Statistical model analysis of local structure of quaternary sphalerite crystals

Abstract

At the 2004 Ural International Winter School, we introduced the statistical strained tetrahedron model and discussed ternary tetrahedron structured crystals. The model allows one to interpret x-ray absorption fine structure (EXAFS) data and extract quantitative information on ion site occupation preferences and on the size and shape of each elemental constituent of the configuration tetrahedra. Here we extend the model to cover quaternary sphalerite crystal structures. We discuss the two topologically different quaternary sphalerite systems: the pseudo balanced A₁₋xBxYyZ₁₋y (2:2 cation:anion ratio), and the unbalanced AxBx C₁₋x₋x Z or AXyYy Z₁₋y₋y (3:1 or 1:3 cation:anion ratios) truly quaternary alloy systems. These structural differences cause preference values in pseudo quaternaries to vary with the relative contents, but to remain constant in truly quaternary compounds. We give equations to determine preference coefficient values from EXAFS or phonon spectra and to extract nearest-neighbour inter-ion distances by EXAFS spectroscopy. The procedure is illustrated and tested on CdMnSeTe, GaInAsSb, and ZnCdHgTe quaternary alloys.