EXAFS studies of the local environment of lead and selenium atoms in PbTe$_{1-x}$Se$_x$ solid solution

Abstract

EXAFS spectroscopy is used to study the local environment of lead and selenium atoms in PbTe$_{1-x}$Se$_x$ solid solution. In addition to a bimodal distribution of bond lengths in the first shell, unusually large Debye--Waller factors for the Pb--Pb interatomic distances in the second shell and a substantial deviation of these distances from Vegard's law are observed. Valence force field (VFF) calculations show that these observations are due to the complex structure of the distribution function for Pb--Pb distances. It is found that the number of Se--Se pairs in the second shell surpasses the statistical value, which indicates that chemical factors play an important role in the structure of the solid solution. The contribution of these chemical factors to the enthalpy of mixing of the solid is estimated to be approximately 0.5 kcal/mole, which is comparable to the strain contribution.

Figures (10)

• Figure 1: EXAFS $k \chi(k)$ spectra obtained at the $K$ absorption edge of Se for PbTe$_{1-x}$Se$_x$ samples. $x$: 1 --- 0.1, 2 --- 0.25, 3 --- 0.5, 4 --- 0.75, 5 --- 1. The arrow denotes the location of a glitch.
• Figure 2: EXAFS $k \chi(k)$ spectra obtained at the $L_{\rm III}$ absorption edge of Pb for PbTe$_{1-x}$Se$_x$ samples. $x$: 1 --- 0, 2 --- 0.1, 3 --- 0.25, 4 --- 0.5, 5 --- 0.75, 6 --- 1. The arrows indicate the locations of glitches.
• Figure 3: Pb--Se (1) and Pb--Te (2) bond lengths as a function of composition $x$ of PbTe$_{1-x}$Se$_x$ solid solution. 3, 4, and 5 are the results obtained from the EXAFS data analysis for $R_{\rm Pb-Te}$, $R_{\rm Pb-Se}$, and $R_{\rm Se-Pb}$, respectively. Solid lines and dashed line are mean Pb--Se, Pb--Se distances, and mean interatomic distance (calculated from the lattice parameter) all obtained from the VFF modeling (Sec. 4).
• Figure 4: Debye--Waller factors for Pb--Te (1) and Pb--Se (2) bonds as functions of the composition $x$ of PbTe$_{1-x}$Se$_x$ solid solution. 3, 4, and 5 are the results of the EXAFS data analysis for Pb--Te, Se--Pb, and Pb--Se bonds, respectively. The solid line is the static contribution to the Debye--Waller factor calculated using the VFF method (Sec. 4).
• Figure 5: Pb--Pb interatomic distances as a function of $x$ in the PbTe$_{1-x}$Se$_x$ solid solution. The points are results of the EXAFS data analysis. The solid line is calculated using the VFF method, the dashed line is the mean interatomic distance calculated from the lattice parameter, and the dotted line presents the results of the EXAFS data analysis for simulated $\chi(k)$ curves (equation (\ref{['eq4']})).