About rms amplitude of zero oscillations of atoms in crystal

It is shown that the values of the energy and amplitude of zero-point vibrations of atoms in a crystal, due to the uncertainty principle, depend on the dynamic characteristics of atoms in the crystal. It was found that the root-mean-square amplitude of thermal and zero-point vibrations of atoms, like other properties, has a periodic dependence on the ordinal number of elements in the Mendeleev's Periodic Table. It is shown that the value of the root-mean-square amplitude of thermal vibrations of atoms in a lattice of elements with a high value of the Debye temperature at room temperature does not differ much from the value of the amplitude of zero-point vibrations of atoms (at T = 0 K). This is explained by the small number of excited vibrations with the maximum frequency in these crystals at room temperature, since the room temperature is much lower than their Debye temperature, at which the entire spectrum of thermal vibrations of atoms in the crystal is excited. The results can be used in materials science and technology to assess the strength and thermo physical characteristics of materials at cryogenic temperatures, without resorting to measuring them directly at absolute zero.

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