MME 467 Ceramics for Advanced Applications Lecture 04 Structure of Ceramics 1 Ref: Barsoum, Fundamentals of Ceramics, Ch03, McGraw-Hill, 2000. Prof. A. K. M. Bazlur Rashid Department of MME, BUET, Dhaka Topics to discuss... 1. Structure of Ceramics 1. Structure of Crystalline Ionic Ceramics 2. Structure of Some Binary Ionic Ceramics 1
STRUCTURE OF CERAMICS Crystalline microstructures range in complexity l from single element structures of carbon (such as diamonds, graphite, and fullerenes) - which are not strictly speaking ceramic materials, although they share several properties with them l through simple compound structures consisting of just two elements (e. g. NaCl) l to more complex structures such as clays and engineering ceramics designed for particular applications such as superconductors. Amorphous microstructures include the vast silicabased family, and are based on short range rather than long range order. STRUCTURE OF IONIC CERAMICS For compound A m B n we expect ionic bonding to predominate when atom A has low electronegativity and atom B has high electronegativity. For ionic compounds the bonding forces are electrostatic and, therefore, omni-directional. l the bonding forces should be maximised by packing as many cations around each anion, and as many anions around each cation as possible. l the coordination numbers are, however, constrained by the stoichiometry of the compound and by the sizes of the atoms. Example: For Na + Cl, there are 6 anions around each cation; because of 1:1 stoichiometry there must also be 6 Na cations around each Cl anoin. For Zr 4+ O 2 2, there are 8 anions around each cation, but there mush be only 4 cations around each anion. 2
Most ionic ceramics structures based on 1. either FCC or HCP close-packing of one type of ion, 2. with the other ions occupying a specific set of interstitial sites. Generally the larger ions (usually anions) form the close-packed structure, with smaller ions (cations) occupying the interstices. Recalling that, although FCC and HCP are the most efficient ways of packing spheres, only 74% of the available space is filled; the 26% free space is in the form of different types of holes or sites, which can be occupied by the smaller cations in the ionic structures. Two principle types of cation sites, tetrahedral (TD) and octahedral (OH), exist between layers of close-packed atoms. l the caions need to fit snugly, so they squeeze into holes that are not quite big enough l funny things happen if the hole size is bigger than the size of inclusion atom!! (as in barium titanate) Having determined what types of holes are available, we must now decide: (a) Which sites are occupied by a given cation è This is determined by the radius ratio. (b) How many sites are occupied è This is determined by the stoichiometry. Location and Density of Interstitial Sites Tetrahedral hole Three anions in one plane, and a single anion in the adjacent plane Octahedral hole Three in each of the two planes The nearest neighbour configuration of oxygen atoms around OH and TD cations is independent of whether the basic structure is derived from FCC or HCP. l FCC and HCP lattices have the same number density of OH and TD sites 3
In compact structures, No. of Tetrahedral (TD) sites = 2n No. of Octahedral (OH) sites = n n = No. of atoms per cell Coordination Number In TD sites 4 In OH sites 6 Octahedral sites are larger O T RED = Octahedral sites = 1/4 x 12 + 1 = 4 per unit cell BLUE = Tetradedral sties = 8 per unit cell 4
Classification of Ionic Ceramic Structures 1. AX - type Structures Rocksalt, CsCl, and ZnS 2. AX 2 - type Structures Fluorite, Rutile 3. A m B n O p - type Structures Spinel, Perovskite Many structures; But what determines which structure will form? Factors Affecting Structures 1. Crystal stoichiometry or Electroneutrality Electrically neutral; charges must be balanced (even when defects are present). Ceramics with AX 2 stoichiometry cannot have ROCKSALT structure. 2. Radius ratio To achieve lowest energy state (E total ), cations and anions tend to pack densely (as determined by the r C /r A ratio), which will maximise attractions and minimise repulsions (and increase the coordination number, CN). An unstable structure cannot be formed. 3. Propensity for covalency and tetrahedral coordination l If the bonding has some covalent character, then packing will be less efficient. l Cations with higher polarising power (Cu 2+, Al 3+, Zn 2+, Hg 2+ ) are bonded with anions that are readily polarisable (I 2-, S 2-, Se 2- ), thereby increasing covalent character of bond and forming tetrahedral crystal. l Atoms that favour sp 3 hybridisation (Se, C, Ge) form tetrahedral crystals. 5
Anion-Cation Coordination Configuration r C /r A > Ideal r C /r A = Ideal r C /r A < Ideal stable stable unstable For a specific CN, there is a critical or minimum radius ratio Coordination Number Geometries for Various Radius Ratios predicting structure based on radius ratio CN Position of cation Range of r C /r A 2 Centre of two linear anions < 0.155 3 Centre of triangle 0.155 0.225 4 Centre of tetrahedron 0.225 0.414 6 Centre of octahedron 0.414 0.732 8 Centre of cube 0.732 1.000 Coordination number increases as r C /r A increases 6
Effect of Stoichiometry If all of one type of site is full, the remainder have to go into the other types of sites. Example: FCC unit cell has 4 OH and 8 TD sites. Now, if for a specific ceramic, each unit cell has 6 cations and the cations prefer OH sites, then 4 will go in OH site, and 2 in TD sites Effect of Bond Hybridisation Significant in covalent bonding, or in ionic bonding with a significant covalent character. Example: SiC Electronegativity: X Si = 1.8, X C = 2.5 Ionic character = 11.5 % only (i.e., 88.5 % covalent bonding) Both Si and C prefer sp 3 hybridisation; So, Si get TD sites Predicting Structure Based on r C /r A Ratio Example Problem 13.2/Callister/P-391 On the basis of ionic radii, which crystal structure would you predict for FeO? Ionic radius: Fe 2+ = 0.077 Fe 3+ = 0.069 O 2- = 0.140 r Fe +2 r O -2 0.077 nm = = 0.550 0.140 nm The value lies between 0.414 and 0.732. Thus the CN is 6. Since both Fe and O has the same valence, both Fe and O have the same CN of 6. Therefore, the predicted crystal structure of FeO will be ROCKSALT. Conclusion: It is not only the chemical formula which determine the crystal structure but also the relative sizes of the cations and anions. 7
Common Ceramic Crystal Structures Structure Structure Atomic CN CN Example Type Name Packing Cation Anion of Structure AX Rock salt FCC 6 6 NaCl, MgO, FeO AX Cesium chloride Simple cubic 8 8 CsCl AX Zinc blende FCC 4 4 ZnS, SiC A m X p Fluorite (AX 2 ) Simple cubic 8 4 CaF 2, UO 2, ThO 2 A m X p Corundum HCP Al 2 O 3, Fe 2 O 3 A m B n X p Perovskite (ABX 3 ) FCC 12(A), 6(B) 6 BaTiO 3, SrZrO 3 A m B n X p Spinel (AB 2 X 4 ) FCC 4(A), 6(B) 4 MgAl 2 O 4, FeAl 2 O 4 8
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STRUCTURE OF SOME BINARY IONIC CERAMICS Cesium Chloride Structures Anions in simple cubic arrangement, with cations in interstices at the cube centres. The radius ratio is 0.94 (>0.732). l The coordination number is 8 for both anions and cations. l Cubic structure. Ceramics having this structure: CsBr, TlCl, TlBr Rocksalt Structure A close-packed FCC array of larger anions, with an FCC array of smaller cations occupying the octahedral sites. It has 1:1 (AX - type) stoichiometry with the coordination number is 6 for both cations and anions. The radius ratio is (0.102 pm/0.181 pm) = 0.563 (which lies between 0.732 and 0.414). Crystal structure of NaCl Example of rocksalt ceramic structure: MgO, CaO, BaO, CdO, MnO, FeO, NiO, all other halides of Na, Li, K and Rb, CsF, AgCl. 10
Zinc Blende Structure Zinc sulfide (ZnS) is a unique compound that forms two types of crystalline structures. Wurtzite hexagonal structure Zinc blende (a.k.a. sphalerite) cubic The radius ratio is (0.074/0.140) = 0.529. The size argument predict Zn 2+ in OH sites, but found in TD sites. So why Zn 2+ in TD sites? Bonding hybridisation of zinc favours TD sites. So Zn 2+ has 4 neighbouring O 2-, instead of 6. In order to satisfy the MX stoichiometry, only one half of the tetrahedral sites are needed to fill with divalent cations. Oxides and sulfides with smaller cations that prefer tetrahedral coordination tend to form this structure, e.g., ZnS, ZnO and BeO, as well as covalent compound such SiC, BN and GaAs. Zinc blende structure can be viewed as a derivative of the fully covalently bonded diamond cubic structure. If all atoms in zinc blende structure are identical, we obtain diamond structure. diamond structure 11
Wurtzite Structure Unit cell of the Wurtzite structure! The wurtzite structure is based on the HCP close-packing of anions, with one-half of TD sites occupied by the cations. Filling of cation is only in tetrahedral of one orientation (apex upward). The coordination number of each ion is 4. This is the same as zinc blende structure. Examples: AgI, ZnO, CdS, AlN, GaN, BN andα-sic. Wurtzite Unit cell Wurtzite structure The grey balls represent metal atoms, and yellow balls represent sulfur atoms. 12
Antifluorite and Fluorite Structures In antifluorite strucutre, the r C /r a ratio is close to 1, which renders it s cubic arrangement. The anions are in FCC arrangement and all tetrahedral sites are filled by cation. The coordination numbers of cation and anion are 4 and 8, respectively. The chemical stoichiometry is M 2 X. The connectivity of the tetrahedra is completely edge sharing; each tetrahedron shares two of its oxygen ions with a neigboring tetahedron. Examples: Oxides of alkaline metals such as Li 2 O, Na 2 O and K 2 O, and chalcogenides such as Li 2 S, Li 2 Se. Fluorite structure is the reverse of antifluorite and the crystal will show stoichiometry as MX 2. The structure is based on FCC closepacking of the cations with all tetrahedral interstices filled by anions. Examples: CaF 2 (the mineral fluorite), BaF 2, ZrO 2, UO 2 and CeO 2,!! (a) Antifluorite structure, typified by compounds Li 2 O (b) (110) plane of the fluorite structure compounds ZrO 2. 13
Rutile Structures Rutile is one polymorph of the mineral TiO 2 (anatase and brookite are being the other structures) The structure is based on quasi-hcp packing of oxygen atoms with cation fill one-half of the available OH site. The unit cell of rutile. Ti atoms are gray; O atoms are red. The radius ratio is 0.745/1.26 = 0.591. With this ratio, the cubic holes are too large (r hole /r = 0.732) to be suitable. The titanium(iv) ions will prefer to occupy OH holes in a FCC structure. Nature chooses to pack the oxide ions in rutile in a HCP structure. The rutile structure has (6,3)-coordination. Observe that none of the TD holes are occupied. The titanium(iv) ions lie in OH holes. The occupation of Ti in OH site is repeated in the third layer of oxygen HCP stacking, resulting in arrangement as TD unit cell. However, the atoms do relax from their positions since partial occupancy of highly charged Ti 4+. Arrangement of Ti 4+ causes anisotropic diffusion of cation; along the c-axis is much faster than in the a-axis direction. This makes TiO 2 having highly anisotropic refractive index, and application for opacifying pigment for paints, paper and fabric.! Unit cell of rutile structure One-half filling of octahedral sites in a close-packed plane (rutile structure) 14
Next Class Lecture 05 Structure of Ceramics 2 Ref: Barsoum, Fundamentals of Ceramics, Ch03, McGraw-Hill, 2000. 15