Longitudinal and Transverse Phonons in Lattice Thermal Conductivity

Analysis of the lattice thermal conductivity and phonon-phonon scattering relaxation rate: Application to Mg2Ge and Mg2Si

“…From these Figures, it is also clear that the values of re(T) used in the calculation of the lattice thermal conductivities of MgzGe and MgzSi lie in the range 1 -4 for transverse phonons and 1 -3 for longitudinal phonons in the entire temperature range 2-1000 K, and the upper limit of Guthrie [31] is not exceeded at any temperature. Thus, they are free from the Guthrie comments [32] too. Therefore, it can be said that the values of rn(T) used in the present analysis of the lattice thermal conductivities of Mg2Ge and MgzSi are more realistic than those used by earlier workers [57,58,61,62].…”

“…9(o)) = co for transverse phonons and o) 2 for longitudinal phonons. The temperature exponent re(T) is a continuous function of temperature T. Guthrie [31,32] commented on the use of the Herring [11] relations z;) h oc T ~ .and zf)h oc T 3 for transverse and longitudinal phonons, respectively, at high temperatures, and suggested that these relations are valid only at low temperatures. It is needed to be stated that Guthrie [31 ] could not give any analytical expression for the exact value of re(T), except that he reported the extreme values of re(T) as: For class I events: …”

“…In these expressions, B's are constants and are known as the scattering strenghts of the respective processes, ~ is constant, 0 is the Debye temperature and qrn~x is the zone boundary of the first Brillouin zone. Suffixes Tand L stand for transverse and longitudinal phonons, respectively, and suffixes N and U refer to threephonon normal and umklapp processes, respectively The three-phonon scattering relaxation rates were further studied by Guthrie [31,32] by dividing the phonon-phonon scattering events into two classes: class I Table 2 The combined scattering relaxation rates. In these expressions, 0)x and 0)~ are the transverse phonon frequencies at 1/2qmax and qrnax, respectively, 0)3 and 0)4 are the same for longitudinal phonons, c% is the Debye frequency, ~ffl and Tyt 1 are the boundary and point-defect scattering relaxation rate, respectively, and the other terms have the same meanings as stated in Table 1 Combined scattering relaxation rates zc 1 Frequency range events, in which the carrier phonon is annihilated by combination, and class II events, in which the carrier phonon is annihilated by splitting.…”

Analysis of lattice thermal conductivity of GaAs at high temperatures

“…Recently, while commenting on the nature of dependence of the phonon conductivity on frequency w and temperature T, Guthrie [6,7] gave an expression for the three-phonon sc~ittering relaxation rate ~h in the form [12] and incorporating the Guthrie ideas, the author and his co-workers [3][4][5] gave an expression for where O is the Debye temperature of the sample and c~ is a constant which has the same meaning as given by Klemens. According to the SDV model, for transverse phonons, the expression for ~ reduces to since only class I events are possible for transverse phonons.…”

“…It was Holland [2] who first introduced the two-mode conduction of phonons to explain the high-temperature data of the lattice thermal conductivities of Si and Ge. Later, the author and his co-workers [3][4][5] proposed a modification of the Holland model, using the Guthrie [6,7] ideas, and this is known as the Sharma-Dubey-Verma (SDV) model [3][4][5] in which the phonon-phonon scattering events are classified into two groups: the class I events, in which a carrier phonon is annihilated by combination, and class II, in which the annihilation takes place by splitting.The phonon conductivity of GaAs has been studied experimentally as well as theoretically by several workers [4,[8][9][10]. However, their studies are limited up to room temperature, i.e.…”