The estimation of the parameter Gruneisen metal hexaborides

Keywords: Gruneisen parameter, Debye characteristic temperature, X-ray characteristic temperature, anharmonicity of oscillations of particles in crystals, Lindemann’s formula, Gruneisen formula


The basis for the estimation of the Gruneisen parameter γ is laid  (θД – Debye’s characteristic temperature, V– molar volume) from which the mathematical expression follows . In previous publications in order to determine θД the Lindemann formula was used. However, due to the ambiguity of the dimensional coefficient C in the Lindemann formula, the authors used the method of high-temperature roentgenography within the limits of 293–973 K. On the basis of analisys of the intensity of one maximum interference (hkl) at different temperatures, was determined by Chipman’s method X-ray characteristic temperature  θр(Т) groups of hexaboard type CaB6, namely CaB6, YB6, LaB6, CeB6, PrB6 , NdB6, ErB6, ThB6, YbB6. Considering, that neither the structure nor the interatomic connections within the temperature search of hexaborides does not change, the value of the parameter γ is determined. Its value was obtained within 2.5–4.7 for CeB6, NdB6, ErB6, YbB6, ThB6 and order 5.5–6.6 for CaB6, YB6, LaB6, PrB6. The parameters of Gruneisen proved to be practically independent of temperature. The presence of the meanings of γ made it possible to divide the implicit and explicit parts of the anagrammonism into a calming measure. The generalizing measure of anharmonism is mainly exhausted by the product γβ (β – the coefficient of the volumetric expansion of the crystalline lattice.


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Fedyshyn, Y., Vadets, D., Garashchenko, O., Romanov, O., & Fedyshyn, T. (2018). The estimation of the parameter Gruneisen metal hexaborides. Scientific Messenger of LNU of Veterinary Medicine and Biotechnologies. Series: Food Technologies, 20(90), 36-39.