Crystal Defects and Non-Stoichiometry

Why defects must exist

The equilibrium concentration rises with temperature, since the entropy term grows in importance. This is why quenching from high temperature can freeze in a higher defect concentration than the material would have at room temperature.

The two main point defects

The density consequence is the standard discriminator. Schottky removes matter from the lattice while the volume stays the same, so density falls; Frenkel merely moves an ion within the crystal, so mass and volume are both unchanged.

The size condition follows from the interstitial site being small: only a substantially smaller ion can fit into it, so Frenkel defects require a marked size difference between the ions.

Metal excess and F-centres

Heating certain ionic solids in metal vapour produces an anion vacancy that traps an electron to maintain neutrality. That trapped electron occupies a quantised set of levels and absorbs visible light, giving the crystal colour.

These are colour centres, and they explain why an otherwise colourless crystal becomes coloured on heating in metal vapour or on irradiation. The colour depends on the host lattice rather than the metal, because it is the vacancy that traps the electron — a point that is often asked and easily got wrong.

Non-stoichiometry

Some compounds deviate measurably from simple whole-number ratios. This requires a mechanism to preserve overall charge neutrality, and that mechanism is a change of oxidation state.

Where a transition metal can exist in two oxidation states, a deficiency of metal ions can be compensated by some of the remaining ions taking the higher state. The formula then departs from the ideal ratio, and the compound is non-stoichiometric.

Non-stoichiometry is therefore largely confined to compounds of elements with accessible multiple oxidation states, which is why it is common among transition metal oxides and sulphides and rare elsewhere. Explaining that restriction is a good discriminating answer.

Consequences for properties

Ionic conduction in solids depends almost entirely on defects. Without vacancies there is no route for an ion to move, so a hypothetical perfect ionic crystal would be an insulator to ionic current. Solid electrolytes are materials engineered to have unusually high defect concentrations for exactly this reason.

Doping

Deliberately introducing a foreign ion of different charge forces vacancies or interstitials to appear in order to preserve neutrality. Adding a divalent cation to a monovalent lattice, for instance, creates one cation vacancy per added ion.

This is how ionic conductivity is engineered, and it is also the ionic analogue of semiconductor doping. Calculating how many vacancies a given dopant level produces is a standard numerical, and it reduces to charge balance.

Frequently asked questions

Why does a Frenkel defect not change density?

Because no ion leaves the crystal — one simply moves from a lattice site to an interstitial site. Total mass and volume are unaffected.

Why do only some compounds show non-stoichiometry?

Because charge neutrality must be maintained. That requires an element able to adopt more than one oxidation state, which restricts it largely to transition metal compounds.

What determines the colour of an F-centre?

The size and environment of the anion vacancy in the host lattice, since the trapped electron's energy levels depend on the potential well it sits in. The colour is characteristic of the host, not of the metal used.

How does doping increase ionic conductivity?

By creating vacancies to preserve charge balance. More vacancies means more sites into which ions can hop, so conductivity rises.