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Elastic and thermodynamic properties of the GeA2O4 (B = Mg, Zn and Cd) cubic spinels: an ab initio study
Zerarga F.1, Bouhemadou A.2, Allali D.3,4
1 University Abderrahmane Mira, Department of Physics, 06000 Bejaia, Algeria
E-mail: zerargafares@yahoo.fr
2 Laboratory for Developing New Materials and their Characterization, University of Setif 1, 19000 Setif, Algeria.
3 Faculte´ de technologie, Universite´ Mohamed Boudiaf-M’sila, B.P 166 Ichbilia, 28000 M’sila, Algeria.
4Physics and Chemistry of Materials Lab, Department of Physics, University Mohamed Boudiaf of M’sila, 28000, M’sila, Algeria.

Abstract
The structural, elastic and thermodynamic properties of the GeA2O4 (A= Mg, Zn and Cd) cubic spinels have been investigated through ab-initio full-potential linearized augmented plane wave calculations [1]. The structural parameters calculated using both the local density [2] and generalized gradient approximations [3] to the exchange-correlation potential are in good agreement with the available experimental and theoretical data. The single crystal elastic constants are numerically estimated using total energy-strain approach with two different sets of distortions [4]. The polycrystalline aggregate elastic parameters are calculated from the single crystal elastic constants via the Voigt–Reuss–Hill approximations [5,7]. Mechanical stability, sound velocities, ductility/brittleness, elastic anisotropy, Debye temperature and pressure dependence of the elastic constants of the title compounds are also assessed. The temperature dependence of the lattice parameter, bulk modulus, volume thermal expansion coefficient, isochoric and isobaric heat capacity and Debye temperature in a wide temperature interval at some different fixed pressures is predicted through the quasi-harmonic Debye model [8].

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