GET212 Lecture Notes on Materials Science and Engineering PDF

Introduction to Materials Science and Engineering “materials science” involves investigating the relationships that exist between the structures and properties of materials. In contrast, “materials engineering” is, on the basis of these structure–property correlations, designing or engineering th...

Introduction to Materials Science and Engineering “materials science” involves investigating the relationships that exist between the structures and properties of materials. In contrast, “materials engineering” is, on the basis of these structure–property correlations, designing or engineering the structure of a material to produce a predetermined set of properties. From a functional perspective, the role of a materials scientist is to develop or synthesize new materials, whereas a materials engineer is called upon to create new products or systems using existing materials, and/or to develop techniques for processing materials. Most graduates in materials programs are trained to be both materials scientists and materials engineers. “Structure” is at this point a nebulous term that deserves some explanation. In brief, the structure of a material usually relates to the arrangement of its internal components. Subatomic structure involves electrons within the individual atoms and interactions with their nuclei. On an atomic level, structure encompasses the organization of atoms or molecules relative to one another. The next larger structural realm, which contains large groups of atoms that are normally agglomerated to gether, is termed “microscopic,” meaning that which is subject to direct observation using some type of microscope. Finally, structural elements that may be viewed with the naked eye are termed “macroscopic.” A property is a material trait in terms of the kind and magnitude of response to a specific imposed stimulus, in service use; all materials are exposed to external stimuli that evoke some type of response. Generally, definitions of properties are made independent of material shape and size. Virtually all- i m p o r t a n t properties of solid materials may be grouped into six different categories: mechanical, electrical, thermal, magnetic, optical, and deteriorative. For each there is a characteristic type of stimulus capable of provoking different responses. Mechanical properties relate deformation to an applied load or force; examples include elastic modulus (stiffness), strength, and toughness. For electrical properties, such as electrical conductivity and dielectric constant, the stimulus is an electric field. The thermal behavior of solids can be represented in terms of heat capacity and thermal conductivity. Magnetic properties demonstrate the response of a material to the application of a magnetic field. For optical properties, the stimulus is electromagnetic or light radiation; index of refraction and reflectivity are representative optical properties. Finally, deteriorative characteristics relate to the chemical reactivity of materials. In addition to structure and properties, two other important components, processing and performance. With regard to the relationships of these four components, the structure of a material will depend on how it is processed. Furthermore, a material’s performance will be a function of its properties. WHY STUDY MATERIALS SCIENCE AND ENGINEERING? All discipline in engineering will be faced with design problems, Dilemma of selecting the right type of material, In-service characteristics being properly characterized, Understanding of deterioration of materials in service, Understanding of properties trade offs, Understanding of material economics. Classification of Materials There are different ways of classifying materials. One way is to describe five groups: 1. metals and alloys; 2. ceramics; 3. polymers (plastics); 4. composite materials; and 5. semiconductors. Materials in each of these groups possess different structures and properties. A brief explanation of these material classifications and representative characteristics is offered next. Metals and Alloys These include steels, aluminum, magnesium, zinc, cast iron, titanium, copper, and nickel. Atoms in metals and their alloys are arranged in a very orderly manner (as discussed in Chapter 3), metallic materials have large numbers of nonlocalized electrons; that is, these electrons are not bound to particular atoms. For these reason, metals are extremely good conductors of electricity (Figure 1.2) and heat, and are not transparent to visible light; a polished metal surface has a lustrous appearance. Metallic materials, in comparison to the ceramics and polymers, are relatively dense (Figure 1.4). With regard to mechanical characteristics, these materials are relatively high strength (Figure 1.5), high stiffness (Figure 1.6), ductility or formability (i.e., capable of large amounts of deformation without fracture) , and shock resistance. They are particularly useful for structural or load–bearing applications. Although pure metals are occasionally used, combinations of metals called alloys provide improvement in a particular desirable property or permit better combinations of properties. Ceramics Ceramics are inorganic materials compounds between metallic and nonmetallic elements; they are most frequently oxides, nitrides, and carbides. Ceramics can be crystalline, non- crystalline, or a mixture of both. For example, common ceramic materials include aluminum oxide (or alumina, Al2O3), silicon dioxide (or silica, SiO2), silicon carbide (SiC), silicon nitride (Si3N4), and, in addition, what some refer to as the traditional ceramics—those composed of clay minerals (i.e., porcelain), as well as cement and glass. With regard to mechanical behavior, ceramic materials are relatively stiff and strong In addition, they are typically very hard. Due to the presence of porosity (small holes), ceramics tend to be brittle (lack of ductility) and are highly susceptible to fracture. New processing techniques make ceramics sufficiently resistant to fracture that they can be used in load-bearing applications, such as impellers in turbine engines. These materials are used for cookware, cutlery, and even automobile engine parts. Ceramics are also used in substrates that house computer chips, sensors and actuators, capacitors, spark plugs, inductors, and electrical insulation. Furthermore, ceramic materials are typically insulative to the passage of heat and electricity, and are more resistant to high temperatures and harsh environments than metals and polymers. Ceramics have exceptional strength under compression. Polymers Polymers include the familiar plastic and rubber materials. Many of them are organic compounds that are chemically based on carbon, hydrogen, and other nonmetallic elements (i.e., O, N, and Si). Furthermore, they have very large molecular structures, often chainlike in nature, that often have a backbone of carbon atoms. These materials typically have low densities (Figure 1.4), whereas their mechanical characteristics are low stiffness and strength (Figures 1.5 and 1.6). Although they have lower strength, polymers have a very good strength-to- weight ratio. Many polymers have very good electrical resistivity. They can also provide good thermal insulation. They are typically not suitable for use at high temperatures. Many polymers have very good resistance to corrosive chemicals. Thermoplastic polymers, in which the long molecular chains are not rigidly connected, have good ductility and formability; thermosetting polymers are stronger but more brittle because the molecular chains are tightly linked. Thermoplastics are made by shaping their molten form. Thermosets are typically cast into molds. Polymers are used in electronic devices and several other applications. Composites Materials The composites are formed from two or more individual materials, which come from the categories previously discussed–metals, ceramics, and polymers. The design goal of a composite is to achieve a combination of properties that is not displayed by any single material, and also to incorporate the best characteristics of each of the component materials. Usual composites have just two phases: matrix (continuous) and dispersed phase (particulates or fibers). In general, the properties of composites depend on: properties of phases; geometry of dispersed phase (particle size, distribution, orientation); and amount of phase. Composite materials can be classified into three main categories: 1. particle-reinforced composites 2. fiber-reinforced composites 3. structural composites (laminates and sandwich panels) One of the most common and familiar composites is fiberglass, sometimes also termed a glass fiber–reinforced polymer composite, abbreviated (GFRP), in which small glass fibers are embedded within a polymeric material (normally an epoxy or polyester). The glass fibers are relatively strong and stiff (but also brittle), whereas the polymer is more flexible. Thus, fiberglass is relatively stiff, strong, and flexible. In addition, it has a low density. Semiconductors Semiconductors have electrical properties that are intermediate between the electrical conductors (i.e., metals and metal alloys) and insulators (i.e., ceramics and polymers), see Figure 1.2. Some of the common and familiar semiconductors known as electronic materials are silicon, germanium, and gallium arsenide. The electrical characteristics of these materials are extremely sensitive to the presence of minute concentrations of impurity atoms, for which the concentrations may be controlled over very small spatial regions to enable their use in electronic devices such as transistors, diodes, etc., that are used to build integrated circuits. Semiconductors have made possible the advent of integrated circuitry that has totally revolutionized the electronics and computer industries over the past three decades. Advanced Materials 1 Materials that are utilized in high-technology (or high-tech) applications are sometimes termed advanced materials. High technology mean a device or product that operates or functions using relatively intricate and sophisticated principles. These advanced materials are typically traditional materials whose properties have been enhanced, and also newly developed, high-performance materials. Furthermore, they may be of all material types (e.g., metals, ceramics, polymers), and are normally expensive. Advanced materials include biomaterials and what we may term materials of the future (that is, smart materials and nanoengineered materials). These advanced materials are using in several applications—for example, materials that are used for lasers, integrated circuits, magnetic information storage, liquid crystal displays (LCDs), and fiber optics. Biomaterials Biomaterials are employed in components implanted into the human body to replace diseased or damaged body parts. These materials must not produce toxic substances and must be compatible with body tissues. All of the preceding materials–metals, ceramics, polymers, composites, and semiconductors–may be used as biomaterials. Smart Materials A smart (or intelligent) materials can sense and respond to an external stimulus such as a change in temperature, the application of a stress, or a change in humidity or chemical environment. Usually a smart-material-based system consists of sensors and actuators that read changes and initiate an action. An example of a passively smart material is lead zirconium titanate (PZT) and shape- memory alloys. When properly processed, PZT can be subjected to a stress and a voltage is generated. This effect is used to make such devices as spark generators for gas grills and sensors that can detect underwater objects such as fish and submarines. Other examples of smart system is used in helicopters to reduce aerodynamic cockpit noise that is created by the rotating rotor blades. Piezoelectric sensors inserted into the blades monitor blade stresses and deformations; feedback signals from these sensors are fed into a computer- controlled adaptive device, which generates noise-canceling antinoise. Nanomaterials One new material class that has fascinating properties and tremendous technological promise is the nanomaterials. Nanomaterials may be any one of the four basic types– metals, ceramics, polymers, and composites. However, unlike these other materials, they are not distinguished on the basis of their chemistry, but rather, size; the nano-prefix denotes that the dimensions of these structural entities are on the order of a nanometer (10–9 m)–as a rule, less than 100 nanometers (equivalent to approximately 500 atom diameters). With the development of scanning probe microscopes, which permit observation of individual atoms and molecules, it has become possible to design and build new structures from their atomic-level constituents. This ability to carefully arrange atoms provides opportunities to develop mechanical, electrical, magnetic, and other properties that are not otherwise possible. Some of the physical and chemical characteristics exhibited by matter may experience dramatic changes as particle size approaches atomic dimensions. For example, materials that are opaque in the macroscopic domain may become transparent on the  nanoscale, chemically stable materials become combustible, and electrical insulators become conductors. Furthermore, properties may depend on size in this nanoscale domain. Some of these effects are quantum mechanical in origin, others are related to surface phenomena. Because of these unique and unusual properties, nanomaterials are using in electronic, biomedical, sporting, energy production, and other industrial applications. Whenever a new material is developed, its potential for harmful and toxicological interactions with humans and animals must be considered. Small nanoparticles have exceedingly large surface area–to–volume ratios, which can lead to high chemical reactivities. Although the safety of nanomaterials is relatively unexplored, there are concerns that they may be absorbed into the body through the skin, lungs, and digestive tract at relatively high rates, and that some, if present in sufficient concentrations, will pose health risks–such as damage to DNA or promotion of lung cancer. References Callister W. D., Rethwisch D. G, Materials Science and Engineering An Introduction, 8th edition, p.4, 2009. Askeland D. R., Fulay P. P, Essentials of Materials Science and Engineering, 2nd edition, p. 8, 2009. ATOMIC STRUCTURE Fundamental Concepts Each atom consists of a very small nucleus composed of protons and neutrons, which is encircled by moving electrons. Both electrons and protons are electrically charged, the charge magnitude being 1.60*10-19 C, which is negative in sign for electrons and positive for protons; neutrons are electrically neutral. Masses for these subatomic particles are infinitesimally small; protons and neutrons have ap proximately the same mass, 1.67*10-27 kg, which is significantly larger than that of an electron, 9.11*10-31 kg. Each chemical element is characterized by the number of protons in the nucleus, or the atomic number (Z). For an electrically neutral or complete atom, the atomic number also equals the number of electrons. This atomic number ranges in integral units from 1 for hydrogen to 92 for uranium, the highest of the naturally occurring elements. The atomic mass (A) of a specific atom may be expressed as the sum of the masses of protons and neutrons within the nucleus. Although the number of protons is the same for all atoms of a given element, the number of neutrons (N) may be variable. Thus atoms of some elements have two or more different atomic masses, which are called isotopes. The atomic weight of an element corresponds to the weighted average of the atomic masses of the atom’s naturally occurring isotopes. The atomic mass unit (amu) may be used for  1 computations of atomic weight. A scale has been established whereby 1 amu is defined as 12 of the atomic mass of the most common isotope of carbon, carbon 12 (12C, A = 12.000000). A = Z + N. Eqn 1 The atomic weight of an element or the molecular weight of a compound may be specified on the basis of amu per atom (molecule) or mass per mole of material. In one mole of a substance there are 6.023*10-23 (Avogadro’s number) atoms or molecules. These two atomic weight schemes are related through the following equation: 1 amu/atom (or molecule) = 1 g/mol For example, the atomic weight of iron is 55.85amu/atom, or 55.85g/mol. Sometimes use of amu per atom or molecule is convenient; on other occasions g (or kg)/mol is preferred. ATOMIC MODELS Duringthelatterpartofthenineteenthcenturyitwasrealizedthatmanyphenomena involving electrons in solids could not be explained in terms of classical mechanics. What followed was the establishment of a set of principles and laws that govern systems of atomic and subatomic entities that came to be known as quantum mechanics. An understanding of the behavior of electrons in atoms and crystalline solids necessarily involves the discussion of quantum-mechanical concepts. How ever, a detailed exploration of these principles is beyond our. One early outgrowth of quantum mechanics was the simplified Bohr atomic model, in which electrons are assumed to revolve around the atomic nucleus in discrete orbitals, and the position of any particular electron is more or less well defined in terms of its orbital. This model of the atom is represented in Figure 2.1. Another important quantum- mechanical principle stipulates that the energies of electrons are quantized; that is, electrons are permitted to have only specific values of energy. An electron may change energy, but in doing so it must make a quantum jump either to an allowed higher energy (with absorption of energy) or to a lower energy (with emission of energy). Often, it is convenient to think of these allowed electron energies as being associated with energy levels or states. These states do not vary continuously with energy; that is, adjacent states are separated by finite energies. These energies are taken to be negative, whereas the zero reference is the unbound or free electron. Of course, the single electron associated with the hydrogen atom will fill only one of these states. Thus,the Bohr model represents an early attempt to describe electrons in atoms, in terms of both position (electron orbitals) and energy (quantized energy levels). This Bohr model was eventually found to have some significant limitations because of its inability to explain several phenomena involving electrons. A resolution was reached with a wave-mechanical model, in which the electron is considered to exhibit both wavelike and particle-like characteristics. With this model, an elec tron is no longer treated as a particle moving in a discrete orbital; but rather, position is considered to be the probability of an electron’s being at various locations around the nucleus. In other words, position is described by a probability distribution or electron cloud. Quantum Numbers Using wave mechanics, every electron in an atom is characterized by four parameters called quantum numbers. The size, shape, and spatial orientation of an electron’s probability density are specified by three of these quantum numbers. Furthermore, Bohr energy levels separate into electron subshells, and quantum numbers dictate the number of states within each subshell. Shells are specified by a principal quantum number n, which may take on integral values beginning with unity; sometimes these shells are designated by the letters K, L, M, N, O, and so on, which correspond, respectively, to n 1,2,3,4,5,... ,as indicated in Table 2.1. It should also be noted that this quantum number, and it only, is also associated with the Bohr model. This quantum number is related to the distance of an electron from the nucleus, or its position. The second quantum number, l, signifies the subshell, which is denoted by a lowercase letter—as s, p, d,or f; it is related to the shape of the electron subshell. In addition, the number of these subshells is restricted by the magnitude of n. Allowable subshells for the several n values are also presented in Table 2.1. The number of energy states for each subshell is determined by the third quantum number, ml. For an s subshell, there is a single energy state, whereas for p, d, and f subshells, three, five, and seven states exist, respectively (Table 2.1). In the absence of an external magnetic field, the states within each subshell are identical. However, when a magnetic field is applied these subshell states split, each state assuming a slightly different energy. Associated with each electron is a spin moment, which must be oriented either up or down. Related to this spin moment is the fourth quantum number, ms, for which two values are possible, + 1⁄2 𝑎𝑛𝑑 − 1⁄2 one for each of the spin orientations. Thus, the Bohr model was further refined by wave mechanics, in which the introduction of three new quantum numbers gives rise to electron subshells within each shell. A comparison of these two models on this basis is illustrated, for the hydrogen atom, ELECTRON CONFIGURATIONS The preceding discussion has dealt primarily with electron states—values of energy that are permitted for electrons. To determine the manner in which these states are filled with electrons, we use the Pauli exclusion principle, another quantum mechanical concept. This principle stipulates that each electron state can hold no more than two electrons, which must have opposite spins. Thus, s, p, d, and f subshells may each accommodate, respectively, a total of 2, 6, 10, and 14 electrons; Table 2.1 summarizes the maximum number of electrons that may occupy each of the first four shells. Of course, not all possible states in an atom are filled with electrons. For most atoms, the electrons fill up the lowest possible energy states in the electron shells and subshells, two electrons (having opposite spins) per state. When all the electrons occupy the lowest possible energies in accord with the foregoing restrictions, an atom is said to be in its ground state. However, electron transitions to higher energy states are possible. The electron configuration or structure of an atom represents the manner in which these states are occupied. In the conventional notation the number of electrons in each subshell is indicated by a superscript after the shell–subshell designation. For example, the electron configurations for hydrogen, helium, and sodium are, respectively, 1s1, 1s2, and 1s2 2s2 2p6 3s1. At this point, comments regarding these electron configurations are necessary. First, the valence electrons are those that occupy the outermost filled shell. These electrons are extremely important; as will be seen, they participate in the bonding between atoms to form atomic and molecular aggregates. Furthermore, many of the physical and chemical properties of solids are based on these valence electrons. In addition, some atoms have what are termed ‘‘stable electron configurations’’; that is, the states within the outermost or valence electron shell are completely filled. Normally this corresponds to the occupation of just the s and p states for the outermost shell by a total of eight electrons, as in neon, argon, and krypton; one exception is helium, which contains only two 1s electrons. These elements (Ne, Ar, Kr, and He) are the inert, or noble, gases, which are virtually unreactive chemically. Some atoms of the elements that have unfilled valence shells assume stable electron configurations by gaining or losing electrons to form charged ions, or by sharing electrons with other atoms. This is the basis for some chemical reactions, and also for atomic bonding in solids. Under special circumstances, the s and p orbitals combine to form hybrid spn orbitals, where n indicates the number of p orbitals involved, which may have a value of 1, 2, or 3. The 3A, 4A, and 5A group elements of the periodic table are those which most often form these hybrids. The driving force for the formation of hybrid orbitals is a lower energy state for the valence electrons. For carbon the sp3 hybrid is of primary importance in organic and polymer chemistries. THEPERIODICTABLE All the elements have been classified according to electron configuration in the periodic table. Here, the elements are situated, with increasing atomic number, in seven horizontal rows called periods. The arrangement is such that all elements that are arrayed in a given column or group have similar valence electron structures, as well as chemical and physical properties. These properties change gradually and systematically, moving horizontally across each period. The elements positioned in Group 0, the right most group, are the inert gases, which have filled electron shells and stable electron configurations. GroupVIIA and VIA elements are one and two electrons deficient, respectively, from having stable structures. The Group VIIA elements (F, Cl, Br, I, and At) are sometimes termed the halogens. The alkali and the alkaline earth metals (Li,Na,K,Be,Mg, Ca, etc.) are labeled as Groups IAandIIA, having, respectively, one and two electrons in excess of stable structures. The elements in the three long periods, Groups IIIB through IIB, are termed the transition metals, which have partially filled d electron states and in some cases one or two electrons in the next higher energy shell. Groups IIIA, IVA, and VA (B, Si, Ge, As, etc.) display characteristics that are intermediate between the metals and nonmetals by virtue of their valence electron structures. As may be noted from the periodic table, most of the elements really come under the metal classification. These are sometimes termed electropositive elements, indicating that they are capable of giving up their few valence electrons to become positively charged ions. Furthermore, the elements situated on the right-hand side of the table are electronegative; that is, they readily accept electrons to form negatively charged ions, or sometimes they share electrons with other atoms. As a general rule, electronegativity increases in moving from left to right and from bottom to top. Atoms are more likely to accept electrons if their outer shells are almost full, and if they are less ‘‘shielded’’ from (i.e.,closer to) the nucleus. PRIMARY INTERATOMIC BONDS IONIC BONDING Perhaps ionic bonding is the easiest to describe and visualize. It is always found in compounds that are composed of both metallic and nonmetallic elements, elements that are situated at the horizontal extremities of the periodic table. Atoms of a metallic element easily give up their valence electrons to the nonmetallic atoms. In the process all the atoms acquire stable or inert gas configurations and, in addition, an electrical charge; that is, they become ions. Sodium chloride (NaCl) is the classical ionic material. A sodium atom can assume the electron structure of neon (and a net single positive charge) by a transfer of its one valence 3s electron to a chlorine atom. After such a transfer, the chlorine ion has a net negative charge and an electron configuration identical to that of argon. In sodium chloride, all the sodium and chlorine exist as ions. The attractive bonding forces are coulombic; that is, positive and negative ions, by virtue of their net electrical charge, attract one another. For two isolated ions, the attractive 𝐴 energy EA is a function of the interatomic distance according to 𝐸𝐴 = − 𝑟 (1) an 𝐵 analogous equation for the repulsive energy is 𝐸𝑅 = 𝑟 𝑛. (2) In these expressions, A, B, and n are constants whose values depend on the particular ionic system. The value of n is approximately 8. Ionic bonding is termed nondirectional, that is, the magnitude of the bond is equal in all directions around an ion. It follows that for ionic materials to be stable, all positive ions must have as nearest neighbors negatively charged ions in a three dimensional scheme, and vice versa. The predominant bonding in ceramic materials is ionic. Bonding energies, which generally range between 600 and 1500 kJ/mol (3 and 8 eV/atom), are relatively large, as reflected in high melting temperatures shown in table 2.3 below. COVALENTBONDING In covalent bonding stable electron configurations are assumed by the sharing of ectrons between adjacent atoms. Two atoms that are covalently bonded will each contribute at least one electron to the bond, and the shared electrons may be considered to belong to both atoms. Covalent bonding is schematically illustrated below, for molecule of methane (CH4). The carbon atom has four valence electrons, whereas each of the four hydrogen atoms has a single valence electron. Each hydrogen atom can acquire a helium electron configuration (two 1s valence electron s) when the carbon atom shares with it one electron. The carbon now has four additional shared electrons, one from each hydrogen, for a total of eight valence electrons. Many nonmetallic elemental molecules (H2, Cl2, F2, etc.) as well as molecules containing dissimilar atoms, such as CH4, H2O, HNO3, and HF, are covalently bonded. Furthermore, this type of bonding is found in elemental solids such as diamond (carbon), silicon, and germanium and other solid compounds composed of elements that are located on the right-hand side of the periodic table, such as gallium arsenide (GaAs), indium antimonide (InSb), and silicon carbide (SiC). The number of covalent bonds that is possible for a particular atom is determined by the number of valence electrons. For N valence electrons, an atom can covalently bond with at most 8 - N other atoms. For example, N = 7 for chlorine, and 8 – N = 1,which means that one Cl atom can bond to only one other atom, as in Cl2. Similarly, for carbon, N = 4, and each carbon atom has 8 - 4, or four, electrons to share. Diamond is simply the three-dimensional interconnecting structure wherein each carbon atom covalently bonds with four other carbon atoms. Covalent bonds may be very strong, as in diamond, which is very hard and has a very high melting temperature, 3550oC (6400F), or they may be very weak, as with bismuth, which melts at about 270oC (518F). Bonding energies and melting temperatures for a few covalently bonded materials are presented in Table 2.3. Polymeric materials typify this bond, the basic molecular structure being a long chain of carbon atoms that are covalently bonded together with two of their available four bonds per atom. The remaining two bonds normally are shared with other atoms, which also covalently bond. METALLIC BONDING Metallic bonding, the final primary bonding type, is found in metals and their alloys. A relatively simple model has been proposed that very nearly approximates the bonding scheme. Metallic materials have one, two, or at most, three valence electrons. With this model, these valence electrons are not bound to any particular atom in the solid and are more or less free to drift throughout the entire metal. They may be thought of as belonging to the metal as a whole, or forming a ‘‘sea of electrons’’ or an ‘‘electron cloud.’’ The remaining non valence electrons and atomic nuclei form what are called ion cores, which possess a net positive charge equal in magnitude to the total valence electron charge per atom. Figure xx below The free electrons shield the positively charged ion cores from mutually repulsive electrostatic forces, which they would otherwise exert upon one another; consequently, the metallic bond is nondirectional in character. In addition, these free electrons act as a ‘‘glue’’ to hold the ion cores together. Bonding energies and melting temperatures for several metals are listed in Table 2.3. Bonding may be weak or strong; energies range from 68 kJ/mol (0.7 eV/atom) for mercury to 850 kJ/mol (8.8 eV/atom) for tungsten. Their respective melting temperatures are 39 and 3410oC (38 and 6170F). Metallic bonding is found for Group IA and IIA elements in the periodic table, and, in fact, for all elemental metals. Some general behaviors of the various material types (i.e., metals, ceramics, polymers) may be explained by bonding type. For example, metals are good conductors of both electricity and heat, as a consequence of their free electrons. By way of contrast, ionically and covalently bonded materials are typically electrical and thermal insulators, due to the absence of large numbers of free electrons. Furthermore, we shall learn that most metals and alloys fail in ductile manner at room temperature; that is, fracture occurs after the materials have experienced significant degrees of permanent deformation. This behavior is explained in terms of deformation mechanism, which is implicitly related to the characteristics of the metallic bond. Conversely, at room temperature ionically bonded materials are intrinsically brittle as a consequence of the electrically charged nature of their component ions. SECONDARY BONDING OR VAN DER WAALS BONDING Secondary, van der Waals, or physical bonds are weak in comparison to the primary or chemical ones; bonding energies are typically on the order of only 10 kJ/mol (0.1 eV/atom). Secondary bonding exists between virtually all atoms or molecules, but its presence may be obscured if any of the three primary bonding types is present. Secondary bonding is evidenced for the inert gases, which have stable electron structures, and, in addition, between molecules in molecular structures that are covalently bonded. Secondary bonding forces arise from atomic or molecular dipoles. In essence, an electric dipole exists whenever there is some separation of positive and negative portions of an atom or molecule. The bonding results from the coulombic attraction between the positive end of one dipole and the negative region of an adjacent one. Dipole interactions occur between induced dipoles, between induced dipoles and polar molecules (which have permanent dipoles), and between polar molecules. Hydrogen bonding, a special type of secondary bonding, is found to exist between some molecules that have hydrogen as one of the constituents. CRYSTAL STRUCTURES FUNDAMENTAL CONCEPTS Solid materials may be classified according to the regularity with which atoms or ions are arranged with respect to one another. A crystalline material is one in which the atoms are situated in a repeating or periodic array over large atomic distances; that is, long-range order exists, such that upon solidification, the atoms will position themselves in a repetitive three-dimensional pattern, in which each atom is bonded to its nearest-neighbor atoms. All metals, many ceramic materials, and certain polymers form crystalline structures under normal solidification conditions. For those that do not crystallize, this long-range atomic order is absent. Some of the properties of crystalline solids depend on the crystal structure of the material, the manner in which atoms, ions, or molecules are spatially arranged. There is an extremely large number of different crystal structures all having long range atomic order; these vary from relatively simple structures for metals, to exceedingly complex ones, as displayed by some of the ceramic and polymeric materials. The present discussion deals with several common metallic and ceramic crystal structures. When describing crystalline structures, atoms (or ions) are thought of as being solid spheres having well-defined diameters. This is termed the atomic hard sphere model in which spheres representing nearest-neighbor atoms touch one another. An example of the hard sphere model for the atomic arrangement found in some of the common elemental metals is displayed in Figure xxx. Sometimes the term lattice is used in the context of crystal structures; in this sense ‘‘lattice’’ means a three-dimensional array of points coinciding with atom positions (or sphere centers). UNIT CELLS The atomic order in crystalline solids indicates that small groups of atoms form a repetitive pattern. Thus, in describing crystal structures, it is often convenient to subdivide the structure into small repeat entities called unit cells. Unit cells for most crystal structures are parallelepipeds or prisms having three sets of parallel faces; one is drawn within the aggregate of spheres (Figure xxx), which in this case happens to be a cube. A unit cell is chosen to represent the symmetry of the crystal structure, wherein all the atom positions in the crystal may be generated by translations of the unit cell integral distances along each of its edges. Thus, the unit cell is the basic structural unit or building block of the crystal structure and defines the crystal structure by virtue of its geometry and the atom positions within. Convenience usually dictates that parallelepiped corners coincide with centers of the hard sphere atoms. Furthermore, more than a single unit cell may be chosen for a particular crystal structure; however, we generally use the unit cell having the highest level of geometrical symmetry. METALLIC CRYSTAL STRUCTURES The atomic bonding in this group of materials is metallic, and thus nondirectional in nature. Consequently, there are no restrictions as to the number and position of nearest- neighbor atoms; this leads to relatively large numbers of nearest neighbors and dense atomic packings for most metallic crystal structures. Also, for metals, using the hard sphere model for the crystal structure, each sphere represents an ion core. Table1 presents the atomic radii for a number of metals. Three relatively simple crystal structures are found for most of the common metals: face-centered cubic, body-centered cubic, and hexagonal close-packed. THE FACE-CENTERED CUBIC CRYSTAL STRUCTURE The crystal structure found for many metals has a unit cell of cubic geometry, with atoms located at each of the corners and the centers of all the cube faces. It is aptly called the face-centered cubic (FCC) crystal structure. Some of the familiar metals having this crystal structure are copper, aluminum, silver, and gold. Figurexxxa shows a hard sphere model for the FCC unit cell, whereas in Figure xxxb the atom centers are represented by small circles to provide a better perspective of atom positions. The aggregate of atoms in Figurexxxc represents a section of crystal consisting of many FCC unit cells. These spheres or ion cores touch one another across a face diagonal; the cube edge length a and the atomic radius R are related through 𝒂 = 𝟐𝑹√𝟐 This result is obtained as an example problem. For the FCC crystal structure, each corner atom is shared among eight unit cells, whereas a face-centered atom belongs to only two. Therefore, one eighth of each of the eight corner atoms and one half of each of the six face atoms, or a total of four whole atoms, may be assigned to a given unit cell. This is depicted in Figure xxxa, where only sphere portions are represented within the confines of the cube. The cell comprises the volume of the cube, which is generated from the centers of the corner atoms as shown in the figure. Corner and face positions are really equivalent; that is, translation of the cube corner from an original corner atom to the center of a face atom will not alter the cell structure. Two other important characteristics of a crystal structure are the coordination number and the atomic packing factor (APF). For metals, each atom has the same number of nearest-neighbor or touching atoms, which is the coordination number. For face-centered cubics, the coordination number is 12. This may be confirmed by examination of Figure xxxa; the front face atom has four corner nearest-neighbor atoms surrounding it, four face atoms that are in contact from behind, and four other equivalent face atoms residing in the next unit cell to the front, which is not shown. The APF is the fraction of solid sphere volume in a unit cell, assuming the atomic hard sphere model, or 𝒗𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝒂𝒕𝒐𝒎𝒔 𝒊𝒏 𝒂 𝒖𝒏𝒊𝒕 𝒄𝒆𝒍𝒍 𝑨𝑷𝑭 = 𝒕𝒐𝒕𝒂𝒍 𝒖𝒏𝒊𝒕 𝒄𝒆𝒍𝒍 𝒗𝒐𝒍𝒖𝒎𝒆 For the FCC structure, the atomic packing factor is 0.74, which is the maximum packing possible for spheres all having the same diameter. Computation of this APF is also included as an example problem. Metals typically have relatively large atomic packing factors to maximize the shielding provided by the free electron cloud. THE BODY-CENTERED CUBIC CRYSTAL STRUCTURE Another common metallic crystal structure also has a cubic unit cell with atoms located at all eight corners and a single atom at the cube center. This is called a body-centered cubic (BCC) crystal structure. A collection of spheres depicting this crystal structure is shown in Figure xxc, whereas Figures xxa and xxb are diagrams of BCC unit cells with the atoms represented by hard sphere and reduced-sphere models, respectively. Center and corner atoms touch one another along cube diagonals, and unit cell length a and atomic radius R are related through 𝟒𝑹 𝒂= √𝟑 Chromium, iron, tungsten, as well as several other metals listed in Table 1 exhibit a BCC structure. Two atoms are associated with each BCC unit cell: the equivalent of one atom from the eight corners, each of which is shared among eight unit cells, and the single center atom, which is wholly contained within its cell. In addition, corner and center atom positions are equivalent. The coordination number for the BCC crystal structure is 8; each center atom has as nearest neighbors its eight corner atoms. Since the coordination number is less for BCC than FCC, so also is the atomic packing factor for BCC lower— 0.68 versus 0.74 THE HEXAGONAL CLOSE-PACKED CRYSTAL STRUCTURE Not all metals have unit cells with cubic symmetry; the final common metallic crystal structure to be discussed has a unit cell that is hexagonal. Figure xx3a shows a reduced-sphere unit cell for this structure, which is termed hexagonal close-packed (HCP); an assemblage of several HCP unit cells is presented in Figure xx3b. The top and bottom faces of the unit cell consist of six atoms that form regular hexagons and surround a single atom in the center. Another plane that provides three additional atoms to the unit cell is situated between the top and bottom planes. The atoms in this midplane have as nearest neighbors atoms in both of the adjacent two planes. The equivalent of six atoms is contained in each unit cell; one-sixth of each of the 12 top and bottom face corner atoms, one-half of each of the 2 center face atoms, and all the 3 midplane interior atoms. If a and c represent, respectively, the short and long unit cell dimensions of Figure xx3a, the c/a ratio should be 1.633; however, for some HCP metals this ratio deviates from the ideal value. The coordination number and the atomic packing factor for the HCP crystal structure are the same as for FCC:12 and 0.74, respectively. The HCP metals include cadmium, magnesium, titanium, and zinc; some of these are listed in Table1. Table 1Atomic Radii and Crystal Structure of Some Metals FCC NUMBER OF ATOMS 8 × = 1 corner atom 6 × = 3 face atoms 4 total atoms. The coordination number is 12. APF = 0.74 What is coordination number? BCC NUMBER OF ATOMS 1 8 × = 1 𝑐𝑜𝑟𝑛𝑒𝑟 𝑎𝑡𝑜𝑚𝑠 8 1 = center atom 2 total atoms in BCC. The coordination number is 8. The Hexagonal Close-Packed Structure A special form of the hexagonal structure, the hexagonal close-packed structure (HCP), is shown in Figure 3.8. The unit cell is the skewed prism, shown separately. Figure 3.8a shows a reduced sphere unit cell for this structure, an assemblage of several HCP unit cells is presented in Figure 3.8b Alternatively, the unit cell for HCP may be specified in terms of the parallelepiped defined by the atoms labeled A through H in Figure 3.8a. Thus, the atom denoted J lies within the unit cell interior. The top and bottom faces of the unit cell consist of six atoms that form regular hexagons and surround a single atom in the center. Another plane that provides three additional atoms to the unit cell is situated between the top and bottom planes. The atoms in this mid plane have as nearest 3×1 = 3 center atoms 2×( ) = 1 face atom 12×( ) = 2 corner atoms  6 total atoms In metals with an ideal HCP structure, the a and c axes are related by the ratio c/a=1.633. Most HCP metals, however, have c/a ratios that differ slightly from the ideal value because of mixed bonding. The coordination number and the atomic packing factor for the HCP crystal structure are the same as for FCC: 12 and 0.74, respectively. The HCP metals include cadmium, magnesium, titanium, and zinc. Metals with HCP are not as ductile as FCC metals. EXAMPLES DENSITY COMPUTATIONS—METALS A knowledge of the crystal structure of a metallic solid permits computation of its theoretical density through the relationship 𝑛𝐴 𝜌= 𝑉𝑐 𝑁𝐴 𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑡𝑜𝑚𝑠 𝑎𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑒𝑑 𝑤𝑖𝑡ℎ 𝑒𝑎𝑐ℎ 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙 𝐴 = 𝑎𝑡𝑜𝑚𝑖𝑐 𝑤𝑒𝑖𝑔ℎ𝑡 𝑉𝑐 = 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙 𝑎𝑡𝑜𝑚𝑠 𝑁𝐴 = 𝐴𝑣𝑜𝑔𝑎𝑑𝑟𝑜′ 𝑠 𝑛𝑢𝑚𝑏𝑒𝑟 (6.023 × 1023 ) 𝑚𝑜𝑙 Example CERAMICS CRYSTAL STRUCTURE Ceramics crystal structures are generally more complex because they are composed of more than one elements and the nature of bonding may be ionic or covalent; electronegativity being a major factor in ionic bonding. For those ceramic materials for which the atomic bonding is predominantly ionic, the crystal structures may be thought of as being composed of electrically charged ions instead of atoms. The metallic ions, or cations, are positively charged, because they have given up their valence electrons to the nonmetallic ions, or anions, which are negatively charged. Two characteristics of the component ions in crystalline ceramic materials influence the crystal structure: the magnitude of the electrical charge on each of the component ions, and the relative sizes of the cations and anions. With regard to the first characteristic, the crystal must be electrically neutral; that is, all the cation positive charges must be balanced by an equal number of anion negative charges. The chemical formula of a compound indicates the ratio of cations to anions, or the composition that achieves this charge balance. For example, in calcium fluoride, each calcium ion has a 2 charge (Ca2+), and associated with each fluorine ion is a single negative charge (F-). Thus, there must be twice as many F as Ca2+ ions, which is reflected in the chemical formula CaF2. The second criterion involves the sizes or ionic radii of the cations and anions, rC and rA, respectively. Because the metallic elements give up electrons when ionized, cations are ordinarily smaller than anions, and, consequently, the ratio rC/rA is less than unity. Each cation prefers to have as many nearest-neighbor anions as possible. The anions also desire a maximum number of cation nearest neighbors. Stable ceramic crystal structures form when those anions surrounding a cation are all in contact with that cation, as illustrated in Figure 4. The coordination number (i.e., number of anion nearest neighbors for a cation) is related to the cation–anion radius ratio. For a specific coordination number, there is a critical or minimum rC/rA ratio for which this cation–anion contact is established (Figure 4), which ratio may be determined from pure geometrical considerations The coordination numbers and nearest-neighbor geometries for various rC/rA ratios are presented in Table 3 For rC/rA ratios less than 0.155, the very small cation is bonded to two anions in a linear manner. If rC/rA has a value between 0.155 and 0.225, the coordination number for the cation is 3. This means each cation is surrounded by three anions in the form of a planar equilateral triangle, with the cation located in the center. The coordination number is 4 for rC/rA between 0.225 and 0.414; the cation is located at the center of a tetrahedron, with anions at each of the four corners. For rC/rA between 0.414 and 0.732, the cation may be thought of as being situated at the center of an octahedron surrounded by six anions, one at each corner, as also shown in the table. The coordination number is 8 for rC/rA between 0.732 and 1.0, with anions at all corners of a cube and a cation positioned at the center. For a radius ratio greater than unity, the coordination number is 12. The most common coordination numbers for ceramic materials are 4, 6, and 8. Example  ̅̅̅̅ = 𝑟𝐴 + 𝑟𝐶 and 𝐴𝑂 ̅̅̅̅ ̅̅̅̅ 𝐴𝑃 Furthermore, the side length ratio 𝐴𝑃⁄̅̅̅̅ is a function of the angle 𝛼 as 𝐴𝑂 = 𝑐𝑜𝑠𝛼. The 𝐴𝑂 ̅̅̅̅ ̅̅̅̅ 𝐴𝑃 𝑟 magnitude of 𝛼 is 30o, since line ̅̅̅̅ 𝐴𝑂 bisects the 60o angle 𝐵𝐴𝐶. Thus, 𝐴𝑂 ̅̅̅̅ = 𝑟 +𝐴𝑟 = 𝐴 𝐶 𝑜 √3 𝑐𝑜𝑠30 = or, solving for the cation-anion radius ratio, 2 𝑟𝐶 1 − √3⁄2 = = 0.155 𝑟𝐴 √3⁄ 2 𝑟 Coordination Numbers and Geometries for Various Cation-Anion Radius Ratio ( 𝐶⁄𝑟𝐴 ) AX-TYPECRYSTALSTRUCTURES Some of the common ceramic materials are those in which there are equal numbers of cations and anions. These are often referred to as AX compounds, where A denotes the cation and X the anion. There are several different crystal structures for AX compounds; they can assume coordination numbers of 4, 6, 8. Example include NaCl, CsCl, MgO, MnS, LiF and FeO, ZnS, ZnTe, SiC. AmXp – Type Crystal Structures If the charges on the cations and anions are not the same, a compound can exist with the chemical formula AmXp where m and/or p ≠ 1. For example 𝐴𝑋2 , for which a common crystals of these form are the fluorite (CaF2), UO2, PuO2, and ThO2. AmBnXp Type of Crystal Structures It is also possible for ceramic compounds to have more than one type of cation; for two types of cations (represented by A and B), their chemical formula may be designated as AmBnXp. Barium titanate (BaTiO3), having both Ba2+ and Ti4+ cations, falls into this classification. This material has a perovskite crystal structure and rather interesting electromechanical properties. Some Common Crystal Structures POLYMORPHISM AND ALLOTROPY Some metals, as well as nonmetals, may have more than one crystal structure, a phenomenon known as polymorphism. When found in elemental solids, the condition is often termed allotropy. The prevailing crystal structure depends on both the temperature and the external pressure. One familiar example is found in carbon: graphite is the stable polymorph at ambient conditions, whereas diamond is formed at extremely high pressures. Also, pure iron has a BCC crystal structure at room temperature, which changes to FCC iron at 912oC(1674F). Most often a modification of the density and other physical properties accompanies a polymorphic transformation. CRYSTAL SYSTEMS Since there are many different possible crystal structures, it is sometimes convenient to divide them into groups according to unit cell configurations and/or atomic arrangements. One such scheme is based on the unit cell geometry, that is, the shape of the appropriate unit cell parallelepiped without regard to the atomic positions in the cell. Within this framework, an x, y, z coordinate system is established with its origin at one of the unit cell corners; each of the x, y, and z axes coincides with one of the three parallelepiped edges that extend from this corner, as illustrated in Figure x5. The unit cell geometry is completely defined in terms of six parameters: the three edge lengths a, b, and c, and the three interaxial angles 𝛼, 𝛽, 𝑎𝑛𝑑 𝛾. These are indicated in Figure x5, and are sometimes termed the lattice parameters of a crystal structure. On this basis there are found crystals having seven different possible combinations of a, b, and c, and 𝛼, 𝛽, 𝑎𝑛𝑑 𝛾, each of which represents a distinct crystal system. These seven crystal systems are cubic, tetragonal, hexagonal, orthorhombic, rhombohedral, monoclinic, and triclinic. CRYSTALLOGRAPHIC DIRECTIONS A crystallographic direction is defined as a line between two points, or a vector. The following steps are utilized in the determination of the three directional indices: 1. A vector of convenient length is positioned such that it passes through the origin of the coordinate system. Any vector may be translated throughout the crystal lattice without alteration, if parallelism is maintained. 2. The length of the vector projection on each of the three axes is determined; these are measured in terms of the unit cell dimensions a, b, and c. 3. These three numbers are multiplied or divided by a common factor to reduce them to the smallest integer values.  4. The three indices, not separated by commas, are enclosed in square brackets, thus: [uvw]. The u, v, and w integers correspond to the reduced projections along the x, y, and z axes, respectively. For each of the three axes, there will exist both positive and negative coordinates. Thus, negative indices are also possible, which are represented by a bar over the appropriate index. For example, the ̅̅̅̅̅̅̅̅̅ [1 1 1] direction would have a component in the -y direction. Also, changing the signs of all indices produces an antiparallel direction; that is [1̅ 1 1̅] is directly opposite to [1 1̅ 1] Example HEXAGONAL CRYSTALS A problem arises for crystals having hexagonal symmetry in that some crystallographic equivalent directions will not have the same set of indices. This is circumvented by utilizing a four-axis, or Miller–Bravais, coordinate system as shown in Figure 3.21. The three a1, a2, and a3 axes are all contained within a single plane (called the basal plane) and at 120o angles to one another. The Z-axis is perpendicular to this basal plane. Directional indices, which are obtained as described above, will be denoted by four indices, as [uvtw]; by convention, the first three indices pertain to projections along the respective a1, a2, and a3 axes in the basal plane. Conversion from the three-index system to the four-index system, [𝑢𝐼 𝑣 𝐼 𝑤 𝐼 ] → [𝑢𝑣𝑡𝑤] is accomplished by the following formulas: 𝑛 𝑢 = (2𝑢𝐼 − 𝑣 𝐼 ) 3 𝑛 𝑣 = (2𝑣 𝐼 − 𝑢𝐼 ) 3 𝑡 = −(𝑢 + 𝑣) 𝑤 = 𝑛𝑤 𝐼 where primed indices are associated with the three-index scheme and unprimed, with the new Miller–Bravais four-index system; n is a factor that may be required to reduce u, v, t, and w to the smallest integers. Several different directions are indicated in the hexagonal unit cell. CRYSTALLOGRAPHIC PLANES Theorientationsofplanesforacrystalstructurearerepresentedinasimilarmanner. Again, the unit cell is the basis, with the three-axis coordinate system as represented in Figure 3.19. In all but the hexagonal crystal system, crystallographic planes are specified by three Miller indices as (hkl). Any two planes parallel to each other are equivalent and have identical indices. The procedure employed in determination of the h, k, and l index numbers is as follows: 1. If the plane passes through the selected origin, either another parallel plane must be constructed within the unit cell by an appropriate translation, or a new origin must be established at the corner of another unit cell. 2. At this point the crystallographic plane either intersects or parallels each of the three axes; the length of the planar intercept for each axis is determined in terms of the lattice parameters a, b, and c. 3. The reciprocals of these numbers are taken. A plane that parallels an axis may be considered to have an infinite intercept, and, therefore, a zero index. 4. If necessary, these three numbers are changed to the set of smallest integers by multiplication or division by a common factor. 5. Finally, the integer indices, not separated by commas, are enclosed within parentheses, thus: (hkl). An intercept on the negative side of the origin is indicated by a bar or minus sign positioned over the appropriate index. Furthermore, reversing the directions of all indices specifies another plane parallel to, on the opposite side of and equidistant from, the origin. Several low-index planes are represented in Figure 3.23. One interesting and unique characteristic of cubic crystals is that planes and directions having the same indices are perpendicular to one another; however, for other crystal systems there are no simple geometrical relationships between planes and directions having the same indices.  Families of Planes The cubic crystal of the following planes ̅̅̅̅̅̅̅̅̅ ̅ ̅̅̅̅̅ ̅ ̅̅̅̅ ̅ ̅ ̅ (1 1 1), (1 1 1), (1, 1 1), (1 1 1), (1 1 1), (1 1 1), (1 1 1), 𝑎𝑛𝑑 (1 1 1) all belong to the family {1 1 1} family. Family representation is important crystallography. Tetragonal and other types of crystal systems can be represented using the families of plane. Crystalline and Noncrystalline Materials Single Crystals For a crystalline solid, when the periodic and repeated arrangement of atoms is perfect or extends throughout the entirety of the specimen without interruption, the result is a single crystal, Figure 3.17. All unit cells interlock in the same way and have the same orientation. Single crystals exist in nature, but they may also be produced artificially. They are ordinarily difficult to grow, because the environment must be carefully controlled. Single crystals have become extremely important in many of our modern technologies, in particular electronic microcircuits, which employ single crystals of silicon and other semiconductors. Figure 3.17 Photograph of a quartz single crystal. Polycrystalline Materials Most crystalline solids are composed of a collection of many small crystals or grains; such materials are termed polycrystalline. Various stages in the solidification of a polycrystalline specimen are represented schematically in Figure 3.18. Initially, small crystals or nuclei form at various positions. These have random crystallographic orientations, as indicated by the square grids. The small grains grow by the successive addition from the surrounding liquid of atoms to the structure of each. The extremities of adjacent grains impinge on one another as the solidification process approaches completion. As indicated in Figure 3.17, the crystallographic orientation varies from grain to grain. Also, there exists some atomic mismatch within the region where two grains meet; this area, called a grain boundary. Figure 3.18 Schematic diagrams of the various stages in the solidification of a polycrystalline material; the square grids depict unit cells. (a) Small crystallite nuclei. (b) Growth of the crystallites. (c) Upon completion of solidification, grains having irregular shapes have formed. (d) The grain structure as it would appear under the microscope; dark lines are the grain boundaries. Adapted from W. Rosenhain, An Introduction to the Study of Physical Metallurgy, 2nd edition, Constable & Company Ltd., London, 1915. Amorphous Materials Any material that exhibits only a short-range order of atoms or ions is an amorphous material; that is, a noncrystalline one. In general, most materials want to form periodic arrangements since this configuration maximizes the thermodynamic stability of the material. Amorphous materials tend to form when, for one reason or other, the kinetics of the process by which the material was made did not allow for the formation of periodic arrangements. Glasses, which typically form in ceramic and polymer systems, are good examples of amorphous materials. Similarly, certain types of polymeric or colloidal gels, or gel-like materials, are also considered amorphous. Similar to inorganic glasses, many plastics are also amorphous. They do contain small portions of material that are crystalline. During processing, relatively large chains of polymer molecules get entangled with each other, like spaghetti. Amorphous silicon is another important example of a material that has the basic short- range order of crystalline silicon. Thin films of amorphous silicon are used to make transistors for active matrix displays in computers. Amorphous silicon and polycrystalline silicon are both widely used for such applications as solar cells and solar panels. References Askeland D. R., Fulay P. P, Essentials of Materials Science and Engineering,2nd edition, p. 66, 2009. Interstitial Defects An interstitial defect is formed when an extra atom or ion is inserted into the crystal structure at a normally unoccupied position, as in Figure 4.1(b). Interstitial atoms or ions, although much smaller than the atoms or ions located at the lattice points, are still larger than the interstitial sites that they occupy. Consequently, the surrounding crystal region is compressed and distorted. Interstitial atoms such as hydrogen are often present as impurities; whereas carbon atoms are intentionally added to iron to produce steel. Unlike vacancies, once introduced, the number of interstitial atoms or ions in the structure remains nearly constant, even when the temperature is changed. A self-interstitial is an atom from the crystal that is crowded into an interstitial site, a small void space that under ordinary circumstances is not occupied. This kind of defect is also represented in Figure 4.2. In metals, a self- interstitial introduces relatively large distortions in the surrounding lattice because the atom is substantially larger than the interstitial position in which it is situated. Consequently, the formation of this defect is not highly probable, and it exists in very small concentrations, which are significantly lower than for vacancies. Substitutional Defects A substitutional defect is introduced when one atom or ion is replaced by a different type of atom or ion as in Figure 4.1(c) and (d). The substitutional atoms or ions occupy the normal lattice sites. Substitutional atoms or ions may either be larger than the normal atoms or ions in the crystal structure, in which case the surrounding interatomic spacings are reduced, or smaller causing the surrounding atoms to have larger interatomic spacings. In either case, the substitutional defects alter the interatomic distances in the surrounding crystal. Again, the substitutional defect can be introduced either as an impurity or as a deliberate alloying addition, and, once introduced, the number of defects is relatively independent of temperature. Examples of substitutional defects include incorporation of dopants such as phosphorus (P) or boron (B) into Si. Similarly, for the copper and nickel alloy, copper atoms will occupy crystallographic sites where nickel atoms would normally be present. The substitutional atoms will often increase the strength of the metallic material. Substitutional defects also appear in ceramic materials. For example, addition of MgO to NiO, Mg+2 ions occupy Ni+2 sites and O–2 ions from MgO occupy O–2 sites of NiO. Whether atoms or ions added go into interstitial or substitutional sites depends upon the size and valence of guest atoms or ions compared to the size and valence of host ions. The crystal structure for metals of both atom types must be the same. Also, the size of the available sites plays a role in this.