1. Lindemann ratio for classical and quantum crystals.
- Author
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Magomedov, Mahach N.
- Subjects
- *
DEBYE temperatures , *MELTING points , *CRYSTAL structure , *AMORPHOUS substances , *ATOMIC hydrogen - 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. The dependence of the Lindemann ratio (LE) on the ratio of the melting point (Tm) to the Debye temperature (Θ) for various structures of solid. [Display omitted] • Lindemann ratio, which can be applied to classical and quantum solids is proposed. • Lindemann ratio (LR) for crystalline and amorphous classical solids is calculated. • For quantum crystals the LR decreases at the pressure increase along the melting line. • For quantum nanocrystals the LR increases with the decrease in the nanocrystal size. • It is incorrect to use the Lindemann criterion to the melting of quantum crystals. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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