# Defect chemistry analysis and thermodynamic characterization of (lead(1-x)tin(x))(1-y)tellurium(y) ternary compounds

#### Abstract

A framework is established for the analysis of defect chemistry of the entire (Pb$\sb{1-x}$Sn$\sb{x}$)$\sb{1-y}$Te$\sb{y}$ system based upon statistical thermodynamic calculations and experimentally measured carrier concentration and tellurium partial pressure data. The energy-band structure, in which inversion of the direct-gap bands occurs, is explicitly incorporated into the analysis for the first time and the non-degenerate assumption is abandoned. The densities of states of the non-ellipsoidal bands and the Fermi levels are calculated numerically. The intrinsic material parameters are determined by the fit to the carrier concentration-partial pressure data. The model established is applied to PbTe and SnTe binary compounds and satisfactory fits obtained. The Fermi level lies in the light-mass valence band of SnTe for all of the observed carrier concentrations so that previous analyses were in error. The 1 at% wide homogeneity range of SnTe is wide enough that a compositional variation in the sum of the chemical potentials of tin and tellurium has been detected experimentally. This variation is theoretically zero in the usual models for narrow homogeneity-range compounds, but is accounted for in this analysis. The partial pressures of Te$\sb2$($g$), PbTe($g$), and SnTe($g$) are measured over (Pb$\sb{1-x}$Sn$\sb{x}$)$\sb{1-y}$Te$\sb{y}$($c$) for $x$ = 0.5 and 0.7, and over the corresponding melts. The Te-rich leg of the three phase curve are constructed and the composition for the solid solutions derived at a series of points with known temperature and Te$\sb2$($g$)-partial pressure. These are the useful information for the subsequent defect chemistry analysis for those ternary compounds. Combining with those over binary compounds, the partial pressures of PbTe($g$) and SnTe($g$) lead to the Gibbs energy of mixing of the ternary solid solutions from their binary components, which is slightly different than that expected for an ideal solution. Together with the previous results of $x$ = 0.13 and 0.2, a more complete picture of the thermodynamics of the pseudobinary solid solution is obtained. The experimental technique consists of measuring the optical absorbance of the vapor coexisting with a solid-solution sample in a sealed optical cell of known volume and temperature. The samples are synthesized by reaction in the sealed cell of weighed amounts of the spectroscopically pure elements.

#### Recommended Citation

Sha, Yi Gao, "Defect chemistry analysis and thermodynamic characterization of (lead(1-x)tin(x))(1-y)tellurium(y) ternary compounds" (1988). *Dissertations (1962 - 2010) Access via Proquest Digital Dissertations*. AAI8925439.

https://epublications.marquette.edu/dissertations/AAI8925439