Energetics of halogen impurities in thorium dioxide

Defect energies for halogen impurity atoms (Cl, Br and I) in thoria are calculated using the generalized gradient approximation and projector augmented plane wave potentials under the framework of density functional theory. The energy to place a halogen atom at a pre-existing lattice site is the incorporation energy. Seven sites are considered: octahedral interstitial, O vacancy, Th vacancy, Th-O di-vacancy cluster (DV) and the three O-Th-O tri-vacancy cluster (NTV) configurations. For point defects and vacancy clusters, neutral and all possible defect charge states up to full formal charge are considered. The most favourable incorporation site for Cl is the singly charged positive oxygen vacancy while for Br and I it is the NTV1 cluster. By considering the energy to form the defect sites, solution energies are generated. These show that in both ThO_2-x and ThO₂ the most favourable solution equilibrium site for halides is the single positively charged oxygen vacancy (although in ThO₂, I demonstrates the same solubility in the NTV1 and DV clusters). Solution energies are much lower in ThO_2-x than in ThO₂ indicating that stoichiometry is a significant factor in determining solubility. In ThO₂, all three halogens are highly insoluble and in ThO_2-x Br and I remain insoluble. Although ½Cl₂ is soluble in ThO_2-x alternative phases such as ZrCl₄ exist which are of lower energy.