Inorganic chemistry

Crystal lattice defects

Real crystals are never perfectly periodic. Vacancies, interstitials, substitutions and dislocations alter transport, colour, strength and reactivity; controlling those defects is central to materials chemistry.

1 Lower secondary 2 Upper secondary 3 Undergraduate 4 Advanced 5 Research

IntuitionIntuition: a missing or misplaced atom changes the whole solid

A vacancy is not merely an empty dot: nearby atoms relax, charge redistributes, and the defect can trap carriers or enable diffusion. The crystal stays mostly ordered, but a dilute defect population can dominate a useful property.

Increase vacancy fraction to see ions removed at random. Real Schottky defects create charge-balanced cation and anion vacancies.

SchoolSchool level: point defects

Common point defects
Defect	Description	Example
Vacancy	Missing atom at a lattice site	Schottky pair in NaCl
Interstitial	Extra atom between sites	C in Fe
Substitutional	Foreign atom replaces host	P in Si

Definition: Schottky and Frenkel defects

In an ionic solid a Schottky defect removes stoichiometric sets of cations and anions, preserving charge neutrality. A Frenkel defect moves an ion from its normal site to an interstitial site, making a vacancy–interstitial pair without changing composition.

\mathrm{Na_{Na}^{x}+Cl_{Cl}^{x}\rightleftharpoons V_{Na}^{\prime}+V_{Cl}^{\bullet}+NaCl_{surface}}

Kröger–Vink notation records the species, lattice site and effective charge relative to the perfect crystal. A prime denotes one negative effective charge, a dot one positive charge, and x a neutral effective charge. It is bookkeeping, not the ion’s absolute oxidation state.

Example: Charge-balanced vacancies in NaCl

If 0.01% of Na⁺ sites are vacant in an otherwise stoichiometric NaCl crystal, what fraction of Cl⁻ sites must be vacant for Schottky disorder?

Solution

The same fraction, 0.01%, because one cation vacancy and one anion vacancy form a neutral pair and preserve the 1:1 site ratio.

UndergraduateUndergraduate: equilibrium concentrations and nonstoichiometry

At finite temperature, forming defects costs enthalpy but increases configurational entropy. Their equilibrium concentration follows mass action and rises approximately exponentially with formation free energy; impurity chemical potentials and oxygen partial pressure can shift defect populations dramatically.

c_v\propto\exp\!\left(-\frac{\Delta G_f}{k_BT}\right)

The ideal dilute-defect approximation breaks down when defects associate, order, change charge state or interact elastically. Charge neutrality couples charged vacancies, interstitials, electrons and holes; a defect diagram maps stable populations as a function of chemical potential and Fermi level.

Example: Thermal vacancy estimate

For a rough estimate, let a vacancy formation free energy be 1.0 eV at 1000 K. Estimate cᵥ using exp(−ΔGf/kBT), with kB = 8.617×10⁻⁵ eV K⁻¹.

Solution

kBT ≈ 0.0862 eV, so cᵥ ≈ exp(−11.6) ≈ 9×10⁻⁶. This simplified estimate neglects formation entropy, interactions and non-ideal defect chemistry.

AdvancedExtended defects and functional control

Dislocations are line defects whose Burgers vector measures the lattice mismatch around a circuit. Grain boundaries are two-dimensional interfaces; stacking faults disrupt the sequence of close-packed layers. These defects govern plastic deformation, grain-boundary diffusion and corrosion pathways.

Doping exploits controlled substitutions: phosphorus on a silicon site is a donor, while boron is an acceptor. Oxygen vacancies in oxides can change oxidation state, electronic conductivity and catalytic activity; the same defect may be beneficial or harmful depending on operating conditions.

ResearchResearch: defect engineering and energy materials

References

Defects in Solids · R. J. D. Tilley, 2008
Relations between the Concentrations of Imperfections in Crystalline Solids · F. A. Kröger, H. J. Vink, 1956