First-principles study of elastic and thermal properties of refractory carbides and nitrides

Abstract

The elastic properties and thermal expansion of TiC, TiN, VC and VN are calculated by means of a precise first-principles electronic structure method. The single-crystal elastic constants are derived from the total energies of distorted structures. For the thermal expansion, the contribution of electronic states is determined within a free-electron model utilizing the density of states at the Fermi energy of the actual materials. The contribution of lattice vibrations to the thermal properties is modelled by Debye's approximation for phonon dispersion. Anharmonic effects are included via Grüneisen's theory requiring the volume dependence of the Debye temperature. For the calculation of the Grüneisen parameter, volume- and pressure-dependent single-crystal elastic constants are needed. Since in reality refractory compounds always contain vacancies, the influence of vacancies is studied for vanadium carbides by a supercell of composition VC_0.75. It is found that vacancies significantly increase the thermal expansion coefficient, in particular at higher temperatures. Because of the modelling procedure, third derivatives of first-principles total energies are needed, which requires a high-quality method as well as a thorough application of it. The accuracy of the calculated values as well as their agreement with the rather sparse experimental data is discussed.