Statistical strained-tetrahedron model of local ternary zinc blende crystal structures

Abstract

The statistical strained-tetrahedron model was developed to overcome two common assumptions of previous models: 1) rigid undistorted ion sublattice of regular tetrahedra throughout all five configurations and 2) random ion distribution. These simplifying assumptions restrict the range of applicability of the models to a narrow subset of ternary alloys for which the constituent binaries have their lattice constants and standard molar enthalpies of formation (∆fH₀) equal or quasi-equal. Beyond these limits predictions of such models become unreliable, in particular, when the ternary exhibits site occupation preferences. The strained-tetrahedron model, free from rigidity and stochastic limitations, was developed to better describe and understand the local structure of ternary zinc blende crystals, and interpret experimental EXAFS and far-IR spectra. It considers five tetrahedron configurations with the shape and size distortions characteristic of ternary zinc blende alloys, allows nonrandom distributions and, hence, site occupation preferences, conserves coordination numbers, respects stoichiometry, and assumes that next-neighbor values determine preferences beyond next-neighbor. The configuration probabilities have three degrees of freedom. The nineteen inter-ion crystal distances are constrained by tetrahedron structures; to avoid destructive stresses, we assume that the average tetrahedron volumes of both sublattices relax to equal values. The number of distance free-parameters ≤ 7. Model estimates, compared to published EXAFS results, validate the model. Knowing the configuration probabilities, one writes the dielectric function for far-infrared absorption or reflection spectra. Constraining assumptions restrict the number of degrees of freedom. Deconvolution of the experimental spectra yields site-occupation- preference coefficient values and/or specific oscillator strengths. Validation again confirms the model.