Point defect basics

Kröger-Vink notation

Defect notations in Kroger-Vink notation. via Dehoff (p.473)

Defect notations in Kroger-Vink notation. via Dehoff (p.474) (X atom on M site is wrong, should be $\ce{X^{''''}_M}$)

Frenkel and Schottky defects

Frenkel and Schottky defects maintain change neutrality, these defects are “intrinsic defects”. Examples of “extrinsic defects” include impurities.

Frenkel defects

$$ \ce{M^x_M -> M_i + V_M} $$

Frenkel defect via Dehoff (p.475)

Schottky defects

$$ \ce{null -> V^{''}_M + V^{..}_X} $$

Schottky defect via Dehoff. (p.478)

Thermodynamics of defects

Types of defects in different crystals

• For elementary crystals (such as metal), usually vacancy and interstitial defects are discussed.
• For compound crystals (such as ionic crystals), usually Frenkel and Schottky defects are discussed.

Derivation of the expression of defect concentration

The expression of defect concentration are obtained from equilibrium constants $K$, usually:

• Get $K$
• $K = \exp -\Delta G / k_BT$.

Defect concentration for different types of defects