Temperature dependence of the heat capacity and times of the establishment of vacancy equilibrium in simple crystals

The concentration range of vacancies that affect the temperature dependence of the heat capacity at constant volume $C_v$ has been determined. The times of the establishment of vacancy equilibrium in spherical samples of simple crystals with different radii due to the thermal motion of atoms have been calculated for the process as close as possible to the equilibrium one with a decrease in the temperature from the melting point to the current value $T$. The free energy of an imperfect crystal has been determined taking into account contributions from interatomic interactions in terms of the Lennard-Jones potential functions and vibrational energies. The properties of an imperfect crystal have been calculated within the Lifshitz approximation linear in the density of vacancies with the frequency distribution function of the perfect crystal with the corresponding corrections, which reflect local vibrations of atoms around vacancies. The free energy of a defect-free perfect crystal has been determined from the calculated frequencies of normal vibrations with the inclusion of up to four nearest neighbors. It has been shown that disregard of acoustic (out-of-phase) parts of the spectrum in the calculation of the heat capacity $C_v$ with increasing temperature leads to a decrease (increase) in $C_v$ from the values calculated for the total vibrational spectrum. A nonequilibrium state of the imperfect crystal can lead to negative values of the heat capacity at constant volume.