Comparison of anharmonic characteristics of ionic crystals

Keywords: anharmonicity of thermal oscillations, mean square displacement of ions, characteristic temperature, Gruneisen parameter, Debye function, universal measure of anharmonicity, average and actual expansion coefficients, displacement of cations and anions


The values of the anharmonic properties of NaCl, KCl, KBr, KI, CsCl, obtained by high-temperature X-ray diffraction on a CRS are compared with each other. The experimental results are presented in numerical form for the temperature dependence of the crystal lattice parameter a(t), the mean and actual coefficients of linear expansion acp(t) and aдійсн.(t); x-ray characteristic temperature Ɵp(T); medium-quadratic dynamic displacements of hypothetical ions, cations and anions , , ; the Gruneisen parameter γ for each substance. Changes in the parameter of crystalline lattices are described by a quadratic temperature dependence. The average and actual coefficients of expansion of crystalline lattices within the investigated temperature range (from 293K to 573K-773K) are described by a linear temperature dependence. The results of the search show that the greatest contribution to the anharmonicity of the thermal vibrations of the lattice is given by the coefficients of bulk expansion β(T). According to this indicator, among the studied substances of the NaCl type, the most anharmonic was KI. X-ray characteristic of temperatures are described by linear downward correlations. The calculations  suggest a simplified formula: , where h – is Plancka’s, T – is the thermodynamic temperature, m – is the mass of the ion, k – is Boltzmann, and Ɵp – is the X-ray characteristic temperature, , Ф(х) – is the Debye function; ; 0,0278 – coefficient of proportionality, which is calculated with  an accuracy of 0,01%. The values of a(t), , Ɵp(t), a(t) within the studied temperature range correlate with literary data. The calculation of the Gruneisen parameter γ with increasing temperature was carried out by the method of the Indian physicist Bansigir both for the group of ionic crystals and for each substance separately. Experimental values of γ with literary data are compared.

It is noticed the proportionality between and α2(t). Taking into account that Ɵp(T, V), for the universal generalizing measure of anharmonism, the value was adopted, where n – is the dimensionless coefficient of proportionality, which turned out to be closer to 1, and not to 2, as it is for pure metals. This is due to the fact that for metals γ 2.

Within the studied temperature range, the values  for crystals of the NaCl type range from –2·10–4К–1 to –3·10–4 К–1. For CsCl it is in the range from –3,7·10–4 К–1 to –4,2·10–4 К–1.


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Fedyshyn, Y., Vadets, D., Garashchenko, O., RomanovО., Fedyshyn, T., & VyhrystО. (2018). Comparison of anharmonic characteristics of ionic crystals. Scientific Messenger of LNU of Veterinary Medicine and Biotechnologies. Series: Food Technologies, 20(85), 9-13.