Within any crystal, there will usually be some defects. To maintain electroneutrality of the crystals, defects that involve loss of a cation will be associated with loss of an anion, i.e. these defects come in pairs. Frenkel defects consist of a cation vacancy paired with a cation interstitial and can be generated anywhere in the bulk of the crystal, occurring most commonly in compounds with a low coordination number and cations that are much smaller than the anions. Schottky defects consist of one vacancy of each type, and are generated at the surfaces of a crystal, occurring most commonly in compounds with a high coordination number and when the anions and cations are of similar size. If the cations have multiple possible oxidation states, then it is possible for cation vacancies to compensate for electron deficiencies on cation sites with higher oxidation numbers, resulting in a non-stoichiometric compound. Another non-stoichiometric possibility is the formation of an F-center, a free electron occupying an anion vacancy. When the compound has three or more ionic components, even more defect types are possible. All of these point defects can be generated via thermal vibrations and have an equilibrium concentration. Because they are energetically costly but entropically beneficial, they occur in greater concentration at higher temperatures. Once generated, these pairs of defects can diffuse mostly independently of one another, by hopping between lattice sites. This defect mobility is the source of most transport phenomena within an ionic crystal, including diffusion and solid state ionic conductivity. When vacancies collide with interstitials (Frenkel), they can recombine and annihilate one another. Similarly, vacancies are removed when they reach the surface of the crystal (Schottky). Defects in the crystal structure generally expand the lattice parameters, reducing the overall density of the crystal. Defects also result in ions in distinctly different local environments, which causes them to experience a different crystal-field symmetry, especially in the case of different cations exchanging lattice sites. This results in a different splitting of d-electron orbitals, so that the optical absorption (and hence colour) can change with defect concentration.
Within any crystal, there will usually be some defects. To maintain electroneutrality of the crystals, defects that involve loss of a cation will be associated with loss of an anion, i.e. these defects come in pairs. Frenkel defects consist of a cation vacancy paired with a cation interstitial and can be generated anywhere in the bulk of the crystal, occurring most commonly in compounds with a low coordination number and cations that are much smaller than the anions. Schottky defects consist of one vacancy of each type, and are generated at the surfaces of a crystal, occurring most commonly in compounds with a high coordination number and when the anions and cations are of similar size. If the ,cations have multiple possible oxidation states, then it is possible for cation vacancies to com.pensate for electron deficiencies on cation sites with higher oxidation numbers, resulting in a non-stoichiometric compound. Another non-stoichiometric possibility is the formation of an F-center, a free electron occupying an anion vacancy. When the compound has three or more ionic components, even more defect types are possible. All of these point defects can be generated via thermal vibrations and have an equilibrium concentration. Because they are energetically costly but entropically beneficial, they occur in greater concentration at higher temperatures. Once generated, these pairs of defects can diffuse mostly independently of one another, by hopping between lattice sites. This defect mobility is the source of most transport phenomena within an ionic crystal, including diffusion and solid state ionic conductivity. When vacancies collide with interstitials (Frenkel), they can recombine and annihilate one another. Similarly, vacancies are removed when they reach the surface of the crystal (Schottky). Defects in the crystal structure generally expand the lattice parameters, reducing the overall density of the crystal. Defects also result in ions in distinctly dif.ferent local environments, which causes them to experience a different crystal-field symmetry, especially in the case of different cations exchanging lattice sites. This results in a different splitt!ing of d-electron orbitals, so that the optical absorption (and hence colour) can change with defect concentration.