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

2. Lattice or point defects: Vacancies (oxygen, cation) Interstitial ions
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)
Extended defects:
Crystallographic shear
Dislocations
Grain boundaries
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.
Binary oxides
(ZnO)
Ternary oxides
(ZnAl2O4)
Cation vacancy
Oxygen vacancy
Interstitial cation
Interstitial oxygen
Foreign ion (donor)
Foreign ion (acceptor)
Antisite defects

3. Rules for defect reactions:
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.
1eV = 96.5 kJ/mol
Frenkel disorder
Schottky disorder

4. Defects and entropy N atoms arranged at (N+n) sites with n vacancies
Thermodynamic probability for distinguishable particles
N0: total number of atoms
ni: number of atoms on the i-th energy state -

5. Defects and nonstoichiometry in binary oxides
Oxygen nonstoichiometry (TiO2, CeO2, Nb2O5, V2O5)
Metal nonstoichiometry (FeO, NiO, MnO)
Fe1-yO

6. Defects and nonstoichiometry in binary oxides
Isolated
defects
Defect complexes
Formation of subphases
Defect ordering
CeO2-x
n = 5
n = 4
n = 15-18
-GO2 (kcal/mol)
- log x in CeO2-x
Equilibrium constant
Electroneutrality
x: fraction of vacant sites in CeO2-x
In general:
n = 6: doubly ionized vacancies
n = 4: singly ionized vacancies
n = 2: neutral vacancies
n ≤6 for isolated defects or defect complexes

8. Defects and nonstoichiometry in binary oxides
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

9. Lattice defects and nonstoichiometry in perovskites
BaTiO3
Partial Schottky disorder (TiO2–rich side)
Partial Schottky disorder (BaO-rich side)
Full Schottky disorder
Oxygen nonstoichiometry
1eV = 96.5 kJ/mol

10. Lattice defects and nonstoichiometry in perovskites
BaTiO3
Ti-rich
Ba-rich

11. 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
Ba-rich
Ti-rich

12. Lattice defects and electrical conductivity in perovskites
Z: numero di cariche; e: carica dell’elettrone; : mobilità
c: concentrazione
Electrical conductivity
(1) At low p(O2) << p0(O2)
n-type
p-type
(1)m = -1/6
(2)m = -1/4
BaTiO3
p0(O2)
n = p
(2a) At intermediate p(O2) and R = Ba/Ti < 1
(2b) At intermediate p(O2) with R = 1 and acceptor impurities
(3) At high p(O2) p(O2) > p0(O2)
Reduction (1): H2-3 eV
Oxidation (3): H1 eV

13. 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
Donor doping: the substitutional impurity has a higher charge than the regular and bring more oxygen into the lattice 13

14. 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);
1200°C
La:BaTiO3
p0(O2)

15. Doping of perovskites: influence of doping on electron conductivity
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.
p0(O2)

16. Doping of perovskites: from isolated defect to oxygen vacancy ordering and formation of layered structures
Due to the high dielectric constant ( ) 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.
Sr2Fe2O5
ABO3
A2B2O5
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.
A4B4O11

17. 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): 
n-type
Fe2+
n-type
p-type
Fe4+
p-type
At high p(O2)

18. Doping of perovskites: excess oxygen, shear planes and layered structures
cubic
distorted
orthorhombic
SrTiO3
La2Ti2O7
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
x = 0, δ = 0 : SrTiO3
x = 1, δ = 0.5 : La2Ti2O7
δ = x/2
The structure can be described as the intergrowth of perovskite layers (SrTiO3) and La2Ti2O7 layers. A layered perovskite with general formula:
La4Srn-4TinO3n+2

19. Aurivillius compounds: ((Bi2O2)2+(Bim-1TimO3m+1)2-)
Layered perovskites
A typical example: Ruddlesden-Popper phases SrO(SrTiO3)n or Srn+1TinO3n+1
Sr3Ti2O7
(n = 2)
SrO P
Sr3Ti2O7
SrTiO3+Sr3Ti2O7
Aurivillius compounds: ((Bi2O2)2+(Bim-1TimO3m+1)2-)
Ferroelectric & piezoelectric materials with high TC