Electronic structure of fluorite-type compounds and mixed crystals

The electronic structures of fluorite-type crystals ${\mathrm{CaF}}_2$, ${\mathrm{SrF}}_2$, ${\mathrm{CdF}}_2$, and ${\mathrm{PbF}}_2$ are studied by means of the linear-muffin-tin-orbitals (LMTO) method. The tight-binding version of the LMTO and its coherent-potential-approximation (CPA) generalization is used to study the electronic states in (Ca,Cd)${\mathrm{F}}_2$, (Pb,Sr)${\mathrm{F}}_2$, and (Ca,Sr)${\mathrm{F}}_2$ mixed crystals. In the case of (Cd,Pb)${\mathrm{F}}_2$, we investigate the effects due to the large lattice-constant mismatch by introducing two extreme models of bond-length variations in the mixed crystals: (i) Mixed-crystal bond lengths preserve their values from pure crystals, and (ii) all bond lengths are varied linearly with the alloy composition between the pure crystal values. A comparison of the results with the photoemission data supports the former model, which is used also for other systems. As a side issue, we discuss the accuracy of the supercell approach to the electronic structure of random alloys by comparing LMTO supercell and LMTO-CPA calculations using the same set of potential parameters.