Estimation of the Gruneisen parameter and an explicit measure of anharmonicity of dodecaborides

Keywords: Gruneisen constant, Debye characteristic temperature, X-ray characteristic temperature, Lindemann formu-la, Gruneisen formula, anharmonicity of oscillations of crystal particles, dodecaborides


In previous works on the ratio   (θД the characteristic temperature of Debye, was calculated according to the Lindemann formula; V – molar volume of hypothetical lattice atoms; γ is the Gruneisen parameter) for the group of dodecaborides (TbB12, DyB12, HoB12, ErB12, TuB12, LaB12, UB12) the average value of γ = 1.3 was determined. However, due to the ambiguity of the coefficient of proportionality in the Lindemann formula by definition θD, the authors selected an independent high-temperature X-ray method for determining the dependence θr (T). Taking into account the immutability of the structure and type of interatomic connection in the temperature interval of the search (293–973 K), the authors evaluated the value and temperature dependence of γ (T) of each dodecaboride separately. The results of the search showed that the value of γ for each given dodecaboride is different, but practically independent from temperature. For some dodecaborides, the parameter γ is about 2–3 units, and for others it is overestimated. The values of γ made it possible to estimate the magnitude of the implicit γβ and the explicit  parts of the universal measure of anharmonicity of dodecaborides , where β – real coefficient of volumetric expansion of the crystalline lattice. Because    (n – dimensionless coefficient of proportionality), then the temperature change n(T) is also determined.


Vadets, D.I., Tymeichuk, O.Iu., & Fedyshyn, Ya.I. (1998). Doslidzhennia teplovykh kolyvan v krystalakh dodekaborydiv metaliv typu UB12. Naukovyi visnyk Lvivskoi derzhavnoi akademii veterynarnoi medytsyny imen S.Z. Gzhytskoho, 1, 132–136 (in Ukranian).

Bansigir, K.G. (1968). Evaluation of the Grüneisen Constant. Journal of Applied Physics, 39(8), 4024–4026. doi: 10.1063/1.1656895.

Samsonov, G.V., & Paderno, Ju.B. (1961). Boridy redkozemel'nyh metallov. Institut metallokeramiki i special'nyh splavov AN USSR. Kiev: Izd-vo AN USSR (in Russian).

Fedyshyn, Ya.I., Vadets, D.I., & Fedyshyn, T.Ia. (2016). Vysokotemperaturne renthenohrafichne doslidzhennia teplovykh vlastyvostei krystalichnykh til. Naukovyi visnyk Lvivskoho nats. un-tu veterynarnoi medytsyny ta biotekhnolohii im. S. Z. Gzhytskoho, 18, 2(68), 111–114. doi: 10.15421/nvlvet6822 (in Ukranian).

Chipman, D.R. (2004). Temperature Dependence of the Debye Temperatures of Aluminum, Lead, and Beta Brass by an X-Ray Method. Journal of Applied Physics, 31(11), 2012–2015. doi: 10.1063/1.1735487.

Fedyshyn, Y.I., & Vadets, D.I. (2017). Considerations to determine the mass of atoms (ions) of crystalline substance. Scientific Messenger LNUVMBT named after S.Z. Gzhytskyj, 19(75), 40–44. doi: 10.15421/nvlvet7508.

Mykhalchenko, V.P., & Kushta, H.P. (1963). Vyznachennia staloi Hriunaizena dvanadtsiaty protsentnoho khromystoho ferytu renthenohrafichnym metodom. UFZh, 8(7), 779–786 (in Ukranian).

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Fedyshyn, Y., Vadets, D., Garashchenko, O., Romanov, O., & Fedyshyn, T. (2018). Estimation of the Gruneisen parameter and an explicit measure of anharmonicity of dodecaborides. Scientific Messenger of LNU of Veterinary Medicine and Biotechnologies. Series: Food Technologies, 20(90), 3-6.