RMS Dynamic Displacements of Atoms and Their Complexes from the Equilibrium Position in Crystals

Authors D.I. Vadets1 , O.V. Garashchenko1 , V.I. Garashchenko1 , O.Y. Romaniv1 , Y.I. Fedyshyn2 , S.L. Forsyuk1

1National University of Water and Environmental Engineering, 11, Soborna St., 33000 Rivne, Ukraine

2Stepan Gzhytskyi National University of Veterinary Medicine and Biotechnologies, 50, Pekars'ka St., 79010 Lviv, Ukraine

Е-mail v.i.harashchenko@nuwm.edu.ua
Issue Volume 12, Year 2020, Number 3
Dates Received 07 February 2020; revised manuscript received 15 June 2020; published online 25 June 2020
Citation D.I. Vadets, O.V. Garashchenko, V.I. Garashchenko, et al., J. Nano- Electron. Phys. 12 No 3, 03018 (2020)
DOI https://doi.org/10.21272/jnep.12(3).03018
PACS Number(s) 61.66.Dk, 65.40.De
Keywords Oscillation anharmonicity, Oscillation amplitudes, RMS dynamic displacements.

The thermal characteristics of a group of ionic crystals of cubic crystal system, CaB6 type hexaborides, and UB12 metal dodecaborides were investigated using high-temperature X-ray diffraction using a KROS camera with a thermal nozzle. On the basis of the X-ray characteristic temperature values, full root mean square (RMS) dynamic displacements of hypothetical atoms or their complexes with average and consolidated masses are calculated. The temperature increase of the oscillation amplitudes and the temperature decrease of the X-ray characteristic temperature are explained. The reasons for the slight difference of the X-ray characteristic temperature values with the literary data are described. It is established that the reduced masses of hypothetical atoms are smaller than their average masses. The growth rate of the RMS dynamic displacements of atoms with increasing temperature for ionic crystals is shown graphically, and for hexaborides and dodecaborides of metals – analytically, in the range from room temperature to 700-973 K. The change in RMS dynamic displacements with the change in masses is observed in ionic crystals and is not observed in metal borides. This is explained by the structure of the interatomic bond change. The values of the general measure of the anharmonicity of thermal oscillations are given for hexaborides and dodecaborides. It is shown that in the group of hexaborides there is a regular decrease of the crystal lattice parameter with the increase of the atomic number of metals, which is explained by lanthanide compression. This is due to the strength of the boron frame, which is a consequence of the increase in the atomic radius. It is explained that the increase in the anharmonicity of thermal oscillations of atoms with increasing temperature leads to a linear decrease in the effective X-ray characteristic temperature. Studies have shown that the RMS dynamic displacements are described by a weak quadratic polynomial with positive velocity, which correlates with the temperature dependence of the general measure of anharmonicity of vibrational motion.

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