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 (D f H 0 ) 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.

Statistical model analysis of local structure of quaternary sphalerite crystals

“…Most semiconductors exhibit SOPs, as experimentally confirmed yielding quantitative SOP coefficient values reliably using different models. The strained tetrahedron model gives a good agreement for both EXAFS data [1,2] and FIR spectra [4,5] of sphalerite ternary A 1-x B x Z and AY y Z 1-y , and now to the Q22 A 1-x B x Y y Z 1-y systems [6]. It also successfully interprets EXAFS data of intermetallic M 3 (XX¢) [3] systems, and within certain limitations may do so for some wurzite crystalline structures [2], returning SOP coefficient values.…”

“…The topological differences between quaternary sphalerite Q31 (Q13) and Q22 structured systems impose different statistical model approaches and thus the statistical analysis of the pseudo and truly-Q compounds is not a simple generalisation. This explains why, after the Q22 compound analysis [4], an ad hoc statistical strained tetrahedron model for quaternary sphalerite Q31 and Q13 systems is developed in Ref. 7.…”

“…In the following, we use the same nomenclature introduced in [1] and used since [2][3][4][5][6] and define cations by A, B, C, anions by X, Y, Z, and the relative contents of site competing ions by x, x′ for cations, and by y, y′ for anions. We thus write AZ for a binary compound, A 1-x B x Z or AY y Z 1-y for a ternary system, and either A 1-x B x Y y Z 1-y (2:2 cation:anion ratios, referred to as Q22) or A 1-x-x′ B x′ C x Z or AX y Y y′ Z 1-y-y′ (with respectively (3:1 or 1:3 cation:anion ratios) for quaternary systems.…”

“…Successively, the model was expanded to treat ternary M 3 (XX′) 1 type intermetallide alloys [3] and then to interpret FIR spectra of ternary sphalerite structure [4,5]. To our knowledge no EXAFS data for truly-Q systems are available in the literature.…”

“…Elemental volumes of the two sublattices, for each of the three strictly ternary configurations, relax pair-by-pair to common values (i.e., three volume relaxation constraints [VRC] on the distance parameters). For FIR spectra, the lines issued from the different configurations by a given ion ij-dipole have an invariant [4,5].…”