Ab initio lattice dynamics and elastic constants of ZrC

Abstract

Abstract. Ab initio calculations and a direct method are applied to derive the phonon dispersion relations and phonon density of states for the ZrC crystal. The results are in good agreement with neutron scattering data. The force constants are determined from the Hellmann-Feynman forces induced by atomic displacements in a 2×2×2 supercell. The elastic constants are found using the deformation method and successfully compare with experimental data. [4,5,6,7]. The electronic structure, bulk modulus, and elastic constants, as well as the phonon dispersion relations have been found for TiC, TiN and TiO compounds by means of first-principles totalenergy calculations [8,9]. Generally, the calculated values show good agreement with experiments. This provides a motivation to extend the investigation to heavier transition metals and to treat zirconium carbide, ZrC. This crystal is an important material in nuclear energy technology, since it provides a filling medium for fuel particles. It is also used for surface hardening and coverage of cathodes of X-ray sources. In this paper we continue to study the lattice dynamics and elastic properties of transition-metal compounds. See [8] and references given there for a more detailed description of the method. PACSThe transition-metal carbide compounds, of which ZrC is a representative, are of considerable scientific and technological interest because of their striking mechanical properties, extreme hardness combined with metallic electrical and thermal conductivities. The ZrC crystal has NaCl structure and it is usually non-stoichiometric, mainly owing to carbon-vacancy defects. The phonon dispersion relations of ZrC have been measured along main symmetry directions by Smith et al [10,11]. Elastic constants, in turn, have been measured for two concentrations of carbon (ZrC 0.89 and ZrC 0.94 ) by Chang and Graham [12].In this paper we extend the first-principle calculations to describe the phonon dispersion curves, phonon density and elastic constants of ZrC. The method which is used, is based on the total energy calculation and HellmannCorrespondence to: jochym@ifj.edu.pl Feynman (HF) forces. The phonon dispersion relations are calculated by the direct method and the Phonon program [13,14,15,16,17,18], in which the force constants of the dynamical matrix are derived from HF forces. Alternatively, one could use the linear-response method [19,20] for the evaluation of ab initio phonon frequencies at a predetermined set of Brillouin zone points. Elastic constants and bulk modulus are estimated by straightforward evaluation of energy derivatives with respect to the deformations.The energies and HF forces of ZrC crystal are calculated by the method of total energy minimization, using norm-conserving pseudopotentials as an approximation for the atomic core-valence electron interaction [21,22,23]. This method allows to include the pressure in calculations as well as anharmonic effects. For the lattice dynamics calculations a 2×2×2 supercell with periodic boundary conditions and 64 ...

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