Type of bonds Four general categories bonds 1.metallic 2. ionic 3. covalent 4. Vander Waals Primary bond is commonly applied to metallic type. ionic covalent ~100 kcal/mol Secondary bonds : Vander Waals ~ <10 kcal/mol There is almost more than one type of bond in a ceramic solid ( ionic + covalent). 1
The metallic bond is equally effective in all three coordinate directions. The coulombic attractions of the ionic bond is also equally effective in all three coordinate directions. The covalent bond is very specifically oriented and is most effective between the two atoms of a pair. The Vander Waals bonds, although weak, are polar and therefore directional. Metalic : Positive ionic are held together by free electrons. Ionic : Positive and negative ions are held together by coulomic attraction. Covalent : Electrons are shared with electron pairs between two positive ions. Vander Waals : The centers of positive and negative charges are not coincident. Therefore an apparent coulombic attraction exist. 2
Ionic bond Materials which derive most of their coherency from coulombic forces of attraction between charged atoms are classified as ionic solids. The net coulombic attraction within an ionic solid. As the positive and negative ions are brought closer together, energy is release. Not until the electron shells around the ions begin to interact are the net coulombic forces of attraction balanced by those of repulsion. (1) Coulombic energy The potential energy E, corresponding to two point charges. : the distance between two points : no. of charges at each point. e : coul 3
All scientific evidence indicates that the lowest energy condition is the most stable. This factor is responsible for the natural tendency of atoms to assume positions in which there is a minimum of free energy. The grouping of atoms in close coordination are due to the attractive repulsive forces between atoms. The equilibrium spacing between atoms is that distance at which the attractive and repulsive force are balanced. (i) Unlike charges give a negative value to E, indicating that energy is given off as the distance is decreased. (when two unlike, monovalent ions are closed) (ii) The energy of two positive ( or two negative ) monovalent ions increases as these are brought closer together. 4
(2) Madelung constant The Madelung constant is the ratio of the potential energy of an ion within a three-dimensional solid to the energy between a single pair of ions. Ex. NaCl The removal of a sodium ion from the interior of a NaCl crystal requires 1.747 times as much energy as it does to separate it from a single ion. Ex. Calculate the Madelung constant for a hypothetical linear array of alternating positive and negative monovalent ions. Ans : 5
(3) Electronic repulsion energy This repulsive energy between the electron shells of adjacent atoms may be expressed by b : constant n : ~9 as determined expertimentally The sum U of the net coulombic attractive and electron repulsive energies is E C + E R. At the interatomic distance a,, ( one monovalent ion within an ionic crystal ) The energy per mol, Since n 9, U = 184 kcal/gm-mole for NaCl is exceedingly close to the experimental value of 182.4 kcal/gm-mole. 6
Covalent bonds This type of bond involves mutual sharing of two electrons by adjacent atoms and is frequently encountered in ceramic materials. Useful qualitative relationship : (1) A covalent bond always involves two electrons. (2) No more then four covalent bonds. (3) Single, double, and triple bonds are possible, involving two, four, and six electrons between an adjacent pair of atoms. Covalent bonds can be very strong. Evidence of this is found in diamond and in refractory and abrasive ceramic compounds which depend extensively on covalent bonding. Polyatomic groups: covalent bonds are associated almost exclusively with the semimetallic and nonmetallic atoms which are located in the upper right-hand corner of the periodic table. Since these elements can share electrons, it is not surprising to find them clustering into larger polyatomic units. Polyatomic groupings may be formed which do not have enough electrons to fill the outer-shell requirement. Such units become more stable if they receive additional electrons from external sources. When this occurs, the unit become a polyatomic anion as shown in Fig. 2-10. 7
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Vander Waals bonds These bonds originate through electrical dipole inside the materials. With the displaced center of charge, the positive end of one dipole can be attracted to the negative end of another dipole. Vander Waals bonds are also evident in compounds that form true molecules, such as, H 2 O, SiF 4, CO 2, they have strong intramolecular forces, but only weak intermolecular attraction; therefore these compounds liquefy and gasify as independent molecules. Dipoles may be induced by an electric field applied. In ceramic material, there are two main structural and behavioral consequences of the Vander Waals force of attraction : (1) they serve as the loci for plastic slip (e.g. in clays) and (2) they serve to promote physical adsorption of atoms, ions or molecules onto solid and liquid surfaces. 9
It should be noted, that neighboring atoms or ions may induce distortion in any particular dipole ; therefore a precise calculation is not always possible. 10
Ex. The H-N-H bond angle in ammonia is 112, and the H-N couple has a dipole moment of 1.7 debyes, what is the dipole moment of NH3? Ans: V : the vertical compound h : the horizontal compound sin 56 x 1.7, sin 60 x h h 1.7 sin 56 1.63 sin 60 v (1.7)2 (1.63)2 0.5 dipole moment of NH3 = 3V = 1.5 debyes 11
Stability of ionic crystal structures The Madelung constant The Madelung constant is a precise definition of the energy of a particular crystal structure relative to the same no. of isolated molecules Ex. KCl K Cl e K e Cl expenditure of 4.34 ev Ionization energy an energy gain of 3.82 ev Electron affinity The energy for ionic bond between a cation and anion pair can be described by two terms : (1) coulombic attraction the basis for the bond. (2) repulsion due to the pauli exclusion principle that becomes strong at very close separation. Electrostatic energy : the permittivity of free space : an empirical constant : the interatomic separation 12
R 0 = R A + R C, at which the total energy is minimum, which we will denote as E 0. a crystal composed of N molecules the energy of whole NE 0. rewrite : cation valence : anion valence α : the summation of the electrostatic interaction 13
Madelung Constant : Represents the electrostatic energy of the crystal relative to the energy of the same no. of isolated molecules. C : the sum of the short-range repulsive interaction. The Madelung Constant is a measure of the magnitude of the electrostatic stabilization, and for stable crystals has a value > 1. 14
It can be seen that the differences between some structures are relatively small. Zincblend the difference in electrostatic energy is minor Wurtzite (~0.2%). When the energy difference between different structure types of the same stoichiometry (polymorphism) is small. For ionic crystals the majority of the interaction energy lies in the electrostatic term, with the short-range repulsion accounting for only about 10% of the interaction. ~10 ~10%, 1 1 4 4 4 0 0 2 0 2 1 0 0 2 0 n n n e Z Z N E C e Z Z N Ec R e Z Z C R R R E A C C A C n A C C 15
Ceramics Inorganic and nonmetallic materials Compounds between metallic and nonmetallic elements Bonding: ionic or ionic + covalent Ceramic 由希臘字 Keramikos 而來, 意謂 burnt stuff, 係指經高溫燃燒處理所得的材料 傳統陶瓷 精密陶瓷 16
Crystal Structure of Ceramics Atomic bonding: Ionic 離子鍵比例 Cations ( 陽離子 ) Anions ( 陰離子 ) 影響陶瓷結構的因素 : 電荷 離子半徑 電荷 : 維持電中性, CaF 2 離子半徑 : r C < r A, r C / r A < 1 每一陽離子欲有最大量陰離子於周圍 每一陰離子欲有最大量陽離子於周圍 17
Crystal Structure of Ceramics Stable structure: 圍繞於陽離子周圍的陰離子都與陽離子接觸 Coordination Number(CN ; 配位數 ): 最靠近陽離子的陰離子總數, 與 r c /r A 比值有關 Critical or minimum r c / r A ratio => 特定 r c / r A 比 Bond strength ( 鍵結強度 ) = 電荷 ( 陽離子 )/CN 18
r C / r A 19
離子半徑 20
Crystal Structure v.s. Close Packing of Anions B layer of close-packed oxygen atoms is positioned with respect to the A layer. The two are identical except for a lateral translation. The B-layer atoms do not lie directly above any of the A-layer atoms. 21
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Crystal Structure v.s. Close Packing of Anions Atomic close packing: FCC, HCP Stacking close-packed planes of large anions => unit cell => Two interstitial sites: Tetrahedral (T) sites => CN No.= 4 Octahedral (O) sites => CN No.= 6 24
Octahedral site : atoms =1:1 Tetrahedral site : atoms =2:1 25
Crystal Structure v.s. Close Packing of Anions For each of anion spheres => one Octa. position and two Tetra. position exist. Consider two factors FCC (ABCABCA..) or HCP (ABABA.) Cations put in Tetra. sites or Octa. sites NaCl => FCC stacking => Na in Octa. sites (CN=6), fill in all Octa. sites Spinel structure 尖晶石結構, AB 2 O 4, e.g. MgAl 2 O 4 => O in FCC stacking, Mg in Tetra. sites, Al in Octa. sites. 26
Pauling s rules : (1) Based on the geometric stability of packing for ions of different size. (2) Simple electrostatic stable argument. Rule 1. Each cation will be coordinated by a polyhedron of anions, the no. of ions in which is determined by the relative sizes of the cation and anion. Rule 2. This rule ensures that the basic coordination polyhedra are arranged in three dimensions in a way that preserve local charge neutrality. Bond strength = valence C.N. Ex. MgO : Octahedrally coordination Mg 2+ have bond strength of 2/6. This is qualitatively a measure of the relative fraction of the 2+ charge that is being allocated to or shared with each of the coordinating anions. The coordination of cations around anions as well as those of anions around cations. Rule 3. Coordination polyhedra prefer linkages where they share corners rather than edges, and edges rather than faces. This rule is simply based on the fact that cations prefer to maximize their distance from other cations in order to minimize electrostatic repulsion. 27
Tetrahedra and octahedra linked by sharing(a) corner,(b) edge, and (c) face. 28
Rule 4. When C.N. is small or the cation valence is high, that rule 3 becomes more important. This also is based on electrostatic. Rule 5. Simple structure are usually preferred over more complicated arrangement. Summary Ex. MO has, cation anion 1 1 Case 1. If octahedral coordination (C.N.= 6) is preferable, all of octahedral sites will be filled, since octahedral sites atoms Case 2. If tetrahedral coordination (C.N.= 4) is preferred, only ½ tetrahedral sites need be filled, since These sites will tend to be filled in a way that maximizes the cation separation, according to Pauling s 3 rd and 4 th rules. tetrahedral sites atoms 1 1 2 1 29
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