Point Defects in Solids

No real crystal is a perfect, infinitely repeating lattice — at any temperature above absolute zero, thermal

vibration and the practical realities of crystal growth introduce localised irregularities called point defects, disruptions confined to a single lattice point or a small cluster of points. Point defects are broadly

divided into two classes: stoichiometric defects, which do not change the overall chemical formula (ratio of

cations to anions) of the compound, and non-stoichiometric defects, which do.

Schottky defect (a stoichiometric defect) arises when an equal number of cations and anions are missing from

their normal lattice sites entirely — leaving vacancies — while the rest of the lattice stays intact. It occurs

mainly in ionic compounds where the cation and anion are of similar size, so that removing one of each maintains

electrical neutrality without geometric strain, and where the coordination number is comparatively high (typically

$6$ or $8$). Sodium chloride and potassium chloride are classic examples. Because atoms/ions are genuinely missing

from the lattice — not just relocated — the Schottky defect decreases the density of the crystal, since the

same mass is now spread over what is effectively the same or a very slightly larger volume with fewer particles in

it.

Frenkel defect (also stoichiometric) arises when a smaller ion — almost always the cation — is dislodged from

its normal lattice site and instead squeezes into a nearby, otherwise-empty interstitial space between lattice

points, leaving a vacancy behind at its original site. This defect is common precisely when there is a large

size difference between the cation and anion, because a much smaller cation can fit into an interstitial gap that

a similarly sized anion cannot; $\text{AgCl}$, $\text{AgBr}$ and $\text{ZnS}$ are typical examples. Because no ion

actually leaves the crystal — it is merely relocated from a regular site to an interstitial one — the total number

of particles and the total volume are essentially unchanged, so a Frenkel defect does not change the density

of the crystal, unlike a Schottky defect.

Non-stoichiometric metal-excess defects arise, for instance, when a crystal like $\text{NaCl}$ is heated in

the vapour of the metal (sodium vapour). Sodium atoms deposit on the crystal surface and diffuse in, each losing

its valence electron to become $\text{Na}^+$ (which occupies a normal cation site) while the freed electron …