Theoretical study of high-pressure phase stability of NaZr2(PO4)3 via elastic constants and equation of state

Abstract

Phase stability of \(\mathrm {NaZr_2(PO_4)_3}\) has been studied through density functional theory calculations of elastic constants, equation of state and enthalpies. The changes in elastic constants as a function of pressure show that the ambient rhombohedral (R\(\bar{3}c\)) \(\mathrm {NaZr_2(PO_4)_3}\) becomes unstable above 8 GPa and this instability is driven by a softening of C\(_{44}\) elastic constant through one of the Born stability criteria. High-pressure equation-of-state and enthalpy calculations further show that the ambient rhombohedral (\(R\bar{3}c\)) structure transforms first into another rhombohedral (R3) phase and subsequently to LiZr\(_2\)(PO\(_4\))\(_3\)-type orthorhombic phase at pressures above 6 and 8 GPa respectively which are in agreement with a recent x-ray diffraction study. Analysis of interatomic distances show that LiZr\(_2\)(PO\(_4\))\(_3\)-type orthorhombic structure allows for shorter Na–O and Zr–P bonds at high pressures which appears to enable strong bonding and stability. Calculated formation enthalpy and bulk modulus of the ambient phase of \(\mathrm {NaZr_2(PO_4)_3}\) are found to be in reasonable agreement with the respective experimental values.