Association energies in Re3+-doped alkaline-earth fluorides studied by computational methods

Association energies of nearest-neighbour and next-nearest-neighbour associates between substitutional, trivalent rare-earth ions and interstitial fluoride ions CaF₂, SrF₂ and BaF₂ are obtained by lattice simulation calculations. The dopant ion-fluoride ion interaction is described (i) with a set of potentials obtained with electron gas methods, and (ii) with a set of potentials derived semi-empirically from the host lattice cation-anion interaction potentials. The calculations successfully simulate the experimentally observed variations of the dopant-interstitial binding energies with the radius of the dopant ion, and with the lattice parameter of the host. The better quantitative agreement is obtained with the semi-empirical potentials. The variations are explained by an evaluation of the displacements of the ions constituting the associates.