Ceramic Their Properties and Material Behavior Engr 2110 Dr. R. Lindeke

Ceramic Bonding • Bonding: • Large vs small ionic bond character: -- Mostly ionic, some covalent. -- % ionic character increases with difference in electronegativity (remember!?!). • Large vs small ionic bond character: CaF2: large SiC: small Adapted from Fig. 2.7, Callister 7e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.

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 The same ideas apply to all “ceramics” Principles of Ceramic Architecture: Size relationships Cation to Anion Electrical Neutrality of the overall structure Crystallographic Arrangements Stoichiometry Must Match

Ionic Bonding & Structure 1. Size - Stable structures: --maximize the # of nearest oppositely charged neighbors. - + unstable - + - + Adapted from Fig. 12.1, Callister 7e. stable stable • Charge Neutrality: --Net charge in the structure should be zero. --General form: CaF 2 : Ca 2+ cation F - anions + A m X p m, p determined by charge neutrality

Coordination # and Ionic Radii cation anion • Coordination # increases with Issue: How many anions can you arrange around a cation? Adapted from Fig. 12.2, Callister 7e. Adapted from Fig. 12.3, Callister 7e. Adapted from Fig. 12.4, Callister 7e. ZnS (zincblende) NaCl (sodium chloride) CsCl (cesium Adapted from Table 12.2, Callister 7e. 2 r cation anion Coord __#__ < 0.155 0.155 - 0.225 0.225 - 0.414 0.414 - 0.732 0.732 - 1.0 3 4 6 8 linear triangular TD OH cubic

Cation Site Size: considering Tetrahedral, Octahedral or Cubic Determine minimum rcation/ranion for OH site (Coor # is 6) OH means Octahedral Site Anion: 8*1/8 = 1 Cation: 1 Equal Stoichiometry! a = 2ranion We compute this one because its easy!

Site Selection II Stoichiometry If all of one type of site is full the remainder have to go into other types of sites! Ex: the 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 then: 4 fill in OH 2 more are in TD (because they have to -- for electrical neutrality but the crystal is less stable)

Site Selection III Bond Hybridization – considers 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 ca. 89% covalent bonding we find that in SiC, TD sites are preferred due to covalence needs even though the radii ratio suggests otherwise

AX Crystal Structures  cubic sites preferred AX–Type Crystal Structures include NaCl, CsCl, and zinc blende Cesium Chloride structure:  cubic sites preferred So each Cs+ has 8 neighboring Cl- (cubic Sites) Adapted from Fig. 12.3, Callister 7e.

AX Crystal Structures Why is Zn2+ in TD sites? Zinc Blende structure Size arguments predict Zn2+ in OH sites, In observed structure Zn2+ in TD sites Why is Zn2+ in TD sites? bonding hybridization of zinc favors TD sites So each Zn2+ has 4 neighboring O2- Adapted from Fig. 12.4, Callister 7e. Ex: ZnO, ZnS, SiC

Example: Predicting Structure of FeO • On the basis of ionic radii, what crystal structure would you predict for FeO? Cation Anion Al 3+ Fe 2 + Ca 2+ O 2- Cl - F Ionic radius (nm) 0.053 0.077 0.069 0.100 0.140 0.181 0.133 • Answer: based on this ratio, --coord # = 6 -- or structure is like NaCl (two interleaved FCC) Data from Table 12.3, Callister 7e.

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 in the Anion FCC lattice Adapted from Fig. 12.2, Callister 7e.

MgO and FeO So each oxygen has 6 neighboring Mg2+ (octahedral sites) MgO and FeO also have the NaCl structure (as we predicted for FeO earlier!) O2- rO = 0.140 nm Mg2+ 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 Mg2+ (octahedral sites)

AX2 Crystal Structures Fluorite structure Calcium Fluorite (CaF2) cations in cubic sites same for UO2, ThO2, ZrO2, CeO2 what about an antifluorite structure? -- cations and anions reversed see Concept Check 12.1 (K2O) Both Cation and Anion is 8 so we should find CsCl structure, but There needs to be twice as many K’s as O’s so K are at cube corners and O’s are alternating Centers of Cube – the opposite of Fluorite! Adapted from Fig. 12.5, Callister 7e.

ABX3 Crystal Structures Perovskite Ex: complex oxide BaTiO3 Adapted from Fig. 12.6, Callister 7e.

Silicate Ceramics Most common elements on earth are Si & O SiO2 (silica) structures are quartz, crystobalite, & tridymite The strong Si-O bond leads to a strong, high melting material (1710ºC) Si4+ O2- Adapted from Figs. 12.9-10, Callister 7e. crystobalite Silicates make up most of the rock, etc.

Amorphous Silica Silica gels - amorphous SiO2 Si4+ and O2- not in well-ordered lattice Charge balanced by H+ (to form OH-) at “dangling” bonds very high surface area > 200 m2/g SiO2 is quite stable, therefore unreactive makes good catalyst support Adapted from Fig. 12.11, Callister 7e.

• Quartz sand is crystalline SiO2: GLASS STRUCTURE • Basic Unit: • Glass is amorphous • Amorphous structure occurs by adding impurities (Na+,Mg2+,Ca2+, Al3+) • Impurities: interfere with formation of crystalline structure. (soda glass) Adapted from Fig. 12.11, Callister, 6e. • Quartz sand is crystalline SiO2: 8

Silica Glass A “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

GLASSES – transparent and easily shaped Noncrystalline Silicates + oxides (CaO, Na2O, K2O, Al2O3) E.g. Soda lime glass = 70wt% SiO2 + 30% [Na2O (soda) and CaO(lime) Table 13.1

GLASS PROPERTIES • Specific volume (1/r) vs Temperature (T): • Crystalline materials: --crystallize at melting temp, Tm --have abrupt change in spec. vol. at Tm • Glasses: --do not crystallize --spec. vol. varies smoothly with T --Glass transition temp, Tg Adapted from Fig. 13.5, Callister, 6e. • Viscosity: --relates shear stress & velocity gradient: --has units of (Pa-s) 9

GLASS VISCOSITY VS T AND IMPURITIES • Viscosity decreases with T increase • Impurities lower Tdeform Adapted from Fig. 13.6, Callister, 6e. (Fig. 13.6 is from E.B. Shand, Engineering Glass, Modern Materials, Vol. 6, Academic Press, New York, 1968, p. 262.) 10

Important Temperatures Melting point = viscosity of 10 Pa.s Working point= viscosity of 1000 Pa.s Softening point= viscosity of 4x107Pa.s Temperature above which glass cannot be handled without altering dimensions) Annealing point= viscosity of 1012 Pa.s. Strain point = viscosity of 3x1013Pa.s Fracture occurs before deformation • Viscosity decreases with T • Impurities lower Tdeform

Silicates Combine SiO44- tetrahedra by having them share corners, edges, or faces Cations such as Ca2+, Mg2+, & Al3+ act to neutralize & provide ionic bonding Adapted from Fig. 12.12, Callister 7e. Mg2SiO4 Ca2MgSi2O7

Layered Silicates Layered silicates (clay silicates) = SiO4 tetrahedra connected together to form 2-D plane (Si2O5)2- So need cations to balance charge = Adapted from Fig. 12.13, Callister 7e.

Layered Silicates Kaolinite clay alternates (Si2O5)2- layer with Al2(OH)42+ layer Adapted from Fig. 12.14, Callister 7e. Note: these sheets loosely bound by van der Waal’s forces

Layered Silicates Can change the counterions Micas: KAl3Si3O10(OH)2 this changes layer spacing the layers also allow absorption of water Micas: KAl3Si3O10(OH)2 Bentonite used to seal wells packaged dry swells 2-3 fold in H2O pump in to seal up well so no polluted ground water seeps in to contaminate the water supply. Used in bonding Foundry Sands and Taconite pellets

Carbon Forms Carbon black – amorphous – surface area ca. 1000 m2/g Diamond tetrahedral carbon hard – no good slip planes brittle – can cleave (cut) it large diamonds – jewelry small diamonds often man made - used for cutting tools and polishing diamond films hard surface coat – cutting tools, medical devices, etc. (C likes to have covalent bonds & tetravalent) Adapted from Fig. 12.15, Callister 7e.

Carbon Forms - Graphite layer structure – aromatic layers weak van der Waal’s forces between layers planes slide easily, good lubricant Adapted from Fig. 12.17, Callister 7e. Like connected benzene rings

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 C60 - also C70 + others Adapted from Figs. 12.18 & 12.19, Callister 7e.

Defects in Ceramic Structures • Frenkel Defect --a cation is out of place. • Shottky Defect --a paired set of cation and anion vacancies. Shottky Defect: Frenkel Defect Adapted from Fig. 12.21, Callister 7e. (Fig. 12.21 is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. 1, Structure, John Wiley and Sons, Inc., p. 78.) • Equilibrium concentration of defects

Lets take a look at 12.31 We must consider Schottky Defects formation energy for an “unknown” MO built in a NaCl structure: given Numbers of Defects and Density for various temperatures -- (a) find energy for defect formation (eV) (b) find Ns at 1000 C (c) Identify the Metal in the oxide

Solving Part (a) T (C)  (g/cc) Ns (m-3) 750 3.50 5.7x109 1000 3.45 ? 1500 3.40 5.8x1017 Now divide (2) by (1) and solve for Qs

Continuing:

Part B:

Part c: Using a modification to Density Models for Ceramics

Impurities • Impurities must also satisfy charge balance leaving Electroneutrality Na + Cl - • Ex: NaCl initial geometry Ca 2+ impurity resulting geometry Na + cation vacancy • Substitutional cation impurity • Substitutional anion impurity initial geometry O 2- impurity Cl - an ion vacancy resulting geometry

Ceramic Phase Diagrams MgO-Al2O3 diagram:  Adapted from Fig. 12.25, Callister 7e.

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 (like charges repel)

Measuring Elastic Modulus • Room T behavior is usually elastic, with brittle failure. • 3-Point Bend Testing often used. --tensile tests are difficult for brittle materials! F L/2 d = midpoint deflection cross section R b d rect. circ. Adapted from Fig. 12.32, Callister 7e. • Determine elastic modulus according to: F x linear-elastic behavior d slope = E = L 3 4 bd 12 p R rect. cross section circ.

Measuring Strength s = 1.5Ff L bd 2 Ff L pR3 x F F • 3-point bend test to measure room T strength. F L/2 d = midpoint deflection cross section R b d rect. circ. location of max tension Adapted from Fig. 12.32, Callister 7e. • Flexural strength: • Typ. values: Data from Table 12.5, Callister 7e. rect. s fs = 1.5Ff L bd 2 Ff L pR3 Si nitride Si carbide Al oxide glass (soda) 250-1000 100-820 275-700 69 304 345 393 Material (MPa) E(GPa) x F Ff d

Mechanical Issues: Properties are significantly dependent on processing – and as it relates to the level of Porosity: E = E0(1-1.9P+0.9P2) – P is fraction porosity fs = 0e-nP -- 0 & n are empirical values Because the very unpredictable nature of ceramic defects, we do not simply add a factor of safety for tensile loading We may add compressive surface loads We often choose to avoid tensile loading at all – most ceramic loading of any significance is compressive (consider buildings, dams, brigdes and roads!)