intrinsic defect equilibrium
Intrinsic defects are the ones a perfectly pure crystal makes all by itself, purely because it is warm — no impurities, no outside doping, just the temperature-driven population that thermodynamics demands. Intrinsic defect equilibrium is the balance point: the specific number of these self-made defects the crystal settles at, once the energy cost of creating them is weighed against the entropy gain of having them scattered about. It is the ionic-crystal cousin of the equilibrium vacancy concentration in metals.
The neat trick is to treat defect formation like a chemical reaction and apply the law of mass action. For Schottky defects in NaCl, the reaction is: perfect crystal goes to one sodium vacancy plus one chlorine vacancy. At equilibrium the product of the two vacancy concentrations is a constant set by temperature: [V_Na][V_Cl] = K_S = exp(-H_S / (k T)), where H_S is the energy to form one Schottky pair. In a pure crystal the two vacancies are made in equal numbers, so each concentration is exp(-H_S / (2 k T)) — note the factor of 2 in the denominator, because the formation energy is shared between the two members of the pair. Frenkel equilibria work the same way, with vacancy and interstitial concentrations equal.
This mass-action view is the foundation of defect chemistry. It explains why intrinsic defect levels are fixed once you know the temperature and the formation energy, and it draws the crucial line between intrinsic behaviour (pure crystal, defects set by temperature) and extrinsic behaviour (impure or deliberately doped crystal, defects set by the added impurities). At low temperature a real crystal's defects are usually dominated by impurities (extrinsic); only when it is hot enough does the thermally generated intrinsic population take over. Knowing which regime you are in is essential to predicting ionic conductivity, diffusion, and colour.
Plot the log of a NaCl crystal's ionic conductivity against 1/T and you see two straight-line regions: a steep intrinsic branch at high temperature, whose slope gives the Schottky formation energy, kinking into a shallower extrinsic branch at low temperature, whose defects are fixed by trace impurities. The kink is precisely where intrinsic defect equilibrium takes over from impurity control.
Intrinsic defects are set by temperature and formation energy; below a crossover, impurities (extrinsic) take over.
Intrinsic means self-generated by heat in a pure crystal, not impurity-driven. Real crystals are almost never pure enough to be intrinsic at room temperature — their low-temperature defects are usually extrinsic, dominated by unavoidable trace impurities.