Defects in crystals,
Non-stoichiometry
Point defects
Vacancy
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Point defects
Interstitial
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Point defects
Substitutional
impurity
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Point defects
Schottky pair
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Point defects
Frenkel defect
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Other defects
Line defects
• Edge dislocation
• Screw dislocation
Plane defects
• Stacking fault
• Small angle grain boundaries
Non-stoichiometry
Example: FeO
 Stoichiometric case: Fe2+ : O2- = 1:1
Usually: partial oxidation of Fe2+ occurs
 non-stoichiometric composition: Fe1-xO
Say for example:
Let:
[Fe3+] = a ;
Fe3+/Fe2+ = 0.05
[Fe2+] = b
a/b = 0.05
charge balance : 3a + 2b = 2
Solving :
a = 0.05; b = 0.93
Therefore the non-stoichiometric composition = Fe0.98O
Effect of defects on properties
Frenkel defects
• AgBr, AgCl
• ionic conduction, photography
Substitutional impurities
• Extrinsic semiconductors
• n-type: P doped Si
• p-type: B doped Si
Relevance of non-stoichiometry
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electrical conductivity
corrosion
electrode surface activity
catalysis
Examples of non-stoichiometric materials
• Tungsten bronzes: NaxWO3  colored materials
• 123 oxides: YBa2Cu3O7-x  high Tc superconductors
Problem Set
1. The average energy required to create a vacancy in a monatomic solid is 1.1515 eV/mol. Compute the ratio of vacancies
at 1000K and 500 K.
2. How are the density of crystals affected by the presence of Schottky and Frenkel defects ?
3. Addition of Ca2+ increases the conductivity of KCl crystal. However, it is found that the conductivity is still due to the
motion of K+ ions rather than the doped Ca2+ ions. Discuss the mechanism for the enhanced conductivity.
4. If the ratio of A3+ to A2+ in a nonstoichiometric sample of an ionic crystal AO is 0.15, what is the nature of the defect ?
Derive the correct formula for AO.
5. Discuss the nature of nonstoichiometry in (a) copper sulfide, (b) zinc oxide, (c) praseodymium oxide. What are the
different structures in the case of (c).
6. NiTe exhibits nonstoichiometry. Draw schematic diagrams to illustrate the crystal structures of the two extreme
formulations.