an intrinsic defect

An intrinsic defect is one the crystal makes all by itself, purely from heat, with no foreign atoms involved. Even a chemically perfect, 100 percent pure crystal at any temperature above absolute zero is riddled with them, because thermal energy keeps knocking ions off their sites and entropy rewards a little disorder. They are the 'born-in' defects, as opposed to extrinsic ones brought in by impurities or doping.

In an ionic ceramic the intrinsic defects must come in charge-neutral packages, and there are two main recipes: the Schottky set (matched cation and anion vacancies) and the Frenkel pair (an ion moved to an interstitial, leaving its vacancy). There is also the intrinsic electronic pair — thermally exciting an electron across the band gap to leave a free electron and a hole, nil ⇌ e' + h•. All three are governed by a Boltzmann factor: their concentration rises exponentially with temperature, roughly exp(-E/2kT) for the ionic pairs and exp(-Eg/2kT) for the electronic pair, where E is the formation energy and Eg the band gap. Higher temperature and lower formation energy both mean more intrinsic defects.

The intrinsic level sets a baseline the material cannot go below at a given temperature. In practice, though, real ceramics at low-to-moderate temperature are usually extrinsic-dominated: even a few hundred parts per million of an aliovalent impurity can create more vacancies than heat alone, so the intrinsic regime only takes over at high temperature where the exponential thermal term finally outruns the fixed impurity contribution. Telling the two regimes apart is exactly what a Brouwer diagram is for.