Atomic scale computer simulations were used to investigate clustering of those defects that resulted from the accommodation of Gd2O3 in a CeO2 host lattice. It was found that binding energies of the defect clusters could be accurately described by a model in which the total binding energy was deconvoluted into its constituent pair terms (though a three body correction was necessary for a specific cluster type). At short defect–defect distances, these interaction energies must be calculated explicitly because of the complexity of the lattice relaxation. At longer distances, binding energies could be approximated by calculating the coulomb interactions between the effective charges of the defects divided by the relative permittivity of the host lattice. This scheme provided a framework within which the total of defect–defect interactions could be determined for a large ensemble of defects disordered throughout this lattice.

A Pair Sum Approximation for Predicting Defect Cluster Binding Energies in Fluorites. J.A.Ball, R.W.Grimes, D.W.Price: Modelling and Simulation in Materials Science and Engineering, 2005, 13, 1353-63