Module 4: Defect Chemistry and Defect Equilibria

Materials in general consist of defects which can be divided into a variety of categories such as point

defects or 0-D defects, line defects or 1-D defects and 2-D or surface defects. These defects play an

important role in determining the properties of ceramic materials and in this context role of point

defects is extremely important. In this module, we will learn about various point defects, role of

stoichiometry i.e. cation and anion excess and deficit, role of foreign atoms on the defect chemistry.

Subsequently, we will adopt a simple thermodynamic basis for calculating their concentration in

equilibrium and then will extend the Gibbs-Duhem relation for chemical systems to the defects in

ceramics considering them to be equivalent to the dilute solutions, an approximation which is fairly

valid. This will lead us to the determination of defect concentrations as a function of partial pressure

of oxygen which is an important exercise to establish the defect concentration vs pO2 diagrams,

called as Brower’s diagrams.

Suggested reading:

1. Nonstoichiometry, Diffusion and Electrical Conductivity in Binary Metal Oxides (Science &

Technology of Materials), P.K. Kofstad, John Wiley and Sons Inc.

2. Physical Ceramics: Principles for Ceramic Science and Engineering, Y.-M. Chiang, D. P. Birnie,

and W. D. Kingery, Wiley-VCH

3. Introduction to the Thermodynamics of Materials, David R. Gaskell, Taylor and Francis

Lecture 4.1

Point Defects

Point defects are caused due to deviations from the perfect atomic

arrangement or stoichiometry. These could be missing lattice ions from

their positions, interstitial ions or substitutional ions (or impurities) and

valence electrons and/or holes.

Usually, point defects in metals are electrically neutral where as in ionic

oxides, these are electrically changed.

Ionic defects

o Occupy lattice positions

o Can be either of vacancies, interstitial ions, impurities and substitutional

ions

Electronic defects

o Deviations from a ground state electron orbital configuration give rise to

such defects when valence electrons are excited into higher energy

orbitals/ levels and lead to formation of electron or holes.

Defects are present in most oxides and are easily understood. Hence most

examples in the following section use examples of oxides.

Kröger–Vink notation in a metal oxide, MO

Regular Sites

Normal or regular occupied metal or cation site MM

Normal or regular occupied oxygen or anion site OO

Point Defects

Oxygen (anion) vacancy : VO

Metal (cation) vacancy : VM

Oxygen (anion) interstitial : OO

Metal (cation) Interstitial : Mi

Vacant interstitial site : Vi

Foreign cation : Mf

Foreign cation on regular metal site : Mfm

Foreign cation on interstitial site : Mfi

A normal cation or anion in an

oxide with zero effective change : MMx or OO

x

Charged oxygen vacancy : VO⦁ or VO

⦁⦁ (⦁ represents one

positive charge)

Charged metal vacancy : VM′or VM" ( ‘ represents one

negative charge)

Charged metal or oxygen interstitial : Mi⦁⦁ 𝑜𝑟 Oi

′′

Neutral cation & anion vacancies : VMx or VO

x

Electron and holes : e′and h

Defect Reactions

Rules for writing defect reactions

o Ratio of regular cation & anion sites is always constant.

o Mass balance to be preserved.

o Electrical neutrality is to be always preserved.

Both ionic and electronic defect compensations are possible determined by

the energetics.

We will assume complete ionization of defects.

Defect Structures in Stoichiometric Oxides

Charged point defect is a defect which ready to be ionized and provides a

complimentary electronic charged defect. Various such combinations are

possible such as

o Cation and anion vacancies (VMand VO)

o Vacancies and interstitial ion of same kind i.e. VO and Oi OR VM and Mi

o Misplaced atoms (MO & OM) − interchanged

o Vacancies and misplaced atoms for same kind of atom (VM + MO)

o Interstitial and misplaced atoms 𝑖. 𝑒. Oi& MO

o Interstitial atoms i.e. Mi & Oi

Among all of these, first two are the most important as these are regularly

seen in many important oxides. First is called as Schottky disorder while second

is called as Frenkel disorder.

a) Schottky Disorder:

This defect normally forms at the outer or inner surfaces or dislocations. It eventually diffuses into the crystal unit equilibrium is reached.

Figure 1 Schottky Disorder

The defect reaction written as

0 (or Null) ⇌ VM ′′ + Vo

⦁⦁

This defects is preferred when cations and anions are of comparable sizes.

Examples are rocksalt structured compounds such as NaCl, MgO,

Corundum, Rutite etc..

VO

VM MM

OO

b) Frenkel Disorder:

Figure 2 Frenkel Defect

This defect can form inside the crystal.

It forms where cations are appreciably smaller then anions

Defect reaction is written as

0 ⇌ VM′′ + Mi

In cases, where anions form the disorder, then it is called as Anti-Frenkel.

Corresponding defect reaction in that case would be

0 ⇌ VO + Oi

′′

Examples of compounds showing this defect are AgBr type compounds such

as AgBr, AgI etc.

c) Intrinsic Ionization

Thermal creation of electron hole pair and is depicted by

0 = e + h

Mi

VM MM

OO

Defect Structures in Non-stoichiometric Oxides:

Mainly of two types:

i) Oxygen deficient (or excess metal)

ii) Metal deficient (or excess oxygen)

Nonstoichiometry necessitates presence of point defects and extent of non-stoichiometry determines the concentration of Defects.

In such oxides, electrical neutrality is preserved via formation of point

defects and electronic changes.

Intrinsic ionization is always a possibility.

d) Oxygen Deficient Oxides

Formation of oxygen vacancies or metal interstitials or both are possible

Formation occurs only at the surface

i) If oxygen vacancies are the dominating defects

Depicted by MO2-x (x is the extent of non-stoichiometry) and overall

reaction as

MO ⇌ MO2−x +x

2O2 ↑

Due to loss of oxygen, possible defect reactions would be

o Electronic compensation leading to creation oxygen vacancies and of

electrons

OO ⇌ VO⦁⦁ +

1

2 𝑂2 + 2�� or

o Ionic compensation leads to formation of oxygen vacancies and

reduction of metal ions on their sites

OO ⇌ VO⦁⦁ +

1

2 O2 + 2MM

′

ii) If metal interstitials are the dominating defects then,

Depicted as 𝐌𝟏+𝐲 𝐎𝟐 (y is the extent of non-stoichiometry)

Possible defect reactions are

o Ionic compensation leading to the formation of metal interstitials and

reduction of metal ions on their sites

MM ⇌ Mi⦁⦁⦁⦁ + 4MM

′ or

o Electronic compensation leading to the formation of metal interstitials

and free electrons

M ⇌ Mi⦁⦁⦁⦁ + 4e

Creation of quasi-free electrons (extra charge is represented as M’)

Conduction occurs due to transport of electrons

Typically n-type conductors.

Example: TiO2, ZrO2, CeO2, Nb2O5

e) Metal Deficient Oxides

Formation of either metal vacancies or oxygen interstitials (excess oxygen)

Formation occurs typically at the surface.

Following cases are possible:

i) If metal deficiency is dominating defect then

Depicted as metal deficient oxide M1-yO (y is the extent of non-

stoichiometry)

Possible defect reaction is that of electronic compensation

1

2O2 ⇌ OO + VM

′′ + 2h

Creation of holes

Conduction due to holes i.e. a p- type conductor

Examples of oxides showing this characteristics are MnO, NiO, CoO, FeO

etc.

ii) If metal deficiency is dominating defect then

Oxides depicted as MO2+x

Oxygen interstitials can form due to following reaction

1

2O2 ⇌ Oi

′′ + 2h

P-type conductor

Example can be an oxide like UO2.

Dissolution of foreign cations in an oxide

a) Case-1: Parent oxide is MO and foreign oxide is Mf2O3.

Following scenarios are likely:

i. Mf 3+ occupies M2+ sites in MO giving rise to an extra positive charge on

the metal site and a free electron according to following defect reaction

Mf2O3⇌2 MfM

⦁ +2OO+1

2O2 ↑+2e (i)

ii. Alternatively for a metal deficient oxide MO, creates metal vacancies as

Mf2O3 ⇌ 2MfM

⦁ + 3OO + VM′′ (ii)

iii. For an oxygen deficient oxide, oxygen vacancies are compensated as

VO

•• +Mf 2O

3Û 2M

fM

• + 3OO

(iii)

Reaction (iii) results is reduction in vacancy concentration, while

reactions (i) & (ii) result in increase in the electron concentration or

metal vacancy concentration.

iv. Reaction (i), for a p-type conductor, can be alternatively expressed as

following

2h + Mf2O3 ⇌ 2MfM

⦁ + 2OO +1

2O2 ↑ (iv)

-

b) Case-2: Parent oxide is MO and foreign oxide is Mf2O.

It is recommended for the students to carry out this exercise.

Summary

In this lecture we have learnt about the existence of point defects as a reality in the materials and

that their presence can be well studied using defects reactions similar to chemical reactions. The

point defects can be neural as well as charged defects in most materials and they are denoted by

Kroger-Vink notation. The guiding principle to form a point defect is that solid has to remain charge

neutral. The point defect formation in a stoichiometric solid takes places by formation of cation and

anion vacancies in stocihiomtetic amounts, called as Schottky defects or by formation of Frenkel (or

anti-Frenkel) defects via formation of a vacancy of cation (or anion) and an interstitial of the same

ion. On the other hand, in non-stoichiometric solids, defect formation also gives rise to a

compensating electron or hole or oxidation or reduction for maintaining charge neutrality. We also

looked at how impurities in the ionic solids can change their defect chemistry which can be used in a

useful manner.