Analysis of lattice thermal conductivities of rare-earth sulphides at high temperatures

Abstract

The lattice thermal conductivities of rare-earth sulphides have been analyzed at high temperatures in the frame of the two-mode conduction of phonons for the first time by studying the total lattice thermal conductivities of GdS and LaS in the entire temperature range 100--1000 K. The temperature exponents for the three-phonon scattering relaxation rates are reported for the transverse as well as for the longitudinal phonons. The separate percentage contributions due to the transverse and longitudinal phonons towards the total lattice thermal conductivities of the above samples have similarly been studied. The role of the four-phonon processes too has been included in the present investigation.The lattice thermal conductivities of numerous samples have been studied by a number of workers [1-10], experimentally as well as theoretically, at high and at low temperature, and it is now well established that high-temperature lattice thermal conductivity data can not be explained by one conductivity integral as proposed by Callaway [11]. It was Holland [12] who first introduced the twomode conduction of phonons to explain the lattice thermal conductivities of Ge and Si at high temperatures. Later, following Guthrie [13,14], the author and his co-workers [15][16][17][18] proposed a modification to the Holland model, which is known as the Sharma-Dubey-Verma (SDV) model [15][16][17][18]. In the SDV model [15][16][17][18], the phonon-phonon scattering events have been classified into two classes: class 1 events in which a carrier phonon is annihilated by combination, and class II events in which annihilation takes place by splitting. From their studies, it is clear that the SDV model gives a very good response in explaining experimental lattice thermal conductivity data at high temperatures. At the same time, the temperature-dependence of the phonon-phonon scattering relaxation rate used in the SDV model is also free from the Guthrie comments [13,14].Khusnutdinova et al. [19] tried to explain the high-temperature lattice thermal conductivity data on GdS and LaS by using an analytical expression obtained in the frame of the Callaway [1 1 ] expression based on the high-temperature approxi--1 2 mations. They used an expression -t-3ph~wT for the three-phonon scattering relaxation rate, which is valid for longitudi.nal phonons only. At the same time, all of their calculations are based on the Callaway expression, which gives a good response to the experimental lattice thermal conductivity data at low temperatures only. Thus, it is interesting to analyse the lattice thermal conductivities of the above samples in the frame of the two-mode conduction of phonons.12