Temperature Dependence of Three-Phonon Processes in Solids, with Application to Si, Ge, GaAs, and InSb

Lattice Thermal Conductivity of Gadolinium Monosulphide above Room Temperature in the Frame of Two‐Mode Conduction of Phonons

“…Using the constants reported in Tablel, the temperature exponents mT,I(T) for transverse phonons, and mL,I(T) for longitudinal phonons have been found to vary from 1.04 t o 1.01 and from 1.17 t o 1.05, respectively, when T goes from 300 to 800 K, whereas a t very high temperature mL,Ir(T) is constantly unity as suggested by Guthrie [9]. Using these values of the temperature exponents, the total lattice thermal conductivity of GdS has been calculated in the temperature range 300 to 800K by estimating the separate contributions K , due to transverse phonons and KL due to longitudinal phonons with the help of the numerical integration of the conductivity integrals stated in (7) and (8); the results obtained are shown in Fig.…”

“…Following Guthrie [9], in the SDV model, the phonon-phonon interactions have been classified into two classes: class I in which two phonons are combined to form one phonon and class I1 i n which one phonon is split into two phonons, and the temperature exponents m I ( T ) and mII(T) are given by…”

Thermal conductivity of germanium containing dislocations at low temperatures

“…Guthrie [14] has calculated the temperature dependence of the three-phonon processes by evaluating the exponent for the three-phonon processes a t different temperatures. Guthrie's results can be summarized to our present calculations as follows : (xi;), = Bp.& T3 , The phonon-dislocation scattering processes can be expressed by (1) where zdi and TZ; are the reciprocal relaxation times for the static and the dynamic processes, respectively.…”

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

“…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.…”