Defect Chemistry Crystals are imperfect at T > 0K High purity diamond, quartz: << 1% Reduces free energy of crystal Point Defects: Schottky, Frenkel, color centers, doping, vacancies, solid solutions Line Defects: Dislocations Planar Defects: Boundaries, shear structures, stacking faults West, Ch.2; Smart, Ch.5 Extended Defects Perovskite, high T c ceramic superconductors, WO 3
Chapter 2: Defects Defects cost enthalpy H Increase entropy S e.g. one vacancy: 10 23 possible positions in 1 mol of ions Too many defects, smaller increase in entropy, costs more energy Real materials at equ m: intermediate defect conc. Intrinsic defect Defect conc. T ( G with increasing T) Predominant type of defect gives lowest G = H T S (Table 2.1)
Perovskite, ABX 3 Table 1.18: A = Group I or II metal B = T.M. or lower p-block X = O 2 or X e.g. CaTiO 3, KNbO 3, LaGaO 3 > 300 examples: tunable properties SrTiO 3 Ti 4+ : corners (solid circles, CN = 6) O 2 : edge centers (open circles, CN = 2) Sr 2+ : body center (green circle, CN = 12) Sr + O together = fcc/ccp [1/4 Sr, 3/4 O] Ti in 1/4 O h sites cf. NaCl: fcc/ccp Na +, all O h sites filled West, Ch.1, p.54-57
High-Temperature Superconductors T C of superconductors, pre-1986: Hg (4.2K), PbBi (10K), Nb 3 Ge (23.3K) Ceramic structure based on perovskite YBa 2 Cu 3 O 7 δ T C = 93K (B.P. N 2 = 77K) ρ = 1/σ = 0 below T C 2008: T C = 210K Sn x Ba 4 Ca 2 Cu x+4 O y, x = 6 2010: T C = 254K (Tl 4 Ba)Ba 2 Ca 2 Cu 7 O 13
Defect Perovskite Structure of YBa 2 Cu 3 O 7 Left: 3 perovskite unit cells, CaTiO 3 3 = Ca 3 Ti 3 O 9 Center: Replace 3 Ca with 2 Ba & 1 Y; Ti with Cu YBa 2 Cu 3 O 9 orthorhombic unit cell count Right: Removal of 2/9 of oxygens gives defect perovskite structure, YBa 2 Cu 3 O 7 123 Superconductor CN(Ba) = 10, CN(Y) = 8
Polyhedral View of YBa 2 Cu 3 O 7 δ Chains of corner-sharing CuO 4 square planar units Sheets of corner-sharing CuO 5 square pyramids Superconductivity parallel to sheets Non-stoichiometric compound: 0 δ 1, δ R δ = 0.1 Gradual loss of doublybridging O s on chains upon or P(O 2 ) YBa 2 Cu 3 O 7 δ Y 3+, Ba 2+, O 2 Cu +2.33 2Cu 2+ and Cu 3+ If YBa 2 Cu 3 O 9, 3Cu = 11+ Not possible for Cu 2+ & Cu 3+ Linear CuO 2 units, w/ Cu + δ = 0.5, T C = 60K δ > 0.6: no superconductivity
2001: MgB 2 T c = 39 K 1970s: Salts of tetrathiafulvalene, (C 2 H 2 S 2 C) 2 quasi 1-D, 2-D stacks of donors T C < 13 K
ReO 3 and Tungsten Bronzes ReO 3 : corner-sharing ReO 6 octahedra Empty body center (No Sr) WO 3, UO 3, MoF 3 3D network of open channels Na x W V xw VI 1-xO 3 Some body centers occupied by Na (0 x 1) Low x: pale yellow, semiconducting High x: bright bronze, metallic West, p.63-66
W VI O 6 O 2 WO 3 Unit cell contents: W 6+ : 8 (1/8) = 1 O 2 : 12 (1/4) = 3 Tunable properties and adaptive structure Void space for injection of [H + or Li + or Na + ] + e H 1+ x W V x W VI 1 x O 3 Tungsten Bronzes Electrochromic properties: ph-electrodes, displays, ion-selective electrodes, batteries, sensors, Electrochemical or chemical synthesis of M x WO 3
Electrochromic WO 3 Thin Films Electrochromic Film: Multilayer stacks that behave like batteries Visible indication of their electrical charge Fully charged: opaque Partially charged: partially transparent Fully discharged: transparent Uses: smart windows, displays, mirrors, rechargeable solid state batteries, ph-sensitive electrochemical transistors, selective oxidation catalyst, solar cells, chemical sensors, Chemical Vapor Deposition onto substrate: 2WF 6 + 3O 2 2WO 3 + 6F 2 2W(CO) 6 + 9O 2 2WO 3 + 12CO 2 e into CB of W VI O 3 M + into hole
Electrochemical Injection of M +, e WO 3 thin film: Transparent A x 1+ W xv W 1 x VI O 3 : Color A, x e A + = H +, Li + or Na +, 0 x 1 Absorption of light [A + ] only ~ 1 V required In 2 O 3 -SnO 2 (ITO) Ce/TiO 2 or V 2 O 5 glassy PEO 8 LiSO 3 CF 3 Li x W xv W 1 x VI O 3
Why the Color Change for WO 3? CB [W 6+ (d 0 )] Localized VB [W 5+ (d 1 )] Delocalized VB [W 5+ (d 1 )] VB [O 2 (2pπ)] WO 3 x(m + + e ) M x WO 3 x(m + + e ) M x WO 3 Wide band gap insulator LMCT, UV Narrow band gap semiconductor IVCT, Visible W 5+ + W 6+ W 6+ + W 5+ Metallic IVCT, Visible
Polymorphs of WO 3 Hexagonal Tungsten Bronzes (HTBs) A x WO 3, A = K, Rb, Cs, In, Tl Still chains of corner-sharing WO 6 O h along c-axis (Smart, Fig. 5.36) WO 3 unit cell ratio Larger channels accommodate larger A A cations reside in hexagonal channels 0.19 < x < 0.33 x < 0.19: Mix of WO 3 and HTB, regularly spaced (West Fig. 6.14; Smart Figs. 5.37 & 5.38) Planar intergrowths of SC WO 3 and HTB
Polymorphs of WO 3 Tetragonal Tungsten Bronzes (TTB) A x WO 3, A = Na, K, In, Ba, Pb Still chains of corner-sharing WO 6 octahedra along c-axis WO 3 unit cell ratio Perovskite-type square tunnels Triangular tunnels, as in HTB 2 pentagonal tunnels per square tunnel Ferroelectric West p. 64-6
WO 3 x : Defect Elimination by Crystallographic Shear WO 3 before CS WO 3 x after CS Elimination of oxygen anion vacancies edge-sharing O h CS planes can be random or regularly spaced (x takes on specific values: Magneli phase formation) Change in CN for some anions Some W 6+ W 5+, tuning the band filling of W Planar defect West, Section 2.4.1, p.108-110; Smart, Section 5.8.1, p.252-6)
Planar Defects (Section 2.4) CS Planes of WO 3 x Planar Intergrowths Stacking Faults Common in layered structures e.g. Co ccp/fcc (ABCABC) hcp (ABABAB) ABABABCABABAB Polytypes Subgrain Boundaries Anitphase Boundaries
Line Defects: Dislocations (Section 2.5) Edge dislocations Line defect comes out of page, @ center of diagram Dislocations slip under pressure (Fig. 2.21) Pure metals softer than expected Spirals on crystal surfaces Work hardening Stoichiometric: same overall formula Screw dislocations SS = line of screw dislocation Atoms spiral around line
Point Defects (Section 2.2) Schottky Defect Pair of vacant sites: one anion, one cation Same overall formula ( stoichiometric defect) Missing Cl, net charge of +1 Missing Na +, net charge of 1 120 kj/mol to dissociate vacancy pairs Same as enthalpy of association for NaCl Defect concentration: 1 in 10 15 But 1 grain ~ 1mg ~ 10 19 atoms 10 4 Schottky defects Responsible for electrical, optical properties p.85
Point Defects (Section 2.2) Frenkel Defect Atom displaced from lattice site to empty intersticial site e.g.: AgCl (rock salt), Ag displaced into T d site of Cl fcc/ccp lattice 8 C.N. site (total, Ag + and Cl ) Softer Ag +, more covalency Harder Na +, more ionic, prefers Schottky defects Vacancy ve, intersticial +ve, paired p.85-6
Point Defects (Section 2.2) Color Centers Heat alkali halide in M (g) Na absorbs on crystal surface Electron migrates to anion vacancy Cl migrates to surface F-center e in a box: discrete energy levels, absorbs visible hν color center Color depends on crystal composition (not e ) NaCl + K (g) or Na (g) : green/yellow KCl + K (g) : violet p.90-1
Other Color Centers of Rock Salt H-center Cl 2 ion occupies one anion site Cl 2 parallel to [101] F- and H-centers eliminate each other V-center Cl 2 ion occupies two anion sites Cl 2 parallel to [101] Irradiation with X-rays ionizes Cl p.91
Extrinsic Defects Schottky and Frenkel defects are intrinsic, stoichiometric (overall formula remains same) Extrinsic: doping crystals with aliovalent impurities e.g.: NaCl + CaCl 2 Na 1-x Ca x V Na Cl Formula change ccp Cl ; Na +, Ca 2+, V Na all in octahedral sites 1 vacancy for each Ca 2+, controllable Schottky defect equilibrium cst: K [V Na ][V Cl ] (p. 216, 221) x V Na x But K is constant (if defects << 1%) V Cl x x Effective vacancy migration responsible for conductivity Measure σ vs. T, x H of defect formation, migration p.91-2
Solid Solutions (Section 2.3) Dopant conc. > 1% solid solution Crystalline phase with variable composition Two types: Substitutional and intersticial Substitutional Solid Solution: Al 2 O 3 corundum: hcp O 2, Al 3+ in 2/3 O h sites, white Cr 2 O 3 corundum: hcp O 2, Cr 3+ in 2/3 O h sites, green Mix, high temp ( T S term) Al 2 x Cr x O 3, 0 x 2 x ~ 0.02: ruby gemstone Al 3+ and Cr 3+ randomly distributed over O h sites Probability of Al 3+ or Cr 3+ depends on x, can use average properties, size, etc. Same charge & similar radii (within 15%, p.97) & isostructural for complete solid solution p.95-8
Intersticial Solid Solutions Pd fcc, occludes H 2 gas PdH x, 0 x 0.7 α-fe: bcc Stable below 910 C γ-fe: fcc Stable between 910 C and 1400 C δ-fe: bcc Stable between 1400 C and 1534 C (MP) Steel: solid solution with C only for γ-fe C in O h sites, up to 2 wt.% Larger, undistorted sites for fcc Fe than bcc Fe (p.99, Fig. 2.12) Solid solution formation and allowed x values must be determined experimentally p.98-9
ZrO 2, Zirconia Fluorite-type structure (CaF 2 ) fcc Zr 4+ O 2 in every T d site Unit cell contents: Zr 4+ : 8 (1/8) + 6 (1/2) = 4 O 2 : 8 (1) = 8 ZrO 8 cubes, Zr 4+ at BC of alternate cubes ZrO 2, poor O 2 conductor: all anion sites occupied Add CaO to ZrO 2, creates anion vacancies (non-stoichiometric, extrinsic defect): xcao + (1 x)zro 2 Ca x Zr 1 x O 2 x [V O2 ] x p.101
Lime-Stabilized Zirconia, A Solid Electrolyte for Oxygen Sensors Calcium Zirconium Oxygen Ca x Zr 1 x O 2 x [V O2 ] x, 0 x 0.2 Anion vacancies greatly increase the ionic conductivity of O 2 Interstitialcy: interstitial substitution, knock on knock off mechanism Similar ideas for F ion conductor: Na x Pb 1 x F 2 x
Oxygen Concentration Cell, An Oxygen Gas Sensor Ca x Zr 1 x O 2 x PʹO2 < PʺO2 Measure potential difference, E 500 to 1000 C for sufficiently rapid O 2 transport Combined Nernst equation for half reaction at each electrode: E= RT 4F ln P" O 2 P' O2 Gives P O2, sensitive to 10 16 atm Short-circuits < 10 16 atm; use stabilized thoria, ThO 2 Applications: analysis of exhaust gas, pollution, molten metals, respiration, equilibria (CO/CO 2, H 2 /H 2 O, metal/metal oxide), fuel cells p.427-9