The electronic structures of fluorite-type crystals CaF2, SrF2, CdF2, and PbF2 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)F2, (Pb,Sr)F2, and (Ca,Sr)F2 mixed crystals. In the case of (Cd,Pb)F2, the authors 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, they 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.
 

Physical Review B, 43 12597-606, 1991.