Lindemann ratio for classical and quantum crystals

Abstract

Based on the delocalized of melting criterion, a relatively simple analytical (i.e., without computer simulation) method for calculating the Lindemann ratio is proposed. It is shown that for classical single-component solids (in which the melting point (T_m) is greater than the Debye temperature (Θ): T_m/Θ > 1.5), the Lindemann ratio is determined only by the packing coefficient of the structure. Calculations for various structures of classical solids (both crystalline and amorphous) showed good agreement with the estimates of other authors. For quantum single-component crystals (in which T_m/Θ < 0.4), the Lindemann ratio is determined not only by the crystal structure, but also by the Θ/T_m function. Therefore, when passing from the classical to the quantum area, the T_m(Θ) function changes its functional dependence. It was shown that for quantum crystals, the Lindemann ratio decreases with increasing pressure along the melting line. For quantum nanocrystals, the Lindemann ratio increases with an isobaric decrease in a nanocrystal size. At this, the more noticeably the shape of the nanocrystal deviates from the energy-optimal shape, the greater the sized increase in the Lindemann ratio. Therefore, the use of the Lindemann criterion to study the melting of quantum crystals (as they tried to when studying the melting of atomic metallic hydrogen) showed incorrect results.