The new expression for the three-phonon scattering relaxation rate r g , = ( B , + B , e-OlaT) x x g(w) Twl proposed by Dubey and Misho is used to calculate the lattice thermal conductivity of InSb and GaAs in the entire temperature range 2 to 300 K and 2 to 800 K, respectively and very good agreement is obtained between experimental and calculated values of the phonon conductivity of both the samples, InSb and GaAs, in the entire temperature range investigated. The reduced contribution due to transverse and longitudinal phonons are also studied by calculating the separate contribution due to each mode of phonons. The percentage contributions of threephonon normal and three-phonon umklapp processes are studied. A comparative study of present results with the results obtained by previous workers is also made for both of the samples.

The lattice thermal resistivity of an insulator has been studied by several workers /1 to 5/ at low a s well a s at high temperatures and it has been found that at high temperatures I the lattice thermal resistivity of an insulator is mainly due to three-phonon scattering processes and boundary scattering does not make any significant contribution to the total lattice thermal resistivity of an insulator. Thus, the boundary scattering can be ignored in the study of the lattice thermal resistivity at high temperatures. However, it is also found that at low temperatures, the boundary scattering makes a very large contribution to the total lattice thermal resistivity of an insulator in comparison t o other scattering processes. Therefore, there is a need to study the role of the boundary scattering relaxation rate in the calculation of the lattice thermal resistivity of an insulator at low temperatures. Recently, the authors /6/ studied the phonon conductivity of Ga-As in the temperature range 2 t o 800 K. But their entire study is confined t o the role of three-phonon scattering processes alone while the study of the boundary scattering i s ignored in their previous study. In continuation of the earlier report, the aim of the present note is to study the role of the boundary scattering (i.e. crystal size effect) in the lattice thermal resistivity of an insulator by calculating the phonon conductivity of GaAs in the temperature range 2 to 10 K for different values of the boundary scattering relaxation rate (i.e. for different values of the effective length /7/ of the crystal). The study is limited to the low temperature range due to the fact that boundary scattering plays a dominating role a t these temperatures only.According t o Al-Edani and Dubey /6/, the total phonon conductivity K of an insulator can be expressed a s K = S + K L ,1) Part of the M.Sc. thesis to be submitted to

Absorption edge measurements in triglycine selenate single crystals are made. The data on absorption coefficient versus photon energy are analysed and interpreted in term of three valence bands originated by spin–orbit interaction and crystal field splitting.

The lattice thermal conductivity of gadolinium monosulphide is studied by estimating the separate contributions due to transverse and longitudinal phonons in the temperature range 300 to 800 K and a very good agreement is found between calculated and experimental values. It is also reported that the transverse phonons are mainly responsible for the heat conduction in the present sample. The temperature exponents for the three phonon scattering relaxation rates is also reported for gadolinium monosulphide for the first time.Durch Berechnung der getrennten Beitriige der transversalen und longitudinalen Phononen im Temperaturbereich 300 bis 800 K wird die thermische Gitterleitfghigkeit von Gadoliniummonosulfid untersucht und sehr gute ubereinstimmung zwischen berechneten und experimentellen Werten gefunden. Es wird ebenfalls gezeigt, da13 die transversalen Phononen hauptsachlich fur die Wiirmeleitung in der untersuchten Probe verantwortlich sind. Erstmalig werden such fur Gadoliniummonosulfid die Temperaturexponenten fur die drei Phononenstreurelaxationsraten angegeben.

The role of the point-defect scattering relaxation rate has been studied in the lattice thermal conductivity of ah insulator by calculating the lattice thermal conductivity of GaAs for the different va]ues of the point-defect scattering strength. All calculations have been pcrformed in the frame of the recently proposed model of DuB~,Y and MISHO of the phonon conductivity of an insulator. The study is made for low as well as high values of the point-defcct scattering strength in the entire temperature range 4--100 K.The lattice thermal resistivity of ma insulator has been studied by several workers and is found that the transportation of heat by lattice waves in a solid is governed by the anharmonicities of the lattice forees such as various imperfections of the crystal lattice and by the external boundary. It is well known [1--4] that the point-defects (isotopic impurities) are one of the very important seatterers of phonons at temperatures near the conductivity maxima, and the lattice thermal resistivity of an insulator is mainly due to the point-defeet seattering relaxation tate at these temperatures. Thus, there is a need to study the role of the point-defect seattering relaxation tate in the caleulation of the lattiee thermal conduetivity. Reeently, the authors [4, 6] studied the phonon eonductivity of GaAs in the entire temperature rmage 2--800 K. But their studies ate eonfined to see the tole of the three phonon and boundary scattering processes only, while the study of the tole of the point-defeet seattering has been totally ignored in their previous studies. In eontinuation of the earlier study, the airo of the present note is to study the tole of the point-defect seattering relaxation rate in the ealeulation of the lattice thermal eonductivity.The study is performed by introducing a new parameter "p" whieh is the ratio of the point-defeet seattering strengths of the normal sample and the sample under study (having ah impurity coneentration different from the normal sample), similar to the previous study of the tole of the boundary scattering [6]. The new parameter "p" can be defined as p = (point-defect seattering strength for the sample under study)/(point-defect seattering strength of the normal sample) and it depends totally on the extra impurities present in the normal sample. GaAs is taken as ma example mad its lattice thermal eonduc-4* .Acta Physir A~miae Sr II~~'ir 46 1979

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