Heat Capacity of PbS: Isotope Effects

TL;DR

This study investigates how isotopic variations in lead sulfide affect its heat capacity, combining experimental measurements with ab initio calculations to understand the influence of atomic mass differences on thermal properties.

Contribution

It provides the first detailed analysis of isotope effects on the heat capacity of PbS, comparing experimental data with theoretical predictions based on lattice dynamics.

Findings

Isotope substitution significantly affects PbS heat capacity.

Experimental results align with ab initio calculations, with some deviations.

Differences in atomic mass of Pb and S lead to distinct isotope effects.

Abstract

In recent years, the availability of highly pure stable isotopes has made possible the investigation of the dependence of the physical properties of crystals, in particular semiconductors, on their isotopic composition. Following the investigation of the specific heat ($C_p$, $C_v$) of monatomic crystals such as diamond, silicon, and germanium, similar investigations have been undertaken for the tetrahedral diatomic systems ZnO and GaN (wurtzite structure), for which the effect of the mass of the cation differs from that of the anion. In this article we present measurements for a semiconductor with rock salt structure, namely lead sulfide. Because of the large difference in the atomic mass of both constituents ($M_{\rm Pb}$= 207.21 and ($M_{\rm S}$=32.06 a.m.u., for the natural isotopic abundance) the effects of varying the cation and that of the anion mass are very different for this canonical semiconductor. We compare the measured temperature dependence of $C_p \approx C_v$, and the corresponding derivatives with respect to ($M_{\rm Pb}$ and $M_{\rm S}$), with \textit{\textit{ab initio}} calculations based on the lattice dynamics obtained from the local density approximation (LDA) electronic band structure. Quantitative deviations between theory and experiment are attributed to the absence of spin-orbit interaction in the ABINIT program used for the electronic band structure calculations.