lattice defects in oxides. correlations between defects, properties and crystal structures

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Lattice defects in oxides. Correlations between defects, properties and crystal structures

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Page 1: Lattice defects in oxides. Correlations between defects, properties and crystal structures

Lattice defects in oxides.

Correlations between defects, properties and

crystal structures

Page 2: Lattice defects in oxides. Correlations between defects, properties and crystal structures

Defects in oxides

Lattice or point defects:

• Vacancies (oxygen, cation)• Interstitial ions• Foreign atoms at regular sites (doping/solid solutions)• Defect pairs and clusters• Electronic defects (free electrons and holes)

Defect chemistry. Lattice defect can be treated as chemical entities (energy of formation) using defect reactions (mass-action law, equilibrium constant).

Kroger-Vink notation for defects. Defect charge is referred to the perfect crystal.

Extended defects:

• Crystallographic shear• Dislocations• Grain boundaries

Cation vacancy Oxygen vacancy

Interstitial cation Interstitial oxygen

Foreign ion (donor) Foreign ion (acceptor)

Antisite defects

''ZnV

OV

iZn ''

iO

'ZnNa

ZnAl

Binary oxides (ZnO)

Ternary oxides (ZnAl2O4)

ZnAl '

AlZn

Page 3: Lattice defects in oxides. Correlations between defects, properties and crystal structures

Defects in oxides

Rules for defect reactions:

• Site relation. The number of sites must be in the correct proportion (MaXb: M/X = a/b).• Sites can be created or destroyed taking into account the site relation.• Mass balance.• Electroneutrality condition.

surfsurfOMgMgO

OMg OMgVVOMg ''

OMgMgO VVzero ''

Schottky disorder

Frenkel disorder

'Agi

AgBriAg VAgVAg

1eV = 96.5 kJ/mol

Page 4: Lattice defects in oxides. Correlations between defects, properties and crystal structures

vibrconfv SnSTHnGG 0

Defects and entropy

!!

!lnln

nN

nNkWkS BBconf

N atoms arranged at (N+n) sites with n vacancies

0;0;0 vibrconfv SSH

-

-

-

-

Thermodynamic probability for distinguishable particles

!!...!!

!

21 ro

o

nnnn

NW

N0: total number of atomsni: number of atoms on the i-th energy state

Page 5: Lattice defects in oxides. Correlations between defects, properties and crystal structures

Oxygen nonstoichiometry (TiO2, CeO2, Nb2O5, V2O5)

Metal nonstoichiometry (FeO, NiO, MnO)

Defects and nonstoichiometry in binary oxides

Fe1-yO

22

12

'2 OCeVO CeO

CeOO

2'

2

122 OeVO O

CeOo 3' CeCeCe

FeFeOFeO FeVOO 2

2

1 ''2

hVOO FeOFeO 2

2

1 ''2

3FeFeFe

Page 6: Lattice defects in oxides. Correlations between defects, properties and crystal structures

2'

2

122 OeVO O

CeOo

2/121 2

][ OO pnVK Equilibrium constant

OVn 2 Electroneutrality

2/132/13'1 22

][ OOO pxpVK

xVO 2

1 x: fraction of vacant sites in CeO2-x

6/1

2

Opx

nOpx /1

2

xnRTpRTG OOOO lnln2222

0

In general:

n = 6: doubly ionized vacanciesn = 4: singly ionized vacanciesn = 2: neutral vacancies

n ≤6 for isolated defects or defect complexes

Defects and nonstoichiometry in binary oxides

'en

Iso

late

d d

efec

ts

Def

ect

com

ple

xes

Def

ect

ord

erin

gF

orm

atio

n o

f su

bpha

ses

CeO2-x

n =

5

n =

4

n =

15-

18

-G

O2 (

kca

l/mol

)

- log x in CeO2-x

Page 7: Lattice defects in oxides. Correlations between defects, properties and crystal structures
Page 8: Lattice defects in oxides. Correlations between defects, properties and crystal structures

Defects and nonstoichiometry in binary oxides. Formation of shear planes

Ordering of defects and formation of superstructures is observed for large deviations from stoichiometry (TiO2-δ, Nb2O5-δ, WO3-δ, ReO3-δ, etc.). Elimination of oxygen vacancies by formation of metal-rich shear planes is a common mechanisms (crystallographic shear).

Formation of shear planes in ReO3 (left) and WO3 (right) by elimination of oxygen vacancies

Page 9: Lattice defects in oxides. Correlations between defects, properties and crystal structures

Lattice defects and nonstoichiometry in perovskites

Partial Schottky disorder (BaO-rich side)

Full Schottky disorder

Oxygen nonstoichiometry

Partial Schottky disorder (TiO2–rich side)

BaTiO3

1eV = 96.5 kJ/mol

Page 10: Lattice defects in oxides. Correlations between defects, properties and crystal structures

Lattice defects and nonstoichiometry in perovskites

BaTiO3

Ti-rich

Ba-

rich

Page 11: Lattice defects in oxides. Correlations between defects, properties and crystal structures

Lattice defects, nonstoichiometry and phase transitions in perovskites

Cubic (paraelectric) – tetragonal (ferroelectric) phase transition in BaTiO3

1200°C

Ti-rich

Ba-rich

Enthalpy of transition

1320°C

Transition temperature

Ti-rich

Ba-rich

Page 12: Lattice defects in oxides. Correlations between defects, properties and crystal structures

Lattice defects and electrical conductivity in perovskites

Electrical conductivity iii cez Z: numero di cariche; e: carica dell’elettrone; : mobilitàc: concentrazione

'2 2

2

1eVOO OO

(1) At low p(O2) << p0(O2)

6/12/121 22

2 OOOO pnVnpnVK

(2a) At intermediate p(O2) and R = Ba/Ti < 1

4/1''

2

OOBa pnaRVV

(2b) At intermediate p(O2) with R = 1 and acceptor impurities

4/1

22 OO pnVA

(3) At high p(O2) p(O2) > p0(O2)

hOVO OO 22

12

4/12/1122 22

OOOO pVppVpKReduction (1): H2-3 eVOxidation (3): H1 eV

hpen ;'

n-type p-type

(1)m = -1/6

(2)m = -1/4

BaTiO3

p0(O2)n = p

Page 13: Lattice defects in oxides. Correlations between defects, properties and crystal structures

Doping of perovskites: controlling defect nature and concentration

Acceptor doping: the substitutional impurity has a lower charge than the regular and bring less oxygen into the lattice

OOTiBaBaTiO OVFeBaBaOOFe 5222 '

323

OOTiBaBaTiO OVTiNaTiOONa 5222 '

223

OTiBaBaTiO OhFeBaBaOOFeO 62222

2

1 '322

3

Donor doping: the substitutional impurity has a higher charge than the regular and bring more oxygen into the lattice

OTiBaBaTiO OeTiLaOTiOOLa 6222

2

12 '

22323

OTiBaBaBaTiO OTiVLaTiOOLa 9223 ''

2323

OBaTiBaTiO OeBaNbOBaOONb 6222

2

12 '

2523

OBaBaTiBaTiO OBaVNbBaOONb 62 ''

523

Page 14: Lattice defects in oxides. Correlations between defects, properties and crystal structures

Doping of perovskites: influence of doping on electron conductivity

Donor doped compounds:• Black colour;• Good conductivity (>10-2 S/cm) even at RT;• Some show metallic conduction (103 S/cm, La:SrTiO3);

OTiBaBaBaTiO OTiVLaTiOOLa 9223 ''

2323

1200°CLa:BaTiO3

OTiBaBaTiO OeTiLaOTiOOLa 6222

2

12 '

22323

'2 2

2

1eVOO OO

p0(O2)

Page 15: Lattice defects in oxides. Correlations between defects, properties and crystal structures

Acceptor doped compounds• Light colour;• Good conductivity at high temperature• Many are insulators at RT;• Can be fired in reduced atmosphere retaining their dielectric properties.

Doping of perovskites: influence of doping on electron conductivity

p0(O2)

OOTiBaBaTiO OVMnBaBaOOMn 5222 '

323

OTiBaBaTiO OhMnBaBaOOMnO 62222

2

1 '322

3

Page 16: Lattice defects in oxides. Correlations between defects, properties and crystal structures

Doping of perovskites: from isolated defect to oxygen vacancy ordering and formation of layered structures

Due to the high dielectric constant (20-1000) and structural stability, perovskites can accomodate a large concentration of foreign aliovalent impurities (good solvent) and related charge compensating defects (cation or oxygen vacancies). The simple model of randomly distributed isolated defects (no association) holds up to high dopant concentration (few at.% for acceptors, 10 at.% for donors). At higher dopant concentration, ordering of defects, formation of shear planes and layered structures is observed.

OOTiSrSrTiO OVFeSrSrOOFe 5222 '

323

OTixxx VFeOTiSrFe 2; '

2/31

x = 0: SrTiO3; x = 1: Sr2Fe2O5

At T < 700°C, oxygen vacancy ordering occurs in Sr2Fe2O5 (brownmillerite structure).For intermediate compositions, intergrowth of perovskite blocks and brownmillerite layer with general formula AnBnO3n-1.Perovskites doped with high concentration of acceptor impurities (10-20 at.%) shows high ionic (oxygen) and electronic (holes related to transition metals Ti, Fe, Co, Nb) conductivity. Application as mixed conductors in electrochemical devices.

A4B4O11Sr2Fe2O5

ABO3 A2B2O5

Page 17: Lattice defects in oxides. Correlations between defects, properties and crystal structures

Doping of perovskites: from isolated defect to oxygen vacancy ordering and formation of layered structures

La1-xSrxFeO3 with 0 < x <0.25 can be accurately described as an acceptor-doped perovskite with randomly distributed defects

At low p(O2): OOFeLaLaFeO OVFeSrOFeSrO 52222 '

323

'2 2

2

1eVOO OO

n-typeFe2+

hOVO OO 22

12 Fe4+ p-typeAt high p(O2)

n-type

p-type

Page 18: Lattice defects in oxides. Correlations between defects, properties and crystal structures

La4Srn-4TinO3n+2

31

232 )1(2

TiOSrLa

TiOSrOxOLax

xx

δ = x/2

231

232

2

)1(2

Ox

TiOSrLa

TiOSrOxOLax

xx

cubic distortedorthorhombic

SrTiO3 La2Ti2O7

x = 0, δ = 0 : SrTiO3

x = 1, δ = 0.5 : La2Ti2O7

Doping of perovskites: excess oxygen, shear planes and layered structures

Reducing atmosphere, black conducting ceramics (up to 103 Scm-1) , random distribution of defects, x up to 0.3

Oxidizing atmosphere, less conducting, O excess accomodated by formation of shear planes when x > 0.17, by small isolated defects when x<0.17

The structure can be described as the intergrowth of perovskite layers (SrTiO3) and La2Ti2O7 layers. A layered perovskite with general formula:

Page 19: Lattice defects in oxides. Correlations between defects, properties and crystal structures

Layered perovskites

A typical example: Ruddlesden-Popper phases SrO(SrTiO3)n or Srn+1TinO3n+1

Sr3Ti2O7

(n = 2)

SrO

SrO

P

P

P

Sr3Ti2O7

SrTiO3+Sr3Ti2O7

Aurivillius compounds: ((Bi2O2)2+(Bim-1TimO3m+1)2-) Ferroelectric & piezoelectric materials with high TC

Page 20: Lattice defects in oxides. Correlations between defects, properties and crystal structures