Three-Phonon Scattering and Guthrie's Limits for Its Temperature Dependence

Sharma, Priyanka; Dubey, K. S.; Verma, G. S.

doi:10.1103/physrevb.4.1306

Cited by 46 publications

(30 citation statements)

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“…Incorporating the Guthrie ideas and following Klemens [21], the author and his co-workers [15][16][17][18] gave an expression for z -1 3 ph as T3ph--1 oc g(w) Tm(X)e -~ (2) where 19 is the Debye temperature and ~ is a constant which has the same meaning as given by Klemens [21]. According to the SDV model, the three-phonon -1 for transverse phonons is given by scattering relaxation rate Zaph, T …”

Section: Phonon Conductivity Integral and Temperature Exponent M(t)mentioning

confidence: 99%

“…[4,[15][16][17][18]), %,~f and %,L are the combined scattering relaxation times due to transverse phonons and longitudinal phonons, respectively, and can be expressed as…”

Section: Taph Oc G(og)f(t)mentioning

confidence: 99%

“…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.…”

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confidence: 99%

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

Dubey

1981

Journal of Thermal Analysis

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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

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Section: Phonon Conductivity Integral and Temperature Exponent M(t)mentioning

confidence: 99%

“…[4,[15][16][17][18]), %,~f and %,L are the combined scattering relaxation times due to transverse phonons and longitudinal phonons, respectively, and can be expressed as…”

Section: Taph Oc G(og)f(t)mentioning

confidence: 99%

mentioning

confidence: 99%

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

Dubey

1981

Journal of Thermal Analysis

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“…The coefficients C,(G) will be deduced from the equation for the conservation of the generalized momentum L7 = P -GN Using the expansion (6), we get from ( 1 2 ) I n spherical coordinates (w, 0, q~), 2 1 d3k = k2 sin2 e d k ae d p = -bff, -dw, sin2 e de dpl .…”

Section: In the Formmentioning

confidence: 99%

“…Here y! are constants that can be calculated from experimental dispersion curves [ 2 ] . If we take into consideration the dispersion equations (4), this will cause a distinction between phonon group velocity vkj = dokj/dk and phonon phase velocity vk,j = @kj/k.…”

Section: Introductionmentioning

confidence: 99%

The Contribution of Reciprocal Lattice Vectors to Processes of Phonon‐Phonon Interaction and Lattice Thermal Conductivity

Segal¹

1980

Physica Status Solidi (b)

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On the basis of a reformulation of the known wave vector conservation law in interaction processes with three phonons, the Boltzmann equation is solved and an equation of the lattice thermal conductivity is obtained. I n this equation the average value of reciprocal lattice vectors occurs, which contribute to the three phonon interaction processes. An application of the equation obtained for different substances would offer information regarding the reciprocal lattice vectors which contribute to these processes.Aux termes d'une nouvelle expression de la loi de la conservation du vecteur d'onde dans les processus d'interaction avec trois phonones on rBsout 1'6quation de Boltzmann et on obtient une expression de la conductivite thermique du rbseau. Dam cette expression appara'it la valeur moyenne des vecteurs du rkseau rbciproque qui interviennent dans les processus d'interaction avec trois phonones. L'application de la relation obtenue it differentes donnBes exphimentales pourrait nous offrir des informations sur les vecteurs du reseau rbciproque qui contribuent it ces processus.

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Nonlinear Heat Transfer in a Lattice Containing Impurities

Dubey

1973

Physica Status Solidi (b)

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Nonlinear heat transfer in a lattice has been studied considering two scattering mechanisms, isotopic scattering and dislocation scattering as impurity scattering process. A sufficiently good agreement is observed between the experimental conductivity of NaF in the entire temperature range 2 to 10 OK.Es wird die nichtlineare Warmeiibertragung in einem Gitter unter Beriicksichtigung von zwei Streumechanismen, isotopischer und Versetzungsstreuung als FehlstellenstreuprozeD, untersucht. Eine geniigend gute Ubereinstimmung mit der experimentellen Leitfiihigkeit von NaF wird im gesamten Temperaturbereich von 2 bis 10 "K beobachtet.

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Three-Phonon Scattering and Guthrie's Limits for Its Temperature Dependence

Cited by 46 publications

References 8 publications

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

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

The Contribution of Reciprocal Lattice Vectors to Processes of Phonon‐Phonon Interaction and Lattice Thermal Conductivity

Nonlinear Heat Transfer in a Lattice Containing Impurities

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