X-ray diffraction analysis of stannite, wurtz-stannite and pseudo-cubic quaternary compounds by Rietveld method

Abstract

Room temperature X-ray powder diffraction measurements were carried out on nine polycrystalline samples of the Cu$_{2}$B$^{II}$C$^{IV}$X$_{4}$ (B=Mn, or Fe, or Co; C=Si, or Ge, or Sn; X=S, or Se, or Te) magnetic semiconductor compounds. The diffraction patterns were used to show the equilibrium conditions and to derive crystalline parameter values. The results showed that four of these compounds have a tetragonal stannite structure with space group $\mbox{I}\bar {4}2\mbox{m}$(N$^{\circ}$ 121), two an orthorhombic wurtz-stannite structure with space group Pmn2$_{1 }$(N$^{\circ}$ 31) and three of them an orthorhombic pseudo-cubic structure with space group F222 (N$^{\circ}$~22). In each case, the structure was refined using the Rietveld method. When the obtained atomic parameter values for the tetragonal compounds were plotted as a function of molecular weight $W$, it was found that the values of the atomic positions, the cation-anion bond distances, tetragonal distortion and internal distortion of the compounds containing S and/or Se lay on different lines. Also, it was found that when the experimental points of the cation-anion bond distances $d_{Cu - VI}$, $d_{II - VI}$ and $d_{IV - VI}$ were plotted against the effective lattice parameter $a_{e}$ = ($V$/$N)^{1 / 3}$, a linear variation of these distances with $a_{e}$ was obtained. Values of the ionic energy gap $C_{i}$ and homopolar energy gap $E_{h}$ using the Phillips-Van Vechten scheme, with the present experimental crystallographic results as well as using the atomic data, were determined. It was found that the observed and predicted values of $C_{i}$ and $E_{h}$ lie on the same straight line.