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Статья
2021

Root-Mean-Square Amplitude of Zero-Point Vibrations in a Crystal


I. KhidirovI. Khidirov, S. Dzh. RakhmanovS. Dzh. Rakhmanov, Sh. A. MakhmudovSh. A. Makhmudov
Российский физический журнал
https://doi.org/10.1007/s11182-021-02448-6
Abstract / Full Text

The paper shows that the values of zero-point energy and vibrations of atoms in a crystal determined by the uncertainty principle, depend on the dynamic response of atoms. It is found that the root-mean-square (rms) amplitude of thermal and zero-point vibrations of atoms in crystal lattices of elements from the periodic table, has a periodic dependence on the atomic number of elements. It is shown that the rms amplitude of thermal vibrations of atoms in crystal lattices of elements with high Debye temperature, does not strongly differ from their zero-point vibrations at room temperature. This is explained by a small number of excited vibrations with the maximum frequency at room temperature, since the latter is significantly lower than their Debye temperature, at which the whole range of thermal vibrations of atoms in the crystal excites. The obtained results can be used in materials science and technology to estimate the strength and thermal characteristics of materials at cryogenic temperatures, without their direct measurements at the absolute-zero temperature.

Author information
  • Institute of Nuclear Physics of the Academy of Sciences of Uzbekistan, Tashkent, Republic of UzbekistanI. Khidirov, S. Dzh. Rakhmanov & Sh. A. Makhmudov
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