First principles investigation of temperature and pressure dependent elastic properties of ZrC and ZrN using Debye–Gruneisen theory

Abstract

We investigated the effects of temperature and pressure on the elastic properties of ZrC and ZrN using first-principles calculations and quasi-harmonic Debye–Gruneisen theory. Three expressions, the Slater, Dugdale–MacDonald (DM), and free volume expressions, were employed in the Debye–Gruneisen theory to obtain the Gruneisen parameter, γ. The DM expression agreed well with the experimental measurements of the ZrN volume expansion. The volume expansion of ZrC, on the other hand, did not agree well with any expression investigated here. ZrC calculations, therefore, require a modified expression. Variations in the Debye temperature, the Gruneisen parameter, the bulk (B), shear (G), and Young’s (E) moduli were calculated as a function of temperature and pressure. The temperature-dependent properties at room pressure agreed well with previous experimental results and other calculated results; however, the pressure effects at the various temperatures were not easily compared with the results from other experimental and computational results because their effects on the elastic properties of ZrC and ZrN remain largely unknown.