Defect Chemistry. Extended Defects

Transcription

1 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

2 Chapter 2: Defects Defects cost enthalpy H Increase entropy S e.g. one vacancy: 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)

3 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

4 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 = : T C = 254K (Tl 4 Ba)Ba 2 Ca 2 Cu 7 O 13

5 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 Superconductor CN(Ba) = 10, CN(Y) = 8

6 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 Cu 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

7 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

8 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

9 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

10 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 CO 2 e into CB of W VI O 3 M + into hole

11 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

12 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

13 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 & 5.38) Planar intergrowths of SC WO 3 and HTB

14 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

15 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 ; Smart, Section 5.8.1, p.252-6)

16 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

17 Line Defects: Dislocations (Section 2.5) Edge dislocations Line defect comes out of 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

18 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 kj/mol to dissociate vacancy pairs Same as enthalpy of association for NaCl Defect concentration: 1 in But 1 grain ~ 1mg ~ atoms 10 4 Schottky defects Responsible for electrical, optical properties p.85

19 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

20 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

21 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

22 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

23 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

24 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

25 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

26 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

27 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 atm Short-circuits < 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