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

• Perovskite, high Tc ceramic superconductors, WO3

Extended Extended Extended Extended

DefectsDefectsDefectsDefects

Chapter 2:

Defects

• Defects cost enthalpy ∆H

• Increase entropy ∆S

• e.g. one vacancy: 1023 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, ABX3• Table 1.18: A = Group I or II metal

B = T.M. or lower p-block

X = O2– or X–

• e.g. CaTiO3, KNbO3, LaGaO3

• > 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 filledWest, 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: Removal of 2/9 of oxygens gives defect

perovskite structure, YBa2Cu3O7

• “123” Superconductor

• CN(Ba) = 10, CN(Y) = 8

Polyhedral View of YBa2Cu3O7–δδδδ

• Chains of corner-sharing

CuO4 square planar units

• Sheets of corner-sharing

CuO5 square pyramids

• Superconductivity parallel

to sheets

• Non-stoichiometric

compound: 0 ≤ δ ≤ 1, δ ∈ R

• δ = 0.1

• Gradual loss of doubly-

bridging O’s on chains

upon ∆ or ↓ P(O2)

• Linear CuO2 units, w/ Cu+

• δ = 0.5, TC = 60K

• δ > 0.6: no

superconductivity

• YBa2Cu3O7–δ

• Y3+, Ba2+, O2– ⇒ Cu+2.33 ⇒ 2Cu2+ and Cu3+

• If YBa2Cu3O9, 3Cu = 11+

• Not possible for Cu2+ & Cu3+

2001: MgB2 Tc = 39 K

1970s: Salts of

tetrathiafulvalene,

(C2H2S2C)2

““““quasi”””” 1-D, 2-Dstacks 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

• NaxWV

xWVI

1-xO3

• Some body centers occupied by Na (0 ≤ x ≤ 1)

• Low x: pale yellow, semiconducting

• High x: bright “bronze”, metallic

• West, p.63-66

WO3

Unit cell contents:

W6+ : 8×(1/8) = 1

O2– : 12×(1/4) = 3

WVIO6 O2–

• Tunable properties and adaptive structure

• Void space for injection of [H+ or Li+ or Na+] + e–

→ Hx1+ Wx

V 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: 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, O

e– into CB

of WVIO3

M+ into hole

Chemical Vapor Deposition

onto substrate:

2WF6 + 3O2 → 2WO3 + 6F2

2W(CO)6 + 9O2 → 2WO3 + 12CO2

Electrochemical Injection of M+, e–

Ce/TiO2 or V2O5

WO3 thin film: Transparent

Ax1+Wx

VW1–xVIO3: Color ∝ A, x

• A+ = H+, Li+ or Na+, 0 ≤ x ≤ 1

• Absorption of light ∝ [A+]

• only ~ 1 V required

e–

In2O3-SnO2 (ITO)

glassy PEO8LiSO3CF3

LixWxVW1–x

VIO3

Why the Color Change for WO3?

WO3

Wide band gap

insulator

LMCT, UV

VB

[O2– (2pπ)]

CB

[W6+ (d0)]

MxWO3

Metallic

IVCT, Visible

x(M+ + e–)

Delocalized

VB [W5+ (d1)]

x(M+ + e–)MxWO3

Narrow band gap

semiconductor

IVCT, Visible

Localized VB

[W5+ (d1)]

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

• 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)

WO3–x

after

CS

WO3

before

CS

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)

OABABABCABABABO

Subgrain Boundaries Anitphase Boundaries

Polytypes

Line Defects:

Dislocations

(Section 2.5)

• Pure metals softer than expected

• Spirals on crystal surfaces

• Work hardening

• Stoichiometric: same overall formula

Edge dislocations

• Line defect comes out of

page, @ center of diagram

• Dislocations slip under

pressure (Fig. 2.21)

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

• 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

Point Defects (Section 2.2)

Color Centers

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

• Formula change

• ccp Cl–; Na+, Ca2+, VNa all in octahedral sites

• 1 vacancy for each Ca2+, controllable

• Schottky defect equilibrium cst: K ∝ [VNa][VCl] (p. 216, 221)

• x↑ ⇒ VNa ↑

• But K is constant (if defects << 1%) ⇒ VCl↓

• Effective vacancy migration responsible for conductivity

• Measure σ vs. T, x ⇒ ∆H of defect formation, migration

x

x

x

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:

• 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: 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 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

• 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

Calcium

Zirconium

Oxygen

Oxygen Concentration Cell,

An Oxygen Gas Sensor

• Measure potential difference, E

• 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

• 500 to 1000°C for

sufficiently rapid O2–

transport

• Combined Nernst

equation for half reaction

at each electrode:

′

CaxZr1–xO2–x

PʹO2< PʺO2

p.427-9

E =RT

4FlnP"

O2

P 'O2