a convenient semi=log plot data. Taking the logarithm of each side of Eq.6 gives ln (n v/ n sites ) = ln C - (E v)/kT

(7)

Fig. 5.4 shows the linear plot of ln (n v/ n sites ) versus 1/T. The slope of this Arrhenius plot is (E v)/k. These experimental data indicate that the energy required to create q vacancy in the Al crystal structure is 0.76 eV. 5.3 Point defects and solid-state diffusion At sufficient temperatures, atoms and molecules can be quite mobile in both liquids and solids. Watching a drop of ink fall into a breaker of water and spread out until all the water is evenly colored gives a simple demonstration of diffusion, the movement of molecules from an area of higher concentration to an area of lower concentration. But diffusion is not restricted to different materials. At room temperature, H2O molecules in pure water are in continuous motion and migrating through the liquid as an example of self-diffusion. This atomic-scale motion is relatively rapid in liquids and relatively easy to visualize. It is more difficult to visualize diffusion in rigid solids. Nonetheless, diffusion does occur in the solid state. A primary difference between solid-state and liquid-state diffusion is the low rate of diffusion in solids. Looking back at the crystal structures, we can appreciate that diffusion of atoms or ions through those generally tight structures is difficult. In fact, the energy requirements to squeeze most atoms or ions through perfect crystal structures are so high as to make diffusion nearly impossible. To make solid-state diffusion practical, point defects are generally required. Fig. 5.5 illustrates how atomic migration becomes possible without major crystal structure distortion by means of a vacancy migration mechanism.

121

Fig.5.5 Atomic migration occurs by a mechanism of vacancy migration. Note that the overall direction of material flow (the atom) is opposite to the direction of vacancy flow.

It is important to note that the overall direction of material flow is opposite to the direction of vacancy flow. Fig. 5.6 shows diffusion by an interstitialcy mechanism and illustrates effectively the random walk nature of atomic migration. This randomness does not preclude the net flow of material when there is an overall variation in chemical composition. This frequently occurring case is illustrated in Fig. 5.7 and 5.8. Although each atom of solid A has an equal probability of randomly “walking” in any direction, the higher initial concentration of A on the left side of the system will cause such random motion to produce interdiffusion, a net flow of A atoms into solid B. Similarly solid diffuses into solid A.

122

Fig.5.6. Diffusion by an interstitialcy mechanism illustrating the random walk nature of atomic migration.

The formal mathematical treatment of such diffusional flow begins with an expression known as Fick’s first law,

J

x

 D

c x

(8)

where Jx is the flux, or flow rate, of the diffusing species in the xdirection due to a concentration gradient (∂c/∂x). D – proportionality coefficient (called the diffusion coefficient or, simply, the diffusivity). The geometry of Eq. (8) is illustrated in Fig. 5.9. Fig. 5.7 reminds us that the concentration gradient at a specific point along the diffusion path changes with time, t. This transient condition is represented by a second-order differential equation also known as Fick’s second law, Cx t



   C D x  x 123

x

   

(9)

Fig.5.7. The inter diffusion of materials A and B. Although any given A or B atom is equally likely to “walk” in any random direction (see Figure 5.6), the concentration gradients of the two materials can result in a net flow of A atoms into the B material, and vice versa.

Fig. 5.8. The interdiffusion of materials on an atomic scale was illustrated Fig.5.7. A comparable example on the microscopic scale is this interdiffusion of Cu and Ni. 124

Fig. 5.9. Geometry of Fick’s first law

For many practical problems, one can assume that D is independent of C, leading to a simplified version of Eq.9:  D  C2 x t x 2

 cx

(10)

Fig. 5.10. Solution to Fick’s second law (Eq.10) for the case of a semi-infinite solid, constant surface concentration of the diffusing species Cs,, initial bulk concentration Co , and a constant diffusion coefficient D.

125

Fig.5.10 illustrates a common application of Eq.10; the diffusion of material into a semi-infinite solid while the surface concentration of the diffusing species, Cs, remains constant. Two examples of this system would be the plating of metals and the saturation of materials with reactive atmospheric gases. Specifically, steel surfaces are often hardened by carburization, the diffusion of carbon atoms into the steel from a carbon-rich environment. The solution to this differential eq. With the given boundary conditions is

c c c c x

0

s

0

x    1  erf    2* D *t 

(11)

where C0 is the initial bulk concentration of the diffusing species and erf - refers to the Gaussian error function, based on the integration of the “bell-shaped” curve with values readily available in mathematical tables. A great power of this analysis is that the result (Eq. 11) allows all of the concentration profiles of Fig.5.10 to be redrawn on a single master plot.

Fig. 5.11. Master plot summarizing all of the diffusion result of Fig. 5.10 on a single curve. 126

Such a plot permits rapid calculation of the time necessary for relative saturation of the solid as a function of x, D, t. Fig. 5.12. shows similar saturation curves for various geometries. Remember: It is important to keep in mind that these results are but a few of the large number of solutions that have been obtained by materials scientists for diffusion geometries in various practical processes. The preceding mathematical analysis of diffusion implicitly assumed a fixed temperature. Our previous discussion of the dependence of diffusion on point defects causes us to expect strong temperature dependence for diffusivity by analogy to Eq. (5) – and this is precisely the case. Diffusivity data are perhaps the best known examples of an Arrhenius eq.:

D

q

D0 * e kT

(12)

where Do – preexponential constant; q – the activation energy for defect motion.

Fig. 5.12. Saturation curves similar to Fig. 5.11 for various geometries. The parameter Cm – is the average concentration of diffusing species within the sample. Again, the surface concentration Cs and diffusion coefficient D are assumed to be constant. 127

Remember: In general, q is not equal to the E defects of Eq. (5). E defects represents the energy required for defect formation,  while q represents the energy required for movement of that defect through the crystal structure (E defect motion) for interstitial diffusion. For the vacancy mechanism, vacancy formation is an integral part of the diffusional process ( see Fig.5.5) and q = E defects+ E defect motion It is more common to tabulate diffusivity data in terms of molar quantities, that is, with activation energy, Q, per mole of diffusing species:

D

Q

D0 * e RT

(13)

where R is the universal gas constant R = NA ·k. Fig. 5.13 shows an Arrhenius plot of the diffusivity of carbon in This is example of an interstitialcy mechanism as sketched in Fig. 5.6. Fig. 5.14 collects diffusivity data for a number of metallic systems. Let’s compare different data sets. 1) For instance, C can diffuse by in interstitialcy mechanism through bcc Fe more readily than through fcc Fe (Qbcc < Q fcc). 2) The greater openness of the bcc structure makes this understandable. 3) Similarly, the self-diffusion of Fe by a vacancy mechanism is greater in bcc Fe than in fcc Fe. Fig. 5.15 gives comparable diffusivity data for several nonmetallic systems. In many compounds, such as Al2O3, the smaller ionic species (e.g., Al +3) diffuse much more readily through the system. The Arrhenius behavior of ionic diffusion in ceramic compounds is especially analogous to the temperature dependence of semiconductors be discussed later. It is this ionic transport mechanism that is responsible for the semiconducting behavior of certain ceramics such as ZnO; that is, charged ions rather than electrons produce the measured electrical conductivity. 128

Fig. 5.13. Arrhenius plot of the diffusivity of carbon in α–Fe over a range of temperatures. Note also related Fig. 4.4 and Fig. 5.6 and other metallic diffusion data in Fig. 5.14.

Polymer data are not included with the other nonmetallic systems. Because most commercially important diffusion mechanisms in polymers involve the liquid state or the amorphous solid state, where the point defect mechanism of this section do not apply. 5.4 Steady- state diffusion The change in the concentration profile with time for processes such as carburization was shown in Fig. 5.10. A similar observation for a process with slightly different boundary conditions is shown in Fig. 5.16.

129

Fig.5.14. Arrhenius plot of diffusivity data for a number of metallic systems.

Fig.5.15. Arrhenius plot of diffusivity data for a number of nonmetallic systems. 130

Fig. 5.16. Solution to Fick’s 2-d law for the case of a solid thickness xo, constant surface concentrations of the diffusing species ch and cl, and a constant diffusion coefficient D. For long times, e.g., t3 the linear concentration profile is an example of steady-state diffusion.

In this case, the relatively high surface concentration of the diffusing species, ch , is held constant with time, just as cs was held constant in Fig.5.10, but the relatively low concentration, cl, at x0 is also held constant with time. As a result the nonlinear concentration profiles at times greater than zero (e.g., at t1 and t2 in Fig. 5.16) approach a straight line after a relatively long time (e.g., at t3 in Fig.5.16). This linear concentration profile is unchanging with additional time as long as ch and cl remain fixed. This limiting case is an example of steady –state diffusion (i.e., mass transport that is unchanging with time). The concentration gradient defined by Eq. 5.8

J

x

 D

c x

131

takes an especially simple form in this case:

c c ch  c1     ch  c1  / x0 x x 0  x0 

(14)

In the case of carburization represented by Fig. 5.10, the surface concentration, cs was held fixed by maintaining a fixed carbonsource atmospheric pressure at the x = 0 surface. That is also how both ch and cl are maintained fixed in the case represented by Fig. 5.16. Example N2: A plate of material with a thickness of xo is held between 2 gas atmospheres:  a high-pressure atmosphere on the x = 0 surface, which produces the fixed concentration ch, and  low-pressure atmosphere on the x = x0 surface, which produces the fixed concentration cl, (Fig. 5.17) A common application of steady-state diffusion is the use of materials as gas purification membranes. Example N3: Thin sheet of palladium Pd metal is permeable to hydrogen gas but not to common atmospheric gases such as oxygen, nitrogen, and water vapor. By introducing the “impure” gas mixture on the high pressure side (Fig.5.17b) and maintaining a constant, reduced hydrogen pressure on the low-pressure side, a steady flow of purified hydrogen passes through the Pd sheet. 5.5 Alternative diffusion paths Let’s see some specific diffusivity data and analyze a particular material process. Fig. 5.18 shows that the self-diffusion coefficients for silver Ag vary by several orders of magnitude, depending on the route for diffusional transport.

132

Fig. 5.17 Schematic of sample configurations in gas environments that lead, after a long time, to the diffusion profiles representative of (a) non-steady state diffusion (Fig. 5.10); (b) steady-state diffusion (Fig. 5.16).

To this point, we have considered volume diffusion or bulk diffusion, through a material’s crystal structure by means of some 133

detect mechanism. However, there can be “short circuits” associated with easier diffusion paths.

Fig.5.18. Self-diffusion coefficients for Ag depend on the diffusion path. In general, diffusivity is greater through less restrictive structural regions.

Explanation:  As seen in Fig. 5.18, diffusion is much faster (with a lower Q) along a grain boundary. As well saw in Chapter 4, this region of mismatch between adjacent crystal grains in the material’s microstructure is a more open structure, allowing 134



enhanced grain boundary diffusion. The crystal surface is an even more open region, and surface diffusion allows easier atom transport along the free surface less hindered by adjacent atoms. The overall result is that

Q volume > Q grain boundary > Q surface D volume > D grain boundary > D surface

and

Fig.5.19. Schematic illustration of how a coating of impurity B can penetrate more deeply into grain boundaries and even further along a free surface of polycrystalline A, consistent with the relative values coefficients (D volume < D grain boundary < D surface )

135

Remember: 1) This does not mean that surface diffusion is always the important process just because D surface is greatest. 2) More important is the amount of diffusing region available. In most cases, volume diffusion dominates. 3) For the material with a small average grain boundary and therefore large grain boundary area, grain boundary diffusion can dominate. 4) Similarly, in a fine-grained powder with large surface area, surface diffusion can dominate. For a given polycrystalline microstructure, the penetration of a diffusing species will tend to be greater along grain boundaries and even greater along the free surface of the sample (Fig.5.19). Conclusion

4) 5)

6)

7)

1) Point defect concentrations increase exponentially with absolute T following an Arrhenius expression. 2) Solid-state diffusion in crystalline materials occurs via a point defect mechanism. 3) The diffusivity , as defined by Fick’s laws, also increases exponentially with absolute T in another Arrhenius expression. The mathematics of diffusion allows a relatively precise description of the chemical concentration profiles of diffusing species. For some samples geometries, the concentration profile approaches a simple, linear form after a relatively long time. This steady-state diffusion is well illustrated by gas transport across thin membranes. In the case of fine-grained polycrystalline materials or powders, material transport may be dominated by grain boundary diffusion or surface diffusion, respectively. This is because, in general, (D volume < D grain boundary < D surface ) Another result is that, for a given polycrystalline solid, impurity penetration will be greater along grain boundaries and even greater along the free surface. 136

CHAPTER 6 Mechanical Behavior

137

CHAPTER 6 MECHANICAL BEHAVIOR 6.1 Stress versus strain Metals generally used as structural elements. a) How strong they are? b) How much deformation must I expect given a certain load? Answer: The basic description of the material is obtained by the tensile test. Fig. 6.1. illustrates this simple pull test.

Fig. 6.1. Tensile test

138

The load necessary to produce a given elongation is monitored as the specimen is pulled in tension at a constant rate. A load-versuselongation curve (Fig.6.2) is the immediate result of such a test. A more general statement about material characteristics is obtained by normalizing the data of Fig. 6.2 for geometry. The resulting stressversus-strain curve is given in Fig. 6.3. Here, the engineering stress, σ, is defined as σ = P/A0

(1)

where P is the load on the sample with an original (zero stress) crosssectional area, A0. Sample cross section refers to the region near the center of the specimen’s length.

Fig. 6.2. Load-versus-elongation curve obtained in a tensile test. The specimen was Al-2084-T81.

Specimens are machined such that the cross-sectional area in this region is uniform and smaller than at the ends gripped by the 139

testing machine. This smallest area region, referred to as the gage length, experiences the largest stress concentration so that any significant deformation at higher stresses is localized there. The engineering strain ε, is defined as ε = (l – lo) /lo = Δ/lo

(2)

where l is the gage length at a given load, and lo is the original (zerostress) length. Fig. 6.3 is divided into 2 distinct regions: 1) elastic deformation; 2) plastic deformation.

Fig. 6.3. Stress-versus-strain curve obtained by normalizing the data of (Fig. 6.2) for specimen geometry.

Elastic deformation is temporary deformation. It is fully recovered when the load is removed. The elastic region of the stress-strain 140

curve is the initial linear portion. Plastic deformation is permanent deformation. It is not recovered when the load is removed, although a small elastic component is recovered. The plastic region is the nonlinear portion generated once the total strain exceeds its elastic limit. It is often difficult to specify precisely the point at which the stress-strain curve deviates from linearity and enters the plastic region. The usual convention is to define as yield strength the intersection of the deformation curve with a straight –line parallel to the elastic portion and offset 0.2 % on the strain axis (Fig. 6.4). The yield strength represents the stress necessary to generate this small amount (0,2 %) of permanent deformation.

Fig. 6.4. The yield strength is defined relative to the intersection of the stress-strain curve with a “0.2 % offset”. This is a convenient indication of the onset of plastic deformation.

Fig. 6.5 indicates the small amount of elastic recovery that occurs when a load well into the plastic region is released. 141

Fig. 6.6 summarizes the key mechanical properties obtained from the tensile test. The slope of the stress-strain curve in the elastic region is the modulus of elasticity, E, also known as Young’s modulus. The linearity of the stress-strain plot in the elastic region is a graphical statement of Hook’s law: σ= E ε

(3)

Fig. 6.5. Elastic recovery occurs when stress is removed from a specimen that has already undergone plastic deformation.

The modulus E is a highly practical piece of information. It represents the stiffness of the material that is its resistance to elastic strain. This manifests itself as the amount of deformation in normal use below the yield strength and the springiness of the material during forming. As with E, the yield strength has major practical significance. It shows the resistance of the metal to permanent deformation and indicates rolling and drawing operations can form the ease with the metal. Although we are concentrating on the behavior of metals under tensile loads, the testing apparatus illustrated in Fig. 6.1. is routinely used in a reversed mode producing a compressive test. The elastic

142

modulus in fact, tends to be the same for metal alloys tested in either tensile or compressive modes. Remember: 1) Many design engineers, especially in the aerospace field, are more interested in strength-per-unit density than strength or density individually (If 2 alloys each have adequate strength, the lower density one is preferred for potential fuel savings). 2) The strength-per-unit density is generally termined specific strength, or strength-to-weight ratio, and is discussed relative to composite properties later. 3) Another term of practical engineering importance is residual stress, defined as the stress remaining within a structural material after all applied loads are removed. This commonly occurs following various thermo mechanical treatment such as welding and machining.

Fig. 6.6. The key mechanical properties obtained from tensile test: modulus of elasticity, E; 2) yield strength Y.S.; 3) tensile strength, T.S.; 4) ductility, 100 x εfailure ( note that elastic recovery occurs after fracture); 5) toughness = ∫σ dε ( measured under load; hence the dashed line is vertical). 143

As the plastic deformation represented in Fig. 6.6 continues at stresses above the yield strength, the engineering stress continues to rise toward a maximum. This maximum stress is termed the ultimate tensile strength, or simply the tensile strength (T.S.). Within the region of the stress-strain curve between Y.S. and T.S., the phenomenon of increasing strength with increasing deformation is referred to as strain hardening. This is an important factor in shaping metals by cold working, that is, plastic deformation occurring well below one-half times the absolute melting point. It might appear from Fig.6.6 that plastic deformation beyond T.S. softens the material because the engineering stress falls. Instead, this drop in stress is simply the result of the fact that the engineering stress and strain are defined relative to original sample dimensions. At the ultimate tensile strength, the sample begins to neck down within the gage length. (Fig. 6.7). The true stress ( σtr = P/A actual) continues to rise to the point of fracture (Fig. 6.8). For many metals and alloys, the region of the true stress (σT ) versus true strain (εT) curve between the onset of plastic deformation (corresponding to the yield stress in the engineering stress versus engineering strain curve) and the onset of necking (corresponding to the tensile stress in the engineering stress versus engineering strain curve) can be approximated by

(εT) = K εTn

(4)

where K and n are constants with values for a given metal or alloy depending on its thermo mechanical history (e.g., degree of mechanical working, heat treatment, etc). In order words, the true stress versus true strain curve in this region is nearly straight when plotted on logarithmic coordinates. The slope of the log – log plot is the parameter n, which is termed the strainhardening exponent. For low-carbon steels used to form complex shapes, the value of n will normally be approximately 0,22. Higher values, up to 0.26, indicate an improved ability to be deformed during the shaping process without excess thinning or fracture of the piece. The engineering stress at failure in Fig.6.6 is lower than T.S. and occasionally even lower than Y.S. Unfortunately; the 144

complexity of the final stages of neck down causes the value of the failure stress to vary substantially from specimen to specimen.

Fig.6.7. Neck down of a tensile test specimen within its gage length after extension beyond the tensile strength.

More useful is the strain at failure. Ductility is frequently quantified as the percent elongation at failure (= 100 x εfailure ). A less used definition is the percent reduction in area [ A0-Afinal]/A0]. The values for ductility from the 2 different definitions are not, in general, equal. It should also be noted that the value of percent elongation at failure is a function of the gage length used. Tabulated values are frequently 145

specified for a gage length of 2 in. Ductility indicates the general ability of the metal to be plastically deformed.

Fig. 6.8 True stress ( == load divided by actual area in the necked-down region) continues to rise to the point of fracture, in contrast to the behavior of engineering stress.

Practically implications of this ability include formability during fabrication and relief of locally high stress at crack tips during 146

structural loading. It is also useful to know whether an alloy is both strong and ductile. A high-strength alloy that is also highly brittle may be as unusable as a deformable alloy with unacceptably low strength. Fig. 6.9 compares these 2 extremes with an alloy with both high strength and substantial ductility.

Fig.6.9. The toughness of an alloy depends on a combination of strength and ductility

The term toughness is used to describe this combination of properties. Fig. 6.6 shows that this is conveniently defined as the total area under the stress-strain curve. Since integrated σ - ε data are not routinely available, we shall be required to monitor the relative magnitude of strength (Y.S. and T.S.) and ductility (percent elongation at fracture. The general appearance of the stress-versusstrain curve in Fig.6.3 is typical of a wide range of metal alloys. For certain alloys (especially low-carbon steels), the curve of Fig. 6.10 is obtained. The obvious distinction for this latter case is a distinct break from the elastic region at a yield point, also termed an upper yield point. The distinctive ripple pattern following the yield point is associated 147

with non-homogeneous deformation that begins at a point of stress concentration (often near the specimen grips”). A lower yield point is defined at the end of the ripple pattern and at the onset of general plastic deformation.

Fig. 6.10. For a low-carbon steel, the stress-versus-strain curve includes both an upper and lower yield point

Figure 6.11 illustrates another important feature of elastic deformation, namely a contraction perpendicular to the extension caused by a tensile stress. This effect is characterized by the Poisson’s ratio, v:

v = - ε x / εz

(5)

where the strains in the x and z directions are defined by Fig. 6.11. (There is a corresponding expansion perpendicular to the compression caused by a compressive stress). Although the Poisson’s ratio does not appear directly on the stress-versus-strain 148

curve, it is along with the elastic modulus, the most fundamental description of the elastic behavior of engineering materials. Note that values fall within the relatively narrow band of 0.29 to 0.35.

Fig. 6.11. The Poisson’s ratio characterizes the contraction perpendicular to the extension caused by a tensile stress.

Fig. 6.12. illustrates the nature of elastic deformation in a pure shear loading. The shear stress, τ , is defined as τ=Ps/As

(6)

where P s is the load on the sample and A s is the area of the sample parallel (rather than perpendicular) to the applied load. The shear stress produces an angular displacement (α) with the shear strain , γ , being defined as

γ = tan α

(7)

which is equal to Δy/zo in Fig. 6.12. The shear modulus, or modulus of rigidity, G, is defined (in a manner comparable to Eq. 3) as

G =τ/γ 149

(8)

The shear modulus G and the elastic modulus E are related, for small strains, by Poisson’s ratio; namely, E = 2 G (1+v)

(9)

As the 2 moduli are related by v (Eq. 9) and v falls within a narrow band, the ratio of G/E is relatively fixed for most alloys at about 0.4.

Fig.6.12. Elastic deformation under a shear load.

6.2 Ceramics & Glasses Many of the mechanical properties discussed for metals are equally important for ceramics and glasses used in structural applications. In addition, the different nature of these nonmetals leads to some unique mechanical behavior. Metal alloys generally demonstrate a significant amount of plastic deformation in a typical tensile test. In contrast, ceramics and glasses generally do not. Fig. 6.13 shows characteristic results for uniaxial loading of dense, polycrystalline Al2O3. In Fig. 6.13a, failure of the sample occurred in the elastic region. This brittle fracture is characteristic of ceramics and glasses. Fig.6.13a illustrates the breaking strength in a tensile test (280 MPa), while Fig. 6.13b is the same for a compressive test (2100 MPa). This is an especially dramatic example of the fact that the ceramics are relatively weak in tension but relatively strong in compression. This behavior is shared by some cast irons and concrete. 150

(a) Tension

(b) Compression

Fig. 6.13. The brittle nature of fracture in ceramics is illustrated by these stressstrain curves, which show only linear, elastic behavior. In (a) fracture occurs at a tensile stress of 280 MPa. In (b) a compressive strength of 2100 MPa is observed. The sample in both tests is a dense, polycrystalline Al2O3.

The strength parameter is the modulus of rupture, a value calculated from data in a bending test. The modulus of rupture (MOR) is given by MOR =3FL/2bh2

(10)

Where F is the applied force, b, h and L are dimensions defined in Fig. 6.14. The MOR is sometimes referred to as the flexural strength (F.S.) and is similar in magnitude to the tensile strength, as the failure mode in bending is tensile (along the outermost edge of the sample). The bending test, illustrated in Fig. 6.14, is frequently easier to conduct on brittle materials than the traditional tensile test. One can note that v for metals is typically ~1/3 and for ceramics ~ 1/4. To appreciate the reason for the mechanical behavior of structural ceramics, we must consider the stress concentration at a crack tips. For purely brittle material, the simple Griffith crack model is applicable. Griffith assumed that in any real material there would be numerous elliptical cracks at the surface and/or in the interior. It can be shown that the highest stress (σm) at the tip of such a crack is

σm = 2 σ (c/ρ)1/2 151

(11)

Fig. 6.14. The bending test that generates a modulus of rupture. This strength parameter is similar in magnitude to a tensile strength. Fracture occurs along the outermost sample edge, which is under a tensile load.

where σ is the applied stress, c the crack length as defined in Fig. 6.15, and ρ is the radius of the crack tip. Since the crack tip radius can be as small as an interatomic spacing, the stress intensification can be quite large. Routine production and handling of ceramics and glasses make Griffith flaws inevitable. Hence, these materials are relatively weak in tension. A compressive load tends to close, not open, the Griffith flaws and consequently does not diminish the inherent strength of the ionically and covalently bonded material. The drawing of small-diameter glass fibers in a controlled atmosphere is one way to avoid Griffith flaws. The resulting fibers can demonstrate tensile strengths approaching the theoretical atomic bond strength of the material. This helps to make them excellent reinforcing fibers for composite systems. 6.3 Polymers As with ceramics, the mechanical properties of polymers can be described with much of the vocabulary introduced for metals. 152

Fig. 6.15. Stress (σm) at the tip of a Griffith crack

Tensile strength and modulus of elasticity are important design parameters for polymers as well as inorganic structural materials.

153

With the increased availability of engineering polymers for metals substitution, a greater emphasis has been placed on presenting the mechanical behavior of polymers in a format similar to that used for metals. Primary emphasis is on the stress-versus-strain data. Although strength and modulus values are important parameters for these materials, design applications frequently involve a bending, rather than tensile mode. As a result, flexural strength and flexural modulus are frequently quoted. As noted earlier, flexural strength (F.S.) is equivalent to the modulus of rupture defined for ceramics in Eq. 10. and Fig. 6.14. For the same test specimen geometry, the flexural modulus, or modulus of elasticity in bending ( E flex), is

E flex = L3m/4bh3

(12)

Where m is the slope of the tangent to the initial strain-line portion of the load-deflection curve and all other terms are defined relative to Eq. 10 and Fig. 6.14. An important advantage of the flexural modulus for polymers is that it describes the combined effects of compressive deformation (adjacent to the point of applied load in Fig. 6.14) and tensile deformation (on the opposite side of the specimen). For metals, as noted before, tensile and compressive moduli are generally the same. For many polymers, the tensile and compressive moduli differ significantly. Some polymers, especially the elastomers, are used in structures for the purpose of isolation and absorption of shock and vibration. For such applications, a “dynamic” elastic modulus is more useful to characterize the performance of the polymer under an oscillating mechanical load. For elastomers in general, the dynamic modulus is greater than the static modulus. For some compounds, the 2 moduli may differ by a factor of 2. The dynamic modulus of elasticity, E dyn (in MPa) , is

E dyn = CIf2

(13)

Where C is a constant dependent upon specific test geometry, I the moment of inertia (in kg m2) of the beam and weights used in the 154

dynamic test, and f the frequency of vibration (in cycles/s) for the test. Eq. (13) holds for both compressive and shears measurements, with the constant C having a different value in each case.

Fig. 6.16. Stress-versus-strain curves for a polyester engineering polymer.

Fig. 6.16 shows typical stress-versus-strain curves for an engineering polymer, polyester. Although these plots look similar to common stress-versus-strain plots for metals, there is a strong effect of temperature. On the other hand, this mechanical behavior is 155

relatively independent of atmospheric moisture. Both polyester and acetal engineering polymers have these advantages.

Fig. 6.17. Stress-versus-strain curves for a nylon 66 at 23 C showing the effect of relative humidity.

However, relative humidity is a design consideration for the use of nylons, as shown in Fig. 6.17. Also demonstrated in Fig. 6.17 is the difference in elastic modulus (slope of the plots near the origin) for tensile and compressive loads. You can find some mechanical properties of the thermoplastic polymers (those that become soft and deformable upon-heating) in tables. Some table gives similar properties for the thermosetting polymers (those which become hard and rigid upon heating). Note, that the dynamic modulus values in the table are not, in general, greater than the tensile modulus values. The statement that the dynamic modulus of an elastomer is generally greater than the 156

static modulus is valid for a given mode of stress application. The dynamic shear modulus value are, in general, greater than static shear modulus values. 6.4 Elastic deformation Fig. 6.18 shows that the fundamental mechanism of elastic deformation is the stretching of atomic bonds.

Fig.6.18. Relationship of elastic deformation to the stretching of atomic bond.

The fractional deformation of the material in the initial elastic region is small so that, on the atomic scale, we are dealing only with the portion of the force-atom separation curve in the immediate vicinity 157

of the equilibrium atom separation distance (a0 corresponding to F =0). The nearly straight – line plot of F versus a across the a axis implies that similar elastic behavior will be observed in a compressive, or push, test as well as in tension. This is often the case, especially for metals. 6.5 Plastic deformation The fundamental mechanism of plastic deformation is the distortion and reformation of the atomic bonds. We know, that atomic diffusion in crystalline solids is extremely difficult without the presence of point defects. Similarly, the plastic (permanent) deformation of crystalline solids difficult without dislocations, the linear defects. Frenkel first calculated the mechanical stress necessary to deform a perfect crystal. This would occur by sliding 1 plane of atoms over an adjacent plane, as shown in Fig. 6.19.

Fig. 6.19. Sliding of one plane of atoms past an adjacent one. This high-stress process is necessary to plastically (permanently) deform a perfect crystal.

The shear stress associated with this sliding action can be calculated with knowledge of the periodic bonding forces along the slip plane. The result obtained by Frenkel was that the theoretical 158

critical shear stress is roughly one order of magnitude less than the bulk shear modulus, G, for material. For a typical metal such a copper, the theoretical critical shear stress represents a value well over 1000 MPa. The actual stress necessary to plastically deform a sample of pure copper (i.e., slide atomic planes past each other) is at least an order of magnitude less than this. Our everyday experience with metallic alloys (opening aluminum cans or bending automobile fenders) represents deformations generally requiring stress levels of only a few hundred megapascals (MPa). Question: What is the basis of the mechanical deformation? Answer: Dislocation Fig. 6.20 illustrates the role a dislocation can play in the shear of a crystal along a slip plane.

Fig.6.20. A low-stress alternative for plastically deforming a crystal involves the motion of a dislocation along a slip plane. 159

The key point to observe is that only a relatively small shearing force needs to operate and only in the immediate vicinity of dislocation in order to produce a step-by-step shear that eventually yields the same overall deformation as the high stress mechanism of Fig. 6.19. Reflecting on Fig. 6.20, we can appreciate that the stepwise slip mechanism would tend to become more difficult as the individual atomic step distances are increased. As a result, slip is more difficult on a low-atomic-density plane than on a high-atomic-density plane. Fig. 6.21 shows this schematically.

Fig.6.21. Dislocation slip is more difficult along (a) a low-atomic-density plane than along (b) a high-atomic-density plane. 160

In general, the micromechanical mechanism of slip-dislocation motion-will occur in high-atomic-density planes and in high-atomicdensity directions. Slip system – a combination of families of crystallographic planes and directions corresponding to dislocation motion (Fig.6.22). Fig. 6.23 illustrates the micromechanical basis of solution hardening of alloys, that is restricting plastic deformation by forming solid solutions. Hardening, or increasing strength, occurs because the elastic region is extended, producing a higher yield strength. Useful rule: The temperature at which atomic mobility is sufficient to affect mechanical properties is approximately one-third to one-half times the absolute melting point, Tm

Fig.6.22. Slip systems for (a) fcc aluminum and (b) hcp magnesium.

161

Fig.6.23. How an impurity atom generates a strain field in a crystal lattice, causing an obstacle to dislocation motion.

Fig. 6.24 defines the resolved shear stress, , which is the actual stress operating on the slip system (in the slip plane and in the slip direction) resulting from the application of a simple tensile stress,  = F/A; F=F cos . A= A/cos .  = F/A cos  cos  =  cos  cos  ; where  is the applied tensile stress. 6.6 Hardness The hardness test (Fig.6.25) is available as a relatively simple alternative to the tensile test of Fig. 6.1. The resistance of the material to indentation is a qualitative indication of its strength. The indenter can be either rounded or pointed and is made of a material much harder than the test piece, for example, hardened steel, tungsten carbide, or diamond. Empirical hardness numbers are calculated from appropriate formulas using indentation geometry measurements. Microhardness measurements are made using a highpower microscope. Rockwell hardness is widely used with many scales available for different hardness ranges. 162

Fig.6.24. Definition of the resolved shear stress, τ , which directly produces plastic deformation (by a shearing action) as a result of the external application of a simple tensile stress, σ .

6.7 Creep and stress relaxation The tensile test alone cannot predict the behavior of a structural material used at elevated temperatures. The strain induced in a typical metal bar loaded below its yield strength at room temperature 163

can be calculated from Hook’s law. This strain will not generally change with time under a fixed load (Fig. 6.26).

Fig.6.25. Hardness test.

Fig.6.26. Elastic strain induced in an alloy at room temperature is independent of time.

Repeating this experiment at a “high” temperature (T greater than 1/3 to 1/2 times the melting point on an absolute temperature scale) 164

produces dramatically different results. Fig. 6.27 shows a typical test design, and Fig. 6.28 shows a typical creep curve in which the strain, , gradually increases with time after the initial elastic loading.

Fig.6.27. Typical creep test

Creep can be defined as plastic (permanent) deformation occurring at high temperature under constant load over a long time period. After the initial elastic deformation at t ~0, Fig. 6.28 shows three stages of creep deformation. The primary stage is characterized by a decreasing strain rate (slope of the  vs.t curve). The relatively rapid 165

increase in length induced during this early time period is the direct result of enhanced deformation mechanisms.

Fig.6.28. Creep curve. In contrast to Figure 6.26, plastic strain occurs over time for a material stressed at high temperatures (above about one-half the absolute melting point).

A common example for metal alloys is dislocation climb as illustrated in Fig. 6.29. The secondary stage of creep deformation is characterized by straight-line, constant-strain-rate data. In this region, the increased ease of slip due to high-temperature mobility is balanced by increasing resistance to slip due to the buildup of dislocations and other microstructural barriers. In the final tertiary stage, strain rate increases due to an increase in true stress resulting from cross-sectional area reduction due to necking or internal cracking. In some cases, fracture occurs in the secondary stage, eliminating this final stage. A demonstration of this is an Arrhenius plot of the logarithm of the steady-state creep rate from the 166

secondary stage against the inverse of absolute temperature (Fig.6.30).

Fig. 6.29. Mechanism of dislocation climb. Obviously, many adjacent atom movements are required to produce climb of an entire dislocation line.

Fig.6.30. Arrhenius plot of ln є’ versus 1/T , where є’ is the secondary stage creep rate and T is the absolute temperature. The slope gives the activation energy for the creep mechanism. Extension of high - temperature, short-term data permits prediction of longterm creep behavior at lower service temperatures. 167

As with other thermally activated processes, the slope of the Arrhenius plot is important in that it provides activation energy, Q. for the creep mechanism from the Arrhenius expression ’ = Ce -Q/RT where C is the preexponential constant, R the universal gas constant, and T the absolute temperature. Another powerful aspect of the Arrhenius behavior is its predictive power. The dashed line in Fig. 6.30 shows how high-temperature strain-rate data, which can be gathered in short-time laboratory experiments, can be extrapolated to predict long-term creep behavior at lower service temperatures. This extrapolation is valid as long as the same creep mechanism operates over the entire temperature range.

Fig.6.31. Creep rupture data for the nickel-based superalloy Inconel 718.

Many elaborate semi-empirical plots have been developed, based on this principle, to guide design engineers in material selection. Creep is probably more important in ceramics than in metals because high-temperature applications are so widespread. The role of diffusion mechanisms in the creep of ceramics is more complex than in the case of metals because diffusion, in general, is more complex in ceramics. The requirement of charge neutrality and different diffusivities for cations and anions contribute to this complexity. As 168

a result, grain boundaries frequently play a dominant role in the creep of ceramics. Sliding of adjacent grains along these boundaries provides for microstructural rearrangement during creep deformation.

Fig.6.32. Arrhenius-type plot of creep-rate data for several polycrystalline oxides under an applied stress of 50 psi (345 x 103 Pa).Note that the inverse temperature scale is reversed (i.e., temperature increases to the right).

For metals and ceramics, we have found creep deformation to be an important phenomenon at high temperatures (greater than 1/2 the absolute melting point). Creep is a significant design factor for polymers given their relatively low melting points. Fig. 6.33 shows creep data for nylon 66 at moderate temperature and load. A related phenomenon, termed stress relaxation, is also an important design 169

consideration for polymers. A familiar example is the rubber band, under stress for a long period of time, which does not snap to its original size upon stress removal. Creep deformation involves increasing strain with time for materials under constant stresses. By contrast, stress relaxation involves decreasing stress with polymers under constant strain. The mechanism of stress relaxation is viscous flow; that is molecules gradually sliding past each other over an extended period of time.

Fig.6.33. Creep data for a nylon 66 at 60oC and 50% relative humidity.

Viscous flow converts some of the fixed elastic strain into nonrecoverable plastic deformation. Stress relaxation is characterized by a relaxation time, , defined as the time necessary for the stress () to fall to 0.37 (=1/e) of the initial stress (0). The exponential decay of stress with time (t) is given by

 = 0 e –t/ In general, stress relaxation is an Arrhenius phenomenon, as was creep for metals and ceramics. The form of the Arrhenius equation for stress relaxation is

1/ = C e –Q/RT 170

where C is a preexponential constant, Q the activation energy (per mole) for viscous flow, R the universal gas constant, and T the absolute temperature. 6.8 Viscoelastic deformation We know that materials generally expand upon heating. This thermal expansion is monitored as an incremental increase in length, L, divided by its initial length, L0. Two unique mechanical responses are found in measuring the thermal expansion of an inorganic glass or an organic polymer (Fig. 6.34).

Fig.6.34. Typical thermal expansion measurement of an inorganic glass or an organic polymer indicates a glass transition temperature, Tg, and a softening temperature, Ts.

First, there is a distinct break in the expansion curve at the temperature Tg. There are two different thermal expansion coefficients (slopes) above and below Tg. The thermal expansion coefficient below Tg is comparable to that of a crystalline solid of the same composition. The thermal expansion coefficient above Tg is 171

comparable to that of a crystalline solid of the same composition. The thermal explanation coefficient above Tg is comparable to that for a liquid. As a result, Tg is referred to as the glass transition temperature. Below the material is a true glass (a rigid solid), and above Tg it is a super cooled liquid. In terms of mechanical behavior, elastic deformation occurs below Tg, while viscous (liquid-like) deformation occurs above Tg. continuing to measure thermal expansion above Tg leads to a precipitations drop in the data curve at the temperature Ts. This is the softening temperature and marks the point where the material has become so fluid that it can no longer support the weight of the length-monitoring probe (a small refractory rod).

Fig.6.35. Upon heating, a crystal undergoes modest thermal expansion up to its melting point (Tm), at which a sharp increase in specific volume occurs. Upon further heating, the liquid undergoes a greater thermal expansion. Slow cooling of the liquid would allow crystallization abruptly at Tm and a retracing of the melting plot. Rapid cooling of the liquid can suppress crystallization producing a supercooled liquid. In the vicinity of the glass transition temperature (Tg), gradual solidification occurs. A true glass is a rigid solid with thermal expansion similar to the crystal but an atomic-scale structure similar to the liquid. 172

The viscous behavior of glasses (organic or inorganic) can be described by the viscosity, , which is defined as the proportionality constant between a shearing force per unit area (F/A) and velocity gradient (dv/dx): F/A = dv/dx The units for viscosity are traditionally the poise [ 1g/(cm s)], which is equal to 0.1 Pa s. 6.9 Inorganic glasses The viscosity of a typical soda-lime-silica glass from room temperature to 1500 0C is summarized in Fig.6.36. The melting range is the temperature range (between about 1200 and 1500 0C for soda-lime-silica glass), where  is between 50 and 500 P. This represents a very fluid material for a silicate liquid. Water and liquid metals, however, have viscosities of only about 0.01 P. The forming of product shapes is practical in the viscosity range of 104 to 108 P, the working range (between about 700 and 900 0C for soda-limesilica glass). The softening point is formally defined at  value of 107.6 P (~700 0C for soda-lime-silica glass) and is at the lower temperature end of the working range. After a glass product is formed, residual stresses can be relieved by holding in the annealing range of  from 1012. 5 P to 1013. 5 P. The annealing point is defined as the temperature at which  = 1013. 4 P and internal stresses can be relieved in about 15 min (~ 450 0C for soda-lime-silica glass). The glass transition temperature occurs around the annealing point. Above the glass transition temperature, the viscosity data follow an Arrhenius form with

 = 0 e +Q/RT where 0 is the pre-exponential constant, Q the activation energy for viscous deformation, R the universal gas constant, and T the absolute temperature. Note that the exponential term has a positive sign rather than the usual negative sign associated with diffusivity data. This is simply the nature of the definition of viscosity, which decreases rather than increases with temperature. Fluidity, which could be 173

Fig.6.36. Viscosity of a typical soda-lime-silica glass from room temperature to 1500oC. Above the glass transition temperature (~450oC in this case), the viscosity decreases in the Arrhenius fashion.

defined as 1/, would, by definition, has a negative exponential sign comparable to the case for diffusivity. A creative application of viscous deformation is tempered glass. Fig. 6.37 shows how the glass is first equilibrated above the glass transition temperature, Tg, followed by a surface quench that forms a rigid surface “skin” at a temperature below Tg . Because the interior is still above Tg, interior compressive stresses are largely relaxed, although a modest tensile stress is present in the surface “skin”. Slow cooling to room temperature allows the interior to contract considerably more than the surface, causing a net 174

Fig.6.37. Thermal and stress profiles occurring during the production of tempered glass. The high breaking strength of this product is due to the residual compressive stress at the material surfaces.

compressive residual stress on the surface balanced by a smaller tensile residual stress in the interior. This is an ideal situation for a brittle ceramic. So the material must be subjected to a significant tensile load before the residual compressive load can be neutralized. An additional tensile load is necessary to fracture the material. The breaking strength becomes the normal breaking strength plus the magnitude of the surface residual stress. A chemical rather than 175

thermal technique to achieve the same results is to chemically exchange larger radius K+ ions for the Na + ions in the surface of a sodium-containing silicate glass. The compressive stressing of the silicate network produces a product known as chemically strengthened glass. For organic polymers, the modulus of elasticity is usually plotted instead of viscosity. Fig.6.38 illustrates the drastic and complicated drop in the modulus with temperature for a typical commercial thermoplastic with approximately 50 % crystallinity and shows 4 distinct regions.

Fig.6.38. Modulus of elasticity as a function of temperature for a typical thermoplastic polymer with 50% crystallinity. There are four distinct regions of visco-elastic behavior: (1) rigid, (2) leathery, (3) rubbery, and (4) viscous.

At “low” temperatures (well below Tg), a rigid modulus occurs corresponding to mechanical behavior reminiscent of metals and 176

ceramics. However, the substantial component of secondary bonding in the polymers causes the modulus for these materials to be substantially lower than the ones found for metals and ceramics, which were fully bonded by primary chemical bonds (metallic, ionic, and covalent). In the glass transition temperature (Tg ) range, the modulus drops precipitously and the mechanical behavior is leathery. Just above Tg, a rubbery plateau is observed. These 2 regions (leathery and rubbery) extend our understanding of elastic deformation. For metals and ceramics elastic deformation meant a relatively small strain directly proportional to applied stress. For polymers, extensive nonlinear deformation can be fully recover and is, by definition, elastic. As the melting point (Tm) is approached, the modulus again drops precipitously as we enter the liquid-like viscous region. Fig. 6.38 represents a linear, thermoplastic polymer with approximately 50 % crystallinity. Fig.6.39 shows how that behavior lies midway between that for a fully amorphous material and a fully crystalline one.

Fig.6.39. In comparison to the plot of Figure 6-38, the behavior of the completely amorphous and completely crystalline thermoplastics falls below and above that for the 50% crystalline material. The completely crystalline material is similar to a metal or ceramic in remaining rigid up to its melting point. 177

Fig.6.40. Cross-linking produces a network structure by the formation of primary bonds between adjacent linear molecules.

Fig.6.41. Increased cross-linking of a thermoplastic polymer produces increased rigidity of the material.

The fully crystalline polymer is relatively rigid up to its melting point. This is consistent with the behavior of crystalline metals and ceramics. Another structural feature that can affect mechanical 178

behavior in polymers is the cross-linking of adjacent linear molecules to produce a more rigid, network structure (Fig. 6.40). Fig.6.40. is the classic example shown here is the vulcanization of rubber. Sulfur atoms form primary bonds with adjacent polyisoprene mers. This is possible because the polyisoprene chain molecule still contains double bonds after polymerization. [It should be noted that sulfur atoms can themselves bond together to form a molecule chain. Sometimes, cross-linking is by an (S)n chain, where n > 1.] Fig. 6.41 shows how increased cross-linking produces an effect comparable to increased crystallinity. The similarity is due to the increased rigidity of the cross-linked structure, in that cross-linked structures are generally noncrystalline. 6.10 Elastomers For the polymers known as elastomers, the rubbery plateau is pronounced and establishes the normal, room-temperature behavior of these materials. Fig. 6.42 shows the plot of log (modulus) versus temperature for an elastomer.

Fig.6.42. The modulus of elasticity versus temperature plot of an elastomer has a pronounced rubbery region. 179

This subgroup of thermoplastic polymers includes the natural and synthetic rubbers, such as polyisoprene. These materials provide a dramatic example of the uncoiling of a linear polymer (Fig.6.43). As a practical matter, the complete uncoiling of the molecule is not achieved, but huge elastic strains do occur.

Fig.6.43. Schematic illustration of the uncoiling of (a) an initially coiled linear molecule under (b) the effect of an external stress. This indicates the molecular-scale mechanism for the stress versus strain behavior of an elastomer, as shown in Fig.6.44.

Fig. 6.44 shows a stress-strain curve for the elastic deformation of an elastomer. This is in dramatic contrast to the stress-strain curve for a common metal. In Fig.6.44 the elastic modulus (slope of the stressstrain curve) increases with increasing strain. For low strains (up to ~15%), the modulus is low corresponding to the small forces needed to overcome secondary bonding and to uncoil the molecules. For high strains, the modulus rises sharply, indicating the greater force needed to stretch the primary bonds along the molecular backbone. In the both regions, however, there is a significant component of secondary bonding involved in the deformation mechanism, and the moduli are much lower than those for common metals and ceramics. The dashed line in 6.44 indicates, the recoiling of the molecules 180

(during unloading) has a slightly different path in the stress-versusstrain plot than does the uncoiling (during loading).

Fig.6.44. The stress-strain curve for an elastomer is an example of nonlinear elasticity. The initial low-modulus (i.e., low-slope) region corresponds to the uncoiling of molecules (overcoming weak, secondary bonds), as illustrated by Figure 6.43. The high-modulus region corresponds to elongation of extended molecules (stretching primary, covalent bonds), as shown by Figure 6.43b. Elastomeric deformation exhibits hysteresis; that is, the plots during loading and unloading do not coincide.

The different plots for loading and unloading define hysteresis.

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Conclusion 1) The tensile test gives the most basic design data, including modulus of elasticity, yield strength, tensile strength, ductility, and toughness. 2) The fundamental mechanism of elastic deformation is the stretching of atomic bonds. 3) Dislocations facilitate atom displacement by slipping in high-density atomic planes along high-density atomic directions. Without dislocation slip, exceptionally high stresses are required to deform these materials permanently. 4) The hardness test is a simple alternative to the tensile test that provides an indication of alloy strength. 5) The creep test indicates that above a temperature of about 1/2 times the absolute melting point, an alloy has sufficient atomic mobility to deform plastically at stresses below the room-temperature yield stress.

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CHAPTER 7 Thermal Behavior

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CHAPTER 7 THERMAL BEHAVIOR 7.1 Heat capacity As a material absorbs heat from its environment, its temperature rises. This common observation can be quantified with a fundamental material property, the heat capacity, C, defined as the amount of heat required to raise its temperature by 1K (=10C): C = Q/ T

(1)

With Q being the amount of heat producing a temperature change  T. It is important to note that, for incremental temperature changes, the magnitude of  T is the same in either the Kelvin (K) or Celcius (0C) temperature scales. The magnitude of C will depend on the amount of material. The heat capacity is ordinarily specified for a basis of one gram-atom (for elements) or one mole (for compounds) in units of J/g-atom K or J/mol K. A common alternative is the specific heat using a basis of unit mass, such as J/kg K. Along with the heat and the mass, the specific heat is designated by lowercase letters: C=q/ m  T

(2)

There are 2 common ways in which heat capacity (or specific heat) is measured. One is while maintaining a constant volume, Cv (cv), and the other is while maintaining a constant pressure, Cp (cp). The magnitude of Cp is always greater than Cv, but the difference is minor for most solids at room temperature or below. Because we ordinarily use mass-based amounts of engineering materials under a fixed, atmospheric pressure, we will tend to use Cp data in this lecture. Fundamental studies of the relationship between atomic vibrations and heat capacity in the early part of the 20-th century led to the discovery that, at very low temperatures, Cv rises sharply from zero at 0 K as Cv = AT3 (3) 184

where A is a temperature-independent constant. Furthermore, above a Debye temperature ( D), the value of Cv was found to level off at approximately 3R, where R is the universal gas constant. Fig. 7.1 summarizes how Cv rises to an asymptotic value of 3R above D. As D is below room temperature for many solids and Cp~ Cv, we have a useful rule of thumb for the value of the heat capacity of many engineering materials.

Fig.7.1. The temperature dependence of the heat capacity at constant volume, Cv. The magnitude of Cv rises sharply with temperature near 0 K and, above the Debye temperature (θD), levels off at a value of approximately 3R.

Finally, it can be noted that there are other energy-absorbing mechanisms, besides atomic vibrations, that can contribute to the magnitude of heat capacity. 7.2 Thermal expansion An increase in temperature leads to greater thermal vibration of the atoms in a material and an increase in the average separation distance of adjacent atoms (Fig. 7.2). In general, the overall dimension of the material in a given direction, L, will increase with 185

increasing temperature, T. This is reflected by the linear coefficient of thermal expansion, , given by  = dL/LdT

(4)

with  having units of mm/(mm 0C). Note that the thermal expansion coefficients of ceramics and glasses are generally smaller than those for metals, which are, in turn, smaller than those for polymers. The differences are related to the asymmetrical shape of the energy well in Fig. 7.2. The ceramics and glasses generally have deeper wells (i.e., higher bonding energies) associated with their ionic and covalent-type bonding. The result is a more symmetrical energy well, with relatively less increase in interatomic separation with increasing temperature, as shown in Fig. 7.2b.

Fig.7.2. Plot of atomic bonding energy versus inter-atomic distance for (a) weakly bonded solid and (b) a strongly bonded solid. Thermal expansion is the result of a greater inter-atomic distance with increasing temperature. The effect (represented by the coefficient of thermal expansion in Equation (4) is greater for the more asymmetrical energy well of the weakly bonded solid.

The elastic modulus is directly related to the derivative of the bonding energy curve near the bottom of the well (Fig. 6.18), and it follows that the deeper the energy well, the larger the value of that derivative and hence the greater the elastic modulus. Furthermore, 186

the stronger bonding associated with deeper energy wells corresponds to higher melting points. The thermal expansion coefficient itself is a function of temperature. A plot showing the variation in the linear coefficient of thermal expansion of some common ceramic materials over a wide temperature range is shown in Fig. 7.3. 7.3 Thermal conductivity The mathematics for the conduction of heat in solids is analogous to that for diffusion. The analog for diffusivity, D, is thermal conductivity, k, which is defined by Fourier’s law: k = - (dQ/dt) / A(dT/dx)

(5)

where dQ/dt is the rate of heat transfer across an area, A.

Fig.7.3. Linear thermal expansion coefficient as a function of temperature for three ceramic oxides (mullite = 3Al2O3 ·2SiO2). 187

Due to a temperature gradient dT/dx. Fig. 7.4 relates the various terms of Eq. (5) and should be compared with the illustration of Fick’s first law in Fig. 5.9, The units for k are J/(s m K). For steadystate heat conduction through a flat slab, the differentials of Eq. 7.5 become average terms: K = - (Q/t) / A(T/x)

(6)

Eq. 6 is appropriate for describing heat flow through refractory walls in high-temperature furnaces. A plot of thermal conductivity for several common ceramic materials over a wide temperature range is shown in Fig. 7.5. The conduction of heat in engineering materials involves 2 primary mechanisms, atomic vibrations and the conduction of free electrons. For poor electrical conductors such as ceramics and polymers, thermal energy is transported primarily by the vibration of atoms. For electrically conductive metals, the kinetic energy of the conducting (or “free”) electrons can provide substantially more efficient conduction of heat than atomic vibrations.

Fig.7.4. Heat transfer is defined by Fourier's law (5).

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Fig.7.5. Thermal conductivity of several ceramics over a range of temperatures.

The increasing vibration of the crystal lattice at increasing temperature, then, generally results in a decrease in thermal conductivity. Similarly, the structural disorder created by chemical impurities results in a similar decrease in thermal conductivity. As a result, metal alloy tend to have lower thermal conductivities than pure metals. For ceramics and polymers, atomic vibrations are the predominant source of thermal conductivity, given the very small number of 189

conducting electrons. These lattice vibrations are, however, also wavelike in nature and are similarly impeded by structural disorder. As a result, glasses will tend to have a lower thermal conductivity than crystalline ceramics of the same chemical compositions. In the same way, amorphous polymers will tend to have a greater thermal conductivity than crystalline polymers of comparable compositions. Also, the thermal conductivities of ceramics and polymers will drop with increasing temperature due to the increasing disorder caused by the increasing degree of atomic vibration. For some ceramics, conductivity will eventually begin to rise with further increase in temperature due to radiant heat transfer. Significant amounts of infrared radiation can be transmitted through ceramics, that tend to be optically transparent. The thermal conductivity of ceramics and polymers can be further reduced by the presence of porosity. The gas in the pores has a very low thermal conductivity, giving a low net conductivity to the overall microstructure. 7.4 Thermal shock The common use of some inherently brittle materials, especially ceramics and glasses, at high temperatures leads to a special engineering problem called thermal shock. This can be defined as the fracture (partial or complete) of the material as a result of a temperature change (usually a sudden cooling). The mechanism of thermal shock can involve both thermal expansion and thermal conductivity. Thermal shock follows from these properties in one or 2 ways. First, a failure stress can be built up by constraint of uniform thermal expansion. Second, rapid temperature changes produce temporary temperature gradients in the material with resulting internal residual stress. Fig. 7.6 shows a simple illustration of the first case. It is equivalent to allowing free expansion followed by mechanical compression of the rod back to its original length. More than one furnace design has been flawed by inadequate allowance for expansion of refractory ceramics during heating. Similar consideration must be given to expansion coefficient matching of coating and substrate for glazes (glass coatings on ceramics) and enamels (glass coatings on metals). 190

Fig 7.6. Thermal shock resulting from constraint of uniform thermal expansion. This process is equivalent to free expansion followed by mechanical compression back to the original length.

Even without external constraint, thermal shock can occur due to the temperature gradients created because of a finite thermal conductivity. Fig.7.7 illustrates how rapid cooling of the surface of a high-temperature wall is accompanied by surface tensile stresses. The surface contracts more than the interior, which is still relatively hot. As a result, the surface “pulls” the interior into compression and is itself “pulled” into tension. With the inevitable presence of Griffith flaws at the surface, this surface tensile stress creates the clear potential for brittle fracture. The ability of a material to withstand a given temperature change depends on a complex combination of thermal expansion, thermal conductivity, overall geometry, and the inherent brittles of that material. Fig.7.8 shows the kinds of thermal quenches (temperature drops) necessary to fracture various ceramics and glasses by thermal shock. Conclusion 1. The heat capacity indicates the amount of heat necessary to raise the temperature of a given amount of material. 2. The term specific heat is used when the property is determined for a unit mass of the material.

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Fig.7.7. Thermal shock resulting from temperature gradients created by a finite thermal conductivity. Rapid cooling produces surface tensile stresses.

3.Fundamental understanding of the mechanism of heat absorption by atomic vibrations leads to a useful rule of thumb for estimating heat capacity of materials at room temperature and above (Cp ~ Cv ~3R). 4.The increasing vibration of atoms with increasing temperature leads to increasing interatomic separations and, generally, a positive coefficient of thermal expansion. A careful inspection of the relationship of this expansion to the atomic bonding energy curve 192

reveals that strong bonding correlates with low thermal expansion as well as high elastic modulus and high melting point.

Fig.7.8. Thermal quenches that produce failure by thermal shock are illustrated. The temperature drop necessary to produce fracture (T0-T‘) is plotted against a heat transfer parameter (rmh). More important than the values of rmh are the regions corresponding to given types of quench (e.g., “water quench” corresponds to an rmh around 0.2 to 0.3).

The inherent brittleness of ceramics and glasses, combined with thermal expansion mismatch or low thermal conductivities, can lead to mechanical failure by thermal shock.

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CHAPTER 8 Failure Analysis and Prevention

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CHAPTER 8 FAILURE ANALYSIS AND PREVENTION 8.1 Introduction Why it is necessary to know Failure analysis and prevention?  At room temperature metal alloys and polymers stressed beyond their elastic limit eventually fracture following a period of nonlinear plastic deformation.  Brittle ceramics and glasses typically break following elastic deformation, without plastic deformation. The inherent brittleness of ceramics and glasses combined with their common use at high temperatures make thermal shock a major concern. Conclusion: With continuous service at high temperatures, any engineering material can fracture when creep deformation reaches its limit. We are planning in this Chapter: 1) To look at additional ways in which materials fail. 2) For the rapid application of stress to materials with preexisting surface flaws, the measurement of the impact energy corresponds to the measurement of toughness, or area under the stress-versusstrain curve. 3) Monitoring impact energy as a function of temperature reveals that, for bcc metal alloys, there is a distinctive ductile - to- brittle transition temperature, below which otherwise ductile materials can fail in a catastrophic, brittle fashion. 4) The general analysis of the failure of structural materials with preexisting flaws is termed - fracture mechanics. The important property - fracture toughness, which is large for materials such as pressure-vessel steels and small for brittle materials such as typical ceramics and glasses. 5) Under cyclic loading conditions, otherwise ductile metal alloys and engineering polymers can eventually fail in a brittle fashion, a phenomenon appropriately termed fatigue. Ceramics and glasses can exhibit static fatigue without cyclic loading due to a chemical reaction with atmospheric moisture. 196

6) Nondestructive testing - evaluation of engineering materials without impairing their future usefulness (it is very important technology for identifying microstructural flaws). Such flaws include surface and internal cracks, so it plays central role in the failure of materials. Conclusion Failure analysis can be defined as the systematic study of the nature of the various modes of material failure. The related goal of failure prevention - to apply the understanding provided by failure analysis to avoid future disasters. 8.2 Impact energy Impact energy - necessary energy to fracture a standard test piece under an impact load (= analog of toughness). The most common Lab. measurement of impact energy - Charpy test, illustrated in Fig. 8.1. Test principle - straight-forward. The energy necessary to fracture the test piece is directly calculated from the difference in initial and final heights of the swinging pendulum. To provide control over the fracture process, a stress-concentrating notch is machined into side of the sample subjected to maximum tensile stress. The net test result is to subject the sample to elastic deformation, plastic deformation, and fracture in rapid succession. Although rapid, the deformation mechanisms involved are the same as those involved in tensile testing the same material. The load impulse must approach the ballistic range before fundamentally different mechanisms come into play. In effect Charpy test takes the tensile test to completion very rapidly. The impact energy from the Charpy test correlates with the area under the total stress-strain curve. ( i.e., toughness). We expect alloys with large values of both strength (Y.S. and T.S.) and ductility (percent elongation at fracture) to have large impact energy. 197

Remember: The impact data are sensitive to test conditions:  Increasingly sharp notches can give lower impact energy values due to the stress concentration effect at the notch tip.  The nature of stress concentration at notch and crack tips is explored further in the next section.

Fig.8.1. Charpy test of impact energy.

For polymers, impact energy values are typically measured with the Izod test. These 2 standardized tests differ primarily in the 198

configuration of the notched test specimen. Impact test temperature can also be a factor. Examples: 1. Face-centered cubic alloys generally show ductile fracture modes in Charpy testing; 2. Hexagonal close-packed alloys - generally brittle; (Fig. 8.2). 3. Body-centered cubic alloys show a dramatic variation in fracture mode with temperature. In general, they fail in a brittle mode at relatively low temperatures and in a ductile mode at relatively high temperatures.

Fig.8.2 Impact energy for a ductile fcc alloy (copper C23000- 061, “red brass) is generally high over a wide temperature range. Conversely, the impact energy for a brittle hcp alloy (magnesium AM100A) is generally low over the same range.

Fig. 8.3 shows the microscopic fracture surface of the hightemperature ductile failure. It has a dimpled texture with many 199

cuplike projections of deformed metal. Brittle fracture is characterized by cleavage surfaces. Near the transition temperature between brittle and ductile behavior the fracture surface exhibits a mixed texture. Remember: 1. The ductile-to-brittle transition temperature is of great practical importance. Why? If alloy exhibits a ductile-to-brittle transition it loses toughness and it is susceptible to catastrophic failure below this transition temperature. 2. The transition temperature can fall between roughly (-100 and +100)oC, depending on alloy composition and test condition! 3. Low-carbon steels that were ductile in room-temperature tensile tests became brittle when exposed to lower temperature ocean environments (several disastrous failures of Liberty ships occurred during World War II).

Fig.8.3. (a) Typical “cup and cone” ductile fracture surface. Fracture originates near the center and spreads outward with a dimpled texture. Near the surface, the stress state changes from tension to shear with fracture continuing at approximately 45o. (b) Typical cleavage texture of brittle fracture surface.

8.3 Fracture toughness Fracture toughness (symbol Kic ) - "kay-one-cee) - is the critical 200

value of the stress intensity factor at a crack tip necessary to produce catastrophic failure under simple uniaxial loading. "1" - means "mode1" = uniaxial loading; "c" - "critical". Example of the concept of Fracture toughness blowing up a balloon containing a small pinhole. When the internal pressure of the balloon reaches a critical value, catastrophic failure originates at the pinhole. In general, the value of Fracture toughness is given by

Kic = Yf a

(1)

where Y - dimensionless geometry factor on the order of 1; f is the overall applied stress at failure; a - is the length of a surface crack (or 1/2 the length of an internal crack). Fracture toughness Kic has units of MPam . Fig. 8.4 shows a typical measurement of Kic

Fig.8.4. Fracture toughness test

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Remember: Kic is associated with so-called plane strain conditions in which the specimen thickness (Fig.8.4) is relatively large compared with the notch dimension. 1. For thin specimens we say ("plane stress" conditions) Fracture toughness is denoted KC and is a sensitive function of specimen thickness. Plane strain conditions generally prevail when thickness  2.5 (Kic /Y.S.)2. 2. Failure by general yielding is preceded by observable deformation, whereas flaw-induced fracture occurs with no such warning. It is big progress in the range of applications of structural ceramics. Fig. 8.5(a) illustrates the mechanism of transformation toughening in partially stabilized zirconia (PSZ).

Fig.8.5. Two mechanisms for improving fracture toughness of ceramics by crack arrest. (a)Transformation toughening of partially stabilized zirconia involves the stress-induced transformation of tetragonal grains to the monoclinic structure which has a larger specific volume. The result is a local volume expansion at the crack tip, squeezing the crack shut and producing a residual compressive stress. (b) Microcracks produced during fabrication of the ceramic can blunt the advancing crack tip.

Explanation: Having second-phase particles of tetragonal zirconia in a matrix of cubic zirconia is the key to improved toughness. 202



A propagating crack creates a local stress field that induces a transformation of tetragonal zirconia particles to the monoclinic structure in that vicinity.  The slightly larger specific volume of the monoclinic phase causes an effective compressive load locally and, in turn, the "squeezing" of the crack shut. Fig. 8.5(b) shows the second technique of crack arrest.  Micro-cracks purposely introduced by internal stresses during processing of the ceramic are available to blunt the tip of an advancing crack. The larger tip radius can dramatically reduce the local stress at the crack tip. Traditional ceramics and glass The absence of plastic deformation on the macroscopic scale (the stress - strain curve) is matched by a similar absence on the microscopic scale. This is reflected in the characteristically low fracture toughness (Kic) values ( 5 MPam) for ceramics and glass. Most (Kic) values are lower than those of the most brittle metals. Only the recent developed transformation - toughened PSZ is competitive with some of the moderate toughness metal alloys. 8.4 Fatigue Before we characterized the mechanical of metals under a single load application either slowly (e.g., the tensile test) or rapidly (e.g., the impact test). Many structural applications involve cyclic rather than static loading, and a special problem arises. Fatigue - is the general phenomenon of material failure after several cycles of loading to a stress level below the ultimate tensile stress Fig.8.6. Fig. 8.7 illustrates a common Lab test used to cycle a test piece rapidly to a predetermined stress level. Fig. 8.8 - is a typical fatigue curve. This plot of stress (S) versus number of cycles (N), on a logarithmic scale, at a given stress is also called the S-N curve. The data indicate that while the material can withstand a stress of 800 MPa (T.S.) in a single loading (N=1) , it fractured after 10000 applications ( N=104) of a stress less than 600 MPa. The reason for this decay in strength is a subtle one. 203

Fig.8.6. Fatigue corresponds to the brittle fracture of an alloy after a total of N cycles to a stress below the tensile strength.

Fig.8.7. Fatigue test.

Fig.8.8. Typical fatigue curve.

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Fig. 8.9 shows how repeated stress applications can create localized plastic deformation at the metal surface, eventually manifesting as sharp discontinuities (extrusions and intrusions).

Fig.8.9. An illustration of how repeated stress applications can generate localized plastic deformation at the alloy surface leading eventually to sharp discontinuities.

These intrusions once formed, continue to grow into cracks, reducing the load-carrying ability of the material and serving as stress concentrators. In particular, crack growth continues until the crack length reaches the critical value as defined by

Kic = Yf a 205

Fig. 8.10 shows how once the stress exceeds some threshold value, crack length increases, as indicated by the slope of the plot (da/dN), the rate of crack growth. At a given stress level, the crack growth rate increases with increasing crack length, and for a given crack length, the rate of crack growth is significantly increased with increasing magnitude of stress.

Fig.8.10. Illustration of crack growth with number of stress cycles, N, at two different stress levels. Note that, at a given stress level, the crack growth rate, da/dN, increases with increasing crack length, and, for a given crack length such as a1, the rate of crack growth is significantly increased with increasing magnitude of stress.

Let's see Fig. 8.11. This is illustration of logarithmic relationship between crack growth rate (da/dN) and the stress intensity factor range ( K). Region I corresponds to non-propagating fatigue cracks. Region II corresponds to a linear relationship between log (da/dN) and log ( K). (da/dN) = A ( K)m

(2)

where A and m are material parameters dependent on environment, test frequency, and the ratio of minimum and maximum stress 206

applications, and K - is the stress intensity factor range at the crack tip. K = K max - K min = Ya = Y ( max -  min)a

(3)

(2) and (3) to note that the K is the more general stress intensity factor rather than the more specific fracture toughness, Kic. N - is the number of cycles associated with a given crack length prior to failure rather than the total number of cycles to fatigue failure associated with an S-N curve.

Fig.8.11. Illustration of logarithmic relationship between crack growth rate, da/dN, and the stress intensity factor range, 1K. Region I corresponds to nonpropagating fatigue cracks. Region II corresponds to a linear relationship between log da/dN and log 1K. Region III represents unstable crack growth prior to catastrophic failure. 207

In the region II values of m typically range between 1 - 6. Region III corresponds unstable crack growth prior to catastrophic failure. Fig. 8.8 showed that the decay in strength with increasing numbers of cycles reaches a limit. This fatigue strength, or endurance limit, is characteristic of ferrous alloys. Nonferrous alloys tend not to have such a distinct limit, although the rate of decay decreases with N. Fatigue strength usually falls between 1/4 and 1/2 of the tensile strength. Metal fatigue has been defined as a loss of strength created by microstructural damage generated during cyclic loading. Attention: fatigue phenomenon is also observed for ceramics and glasses, but WITHOUT cyclic loading (because of chemical and not mechanical mechanism).

a)

b)

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(с) Fig.8.12. Characteristic fatigue fracture surface. (a) Photograph of an aircraft throttle-control spring (1,5x) that broke in fatigue after 274 h of service. The alloy is 17-7PH stainless steel. (b) Optical micrograph (10x) of the fracture origin (arrow) and the adjacent smooth region containing a concentric line pattern as a record of cyclic crack growth (an extension of the surface discontinuity shown in Figure 810). The granular region identifies the rapid crack propagation at the time of failure. (c) Scanning electron micrograph (60x), showing a close up of the fracture origin (arrow) and adjacent “clamshell” pattern.

Static fatigue - the drop in strength of glasses with duration of load (and without cyclic load applications) Fig.8.13. Remember: 1) it occurs in water-containing environments; 2) it occurs around room temperature. The role of water in static fatigue is shown in Fig. 8.14. Explanation: By chemically reacting with the silicate network, an H2O molecule generates 2 Si-OH units. The hydroxyl units are not bonded to each other, leaving a break in the silicate network. When this reaction occurs at the tip of a surface crack, the crack is lengthened by one atomic-scale step. 209

Fig.8.13. The drop in strength of glasses with duration of load (and without cyclic load applications) is termed static fatigue.

Fig.8.14. The role of H2O in static fatigue depends on its reaction with the silicate network. One H2O molecule and one –Si-O-Si- segment generate two Si-OH units. This is equivalent to a break in the network. 210

Fig.8.15. Comparison of (a) cyclic fatigue in metals and (b) static fatigue in ceramics.

Fig. 8.15 shows comparison of (a) cyclic fatigue in metals and (b) static fatigue in ceramics. Because of the chemical nature of the mechanism in ceramics and glasses, the phenomenon is found predominantly around room temperature. At relatively high temperatures (above about 150 oC), the hydroxyl reaction is so fast that the effects are difficult to monitor. At those temperatures, other factors such as viscous deformation can also contribute to static fatigue. At low temperatures (below - 100 oC), the rate of hydroxyl 211

reaction is too low to produce a significant effect in practical time periods. Analogies to static fatigue in metals would be stress corrosion cracking and hydrogen embrittlement, involving crack growth mechanisms under severe environments. Fatigue in polymers is treated in a way similar to metal alloys. The fatigue limit for polymers = 106 cycles; for commonly used nonferrous alloys = 108 cycles. 8.5 Nondestructive testing Nondestructive testing is the evaluation of engineering materials without impairing their usefulness. Central focus of many Nondestructive testing techniques is:  The identification of potentially critical flaws (such as surface and internal cracks).  The analysis of existing failure  To prevent future failures. Dominant techniques: 1) X-radiography; 2) ultrasonic. 8.6

X-radiography

X-radiography produces a "shadow-graph" of the internal structure of a part with a much coarser resolution ( typically the order of 1 mm). Principle: it based on a portion of the electromagnetic spectrum with relatively short wavelengths (typically < 1 nm) in comparison of the visible region.  Medical chest x-ray is common example;  Industrial X-radiography used for inspecting castings and weldments  For a given material being inspected by a given energy x-ray beam, the intensity of the beam I, transmitted through a thickness of material ( x )

I = Io e - x

Beer's law

where Io is the incident beam intensity and  the linear absorption coefficient for the material. 212

(4)

Fig.8.16. A schematic of x-radiography.

8.7 Ultrasonic testing Principle: it based on a portion of the acoustic spectrum (typically 1 to 25 MHz) with frequencies well above those of the audible range (20 to 20000 Hz) . Distinction ( between X-radiography and ultrasonic testing): 1) the ultrasonic waves are mechanical in nature, 2) requiring a transmitting medium, while electromagnetic waves can be transmitted in a vacuum. A typical ultrasonic source involving a piezoelectric transducer is shown in Chapter 15 and schematic of a "pulse echo" of ultrasonic test in Fig. 8.17. 213

Main idea of ultrasonic test - is the reflection of the ultrasonic waves at interfaces of dissimilar materials. The reflection coefficient R defined as the ratio of reflected beam intensity Ir to incident beam, intensity I i

Fig.8.17. A schematic of “pulse echo” ultrasonic test.

214

R = Ir / Ii = [(Z2 -Z1) / (Z2 +Z1)]2

(5)

Where Z is the acoustic impedance, defined as the product of the material's density and velocity of sound, with subscription 1 and 2 referring to the 2 dissimilar materials on either side of the interface. The high degree of reflectivity by a typical flaw such as an internal crack, is the basic for defect inspection. REMEMBER: This technique is not suitable for use on complex-shaped parts, and there is a tendency for ultrasonic waves to scatter due to microstructural features such as porosity and precipitates. 8.8 Other nondestructive tests A wide spectrum of additional methods is available for nondestructive testing. Eddy-current testing The impedance of an inspection coil is affected by the presence of an adjacent, electrically conductive test piece, in which alternating, or eddy currents have been induced by the coil. The net impedance is a function of the composition and /or geometry of the test piece. The popularity of this test is due to its convenience, rapidity, non-contact nature. By varying the test frequency, the method can be used for both surface and subsurface flaws. Limitations: qualitative nature and the requirement of electrical conductivity. Magnetic-particle testing A fine powder of magnetic particles (Fe or Fe3O4) is attracted to the magnetic leakage flux around a discontinuity, such as a surface or near-surface crack in a magnetized test piece. It is simple, traditional technique widely used because of its convenience and low cost. Limitations:  A primary limitation is the restriction to magnetic materials.  An enormous volume of structural steels used in engineering is magnetic.

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Liquid-penetrate testing The capillary action of a fine powder on the surface of a sample draws our a high-visibility liquid that has previously penetrated into surface defects. Like magnetic-particle testing, it is an inexpensive and convenient technique for surface defect inspection. Liquidpenetrate testing is largely used on nonmagnetic materials for which magnetic-particle inspection is not possible! Limitations: The inability to inspect subsurface flaws and a loss of resolution on porous materials. Acoustic- emission testing This method measures the ultrasonic waves produced by defects within the microstructure of a material in response to an applied stress. It has assumed a unique role in failure prevention. In addition to being able to locate defects, it can provide an early warning of impending failure due to those defects. Distinction (between conventional ultrasonic testing and Acousticemission testing):  In conventional ultrasonic testing a transducer provides the source of ultrasound, the material is the source of ultrasonic acoustic emissions.  Transducers serve as only receivers.  The rate of acoustic-emission events rises sharply just prior to failure. By continuously monitoring these emissions, the structural load can be removed in time to prevent failure.  A primary example of this application is in the continuous surveillance of pressure vessels. 8.9 Failure analysis and prevention Failure analysis is very important for application of materials in engineering design. Failure prevention is equally important for avoiding future disasters. Ductile fracture - is observed in a large number of the failures occurring in metals due to "overload" (i.e., taking a material beyond the elastic limit and, subsequently, to fracture). 216

Conclusion 1. Brittle fracture - is characterized by rapid crack propagation without significant plastic deformation on a macroscopic scale. 2. Fatigue failure - by a mechanism of slow crack growth gives the distinctive "clamshell" fatigue 3.

4.

5.

6.

7.

8.

9.

fracture surface. Corrosion - fatigue failure is due to the combined actions of a cyclic stress and a corrosive environment. In general, the fatigue strength of metal will be decreased in the presence of an aggressive, chemical environment. Stress -corrosion cracking (SCC) - combined mechanical and chemical failure mechanism in which a non-cyclic tensile stress (below the yield strength ) leads to the initiation and propagation of fracture in a relatively mild chemical environment. Stress - corrosion cracks may be inter granular, trans granular, or a combination. Wear failure is a term encompassing a broad range of relatively complex, surface-related damage phenomena. Both surface damage and wear debris can constitute "failure" of materials intended for sliding contact applications. Liquid-erosion failure is a special form of wear damage in which a liquid is responsible for the removal of material. Liquid-erosion damage typically results in a pitted or honeycomb-like surface region. Liquid-metal embrittlement involves the material losing some degree of ductility or fracturing below its yield stress in conjunction with its surface being wetted by a lower-meltingpoint liquid metal. Hydrogen embrittlement is the most notorious form of catastrophic failure in high-strength steels. A few parts-permillion of hydrogen dissolved in these materials can produce substantial internal pressure, leading to fine, hairline cracks and a loss of ductility Creep and stress-rupture failures can occur near room temperature for many polymers and certain low-melting point 217

metals, such as lead, but may occur above 1000 oC in many ceramics and certain high-melting point metals, such as the superalloys. 10. Complex failure are those in which the failure occurs by the sequential operation of two distinct fracture mechanisms. An example would be initial cracking due to stress -corrosion cracking and, then, ultimate failure by fatigue after a cyclic load is introduced simultaneously with the removal of the corrosive environment. Remember: Fracture toughness for metals and alloys 20 - 200 MPam Fracture toughness for ceramics and glass 1 - 9 MPam Fracture toughness for polymers 1 - 4 MPam Fracture toughness for composites 10 - 60 MPam

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CHAPTER 9 Phase Diagrams. Equilibrium Microstructural Development

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CHAPTER 9 PHASE DIAGRAMS – EQUILIBRIUM MICROSTRUCTURE DEVELOPMENT To appreciate fully the nature of the many microstructuresensitive properties of engineering materials, we must spend some time exploring the ways in which microstructure is developed. An important tool in this exploration is the phase diagram, which is a "map" that will guide us in answering the general question: What microstructure should exist at a given temperature for a given material composition? This is a question with a specific answer based in part on the equilibrium nature of the material. 9.1 The phase rule We begin with definition of terms you need to understand the following discussion. PHASE – is a chemically and structurally homogeneous portion of the microstructure. Single-phase microstructure can be polycrystalline (Fig.9.1), but each crystal grain differs only in crystalline orientation, not in chemical composition.

Fig.9.1 Single-phase microstructure of commercially pure molybdenum, 200x. Although there are many grains in this microstructure, each grain has the same, uniform composition. 220

COMPONENT – distinct chemical substance from which the phase is formed. In Cu-Ni alloy we find 1 single phase (solid solution) and 2 components. DEGREES of FREEDOM – are the number of independent variables available to the system. Example: a pure metal at precisely its melting point has no degrees of freedom. At this condition or state, the metal exists in two phases in equilibrium, that is, in solid and liquid phases simultaneously. Any increase in temperature will change the state of the microstructure. Similarly, a slight reduction in temperature will completely solidify the material. IMPORTANT STATE VARIABLES: temperature, pressure, composition. The general relationship between microstructure and these state variables is given by the Gibbs phase rule, F=C–P+2

(1)

where F – is the number of degrees of freedom, C – the number of components, P – the number of phases 2 – comes from limiting the state variables to two ( temperature and pressure) Remember: For most routine materials processing involving condensed systems, the effect of pressure is slight, and we can consider pressure to be fixed at 1 atm. In this case the phase rule can be rewritten to reflect one less degree of freedom: F=C–P+1

(2)

Example N1: pure metal at its melting point: C =1, P = 2 (solid + liquid), giving F= 1-2+1 =0, as we had noted previously. Example N2: metal with a single impurity (i.e. with 2 components) at its melting point. Solid and liquid phases can usually coexist over a range of temperatures: C =2, P = 2 (solid + liquid), giving F= 2-2+1 =1. 221

Conclusion: the single degree of freedom means simply that we can maintain this two-phase microstructure while we vary the temperature of the material. However, we have only one independent variable (F=1)!!!!!! By varying temperature, we indirectly vary the compositions of the individual phases. Composition is, then, a dependent variable. Fig.9.3. (b) A projection of the phase diagram information at 1 atm generates a temperature scale labeled with the familiar transformation temperatures for H2O (melting at 0oC and boiling at 100oC). This figure summarizes the phases present for water as a function of temperature and pressure. For the fixed pressure of 1 atm, we find a single , vertical temperature scale labeled transformation. Solid H2O (ice) transforms to liquid H2O (water) at 0 0 C, then water transforms to gaseous H2O (steam) at 1000 C.

Fig.9.2. Two-phase microstructure of pearlite found in a steel with 0.8 wt % C, 500x. This carbon content is an average of the carbon content in each of the alternating layers of ferrite (with 25 %) = Automobile tires are a rubber with roughly 1/3 carbon black particles.  Cermet – ceramic –metal composite (high –hardness carbide in a ductile metal matrix)

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Fig.14.9 Filling the volume of concrete with aggregate is aided by a wide particle size distribution. The smaller particles fill spaces between larger ones. This view is, of course, a two-dimensional schematic.

14.3 Property averaging Properties of composites represent an average of the properties of their individual components. So the precise nature of the “average’ is a sensitive function of microstructural geometry. 14.3.1 Three idealized geometries We know 1 – direction parallel to continuous fibers in a matrix (phases in parallel); 2 - direction perpendicular to the direction of the continuous fibers (phases in series.); 3 - direction relative to a uniformly dispersed aggregate composite. 1 and 2 represent extremes in the highly anisotropic nature of fibrous composites such as fiberglass and wood. 3 represents an idealized model of the relatively isotropic nature of concrete. 332

Fig. 14.10. Three idealized composite geometries: (a) a direction parallel to continuous fibers in a matrix, (b) a direction perpendicular to continuous fibers in a matrix, and (c) a direction relative to a uniformly dispersed aggregate composite.

Fig. 14.11. Uniaxial stressing of a composite with continuous fiber reinforcement. The load is parallel to the reinforcing fibers. 333

14.3.2 Loading parallel to reinforcing fibers – ISOSTRAIN The uniaxial stressing of the geometry of Fig. 14.10a was shown in 14.11. If the matrix is the intimately bonded to the reinforcing fibers, the strain of both the matrix and the fibers must be the same.

Fig. 14.12. Simple stress-strain plots for a composite and its fiber and matrix components. The slope of each plot gives the modulus of elasticity.

This isostrain condition is true even though the elastic moduli of the components will tend to be quite different. Fig. 14.12 shows the modulus as the slope of a stress-strain curve for a composite with 70 % reinforcing fibers. ( For matrix modulus = 6.9 x 103 MPa; for fiber 72.4 x 103 MPa; for composite =52.8 x 103 MPa = composite modulus is higher than for the matrix. 14.3.3 Loading perpendicular to reinforcing fibers – ISOSTRESS The isostress condition with perpendicular loading of the reinforcing fibers produces a substantially different result from the isostrain condition with parallel loading (Fig. 14.13).

334

Fig. 14.13. Uniaxial loading of a composite perpendicular to the fiber reinforcement can be simply represented by this slab.

Fig. 14.14 shows that the matrix modulus dominates the composite modulus except with very high concentration of fibers. 14.3.4 Loading a uniformly dispersed aggregate composite The uniaxial stressing of the isotropic geometry of Fig. 14.10c is shown in Fig. 14.15. A rigorous treatment of this system can become quite complex depending on the specific nature of the dispersed and continuous phases. Fortunately, the results of the 2 previous cases (isostrain and isostress fiber composite) serve as upper and lower bounds for the aggregate case.

Fig. 14.14. The composite modulus, Ec, is a weighted average of the moduli of its components (Em = matrix modulus and Ef = fiber modulus 335

Fig. 14.15. Uniaxial stressing of an isotropic aggregate composite

14.3.5 Interfacial strength The interface between the matrix and discontinuous phase must be strong enough to transmit the stress (сжимание) or strain (растяжение) due to a mechanical load from one phase to the other. Without this strength, the dispersed phase can fail to “communicate” with the matrix. Reinforcing fibers easily slipping out of a matrix. Fig. 14.16 illustrates the contrasting microstructure of (a) poorly bonded and (b) well-bonded interfaces in a fiberglass composites.

(a)

(b)

Fig. 14.7. The utility of a reinforcing phase in this polymer-matrix composite depends on the strength of the interfacial bond between the reinforcement and the matrix. These scanning electron micrographs contrast (a) poor bonding with (b) a well-bonded interface. In metal-matrix composites, high interfacial strength is also desirable to ensure high overall composite strength. (Courtesy of Owens-Corning Fiberglas Corporation)

14.4 How to control interfacial strength? Surface treatment, chemistry, and temperature are a few considerations in the “art and science” of interfacial bonding. It is required in all composites to ensure that 336

  



property averaging is available at relatively low stress levels. 2 different behavior of fiber composites at high stress levels for polymer-matrix and metal matrix composites, failure originates in or along the reinforcing fibers. (Fig. 14.16) – high interfacial strength is desirable to maximize the overall composite strength. In ceramic-matrix composites, failure generally originates in the matrix phase. To maximize the fracture toughness for these materials, it is desirable to have a relatively weak interfacial bond allowing fibers to pull out. As a result, a crack initiated in the matrix is deflected along the fibermatrix interface. This increased crack path length significantly improves fracture toughness. The mechanism of fiber pullout for importing fracture toughness is shown in Fig. 14.17.

Fig. 14.17. For ceramic-matrix composites, low interfacial strength is desirable. We see that (a) a matrix crack approaching a fiber is (b) defected along the fiber-matrix interface. For the overall composite (c), the increased crack path length due to fiber pull-out significantly improves fracture toughness.

337

Fig.14.18. Si3N4; SiC/Al2O3; SiC/SiC; SiC/Si3N4. The fracture toughness of these structural ceramics is substantially increased by the use of a reinforcing phase. (Note the toughening mechanism illustrated in Figure 14.17.)

14.5 Processing of composites Fig. 14.19 illustrates the fabrication of typical fiberglass configurations. These are often standard polymer processing methods with glass fiber added at an appropriate point in the procedure. A major factor affecting properties is the orientation of the fibers. Table 14.1 Major processing methods for three representative composites Composite Fiberglass Wood Concrete

Processing methods Open mold Pre-forming Closed mold Sawing Kiln drying Manufacturing of Portland cement Mix design (mixing of cement, aggregate, water) Reinforcement (with steel bars, etc) 338

Fig. 14.19. Summary of the diverse methods of processing fiberglass products: (a) open-mold processes.

339

.

Fig.14.19 (Continued) (b) preforming methods, (c) closed-mold processes

Note: The open-mold processes include pultrusion, which is especially well suited for producing complex cross-section products continuously.

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CHAPTER 15 Electrical Behavior

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CHAPTER 15 ELECTRICAL BEHAVIOR 15.1 Charge carries and conduction The condition of electricity in materials is by means of species called charge carriers. Example: Electron – a particle with 0.16 x 10 –18 C of negative charge. Electron hole – it is a missing electron in an electron cloud. The absence of negatively charged electron gives the electron hole an effective positive charge of 0.16 x 10 –18 C (play a central role in semiconductors). In ionic materials, anions can serve as negative charge carriers and cations as positive carriers. Fig. 15.1 – simple method for measurement of electrical conduction. I – current flow through the circuit with resistance R and voltage V. V=IR

Ohm’s law

(1)

V – in Volts, I – in Amperes (1A=1C/s); R –in Ohm R = A /l

(2)

l – sample length; A – sample area; - resistivity. Units for resistivity -  m.  conductivity – is the reciprocal of resistivity ( it is most convenient parameter for material of electrical classification). = 1/

(3)

 = nq

(4)

n – is the density of charge carriers, q – charge of carrier, - mobility of each carrier. - mobility of each carrier = average carrier velocity or drift velocity (v) divided by electrical field strength E.  = v/E (5) 342

Electric field strength E = V/l For semiconductors:  = nnqnn + npqpp

(6)

The subscripts n and p refer to the negative and positive carriers.

Fig. 15.1. Schematic of a circuit for measuring electrical conductivity. Sample dimensions relate to Equation (2).

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15.2 Energy levels and energy bands Fig. 15.2 shows an energy-level diagram for a single sodium atom. Electronic configuration is 1s22s22p63s1

Fig. 15.2. Energy level diagram for an isolated sodium atom.

Energy – level diagram indicates that there are actually 3 orbitals associated with the 2p energy level and that each of the 1s and 2s and 2p orbitals is occupied by 2 electrons. This distributions of electrons among the various orbitals is a manifestation of the Pauli exclusion principle, an important concept from quantum mechanics that indicates that no 2 electrons can occupy precisely the same state. Fig. 15-2 each horizontal line represents a different orbital (i.e., a unique set of 3 quantum numbers). Remember: 1) Each such orbital can be occupied by 2 electrons because they are in 2 different states; that is, they have opposite or anti-parallel electron spin. 2) In general, electron spins can be parallel or anti-parallel. 3) The outer orbitals (3s) is half-filled by a single electron. Fig.15.3. shows diagram for hypothetical Na4 molecule. The 4 shared, outer orbital electrons are “split” into 4 slightly different energy levels, as predicted by the Pauli exclusion principle. 344

Fig. 15.3. Energy-level diagram for a hypothetical Na4 molecule. The four shared, outer orbital electrons are .split. into four slightly different energy levels, as predicted by the Pauli exclusion principle.

In fact, electron pairing in a given orbital tends to be delayed until all levels of a given energy have a single electron. This is referred to as Hund’s rule. Example N2 ( N – element 7) Nitrogen has 3 2p electrons, each in a different orbital of equal energy. Pairing of 2 in 2p electrons of opposite spin in a single orbital does not occur until element 8 – oxygen. The result of this splitting is a narrow band of energy levels corresponding to what was a single 3s level in the isolated atom. Note: 1) In the 3s level of the isolated atom, the 3s band of the Na4 molecule is only half-filled. As a result, electron mobility between adjacent atoms is quite high. 2) The valence electron energy band in the metallic solid is only half-filled, permitting high mobility of outer orbital electrons throughout the solid. 3) Produced from valence electrons, the energy band of Fig. 15.4 is termed the valence band. (The valence band is 345

completely full up to the midpoint of the band and ). Note, that this is true only at a temperature of absolute zero (0K). Conclusion: Metals are good electrical conductors because their valence band is only partially filled.

Fig. 15.4. Energy-level diagram for solid sodium. The discrete 3s energy level of Figure 15.2 has given way to a pseudo continuous energy band (half-filled). Again, the splitting of the 3s energy level is predicted by the Pauli exclusion principle.

The energy of the highest filled state in the energy band (at 0 K) is known as the Fermi level (Ef). Fermi function represents the probability that energy level, E, is occupied by an electron and can have values between 0 and 1. At 0K, f(E) is equal to 1 up to EF and equal to 0 above EF Since the energy levels below EF are full, conduction requires electrons to increase their energy to some level just above EF (i.e., to unoccupied levels). Note: This energy promotion requires some external energy source. (from thermal energy obtained by heating the material to some temperature above 0K). 346

Fig.15.5 The Fermi function, f (E), describes the relative filling of energy levels. At 0 K, all energy levels are completely filled up to the Fermi level, EF , and completely empty above EF .

At these levels (E > EF), the accessibility of unoccupied levels in adjacent atoms yields high mobility of conduction electrons known as free electrons through the solid. Fig. 15.6 promotion of an electron from the valence band to the conduction band requires going above an energy band gap, Eg. Conclusion: 1) f(E) is equal to 1 throughout the valence band; 2) f(E) is equal to 0 throughout the conduction band

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Fig. 15.6. At T > 0 K, the Fermi function, f (E), indicates promotion of some electrons above EF .

Fig.15.7 Variation of the Fermi function, f (E), with the temperature for a typical metal (with EF = 5 eV). Note that the energy range over which f (E) drops from 1 to 0 is equal to a few times kT . 348

Fig.15.8 Comparison of the Fermi function, f(E), with the energy band structure for an insulator. Virtually no electrons are promoted to the conduction band [f (E)= 0 there] because of the magnitude of the band gap (> 2 eV).

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Fig.15.9 Comparison of the Fermi function, f (E), with the energy band structure for a semiconductor. A significant number of electrons is promoted to the conduction band because of a relatively small band gap (1 for the solid. Many glasses and glazes contain “opacifiers”, which are second-phase particles such as SnO2 with an index of refraction (n=2) greater than that of the glass (n =1.5).The degree of opacification caused by the pores or particles depends on their average size and concentration as well as mismatch of indices of refraction. If individual pores or particles are significantly smaller than the wavelength of light (400 to 700 nm), they ineffective scattering centers. The scattering effect is maximized by pore or particle sizes within the range of 400 to 700 nm. Pore-free polymers are relatively easy to produce. In polymers, opacity is frequently due to the presence of inert additives. 16.4 Color The opacity of ceramics, glasses, and polymers was just seen to be based on a scattering mechanism. By contrast, the opacity of metals is the result of an absorption mechanism intimately associated 372

with their electrical conductivity. The conduction electrons absorb photons in the visible light range, giving a characteristic opacity to all metals. The absence of conduction electrons in ceramics and glasses accounts for their transparency. However, there is an absorption mechanism for these materials that leads to an important optical property, color. In ceramics and glasses, coloration is produced by the selective absorption of certain wavelength ranges within the visible spectrum due to electron transition in transition metal ions. Fig. 16.10 shows an absorption curve for a silicate glass containing about 1% cobalt oxide (with the cobalt in the form of Co2+ ions).

Fig. 16.10. Absorption curve for a silicate glass containing about 1% cobalt oxide. The characteristic blue color of this material is due to the absorption of much of the red end of the visible-light spectrum.

While much of the visible spectrum is efficiently transmitted, much of the red, or long-wavelength, end of the spectrum is absorbed. With the red end of the spectrum subtracted out, the net glass color is blue. The colors provided by various metal ions are summarized in Table 16.1.

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Table16.1. Colors Provided by Various Metal Ions in Silicate glasses In glass network Ion Coordination number Cr2+ Cr3+ Cr6+ 4 Cu2+ 4 Cr+ Co2+ 4

Color

In modifier position Coordination Color number Blue 6 Green

Yellow Blue-green Colorless Pink

Ni2+

Bluepurple Purple

6 8 6-8 6-8

Mn2+

Colorless

8

Mn3+ Fe2+ Fe3+

Yellowgreen Weak orange

Purple

6 6-8 6

Deep brown Orange

U6+ V3+ V4+ V5+

6-10 6 6

4

Blue-green Weak yellow Weak yellow Green Blue

Colorless

In polymers, the additives include colorants, inert pigments such as titanium oxide that produce opaque colors. Transparent color is provided by dyes that dissolve in the polymer, eliminating the mechanism of light scattering. The specific mechanism of color production in dyes is similar to that for pigments (and ceramics); that is part of the visible light spectrum is absorbed. 16.5 Luminescence We have just seen that color is a result of the absorption of some of the photons within the visible light spectrum. In luminescence photon absorption is accompanied by the reemission of some 374

photons of visible light. The term luminescence is also used to describe the emission of visible light accompanying the absorption of other forms of energy (thermal, mechanical, and chemical) or particles (e.g., high-energy electrons). Fig. 16.11 shows that atoms of a material emit photons of electromagnetic energy when they return to the ground state after having been in an exited state due to the absorption of energy.

Fig.16.11.Schematic illustration of a mechanism for luminescence. Various trap and activator energy levels within the energy band gap are produced by impurity additions to the insulating material. Following the excitation of an electron from the valence band to the conduction band, the electron moves among the traps without emitting radiation, is thermally promoted back to the conduction band, and eventually decays to the activator level with the emission of a photon of light.

Time is a factor in distinguishing 2 types of luminescence: 1) Fluorescence – if reemission occurs rapidly (in less than about 10 nanoseconds). 2) Phosphorescence – for longer times.

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Fig. 16.12. Reflection of light at the surface of an opaque metal occurs without refraction.

Example: inside of the TV screen is coated with a material that fluoresces as an electron beam is scanned rapidly back and forth.

16.6. Reflectivity and opacity of metals The opacity of metals is the result of the absorption of the entire visible light spectrum by the metal’s conduction electrons. Metal films greater than about 100 nm are totally absorbing. The entire range of visible light wavelength is absorbed because of the continuously available empty electron states, represented by the unfilled valance band of Fig. 15.6. Between 90% and 95% of the light absorbed at the outer surface of the metal is reemitted from the surface in the form of visible light of the same wavelength. The remaining 10% to 5% of the energy is dissipated as heat. The reflectivity of the metal surface is illustrated by Fig. 16.12, where you can find reflection of light at the surface of an opaque metal occurs without refraction. The distinctive color of certain metals is the result of a wavelength dependency for the reflectivity. Copper (red-orange) and gold (yellow) have a lower reemission of the short wavelength (blue) end of the visible spectrum. The bright, silvery appearance of Al and silver is the result of the uniform reemission of wavelengths across the entire spectrum (i.e., white light).

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16.7 Optical systems and devices 16.7.1 Lasers Traditional light source is incoherent, because the electron transitions that produce the light waves occur randomly so that the light waves are out of phase with each other. 1950’s – discovery was light amplification by stimulated emission of radiation, known now simply by the acronym laser, which provides a coherent light source in which the light waves are in phase. Several types of lasers have been developed, but the principle of operation can be demonstrated by a common solid-state design. Single-crystal Al2O3 is sometimes called sapphire when relatively pure and ruby when it contains enough Cr2O3 in solid solution to provide a characteristic red color due to the Cr3+ ions.

Fig. 16.13. Schematic illustration of a ruby laser

The ruby is illuminated by 560 nm wavelength photons from the surrounding xenon flash lap, exciting electrons in Cr3+ ions from their ground states to an excited state (Fig. 16.15).

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Fig. 16.14. Schematic illustration of the mechanism for the excitation and decay of electrons of a Cr3C ion in a ruby laser. Although a ground-state electron can be promoted to various activated states, only the final decay from the metastable to the ground state produces laser photons of wavelength 694.3 nm. A residence time of up to 3 ms in the metastable state allows a large number of Cr3C ions to emit together, producing a large light pulse.

Although some electrons can decay directly back to the ground state, others decay into a metastable, intermediate state, as shown in Fig. 16.15, where they may reside for up to 3 ms before decaying to the ground state. The time span of 3 ms is sufficiently long that several Cr3+ ions can reside in this metastable excited state simultaneously. Then an initial, spontaneous decay to the ground state by a few of these electrons produces photon emissions that trigger an avalanche of emission from the remaining electrons in the metastable state. A schematic of the overall sequence of stimulated emission and light amplification is shown in Fig. 16.15.

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Fig. 16. 15. Schematic illustration of stimulated emission and light amplification in a ruby laser.

Note: 1) One end of the cylindrical ruby crystal is fully silvered and the other end is partially silvered. 2) Photons can be emitted in all directions, but those traveling nearly parallel to the long axis of the ruby crystal are the ones that contribute to the laser effect. 379

3) Overall, the light beam is reflected back and forth along the rod, and its intensity increases as more emissions are stimulated. Table 16.2. Some Important Commercial Lasers Laser Gas He-Ge Liquid

Wavelengths 0.5435-3.39

0.37-1.0 0.32-1.0

CW, to a few Watts Pulsed, to tens of Watts

1.061

Pulsed, to 100 W

0.694

Pulsed, to a few Watts

1.2-1.6

CW, to 100 mW

Dye Dye Glass

Output type and power CW, 1-50 mW

Nd-silicate Solid-state Ruby Semiconductor InGaAsP CW – continuous wave 4) The net result is a high-intensity, coherent, and highly collimated laser beam pulse transmitted through the partially silvered end. 5) The resulting single value (monochromatic) wavelength of 694.3 nm is in the red end of the visible spectrum.

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It’s Important!!! 1) Lasers have been constructed from 100-s of materials giving emissions at several thousand different wavelengths in Lab. around the world. 2) Widely used lasers: a) easy to operate; b) high in power, c) energetically efficient (where a 1% conversion of the input energy into light is considered good). 3) The laser medium can be a gas, liquid, solid (insulator or semiconductor). 4) The power in a continuous beam, commercial laser can range from mW to 25kW and more – megawatt. 5) Focused laser beams can provide local heating for cutting, welding and even for surgical procedures. 16.7.2. Optical fibers Phenomenon in telecommunications area: Transition from traditional metal cable to optical glass fibers. (Fig. 16.16). Fig. 16.16. The small cable on the right contains 144 glass fibers and can carry more than three times as many telephone conversations as the traditional (and much larger) copper wire cable on the left. (Courtesy of the San Francisco Examiner.)

1970 – researchers at Corning Glass Works had developed an optical fiber with loss as low as 20 dB/km at a wavelength of 630 nm (within the visible range). 1980 –silica fibers had developed with losses as low as 0.2 dB/km at a wavelength of 1.6 m (in the infrared range) => Result: telephone conversations and any other form of digital 381

data can be transmitted as laser light pulses rather than the electrical signals used in copper cables. Glass fibers are excellent examples of photonic materials in which signal transmission is by photons rather than by the electrons of electronic materials. Glass fibers advantages: a) Reduced expense; b) reduced size; c) combined with an enormous capacity for data transmission => rapid growth of optical communication systems. b) Light can pass along a glass fiber with great efficiency because of total internal reflection and no losses due to refraction to the surrounding environment. Fig. 16.17 – commercial optical fibers: glass – is a core, embedded in a cladding (плакирование) that is, in turn, covered by a coating.

Fig. 16.17. Schematic illustration of the coaxial design of commercial optical fibers.

Remember: 1) The light pulse signals pass along the core ( nearly parallel to the glass/air surface and at  critical angle = 43,3o. Light can travel along such fibers for several km with only modest transmission losses. 2) The cladding is a lower index of refraction glass, providing the phenomenon of total internal reflection (  critical angle = 43,3o =>  refraction = 90 o), although the critical angle will be larger because the cladding index of refraction is much closer to that of the core than to air. 382

3) The coating protects the core and cladding from environmental damage. 4) The core is mode from a high-purity silica glass ranging in diameter from 5m to 100m. Fig. 16.18 – shows common configurations for commercial optical fibers. Fig. 16.18a – the step-index fiber, which has a large core ( up to 100m and a sharp step-down in index of refraction at the core/cladding interface. Those light rays following various zigzag paths along the core take different times to traverse (пересекать) the entire fiber; this phenomenon leads to a broadening of the light pulse and limits the number of pulses that can be transmitted per second. Application: for small transmission distances such as medical endoscopes. Fig. 16.18b – the graded-index fiber, in which a parabolic variation in the index of refraction within the core (produced by systematic additions of other glass formers such as B2O3 and GeO2 to the silica glass), causes helical rather than zigzag paths. The various paths arrive at a receiver at nearly the same time as the beam going along the fiber axis. Application: for local area networks. Fig. 16.18c – the single-mode fiber, which has a narrow core (from 5m to 8m), in which light travels largely parallel to the fiber axis with little distortion of the digital pulse. Single-mode refers to the essentially singular, axial path and correspondingly undistorted pulse shape. By contrast, the step-index and graded-index designs are termed multimode. Application: in telephone and cable TV networks.

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Fig. 16.18. Schematic illustration of (a) step-index, (b) graded-index, and (c) single-mode optical fiber designs.

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CHAPTER 17 Semiconductor Materials

385

CHAPTER 17 SEMICONDUCTOR MATERIALS 17.1. Intrinsic, elemental Semiconductors Semiconductors can be intrinsic or extrinsic. Intrinsic means that electrical conductivity does not depend on impurities, thus intrinsic means pure. In extrinsic semiconductors the conductivity depends on the concentration of impurities.

Fig. 17.1. Variation in electrical conductivity with temperature for semiconductor silicon.

Conduction is by electrons and holes. In an electric field, electrons and holes move in opposite direction because they have opposite charges. The conductivity of an intrinsic semiconductor is:

= nn qn n + np qp p For a solid such as elemental Si (silicon), conduction results from the thermal promotion of electrons from a filled valence band to an empty conduction band. There, the electrons are negative charge carriers. The removal of electrons from the valence band produces electron holes, which are positive charge carriers. Because the density of conduction electrons (nn) is identical to the density of electron holes (np) , we may rewrite Eq. 1 386

= n q (n + p )

(2)

You know, that conductivity of metallic conductors dropped with increasing temperature. By contrast, the conductivity of semiconductors increases with increasing temperature (Fig.17.1). Fig. 17.2 illustrates how increasing temperature extends the Fermi function, giving more overlap (i.e., more charge carriers).

Fig. 17.2. Schematic illustration of how increasing temperature increases overlap of the Fermi function, f(E), with the conduction and valence bands giving increasing numbers of charge carriers.

The precise nature of  (T) for s-r follows from the nature of charge carriers production in Fig. 17.2 – thermal activation. For this mechanism, the density of carriers increases exponentially with temperature; like this: n  e –Eg/2kT where Eg is the band gap (ширина запрещенной зоны)

387

(3)

Fig. 17.3. Arrhenius plot of the electrical conductivity data for silicon given in Figure 17.1. The slope of the plot is −Eg/2k.

Note, that (3) differs slightly from general Arrhenius form (5.1). There is a factor of 2 in the exponent of Eq.(3) arising from the fact that each thermal promotion of an electron produces 2 charge carriers: electron – hole pair. We see that  is determined by the temperature dependence of e and h as well as n.

 = 0 e –Eg/2kT

(4)

where  0 is a preexponential constant of the type associated with Arrhenius eq. By taking the logarithm of each side of Eq. 4, we obtain ln  = ln  0 – Eg/ 2kT

(5)

which indicates that a semilog plot of ln  versus T-1 gives a straight line with a slope of – Eg/ 2kT. Fig. 17.3 demonstrates this linearity with the data of Fig. 17.1 replotted in an Arrhenius plot. Intrinsic, elemental semiconductor of 4 group of the periodic table are; Si (silicon), Ge (germanium), and tin Sn (they have small values 388

of Eg). Si for electronics industry what steel is to the automotive and construction industries. Gray tin (Sn) transforms to white tin at 13 0C. The transformation from the diamond cubic to a tetragonal structure near ambient temperature prevents gray tin from having any useful device application. One finds that electrons move much faster than holes: e >p 17.2. Extrinsic, elemental Semiconductors Extrinsic semiconduction results from impurity additions known as dopants, and the process of adding these components is called doping.

Fig.17.4 Small section of the periodic table of elements. Silicon, in group IVA, is an intrinsic semiconductor. Adding a small amount of phosphorus from group VA provides extra electrons (not needed for bonding to Si atoms). As a result, phosphorus is an n-type dopant (i.e., an addition producing negative charge carriers). Similarly, aluminum, from group IIIA, is a p-type dopant in that it has a deficiency of valence electrons leading to positive charge carriers (electron holes).

Unlike intrinsic semiconductors, an extrinsic semiconductor may have different concentrations of holes and electrons. It is called ptype if p>n (positive charge carriers dominate) and n-type if n>p. They are made by doping, the addition of a very small concentration of impurity atoms. Two common methods of doping are diffusion and ion implantation. 389

Pay attention to: 1) The intrinsic semiconductor Si has 4 valence (outer-shell) electrons. 2) Excess electron carriers are produced by substitutional impurities that have more valence electron per atom than the semiconductor matrix. 3) For instance (P) phosphorous, with 5 valence electrons, is an electron donor in Si since only 4 electrons are used to bond to the Si lattice when it substitutes for a Si atom. 4) Thus, elements in columns V and VI of the periodic table are donors for semiconductors in the IV column, Si and Ge. 5) The energy level of the donor state is close to the conduction band, so that the electron is promoted (ionized) easily at room temperature, leaving a hole (the ionized donor) behind. Since this hole is unlike a hole in the matrix, it does not move easily by capturing electrons from adjacent atoms. This means that the conduction occurs mainly by the donated electrons (thus n-type). 6) Excess holes are produced by substitutional impurities that have fewer valence electrons per atom than the matrix. This is the case of elements of group II and III in column IV semiconductors, like B in Si. The bond with the neighbors is incomplete and so they can capture or accept electrons from adjacent silicon atoms. They are called acceptors. The energy level of the acceptor is close to the valence band, so that an electron may easily hop from the valence band to complete the bond leaving a hole behind. This means that conduction occurs mainly by the holes (thus p-type). 17.3 The Temperature Variation of Conductivity and Carrier Concentration Temperature causes electrons to be promoted to the conduction band and from donor levels, or holes to acceptor levels. The dependence of conductivity on temperature is like other thermally activated processes:  = 0 exp(–Eg/2kT), where A is a constant (the mobility varies much more slowly with temperature). Extrinsic semiconductors have, in addition to this dependence, one due to the thermal promotion of electrons from donor levels or holes from acceptor levels. The dependence on temperature is also exponential but it eventually saturates at high temperatures where all the donors are emptied or all the acceptors are filled. This means that at low temperatures, extrinsic semiconductors have larger conductivity than 390

intrinsic semiconductors. At high temperatures, both the impurity levels and valence electrons are ionized, but since the impurities are very low in number and they are exhausted, eventually the behavior is dominated by the intrinsic type of conductivity. a) For n-type s-r, we can write:

 = 0 exp -(Eg –Ed)/kT),

where Eg = bottom of conduction band; Ed = donor level ( from Fig. 17.5).

Fig. 17.5. Energy band structure of an n-type semi-conductor. The extra electron from the group VA dopant produces a donor level (Ed ) near the conduction band. This provides relatively easy production of conduction electrons.

391

Fig.17.6 Schematic of the production of a conduction electron in an n-type semiconductor. (a) The extra electron associated with the group VA atom can (b) easily break away, becoming a conduction electron and leaving behind an empty donor state associated with the impurity atom.

Note: 1) There is no factor of 2 in the exponent of Equation 2) In extrinsic s-r, thermal activation produces a single charge carrier as opposed to the 2 carriers produced in intrinsic semiconductor. Fig.17.7 and Fig. 17.8 illustrates plots for both extrinsic and intrinsic behavior. 392

Fig. 17.7. Arrhenius plot of electrical conductivity for an n-type semiconductor. This can be contrasted with the similar plot for intrinsic material in Figure 17.3.

Do you know? 1) that the value of 0 for each region will be different. 2) At low temperatures (large 1/T values), extrinsic behavior dominates. 3) The exhaustion range ( область истощения) is a nearly horizontal plateau in which the number of charge carriers is fixed ( = number of dopant atoms). 4) As temperature continues to rise, the conductivity due to the intrinsic material (pure Si) eventually is greater than that due to the extrinsic charge carriers (Fig. 17.9). 5) In the exhaustion range, conductivity is nearly constant with temperature.

393

Fig. 17.8. Arrhenius plot of electrical conductivity for an n-type semiconductor over a wider temperature range than shown in Figure 17.7. At low temperatures (high 1/T ), the material is extrinsic. At high temperatures (low 1/T ), the material is intrinsic. In between is the exhaustion range, in which all “extra electrons” have been promoted to the conduction band.

b) For p-type s-r, we can write Arrhenius equation:

 = 0 exp (-Ea /kT) where Ea is acceptor level from Fig. 17.8. Fig. 17.8 shows the Arrhenius plot of ln versus 1/T for a p-type material. It is quite similar to Fig. 17.8 for n-type. The plateau in conductivity between the extrinsic and intrinsic regions is termed the saturation range for p-type behavior rather than exhaustion range. Saturation occurs when all acceptors levels (= number of group III A atoms) have become occupied with electrons.

394

Fig. 17.9. Energy band structure of a p-type semiconductor. The deficiency of valence electrons in the group IIIA dopant produces an acceptor level (Ea) near the valence band. Electron holes are produced as a result of thermal promotion over this relatively small energy barrier.

Fig.17.10 Schematic of the production of an electron hole in a p-type semiconductor. (a) The deficiency in valence electrons for the group IIIA atom creates an empty state, or electron hole, orbiting about the acceptor atom. (b) The electron hole becomes a positive charge carrier as it leaves the acceptor atom behind with a filled acceptor state. (The motion of electron holes, of course, is due to the cooperative motion of electrons.)

REMEMBER: (comparison between semiconductors and metals) 1) for metals small impurity additions decreased conductivity; 395

2) for metals increases in temperature decreased conductivity. Conclusion: Both effects were due to reductions in electron mobility resulting from reductions in crystalline order. 3) For semiconductors appropriate impurities and increasing temperature increase conductivity, and so both effects are described by energy band model and Arrhenius behavior. 17.4 Compound Semiconductors A large number of compounds formed from elements near group IV A in a periodic table are semiconductors. Many compounds have the zinc blende structure, which is the diamond cubic structure with cations and anions alternating on adjacent atom sites. III-V compounds (AIIIBV) combine (3+ valence element and 5+ valence element). And the average of 4+ matches the valence of the group IV A elements, leads to a band structure. II-VI compounds (AIIBVI) combine (2+ valence element and 6+ valence element). And the average of 4 valence electrons per atom is a good rule of thumb for semiconductors. But like all such rules, there are exceptions. Some IV-VI compounds (such as GeTe) are examples. Fe3O4 (= FeO Fe2O3) is another. Large electron mobility are associated with Fe2+ - Fe3+ interchanges. 17.5 Amorphous semiconductors You know about the economic advantage of amorphous semiconductors. However, these materials have yet to replace traditional, crystalline semiconductors on a large scale. The scientific understanding of semiconducting in non-crystalline solids is much less developed. Commercial development of amorphous semiconductors appears to be on the threshold of a wide market. Already, these materials account for approximately 1/4 (one-quarter) of the photovoltaic (solar cell) market, largely for portable consumer products. Amorphous selenium Se has played a central role in the xerography process (as a photoconductive coating that permits the formation of the charged image).

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17.6 Processing of semiconductors The most striking feature of semiconductor processing is the ability to produce materials of unparalleled structural and chemical perfection. Pay attention to: 1) Structural perfection of the original semiconductor crystal is the result of the highly developed technology of crystal growing. 2) The chemical perfection is due to a special heat treatment prior to the crystal-growing step. The phase diagram illustrates that the impurity content in the liquid is substantially greater than in the solid. This allows us to define a segregation coefficient, K: K= Cs/Cl

(9)

Where Cs and Cl are the impurity concentrations in solid and liquid. Of course, K is much less than 1, and near the edge of the phase diagram, the solidus and liquidus lines are fairly straight, giving a constant value of K over a range of temperatures. This phenomenon allows a single pass of the heating coil along the bar to “sweep” the impurities along with the liquid zone to 1 end. Multiple sweeps leads to substantial purification. Eventually, substantial levels of contamination will be swept to one end of the bar. That end is simply sawed off and discarded. Impurity levels in the part per billion (ppb) range are practical and, in fact, were necessary to allow the development of solid-state electronics, as we know it today. Note: 1) Structural defects, such as dislocations, are a common byproduct of O solubility in the silicon. A process known as gettering is used to “getter” ( or capture) the O, removing it from the region of the Si where the device circuitry is developed. 2) Ironically, the dislocation-producing oxygen is often removed by introducing dislocations on the “back” side of wafers, where the “front” side is defined as that where the circuitry is produced. 3) Mechanical damage (by abrasion, laser impact, etc.) produces dislocations that serve as gettering sites at which SiO2 precipitates are formed. This approach is known as extrinsic gettering. 4) A more subtle approach is to heat treat the Si wafer so that SiO2 397

precipitates form within the wafer but sufficiently far below the front face to prevent interference with circuit development. This latter approach is known as intrinsic gettering and may involve as many as 3 separate annealing steps between 600 and 1250 oC extending over a period of several hours. Do you know? Many modern electronic devices are based on the buildup of thinfilm layers of 1 semiconductor on another while maintaining some particular crystallographic relationship between the layer and the substrate. 1) Vapor deposition technique is called epitaxy. 2) Homoepitaxy – deposition of a thin film of the same material as the substrate ( for example, Si on Si substrate); 3) Heteroepitaxy – involves 2 materials of different compositions ( AlxGa1-xAs on GaAs). 17.7. Semiconductor Devices A semiconductor diode is made by the intimate junction of a ptype and an n-type semiconductor (an n-p junction). Unlike a metal, the intensity of the electrical current that passes through the material depends on the polarity of the applied voltage. If the positive side of a battery is connected to the p-side, a situation called forward bias (прямое смещение), a large amount of current can flow since holes and electrons are pushed into the junction region, where they recombine (annihilate). If the polarity of the voltage is flipped, the diode operates under reverse bias (обратное смещение). Holes and electrons are removed from the region of the junction, which therefore becomes depleted of carriers and behaves like an insulator. For this reason, the current is very small under reverse bias. The asymmetric current-voltage characteristics of diodes is used to convert alternating current (переменный ток- AC) into direct current (постоянный ток - DC). This is called rectification (выпрямление).

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Fig. 17.11. Current flow as a function of voltage in (a) an ideal rectifier and (b) an actual device

A p-n-p junction transistor contains 2 diodes back-to-back. The central region is very thin and is called the base. A small voltage applied to the base has a large effect on the current passing through the transistor, and this can be used to amplify electrical signals (Fig. 17.12).

Fig.17.12 Comparison of a vacuum-tube rectifier with a solid-state counterpart. Such components allowed substantial miniaturization in the early days of solid-state technology. (Courtesy of R. S.Wortman.)

399

Fig.17.13 Schematic of a field-effect transistor (FET). A negative voltage applied to the gate produces a field under the vitreous silica layer and a resulting p-type conductive channel between the source and the drain. The width of the gate is less than 1 μm in contemporary integrated circuits.

Fig.17.14 A silicon wafer (1.5 mm thick , 150 mm diameter) containing numerous chips. (Courtesy of R. D. Pashley, Intel Corporation)

400

Fig.17.15. Schematic illustration of the lithography process steps for producing metal patterns on a silicon wafer.

Fig.17.16. Schematic illustration of the two-step doping of a silicon wafer with arsenic producing an n-type region beneath the vitreous SiO2 mask

401

(a)

(b)

Fig.17.17 Typical metal wire bond to an integrated circuit

Another common device is the MOSFET transistor where a gate serves the function of the base in a junction transistor. Control of the current through the transistor is by means of the electric field induced by the gate, which is isolated electrically by an oxide layer.

402

CHAPTER 18 Magnetical Behavior

403

CHAPTER 18 MAGNETICAL BEHAVIOR 18.1 Introduction to the magnetism Materials may be classified by their response to externally applied magnetic fields as diamagnetic, paramagnetic, or ferromagnetic.

These magnetic responses differ greatly in strength. Diamagnetism is a property of all materials and opposes applied magnetic fields, but is very weak. Paramagnetism, when present, is stronger than diamagnetism and produces magnetization in the direction of the applied field, and proportional to the applied field. Ferromagnetic effects are very large, producing magnetizations sometimes orders of magnitude greater than the applied field and as such are much larger than either diamagnetic or paramagnetic effects. The magnetization of a material is expressed in terms of density of net magnetic dipole moments µ in the material. We define a vector quantity called the magnetization M by M = μtotal/V Then the total magnetic field B in the material is given by B = B0 + μ0M where μ0 is the magnetic permeability of space and B0 is the externally applied magnetic field. 404

Fig.18.3 Attraction of two adjacent bar magnets.

When magnetic fields inside of materials are calculated using Ampere's law or the Biot-Savart law, then the μ0 in those equations is typically replaced by just μ with the definition μ = Kmμ0 where Km is called the relative permeability. If the material does not respond to the external magnetic field by producing any magnetization, then Km = 1. Another commonly used magnetic quantity is the magnetic susceptibility which specifies how much the relative permeability differs from one. Magnetic susceptibility χm = Km – 1 For paramagnetic and diamagnetic materials the relative permeability is very close to 1 and the magnetic susceptibility very close to zero. For ferromagnetic materials, these quantities may be very large.

405

Another way to deal with the magnetic fields which arise from magnetization of materials is to introduce a quantity called magnetic field strength H . It can be defined by the relationship H = B0/μ0 = B/μ0 - M and has the value of unambiguously designating the driving magnetic influence from external currents in a material, independent of the material's magnetic response. The relationship for B above can be written in the equivalent form B = μ0(H + M), H and M will have the same units, amperes/meter. Ferromagnetic materials will undergo a small mechanical change when magnetic fields are applied, either expanding or contracting slightly. This effect is called magnetostriction.

406

18.2 Hysteresis When a ferromagnetic material is magnetized in one direction, it will not relax back to zero magnetization when the imposed magnetizing field is removed. It must be driven back to zero by a field in the opposite direction. If an alternating magnetic field is applied to the material, its magnetization will trace out a loop called a hysteresis loop. The lack of retraceability of the magnetization curve is the property called hysteresis and it is related to the existence of magnetic domains in the material. Once the magnetic domains are reoriented, it takes some energy to turn them back again.

Fig.18.5. Hysteresis Loop. In contrast to Figure 18.4, the B-H plot for a ferromagnetic material indicates substantial utility for engineering applications. A large rise in B occurs during initial magnetization (shown by the dashed line). The induction reaches a large, “saturation” value (Bs) upon application of sufficient field strength. Much of that induction is retained upon removal of the field (Br = remanent induction). A coercive field (Hc) is required to reduce the induction to zero. By cycling the field strength through the range indicated, the B-H plot continuously follows the path shown as a solid line. This is known as a hysteresis loop.

This property of ferrromagnetic materials is useful as a magnetic "memory". Some compositions of ferromagnetic materials will retain 407

an imposed magnetization indefinitely and are useful as "permanent magnets". The magnetic memory aspects of iron and chromium oxides make them useful in audio tape recording and for the magnetic storage of data on computer disks. It is customary to plot the magnetization M of the sample as a function of the magnetic field strength H, since H is a measure of the externally applied field which drives the magnetization . 18.3 Hysteresis in Magnetic Recording Because of hysteresis, an input signal at the level indicated by the

dashed line could give a magnetization anywhere between C and D, depending upon the immediate previous history of the tape (i.e., the signal which preceded it). This clearly unacceptable situation is remedied by the bias signal which cycles the oxide grains around their hysteresis loops so quickly that the magnetization averages to zero when no signal is applied. The result of the bias signal is like a magnetic eddy which settles down to zero if there is no signal superimposed upon it. If there is a signal, it offsets the bias signal so that it leaves a remnant magnetization proportional to the signal offset. 18.4 Variations in Hysteresis Curves There is considerable variation in the hysteresis of different magnetic materials (Fig.18.7). 408

Fig.18.7. Variations in Hysteresis Curves

18.5 Diamagnetism The orbital motion of electrons creates tiny atomic current loops, which produce magnetic fields. When an external magnetic field is applied to a material, these current loops will tend to align in such a way as to oppose the applied field. This may be viewed as an atomic version of Lenz's law: induced magnetic fields tend to oppose the change which created them. Materials in which this effect is the only magnetic response are called diamagnetic. All materials are inherently diamagnetic, but if the atoms have some net magnetic moment as in paramagnetic materials, or if there is long-range ordering of atomic magnetic moments as in ferromagnetic materials, these stronger effects are always dominant. Diamagnetism is the residual magnetic behavior when materials are neither paramagnetic nor ferromagnetic. Any conductor will show a strong diamagnetic effect in the presence of changing magnetic fields because circulating currents will be generated in the conductor to oppose the magnetic field changes. A superconductor will be a perfect 409

diamagnet since there is no resistance to the forming of the current loops. 18.6 Paramagnetism Some materials exhibit a magnetization which is proportional to the applied magnetic field in which the material is placed. These materials are said to be paramagnetic and follow Curie's law:

All atoms have inherent sources of magnetism because electron spin contributes a magnetic moment and electron orbits act as current loops which produce a magnetic field. In most materials the magnetic moments of the electrons cancel, but in materials which are classified as paramagnetic, the cancelation is incomplete. Table 18.1 Magnetic Susceptibilities of Paramagnetic and Diamagnetic Materials at 20°C Here the quantity Km is called the χm=Km-1 relative permeability, a quantity which Material -5 measures the ratio of the internal (x 10 ) magnetization to the applied magnetic Paramagnetic field. If the material does not respond to the magnetic field by magnetizing, then Iron oxide the field in the material will be just the 720 applied field and the relative (FeO) permeability Km =1. A positive relative permeability greater than 1 implies that Iron the material magnetizes in response to amonium 66 the applied magnetic field. The quantity alum χm is called magnetic susceptibility, and it is just the permeability minus 1. The Uranium 40 magnetic susceptibility is then zero if the material does not respond with any Platinum 26 magnetization. So both quantities give the same information, and both are Tungsten 6.8 dimensionless quantities. 410

Cesium

5.1

Aluminum

2.2

Lithium

1.4

Magnesium

1.2

Sodium

0.72

Oxygen gas

0.19

Diamagnetic Ammonia

-.26

Bismuth

-16.6

Mercury

-2.9

Silver

-2.6

Carbon (diamond) Carbon (graphite) Lead

-2.1

-1.6 -1.8

For ordinary solids and liquids at room temperature, the relative permeability Km is typically in the range 1.00001 to 1.003. We recognize this weak magnetic character of common materials by the saying "they are not magnetic", which recognizes their great contrast to the magnetic response of ferromagnetic materials. More precisely, they are either paramagnetic or diamagnetic, but that represents a very small magnetic response compared to ferromagnets. The gases N2 and H2 are weakly diamagnetic with susceptabilities 0.0005 x 10-5 for N2 and -0.00021 x 10-5 for H2. That is in contrast to the large paramagnetic susceptability of O2 in the table. 18.7 Ferromagnetism Iron, nickel, cobalt and some of the rare earths (gadolinium, dysprosium) exhibit a unique magnetic behavior which is called ferromagnetism because iron (ferrum in Latin) is the most common and most dramatic example. Samarium and neodymium in alloys with cobalt have been used to fabricate very strong rare-earth magnets.

Ferromagnetic materials exhibit a long-range ordering phenomenon at the atomic level which causes the unpaired electron spins to line up parallel with each other in a region called a domain. Within the domain, the magnetic field is intense, but in a bulk sample the material will usually be unmagnetized because the many domains will themselves be randomly oriented with respect to one another. 411

Table 18.2 Magnetic Properties of Ferromagnetic Materials

Initial Maximum Coercive Treatment Relative Relative Force Permeability Permeability (oersteds)

Material Iron, pure

99.8%

Iron, pure

99.95%

Remanent Flux Density (gauss)

Annealed

150

5000

1.0

13,000

Annealed in hydrogen

10,000

200,000

0.05

13,000

Annealed, quenched

8,000

100,000

.05

7,000

100,000

1,000,000

0.002

7,000

Annealed

70

250

10

5,000

Annealed

110

600

0.7

4,000

Steel, 0.9% C

Quenched

50

100

70

10,300

Steel, 30% Co

Quenched

...

...

240

9,500

Alnico 5

Cooled in magnetic field

4

...

575

12,500

Silmanal

Baked

...

...

6,000

550

Pressed

...

...

470

6,000

78 Permalloy

Annealed in Superpermalloy hydrogen, controlled cooling Cobalt, pure

99%

Nickel, pure

99%

Iron, powder

fine

Ferromagnetism manifests itself in the fact that a small externally imposed magnetic field, say from a solenoid, can cause the magnetic domains to line up with each other and the material is said to be magnetized. The driving magnetic field will then be increased by a large factor which is usually expressed as a relative permeability for 412

the material. There are many practical applications of ferromagnetic materials, such as the electromagnet. Ferromagnets will tend to stay magnetized to some extent after being subjected to an external magnetic field. This tendency to "remember their magnetic history" is called hysteresis. The fraction of the saturation magnetization which is retained when the driving field is removed is called the remanence of the material, and is an important factor in permanent magnets. All ferromagnets have a maximum temperature where the ferromagnetic property disappears as a result of thermal agitation. This temperature is called the Curie temperature. Ferromagntic materials will respond mechanically to an impressed magnetic field, changing length slightly in the direction of the applied field. This property, called magnetostriction, leads to the familiar hum of transformers as they respond mechanically to 60 Hz AC voltages. In the Table 18.2 the remanent flux density is the retained magnetic field B, and the SI unit for B is the Tesla (T). 1 Tesla = 10,000 gauss. The "coercive force" is the applied reverse magnetic field strength H required to force the net magnetic field back to zero after magnetization. The SI unit for H is A/m, and 1 A/m = 0.01257 Oersteds. 18.8 Relative Permeability The magnetic constant μ0 = 4π x 10-7 T m/A is called the permeability of space. The permeabilities of most materials are very close to μ0 since most materials will be classified as either paramagnetic or diamagnetic. But in ferromagnetic materials the permeability may be very large and it is convenient to characterize the materials by a relative permeability. Table 18.3 Magnetic properties

413

When ferromagnetic materials are used in applications like an iron-core solenoid, the relative permeability gives you an idea of the kind of multiplication of the applied magnetic field that can be achieved by having the ferromagnetic core present. So for an ordinary iron core you might expect a magnification of about 200 compared to the magnetic field produced by the solenoid current with just an air core. This statement has exceptions and limits, since you do reach a saturation magnetization of the iron core quickly, as illustrated in the discussion of hysteresis. 18.9 Magnetic Field Magnetic fields are produced by electric currents, which can be macroscopic currents in wires, or microscopic currents associated with electrons in atomic orbits. The magnetic field B is defined in terms of force on moving charge in the Lorentz force law. The interaction of magnetic field with charge leads to many practical applications. Magnetic field sources are essentially dipolar in nature, having a north and south magnetic pole. The SI unit for magnetic field is the Tesla, which can be seen from the magnetic part of the Lorentz force law Fmagnetic = qvB to be composed of (Newton x second)/(Coulomb x meter). A smaller magnetic field unit is the Gauss (1 Tesla = 10,000 Gauss).

Fig.18.8 Examples of magnetic fields

414

CHAPTER 19

415

CHAPTER 19 NANOTECHNOLOGY Nanostructured materials are becoming of major significance and the technology of their production and use is rapidly growing into a powerful industry” Prof. George A. Olah Nobel Laureate Chemistry, 1994

Chemistry and physics are two fields of science that evolved in an intermingled way and are still inseparable in any practical sense. However, if we view chemistry as the study of atoms and molecules, a realm of matter whose dimensions are generally less than 1 nm, while a major branch of physics deals with solids of essentially an infinite array of bound atoms or molecules of greater than 100 nm, a significant gap exists between the regimes. Size scale

Combination of solid/phase systems (explanation of Table) • Atomizated vapors  • Molecules  • Associates  • Clusters 

416

• • • •

(CLATHRATES) Assembles  Nanoparticles  Nanocomposites  Solid  (DISORDERING, DEFECTS

Nanotechnology comprises technological developments on the nanometer scale, usually 0.1 to 100 nm. (One nanometer equals one thousandth of a micrometre or one millionth of a millimeter.) The term has sometimes been applied to microscopic technology. This article discusses nanotechnology, nanoscience, and "molecular nanotechnology." The prefix nano- means nanotechnology or nanometer scale. These fascinating materials whose dimension range for 1-100 nanometer (1nm =10-9 m) include: quantum dots, wires, nanotubes, nanorods, nanofilms, nanosize metals, semiconductors, polymers, functional devices, biomaterials, etc…. Table illustrates this gap, which deals with particles of 1 to 100 nm, or approximately from 10 to 106 atoms or molecules per particle. In this nanoscale regime neither quantum chemistry nor classical laws of physics hold. In materials (metals, semiconductors, or insulators) where strong chemical bonding is present, delocalization of valence electrons can be extensive, and the extent of delocalization can vary with size. This effect, coupled with structural changes with size variation, can lead to different chemical and physical properties, depending on size. Indeed, it has now been demonstrated that a host of properties depend on the size of such nano-scale particles, including magnetic, optical, melting points, specific heats, and surface reactivity. Furthermore, when such ultrafine particles are consolidated into macroscale solids, these bulk materials sometimes exhibit new properties (e.g., enhanced plasticity). The interest in these materials has been stimulated by the fact that, owing to the small size of the building blocks (particle, grain, or phase) and high surface-to-volume ratio, these materials are expected 417

to demonstrate unique mechanical, optical, electronic and magnetic properties. Remember: • Atoms have a size of 0.1-0.4 nm • DNA double-helix has a diameter 2 nm • Ribosomes have a diameter 25 nm • Human hair has a diameter 50-100 µm 19.1. Definitions and History Nanotechnology is any technology which exploits phenomena and structures that can only occur at the nanometer scale, that is, the scale of single atoms and small molecules. The United States' National Nanotechnology Initiative website defines it as follows: "Nanotechnology is the understanding and control of matter at dimensions of roughly 1 to 100 nanometers, where unique phenomena enable novel applications." Such phenomena include quantum confinement--which can result in different electromagnetic and optical properties of a material between nanoparticles and the bulk material, the Gibbs-Thomson effect--which is the lowering of the melting point of a material when it is nanometers in size, and such structures including carbon nanotubes. Nanoscience and nanotechnology are an extension of the field of materials science, and materials science departments at universities around the world in conjunction with physics, mechanical engineering, bioengineering, and chemical engineering departments are leading the breakthroughs in nanotechnology. Few technologies branded with the term 'nano' actually fit this definition, and there is a danger that a nano bubble will form since it has become a buzzword used by scientists and entrepreneurs to garner funding, regardless of (and usually despite a lack of) interest in the transformative possibilities of genuine work. On the other hand, some have argued that the publicity and competence in related areas generated by supporting such 'soft nano' projects is valuable, even if indirect, progress towards genuine nanotechnology. The first mention of some of the distinguishing concepts in nanotechnology (but predating use of that name) was in "There's 418

Plenty of Room at the Bottom", a talk given by Richard Feynman at an American Physical Society meeting Caltech on December 29, 1959. Feynman described a process by which the ability to manipulate individual atoms and molecules might be developed, using one set of precise tools to build and operate another proportionally smaller set, so on down to the needed scale. In the course of this, he noted, scaling issues would arise from the changing magnitude of various physical phenomena: gravity would become less important, surface tension and Van der Waals attraction would become more important, etc. This basic idea appears feasible, and exponential assembly enhances it with parallelism to produce a useful quantity of end products. The term "nanotechnology" was defined by Tokyo Science University professor Norio Taniguchi in a 1974 paper (N. Taniguchi, "On the Basic Concept of 'Nano-Technology'," Proc. Intl. Conf. Prod. Eng. Tokyo, Part II, Japan Society of Precision Engineering, 1974.) as follows: "'Nano-technology' mainly consists of the processing of, separation, consolidation, and deformation of materials by one atom or one molecule." In the 1980s the basic idea of this definition was explored in much more depth by Dr. Eric Drexler, who promoted the technological significance of nano-scale phenomena and devices through speeches and the books Engines of Creation: The Coming Era of Nanotechnology and Nanosystems: Molecular Machinery, Manufacturing, and Computation, (ISBN 0471-57518-6), and so the term acquired its current sense. Nanotechnology came to be considered in recent years to address the problems the semiconductor industry is facing and anticipating in increasing performing according to Moore's Law. In the field of microelectronics, the drive towards miniaturization continues and transistor gate lengths of 65 nm are routinely fabricated in prototype circuits. The device density of modern computer electronics (i.e. the number of transistors per unit area) has grown exponentially, and this trend is expected to continue for some time (see Moore's law). However, both economics and fundamental electronic limitations prevent this trend from continuing indefinitely. Thus, since technologies in use on chips in 2005 are already at the 65nm scale 419

and becoming more and more difficult to further miniaturize, it may require breakthroughs in nanotechnology to continue to see the constant increases in speed and decreases in price for computers that many take for granted. The problems facing the semiconductor industry are outlined in the "semiconductor roadmap," and many will ultimately require solutions which involve completely novel nanoscale devices and phenomena to achieve higher device densities semiconductor roadmap. Microchips have consistently gotten smaller, faster, and cheaper at once because creating smaller devices allows them to have a smaller capacitance, which allows greater switching speeds and thus processor clock speeds; in turn, the ability to pack more of these smaller transistors into a given area means greater economies of scale lead to cheaper chips.

More broadly, nanotechnology includes the many techniques used to create structures at a size scale below 100 nm, including those used for fabrication of nanowires, those used in semiconductor fabrication such as deep ultraviolet lithography, electron beam lithography, focused ion beam machining, atomic layer deposition, and molecular vapor deposition, and further including molecular self-assembly techniques such as those employing di-block copolymers. It should be noted, however, that all of these techniques preceeded the nanotech era, and are extensions in the development of scientific advancements rather than techniques which were devised with the sole purpose of creating nanotechnology or which were results of nanotechnology research. The term nanoscience is used to describe the interdisciplinary fields of science devoted to the study of nanoscale phenomena employed in nanotechnology. This is the world of atoms, molecules, macromolecules, quantum dots, and macromolecular assemblies, and 420

is dominated by surface effects such as Van der Waals force attraction, hydrogen bonding, electronic charge, ionic bonding, covalent bonding, hydrophobicity, hydrophilicity, and quantum mechanical tunneling, to the virtual exclusion of macro-scale effects such as turbulence and inertia. For example, the vastly increased ratio of surface area to volume opens new possibilities in surfacebased science, such as catalysis. The term nanotechnology is sometimes conflated with molecular nanotechnology (also known as "MNT"), a theoretical advanced form of nanotechnology believed by some to be achievable at some point in the future, based on productive nanosystems. Molecular nanotechnology would fabricate precise structures using mechanosynthesis to perform molecular manufacturing. Molecular nanotechnology, though not yet existent, is expected to have a great impact on society if realized. 19.2 New materials, devices, technologies As science becomes more sophisticated it naturally enters the realm of what is arbitrarily labeled nanotechnology. The essence of nanotechnology is that as we scale things down they start to take on novel characteristics. Nanoparticles (clusters at nanometre scale), for example, have very interesting properties and have proved useful as catalysts and in other uses since, for example when Charles Goodyear invented vulcanized rubber in 1839 or when the Mesoamericans achieved the same result some 2400 years earlier. If we ever do make nanobots, they will not be scaled down versions of contemporary robots. It is the same scaling effects that make nanodevices so special that prevent this. Nanoscaled devices will probably bear much stronger resemblance to nature's nanodevices: proteins, DNA, membranes etc. Supramolecular assemblies are a good example of this. Nanotechnology = synthesis + processing + application These enhanced properties have been shown to be much more beneficial and valuable to mankind than conventional materials in the micron size range prompting many scientists and industry experts 421

to predict that "nanotechnology initiatives (will) ... lead to the next industrial revolution having the same profound impact on economy and society as Information Technology and Bio-Technology." The cost of nanomaterials produced using the proprietary HGRP technology platform is lower than that by other conventional technologies. This cost saving will help to lower the barrier and pave the road for broad application of nanomaterials into many industrial and consumer products. One fundamental characteristic of nanotechnology is that nanodevices self-assemble. That is, they build themselves from the bottom up. Scanning probe microscopy is an important technique both for characterization and synthesis of nanomaterials. Atomic force microscopes and scanning tunneling microscopes can be used to look at surfaces and to move atoms around.

Supramolecutar and Cluster Compounds. It was shown that metal atoms can be grown to small, isolated metal clusters. If we continue this approach, starting with the smallest and building toward larger particles, and also consider molecular growth, the areas of "supramolecular chemistry"(large molecule) and cluster compounds come into focus. Fascinating structures are being synthesized: For 422

example, C60, clusters of C60, a "molecular Ferric wheel, "selfassembled and self-replicating structures, and cluster compounds have been reported. However, since these topics cannot be covered here, and because an extensive review of free atoms, clusters, and nanoscale particles has appeared that covered mainly particles of 1 to 1000 atoms or 1 to 3 nm, we will generally be concerned here with the regime 3 to 10 nm. Furthermore, mainly inorganic nanoparticles will be of interest as opposed to organic and/or van der Waals clusters. By designing different tips for these microscopes, they can be used for carving out structures on surfaces and to help guide selfassembling structures. Atoms can be moved around on a surface with scanning probe microscopy techniques, but it is cumbersome, expensive and very time-consuming, and for these reasons it is quite simply not feasible to construct nanoscaled devices atom by atom. You don't want to assemble a billion transistors into a microchip by taking an hour to place each transistor, but these techniques can be used for things like helping to guide self-assembling systems. One of the problems facing nanotechnology is how to assemble atoms and molecules into smart materials and working devices. Supramolecular chemistry is here a very important tool. Supramolecular chemistry is the chemistry beyond the molecule, and molecules are being designed to self-assemble into larger structures. In this case, biology is a place to find inspiration: cells and their pieces are made from self-assembling biopolymers such as proteins and protein complexes. One of the things being explored is synthesis of organic molecules by adding them to the ends of complementary DNA strands such as ----A and ----B, with molecules A and B attached to the end; when these are put together, the complementary DNA strands hydrogen bonds into a double helix, ====AB, and the DNA molecule can be removed to isolate the product AB.  Synthesis in nano-reactor There are the ligand-stabilized clusters that constitute small metal clusters that have been trapped by strongly bound ligands to the extent that they are now stable, soluble molecules. Unfortunately, such cluster compounds are usually limited to a metal core of about 40 atoms, much smaller than of interest to us here. 423

Inverted micelle

Synthesis in liquid crystal

Self-assembled layers

Lamgmuir-Blodgett films Natural or man-made particles or artifacts often have qualities and capabilities quite different from their macroscopic counterparts. Gold, for example, which is chemically inert at normal scales, can serve as a potent chemical catalyst at nanoscales.

424

"Nanosize" powder particles (a few nanometres in diameter, also called nano-particles) are potentially important in ceramics, powder metallurgy, the achievement of uniform nanoporosity, and similar applications.

W powder

Co particles

The strong tendency of small particles to form clumps ("agglomerates") is a serious technological problem that impedes such applications. However, a few dispersants such as ammonium citrate (aqueous) and imidazoline or oleyl alcohol (nonaqueous) are promising additives for deagglomeration. (Those materials are discussed in "Organic Additives And Ceramic Processing," by D. J. Shanefield, Kluwer Academic Publ., Boston.)

Fig.18.1 Fe-whisker in mezo-porous matrix. (a) longitudinal section particle diameter 1-2 nm; (b) cross-section length >100 nm

425

Fig.18.2 Aggregation of Pd-nanowires

In October 2004, researchers at the University of Manchester succeeded in forming a small piece of material only 1 atom thick called graphene. Robert Freitas has suggested that graphene might be used as a deposition surface for a diamondoid mechanosynthesis tool. As of August 23 2004, Stanford University has been able to construct a transistor from single-walled carbon nanotubes and organic molecules. These single-walled carbon nanotubes are basically a rolled up sheet of carbon atoms. They have accomplished creating this transistor making it two nanometers wide and able to maintain current three nanometers in length. To create this resistor they cut metallic nanotubes in order to form electrodes, and afterwards placed one or two organic materials to form a semiconducting channel between the electrodes. It is projected that this new achievement will be available in different applications in two to five years. News.com reported on March 1st 2005 that Intel is preparing to introduce processors with features measuring 65 nanometers. The company’s current engineers believe that 5 nanometer processes are actually proving themselves to be more and more feasible. The company showed pictures of these transistor prototypes measuring 65, 45, 32, and 22 nanometers. However, the company spoke about 426

how their expectations for the future are for new processors featuring 15,10, 7, and 5 nanometers.

(a)

(b)

Fig.18.3. Nano-chips. (a) Micro-printing: organic layer as switch key; (b) Nerve cells on the micro-relief surface

Moving from the metals to semiconductors opens another wide array of nanoparticles, including Si, Ge, ZnO, TiO2, CdS, and CdSe.

Fig.18.4 Types of photo elements

These are particularly unusual materials because a unique properly of semiconductors, the band-gap energy, changes with particle size, which of course has immense interest for solar cells, energy storage, photovoltaic cells, and much more. 427

Remember: In 1959 - 1 chip held 1 transistor; Today - 1 chip > 1.000.000 transistors; Circuits are 10.000 times faster. Currently the prototypes use CMOS (complementary metal-oxide semiconductors); however, according to Intel smaller scales will rely on quantum dots, polymer layers, and nanotube technology.

a

b

d

с

e

Fig.19.5 Atomic letter. Dots in letters are from fragments of organic molecules

Fig.19.6 Nanofullerens

428

Question: Can simple, ionic, insulator particles (e.g., NaCI, MgO, CaF2, or TiO2) be unique due to particle size? The answer is definitely "yes." If we consider that nanoparticles of crystalline substances have about 1019interfaces/cm3 and range in surface areas up to 500 or even 800 m2/g, fascinating possibilities come to mind. For example, if we compact but do not grow the nanocrystals, solids with multitudinous grain boundaries are formed. In the cases of CaF2 and TiO2, solid samples arc obtained which undergo plastic deformation at room temperature, presumably by diffusional creep.

429

Fig.19.7 Transmission electron microscope (TEM) image showing multi-walled nanotubes of different diameters. These are large-diameter tubes, from a set obtained for testing as AFM probes. Single-walled tubes are much smaller, from 1 to 5 nm in diameter

PhysOrg.com writes about the use of plasmons in the world. Plasmons are waves of electrons traveling along the surface of metals.

Fig.19.8 Application of magnetic properties for saving information 430

They have the same frequency and electromagnetic field as light; however, the sub-wavelength size allows them to use less space. These plasmons act like light waves in glass on metal, allowing engineers to use any of the same tricks such as multiplexing, or sending multiple waves. With the use of plasmons information can be transferred through chips at an incredible speed; however, these plasmons do have drawbacks. For instance, the distance plasmons travel before dying out depends on the metal, and even currently they can travel several millimeters, while chips are typically about a centimeter across from each other. In addition, the best metal currently available for plasmons to travel farther is aluminum. However, most industries that manufacture chips use copper over aluminum since it is a better electrical conductor. Furthermore, the issue of heat will have to be looked upon. The use of plasmons will definitely generate heat but the amount is currently unknown. Further developments in the field of nanotechnology focuses on the oscillation of a nanomachine for telecommunication. The article states that in Boston an antenna-like sliver of silicon one-tenth the width of a human hair oscillated in a lab in a Boston University basement. This team led by Professor Pritiraj Mohanty developed the sliver of silicon. Since the technology functions at the speeds of gigahertz this could help make communication devices smaller and exchange information at gigahertz speeds. This nanomachine is comprised of 50 billion atoms and is able to oscillate at 1.49 billion times per second. The antenna moves over a distance of one-tenth of a picometer. 19.3. Synthesis of nanostructured materials The properties of nanostructured depend on the following 4 common microstructural features: (1) fine grain size and size distribution (< 100 nm); (2) chemical composition of the constituent phases; (3) presence of interfaces, more specifically, grain boundaries, hetero-phase interfaces, or the 431

free surface; (4) interactions between the constituent domains. The presence and interplay of these 4 features largely determine the unique properties of nanomaterials. There are basically 2 broad areas of synthetic techniques: (1) physical methods and (2) chemical methods Physical methods: (1) Inert-gas evaporation technique (for metals and ceramic oxides); (2) Sputtering (for clusters as well as a variety of thin films); (3) Structural degradation of coarser-grained structures induced by the application of high mechanical energy Chemical methods: (1) Chemical Vapor Deposition or Chemical Vapor Condensation; (2) Colloids – Micelles – Vesicles; (3) High Gravity Reactive Precipitation Laser ablation of solids in liquid environment Idea: sol formation of metal nanoclusters by irradiation of the corresponding metal plate immersed into the liquid.

Fig. 19.9 TEM view of Au nanoparticles: (a) Au clusters in water; (b)after 3h sol irradiation (bar denotes 100 nm)

432

Visible range Cu vapor laser was used in this method and Laser beam was focused (spot diameter about 50 m) on the metal surface through a liquid layer (~ several mm).The irradiation of the metal surface results in fast removal of material confined to the laser spot. Explanation: 1.Formation of metal clusters under laser irradiation of metal target is due to a strong interaction of the evaporated metal with water vapor. 2. Thin layer of metal is heated above its melting temperature during the laser pulse (duration of the laser pulse ~20ns). Adjacent water layer (~ 0.3 m) is heated to the same temperature. 3) T of water layer >> than T boiling point, so its pressure ~ tens atmospheres. 4) High vapor density induces a very high number of molecular collisions per second. The interaction of metal and solvent vapors leads to the fast agglomeration of the metal atoms to clusters. From tiny grains, huge gains All materials composed of grains, which consist of many atoms (one nm ~ 3-5 atoms). Grain size on the order of around 10-9 m (1 nm); Extremely large specific surface area; Manifest fascinating and useful properties; Structural and nonstructural applications; Stronger, more ductile materials; Chemically very active materials 433

W-Ni alloy

Fe-Co alloy

AlN

V2O5

Nano talc Fig.19.10. Examples of nano-powder materials 434

Synthesis of calcium carbonate It may be possible to form materials with a large fraction of atoms at grain boundaries, perhaps in atomic arrangements that areunique. It may also be possible to produce binary materials of normally immiscible compounds or elements. Another aspect to consider is that smaller and smaller particles may take on different crystalline forms or at least different morphologies, and this could affect their surface reactivity and/or adsorption properties.

Fig.19.11 NANO-PRECIPITATED CALCIUM CARBONATE (NPCC) (Average particle size 15 nm & above; Narrow distribution (15-40 nm); BET surface area 40 m2/g; ·No chemical inhibitor (no contamination).Commercialized Product in China (Shanxi Province); in NMT Singapore.

Application as filler: Nanocomposites in PVC/PP/PE; Paint /coating; Ink, pulp & paper; Rubber; Epoxy; Adhesives. In 1 plant calcium carbonate particles of 15-40 nm size are being produced in a 10.000m.t./year. Idea: In the process, an aqueous slurry of calcium hydroxide is combined with carbon dioxide in a reactor that rotates at "several hundred to several thousand rpm." President Patrick Chui said: ”This process is the first example of cost-effective production of nanoparticles on a truly commercial scale. In terms of 435

capital costs and process economics, he says, the process compares favorably with the conventional bubble-column process, which can only achieve particle sizes down to 80 nm when using crystal growth inhibitors”. Synthesis of Mg1-xAlx(OH)2[Fe(edta)x]

10% mol

14% mol

20% mol

25% mol

33% mol

M2+1-x M3+x(OH)2[(anion n-)x/n mH2O]

If we consider that the periodic table of the elements "is a puzzle that has been given to us by God" that holds a huge treasure chest of new 436

solid materials, think of what this means in the realm of nanoparticles. Every known solid substance and every material yet to be discovered will yield a new set: of properties, dependent on size. Optical properties, magnetic properties, melting points, specific heats, and crystal morphologies can all be influenced because nanophase materials serve as a bridge between the molecular and condensed phases. It would seem that the likelihood of new discoveries and new applications is extremely high. Many scientists look forward to the art and the science of nanophase materials. Milling & disintegration "Every gemstone, every metallic alloy, every superconductor, every speck of dust, every semiconducting crystal, every piece of biological tissue, absolutely every material that ever was, is, or will be remains latent within the periodic-table until someone or something puts its atomic building blocks together."This quote is the essence of the frontiers of materials chemistry, and it takes on a fourth dimension when we add the fact that this infinite array of materials can have different properties with change in particle size! We now examine how chemists have approached the synthesis of these exciting new structures.

Fig.19.12 Scheme of planetary mil

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Perhaps the most straightforward approach to producing metallic nanoparticles is by controlled aggregation of atoms.

Fig.19.13 Structure of sub-micrometer particles after milling: disintegration + activation = aggregation

This method is very useful in generating commercial quantities of the material.

Fig.19.14 Photo of mechano-chemical synthesized CaCO3

Disadvantage: Contamination problems from the grinding media. 19.4 Radical nanotechnology Radical nanotechnology is a term given to the hypothetical idea of sophisticated nanoscale machines operating on the molecular scale. 438

By the countless examples found in biology it is currently known that billions of years of evolutionary feedback can produce sophisticated, stochastically optimized biological machines, and it is hoped that radical nanotechnology will make possible their construction by some shorter means, perhaps using biomimetic principles. However, it has been suggested by K Eric Drexler and other researchers that radical nanotechnology, although initially implemented by biomimetic means, might ultimately be based on mechanical engineering principles. Drexler's idea of a diamondoid molecular nanotechnology is controversial, but determining a set of pathways for its development is now an objective of a broadly based technology roadmap project led by Battelle (the manager of several U.S. National Laboratories) and the Foresight Institute. That roadmap should be developed by late 2006. 19.5 Interdisciplinary ensemble A definitive feature of nanotechnology is that it constitutes an interdisciplinary ensemble of several fields of the natural sciences that are, in and of themselves, actually highly specialized. Thus, physics plays an important role - alone in the construction of the microscope used to investigate such phenomena but above all in the laws of quantum mechanics. Nanoparticles display new physical properties for two reasons: (1) finite-size effects in which electronic bands give way to molecular orbital as the size decreases, and (2) surface/interface effects (surface atoms/bulk atoms is about 1 in a 3nm particle, or 50% surface atoms). The latter circumstance, that small particles represent surface matter in macroscopic quantities, is often not fully appreciated in interpretive schemes. A classical droplet model provided a good fit to cluster atomization energies and correctly extrapolated to the bulk cohesive energies. In general, these calculations showed that the atomization energy per atom for spherical clusters increased somewhat irregularly on going from 1 to 500 atoms. If the atoms are more weakly bound in the smaller metal clusters, this should translate into lower melting points for the smaller clusters. In fact, there is experimental evidence for this. 439

Achieving a desired material structure and certain configurations of atoms brings the field of chemistry into play. Molecular sieves

As mentioned earlier, if nanoparticies are small enough, a very significant portion of the total atoms are on the surface; for example, a 3-nni particle has 50% surface atoms. In addition, we might expect intrinsically different surface chemistry due to unusual morphologies, unusual surface defects perhaps in high concentrations, and unusual electronic states affecting surface chemistry. Fig.19.15. Fluorescent marks from CdSe nanoparticles inside the ill cells

In the following discussion we consider what is known about surface chemistry of nanoparticies with differences in surface chemistry 440

versus bulk samples as the primary concern. In medicine, the specifically targe-ted deployment of nanoparticles promi-ses to help in the treatment of certain diseases.

Fig.19.16 Propeller structure of CdSe

Here, science has reached a point at which the boundaries separating discrete disciplines become blurred, and it is for precisely this reason that nanotechnology is also referred to as a convergent technology. 19.6 Potential risk Goo An often cited worst-case scenario is "grey goo", a hypothetical substance into which the surface objects of the earth might be transformed by self-replicating nanobots running amok, a process which has been termed global ecophagy. Defenders point out that smaller objects are more susceptible to damage from radiation and heat (due to greater surface area-to-volume ratios): nanomachines would quickly fail when exposed to harsh climates. This argument 441

depends on the speed of which such nanomachines might be able to reproduce. Recently, new analysis has shown that this "grey goo" danger is less likely than originally thought. K. Eric Drexler considers an accidental "grey goo" scenario extremely unlikely and says so in later editions of Engines of Creation. The "grey goo" scenario begs the Tree Sap Answer: what chances exist that one's car could spontaneously mutate into a wild car, run off-road and live in the forest off tree sap? However, other long-term major risks to society and the environment have been identified. A variant on this is "Green Goo", a scenario in which nanobiotechnology creates a self-replicating nano machine which consumes all organic particles, living or dead, creating a slime -like non-living organic mass. Poison/Toxicity For the near-term, critics of nanotechnology point to the potential toxicity of new classes of nanosubstances that could adversely affect the stability of cell walls or disturb the immune system when inhaled or digested. Objective risk assessment can profit from the bulk of experience with long-known microscopic materials like carbon soot or asbestos fibres. There is a possibility that nanoparticles in drinking water could be dangerous to humans and/or other animals. Colon cells exposed to nano titanium dioxide particles have been found to decay at a quicker than normal rate. Titanium dioxide nanoparticles are often used in sunscreens, as they appear transparent, compared to natural titanium dioxide particles, which appear white. 19.7 Famous USA Nanotechnology company Using nanoscale-based synthetic design strategies, ATFI – Applied Thin Films Incorporation has developed several innovative thin film materials. Processing methods are scalable, environmentally safe and include solution-based, PVD (sputtering), CVD, and plasma spray deposition. Several US patents have been issued and many applications, 442

including PCTs, have been filed. ATFI intends to commercialize these products through strategic partnerships/licensing and generate revenue through sale of raw materials, know-how, and expertise. Over $5M in R&D funds received from our sponsors including MDA, AFOSR, NSF, Army, NASA, and DOE has enabled the development of these technologies. A brief description of each of the four platform technologies is given below. Cerablak™ Technology A low-cost solution-based process (dip/spray/brush/flow) that yields a thin (50 nm - 1 µm), hermetic oxide film (aluminum phosphate compositions), stable above 1400°C, with excellent adhesion on metal, glass, and ceramic substrates. A recently-released Frost & Sullivan advanced materials report listed Cerablak™ as the first among the top ten new advanced materials in the market. With the commercial attributes of a disruptive technology, it promises new surface modification strategies across broad industrial segments and will enable quantum improvements in performance or life extension of critical components at an affordable price. (Patents: US6036762 & US6461415) Nano-engineered Thermal barrier coating Conventional yttria-stabilized zirconia (YSZ)-based TBCs used in gas turbines for thermal protection do not offer adequate durability and are prone to cracking and spallation due to stresses induced by sintering, phase transformation, and thermal cycling. New material design strategies are required to 443

overcome this longstanding problem. ATFI has developed a new TBC material based on layered perovskite compositions (BaNd2Ti3O10) that offers extremely low thermal conductivity (0.7 W/mK above 1300°C) combined with excellent strain tolerance and tailorable CTE to match substrates. Extensive crystalline disorder at the atomic scale and compliant atomic layers offer these unique benefits. Dense and thermally stable coatings have been developed using atmospheric plasma spray process. ECONO Process Oxide epitaxial templates are being sought for numerous microelectronic, optical, and superconductor device applications. Using an innovative method termed “Epitaxial Conversion to Oxide via Nitride Oxidation”, ATFI has developed highquality YSZ epitaxial layers on metal, alloy, and silicon substrates. An epitaxial yttrium zirconium nitride (YZN) is deposited using high rate reactive sputtering and converted to epitaxial YSZ by thermal treatment in oxidizing environment (in-situ and ex-situ). This unique process offers high quality films and significantly reduces the cost by eliminating deposition of additional layers, thus enabling a scalable manufacturing technique. The current focus is on developing a suitable buffer layer for next-generation superconductor wires (HTS coated conductors). A non-exclusive license has been executed with a leading manufacturer of HTS wires. (Patent: US6645639). Alumina films by CVD With increasing demand for miniaturization and evolution of MEMS devices, new surface modification treatments are needed to provide hermetic protection for underlying metals and ceramics. Depositing thermally stable and robust ceramic films is a challenge due to the complex-geometry at the micro- or nano-scale requiring processes 444

with high infiltration efficiencies. ATFI’s proprietary CVD process offers deposition of smooth, hermetic, and uniform alumina (amorphous) films with excellent infiltration efficiencies at relatively high rates. Benefits include high throughput, relatively low capital cost, and little or no exhaust treatment. Hundreds of metering valves for a medical application were coated in one run with excellent uniformity and consistency. It becomes obvious that interdisciplinary research is required for progress to be made. The most important aspects are synthesis, physical properties, and chemical properties, but the most important of these at this time is synthesis. The nano-particles under study are almost always prepared in the laboratory (as opposed to naturally occurring), are sometimes reactive with oxygen and water, and are difficult to produce in a monodisperse (one size only) form. Thus creative synthesis schemes that lead to gram or kilogram quantities of pure materials are absolutely essential before this new field of science can be developed for the benefit of humankind. 19.8. More about possible applications of nanoparticles Destructive Adsorbents The intrinsic surface reactivities coupled with high surface areas allow nanoparticle metal oxides to be considered a new family of adsorbents that strongly chemisorb the incoming species usually by dissociative processes. Thus the term destructive adsorbent is appropriate. Two possible applications come to mind:  Use in air-purification cartridges for buildings, military vehicles, air- planes, and other enclosed areas.  As an alternative to incineration of toxic substances, such as chlorocarbons, PCBs, military agents, and other toxic chemicals. Temperatures are much lower than incineration temperatures, and large volumes of hot, flowing gases are not necessary. Water Purification Nanoparticles of metals such as Fe, Zn, and Sn have demonstrated high reactivities for chlorocarbons in an aqueous environment. These results imply that membranes or flow-through chambers could be constructed that might He used for groundwater decontamination: 445

4Zn + CC14 + 4H2O -> CH4 + 2Zn(OH)2 + 2ZnCI New Catalysts Within the field of heterogeneous catalysis was the first true application of nanoparticles, especially supported metal particles on catalyst supports. In a sense, research on nanoparticle catalysis has been going on for decades and to an industry that is vital to the country's economy to the extent of 20% of the GDP. Thus nanoparticles are already extremely important in commerce. Nonetheless, new catalytic applications are still very probable. This has been shown to be especially true for ultrafine particulates produced by the solvated metal atom dispersion (SMAD) method. It was shown that dehydrogenation, hydroformylation, hydrogen at ion, mcthanation, isomerization, Fischer-Tropsch reactions, and other catalytic processes can be enhanced by the use of new nanoparticlcs and bimetallic nanoparticles. With the availability of effective reducing reagents, for treating transition metal salts in i cither aqueous or nonaqueous media, nanoscale catalytic metal particles arc becoming readily available to all scientists. Information Storage In this area nanoparticles have also already found their way into important commerce. All modern audio and video tapes depend on the magnetic properties of fine particles. However, we are now learning how to produce ever smaller, more highly magnetic materials with better control of coercivity. Further work should allow much enhanced clarity for lower costs, and possibly applications not yet imagined. Refrigeration The promise of refrigerators and air conditioners that do not need refrigeration fluids (Freons, HFCs, etc.) is emboldened in new research on magnetic nanoparticles, It has already been demonstrated on a small scale that an entropic advantage can be gained in magnetic particle field reversal. That is, upon application of a magnetic field, the entropy of a magnetic species changes, and if adiabatic conditions are maintained, the field application will result in a temperature change. This ∆T is called the magnetocaloric effect, and the magnitude depends on the size of the magnetic moment, heat capacity, and temperature dependence of magnetization. With 446

nanoparticles these parameters are quite different from consolidated bulk materials, and they hold promise for the construction of better magnetocaloric refrigeration units than have been possible to date. If further research on the synthesis of better magnetic nanoparticles with engineering advantages is successful, it is hard to overestimate the tremendous improvements this could mean for society and the environment. Solar Cells and Environmental Cleanup

Semiconductor nanoparticles hold the potential for more efficient solar cells for both photovoltaic (electricity production) and water splitting (hydrogen production). In addition, these particles show promise for decontamination of water through photo-oxidation and photoreduction of contaminants. Optical Computers Another dream of scientists in this field concerns the use of quantum confined semiconductor systems for optical transitions, spatial light modulators, and other devices depending on nonlinear optical properties. Improved Ceramics and Insulators It has been shown that nanoparticles of ceramic materials can be compressed at relatively 447

low temperatures into solids that possess better flexibility and malleability. After further development the use of ceramics as a replacement for metals may be possible. It should also be noted that aerogel-prepared materials generally have very low densities, can be translucent or transparent, and have low thermal conductivities and unusual acoustic properties. They have found various applications, including detectors for radiation, super-insulators, solar concentrators, coatings, glass precursors, catalysts, insecticides, and destructive adsorbents. Cosmetics Ultrafine particles should prove useful in the cosmetics industry, where lightness, texture, and coverage are so important. Thin Films The discovery of stable nonaqueous metallic colloidal solutions has given us a new precursor material for the formation of thin metallic films. Conclusion 1. There are several major research and development Government programs on nanostructured materials and nanotechnology in the USA, Europe, Japan and Korea 2. Nanotechnology is expected to grow to a multibillion- dollar industry and will become the most dominant technology of the 21 century. 3. For the realization of great potential of Nanotechnology will require multi-disciplinary interactions and collaborations between material scientists + chemists + engineers in order to control and improve the properties of nanophase materials. Figures at Chapters Figure at Chapter 1: The modern automobile is a case study in the selection of a wide range of traditional and advanced materials. For example the large air scoops that extend from the front of this vehicle to the 448

doors are an integral part of the fenders, which are made of a sophisticated, moldable polymer. (Courtesy of Dow Automotive Division of Dow Chemical Corporation) Figure at Chapter 2: The scanning tunneling microscope (Section 4.7) allows the imaging of individual atoms bonded to a material surface. In this case, the microscope was also used to manipulate the atoms into a simple pattern. Four lead atoms are shown forming a rectangle on the surface of a copper crystal. (From G. Meyer and K. H. Rieder, MRS Bulletin 23 28 [1998].) Figure at Chapter 3: The transmission electron microscope (Section 4.7) can be used to image the regular arrangement of atoms in a crystalline structure. This atomic-resolution view is along individual columns of gallium and nitrogen atoms in gallium nitride. The distance marker is 113 picometers or 0.113 nm. (Courtesy of C. Kisielowski, C. Song, and E. C. Nelson, National Center for Electron Microscopy, Berkeley, California.) Figure at Chapter 4: As with the chapter-opening photograph for Chapter 3, this transmission electron micrograph provides an atomic-resolution image of a crystalline compound, viz. a small crystal of zinc selenide embedded in a glass matrix. By viewing individual crystal lattice planes in ZnSe, we can see a distinctive image of a vertical twin boundary This ZnSe “quantum dot” is the basis of a blue light laser. (Courtesy of V. J. Leppert and S. H. Risbud, University of California, Davis and M. J. Fendorf, National Center for Electron Microscopy, Berkeley, California.) Figure at Chapter 5: In addition to superconductivity and high melting point which lead to various important industrial applications, niobium is a metal which forms oxide coatings readily by the interdiffusion of oxygen and niobium atoms near the metal surface. Jewelry manufacturers use this fact to produce colorful earring designs. (Courtesy ofTeledyneWah Chang, Albany, Oregon.) Figure at Chapter 6: Mechanical testing machines can be automated to simplify the analysis of the mechanical performance of materials in a variety of product applications. (Courtesy of MTS Systems Corporation.) Figure at Chapter 7: Refractories are high-temperature resistant ceramics used in applications such as metal casting. The most effective refractories have low values of thermal expansion and thermal conductivity. (Courtesy of R. T. Vanderbilt Company, Inc.) 449

Figure at Chapter 8: The repetitive loading of engineering materials opens up additional opportunities for structural failure. Shown here is a mechanical testing machine, introduced in Chapter 6, modified to provide rapid cycling of a given level of mechanical stress. The resulting fatigue failure is a major concern for design engineers. ( Courtesy of Instron Corporation) Figure at Chapter 9: The microstructure of a slowly cooled .eutectic. soft solder ( 38 wt % Pb - wt % Sn) consists of a lamellar structure of tin-rich solid solution (white) and lead-rich solid solution (dark), 375X. (From ASM Handbook, Vol. 3: Alloy Phase Diagrams, ASM International, Materials Park, Ohio, 1992.) Figure at Chapter 10: The microstructure of a rapidly cooled .eutectic. soft solder (38 wt % Pb - 62 wt % Sn) consists of globules of lead-rich solid solution (dark) in a matrix of tin-rich solid solution (white), 375X. The contrast to the slowly cooled microstructure at the opening of Chapter 9 illustrates the effect of time on microstructural development. (From ASM Handbook, Vol. 3: Alloy Phase Diagrams, ASM International, Materials Park, Ohio, 1992.) Figure at Chapter 11: These automotive steering and suspension components are made of wrought aluminum to provide reduced weight and improved fuel economy. (Courtesy of TRW.) Figure at Chapter 12: Ceramics have traditionally been used in hightemperature engineering applications. For the interior architecture of furnaces, silicon carbide provides good dimensional stability at temperatures up to 1650o C, along with high resistance to thermal shock and corrosion and a low density. (Courtesy of Bolt Technical Ceramics.) Figure at Chapter 13: A molded engineering polymer serves as a lightweight and cost-effective air-intake manifold for automotive applications. (Courtesy of Solvay Automotive, Inc., Troy, Michigan.) Figure at Chapter 14: The hull of this sailing yacht is a sandwich structure, with the outer skin made of an epoxy resin reinforced with Kevlar fibers. The core is an expanded polyvinyl chloride foam. This composite material system is light weight while providing high impact strength and tear resistance. In addition, the sail is not mere cloth but a fiber-reinforced Mylar -lm. (Courtesy of Allied Signal.) 450

Figure at Chapter 15: Electrical behavior is often a critical factor in materials selection. An example is the electrical flex connector seen in the lower left-hand corner of this computer hard disk drive assembly. The metal plate in the disk drive spins at 7200 rpm, generating a temperature between 260 and 315oC.Apolyphenylee sulfide (PPS) polymer was chosen for the connector due to its unique combination of good electrical insulation and creep resistance. (Courtesy of Seagate Technology.) Figure at Chapter 16: Optical behavior is often a critical factor in materials selection. An example is this auto- mobile headlamp bezel constructed of a metal- coated polybutylene terephthalate (PBT) polymer. The bezel is placed between the reflector and the lens to enhance the aesthetics of the headlamp. The PBT polymer was chosen due to its combination of good optical reflectivity (after metal-coating), processing ability, and low warpage. (Courtesy of DuPont Automotive.) Figure at Chapter 17: Each of these steel billets is being heated uniformly in a cost-effective way by two adjacent coils which utilize an oscillating electrical current to produce an oscillating magnetic flux and the resulting heating due to the hysteresis of a ferromagnetic core material. (Courtesy of CoreFlux Heating Systems.) Figure at Chapter 18: The modern microprocessor is a state-of-the- art application of semiconductor materials encased in a package of conventional structural materials. This 500 MHz processor contains 10 million transistors on a single silicon chip. (Courtesy of Intel.) Figure at Chapter 19: A mite next to a gear set produced using MEMS, the precursor to nanotechnology. Courtesy Sandia National Laboratories, SUMMiTTM Technologies

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References William D., Jr. Callister, Materials Science and Engineering: An Introduction , 2006 William D. Callister, Fundamentals of materials science and engineering: an integrated approach, international, 2008. Serway, R. A. & Beichner, R. J., Physics for Scientists and Engineers, 5th Ed., Saunders College Publishing, 2000. Simpson, Robert E., Introductory Electronics for Scientists and Engineers, 2nd Ed., Allyn and Bacon, 1987 Summit Electrical, searchable database for technical information about electrical products, http://www.summit.com/site map/search.htm . Tipler, Paul A., Physics for Scientists and Engineers, 3rd Ed, Extended, Worth Publishers, 1991 Brown, W. F., Magnetic Materials, Ch 8 in the Handbook of Chemistry and Physics, Condon and Odishaw, eds., McGraw-Hill, 1998. Fishbane, Paul M., Gasiorowicz, Stephen, and Thornton, Stephen, Physics for Scientists and Engineers, 2nd Ed extended, Prentice Hall, 1996 Simpson, Robert E., Introductory Electronics for Scientists and Engineers, 2nd Ed., Allyn and Bacon, 1987

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Glossary Absorption. What happens when wave passes through a medium and gives up some of its energy Ammeter. A device for measuring electrical current. Ampere. The metric unit of current, one coulomb per second; also "amp." Amplitude. The amount of vibration, often measured from the center to one side; may have different units depending on the nature of the vibration. Atom. The basic unit of one of the chemical elements. Atomic mass. The mass of an atom. Atomic number. The number of protons in an atom's nucleus; determines what element it is. Attractive. Describes a force that tends to pull the two participating objects together. Cf. repulsive, oblique. Cathode ray. The mysterious ray that emanated from the cathode in a vacuum tube; shown by Thomson to be a stream of particles smaller than atoms. Charge. A numerical rating of how strongly an object participates in electrical forces. Circuit. An electrical device in which charge can come back to its starting point and be recycled rather than getting stuck in a dead end. Coherent. A light wave whose parts are all in phase with each other. Concave. Describes a surface that is hollowed out like a cave. Convex. Describes a surface that bulges outward. Coulomb (C). The unit of electrical charge. 453

Current. The rate at which charge crosses a certain boundary Damping. the dissipation of a vibration's energy into heat energy, or the frictional force that causes the loss of energy. Diffraction. The behavior of a wave when it encounters an obstacle or a non-uniformity in its medium; in general, diffraction causes a wave to bend around obstacles and make patterns of strong and weak waves radiating out beyond the obstacle. Diffuse reflection. Reflection from a rough surface, in which a single ray of light is divided up into many weaker reflected rays going in many directions. Electric dipole. An object that has an imbalance between positive charge on one side and negative charge on the other; an object that will experience a torque in an electric field. Electric field. The force per unit charge exerted on a test charge at a given point in space. Electrical force. One of the fundamental forces of nature; a noncontact force that can be either repulsive or attractive. Electron. Thomson's name for the particles of which a cathode ray was made; a subatomic particle. Field. A property of a point in space describing the forces that would be exerted on a particle if it was there. Focal length. A property of a lens or mirror, equal to the distance from the lens or mirror to the image it forms of an object that is infinitely far away. Frequency. The number of cycles per second, the inverse of the period (q.v.). Image. A place where an object appears to be, because the rays diffusely reflected from any given point on the object have been bent 454

so that they come back together and then spread out again from the image point, or spread apart as if they had originated from the image. Index of refraction. An optical property of matter; the speed of light in a vacuum divided by the speed of light in the substance in question. Independence. The lack of any relationship between two random events. Induction. The production of an electric field by a changing magnetic field, or vice-versa. Ion. An electrically charged atom or molecule. Isotope. One of the possible varieties of atoms of a given element, having a certain number of neutrons Light. Anything that can travel from one place to another through empty space and can influence matter, but is not affected by gravity. Lorentz transformation. The transformation between frames in relative motion. Magnetic dipole. An object, such as a current loop, an atom, or a bar magnet, that experiences torques due to magnetic forces; the strength of magnetic dipoles is measured by comparison with a standard dipole consisting of a square loop of wire of a given size and carrying a given amount of current. Magnetic field. A field of force, defined in terms of the torque exerted on a test dipole Magnification. The factor by which an image's linear size is increased (or decreased). Cf. angular magnification. Mks system. The use of metric units based on the meter, kilogram, and second. Example: meters per second is the mks unit of speed, not cm/s or km/hr. 455

Molecule. A group of atoms stuck together Neutron. An uncharged particle, the other types that nuclei are made of. Ohm. The metric unit of electrical resistance, one volt per ampere. Ohmic. Describes a substance in which the flow of current between two points is proportional to the voltage difference between them. Open circuit. A circuit that does not function because it has a gap in it. Period. The time required for one cycle of a periodic motion (q.v.). Periodic motion. Motion that repeats itself over and over. Photon. A particle of light. Photoelectric effect. The ejection, by a photon, of an electron from the surface of an object. Proton. A positively charged particle, one of the types that nuclei are made of. Real image. A place where an object appears to be, because the rays diffusely reflected from any given point on the object have been bent so that they come back together and then spread out again from the new point. Cf. virtual image. Reflection. What happens when light hits matter and bounces off, retaining at least some of its energy. Refraction. The change in direction that occurs when a wave encounters the interface between two media. Repulsive. Describes a force that tends to push the two participating objects apart. Cf. attractive, oblique. Resistance. The ratio of the voltage difference to the current in an object made of an ohmic substance. 456

Resonance. The tendency of a vibrating system to respond most strongly to a driving force whose frequency is close to its own natural frequency of vibration. Short circuit. A circuit that does not function because charge is given a low-resistance "shortcut" path that it can follow, instead of the path that makes it do something useful. Specula reflection. Reflection from a smooth surface, in which the light ray leaves at the same angle at which it came in. Spin. The built-in angular momentum possessed by a particle even when at rest. System International. Fancy name for the metric system. Virtual image. Like a real image, but the rays don't actually cross again; they only appear to have come from the point on the image. Cf. real image. Volt. The metric unit of voltage, one joule per coulomb. Voltage. Electrical potential energy per unit charge that will be possessed by a charged particle at a certain point in space. Voltmeter. A device for measuring voltage differences. Wave-particle duality. The idea that light is both a wave and a particle. Wave function. The numerical measure of an electron wave, or in general of the wave corresponding to any quantum mechanical particle. (Electrical behavior) Field - a property of a point in space describing the forces that would be exerted on a particle if it was there Sink - a point at which field vectors converge Source - a point from which field vectors diverge; often used more inclusively to refer to points of either convergence or divergence 457

Electric field - the force per unit charge exerted on a test charge at a given point in space Gravitational field - the force per unit mass exerted on a test mass at a given point in space Electric dipole - an object that has an imbalance between positive charge on one side and negative charge on the other; an object that will experience a torque in an electric field (Optical behavior) Absorption. What happens when light hits matter and gives up some of its energy. Angular magnification. The factor by which an image’s apparent angular size is increased (or decreased). Cf. magnification. Coherent. A light wave whose parts are all in phase with each other. Concave. Describes a surface that is hollowed out like a cave. Convex. Describes a surface that bulges outward. Diffraction. The behavior of a wave when it encounters an obstacle or a nonuniformity in its medium; in general, diffraction causes a wave to bend around obstacles and make patterns of strong and weak waves radiating out beyond the obstacle. Diffuse reflection. Reflection from a rough surface, in which a single ray of light is divided up into many weaker reflected rays going in many directions. Focal length. A property of a lens or mirror, equal to the distance from the lens or mirror to the image it forms of an object that is infinitely far away. Image. A place where an object appears to be, because the rays diffusely reflected from any given point on the object have been bent so that they come back together and then spread out again from the image point, or spread apart as if they had originated from the image. Index of refraction. An optical property of matter; the speed of light in a vacuum divided by the speed of light in the substance in question. Magnification. The factor by which an image’s linear size is increased (or decreased). Cf. angular magnification. Real image. A place where an object appears to be, because the rays diffusely reflected from any given point on the object have been bent so that they come back together and then spread out again from the new point. Cf. virtual image. 458

Reflection. What happens when light hits matter and bounces off, retaining at least some of its energy. Refraction. The change in direction that occurs when a wave encounters the interface between two media. Specular reflection. Reflection from a smooth surface, in which the light ray leaves at the same angle at which it came in. Virtual image. Like a real image, but the rays don’t actually cross again; they only appear to have come from the point on the image. Cf. real image. (Magnetical behavior) Magnetic field - a field of force, defined in terms of the torque exerted on a test dipole Magnetic dipole - an object, such as a current loop, an atom, or a bar magnet, that experiences torques due to magnetic forces; the strength of magnetic dipoles is measured by comparison with a standard dipole consisting of a square loop of wire of a given size and carrying a given amount of current Induction - the production of an electric field by a changing magnetic field, or vice-versa

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PRESENT FOR YOU

TESTS Introduction to Materials Science for Engineers

Quiz #1 1. (50%) Answer the following questions briefly, (a) List kind of dislocations and comment on the orientation of their burger’s vectors with respect to dislocation lines? (b) What is the main cause for the secondary bonding? (c) The operating principles of the powder method for X-ray diffraction, (d) What kind of peaks do you expect to see with aluminum (fcc) powder as the diffraction angle increases from 0 degree? Why? (e) Which plane will have the highest peak among various reflection planes? Why? (f) What are the point defect structures commonly we can see in compound structures? Show graphically. 2. (10%) (a) Sketch, in a cubic unit cell, a [110] and a [111] lattice direction, (b) use a trigonometric calculation to determine the angle between the two directions in (a); and (c) use the vector product for cubic systems to determine the arcos angle. 3. (10%) Calculate the linear density of ions in the [111] direction of MgO (structure NaCl- type). r Mg2+ = 0.078 nm; r O2- = 0.132 nm; 460

4. (10%) Calculate the ionic packing factor (IPF) of MgO, which has the NaCl type structure and r Mg2+ = 0.078 nm; r O2- = 0.132 nm; 5. (10%) Calculate the magnitude of the Burgers vector for (a) Al and (b) Al2O3. r Al = 0.143 nm; r O2- =0.132 nm 6. (10%) Show why α-Fe has a lower solubility of carbon and considerable strain locally? The radii of Fe and C and 0.124 and 0.077 nm, respectively.

Selected Questions from Past Test Multiple Choice

1. Which of the following bond types is characterized by shared electrons in the bond? (a) covalent (b) metallic (c) ionic (d) van der Waals 2. Which of the following is not a point defect? (a) interstitial atom (b) substitutional atom (c) edge dislocation (d) none of these are point defects 3. Which of these does not affect diffusion for a case that is described by Fick’s first law? (a) temperature (b) concentration (c) number of vacancies (d) time 4. A dislocation with a Burger’s vector that is perpendicular to the dislocation line is (a) an edge dislocation (b) a screw dislocation (c) a mixed dislocation (d) can be either a) or b) Problems 1. Rhodium has an FCC crystal structure, an atomic radius of 0.1345 nm and an atomic weight of 102.9 g/mol. Calculate the density of rhodium. (a) 6.20 g/cm3 (b) 9.30 g/cm3 (c) 12.4 g/cm3 (d) 24.82 g/cm3 461

2. How many moles are there in 1 liter of water? Water has a density of 1 g/l. Quiz #2 1. Do you know the Maxwell-Boltzmann distribution of molecular energies in gases? a) rate = C · e –q/kT b) P = ∞ e - ∆E/kT c) rate = Ce –Q/RT 2. What is the clue to the nature of the activation energy? a) It is the energy barrier that must be overcome by thermal activation. b) It is the characteristic of process mechanism. c) It is the atoms diffusion. 3. The concentration of points defects increases: a) when temperature decrease b) with linear increasing the temperature c) exponentially with increasing the temperature 4) What is the diffusion? a) the movement of molecules from an area of lower concentration to an area of higher concentration; b) the movement of molecules from an area of higher concentration to an area of lower concentration. 5) To make solid-state diffusion practical, what are generally required? a) point defects b) perfect crystal structures 6) Do you know, what is correct expression? a) “the overall direction of material flow is opposite to the direction of vacancy flow.” b) “the overall direction of material flow is the same to the direction of vacancy flow”. 7) What Fick’s law show us that the concentration gradient at a specific point along the diffusion path changes with time, t? a) Fick’s first law, b) Fick’s second law 8) Steel surfaces are often hardened by carburization, the diffusion of carbon atoms 462

into the steel from a carbon-rich environment. What is the solution to this differential equation? a) Jx = - D ∂c/∂x; ∂2 Cx b) ∂Cx ---- = D -------∂t ∂x2 Cx – C0 c) --------- =1 – erf ( x/ 2√Dt ) Cs – C0 9) The steady –state diffusion characterized by: a) non-linear concentration profile; b) linear concentration profile; c) exponential concentration profile 10) In the case of fine-grained polycrystalline materials or powders, material transport may be; a) D volume < D grain boundary < D surface b) D volume > D grain boundary > D surface 11) The basic description of the mechanical behavior of material is obtained by the a) tensile test; b) bending test; c) rupture test; d) Griffith crack model 12) What are correct expressions: a) Elastic deformation is temporary deformation; b) Elastic deformation is permanent deformation c) Plastic deformation is temporary deformation. d) Plastic deformation is permanent deformation. 13) How do we call the slope of the stress-strain curve in the elastic region? a) yield strength; b) the modulus of elasticity; c)Young’s modulus; d) tensile strength 14) How many mechanical properties do you obtain from tensile test? 463

a) modulus of elasticity; yield strength; tensile strength b) ductility, modulus of elasticity; yield strength; tensile strength c) modulus of elasticity; yield strength; tensile strength, toughness d) toughness, modulus of elasticity; yield strength; tensile strength, ductility 15) The stiffness of the material represents: a) the yield strength; b) its resistance to elastic strain. c) springiness; d) toughness 16) How you defined the residual stress? a) It is very small stress; b) stress remaining within a structural material after all applied loads are removed; c) ultimate tensile strength, or simply the tensile strength 17) What is the formula for Poisson’s ratio? a) (εT) = K εTn b) τ = P s / A s c) v = - εx / εz d) G =τ/γ 18) What are the correct expressions? a) Metal alloys generally demonstrate a significant amount of plastic deformation in a typical tensile test. b) Ceramics and glasses do not demonstrate a significant amount of plastic deformation in a typical tensile test. c) The ceramics are relatively weak in tension but relatively strong in compression. 19) What are the main mechanical properties for ceramics? a) Modulus of elasticity and modulus of strength; b) Modulus of rupture, modulus of elasticity and modulus of strength; c) Modulus of elasticity and modulus of rupture 20) What are the main mechanical properties for polymers? a) Modulus of elasticity, flexural strength; b) Modulus of rupture, modulus of elasticity and modulus of strength; c) Modulus of elasticity, tensile strength, percent elongation at failure

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21) The temperature, at which atomic mobility is sufficient to affect mechanical properties is approximately: a) one-third times the absolute melting point, Tm b) one-half times the absolute melting point, Tm c) one-third to one-half times the absolute melting point, Tm 22) The resistance of the material to indentation is a qualitative indication of its strength and you can measure it by: a) bending test b) hardness test c) tensile test d) creep test 23) What kind of test do you use to predict the behavior of a structural material at elevated temperatures? a) bending test b) hardness test c) tensile test d)creep test 24). Below Tg (glass transition temperature) material is a) true glass (a rigid solid), b) supercooled liquid; c) viscous liquid 25) The viscous behavior of glasses (organic or inorganic) can be described by the viscosity, , which is defined as the proportionality constant between: a) shearing force per unit area (F/A); b) shearing force per unit area (F/A) and velocity gradient (dv/dx): c)velocity gradient (dv/dx) 26) For organic polymers, the modulus of elasticity is usually plotted instead of a) residual stress; b) temperature; c) viscosity; d)rigid modulus 27) What are the correct expressions? a) For metals and ceramics elastic deformation means a relatively small strain directly proportional to applied stress. 465

b) For polymers, extensive nonlinear deformation can be fully recovered and is, by definition, elastic. c) The fully crystalline polymer is relatively rigid up to its melting point. 28) How many distinct regions of viscoelastic deformation do you know for polymers? a) 2 b) 3 c) 4 d) 5 e) 6 29) The heat capacity, C, defined as the amount of heat required to raise its temperature by: a) 1K ; b) 10 K c) 100 K d) 1 F e) 1C 30) How many heat capacity do you know? a) CV b) CV, CT; c) CV, CP (c ) 31) Strongly bonded solids correlated with: a) high melting points, low elastic modulus; low thermal expansion coefficient; b) high melting points, high elastic modulus; high thermal expansion coefficient c) low thermal expansion coefficient; high melting points, high elastic modulus 32) The thermal conductivity is the analog to: a) thermal expansion; b) diffusivity; c) viscosity; d) elasticity 33) Porosity is especially effective in a) decreasing thermal conductivity; b) increasing thermal conductivity 466

34) What is the impact energy? a) notched test specimen b) analog of the toughness c) area under the stress -versus-strain curve 35) How to identify the ductile-to-brittle transition temperature of bcc metal alloy? a) to study structural steel behavior b) monitor the impact energy over a range of environmental temperatures 36) What is necessary to know for design applications of metal alloys? a) useful and quantitative material parameters b) to study fracture mechanics c) fracture toughness 37) What does help to you to define the critical flaw size at the boundary between more desirable, general yielding and catastrophic, fast fracture? a) preliminary examination b) control of fracture surface c) mechanical testing d) fracture toughness 38.What kind of materials exhibits fatigue? a) ceramics; b) metal alloys c) glass d) polymers 39) Fracture mechanics can provide a) quantitative treatment of the approach to failure? b) Qualitative treatment of the approach to failure? 40) What kind of primary examples of nondestructive testing do you know? a) Magnetic-particle testing b) Liquid-penetrant testing c) X-radiography d) Ultrasonic testing e) Eddy-current testing

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TEST N3

41) Is it true that for compounds in solid solution we can find the components dissolve as a discrete molecular unit? a) Yes, it is; b) No, it is not 42) Do you know the important state variables over which the materials engineer has control in establishing microstructure? 43) Put the correct definitions of terms: a) ? – distinct chemical substance from which the phase is formed. b) ?– are the number of independent variables available to the system. c) ? - is a chemically and structurally homogeneous portion of the microstructure 44) Write down the correct name of reactions: cooling a) L (??????) ----  +  cooling b)  (????????) ----  +  heating c) AB --- L + B (????????) 45) How do you write? a) phase rule? b) Lever rule? 46) How you can analyze the development of microstructure during slow cooling of materials from the liquid state? a) using lever rule; b) using phase diagrams; c) using SEM and TEM photos 47) What you can see from phase diagrams? a) different compounds; b) amounts of phases; c) amounts and compositions of phases that are stable at given temperatures 468

48) What is the two-phase diagram? a) Liquid solution + liquid solution; b) Liquid solution + solid solution; c) Solid solution + solid solution 49) How did the composition of each phase indicate in the two-phase diagram? a) by straight line; b) by tie line ; c) stretch line 50) What kind of system is very important for steel industries? a) Fe-C; b) Fe3C; c) Fe-Fe3C 51) At 200 0C a 50:50 Pb-Sn solder alloy exists as 2 phases = liquid (L) + . The composition of  is ~ 18 wt. % Sn and of L ~ 54 wt% Sn. Using the Lever rule determine their relative amounts ( in weight percent).

Answer for test #2 1(b); 2(a); 3(c); 4(b); 5(a); 6(a); 7(b); 8(c); 9(b); 10(a); 119a); 12(a,d); 13 (b,c); 14 (d); 15(b); 16 (b); 17(c); 18 (a,b,c); 19(a,c); 20 (c); 21(c); 22(b); 23(d); 24(a); 25(b); 26(c); 27 (a,b,c); 28 ( c ); 29 (a,e); 30 (c ); 31 (c ); 32(b); 33 (a); 34 (b,c); 35(b); 36 (c ); 37 (d); 38 (b,d); 39 (a); 40 (c,d).

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CONTENTS Chapter 1

Chapter 2

Chapter 3

Chapter 4

MATERIALS FOR ENGINEERING 1.1 Material world 1.2 Types of Materials 1.3 Semiconductors 1.4 “Compound – structure – properties” 1.5 Processing materials 1.6 Selection of materials ATOMIC BONDING 2.1 Atomic structure 2.2 The ionic bond 2.3 Coordination number 2.4 The covalent bond 2.5 The metallic bond 2.6 The secondary bond ( Van der Waals) 2.7 Materials – the bonding classification CRYSTALLINE STRUCTURE – PERFECTION 3.1 Seven Systems and Fourteen Lattices 3.2 Metal structures 3.3 Ceramic structures 3.4 Polymeric structures 3.5 Semiconductor structures 3.6 Lattice positions, directions, and planes 3.7 X-ray diffraction CRYSTAL DEFECTS AND NONCRYSTALLINE STRUCTURE – IMPERFECTION 4.1 The solid solution – chemical imperfection 4.2 Hume-Rothery rules 4.3 Point defects – zero- dimensional imperfections 4.4 Linear defects, or dislocations – onedimensional imperfection 4.5 Planar defects – two-dimensional imperfections 4.6 Noncrystalline solids – threedimensional imperfections 4.7 Quasicrystals 4.8 Microscopy 470

5 6 7 13 14 16 18 21 22 24 28 29 32 33 35 39 40 42 45 53 55 58 64 73 74 76 80 82 86 93 99 103

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

DIFFUSION 5.1 Thermally activated processes 5.2 Thermal production of point defects 5.3 Point defects and solid-state diffusion 5.4 Steady- state diffusion 5.5 Alternative diffusion paths MECHANICAL BEHAVIOR 6.1 Stress versus strain 6.2Ceramics & Glasses 6.3 Polymers 6.4 Elastic deformation 6.5 Plastic deformation 6.6 Hardness 6.7 Creep and stress relaxation 6.8 Viscoelastic deformation 6.9 Inorganic glasses 6.10 Elastomers THERMAL BEHAVIOR 7.1 Heat capacity 7.2.Thermal expansion 7.3.Thermal conductivity 7.4 Thermal shock FAILURE ANALYSIS AND PREVENTION 8.1 Introduction 8.2 Impact energy 8.3 Fracture toughness 8.4 Fatigue 8.5 Nondestructive testing 8.6.X-radiography 8.7 Ultrasonic testing 8.8 Other nondestructive tests 8.9 Failure analysis and prevention PHASE DIAGRAMS – EQUILIBRIUM MICROSTRUCTURE DEVELOPMENT 9.1 The phase rule 9.2 The Phase Diagram 9.3 General binary diagrams 9.4 The lever rule 9.5 Microstructure development during slow cooling 9.6 Eutectic composition 471

113 114 117 121 129 132 137 138 150 152 157 158 162 163 171 173 179 183 184 185 187 190 195 196 197 200 203 212 212 213 215 216 219 220 224 237 240 243 244

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14

Chapter 15

Chapter 16

KINETICS – HEAT TREATMENT 10.1 Time – the third dimension 10.2 The TTT diagram 10.3 Hardenability 10.4 Precipitation hardening 10.5 Annealing 10.6 The kinetics of phase transformations for Nonmetals METALS 11.1Ferrous alloys 11.2 Non-ferrous alloys 11.3 Processing of metals CERAMICS AND GLASSES 12.1 Ceramics – crystalline materials 12.2 Glasses – non-crystalline materials 12.3 Glass-ceramics 12.4 Processing of ceramics and glasses POLYMERS 13.1 Introduction to the polymers 13.2 Structural features of polymers 13.3 Thermoplastic polymers 13.4 Thermosetting polymers 13.5 Additives 13.6 Processing of polymers COMPOSITES 14.1 Fiber-reinforced composites 14.2Aggregate composites 14.3 Property averaging 14.4 How to control interfacial strength? 14.5 Processing of composites ELECTRICAL BEHAVIOR 15.1Charge carries and conduction 15.2Energy levels and energy bands 15.3Conductor 15.4 Superconductors 15.5 Insulators 15.6 Semiconductors 15.7 Electrical classification of materials OPTICAL BEHAVIOR 16.1 Visible light 472

247 248 253 263 265 268 271 277 278 282 285 295 296 299 301 304 307 308 314 319 319 319 320 325 326 330 332 336 338 341 342 344 350 355 358 359 363 365 366

Chapter 17

Chapter 18

Chapter19

16.2Optical properties 16.3 Transparency, translucency, and opacity 16.4 Color 16.5 Luminescence 16.6 Reflectivity and opacity of metals 16.7 Optical systems and devices SEMICONDUCTOR MATERIALS 17.1. Intrinsic, elemental Semiconductors 17.2. Extrinsic, elemental Semiconductors 17.3 The Temperature Variation of Conductivity and Carrier Concentration 17.4 Compound Semiconductors 17.5 Amorphous semiconductors 17.6 Processing of semiconductors 17.7 Semiconductor Devices MAGNETICAL BEHAVIOR 18.1. Introduction to the magnetism 18.2. Hysteresis 18.3 Hysteresis in Magnetic Recording 18.4 Variations in Hysteresis Curves 18.5 Diamagnetism 18.6 Paramagnetism 18.7. Ferromagnetism 18.8. Relative Permeability 18.9. Magnetic Field NANOTECHNOLOGY 19.1 Definitions and History 19.2 New materials, devices, technologies 19.3 Synthesis of nanostructured materials 19.4 Radical nanotechnology 19.5 Interdisciplinary ensemble 19.6 Potential risk 19.7 Famous USA Nanotechnology company 19.8 More about possible applications of nanoparticles Figures at Book chapters References Glossary Tests Contents 473

367 371 372 374 376 377 385 386 389 390 396 396 397 398 403 404 407 408 408 409 410 411 413 414 415 418 421 431 438 439 441 442 445 449 452 453 460 470

"Introduction to the material science" N. Korobova, Sh. Sarsembinov Material Science - the study of engineering materials - has become a notable addition to engineering education during past decade, it has gained its position in the curriculum in part because of the increased level of sophistication required of engineers in a rapidly changing technological society. The properties and characteristics of materials figure prominently in almost every modern engineering design, providing problems as well as opportunities for new invention, and setting limits for many technological advances. The study of solids and the relationship between structure and physical properties is therefore an important component of modern engineering education. Chapters 1-18 were written by Prof. Korobova N., Chapter 19 was devoted to nanotechnology and written by Academician Sarsembinov Sh. Richly illustrated with 19 tables, 385 figures and based on reviewing of new trends with more than 9 references the book describes conceptual framework for understanding the behavior of engineering materials by emphasizing important relationships between internal structure and properties. It attempts to present a general picture of the nature of materials and the mechanisms that act upon, modify, and control their properties. The subject matter in this book is meant to provide prospective engineers with sufficient background and understanding for them to appreciate existing materials and to exploit new materials development effectively. 474 pages.

Коробова Наталья Егоровна Сарсембинов Шамши Шарипович

INTRODUCTION TO THE MATERIAL SCIENCE  

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