Influence of the phonon subsystem on the probability of formation of proper point defects in nonmetallic crystals

A selfconsisten t equation is obtained for the mean concentration of vacancies in a crystal , allowance being made for phonons. The change in the phonon spectrum of the lattice when defects are present is taken into account. It is shown that the appearance of a resonance level in the vibrational spectrum can lead to an appreciable lowering of the vacancy activation energy at sufficiently low temperatures.