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 A 1-x B x Y y Z 1-y (2:2 cation:anion ratio), and the unbalanced A x B x′ C 1-x-x′ Z or AX y Y y′ Z 1-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. PACS: 61.43. Dq Amorphous semiconductors; metals and alloys.

Local crystalline structure of multinary semiconducting alloys: Random vs. ordered distributions

“…These contributions to the distribution probabilities P 0 and P 4 are discussed Ref. [2] and more recently in Ref. [14] (see Fig.…”

“…The Strained-tetrahedra model [12,13] served also to interpret the pseudo quaternary Ga x In 1-x As y Sb 1-y [21] and Cd x Mn 1-x Te y Se 1-y [23,24], as well as the truly quaternary Zn x Cd y Hg 1-x-y Te [26] and InAs x P y Sb 1-x-y [27]. For the latter, W k and C k values are identified by two subsets W kj and C kj [2]. More than a decade ago, the theoretical Statistical model started to be developed [28] to interpret also FIR observations of transverse optical (TO) frequencies and intensities or oscillator strengths (OS) [28].…”

“…More than a decade ago, the theoretical Statistical model started to be developed [28] to interpret also FIR observations of transverse optical (TO) frequencies and intensities or oscillator strengths (OS) [28]. Several ternary alloys (ZnCdTe [2,29], CdHgTe and ZnHgTe [29]) and quaternary alloys [2] (Cd x Mn 1-x Te y Se 1-y [25] and Zn x Cd y Hg 1-x-y Te [26] were analyzed. The theoretical Statistical model successfully compared information derived from the FIR frequency and intensity of phonon vibration spectra to the information obtained by EXAFS.…”

“…The first that we identified as truly quaternary with ABCX (Q 31 ) or AXYZ (Q 13 ) formulas consists of fifteen different tetrahedron configurations: 3 binary, 9 ternary, and 3 quaternary while the second described as ABXY(Q 22 ) consists canonically of 4 binary, 12 ternary configurations, and ruling out the presence of antisites has no quaternary. The latter are referred in the next as pseudo-quaternary alloys [2].…”