Defect Chemistry. • Crystals are imperfect at T > 0K. • High purity diamond, quartz
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Defect Chemistry • Crystals are imperfect at T > 0K • High purity diamond, quartz: 300 examples: tunable properties • • • •
SrTiO3 Ti4+: corners (solid circles, CN = 6) O2–: edge centers (open circles, CN = 2) Sr2+: body center (green circle, CN = 12)
• Sr + O together = fcc/ccp [1/4 Sr, 3/4 O] • Ti in 1/4 Oh sites • cf. NaCl: fcc/ccp Na+, all Oh sites filled
West, Ch.1, p.54-57
High-Temperature Superconductors • TC of superconductors, pre-1986: Hg (4.2K), PbBi (10K), Nb3Ge (23.3K) • Ceramic structure based on perovskite • YBa2Cu3O7–δ • TC = 93K (B.P. N2 = 77K) •
ρ = 1/σ = 0 below TC
• 2008: TC = 210K SnxBa4Ca2Cux+4Oy, x = 6 • 2010: TC = 254K (Tl4Ba)Ba2Ca2Cu7O13
Defect Perovskite Structure of YBa2Cu3O7
•
Left: 3 perovskite unit cells, CaTiO3 × 3 = Ca3Ti3O9
•
Center: Replace 3 Ca with 2 Ba & 1 Y; Ti with Cu → YBa2Cu3O9 orthorhombic unit cell count
•
Right:
•
“123” Superconductor
•
CN(Ba) = 10, CN(Y) = 8
Removal of 2/9 of oxygens gives defect perovskite structure, YBa2Cu3O7
Polyhedral View of YBa2Cu3O7–δδ
•
YBa2Cu3O7–δ
•
Y3+, Ba2+, O2– ⇒ Cu+2.33 ⇒ 2Cu2+ and Cu3+
•
If YBa2Cu3O9, 3Cu = 11+
•
Not possible for Cu2+ & Cu3+
•
Chains of corner-sharing CuO4 square planar units
•
Sheets of corner-sharing CuO5 square pyramids
•
Superconductivity parallel to sheets
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Non-stoichiometric compound: 0 ≤ δ ≤ 1, δ ∈ R
•
δ = 0.1
•
Gradual loss of doublybridging O’s on chains upon ∆ or ↓ P(O2)
•
Linear CuO2 units, w/ Cu+
•
δ = 0.5, TC = 60K
•
δ > 0.6: no superconductivity
2001: MgB2 Tc = 39 K
1970s: Salts of tetrathiafulvalene, (C2H2S2C)2 “quasi” ” 1-D, 2-D stacks of donors TC < 13 K
ReO3 and Tungsten Bronzes • ReO3: corner-sharing ReO6 octahedra • Empty body center (No Sr) • WO3, UO3, MoF3 • 3D network of open channels • NaxWVxWVI1-xO3 • Some body centers occupied by Na (0 ≤ x ≤ 1) • Low x: pale yellow, semiconducting • High x: bright “bronze”, metallic • West, p.63-66
WVIO6
O2–
WO3 Unit cell contents: W6+ : 8×(1/8) = 1 O2– : 12×(1/4) = 3
• Tunable properties and adaptive structure • Void space for injection of [H+ or Li+ or Na+] + e– → Hx1+ WxV W1–xVI O3 “Tungsten Bronzes” • Electrochromic properties: pH-electrodes, displays, ion-selective electrodes, batteries, sensors, O • Electrochemical or chemical synthesis of MxWO3
Electrochromic WO3 Thin Films Electrochromic Film: • Multilayer stacks that behave like batteries • Visible indication of their electrical charge • Fully charged: • Partially charged: • Fully discharged:
opaque partially transparent transparent
• Uses: smart windows, displays, mirrors, rechargeable solid state batteries, pH-sensitive electrochemical transistors, selective oxidation catalyst, solar cells, chemical sensors, O
Chemical Vapor Deposition onto substrate: 2WF6 + 3O2 → 2WO3 + 6F2 2W(CO)6 + 9O2 → 2WO3 + 12CO2
e– into CB of WVIO3 M+ into hole
Electrochemical Injection of M+, e– WO3 thin film: Transparent Ax1+WxVW1–xVIO3: Color ∝ A, x • A+ = H+, Li+ or Na+, 0 ≤ x ≤ 1 • Absorption of light ∝ [A+] • only ~ 1 V required
In2O3-SnO2 (ITO) Ce/TiO2 or V2O5 glassy PEO8LiSO3CF3 LixWxVW1–xVIO3
e–
Why the Color Change for WO3? CB (d0)]
[W6+
Delocalized VB [W5+ (d1)]
Localized VB [W5+ (d1)]
VB [O2– (2pπ)]
WO3
x(M+ + e–)
MxWO3
x(M+ + e–)
MxWO3
Wide band gap insulator
Narrow band gap semiconductor
Metallic
LMCT, UV
IVCT, Visible
IVCT, Visible
W5+ + W6+ → W6+ + W5+
Polymorphs of WO3 Hexagonal Tungsten Bronzes (HTBs) AxWO3, A = K, Rb, Cs, In, Tl • Still chains of corner-sharing WO6 Oh
along c-axis (Smart, Fig. 5.36) • WO3 unit cell ratio • Larger channels accommodate larger A • A cations reside in hexagonal channels • 0.19 < x < 0.33 • x < 0.19: Mix of WO3 and HTB, regularly spaced (West Fig. 6.14; Smart Figs. 5.37 & 5.38) • Planar intergrowths of SC WO3 and HTB
Polymorphs of WO3 Tetragonal Tungsten Bronzes (TTB) AxWO3, A = Na, K, In, Ba, Pb • Still chains of corner-sharing WO6 octahedra along c-axis • WO3 unit cell ratio • Perovskite-type square tunnels • Triangular “tunnels”, as in HTB • 2 pentagonal tunnels per square tunnel • Ferroelectric • West p. 64-6
WO3–x: Defect Elimination by Crystallographic Shear WO3 before CS
WO3–x after CS
• Elimination of oxygen anion vacancies → edge-sharing Oh • CS planes can be random or regularly spaced (x takes on specific values: Magneli phase formation) • Change in CN for some anions • Some W6+ → W5+, 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 WO3–x
Planar Intergrowths
Stacking Faults • Common in layered structures • e.g.
Co
ccp/fcc (ABCABC) hcp (ABABAB)
Polytypes
OABABABCABABABO 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 1015 • But 1 grain ~ 1mg ~ 1019 atoms ⇒ 104 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 Td 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 • Cl2– ion occupies one anion site • Cl2– parallel to [101] • F- and H-centers eliminate each other
V-center • Cl2– ion occupies two anion sites • Cl2– 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 + CaCl2 → Na1-xCaxVNa Cl x • Formula change • ccp Cl–; Na+, Ca2+, VNa all in octahedral sites • 1 vacancy for each
x
Ca2+,
controllable
• Schottky defect equilibrium cst: K ∝ [VNa][VCl] (p. 216, 221) • x↑ ⇒ VNa ↑ x
• But K is constant (if defects 1% ≡ solid solution • Crystalline phase with variable composition • Two types: Substitutional and intersticial
Substitutional Solid Solution: • Al2O3 corundum: hcp O2–, Al3+ in 2/3 Oh sites, white • Cr2O3 corundum: hcp O2–, Cr3+ in 2/3 Oh sites, green • Mix, high temp (↑ T∆S term) → Al2–xCrxO3, 0 ≤ x ≤ 2 • x ~ 0.02: ruby gemstone • Al3+ and Cr3+ randomly distributed over Oh sites • Probability of Al3+ or Cr3+ 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 H2 gas → PdHx, 0 ≤ x ≤ 0.7 α-Fe: γ-Fe: δ-Fe: (MP)
bcc fcc bcc
Stable below 910°C Stable between 910°C and 1400°C Stable between 1400°C and 1534°C
• Steel: solid solution with C only for γ-Fe • C in Oh 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
ZrO2, Zirconia • Fluorite-type structure (CaF2) • fcc Zr4+ • O2– in every Td site Unit cell contents: Zr4+: 8×(1/8) + 6 ×(1/2) = 4 O2–: 8×(1) = 8 • ZrO8 cubes, Zr4+ at BC of alternate cubes • ZrO2, poor O2– conductor: all anion sites occupied • Add CaO to ZrO2, creates anion vacancies (non-stoichiometric, extrinsic defect): xCaO + (1–x)ZrO2 ↔ CaxZr1–xO2–x [VO2–]x p.101
Lime-Stabilized Zirconia, A Solid Electrolyte for Oxygen Sensors Calcium Zirconium Oxygen
• CaxZr1–xO2–x [VO2–]x , 0 ≤ x ≤ 0.2 • Anion vacancies greatly increase the ionic conductivity of O2– • Interstitialcy: interstitial substitution, knock on – knock off mechanism • Similar ideas for F– ion conductor: NaxPb1–xF2–x
Oxygen Concentration Cell, An Oxygen Gas Sensor • 500 to 1000°C for sufficiently rapid O2– transport
′
• Combined Nernst equation for half reaction at each electrode:
CaxZr1–xO2–x
PʹO2 < PʺO2 • Measure potential difference, E
RT P"O2 E= ln 4F P'O2
• Gives P’O2 , sensitive to 10 –16 atm • Short-circuits < 10 –16 atm; use stabilized thoria, ThO2 • Applications: analysis of exhaust gas, pollution, molten metals, respiration, equilibria (CO/CO2, H2/H2O, metal/metal oxide), fuel cells p.427-9
