The Boltzmann Equation Of Phonon Thermal Transport Solved In the Relaxation Time Approximation – II – Data Analysis

<- Back to II. Mechanical Engineering & Physics Vol.3

Cite the paper

Sparavigna, Amelia Carolina

The Boltzmann Equation Of Phonon Thermal Transport Solved In the Relaxation Time Approximation – II – Data Analysis Journal Article

Mechanics, Materials Science & Engineering, 3 (1), pp. 58-67, 2016, ISSN: 2412-5954.

Abstract | Links | BibTeX

Author: Amelia Carolina Sparavigna

ABSTRACT. As discussed in a previous paper [1], the thermal transport in dielectric solids can be obtained by using the Boltzmann equation of an assembly of phonons subjected to a thermal gradient. Solving this equation in the framework of the relaxation time approximation, from the phonon distribution that we obtain, the thermal conductivity of the solid can be easily given. Here we use such an approach to analyse the data of the thermal conductivities of some dielectric materials.

Keywords: thermal conductivity, phonons, Boltzmann equation

DOI 10.13140/RG.2.1.2026.4724

References

[1] Sparavigna, A.C. (2016). The Boltzmann equation of phonon thermal transport solved in the relaxation time approximation – I – Theory. Mechanics, Materials Science & Engineering Journal, March 2016, 1-13., DOI: 10.13140/RG.2.1.1001.1923

[2] Ziman, J.M. (1962). Electrons and phonons: The theory of transport phenomena in solids. Clarendon Press. Reprint Edition in 2001. ISBN-10: 0198507798, ISBN-13: 978-0198507796

[3] Gurevich, V.L. (1986). Transport in phonon systems. North-Holland. ISBN-10: 044487013X, ISBN-13: 978-0444870131

[4] Srivastava, G.P. (1990). The physics of phonons. Taylor and Francis. ISBN-10: 0852741537, ISBN-13: 978-0852741535

[5] Omini, M., & Sparavigna, A. (1995). An iterative approach to the phonon Boltzmann equation in the theory of thermal conductivity. Physica B, 212(2), 101-112. DOI: 10.1016/0921-4526(95)00016-3

[6] Omini, M., & Sparavigna, A. (1997). Effect of phonon scattering by isotope impurities on the thermal conductivity of dielectric solids. Physica B, 233(2-3), 230-240. DOI: 10.1016/s0921-4526(97)00296-2

[7] Omini, M., & Sparavigna, A. (1996). Beyond the isotropic-model approximation in the theory of thermal conductivity. Physical Review B, 53(14), 9064-9073. DOI: 10.1103/physrevb.53.9064

[8] Omini, M., & Sparavigna, A. (1997). Heat transport in dielectric solids with diamond structure. Nuovo Cimento D, 19(10), 1537-1564.

[9] Sparavigna, A.C. (2015). Thermal conductivity of zincblende crystals. Mechanics, Materials Science & Engineering Journal, October 2015, 1-8. DOI: 10.13140/RG.2.1.1758.0565

[10] Callaway, J. (1961). Low-temperature lattice thermal conductivity. Physical Review, 122(3), 787-790. DOI: 10.1103/physrev.122.787.

[11] Callaway, J., & von Baeyer, H.C. (1960). Effect of point imperfections on lattice thermal conductivity. Physical Review, 120(4), 1149-1154. DOI: 10.1103/physrev.120.1149

[12] Callaway, J. (1959). Model for lattice thermal conductivity at low temperatures. Physical Review, 113(4), 1046-1051. DOI: 10.1103/physrev.113.1046

[13] Klemens, P.G. (1951). The thermal conductivity of dielectric solids at low temperatures. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 208(1092), 108-133. DOI: 10.1098/rspa.1951.0147

[14] Herring, C. (1954). Role of low-energy phonons in thermal conduction. Physical Review, 95(4), 954-965. DOI: 10.1103/physrev.95.954

[15] Peierls, R.E. (1955). Quantum Theory of Solids. Oxford University Press, New York. ISBN-13: 9780198507819, DOI: 10.1093/acprof:oso/9780198507819.001.0001

[16] Slack, G.A. (1957). Effect of isotopes on low-temperature thermal conductivity. Physical Review, 105, 829.831. DOI: 10.1103/PhysRev.105.829

[17] Geballe, T.H., & Hull, G.W. (1958). Isotopic and other types of thermal resistance in Germanium. Physical Review, 110, 773-775. DOI: 10.1103/physrev.110.773

[18] Sparavigna, A. (2002). Influence of isotope scattering on the thermal conductivity of diamond. Physical Review B, 65, 064305. DOI: 10.1103/PhysRevB.65.064305

[19] Capinski, W.S., Maris, H.J., & Tamura, S. (1999). Analysis of the effect of isotope scattering on the thermal conductivity of crystalline silicon. Physical Review B, 59(15), 10105-10110. DOI: 10.1103/physrevb.59.10105

[20] Wei, L., Kuo, P.K., Thomas, R.L., Anthony, T., & Banholzer, W. (1993). Thermal conductivity of isotopically modified single crystal diamond. Physical Review Letters, 70(24), 3764-3767. DOI: 10.1103/PhysRevLett.70.3764

[21] John, P., Polwart, N., Troupe, C.E., & Wilson, J.I.B. (2002). The oxidation of (100) textured diamond. Diamond and Related Materials, 11 (3–6), 861-866. DOI: 10.1016/S0925-9635(01)00673-2

[22] Holland, M.G. (1963). Analysis of lattice thermal conductivity. Physical Review, 132(6), 2461-2471. DOI: 10.1103/physrev.132.2461

[23] Klemens, P. (1976). Thermal Conductivity, Springer. DOI: 10.1007/978-1-4899-3751-3

[24] Broido, D.A., Ward, A., & Mingo, N. (2005). Lattice thermal conductivity of silicon from empirical interatomic potentials. Physical Review B, 72(1), 014308. DOI: 10.1103/physrevb.72.014308

[25] Kaburaki, H., Li, J., Yip, S., & Kimizuka, H. (2007). Dynamical thermal conductivity of argon crystal. Journal of Applied Physics, 102(4), 043514. DOI: 10.1063/1.2772547

[26] Turney, J.E., Landry, E.S., McGaughey, A.J.H., & Amon, C.H. (2009). Predicting phonon properties and thermal conductivity from anharmonic lattice dynamics calculations and molecular dynamics simulations. Physical Review B, 79(6), 064301. DOI: 10.1103/physrevb.79.064301

[27] McGaughey, A.J., & Kaviany, M. (2004). Quantitative validation of the Boltzmann transport equation phonon thermal conductivity model under the single-mode relaxation time approximation. Physical Review B, 69(9), 094303. DOI: 10.1103/physrevb.69.094303

[28] Li, W., Carrete, J., Katcho, N.A., & Mingo, N. (2014). ShengBTE: A solver of the Boltzmann transport equation for phonons. Computer Physics Communications, 185(6), 1747-1758. DOI: 10.1016/j.cpc.2014.02.015

Creative Commons Licence
Mechanics, Materials Science & Engineering Journal by Magnolithe GmbH is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at www.mmse.xyz.