Expressions for the calculation of the thermodynamic potential, enthalpy, entropy and volume of vacancy formation in a simple crystal at temperatures close to absolute zero were derived. It was established that the vacancy concentration as a function of the temperature T exhibited a minimum at a certain temperature T0 . At T < T0 , the vacancy concentration function increased with decreasing temperature; the entropy value changed sign at T = T0, and was negative at T < T0 . It was shown that the existence of the so-called zero-point vacancies did not violate the third law of thermodynamics. Three new effects were predicted, and the prospects for their experimental observation were considered.

The Features of Vacancy Formation at Low Temperatures. M.N.Magomedov: Technical Physics Letters, 2001, 27[9], 773-5