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Published in: Continuum Mechanics and Thermodynamics 6/2019

04-07-2019 | Original Article

Relation between defects and crystalline thermal conduction

Authors: A. A. Le-Zakharov, A. M. Krivtsov, A. V. Porubov

Published in: Continuum Mechanics and Thermodynamics | Issue 6/2019

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Abstract

Modeling of the heat transfer in ideal crystal lattice with defects is performed for measuring the heat conductivity coefficient. A non-steady process in closed system is studied. The method is based on comparison of the results of molecular dynamics simulation and solution of the heat equation. Two-dimensional and three-dimensional structures with dense packing of particles are considered. Defects are modeled by removing or changing the mass of randomly selected lattice atoms. Based on the results of molecular-dynamics modeling, an empirical dependence of the thermal diffusivity on the density of defects is elaborated. It also turns out in a good agreement with experimental data.

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Literature
1.
go back to reference Lepri, S. (ed.): Thermal Transport in Low Dimensions: From Statistical Physics to Nanoscale Heat Transfer. Lecture Notes in Physics, vol. 921. Springer, Switzerland (2016) Lepri, S. (ed.): Thermal Transport in Low Dimensions: From Statistical Physics to Nanoscale Heat Transfer. Lecture Notes in Physics, vol. 921. Springer, Switzerland (2016)
2.
go back to reference Hoover, W.G., Hoover, C.G.: Simulation and Control of Chaotic Nonequilibrium Systems. Advanced Series in Nonlinear Dynamics, vol. 27. World Scientific, Singapore (2015)CrossRef Hoover, W.G., Hoover, C.G.: Simulation and Control of Chaotic Nonequilibrium Systems. Advanced Series in Nonlinear Dynamics, vol. 27. World Scientific, Singapore (2015)CrossRef
3.
go back to reference Callaway, J.: Model for lattice thermal conductivity at low temperature. Phys. Rev. 113(4), 1046–1051 (1959)ADSCrossRef Callaway, J.: Model for lattice thermal conductivity at low temperature. Phys. Rev. 113(4), 1046–1051 (1959)ADSCrossRef
4.
go back to reference Ma, J., Luo, X.: Examining the Gallaway model for lattice thermal conductivity. Phys. Rev. B 90, 035203 (2014)ADSCrossRef Ma, J., Luo, X.: Examining the Gallaway model for lattice thermal conductivity. Phys. Rev. B 90, 035203 (2014)ADSCrossRef
5.
go back to reference Klemens, P.G.: The scattering of low-frequency lattice waves by static imperfections. Proc. Phys. Soc. A 68, 1113–1128 (1955)ADSCrossRef Klemens, P.G.: The scattering of low-frequency lattice waves by static imperfections. Proc. Phys. Soc. A 68, 1113–1128 (1955)ADSCrossRef
6.
go back to reference Polanco, C.A., Lindsay, L.: Thermal conductivity of \(InN\) with point defects from first principles. Phys. Rev. B 98, 014306 (2018)ADSCrossRef Polanco, C.A., Lindsay, L.: Thermal conductivity of \(InN\) with point defects from first principles. Phys. Rev. B 98, 014306 (2018)ADSCrossRef
7.
go back to reference Rieder, Z., Lebowitz, J.L., Lieb, E.: Properties of a harmonic crystal in a stationary nonequilibrium state. J. Math. Phys. 8, 10731078 (1967)CrossRef Rieder, Z., Lebowitz, J.L., Lieb, E.: Properties of a harmonic crystal in a stationary nonequilibrium state. J. Math. Phys. 8, 10731078 (1967)CrossRef
8.
go back to reference Bonetto, F., Lebowitz, J.L., Rey-Bellet, L.: Fourier’s law: a challenge to theorists. In: Fokas, A., et al. (eds.) Mathematical Physics 2000, pp. 128–150. Imperial College Press, London (2000)CrossRef Bonetto, F., Lebowitz, J.L., Rey-Bellet, L.: Fourier’s law: a challenge to theorists. In: Fokas, A., et al. (eds.) Mathematical Physics 2000, pp. 128–150. Imperial College Press, London (2000)CrossRef
9.
10.
11.
go back to reference Le-Zakharov, A.A., Krivtsov, A.M.: Molecular dynamics investigation of heat conduction in crystals with defects. Dokl. Phys. 53(5), 261–264 (2008)ADSCrossRef Le-Zakharov, A.A., Krivtsov, A.M.: Molecular dynamics investigation of heat conduction in crystals with defects. Dokl. Phys. 53(5), 261–264 (2008)ADSCrossRef
12.
go back to reference Gendelman, O.V., Savin, A.V.: Normal heat conductivity in chains capable of dissociation. Europhys. Lett. 106, 34004 (2014)ADSCrossRef Gendelman, O.V., Savin, A.V.: Normal heat conductivity in chains capable of dissociation. Europhys. Lett. 106, 34004 (2014)ADSCrossRef
13.
14.
go back to reference Krivtsov, A.M.: The ballistic heat equation for a one-dimensional harmonic crystal. In: Altenbach, H., et al. (eds.) Dynamical Processes in Generalized Continua and Structures. Advanced Structured Materials, vol. 103, pp. 345–358. Springer, Switzerland (2019) Krivtsov, A.M.: The ballistic heat equation for a one-dimensional harmonic crystal. In: Altenbach, H., et al. (eds.) Dynamical Processes in Generalized Continua and Structures. Advanced Structured Materials, vol. 103, pp. 345–358. Springer, Switzerland (2019)
16.
go back to reference Gavrilov, S.N., Krivtsov, A.M., Tsvetkov, D.V.: Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply. Contin. Mech. Thermodyn. 31, 255–272 (2019)ADSMathSciNetCrossRef Gavrilov, S.N., Krivtsov, A.M., Tsvetkov, D.V.: Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply. Contin. Mech. Thermodyn. 31, 255–272 (2019)ADSMathSciNetCrossRef
17.
18.
go back to reference Babenkov, M.B., Ivanova, E.A.: Analysis of the wave propagation processes in heat transfer problems of the hyperbolic type. Contin. Mech. Thermodyn. 26, 483–502 (2014)ADSMathSciNetCrossRef Babenkov, M.B., Ivanova, E.A.: Analysis of the wave propagation processes in heat transfer problems of the hyperbolic type. Contin. Mech. Thermodyn. 26, 483–502 (2014)ADSMathSciNetCrossRef
19.
go back to reference Adamyan, V., Zavalniuk, V.: Lattice thermal conductivity of graphene with conventionally isotopic defects. J. Phys. Condens. Matter 24(41), 415401 (2012)CrossRef Adamyan, V., Zavalniuk, V.: Lattice thermal conductivity of graphene with conventionally isotopic defects. J. Phys. Condens. Matter 24(41), 415401 (2012)CrossRef
20.
go back to reference Pop, E., Varshney, V., Roy, A.K.: Thermal properties of graphene: fundamentals and applications. MRS Bull. 37, 1273–1281 (2012)CrossRef Pop, E., Varshney, V., Roy, A.K.: Thermal properties of graphene: fundamentals and applications. MRS Bull. 37, 1273–1281 (2012)CrossRef
21.
go back to reference Liu, D., Yang, P., Yuan, X., Guo, J., Liao, N.: The defect location effect on thermal conductivity of graphene nanoribbons based on molecular dynamics. Phys. Lett. A 379(9), 810–814 (2015)CrossRef Liu, D., Yang, P., Yuan, X., Guo, J., Liao, N.: The defect location effect on thermal conductivity of graphene nanoribbons based on molecular dynamics. Phys. Lett. A 379(9), 810–814 (2015)CrossRef
22.
go back to reference Li, M., et al.: Effect of defects on the mechanical and thermal properties of graphene. Nanomaterials 9, 347 (2019)CrossRef Li, M., et al.: Effect of defects on the mechanical and thermal properties of graphene. Nanomaterials 9, 347 (2019)CrossRef
23.
go back to reference Yang, Y., et al.: Thermal conductivity of defective graphene oxide: a molecular dynamic study. Molecules 24, 1103 (2019)CrossRef Yang, Y., et al.: Thermal conductivity of defective graphene oxide: a molecular dynamic study. Molecules 24, 1103 (2019)CrossRef
24.
go back to reference Kang, Y., et al.: Thermal transport of graphene sheets with fractal defects. Molecules 23, 3294 (2018)CrossRef Kang, Y., et al.: Thermal transport of graphene sheets with fractal defects. Molecules 23, 3294 (2018)CrossRef
25.
go back to reference Ding, Z., Pei, Q.-X., Jiang, J.-W., Zhang, Y.-W.: Manipulating the thermal conductivity of monolayer MoS2 via lattice defect and strain engineering. J. Phys. Chem. C 119(28), 16358–16365 (2015)CrossRef Ding, Z., Pei, Q.-X., Jiang, J.-W., Zhang, Y.-W.: Manipulating the thermal conductivity of monolayer MoS2 via lattice defect and strain engineering. J. Phys. Chem. C 119(28), 16358–16365 (2015)CrossRef
26.
go back to reference Park, J., et al.: Sensitivity of thermal transport in thorium dioxide to defects. J. Nucl. Mater. 504, 198–205 (2018)ADSCrossRef Park, J., et al.: Sensitivity of thermal transport in thorium dioxide to defects. J. Nucl. Mater. 504, 198–205 (2018)ADSCrossRef
28.
go back to reference Banholzer, W.F., Anthony, T.R.: Diamond properties as a function of isotopic composition. Thin Solid Films 212(1–2), 1–10 (1992)ADSCrossRef Banholzer, W.F., Anthony, T.R.: Diamond properties as a function of isotopic composition. Thin Solid Films 212(1–2), 1–10 (1992)ADSCrossRef
29.
go back to reference Anthony, T.R., Banholzer, W.F.: Properties of diamond with varying isotopic composition. Diam. Relat. Mater. 1, 71–726 (1992)CrossRef Anthony, T.R., Banholzer, W.F.: Properties of diamond with varying isotopic composition. Diam. Relat. Mater. 1, 71–726 (1992)CrossRef
30.
go back to reference Wei, Lanhua, et al.: Thermal conductivity of isotopically modified single crystal diamond. Phys. Rev. Lett. 70, 3764–3767 (1993)ADSCrossRef Wei, Lanhua, et al.: Thermal conductivity of isotopically modified single crystal diamond. Phys. Rev. Lett. 70, 3764–3767 (1993)ADSCrossRef
31.
go back to reference Qiu, Y.Z., et al.: Thermal conductivity of natural and synthetic diamonds with differing isotope contents. Thermochim. Acta 218, 257–268 (1993)CrossRef Qiu, Y.Z., et al.: Thermal conductivity of natural and synthetic diamonds with differing isotope contents. Thermochim. Acta 218, 257–268 (1993)CrossRef
32.
go back to reference Hoover, W.G., Hoover, C.G.: Hamiltonian thermostats fail to promote heat flow. Commun. Nonlinear Sci. Numer. Simul. 18, 3365–3372 (2013)ADSMathSciNetCrossRef Hoover, W.G., Hoover, C.G.: Hamiltonian thermostats fail to promote heat flow. Commun. Nonlinear Sci. Numer. Simul. 18, 3365–3372 (2013)ADSMathSciNetCrossRef
33.
go back to reference Krivtsov, A.M., Myasnikov, V.P.: Modelling using particles of the transformation of the inner structure and stress state in material subjected to strong thermal action. Mech. Solids 1, 72–85 (2005) Krivtsov, A.M., Myasnikov, V.P.: Modelling using particles of the transformation of the inner structure and stress state in material subjected to strong thermal action. Mech. Solids 1, 72–85 (2005)
34.
go back to reference Krivtsov, A.M.: Molecular dynamics simulation of plastic effects upon spalling. Phys. Solid State 46(6), 1055–1060 (2004)ADSCrossRef Krivtsov, A.M.: Molecular dynamics simulation of plastic effects upon spalling. Phys. Solid State 46(6), 1055–1060 (2004)ADSCrossRef
35.
go back to reference Hoover, W.G.: Canonical dynamics: equilibrium phase-space distributions. Phys. Rev. A 31, 1695–1697 (1985)ADSCrossRef Hoover, W.G.: Canonical dynamics: equilibrium phase-space distributions. Phys. Rev. A 31, 1695–1697 (1985)ADSCrossRef
36.
go back to reference Chang, C.W., Okawa, D., Garcia, H., Majumdar, A., Zettl, A.: Breakdown of Fourier’s law in nanotube thermal conductors. Phys. Rev. Lett. 101, 075903 (2008)ADSCrossRef Chang, C.W., Okawa, D., Garcia, H., Majumdar, A., Zettl, A.: Breakdown of Fourier’s law in nanotube thermal conductors. Phys. Rev. Lett. 101, 075903 (2008)ADSCrossRef
37.
go back to reference Xu, X., et al.: Length-dependent thermal conductivity in suspended single-layer graphene. Nat. Commun. 5, 3689 (2014)ADSCrossRef Xu, X., et al.: Length-dependent thermal conductivity in suspended single-layer graphene. Nat. Commun. 5, 3689 (2014)ADSCrossRef
38.
go back to reference Goldstein, R.V., Morozov, N.F.: Mechanics of deformation and fracture of nanomaterials and nanotechnology. Phys. Mesomech. 10, 235–246 (2007)CrossRef Goldstein, R.V., Morozov, N.F.: Mechanics of deformation and fracture of nanomaterials and nanotechnology. Phys. Mesomech. 10, 235–246 (2007)CrossRef
39.
go back to reference Shtukin, L.V., Berinskii, I.E., Indeitsev, D.A., Morozov, N.F., Skubov, D.Y.: Electromechanical models of nanoresonators. Phys. Mesomech. 19(3), 248254 (2016)CrossRef Shtukin, L.V., Berinskii, I.E., Indeitsev, D.A., Morozov, N.F., Skubov, D.Y.: Electromechanical models of nanoresonators. Phys. Mesomech. 19(3), 248254 (2016)CrossRef
Metadata
Title
Relation between defects and crystalline thermal conduction
Authors
A. A. Le-Zakharov
A. M. Krivtsov
A. V. Porubov
Publication date
04-07-2019
Publisher
Springer Berlin Heidelberg
Published in
Continuum Mechanics and Thermodynamics / Issue 6/2019
Print ISSN: 0935-1175
Electronic ISSN: 1432-0959
DOI
https://doi.org/10.1007/s00161-019-00807-w

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