Chapter 12: Structures & Properties of Ceramics • Structures of ceramic materials: How do they differ from those of metals? • Point defects: How are they different from those in metals? • Impurities: How are they accommodated in the lattice and how do they affect properties? • Mechanical Properties: What special provisions/tests are made for ceramic materials? 1 Ceramic Bonding • Bonding: -- Mostly ionic, some covalent. -- % ionic character increases with difference in electronegativity. • Large vs small ionic bond character: CaF 2: large SiC: small Adapted from Fig. 2.7, Callister 7e. 2 Ionic Crystals Note: larger anion radius Cation Radius (nm) Anion Radius (nm) 0.100 0.133 0.072 0.14 0.102 0.182 0.053 0.140 0.040 0.140 Most ionic crystals can be considered as close-packed structure of anions with cations in the interstitial sites. Cations: metallic ions, positively charged Anions: nonmetallic ions, negatively charged 3 Ceramic Crystal Structures Oxide structures – oxygen anions much larger than metal cations – close packed oxygen in a lattice (usually FCC) – cations in the holes of the oxygen lattice 4 Site Selection Which sites will cations occupy? 1. Size of sites – does the cation fit in the site 2. Stoichiometry – if all of one type of site is full, the remainder have to go into other types of sites. 3. Bond Hybridization 5 Ionic Bonding & Structure 1. Size - Stable structures: --maximize the # of nearest oppositely charged neighbors. - - - - - - Adapted from Fig. 12.1, + + + Callister 7e. -- - - - - unstable stable stable • Charge Neutrality : F- --Net charge in the 2+ structure should CaF : Ca + 2 cation anions be zero. F- --General form: AmXp m, p determined by charge neutrality 6 Coordination # and Ionic Radii rcation • Coordination # increases with ranion Issue: How many anions can you arrange around a cation? rcation Coord ZnS (zincblende) ranion # Adapted from Fig. < 0.155 2 linear 12.4, Callister 7e. 0.155 - 0.225 3 triangular NaCl (sodium 0.225 - 0.414 4 TD chloride) Adapted from Fig. 12.2, Callister 7e. 0.414 - 0.732 6 OH CsCl (cesium chloride) 0.732 - 1.0 8 cubic Adapted from Fig. Adapted from Table 12.2, 12.3, Callister 7e. Callister 7e. 7 Cation-anion stable configuration r e.g. 3-coordinate when cos α = A rA + rC Rewrite as r 1 C = −1 rA cos α With α = 30 o rC Minimum ratio for 3-coordinate = .0 155 rA 8 Cation Site Size • Determine minimum rcation /r anion for O H site (C.N. = 6) 2 ranion + 2rcation = 2a a = 2ranion 2 ranion + 2rcation = 2 2ranion r anion + rcation = 2ranion r cation = ( 2 −1)ranion r cation = 0.414 ranion 9 Site Selection II 2. Stoichiometry – If all of one type of site is full, the remainder have to go into other types of sites. Ex: FCC unit cell has 4 OH and 8 TD sites. If for a specific ceramic each unit cell has 6 cations and the cations prefer OH sites 4 in OH 2 in TD 10 Interstitial sites in FCC Octahedral (O ) sites h Tetrahedral (T d) sites 12 middle of the 1 at the center edge sites (each Net 8 T sites/unit cell shared by 4 unit d Net 4 O h sites/unit cell cells) 11 Site Selection III 3. Bond Hybridization – significant covalent bonding – the hybrid orbitals can have impact if significant covalent bond character present – For example in SiC • XSi = 1.8 and XC = 2.5 2 % ionic character = 100 {1 - exp[-0.25( XSi − XC ) ]} = 11 .5% • ca. 89% covalent bonding • both Si and C prefer sp 3 hybridization • Therefore in SiC get TD sites 12 Example: Predicting Structure of FeO • On the basis of ionic radii, what crystal structure would you predict for FeO? Cation Ionic radius (nm) • Answer: 3+ Al 0.053 rcation 0.077 2+ = Fe 0.077 ranion 0.140 3+ Fe 0.069 = 0.550 Ca 2+ 0.100 based on this ratio, --coord # = 6 Anion --structure = NaCl O2- 0.140 Cl - 0.181 Data from Table 12.3, F- 0.133 Callister 7e. 13 Rock Salt Structure Same concepts can be applied to ionic solids in general. Example: NaCl (rock salt) structure rNa = 0.102 nm rCl = 0.181 nm rNa /rCl = 0.564 ∴ cations prefer OH sites Adapted from Fig. 12.2, Callister 7e. 14 MgO and FeO MgO and FeO also have the NaCl structure 2- O rO = 0.140 nm 2+ Mg rMg = 0.072 nm rMg /rO = 0.514 ∴ cations prefer OH sites Adapted from Fig. 12.2, Callister 7e. So each oxygen has 6 neighboring Mg 2+ 15 AX Crystal Structures AX–Type Crystal Structures include NaCl, CsCl, and zinc blende Cesium Chloride structure: r + .0 170 Cs = = .0 939 r .0 181 Cl − ∴ cubic sites preferred So each Cs + has 8 neighboring Cl - Adapted from Fig. 12.3, Callister 7e. 16 AX Crystal Structures Zinc Blende structure r 2+ .0 074 Zn = = .0 529 ⇒ O ?? r .0 140 H O2− • Size arguments predict Zn 2+ in OH sites, • In observed structure Zn 2+ in TD sites 2+ • Why is Zn in TD sites? – bonding hybridization of zinc favors TD sites 2+ 2- Adapted from Fig. So each Zn has 4 neighboring O 12.4, Callister 7e. Ex: ZnO, ZnS, SiC 17 AX 2 Crystal Structures Fluorite structure • Calcium Fluorite (CaF 2) • cations in cubic sites • UO 2, ThO 2, ZrO 2, CeO 2 • antifluorite structure – cations and anions reversed Adapted from Fig. 12.5, Callister 7e. 18 ABX 3 Crystal Structures • Perovskite Ex: complex oxide BaTiO 3 Adapted from Fig. 12.6, Callister 7e. 19 Mechanical Properties We know that ceramics are more brittle than metals. Why? • Consider method of deformation – slippage along slip planes • in ionic solids this slippage is very difficult • too much energy needed to move one anion past another anion 20 Ceramic Density Computation Number of formula units/unit cell n′(ΣA + ΣA ) ρ = C A VCNA Volume of unit cell n’ = number of cations in unit cell AC = atomic weight of cation nA = number of anions in unit cell AA = atomic weight of anion VC = volume of unit cell NA = Avogadro’s number 21 Theoretical Density Calculation of NaCl n′(ΣA + ΣA ) ρ = C A VCNA ANa = 22.99 g/mol ACl = 35.45 g/mol a=2(r Na+ +r Cl -) a = 2(r Na+ +r Cl -) = 2(0.102+0.181) nm 3 3 Thus, Vc = a = (2r Na+ +2r Cl-) And n’ is 4 pair of Na and Cl in one unit cell, finally, n (' ANa + ACl ) 3 ρ = 3 = 14.2 g / cm 2( rNa + + 2rCl − ) N A Cl - Na + 22 Silicate Ceramics Most common elements on earth are Si & O Si 4+ O2- Adapted from Figs. 12.9-10, Callister 7e. crystobalite • SiO 2 (silica) structures are quartz, crystobalite, & tridymite • The strong Si-O bond leads to a strong, high melting material (1710ºC) 23 Amorphous Silica • Silica gels - amorphous SiO 2 – Si 4+ and O 2- not in well-ordered lattice – Charge balanced by H + (to form OH -) at “dangling” bonds • very high surface area > 200 m 2/g – SiO 2 is quite stable, therefore unreactive • makes good catalyst support Adapted from Fig. 12.11, Callister 7e. 24 Silica Glass • Dense form of amorphous silica – Charge imbalance corrected with “counter cations” such as Na + – Borosilicate glass is the pyrex glass used in labs • better temperature stability & less brittle than sodium glass 25 Silicates 4- – Combine SiO 4 tetrahedra by having them share corners, edges, or faces Adapted from Fig. 12.12, Callister 7e. Mg 2SiO 4 Ca 2MgSi 2O7 – Cations such as Ca 2+ , Mg 2+ , & Al 3+ act to neutralize & provide ionic bonding 26 Layered Silicates • Layered silicates (clay silicates) – SiO 4 tetrahedra connected together to form 2-D plane • (Si O )2- Adapted from Fig. 2 5 12.13, Callister 7e. • So need cations to balance charge = 27 Layered Silicates 2- 2+ • Kaolinite clay alternates (Si 2O5) layer with Al 2(OH) 4 layer Adapted from Fig. 12.14, Callister 7e. Note: these sheets loosely bound by van der Waal’s forces 28 Layered Silicates • Can change the counterions – this changes layer spacing – the layers also allow absorption of water • Micas KAl 3Si 3O10 (OH) 2 – smooth surface for AFM sample holder • Bentonite – used to seal wells – packaged dry – swells 2-3 fold in H 2O – pump in to seal up well so no polluted ground water seeps in to contaminate the water supply. 29 Carbon Forms • Carbon black – amorphous – surface area ca. 1000 m 2/g • Diamond – tetrahedral carbon • hard – no good slip planes • brittle – can cut it – large diamonds – jewelry – small diamonds • often man made - used for cutting tools and polishing Adapted from Fig. – diamond films 12.15, Callister 7e. • hard surface coat – tools, medical devices, etc. 30 Carbon Forms - Graphite • layer structure – aromatic layers Adapted from Fig. 12.17, Callister 7e. – weak van der Waal’s forces between layers – planes slide easily, good lubricant 31 Carbon Forms - Graphite 32 Carbon Forms – Fullerenes and Nanotubes • Fullerenes or carbon nanotubes – wrap the graphite sheet by curving into ball or tube – Buckminister fullerenes • Like a soccer ball C 60 - also C 70 + others Adapted from Figs. 12.18 & 12.19, Callister 7e. 33 Diamond-like Carbon Film • Ultralow friction surface • http://en.wikipedia.org/wiki/Diamond- like_carbon 34 Defects in Ceramic Structures • Frenkel Defect -- a cation is out of place. • Shottky Defect -- a paired set of cation and anion vacancies. Shottky Defect: Adapted from Fig. 12.21, Callister 7e. (Fig. 12.21 is from W.G. Moffatt, G.W.