Statistical Model of Sphalerite Structured Quaternary A₁-xBₓYᵧZ₁-y Systems

Tetrahedron coordinated sphalerite quaternary systems of type A₁-xBₓYᵧZ₁-y consist exclusively of binary and ternary elemental tetrahedra, four of the first and four of the latter, each one with three configurations, i. e. , a total of sixteen elemental tetrahedron configurations. These configurations cannot contain all four constituent atoms simultaneously in the same elemental tetrahedron; as a consequence we can consider each ternary tetrahedron composition as diluted in the quaternary compound. Thus, A₁-xBₓYᵧZ₁-y extended x-ray absorption fine structure (EXAFS) data can be treated by using the strained tetrahedron model which, originally developed to deal with ternary systems, has already exhibited excellent agreement with numerous experimental data. To determine ion site occupation preferences of quaternary systems, we applied this model to our EXAFS data for Cd1-xMnxSeyTe1-y and to GaxIn1-xAsySb1-y data available in the literature, and compared them to those derived from ternary data for Cd1-xMnxTe and GaxIn1-xAs. In both sets, as the ternary is diluted in the quaternary system, a drift of the preference values of the pure ternary is observed. The present analysis of experimental reflectivity far infrared (FIR) phonon spectra of quaternary Cd1₁-xMnₓSeᵧTe₁-y crystals confirms the model predictions and leads to an interpretation of the experimental data for A₁-xBₓYᵧZ₁-y quaternary systems