Effects of pressure on the elasticity and stability of zircon (ZrSiO 4): First-principle investigations

Abstract

We investigate the effects of pressure on the elasticity of zircon using the Local Density Approximation (LDA) within the density functional theory. Our LDA calculations predict the elastic constants ( C ij ) with positive pressure derivatives, except C 66 whose pressure derivatives are nearly zero, showing small positive to negative departures with increasing pressure. We calculated Young’s moduli, E 1 and E 3 along the crystallographic axes a and c, respectively. At low pressures (<4 GPa) E 1 < E 3, but the relation reverses at pressures >4 GPa, implying a directional change of axial stiffness of zircon crystals. Our LDA calculated Hill’s average bulk ( B) and shear ( G) moduli show contrasting variations with pressure. B is more sensitive to pressure with positive derivatives varying from 2.25 to 5.63, as compared to much lower pressure derivatives (0.4) of G, which drops to negative values (−0.404) at pressures >7 GPa, and then take up positive values (1.3). The zircon to reidite phase transition, involving “bond switching mechanisms” [1] increases the magnitudes of both B and G, but shows relatively weak effects on their pressure derivatives. This study shows the effects of pressure on the degrees of shear and directional bulk modulus anisotropy of zircon. We also calculated its Debye temperature (708 K) from the elastic wave velocities, which fairly agrees to the available experimental data. Our study predicts that increasing pressure widens the electronic band gap of zircon, implying its greater insulation property at high pressures.