Melting criteria for classical and quantum crystals

It was shown that the Lindemann ratio $(L)$ can be calculated by means of the delocalized criterion of melting for classical crystals, i.e. those with a melting point $(T_m)$ greater than the Debye temperature $(\Theta): T_m/\Theta>$ 1.5. It was shown that for classical single-component crystals, the $L$ value is determined only by the crystal structure. Calculations for various structures of classical crystals showed good agreement with the estimates of other authors. A generalization of the Lindemann relation was obtained for the case of quantum single-component crystals, i.e. for which $T_m/\Theta <$ 0.4. It was shown that for quantum crystals, the Lindemann ratio is determined not only by the crystal structure, but also by the function $\Theta/T_m$. Therefore, when moving from the classical to the quantum domain, the $T_m(\Theta)$ function changes its functional dependence. It was shown that for quantum crystals, the $L$ value decreases with increasing pressure along the melting line. For quantum nanocrystals, the $L$ value increases with an isobaric decrease in the size of the nanocrystal. At the same time, the more noticeably the shape of the quantum nanocrystal deviates from the energy-optimal shape, the greater the sized increase in the Lindemann ratio. A generalization of the delocalized criterion of melting was obtained for the case of quantum single-component crystals.