Modern Ceramic Engineering, 2nd, David W. Richerson, Manuais, Projetos, Pesquisas de Engenharia de Materiais

Baixe Modern Ceramic Engineering, 2nd, David W. Richerson e outras Manuais, Projetos, Pesquisas em PDF para Engenharia de Materiais, somente na Docsity!   • • Properties, Processing, and Use in Design Second Edition, Revised and Expanded   Contents Prel." to the Second Edilion Preface to the First Edition Introd.dion Pad I STRtlCfllRES AND PROPERTIES 1 Atomic: Bonding, and Crystal Structure • vii xi I 3 2 Crystal Chemistry and Speci6c Crystal Structures 32 3 Phase EguUibria and Phue Equilibrium Diagrams 71 4 PbysicaJ and }bennal Behavior 123 5 Mrtblola! Bcbuior and Measurement 162 6 EI.drirl' Behayio[ 204 1 Dieledrict Magnetic. and Optical Behavior 1S1 8 Time, Temperature, and Environmental Elred! on PropeJ1Jes 313 Part II PROCF,sSING OF CERAMICS 373 9 Powder Processing 10 Shape·FonnlllR Processes J 1 D'nqfinlinn 12 Final Macbining 13 Quality Assurance pad II( DESIGN WITH CERAMICS 14 DesI&n Considerations 15 Deslp Approaches 16 FaOure Analysis 17 TougbeDing of Ceramics 18 AppUalions: Material Selection Glossary EWed:ive Ionic Radii (or CalioD' aod AniOBS periodic Table of the Elements lodex 374 418 519 5% 6ZO 649 651 662 680 731 808 833 843 851 .. 4 Chapter 1 The second shell has eight electrons. two in s orbitals and six in p orbitals. All have higher energy than the two electrons in the first shell and are in orbitals farther from the nucleus. (For instance . the s orbitals of the second shell of lithium have a spherical probability distribution at about 3 A radius.) The p orbitals are not spherical. but have dumbbell-shaped probability dis- tributions along the orthogonal axes, as shown in Fig. 1.1. These p electrons have sl ightly higher energy than s electrons of the same shell and are in pairs with opposite spins along each axis when the shell is full. The third quantum shell has d orbitals in addition to sand p orbitals. A full d orbital contains 10 electrons. The fourth and fifth shells contain f orbitals in addition to s. p. and d orbitals. A full f orbital contains 14 e lectrons. A simple notation is used to show the electron configurations within shells. to show the relative energy of the electrons, and thus to show the order in which the electrons can be added to or removed from an atom during bonding. This notation can best be illustrated by a few examples. Example 1.1 Oxygen has eight e lectrons and has the electron notation Is'2s'2p'. The I and 2 preceding the sand p designate the quantum shell. the sand p designate the subshell wi thin each quantum she ll . and the su- perscripts designate the total number of electrons in each subshell. For oxygen the Is and 2s subshells are both full . but the 2p subshell is two electrons short of being full. Example 1.2 As the atomic number and the number of electrons increase . the energy difference between electrons and between shells decreases and overl<.lp between quantum groups occurs. For example . the 45 subshell of iron lills before the 3d subshell is full. This is shown in the electron notation by Figure 1.1 E lectron probability distributions for p orbital s. The highest probability electron positions are along the orthogonal axes. Two electrons. each with opposite spin. are associated with each axis. resulting in a total of six p electrons if all the p orbitals in th e shell are filled . Atomic Bonding and Crystal Structure 5 listing the order of fill of energy levels in sequence from the left of the notation to the right: Fe = 15'252pº35'3p'3c4s? Example 1.3 Electronic notation helps a person visualize which electrons are available for bonding and to estimate the type of bond that is likely to result, Unfilled shells contribute to bonding. Electron notation is often ab- breviated to include only the unfilled and outer shells. The iron electron notation is thus abbreviated to 3dº4sº, which tells the reader that all the subshells up to and including 3s are filled. Yttrium is abbreviated from 1s252pt3d "asd ptad'5s? to 4d!5sº or even more simply, 4d5s”. Figure 1.2 lists the abbreviated electron configurations of the elements arranged according to the periodic table. Another form of abbreviation lists the nearest inert gas of lower atomic number and also identifies the electrons in outer shells. For example, Mg consists of the neon inner structure 1s*2572pº plus 35º and is abbreviated [NeJ3s”. Similarty, Ti can be abbreviated [Ar)3dº4s? and 1 ab- breviated [Kr]4d"Ss'sp*. 12 BONDING The unfilled outermost electron shells are involved tn bonding. The elements He, Ne, Ar, Kr, Xe, and Rn have full outer electron shells and thus are very stable and do not easily form bonds with other elements. Elements with unfilled electron shells are not as stable and interact with other atoms in a controlled fashion such that electrons are shared or exchanged between these atoms to achieve stable full outer shells. The three primary interatomic bonds are referred to as metallic, ionic, and covalent. These provide the bond mechanism for nearly all the solid ceramic and metallic materials discussed in later chapters. Other secondary mechanisms referred to as van der Waals bonds also occur, but are discussed only briefly. Metallic Bonding As the name implies, metallic bonding is the predominant bond mechanism for metals, It is also referred to as electronic bonding, from the fact that the valence electrons (electrons from unfilled shells) are freely shared by all the atoms in the structure, Mutual electrostatic repulsion of the negative charges of the electrons keeps their distribution statistically uniform throughout the structure. At any given time, each atom has enough electrons grouped around it to satisfy its need for a full outer shell, It is the mutual attraction of all the nuclei in the structure to this same cloud of shared electrons that results in the metallic bond. 6 Chapter 1 Because the valence electrons in a metal distribute themselves uniformly and because all the atoms in a pure metal are of the same size, close-packed structures result. Such close-packed structures contain many slip planes along which movement can occur during mechanical loading, producing the ductility that we are so accustomed to for metais. Pure metals typically have very high ductility and can undergo 40 to 60% elongation prior to rupturing. Highly alloyed metais such as the superalloys also have close-packed structures, but the different-size alloying atoms disrupt movement along slip planes and de- crease the ductility. Superalloys typically have 5 to 20% elongation. The free movement of electrons through the structure of a metal results in high electrical conductivity under the influence of an electrical field and high thermal conductivity when exposed to a heat source. These properties are discussed in more detail in Chaps. 4 and 6. Metallic bonding occurs for elements to the left and in the interior of the periodic table (see Fig. 1.2 and the complete periodic table on p. 850). Alkali metals such as sodium (Na) and potassium (K) are bonded by outer s electrons and have low bond energy. These metals have low strength and low melting temperatures-and are not overly stable. Transition metals such as chromium (Cr), iron (Fe), and tungsten (W) are bonded by inner electrons and have much higher bond strengths. Transition metals thus have higher strength and higher melting temperatures and are more stable, Ionic Bonding lonic bonding occurs when one atom gives up one or more electrons and another atom or atoms accept these electrons such that electrical neutrality is maintained and each atom achieves a stable, filled electron shell, This is best illustrated by a few examples. Example 1.4 Sodium chloride (NaCl!) is largely ionically bonded. The Na atom has the electronic structure 18º25º2p“3s. If the Na atom could pet rid of the 3s electron, it would have the stable neon (Ne) structure. The chlorine atom has the electronic structure 15º25º2p*3s'3p*. If the CI atom could obtain one more electron, it would have the stable argon (Ar) structure. During bonding, one electron from the Na is transferred to the Cl, producing a sodium ion (Na*) with a net positive charge and a chlorine ion (Cl”) with an equal negative charge, resulting in a more stable electronic structure for each. This is illustrated in Figure 1.3, The opposite charges provide a Coulombic at- traction that is the source of ionic bonding. To maintain overall electrical neutrality, one Na atom is required for each Cl atom and the formula becomes NaCl. Example 1.5 The aluminum (Al) atom has the electronic structure 157252p*3s"3p!. To achieve a stable Ne structure three electrons would have Table 1.1 Jonic Radii for 6 and 4 Coordination (4 Coordination in Parentheses) Agr Lis (1.02) cr 181 Fe 077 (0.63) Mer 0.72 (0.49) Rb 149 Te 221 ye 089 Apr 0.53 (0.39) cor 0.74 Fe” 0.65 10.49) Mn?” 067 sr 184 Te” 0.56 vp 0.86 Ass 0.50 (0.34) co” 0.61 Ga” 0.62 (0.47) Matt 0.54 se 0.30 (0.12) nº 1.00 Zn 0.75 (0.60) Aut 1.37 ce 0.73 Ga” 0.94 Mo” 0.67 so” 0.61 Tr 0.86 Ze” 0,72 Br 0.23 (0.12) cr 0.62 Ger 0.54 (0.40) Mott 0.65 se” 0.73 Ti” 0.61 pa” 136 cr 0,55 (0.44) ne 971 (0.96) Na” 102 (0.99) Se” 1.98 Tr 1,50 pe 0.35 (027) Cs 1.70 Hg” 102 Nb* 0.64 (0.32) ser 042 (0.29) ne 0.88 Bi” 0.74 cu 0.96 Ho” 0.89 Ne” 1.00 si 0.40 (0.26) ve 097 Br 1.96 cur 073 (0.63) r 220 Ni 0.69 sm” 0.96 us 0.76 0.16 (0.15) Dy* 0.91 we 0.79 o” (1.38) sn 0.93 v> 0.79 ca” 1.00 E 0,88 K 138 0.35 (0.33) Sn” 0.69 vs 0.54 (036) car 0.95 (0.84) Eu 0.95 La” 1.06 pro 1.18 (0.94) se 1.16 we 0,65 Ce” 0.80 133 as Li 0.74 (0.59) pos 0.78 Tat 0.64 0.58 (0,41) Source: Compiled from Refs. | and 2. dampanns JejsÃio pus Sujpuog amuory 10 Chapter 1 Example 1.6 What is the most likely coordination number for a structure made up of Mg'* and O"? Si** and 0-2 Cr'* and 0-9 From Table 1.1, Met 072 o “ o Ta 0.51 coordination number = 6 Sir 0,40 ni o > 40 é 0,29 coordination number = 4 Cr” 062 ar O = Lao 0.44 coordination number = 6 As predicted, Mg”* has a coordination number of 6 in MgO. The O"- ions also have a coordination number of 6 and are arranged in a cubic close- packed structure with the Mg” ions filling the octahedral interstitial positions. This is the same structure that Na* and Cl” bond together to form, This structure is called the rock salt structure after NaCI. Other important ceramic structures are listed in Table 1.2 and are discussed in Chapter 2. Most of the ionic structures are close-packed. Bonding is associated with the s electron shells (which have a spherical probability distribution) and would be nondirectional if purely ionic. However. there is a tendency for increased electron concentration between atom centers, which provides a degree of nonionic character. The degree of ionic character of a compound can be estimated using the electronegativity scale (Fig. 1.5) derived by Pauling [3]. Electronegativity is a measure of an atom's ability to attract electrons and is roughly proportional to the sum of the energy needed to add an electron (electron afânity) and to remove an electron (ionization potential). The larger the electronegativity difference between atoms in a compound, the larger the degree of ionic character. The semiempirical curve derived by Pauling is shown in Fig. 1.6. NOT STABLE STABLE STABLE Figure 1.4 Stable and unstable configurations which determine atomic coordination number within a structure. (Adapted from Ref. 2.) Hm Table 1.2 Ionic Crystal Structures Name of Coordination Coordination structure Packing of anions of anions of cations Examples Rock sait Cubic close-packed 6 6 NaCI, MgO, CaO. LiF. CoO. NiO Zine hlende Cubic close-packed 4 4 ZnS. BeO, SIC Perovskite Cubic close-packed 6 12,6 BaTiO,. CoTiO,. SrZrO, Spinel Cubic close-packed 4 8.6 FeALO, MgALO,. ZnALO, Inverse spinel Cubic close-packed 4 a(o 4 FeMBFcO,. METIMBO, csci Simple cubic 8 8 CsCI, CsBr. Cs Fluorite Simpie cubic 4 8 CaF;, ThO,, CeO.. UO,, ZrO.. HO. Antifuarite Cubic close-packed 8 4 LO. Na;O, KO, Rb:0 Rutile Distorted cubic close-packed 3 6 TIO, GeO:. SnO:, PbO:. VO. Wurtzite Hexagonal close-packed 4 4 ZnS. 2n0, SIC Nickel arsenide Hexagonal close-packed 6 6 NiAs. Fes, CoSe Corundum Hexagonal close-packed 4 6 ALO, FesOy, CO V O Umenite Hexagonal close-packed 4 6.6 FeTIO,. CoTiO,. NÍTIO, Ofivine Hexagonal close-packed 4 6.4 MesSiOs. FesSiO, “First Fe in tetrabiedrai cuordination. second Fe in octahedral coordinatior. Source: Adapted from Ref. 2 14 Chapter 1 (a) DIAMOND STAUCTURE UNIT tb) METHANE MOLECULE Figure 1.7 Schematic example of covalently bonded materials. (a) Diamond with periodic three-dimensional structure. (b) Methane with single-molecular structure. Shaded regions show directional electron probability distributions for pairs of electrons. Carbon has an atomic number of 6 and an electronic structure of 18'2s'2p” and thus has four valence electrons available for bonding. Each 2s and 2p electron shares an orbital with an equivalent electron from another carbon atom, resulting in a structure in which each carbon atom is covalently bonded to four other carbon atoms in a tetrahedra! orientation. This is shown sche- matically in Fig. 1.7a for one tetrahedral structural unit. The central carbon atom has its initial six electrons plus one shared electron from each of the adjacent four carbon atoms, resulting in a total of 10 electrons. This is equiv- alent to the filled outer shell of a neon atom and is à very stable condition. Euch of the four outer carbon atoms of the tetrahedron is bonded directionally to three additional carbon atoms to produce a periodic tetrahedral structure with all the atoms in the structure (except the final outer layer at the surface of the crystal) sharing four electrons to achieve the stable electronic structure of neon. The continuous periodic covalent bonding of carbon atoms in diamond results in high hardness, high melting temperature, and low electrical con- ductivity at low temperature. Silicon carbide has similar covalent bonding and thus high hardness, high melting temperature, and low electrical conductivity at low temperature.” Covalently bonded ceramics typically are hard and strong and have high melting temperatures. However, these are not inherent traits of covalent bonding. For instance, most organic materials have covalent bonds but do not have high hardness or high melting temperatures. The deciding factor is the strength of the bond and the nature of the structure. For instance, methane (CH) forms a tetrahedral structural unit fike diamond, but the valence elec- trons of both the carbon atom and the four hydrogen atoms are satisfied within a single tetrahedron and no periodic structure results. Methane is a *Silicon carbide doped with appropriate impurities has significantly increased electrical conductivity and is an important semiconductor material. Atomic Bonding and Crystal Structure 15 gas under normal ambient conditions. A methane molecule is shown sche- matically in Fig. 1.7b. Organic bonding and structures are discussed in more detail later in the chapter. Diatomic gases (H., O». N., etc.) are another example of covalent bonding where molecules rather than interconnected solid structures are formed. Two hydrogen atoms cach share their 1s electron to form H.. Two oxygen atoms share two electrons to form O». Similarly, two nitrogen atoms share three electrons to form N,. Multiple sharing leads to a particularly strong bond and a stable molecule. N, is often used as a substitute for the inert gases He or Ar. Figure 1.8 illustrates covalent bonding in various diatomic gases. The directional bonding of covalent materials results in structures that are not close packed. This has a pronounced effect on the properties, in particular density and thermal expansion. Close-packed materials such as the metals and ionic-bonded ceramics have relatively high thermal expansion coefhicients. The thermal expansion of each atom is cumulated through each close-packed adjacent atom throughout the structure to yield a large thermal expansion of the whole mass. Covalently bonded ceramics typically have a much lower thermal expansion because some of the thermal growth of the individual atoms is absorbed by the open space in the structure. Covalent bonding occurs between atoms of similar electronegativity which are not close in electronic structure to the inert gas configuration. (Refer to the electronegativity scale in Fig. 1.5.) Atoms such as C, N, Si. Ge. and Te are of intermediate electronegativity and form highly covalent structures. Atoms with a greater difference in electronegativity form compounds having a less covalent bond nature. Figures 1.5 and 1.6 can be used to estimate the relative covalent bond nature. However, the curve in Fig. [.6 is empirical and can be used only as an approximation, especially in intermediate cases. Example 1.8 What is the approximate degree of covalent character of dia- mond? of SiN;? of SiO;? From Fig. 1.5. E -Ec=0 Es — Ex = 1.2 Es — E, =17 From Fig. 1.6. Fraction covalent € = 1 fraction ionic C=1-0=10 Fraction covalent SAN, = 1 — fraction ionic ShN,=10-03= 07 Fraction covalent SiO, = 1 — fraction ionic SO, = 10 — 0,5 = 0,5 16 Chapter 1 iso kas10A (b) Liss 3 os à (e) (d) Figure 1.8 Covalent bonding of diatomic molecules. (From Ref. 10.) In summary, the following properties are characteristic of covalent bond- ing and the resulting ceramic materials: 1. Electron are shared to fill outer electron shells and achieve electrical neutrality. 2. Atoms having similar electronegativity from bonds. 3. Bonding is highly directional. 4. Structures are not close packed, but typically three-dimensional frame-works contain cavities and channels. 5. Compounds typically have high strength, hardness, and melting tem- perature. 6. Structures often have low thermal expansion. Ionic and Covalent Bond Combinations Many ceramic materials have a combination of ionic and covalent bonding. An example is gypsum (CaSO,), from which plaster is manufactured. The sulfur is covalently bonded to the oxygen to produce SO, , which is two electrons short of having full outer electron shells for each of the five atoms. The calcium donates its two valence electrons and is thus bonded ionically to the SOp”: Ca+- Atomic Bonding and Crystal Structure 19 der Waals-type bonds to hold the layers together. Highly anisotropic prop- erties result. All of these layer structures have easy slip between layers. In the clay minerais this property makes possible ptasticity with the addition of water and was the basis of the early use of clay for pottery. In fact, it was the basis of almost all ceramic fabrication technology prior to the twentieth century and is still an important factor in the fabrication of pottery, porcelain, whiteware, brick, and many other items. The easy slip between layers in graphite and hexagonal boron nitride has also resulted in many applications of these materials. Both can be easily machined with conventional cutting tools and provide low-friction. self-lu- bricating surfaces for a wide variety of seals. Both are also used as solid lubricants and as boundary layer surface coatings. The weak bonds between layers of mica and the resulting easy slip has recently led to a new application for these materials. Small synthetic mica crystals are dispersed in glass to form a nonporous composite having excellent electrical resistance properties. The presence of the mica permits machining of the composite to close tolerances with no chipping or breakage. using conventional low-cost machine tools. Although van der Waals forces are weak, they are adequate to cause adsorption of molecules at the surface of a particle. For particles of colloid dimensions (100 À to 3 em), adsorbed ions provide enough charge at the surface of a particle to attract particles of opposite charge and to repel particles of like charge. This has a major effect on the rheology (flow characteristics of particles suspended in a Auid) of particle suspensions used for slip casting and mixes used for extrusion, injection molding. and other plastic-forming techniques (see Chap. 10). The discussions in this chapter of electronic structure, bonding, and crystal structure have been brief and simplified. More detailed discussions are avail- able in Refs. 1 through 7 and in Chapter 2. 1,3 POLYMORPHIC FORMS AND TRANSFORMATIONS As described in the sections on bonding, the stable crystal structure for a composition is dependent on the following: 1. Balance of electrical charge 2. Densest packing of atoms consistent with atom size, number of bonds per atom, and bond direction 3. Minimization of the electrostatic repulsion forces As the temperature of or the pressure on a material change, interatomic distance and the level of atomic vibration change such that the initial structure may not be the most stable structure under the new conditions. Materials 20 Chapter 1 having the same chemical composition but a different crystal structure are called polymorphs and the change from one structure to another is referred to as a polymorphic transformation. Polymorphism is common in ceramic materials and in many cases has a strong impact on useful limits of application. For instance, the stable form of zirconium oxide (ZrO») at room temperature is monoclinic, but it transforms to a tetragonal form at about 1100ºC. This transformation is accompanied by a large volume change that results in internal stresses in the ZrO, body large enough to cause fracture or substantial weakening. In attempts to avoid this problem. it was discovered that appropriate additions of MgO, CaO, or Y,0; to ZrO, produced a cubic form that did not undergo a transformation and was thus useful over a broader temperature range. Before selecting a material for an application, it is necessary for an en- gincer 10 verify that the material does not have an unacceptable transfor- mation. A good first step is to check the phase equilibrium diagram for the composition. Even if more than one polymorph is present within the intended temperature range of the application, the material may be acceptable. The important criterion is that no large or abrupt volume changes occur. This can be determined by looking at the thermal expansion curve for the material, For example, Fig. 1.9 compares the thermal expansion curves for unstabilized ZrO, and stabilized ZrO,. The large volume change associated with the mon- oelinic-tetragonal transformation is readily visible for the unstabilized ZrO». Many ceramic materials exist in different polymorphic forms. Among these materials are SiO», SiC, €, SiN,, BN, TIO,, ZnS, CaTiO,. AbSIO,. FeS,. and As;O.. The properties of some of these are discussed in later chapters. Two types of polymorphic transformations occur. The first, displacive transformation, involves distortion of the structure, such as a chanpe in bond angles, but does not include breaking of bonds. It typically occurs rapidly at a well-defined temperature and is reversible. The martensite transformation in metais às a displacive transformation. So also are the cubictetragonal BaTiO; and tetragonal-monoclinic ZrO, transformations. Displacive transformations are common in the silicate ceramics. In gen- eral, the high-temperature form has higher symmetry, larger specific volume, and larger heat capacity and is always the more open structure. The low- temperature form typically has a collapsed structure achieved by rotating the bond angle of alternating rows of SiO, tetrahedra in opposite directions. The second type of transformation is the reconstructive transformation. Bonds are broken and a new structure formed. Much greater energy is re- quired for this type of transformation than for a displacive transformation. The rate of reconstructive transformation is sluggish, so the high-temperature structure can usually be retained at low temperature by rapid cooling through the transformation temperature. Atomic Bonding and Crystal Structure (a) (b) Pure Fuliy MH 1.5 | stabilized 1.4 1.2 10 0.8 0.6 Linear expansion, % 0.4 0.2 / Er av) LAI O 400 800 1200 O 400 800 1200 Temperature, “ºC Figure 1.9 Thermal expansion curves for (a) unstabilized ZrO. and (b) stabilized ZrO, showing the abrupt volume change in the unstabilized ZrO, due to the mono- clinictetragonal polymorphic phase transformation. (From E. Tyshkewitch and D. W. Richerson. Oxide Ceramics. 2nd ed.. General Ceramics/Academic Press, 1985.) The activation energy for a reconstructive transformation is so high that transformation frequently will not occur unless aided by external factors. For example, the presence of a liquid phase can allow the unstable form to dissolve, followed by precipitation of the new stable form. Mechanical energy can be another means of overcoming the high activation energy. Silica (SiO.) is a good example for illustrating transformations. Both displacive and reconstructive transformations occur in SiO» and play an im- portant role in silicate technology. Figure 1.10 shows the temperature-initiated transformations for SiO». The stable polymorph of SiO, at room temperature is quartz. However. tridymite and cristobalite are also commonly found at room temperature in ceramic components as metastable forms because the reconstructive transformations in SiO, are very sluggish and do not normally occur. Quartz, tridymite, and cristobalite all have displacive transformations in which the high-temperature structures are distorted by changes in bond angle between SiO, tetrahedra to form the low-temperature structures. These displacive transformations are rapid and cannot be restrained from occurring. K is important to note the size of the volume changes associated with displacive transformations in SiO,. These limit the applications, especially of 24 Chapter 1 3. Typically transparent to optical wavelengths, but can be formulated to absorb or transmit a wide variety of wavelengths 4. Typically good electrical and thermal insulators S. Soften before melting. so they can be formed by btowing into intricate hollow shapes Gels Gels are noncrystalline solids that are formed by chemical reaction rather than melting. Silica gel, which is highly useful as a bonding agent in the ceramic and metal industries, is produced by a reaction of ethyl silicate with water in the presence of a catalyst. Si(OH), results, which is then dehydrated to form SiO.. A silica gel can also be formed by the reaction of sodium silicate with acid. Another noncrystalline inorganic gel, AI(H,PO,):. can be produced by reacting aluminum oxide (ALO:) with phosphoric acid (H;PO,). Like the silica gels. this aluminum phosphate gel is produced at room temperature and is an excellent inorganic cement. The technology and important applications of ceramic cements are discussed im Chap. 11. Vapor Deposition An important class of noncrystalline materials is produced by rapid conden- sation of a vapor on a cold substrate or by reaction of a gas at a hot substrate. The vapor can be produced by sputtering, electron-beam evaporation, or thermal evaporation. Vapor contacting a cold substrate solidies so rapidly that the atoms do not have time to rearrange into a crystalline structure. Condensation from a vapor has been used to produce noncrystalline coatings of materials that are difficult or impossible to produce as noncrys- talline solids by other approaches. These coatings are usually nonporous and very fine grained and have unique properties. 1.5 MOLECULAR STRUCTURES So far we have discussed the bonding and structures of metals and ceramics. but have ignored organic materials. Organic materials are extremely important in modern engineering and their general characteristics should be understood just as well as those of metals and ceramics. The majority of organic materials are made up of distinct molecules. The atoms of each molecule are held together strongly by covalent bonds with the outer electron shells filled. Because ail the shelis are filed, the individual molecules are stable and do not have a drive to bond with other molecules (as mentioned earlier for methane). Atomic Bonding and Crystal Structure 25 Organic molecular structures are usually formed from the nonmetallic elements and hydrogen. The most common are the hydrocarbons, which consist prímarily of carbon and hydrogen but may also have halogens (es- pecially CI and F), hydroxide (OH), acetate (C,H:0,), or other groups re- placing one or more of the hydrogens. Other molecular structures include ammonia, which is made up of N and H, and the silicones, which contain Si in the place of carbon. Hydrocarbons The hydrocarbons and modified hydrocarbons are perhaps the most frequently encountered engineering organic materials. Some of the simple compositions and molecular structures are illustrated in Fig. 1.12. The straight lines between the atoms represent individual covalent bonds between pairs of electrons. ETHANE nv H-GE=H HH PHENOL oH Ho Cc MH NANA [A | 1 Pa Pa oco ETHANOL H HH Va H-€-6—0H HH STYRENE HH [1] C=c 11 EA rá [a A c TETRAFLUOROETHYLENE IN FF c n 1] ç º FF Figure 1,12 Hydrocarbon structures. (From Ref. VINYL CHLORIDE n rá H cr FORMALDEHYDE BUTADIENE HH HH SR] G=€-€=6 I H H 10.) 26 Chapter 1 The bond between two carbon atoms has an energy of about 83 kcal/g-mol. The bond energy between a carbon and a hydrogen is about 99 kcal/g-mol and between a carbon and chlorine is about 81 kcal/g-mol. Some pairs of carbon atoms in Fig. 1.12 have two covalent bonds between them. This double bond has an approximate energy of 146 kcal/g-mol [11]. Hydrocarbons with only single bonds have no open structural positions where additional atoms can bond and are thus referred to as saturated. The paraffins are good examples. They have a general formula of C,Hs,... Meth- anc is» = | and ethane is» = 2. These, as well as compositions with n up to 15, are either liquid or gas at room temperature and are used as fuels. As the size of the molecules increase, the melting temperature increases: thus, paralfins with about 30 carbon atoms per molecule are relatively rigid at room temperature. The increase in melting temperature with molecular size is par- tially due to decreased mobility. but mostly to increased van der Waals bond- ing between molecules. The larger molecules have more sites available for van der Waals bonds. Hydrocarbons with double or triple bonds between a pair of carbon atoms are referred to as unsaturated, Under the appropriate conditions, these bonds can be broken and replaced by single bonds that can link small molecules together to form large molecules. This is referred to as polymerization (12. RIR Addition Polymerization When a double bond is broken, it provides two sites at which new bonds may form. and the molecule is referred to as bifunctional. Ethylene, vinyl chloride, tetrafluoroethylene, styrene, and methy! methacrylate are all bi- functional. Addition polymerization can be achieved with bifunctional mol- ecules by applying enough energy to break the double carbon bond. This energy can be in the form of heat, pressure, light, or a catalyst. Once the double bonds of a group of molecules are broken, an unstable electron struc- ture is present and the separate molecular units, called mers, bond together to form a long chain (or polymer). The energy released during addition polymerization is greater than the energy that was required to start the re- action. The following illustrates addition polymerization of vinyl chloride to torm polyvinyl chloride: H H LA CRIA í fi eat, pressure CCC E C—c— (1.1) tight, or catalyst iG ci n n Atomic Bonding and Crystal Structure 29 PHENOL FORMALDEHYDE H OH Se- H LA H—C Se-n + c=O N A” VET H H H / N — H H — Ç OH ou. “e PN NAS H C—L Cc—€C H 48 4 wo HE pe Piu + 2 C=€ c=cC Ho ZE& EH E H H /8 (O) e A (5 . = ) PHENOL-FORMALDEHYDE WATER Figure 1.14 Formation of a network structure by condensation polymerization of phenol and formaidehyde. Pan Pau HHCH H CH HHCHHHCH LU Vl DLL LA Ts T$-E=C-E-66=c e E do nho nllanlla +5—» ss ss H HH H H | | HH | | H | pl I | pl ] CRT LILIII E NG nh CHA "nEMBHCHA Hs Hs H; H; NATURAL RUBBER VULCANIZED RUBBER Figure 1,15 Cross-linking with sulfur in the vulcanization process for natural rubber. (From L. H. Van Vlack, Elements of Materials Science, 2nd ed., O 1964. Addison- Wesley Publishing Co.. Reading, Mass.. Fig. 7.20. Reprinted with permission.) 3 Chapter 1 The shape of the polymer molecules affects the ease and degree of crys- tallization and also the properties. Crystallization occurs most casily if the individual monomers all have identical ordering. Cross-Linking and Branching Crystallization causes moderate changes in properties. Major changes can occur in linear polymers by cross-linking or branching. In cross-linking, ad- jacent chains are bonded together, usually by bridges between unsaturated carbon atoms. The vulcanization of natural rubber with sulfur is a classic example. The reaction is shown in Fig. 1.15. The degree of cross-linking can be controlled by the amount of S added. Both the hardness and strength increase as the amount of cross-linking increases. REFERENCES |. R.D. Shannon and €. T. Prewitt, Effective ionic radii in oxides and fluorides. Acre Crystallogr. B25. 925 (1969). W. D. Kingery. H. K. Bowen, and D. R. Uhimann. fntroduction to Ceramics, 2nd ed., Wiley, New York, 1976. Chap. 2. 3. L. Pauling. The Name of the Chemical! Bond. 3rd ed.. Cornell University Press. Ithaca. New York, 1960. + Anthony R. West. Solid State Chemistry and fis Application. Wiley. New York. 1984. 5. D. W. Oxtoby and N. H. Nachtrieb. Principles of Modern Chemistry, Saunders. Philadelphia. 1986. 6. JF Shackeltord. Introduction to Materials Science for Engineers, 2nd ed., Mac- millan, New York, 1985. 7. WD Callister, Materials Science and Engineering: An introduction, Wiley, New York. 1985. 8. R.H. Doremus, Glass Science, Wiley, New York, 1973. 9. MH. Rawson, lnorganic Glass-Forming Systems, Academic Press, New York, 1967. lo. LH. Van Vlack, Elements of Materials Science, 2nd ed., Addison-Wesley, Reading. Mass., 1964, Chaps. 3. 7, and Appendix F. 4. E W. Billmeyer, Jr.. Texbook of Polymer Science. Interscience, New York, 1962, 2. A. X. Schmidt and C. A. Marlies, Principles of High Polymer Theory and Practice. McGraw-Hill, New York, 1948. 13. G. F. D'Alelio, Fundamento! Principles of Polymerization, Wiley. New York. 1952. 14. D.J. Williams, Polymer Science and Engineering. Prentice-Hall. Englewood Cliffs. N.J.. 1971. 15. R.H. Doremus, Glass Science, Wiley. New York, 1973. 16. Richard Zalten, The Phivsics of Amorphows Solids. Wiley, New York. 1983. to Atomic Bonding and Crystal Structure a PROBLEMS Li 16 Explain why hydrogen and oxygen are present in the atmosphere as H, and O; (diatomic molecules) and helium and argon are present as He and Ar (monatomic molecules). Show the complete electron notation for Co. Why does the 45 shell fill before the 3d shell? How many 3d electrons are in each of the following? (a) Fe (b) Fe"! (c) Fe'* (d) Cut (e) Cu!* What chemical formula would result when yttrium and oxygen combine? What is the most likely coordination number? What is the relative per- cent ionic character? What relative hardness and melting temperature would be expected for yttrium oxide? Titanium has an atomic number of 22. How many electrons does the Ti'* ion contain? How many electrons does Mn** have? Be*7 Y**7 What chemical formula would result when potassium and oxygen com- bine? When calcium and fluorine combine? When tin and oxygen com- bine? When magnesium and oxygen? Titanium and oxygen? Zirconium and oxygen? Silicon and oxygen? Uranium and oxygen? Lanthanum and oxygen? 3 Chapter 2 ÚL to bs Simple cubic Body-centered Face-centered cubic cubie Simple Body-centered Simple Body-centered tetragonal tetragonal orthorhombic orthorhombic Base-centered Face-centered Hexagonal orthorhombre orthorhombic Rhombohedral Simple Base-centered Triclinic monoclinic monoclinic Figure 2.2 Bravais lattices. (From Ref. 1.) at the eight corners plus at the center of each cube, and (3) at the eight corners plus at the center of each face of the cube. These atom positions are referred to as lattice points. Fourteen options are possible for lattice points in the seven crystal systems. These are illustrated in Fig. 2.2 and are referred to as the Bravais lattices. Crystal Directions and Planes The closeness of packing of atoms varies in different planes within the crystaf structure. For example, the planes of the atoms parallel to the Crystal Chemistry and Specific Crystal Structures 35 diagonal of the cube in a face-centered cubic structure are close-packed. Planes in other directions are not close-packed. This variation in packing of atoms results in variations in properties of the crystal along different directions. It is therefore important to have a simple and constant method of identifying the directions and planes within a crystal structure. Since the unit cell is the simplest representation of a crystal structure, it is used as the basis for defining directions and planes within the overall crystal. Figure 2.3 shows a unit cell with three sides lying along the axes of a rectangular coordinate system. This unit cell is generalized and could represent a cubic unit cell (where a = b = c), a tetragonal unit cell (where a =bc),or an orthorhombic unit cell (where a b * c). Crystal directions are identified by the square-bracketed coordinates of a ray that extends from the origin to a corner, edge, or face of the unit cell. For example, a ray along the x axis intersects the corner of the unit cellatx =1,y=0,andz = 0. The direction [Ak!] is thus defined as [100]. If the ray is drawn on the x axis in the negative direction, the crystal direction is [100]. Similarly, a ray along the y axis is the crystal direction [010] and along the 2 axis is [001]. A ray along the diagonal of the unit cell face bounded by the x and z axes intersects the corner of the unit cell atx=1,y=0,andz = 1,so the crystal direction is [101]. A ray across the diagonal of the whole unit cellintersectsatx = 1,y = 1,andz =1 puta [101] c [111] [010] [100] y À a x —b Figure 2,3 Definitions of crystal directions for a cubic, tetragonal or orthorhombic crystal. a, b, and c are lattice dimensions of the unit cell, x, y, and z are the orthogonal axes of a rectangular coordinate system. The rays represent crystal directions with their [Ak!] designations. (From Ref. 2.) % Chapter 2 10) 1 % 1 | I / (010): VZ 4 (MM) (É LA LA hk 4 1 141 == (01 Lil == == 019 aa a O (RB = (A) k 1 1 gj=> 7 Figure 2.4 Examples of Miller indices notations for crystal planes. (From Ref. 2.) so that the crystal direction is [111]. Several of these examples are illustrated in Fig. 2.3. The crystal direction notation is made up of the lowest combination of integers and represents unit distances rather than actual distances. A [222] direction is identical to a [111], so [111] is used. Fractions are not used. For example, a ray that intersects the center of the top face of the unit cell has coordinates x = 1/2, y = 1/2, and z = 1. All have to be multiplied by 2 to convert to the lowest combination of integers [112]. Finally, all parallel rays have the same crystal direction. For instance, the four vertical edges of a unit cell all have the direction [hk!] = [001]. Crystal planes are designated by symbols referred to as Miller indices, The Miller indices are indicated by the notation (AA!) where A, k, and [ are the reciprocals of the intercepts of the plane with the x, y, and z axes. This is illustrated in Fig. 2.4 for a general unit cell. A plane that forms the right side of the unit cell intercepts the y axis at 1, but does not intercept the x or z axes. Thush = 1/00,k = 1/1,and | = 1/2, which gives (010). To distinguish from the notation for directions, parentheses are used for planes. Parallel planes have the same Miller indices, so the left side of the unit cellin Fig. 2.4 also is (010). Similarly, the top and bottom are (001) and the front and back are (100), Determination of Miller indices for several other planes is also illustrated in Fig. 2.4. Structure, Composition, and Coordination Notations Many crystal structures are named after the first chemical composition determined to have the structure. We need a simple notation to distinguish Crystal Chemistry and Specific Crystal Structures 39 nation number, and spin state affect the ionic radius, Let us look at the element iron (Fe). The ferrous ion Fe?* with a valence of +2 has an ionic radius of 9.75 À. The ferric ion Fe?* with a valence of +3 has a smaller ionic radius of 0.69 À. This is not surprising, since the Fe'* has one less electron orbiting the nucleus. Fe?* in the high-spin state has an ionic radius of 0.92 À compared to 0.75 À for Fe?* in the low-spin state. Finally, Fe'* surrounded by six anions (coordination number of 6) has a larger ionic radius (0.92 À) than Fe?“ surrounded by only four anions (CN = 4, r= 0.77). tonic Packing Most of the ionic ceramic crystal structures consist of a three-dimensional stacking of the anions with the smaller cations fitting into interstitial po- sitions. The size of the interstitial position varies depending on the mode of stacking. Eight spheres stacked to form a simple cube have a relatively large interstitial position in the center. For example, in a body-centered cubic metal this position is filled by an atom of the same size as the corner atoms, resulting in a structure that is not quite close-packed. The atom or ion in the center has a coordination number of 8. Six spheres stacked to form an octahedron have a smaller interstitial position (CN of 6), and four spheres stacked to form a tetrahedron have a still smaller interstitial po- sition (CN of 4). The cubic close-packed and hexagonal close-packed struc- tures (discussed later in this chapter) both have interstitial positions of these two types. They are clearly visible in Fig. 2.5, which shows a cutaway of a face-centered cubic (FCC) structure. The larger octahedral sites are visible from the side view and the smaller tetrahedral sites are visible from the diagonal (cutaway) view. There is one octahedral site at the center of the FCC unit cell and one at the midspan of each of the 12 edges. Only ions of an appropriate size range are stable in each interstitial position. An ion that is too small to fill the site completely is not stable. One that closely filis the interstitial site or one that is slightly larger than the site is stable. This was illustrated previously in Fig. 1.4. Note that the ion larger than the interstitial site causes adjacent ions to deviate from close packing. One can calculate using simple geometry the size of a sphere that fits exactly into each interstitial position. This represents the minimum size that is stable. The maximum size is approximately the size of the next larger interstitial position. These size ranges based on the radius ratio of the interstitial cation to the host anion polyhedron are listed in Table 2.1. Ratios smaller than 0.225 typically involve independent tetrahedra or octahedra bonded together by sharing of a corner or edge and result in coordination numbers of 2 or 3. 40 Chapter 2 Figure 2.5 Cutaway of a face-centered cubic structure showing the larger octa- hedral interstitial holes visible from the side view and the smaller tetrahedral interstitial holes visible from the diagonal view. (From Ref. 4, p. 49.) The critical-radius ratios in Table 2.1 are useful in predicting the types of structures that will be formed by various ion combinations, However, as we discussed in Chap. 1, atoms and ions are not really hard spheres. Anmions with high atomic number are large and can be easily deformed, especially by a cation with a high charge. In addition, most materials do not have pure ionic bonding, but have some covalent contribution that Table 2.1 Critical Radius Ratios for Various Coordination Numbers for Cations in Interstitial Positions in Anion Polyhedra Coordination Position Minimum ratio number of anions of ionic radii 4 Corners of tetrahedron 0.225 6 Corners of octahedron 0.414 8 Corners of cube 0.732 Crystal Chemistry and Specific Crystal Structures ai may affect the coordination number. Thus, ions fit into a greater range of coordination number than is indicated by predictions based on the critical- radius ratios of Table 2.1. Table 2.2 identifies deviations that have been observed in ienic bonding between various cations and oxygen. Some cat- ions (AP+, Nat, Ca't, and K*) have been experimentally observed in several different coordinations within ceramic structures. Effect of Charge So far we have only considered the effect of the relative size of the cations and anions on their stacking into a structure. The charge on each ion is equally important. Electrical neutrality is required at the unit cell level as well as throughout the crystal structure. The charge of each cation and anion must be mutually balanced by the combined charge of the surround- ing ions of the opposite charge. This places a limitation on the positions of the ions in the structure. The portion of the charge of each cation is equal to the valence of the cation Vc divided by the coordination number of the cation (CN)c. Like- wise, the portion of the charge of each anion is equal to the valence of the Table 2.2 Coordination Number and Bond Strength of Various Cations with Oxygen Predicted Observed Strength of Radius coordination coordination electrostatic Jon (CN = 4) number number bond B' 0.16 3 3,4 lor3/4 Be? 0.25 4 4 1/72 Lit 0.53 6 4 1/4 Sit 0.29 4 4,6 k AP 0.38 4 4,5,6 3/4 or 1/2 Ge't 0.39 4 4,6 Jor 2/3 Mg'- 0.51 6 6 13 Na* 0.99 6 4,6,8 1/6 Tire 0.44 6 6 2/3 Sc'* 0.52 6 6 112 Cr 0.51 6 6,8 23 or 1/2 Ca? 0.71 6,8 6,7,8,9 1/4 Ce'!* 0.57 6 8 112 Kk* 0.99 8,12 6,7,8,9,10, 12 119 Cs 1.21 12 12 1/12 Source: Ref. 5. 44 Chapter 2 Ordering As the name implies, ordering involves positioning of the host and sub- stitution ions in an ordered, repetitious pattern rather than in a random pattern. This results in a difference between the atom sites of the host and substitution ions, which leads to distortions in the structure or to a change in the dimensions of the unit cell. These result in a change in the behavior of the material. Ordering often results when the size of the substitute ion is significantly different from the size of the host ion. The following are a couple of examples. Example 2.3 Mn?* and Fe?* have ionic radii of 0.97 and 0.92 À such that they distribute randomly in (Mn,Fe)CO, and result in a complete solid solution between MnCO, and FeCO;,. CaCO, and MgCO; have the same structure as MnCO,, FeCO, and (Mn,FejCO;. However, when Ca?* sub- stitutes in MgCO, or Mg?* substitutes in CaCO;, an ordered structure of composition CaMg(CO,), results because of the difference in ionic radii of Cat (r = 1.14 À) and Mg?* (r = 0.86 À). The new structure has alter- nating layers with Ca?* and Mg”* ions. In the Ca layer the CaO interatomic distance is 2.390 À and in the Mg layer the Mg-O distance is 2.095 À [3]. Example 2.4 The ordering in CaMg(CO;); is only in the octahedral lattice site and results in two distinct octahedral crystallographic positions. In some structures, ordering can occur on tetrahedral lattice sites or on both tetrahedral and octahedral sites. For example, in y-Li;ZnMn;0, one Li* ion orders with the Znº* on tetrahedal sites while the other Li* ion orders with the three Mnº* ions on octahedral sites [3]. In this and many other cuses the ordering is induced by the charge difference between the ions. Nonstoichiometry The second type of derivative structure involves stoichiometry and the presence of either lattice vacancies or excess interstitial ions, Stoichiometry refers to the composition of a material and the positioning of the atoms within the crystallographic structure. A stoichiometric ceramic has all lat- tice positions filled according to the ideal structure and composition. A nonstoichiometric ceramic has a deficiency of either cations or anions ac- commodated by vacancies in adjacent positions of oppositely charged ions to allow for charge balance. Wistite has the nonstoichiometric composition Fe, osO [4]. It contains vacancies in some of the cation positions. Similarly, Ca-doped ZrO, (Zr,..Ca,O,.,) contains oxygen vacancies and Zn,.,O has interstitial cations. All of these are types of defect structures and have interesting electrical properties. Crystal Chemistry and Specific Crystal Structures 45 Stuffing The third type of derivative structure is the stuffed derivative, It involves substitution of a lower-valence ion for a higher-valence ion and “stuffing” of an additional ion into the structure to balance the charge. Many of the silicate compositions are stuffed derivatives of forms of SiO;. SiO, consists of SiO, tetrahedra linked into a three-dimensional network structure by sharing of corners. The structure has relatively large open spaces between the tetrahedra. Some of the Si'* ions can be replaced by AP* ions, which are of similar ionic radius. For each of the Si** replaced, the equivalent of an ion with +1 charge is stuffed into open spaces in the structure to obtain charge balance. Typical ions that are stuffed into the structure in- clude Na*, K*, NH£, Ba'*, Ca?t, and Sr'*. In addition to SiO,, a variety of other tetrahedral coordinations can be involved: GeO,, GaO,. AlO,, ZnO,, MgO,, LiQ,, SO,, PO,, BeQO,, BeF,, FeO,, and LiF,. Frequently two different tetrahedra occur in a single structure. In some cases this results in ordering as in KAISiO, or NH,LISO,. In other cases the substi- tution positions are random (disordered), such as BaMgSiO, [3]. The following are additional examples of stufled derivatives: BaAI;O,, BaFe,0O,, CaALO,, NaAISIO,, BaZnGeO,, KLiBeF,, PbGa,0,. CsBePO,, and BaSrFe,O,. Distortion The final derivative structure involves distortion of the original structure. This typically results when ions are substituted that have a significant dif- ference in ionic radius or valence compared to the host ions. The sizes of the tetrahedral or octahedral structural units for the host ion and the substituted ion are different and a more-complex, less-symmetrical struc- ture results. Since separate polyhedral structural units (coordination poly- hedron) are bonded together to form the overall structure, distortions frequently occur in each polyhedron; that is, cation-anion interatomic distances are different for the different ions in the polyhedron. Ordering often accompanies the distortions. 2.3 METALLIC AND CERAMIC CRYSTAL STRUCTURES We now have enough background information on crystal chemistry and on crystal structure notation to begin our review of crystal structures. We will start with the simple metallic structures and then proceed to the ceramic structures. Simple metallic structures are based on single-sized atoms in a close-packed arrangement. Many of the structures consist of close-packed 46 Chapter 2 arrangements of anions with one or more types of cations positioned in octahedral or tetrahedral sites. These structures tend to be dominated by ionic bonding. Other ceramic structures consist of isolated tetrahedra and/ or octahedra that are bonded together by sharing of corners or edges. These are not close-packed and have a higher degree of directional covalent characteristics. Metallic Crystal Structures As we discussed earlier, metallic bonding involves atoms ofa single element immersed in a cloud of free electrons. This forces the atoms into a uniform three-dimensional array with each atom exposed to identical surroundings. Most pure metals have a structure that is face-centered cubic (FCC), body- centered cubic (BCC), or hexagonal close-packed (HCP). The face-centered cubic structure is common among metals (copper, nickel, aluminum, lead, silver). As shown in Fig. 2.6, it consists of atoms at each corner of a cube and at the center of each cube face. Each unit cell contains four atoms. Each atom is surrounded by 12 identical atoms and thus has à coordination number of 12. A CN of 12 is the tightest packing possible for atoms ail of a single size and results in a close-packed structure with a packing factor of 0.74. The packing factor (PF) is deter- mined by using the hard-ball model of a unit cell in Fig. 2.6a. The PF equals the volume of the balls divided by the volume of the total unit cell. As we know from prior discussions, an atom is not a hard ball but mostly open space. However, the electrons orbiting around the nucleus do form a sphere of influence that for the purposes of crystal structure discussions atari) 1orrVD PF = = (3K6413) a a 22 Sasg2 ns £ erero, Di 4 A Segs ADA «AA ly! ly | E (a) tb) te) Figure 2.6 Representations of the face-centered cubic structure. (a) Hard-ball model showing that each unit cell contains a total of four atoms in the closest possible packing (each atom with 12 adjacent atoms), (b) schematic showing the location of atom centers and that each atom is in an equivalent geometric position, and (c) hard-ball model showing the repeating three-dimensional structure. (From Ref. 6, pp. 59, 60.) Crystal Chemistry and Specific Crystal Structures 49 Ceramic Structures with a Single Element Ceramic structures with a single element are rare. The major one is the [diamond] structure. The structure consists of C atoms with each €C co- valently sharing one electron with each of four surrounding C atoms. Thus, each C atom is either at the center of a tetrahedron or at the corner of a tetrahedron. The lattice positions are equivalent. The coordination number is 4 and the coordination formula is CI. Adjacent C atoms are bonded together by very strong covalent forces. This strong bonding results in a high elastic modulus, the highest hardness of any naturally occurring ma- terial, and extremely high temperature stability (over 3700ºC [6700ºF] in a nonoxidizing atmosphere). Binary Ceramic Structures Binary refers to a structure with two distinct atom sites, one typically for an anion and one for a cation. As discussed previously under crystal chem- istry concepts, a variety of elements can substitute in solid solution on these sites without a change in structure. Thus the term binary identifies the number of sites rather than chemical elements. Table 2.4 summarizes im- portant binary structures and some of their characteristics. [Rock Satt] Structure Atx The [rock sait] structure is named for the mineral NaCl. It is also referred to as the [NaCl] structure. The arrangement of ions is illustrated in Fig. 2.10. The structure is cubic with the anions arranged in cubic close packing with all the interstitial octahedral sites occupied by the cations. As is easily seen in Fig. 2.10, the structure consists of alternating cations and anions along each of the three unit cell axes ([100], [010], and [001] crystal di- rections). KCI, LiF, KBr, MgO, CaO, SrO, BaO, CdO, VO, MnO, FeO, CoO, NiQ, and the alkaline earth sulfides all have the [rock salt] structure. The atomic bonding is largely ionic, especially for monovalent ion com- positions. [Nickel Arsenide) Structure A!tXtI The [nickel arsenide] structure involves the same size range of cations as the [NaCI] structure, except that the anions are in an HCP stacking ar- rangement rather than an FCC arrangement. Both the anions and the cations are in sixfold coordination, so the general coordination formula is AISXIS, NiAs, FeS, FeSe, and CoSe have the [NiAs] structure. os Table 2.4 Summary of Binary Ceramic Structures Structure General Coordination Fraction cation name formula formula Anion packing sites occupied Examples [Rock salt] AX APIXIS! Cubic close-packed All octahedral NaCl, KCI, LiF, MgO, VO, NiO [Cesium chloride] AX AMX Simple cubic AM cubic Cs€I, CsBr, Csl [Zinc blende] AX AMIXUI Cubic close-packed 1/2 Tetrahedral ZnS, BeO, j-Si€ [Wirtzite] AX AMI! Hexagonal close-packed 1/2 Tetrahedral ZnS, ZnO, a-SiC, BeO. CdS [Nickel arsenide] AX AlixIS Hexagonal close-packed All octahedra! NiAs, FeS, FeSe, CoSe [Fluorite] AX; Att Simple cubie 1/2 Cubie CaF,, ThO.. CeO.. UO:, ZrO:. HO. [Rutile] AX: AtIxçt Distorted close-packed 1/2 Octahedral TiO,, GO», SnO;, PbO.. VO.. NbO, Sílica types AX: ABXE Comnected tetrahedra — SiO,. GeO, [Amifluorite] AX ABIX Cubic close-packed Alltetrahedral LO, NãO, sulfides [Corundum] AX: At Hexagonal close-packed 2/3 Octahedral ALO, FeiO« CrO,. V;O,. Ga;O,, RhO, Crystal Chemistry and Specific Crystal Structures s1 Na N ta) (o) Figure 2.10 [Rock salt] crystal structure. (From Ref. 4, p. 42.) [Cesium Chloride) Structure APIxBI The [CsCI] structure involves cations that are too large to fit into the octahedral interstitial site. They fit into the larger cavity at the center of a simple cube with the anions at each corner. This is similar to the BCC structure of a metal. Compositions with the [CsCI] structure include CsCI, CsBr, and Csl, [Zinc Blende) and [Wurtzite] Structures AlIXHI Cations too small to be stable in octahedral sites fit into the smaller tetra- hedral interstitia! position and form either the [zinc blende) structure or the [wurtzite] structure. The anions in the [zinc blende] structure are in an FCC arrangement. Those in the [wurtzite] structure are HCP. Note in Table 2.4 that some substances (ZnS and SiC) are listed as having both structures. These are referred to as polymorphic forms. The cubic structure for SiC and ZnsS is stable at low temperatures and the hexagonal structure is stable at high temperatures. The [zinc blende] and [wurtzite] structures are illustrated schematically in Fig. 2.11. Note that the [zinc blende) structure is similar to that of diamond, with the cations and anions alternating in the C atom positions.  (b) Figure 2.13 Illustrations of the [rutile] structure. (a) The tetragonal unit cell of ViO; showing the two different Ti-O bond lengths, and (b) the edge and corner sharing of octahedra to produce a three-dimensional structure. (From Ref. 3, p. 112.) 54  Crystal Chemistry and Specific Crystal Structures 55 the C-direction of the structure. These share corners with adjacent strings of octahedra to form a three-dimensional framework structure. The Silica Structures ANIXBI The silica structures involve small cations with a charge of 4+ . SiO, is the model system. The radius ratio is approximately 0.33, which indicates that tetrahedral coordination is stable for the Si'* cation. The coordination of the anion is determined by: (CNJ = |VAKCN) Ve = (DA = 2 To accommodate this, the Si'* is a1 the center of a tetrahedron of O” anions. Each O? at the corner of each tetrahedron is shared with an adjacent tetrahedron. This results in a directional structure that is not close- packed and that has a combination of ionic and covalent character. SiO; has a wide variety of structures at various temperatures and pres- sures. The high-temperature polymorphs consist of different arrangements of undistorted SiQ, tetrahedra linked together by a sharing of corners. The lower-temperature polymorphs have similar structures but are distorted. Figure 2.14 compares unit cells of the high-temperature cristobalite and tridymite polymorphs of SiO,. A third polymorph of SiO, is quartz. which constitutes a significant percentage of the earth's crust. A schematic illus- trating the uniformity in the high-temperature form of quartz and the distortion in the low-temperature form is shown in Fig. 2.15. The SiO, tetrahedron is the building block of an extensive variety of Cristobalite Tridymite Figure 2.14 Comparison of the high-temperature structures of the cristobalite and tridymite structures of SiO,. (From Ref. 6, p. 218.) 56 Chapter 2 a =» (O 3» “e o es 24 (a) tb) Figure 2.15 Schematic comparing the structure of quartz at (a) high temperature, and (b) low temperature. (From Ref. 4, p. 74.) derivative structures. Many of these structures are discussed later in this chapter under the section on ternary structures. However, at this time it is important that we visualize the relationship of these more complex struc- tures to the silica structures. Figure 2.16 shows some of the ways that SiO, tetrahedra can be linked to form derivative structures. Note that in SiO3”. the tetrahedra are independent and have four bond positions avail- able to link up with cations or other coordination polyhedra. Note also that Si;O$” involves the sharing of one corner and that Si/08", ShOk . (SI0,);" and (SLO ty!” involve the sharing of two corners to yield ring or chain structures. Sheet structures are also possible by linking of (Si-0:), layers of SiO, tetrahedra to AIO(OH), octahedral layers. This occurs, for example, for the important clay mineral kaclinite, Al(Si:0:)(OH),. Finally, additional three-dimensional framework struc- tures are possible by substitution of Al"* or other small cations for Si'* and stufling with other cations to achieve charge neutrality, H should now be apparent to the reader that a variety of derivative structures and hundreds of compositions, cach with different properties, are possible; the important point is that each of these is based upon rel- atively few simple baseline structures. [Corundum] Structure ABIXPI A final binary structure of major importance is the [corundum] structure, ABIXGN, Aluminum oxide (ALO;) is the most important material with this Table 2.5 Summary of Some Ternary Structures Structure General Coordination name name formuta Examples [Spinel) AB;X, AMB FeAbLO,, ZnAbO,, MpALO, [Inverse spinel] ABX, BMADIBRIXIA FeMgFeO,, Fe;O,. MgTiMgO, [Phenacite] ABX, AMB! Be-SiO,, Zn-SÃO,. f-SiN,. LiiMoO, 18-KSOS] ABX, AU AMBUIKIIKEI Rb.So,. K:WS,. Ba:TiS,. NaYSiO, fOlivine) ABX, ABI Mg-SiO,, FesSiO,, ALBeO,. Mg.SnSe, fBarite] ABX, ANIBII BaSO,. KMnO,. CsBeF,, PbCrO,. BaFeO, fZircon] ABX, APIBMIXÇI ZrSiO, YVO, TaBO,, CaBeF,. BiVO, [Ordered SiO.] ABX, AMBIX! AIPO, AIAsO,, FePO, |Calcite] ABX; AMB CaCO:. MgCO:. FeCO,. MTO, [Emenite] ABX: AMIB! FeTiO,, NiTiO,, CoTIO. [Perovskite) ABX; ABI BaTIO,. CaTIO,, SETIO:. SrZrO.. SrSnO:. SrHTO. SaInpanss JEIsà Io DyDadS pus Asian Jeso so Chapter 2 Octahedra! interstice (32 per unit cell) (D Oxygen Qdo 2 cation in octahedral site Tetahedral nterstice (O Cation in tetranadra! site (64 per unit cell) Figure 2,17 Relative atom positions in the normal [spinel) structure. (From A. R. von Hippei, Dielectrics and Waves, Wiley, New York, 1954.) [Phenacite] Structure AbIBHIxIM! The [phenacite] structure is named after the naturally occurring mineral phenacite, BesSiO,. Both the Be'* and Si'* ions are small and fit into fourfold coordination with an oxygen ion at each corner of a tetrahedron, The tetrahedra are linked together into a three-dimensional network struc- ture by sharing of each corner. The resulting structure is not close-packed and has a significant degree of directional covalent character. The unit cell has a rhombohedral symmetry with a cylindrical channel approximately 2 À in diameter aligned parallel to the c axis. Some compositions with the phenacite structure include ZnSiO,, Li;MOO,, LiSeO,, Zn,Ge0O,, and LiBeF.. Table 2,6 Examples of Compositions with the [Spinel] or Closely Related Structure MEALO, MnALO, ZnALO, FeALO, FeO, CoFe.O, MnFe,O, MgFe;O, Mo-GeO, Fe,GeO, Zn,Ge0, Ni,Ge0, Fe.VO, ZnVO, CoTiO, — Me-TiO, AgMoO, NaWO, Zn.SnO, Li;MoO, MgCr:;O, LIALO, LiTi;O, Zn;Sb.O,, LiMeVO, LiCrGeoO, ZnTiO, LiCoTi O; Li,NiF, Fe OsFa« Cu,FeO,F ALON ZnCr8, MnALS, Y,MpSe, CuCrTe, Crystal Chemistry and Specific Crystal Structures o Be-SiO, doped with Mn?* ions was one of the early phosphor materials used for home lighting. ZnSiO, (willenite) doped with Mn?* ions also has strong phosphorescence and was once widely used as a cathodoluminescent material. [B-Silicon Nitride] Structure AVIBVIXYI The [4-Si,N4] structure is essentially the same as the [phenacite) structure, except the unit cell is more compact and of a hexagonal symmetry. The cell dimensions of $-Si,N, are a = 7.607 À and c = 2.911 À compared to BesSiO, with a = 12.472 À and c = 8.252 À. This is because all the Si'* cations are in equivalent crystallographic positions, whereas there are three distinct positions in Be;SiO, (two for the Be?* and one for the Si't). The B-Si:N, has strong covalent bonding. 6-SiNy is an important material for advanced structural applications such as bearings, heat engine components, and metal-cutting tools. It has been determined that considerable A??* and O?- can substitute into f- SiiN, (via solid solution of AbO;N) and still retain the [4-Si;N,] structure. This has led to a series of compositions called sialons with a wide range of properties. [Olivine] Structure APIBNIXI The [olivine] structure is named after the mineral olivine, (Mg, Fe)-SiO,, which is a solid solution between the minerals forsterite (MgSiO,) and fayalite (Fe,SiO,). The structure consists of a slightly distorted, hexagonal, close-packed anion arrangement with the smaller “B” cations positioned in one-eighth of the tetrahedral interstitial sites and the larger “A” cations in half of the octahedral sites. Fe,SiO, has been carefully studied and can be used as an example to help visualize the [olivine] structure. Independent SiO, tetrahedra share corners and edges with FeO, octahedra. This results in distortions of both polyhedra such that the Fe?t have two distinct positions within the struc- ture. One position has two oxygen ions at an interatomic distance of 2.122 À, two at 2.127 À, and two at 2.226 À. The other position has two at 2.088 À, one at 2.126 À, one at 2.236 À, and two at 2.289 À. The tetrahedra have Si-O spacings of one at 1.634 À, two at 1.630 À, and one at 1.649 À. The arrangement of the atoms in the [olivine] structure is illustrated in Fig. 2.18. Many ternary structures are distorted. Such distortions are nec- essary to accommodate the varieties of ion sizes and charges involved. Each size and charge combination results in a slightly different degree or type of distortion. Further modifications result when additional ions are 64 Chapter 2 fore, we provide only the brief summary in Table 2.7 of selected structures and compositions. The major importance of the ABX, compositions is as ores for Ba, W, Zr. Th, Y, and the rare earths (lanthanide series: La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er. Tm, Yb, and Lu). Barite (BaSO,) is a major source of barium. monazite (LnPO,)* for the rare earth elements, zircon (ZrSiO,) for the metal zirconium and the ceramic ZrO;, scheelite (CaWO,) and wolframite (Fes sMns WO.) for tungsten metal, and thorite (ThSIO,) for thorium. Zircon is also used for some ceramics technology applications because it has a low coefficient of thermal expansion. In addition, some [zircon] and [scheelite] compositions are fluorescent. The [zircon] com- position YVO, doped with Eu is a red phosphor once used for color tele- vision, and the [scheelite] composition, CaWOs, doped with Nd, is a laser host. ABX, Structures A variety of materials of extreme importance to modern technology have ABX, structures. These are summarized in Table 2.8. The most important are the [perovskite] structure compositions with ferroelectric properties and with high dielectric constant. Compositions such as BaTiO, and PbZra ss Tio sO; are used for capacitors, ferroelectrics, and piezoelectric transducers. Compositions have been altered by crystal chemical substi- tutions to provide a wide range of properties optimized for specific appli- cations. Other [perovskite] structure compositions of importance include solid solutions between KTaO, and KNbO,, which are used as electro- optic modulators for lasers. Other laser modulator materials are LINDO; and LiTaO;, which have [ilmenite]-related structures. These high-temper- ature ferroelectric materials are also used as piezoelectric substrates, as optical waveguides, and as a holographic-storage medium. Other important ABX; compositions include CaCO, of the [calcite] structure and the rare earth LnFeO, ferrites. Transparent single-crystal calcite is used for Nícol prisms in the polarizing microscope. Compositions in the LnFeO, family are used for magnetic bubble domain devices. [Catcite] Structure AlIBEIXYI The [calcite] structure involves a large cation such as Ca, Mg, Fe, or Mn in the “A” position and a very small cation limited to C**, B** or Nº* in the “B” position. The CaCO, [calcite] composition has been studied in *Ln refers to a variety of substitutions of the lanthanide series rare earth elements. Table 2.8 Summary of Some ABX, Structures Structure name [Caleite] [Aragonite] Ilmenite] [Perovskite] Hexagonal structures (several types) [Pyroxenes] and related structures Source: After Ret. 3. p. 153. Simplified cogrdination formula Cancro, CaMCHO, FetTMO, SHIT, Bal MIO, Mensiio, Special structural features Highly anisotropic, high birefringence Denser packing of COF and Ca't than in [calcite] Example of face-shared octahedra Close-packed structure with corner-shared octahedra Close-packed structure with face-shared octahedra Sharing of two edges of tetrahedra to form single chains Compositional occurrence Trivalent borates, divalent carbonates and alkali nitrates Divalent carbonates and lanthanide borates with larger cations A”B''O, with both A?* and Bº smaller or intermediate-sized cations A"BºO, and A'B”F, with large A and medium-sized B cation As for [Perovskite] but with slightly smaller B cation Smail B cations. medium A cations 66 Chapter 2 detail and is a good example. The structure is illustrated in Fig. 2.19. Each C'* is surrounded by three O?” anions, all in the same plane at a C-O interatomic distance of 1.283 À. Each of these CO, groups has six Ca?* neighbors with a Ca-OQ interatomic distance of 2.36 À. This results in a rhombohedral unit cell that is much longer in one direction than in other directions, resulting in highly anisotropic properties (different properties in different directions). For example, when calcite is heated, it has very high thermal expansion (25 x 10-*/ºC) parallel to the c axis but a negative thermal expansion (—6 x 107*/ºC) perpendicular to the c axis. The an- isotropy is so high that even light is affected when passing through a trans- parent crystal of calcite, When looking through a calcite crystal held in the proper orientation, a double image is seen. A variety of compositions have the [calcite] structure. Some examples include MgCO;, CuCO;, FeCO;, MnCO;, FeBO;, VBO;, TIBO,, CrBO,, LiINO,, and NaNO.. u = upperlayer | = lower layer ec tb) QD ca Oo Figure 2.19 Illustrations of the [calcite] structure. (a) Side view of elongated rhombohedral cell, and (b) projected top view. (º ASM International.) Crystal Chemistry and Specific Crystal Structures 69 Other Structures A few additional structure types need to be mentioned but will not be discussed at this time. These include the [gamet] structure ANBISCHIXIS, the [pyrochlore] structure ABIB$IXEIXIS!, and the [pseudobrookite] struc- ture ALSIBIX,. Carbide and Nitride Structures The structures discussed so far have involved ionic, covalent, or a com- bination of ionic and covalent bonding. Some compositions form structures where the bonding is intermediate between covalent and metallic. This is the case for the transition metal carbides. The large metal atoms form a close-packed structure with the small C ions present in interstitial positions. These materials have some characteristics typical of ceramics and some more typical of metals. Combinations of elements such as Si and € with similar electronegativity have covalent bonds. Nitride structures are similar to carbide structures, except the metal- nitrogen bond is usually less metallic than the metal-carbon bond. REFERENCES 1. J. F. Shackelford, Introduction to Materials Science for Engineers, Macmillan, New York, 1985. 2. D.W. Richerson, Lesson 2: Atomic Bonding and Crystal Structure, introduc- tion to Modern Ceramics, ASM Materials Engineering Institute Course &56, 1990. 3. O.MullerandR. Roy. The Major Ternary Structural Families, Springer-Verlag, Berlin, 1974. 4. W. D. Kingery et al., Introduction to Ceramics, 2nd ed., Wiley, New York. 1976. 5. L. Pauling, Nature of the Chemical Bond, 3rd ed.. Cornell University Press. Ithaca, New York, 1969. 6. L.H. Van Vlack, Elements of Materials Science, 2nd ed., Addison-Wesley, Reading, Mass., 1964. 7. R.C. Evans, An Introduction of Crystal Chemistry, 2nd ed., Cambridge Uni- versity Press, 1964. 8. RW G. Wyckoff, ed.. Crystal Structures, 2nd ed., Vols. 1-5, Wiley, New York, 1963-1971, 9. B. A. Rogers. The Nature of Metals, ASM International, Ohio, 1951. m” Chapter 2 PROBLEMS 2.1 The anion in a binary structure has a valence of — 2 and a coordination number of 4. The cation has a valence of + 4, What is the coordination number of the cation? 2.2 What is the notation for the direction along the c axis of a tetragona! crystal? 2.3 The close-packed plane in a face-centered cubic structure is along the cube diagonal. What are the Miller indices for this plane? 2.4 Which of the following does not have the [perovskite] structure? SrTIO: BaLiF, MgTio, LaAIO; 2.5 Which composition does nor have the [spinel] or closely related struc- ture? Na,WoO, Fe;O, ZrS10, MgALO, 2.6 NaZr(PO,) is the type material for the [NZP] structure. Name sev- eral ions that are likely substitutes for Na in the structure. Name the most likely ion to substitute for P in the tetrahedral position in the structure, 2.7 Copper, nickel, and gold have a face-centered cubic close-packed structure (i.e., unit cubic structure with atoms at the corners and center of the faces of a cube). Assuming that each atom can be modeled by a hard sphere, how many nearest neighbors does each atom have in the structure? Calculate the percent open space present in such a close-packed structure. The remaining space is filled by the spheres and is referred to as the atomic packing factor. 2.8 Draw the following directions for a cubic crystal: [010], [110], [221], [021]. 2.9 Drawthe following planes for a cubic crystal: (001), (111), (120), (101). 3 Phase Equilibria and Phase Equilibrium Diagrams Ceramic materials are generally not pure. They contain impurities or ad- ditions that result in solid solution, noncrystalline phases. multiple crys- talline phases, or mixed crystalline and noncrystalline phases. The nature and distribution of these phases have a strong influence on the properties of the ceramic material, as well as on the fabrication parameters necessary to produce the ceramic. Therefore, before we can progress to a discussion of properties or processing in later chapters, we need to explore ways to estimate the nature and distribution of phases. An understanding of equi- librium and nonequilibrium and phase equilibrium diagrams is a good starting point. 3.1 PHASE EQUILIBRIUM DIAGRAMS A phase equilibrium diagram is a graphical presentation of data that gives considerable information about a single compound (such as SiO,, ALO:, or MgO) or the nature of interactions between more than one compound [1-3]. The following list indicates some of the information that can be read directly from the diagram: 1. Melting temperature of each pure compound 2. The degree of reduction in melting temperature as two or more compounds are mixed 3. The interaction of two compounds (such as SiO, plus ALO;) to form a third compound (3ALO, - 2Si0,. mullite) 4. The presence and degree of solid solution nu 74 Chapter 3 Pressure Crystalline Modification B Crystaltine Modification A Temperature Figure 3.1 Schematic illustrating the phase relations in a one-component system. (From Ref. 5. p. 9.) are also in equilibrium at point 8 (polymorph B, liquid plus vapor). Thus, atbothAandB F=3-P=3-3=õb0 BecauseF =õ0,4andB are referred to as invariant or triple points. Any change in pressure or tem- perature will cause the disappearance of one phase, Curves F-A and A-B are sublimation curves for polymorphs A and B and represent the equilibrium between a solid and vapor. Curve B-C is the vapor pressure curve for the liquid and represents the eguilibrium between the liquid and vapor phases. A-D is the phase transformation (transition) curve between the A and B polymorphs. B-E is the fusion or melting curve where polymorph B and liquid are in equilibrium. For all points along these curves, two phases coexist. Thus, F = 3 — 2 = 1 for these boundary lines. This is referred to as univariant equilibrium and means that pressure and temperature are dependent on each other. The specification of one will automatically fix the other. The regions between boundary lines contain a single phase and are known as fields of stability. É = 3 — | = 2 in these regions. This is re- Pressure Phase Equilibria and Phase Equilibrium Diagrams 7 ferred to as bivariant equilibrium. Within a specific region, the temperature and pressure can be varied independently without a phase change. Other information is available from a single-component diagram. Let us refer again to Fig. 3.1. Point Cis called the critical point, the temperature above which the gas cannot be liquified no matter how high the pressure. The slope of line B-E provides information about the relative density of the liquid and the solid, For most materials, the slope of the curve is positive such that the density of the solid is higher than that of the liquid. Exceptions are HO, Bi, and Sb. Important exceptions in ceramic systems are the glasses of lithium aluminosilicate (beta-spodumene) and magnesium alu- minosilicate (cordierite), which are more dense than the crystalline phases. Figure 3.2a shows the estimated equilibrium phases for SiO,. However, because the rates of change between the SiO; phases are very slow. meta- stable phases are generally present in real materials and often dominate the behavior. The retention of metastable phases is illustrated in Fig. 3.2b. Two-Component Systems A two-component system is referred to as a binary system. Addition of the second component results in a change in the equilibrium of the system and a change in the properties of the resulting materials. It also results in 573ºC aro'c 1470ºC 1713ºC (I0B3CFIN, (1598*F) (2878/F) 2 (3115ºF) | tato £. - 101 kP = ( a, 2 Ê E fé 2 Ê 2 o 8-Cristobalite | & ã g g a-Quart a Ê várte | a BoTridymite Vapor 8-Quartz Temperature Temperature (a) to) Figure 3.2 Comparison of the estimated eguilibrium and metastable phases of SiO». (a) Equilibrium diagram, and (b) diagram including metastable phases. (From W. D. Kingery et al.. Introduction to Ceramics, 2nd ed. p. 274, 275, Wiley. New York, 1976.) 76 Chapter 3 greater complexity and the need for a three-dimensional (p-T-x) diagram to illustrate the equilibrium characteristics for the three variables pressure (p). temperature (7), and composition (x). Figure 3.3 shows a portion of such a diagram with pressure, temperature, and composition as the three orthogonal axes. To the left is the single-component p-T eguilibrium dia- gram for component A and to the right is the similar diagram for component B. In a complete diagram a similar set of "“pseudo-one-component” sub- limation, melting, and vaporization curves would be drawn for each com- position of A + B. The loci of these are curved surfaces that require a three-dimensional model. The general shape of the curved surfaces can be visualized by drawing a plane through the diagram and looking at the intersection of the curved surfaces with the plane. This is illustrated for a simple binary eutectic system [10, 11] (discussed later in this chapter) in Fig. 3.4. The plane is drawn perpendicular to the pressure axis at a constant pressure of 1 atm and parallel to the temperature and composition axes. Only the intersection of the plane with the melting curve is shown. Note that addition of A to Bor Bto A results in a reduction in the melting temperature. For many ceramic systems the effect of pressure is negligible because Temperature Figure 3.3 Schematic illustrating the need for a three-dimensional model to dia- gram the equilibrium of a two-component system as a function of pressure, tem- perature, and composition. (O ASM International.) Phase Equilibria and Phase Equilibrium Diagrams 7 Ta Liquid + A Liguid + & Temperature A+B l , / ! l L 4 j o 10 20 30 40 50 60 70 80 90 100B A100 90 80 70 60 50 40 30 20 40 O Composition Figure 3.5 Schematic of a simple condensed binary eutectic diagram. change in phases. Along the liquidus lines TA — T. and To — T.. two phases coexist, so E = 3 — 2 = 1. The system at each point along these lines is univariant so that temperature and composition are dependent upon each other. A specification of one automatically fixes the other. Three phases (liquid, A, and B) coexist in equilibrium at point 7. This point is called the binary eutectic. Below the eutectic temperature. no liquid can exist in the system under equilibrium. The horizontal line on which T. lies is called the solidus. F = 3 — 3 = O at the binary eutectic. so T. is an invariant point. Any change in temperature or composition results in the loss of one or more phases. For example, an increase in temperature without a change in composition results in the melting of all A and B to form a homogeneous liquid. Conversely, a decrease in tem- perature results in freezing of the liquid by crystallization of a mixture of solid A and B. Similarly, changes in composition to the right of T, results in complete melting of compound A and crystallization of a portion of the compound B, Changes in composition to the left of T, result in complete melting of B and crystallization of a portion of A. These changes in phases resulting from changes in temperature or composition are clearly ilustrated on the binary eutectic diagram. Even the precise percentages of liquid and 80 Chapter 3 solid present at a specific temperature and composition can be calculated. The methods of calculation are discussed later in this chapter. Now let us take a closer look at the binary eutectic system (and two- component systems in general) and explore the significance of the various points and lines on the diagram. First, as we have observed before, addition of a second component causes a reduction in the melting temperature. The steeper the slope of the liguidus line, the greater the effect of the second component on reducing the melting temperature of the first. In Fig. 3.5 the addition of A to B has a greater effect than B to A. A 30% addition of A to B reduces the melting temperature by over 50%, whereas a 30% addition of B to A results in about a 15% reduction. More important though, even a fraction of a percent addition of a second component leads to the presence of liquid at a temperature (the eutectic temperature T.). well below the temperature at which liquid would occur for a pure single component (TA or To). In the case of component A in Fig. 3.5 a small amount of B results in the presence of a liquid at approximately 35% of the melting temperature of pure A. Although the amount of liquid is small for small additions of the second component, the effects on the densification characteristics during fabrication and on the properties of the resulting material can be significant. These effects are discussed in detail in later chapters, especially Chapters 8 and 11. Figure 3.6 gives an example of an actual binary eutectic diagram. This diagram is for the system NaCI-NaF. Note from the diagram that NaCl melts congruently at 800.5ºC (1472.9ºF), NaF melts congruently at 994.5ºC (1822.1ºF). and the binary eutectic is at 680ºC (1256ºF) at a composition of 33.5 mol % NaF and 66.5 mol % NaCl. Note the large drop in tem- perature at which the first liquid forms when a small amount of NaCl is added to NaF. No liquid occurs for pure NaF until 994.5ºC. It is apparent from this example that impurities or controlled additives can have large cfects. Intermediate Compounds Frequently the two components A and B react to form one or more in- termediate compounds such as AB, A;B, or AB,. The intermediate com- pounds can melt congruently (liquid phase and solid phase both of the same composition coexist in equilibrium at the melting temperature), melt incongruently (solid phase changes to a liquid plus a solid phase, both with compositions different from the original phase), or dissociate. Schematic binary diagrams with congruently melting and incongruently melting in- termediate compounds are compared in Figs. 3.7 and 3,8. Figure 3.7 con- sists of two binary eutectic diagrams, A-A;B and A,B-B joined together. Phase Equilibria and Phase Eguilibrinm Diagrams 81 1000 1830 994.5 ºC Liquid 900 1650 o & 6 ê 3 | é 5 z ê E a E a ê Boo “aro mn 700 “290 133.5%) ! j ] l 20 40 60 80 NaCl Mol % NaF Figure 3.6 Simple binary eutectic relationship for NaCI-NaF system. (K. Grjot- heim, T. Halvorsen, and J. H. Holm, Acta. Chem. Scand. 21(8], 2300, 1967.) Liquid Lig. + A q 2 > E 5 Q E o É ez A + AB AB+B A AB B Composition Figure 3.7 Schematic of a binary system with a congruently melting intermediate compound. Bá Chapter 3 2300 7 T + ato N AlOs + Lig. 2100)- Jasio 9 N cas + Lia Ny] 4 2 À 5 1900 | 3 5 Cao + Lig N Ca, + NA 3450 ? 5 N / ê CA + Lig. É MOO cartal NO) £-|3oso & o q CiÃ; " . [= Cao + C;A ti - É Ê & 15005 4 & | + |Sj2730 CA + CA, + |£I]€ C;A + Cry ds $ Õ 1300 j 1 y | 20 40 [60 Teo CGA Cj2A7 CA CAgCAS 1 1 Cao (C5Ag) CaAs AlzOs C=Ca0O; A = ALO,. Figure 3.11 The binary system CaO-AI,O,. The dashed lines indicate regions of the diagram with some uncertainty in the precise position of the boundary lines. (F. M. Lea and C. H. Desch, The Chemistry of Cement and Concrete. 2nd ed., p. 52. Edward Arnold, London, 1956.) UrO, + V,/O: (Cr V,O, = CrVO,). Note that the lowest temperature for liquid formation of V.Oc-rich compositions is controlled by the eutectic temperature 665ºC (1229ºF), and the lowest temperature for liquid for- mation of Cr,Oyrich compositions is controlled by the peritectic temper- ature 810 (1490ºF). Liquid Lig. + B Liquid q DIR TA 2 Lia. + A tiq. + B A+8 A+B A+ AB AB +B A+ AB AB, + B A+B A 8 A B A 8 ta) 10) te Figure 3.12 Representation of dissociating compounds on a phase equilibrium diagram. (a) Lower limit of stability, (b) upper limit of stability, and (c) lower and upper limit. Phase Equilibria and Phase Equilibrium Diagrams ta) COMPLETE SOLIO SOLUTION: NO MAXIMUM, NO MENIMUM 2200 TEMPERATURE Cc SOLUTION 0 2 so so Bo 100 No Mg0 MOL % lb) LIQUID ERA, COMPLETE SOLID SOLUTION WITH MINIMUM SS + LIA. SOLID SOLUTION A B te LIQUID SS + LIQ. COMPLETE SOLID SOLUTION WITH MAXIMUM SOLID SOLUTION A B Figure3.13 Representation of complete solid solution on binary phase equilibrium diagrams. 86 Chapter 3 Some binary systems can contain many intermediate compounds and appear quite complex, An example is the CaO-AJO; system, which con- tains important cementitious and refractory (high-temperature) composi- tions. Although the diagram looks complex, close observation reveals that it is merely a combination of simple eutectic and peritectic diagrams. The final category of intermediate compounds involves compounds that are stable only over a limited temperature range. As illustrated in Fig. 3.12. some have a lower limit of stability, some have an upper limit of stability, and some have both upper and lower limits of stability. Com- pounds that demonstrate these types of solid-solid dissociation are un- common. Examples can be found in the Al0,-Y,0, and SiO,—-Y,O, systems. As an exercise, locate these diagrams in Ref. 5. Solid Solution Solid solution was discussed under crystal chemistry in Chapter 2. Solid solution involves the ability of one atom or group of atoms to substitute into the crystal structure of another atom or group of atoms without re- sulting in a change in structure, Solid solution must be distinguished from mixtures. In a mixture two or more components are present. but they retaín their own identity and crystal structure. Examples of mixtures are component A plus component B in Fig. 3.5 and component A;B plus component B in Fig. 3.7. Similarly, La:O, plus La;NbO, in Fig. 3.9 is a mixture, as is CrVO, plus Cr,;O; in Fig. 3.10. In a solid solution one component is “dissolved” in the other com- ponent such that only one continuous crystallographic structure is detect- able. Crystallographic substitutions take place most casily if two atoms are similar in size and valence. For instance, Mg'*, Co"*, and Ni“ arc all similar in size and can readily replace each other in the cubic [rock salt] structure. In fact, each can replace the other up to 100% in the oxide, resulting in continuous solid solution. Figure 3.13a is the phase equilibrium diagram for the system MgO-NIO, showing complete solid solution be- tween the MgO and NiO [12]. This is the most common type of continuous solid solution. Figure 3.13b and c show less common types in which either a maximum or minimum is present. These maxima and minima are neither compounds nor eutectics. just limits in melting temperature for the solid solution. Solid solution does not have to be complete between two different components and generally is not. Usually, one chemical component will have limited solid solubility in the other. The limits are determined by the similarity in the crystal structures and the size of ions or atoms. Figure 3.14 illustrates partial solid solution for a binary eutectic system and a Phase Equilibria and Phase Equilibrium Diagrams 89 liquidus. In some binary systems, composition regions exist above the liquidus where two distinct liquids coexist. This behavior is referred to as immiscibility and is illustrated schematically in Fig. 3.17. Note that each liquid is a distinct separate phase. When a composition in the two-liquid region is melted and rapidly quenched to a noncrystalline state, the two phases can be observed by transmission electron microscopy. An example is illustrated in Fig. 3.18. The two liquid phases typically have a difference in viscosity, density or surface tension that allows them to maintain an interface between them, One liquid is usually rich in A and one in B. and one is often dispersed as very tiny, nearly spherical droplets in the other. Many SiO» systems with divalent oxides (MgO, CaO, SrO, MnO, ZnO, FeO, NiO, and CoO) exhibit liquid immiscibility. Liquid immiscibility also occurs in many systems consisting of B,O; plus another oxide. An example illustrating liquid immiscibility in a real system is presented in Fig. 3.19. Exsolution We can look at liquid immiscibility in another way. At very high temper- ature only one liquid is present. As the temperature is reduced, two liquids with different characteristics become more stable and “unmixing” occurs. A similar behavior can occur in the solid state in continuous solid solutions. At high temperature, continuous solid solutions are stable. But as the temperature decreases in some systems, two solid solutions become more stable and unmixing or exsolution occurs. Typically, one solid solution is rich in À and one in B. Exsolution occurs in the system SnO.-TIO,. Liquid Temperature, *C do “NjRISdUIS mo Figure 3.17 Schematic representation of liquid immiscibility on a binary phase equilibrium diagram. 90 Chapter 3 . , . • Figure 3.18 Transmission electron micrograph showing an example of liquid im- miscibility. (Courtesy of D. Uhlmann. University of Arizona .) Polymorphism Polymorphic transformations are also shown on phase equilibrium dia- grams. Figure 3.20a is a schematic of a binary eutectic diagram with no solid solution and with three different polymorphs of the A composition. The different polymorphs are usually designated by letters of the greek alphabet. Figure 3.20b is a schematic of a binary eutectic diagram with three A polymorphs. each with partial solid solution of B. Figure 3.21 illustrates a real binary system with polymorphs. Poly- morphic transformations are also present in Fig. 3.19. Three-Component Systems A three-component system is referred to as a tertiary sysfem. The addition of a third component increases the complexity of the system and of the phase equilibrium diagram. The phase rule becomes F = 3 - P + 2 = 5 - P. As with binary ceramic systems. diagrams are usually drawn with pressure as a constant (condensed system). The phase rule for the con- -2570"G TO T ” 2400) / [ 2Liquidis N 200 sistobante + Liaj l jato 1200- *(a-Castoy) sao Temperature, *C E [ETridymite —— a-CaçSiO, + Laço f cao Ja350 ” A mec) 4 Cal ACasSiO, + Lig] 1 Siosoro 70 Elagao | Casio, + d DP alasio, À Cassio, + 1 e-CapSiO, 450 *C “ 8 =] Tridymito +! | Pseudowollastonite 1 His + 2190 P |CajSiO,; + CaO) 1250'0 4 A. 'esnjeseduso B7O*C a-Quartz + Wollastonite uiz5º6 Tridymite + Wollastonite | + Cassio h os) | ce 1 t8-Casio) Sal “ORSIO, + 30 7 âa| | Casho, + &s & +CapSIO, 1470, Ta Si, + 040] 788"€ CaySigO + a-Lapsios (a) Figure 3.19 Liquid immiscibility in the CaO-SiO. binary system. (a) Complete diagram (From B. Phillips Temperature, *C 2200, T T— 3990 Liquid a 2000) 3630 3 3 8 ê E 1800] 3270 2? 1 Pa 1600) E) 20 20 sio, caoo— (5) nd A. Muan, 4. Am. Ceram. Soc.. Fig. 237, 4219] 414. 1959.) (b) Two-liquid region showing complete dome. (Fcom Ya. E Ol'shanskii, Dokt Abd. Nank SSSR 761] 94. 1951.) sueadeig uintaquenha aseua pus srqunby aseud e 94 Chapter 3 Temperature 8 Figure 3.22 Schematic of the three-dimensional model for a condensed simple eutectic ternary system. (O ASM International.) homogeneous ternary liquid is in equilibrium with three solid phases. This is an important invariant point (F = 4 — 4 = 0), as we discuss later in this chapter. Note that the ternary eutectic is at a lower temperature than the binary eutectics. The lines connecting E with e, e», and e, are univariant (E =4-3=1)and are referred to as boundary lines. On boundary line E-e, the two solid phases A and B are in eguilibriaum with a liquid phase. On E-e,. A and € are in equilibrium with liquid. On £-e,, B and €C are in equilibrium with liguid. The three-dimensional diagram in Fig. 3.22 is helpful for showing the relationship of the ternary system to the three binary systems, but is a little too complex for general usage. Three techniques are used to transfer in- formation from the three-dimensional model to a two-dimensional dia- gram. One is to project the boundary lines and contours of the liquidus Phase Equilibria and Phase Equilibriam Diagrams 95 onto a plane, as shown in Fig. 3.23 for a ternary eutectic system. The second is to draw an “isothermal section,” that is. the intersection of a horizontal plane of constant temperature with the three-dimensional dia- gram. Two isothermal sections for the system in Fig. 3.23 are shown in Fig. 3.24. The third technique is to draw a “vertical section," which is the intersection of a vertical plane with each region of the condensed ternary diagram. An example is illustrated in Fig. 3.25 for a system having an intermediate compound BC, Several features on the liquidus projection in Fig. 3.23 require expla- nation. The arrows on the boundary lines indicate directions of decreasing temperature. The points at the apices of the triangle labeled A, B, and € represent the melting temperature of the three pure components. The regions labeled a, b. and c are the “primary fields” of components A, B, and €. They are important for defining the sequence of crystallization of solid phases from a homogeneous liquid melt. For example, all composi- tions within the primary field of A initially crystallize A during, cooling. Final crystallization occurs at the ternary eutectic. Crystallization paths are discussed later in this chapter, Figure 3.23 Two-dimensional projection of the boundary lines and the temper- ature contours of the liquidus surface for the simple eutectic diagram shown in Fig. 3.22. (O ASM International.) % Chapter 3 ta to Figure 3.24 Examples of isothermal sections for temperatures T, and T; for the diagram shown in Fig. 3.23. (O ASM International.) Temperature, *C de '0MeJadua BC A Figure 3.25 Example of a vertical section through the join between component A and an incongruently melting intermediate compound BC. (From Ref. 2, Fig. 6.36.)