Quantum-mechanical calculations of zircon to scheelite transition pathways inZrSiO4

Abstract

Based on accurate quantum-mechanical calculations, a microscopic analysis of mechanistic aspects in the pressure-induced $\text{zircon}\ensuremath{\rightleftharpoons}\text{scheelite}$ phase transition of ${\text{ZrSiO}}_{4}$ is performed under a martensitic scheme at the thermodynamic boundary. Gibbs energy profiles, atomic displacements, bonding reconstruction, and lattice strains are computed across two different transition pathways. After application of a minimum displacement criterion to the atomic positions of consecutive steps in the proposed paths, the trajectories of the 24 atoms involved in each of the unit cells are disclosed. Using the common $I{4}_{1}/a$ symmetry, we show that the group-subgroup relationship between two phases displaying the same metal coordinations is not a sufficient condition to characterize a phase transformation as displacive. A very high activation barrier (236 kJ/mol) accompanies the breaking and formation of four primary Zr-O bonds with oxygen displacements as large as $1.29\text{ }\text{\AA{}}$ from the zircon to the scheelite structure for this tetragonal path. A lower activation energy (80 kJ/mol) is required to nucleate the scheelite phase from zircon according to our fully optimized monoclinic $C2/c$ transition path. Only two oxygen atoms surrounding Zr have similar displacements in this mechanism, yielding the breaking and formation of two primary Zr-O bonds and revealing the reconstructive character of the transformation. Interestingly enough, ${\text{SiO}}_{4}$ tetrahedra are preserved with similar bond lengths and angles when rotating from the zircon to the scheelite phase across the more favorable monoclinic transition pathway.