This article is cited in 31 papers

Physical science of materials

On the Debye temperature and Grüneisen parameters for hexagonal close-packed crystals consisting of p-H$_2$ and o-D$_2$ molecules

M. N. Magomedov

Institute of Geothermy Problems, Makhachkala

Abstract: The expressions for the Debye temperature $(\Theta)$ as well as for the first $(\gamma=-[\partial\ln(\Theta)/\partial\ln(V)]T)$ and second $(q=[\partial\ln(\gamma)/\partial\ln(V)]T)$ Grüneisen parameters are derived based on the Mie–Lennard-Jones pair atomic interaction potential. The conditions imposed on the $\Theta(V/V_0)$, $\gamma(V/V_0)$, and $q(V/V_0)$ dependences for $V/V_0\to$ 0 and for $V/V_0\to\infty$ are analyzed. Here, $V/V_0$ is the ratio of the molar volumes for pressure $P$ at temperature $T$ and for $P=0$ at $T=0$ K. Calculations are performed for crystals of parahydrogen and orthodeuterium at $T=0$ K for $V/V_0$ ranging from 1.30 to 0.01. Good agreement is reached between the calculated dependences and experimental data. The behavior of dependences $\Theta(V/V_0)$, $\gamma(V/V_0)$, and $q(V/V_0)$ upon a variation of the isotopic composition of the crystal is analyzed.

Received: 01.11.2012

 English version: Technical Physics, 2013, 58:9, 1297–1303

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