ABINITIO CLUSTER-IN-THE-LATTICE DESCRIPTION OF VANADIUM-DOPED ZIRCON - ANALYSIS OF THE IMPURITY CENTERS V4+ZRSIO4

A theoretical description of crystal effects induced by the presence of impurity centers V4+ entering the dodecahedral and tetrahedral sites of ZrSiO4 is presented. The computation of the electronic structure and equilibrium geometry of the impurity center in the ionic crystal is carried out using an extension of the ab initio perturbed ion method. This theoretical model consists of a new type of cluster-in-the-lattice scheme that involves the rigorous quantum mechanical solution of clusters of varying size embedded in a quantum crystal lattice. The electronic wavefunction of the doped crystal is expressed as an antisymmetric product of group functions where each represents an ion in the crystal. The crystal is partitioned into active (C) and lattice (L) sets where the positions and wavefunctions of all ions in C, and the positions of some of them, are optimized while those in L are kept frozen. Numerical results are compared with experimental data to analyze the relative stability of V4+ occupying the two possible sites of ZrSiO4. The evolution of the lattice energy in the crystal was examined in terms of the cluster size and the stability property studied by locally optimizing geometries that involve relaxation of various active sets of ions around the substituted centers. Our findings indicate that substitution on the eightfold-coordinated ion site is energetically favorable, whereas that on the fourfold-coordinated site being unstable and very sensitive to the geometry relaxations considered in the calculation.