najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2016-7-6-971-982najo-814Research ArticlePHYSICSФИЗИКАPhonon transmission across an interface between two crystalsMeilakhsA. P.

St. Petersburg

mejlaxs@mail.ioffe.ruIoffe Physical Technical InstituteRussian Federation20161308202576971982Copyright © Meilakhs A.P., 20252025Meilakhs A.P.Meilakhs A.P.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/814

A new model of phonon transmission across interface between two crystals is proposed which takes into account the mismatch of crystal lattices. It has been found that the mismatch of lattices results in phonon scattering at the interface even in the absence of defects. As it has been shown, at the normal incidence, longitudinally polarized phonons have much larger transmission coefficient than that of transversely polarized phonons, excluding special resonance cases. Allowance for this factor results in a calculated Kapitza resistance value that is approximately three times greater. For the quasi one-dimensional case, an exact solution has been obtained.

InterfaceKapitza resistanceLattice dynamicsThe author thanks E. D. Eidelman and G. V. Budkin for helpful critical comments, and A. Ya. Vul for attention to this study. The work was supported by the Russian Foundation for Basic Research (Project No. 16-03-01084 A).ReferencesKidalov S. V., Shakhov F. M. Thermal Conductivity of Diamond Composites. Materials, 2009, 2, P. 2467–2495.Kidalov S. V., Shakhov F. M. Thermal Conductivity of Diamond Composites. Materials, 2009, 2, P. 2467–2495.Zhang C., Wang R., et al. Low-temperature densification of diamond/Cu composite prepared from dual-layer coated diamond particles. J. Material Science, 2015, 26, P. 185-190.Zhang C., Wang R., et al. Low-temperature densification of diamond/Cu composite prepared from dual-layer coated diamond particles. J. Material Science, 2015, 26, P. 185-190.Li B., Wang L., Casati G. Negative differential thermal resistance and thermal transistor. Appl. Phys. Lett., 2006, 88, 143501.Li B., Wang L., Casati G. Negative differential thermal resistance and thermal transistor. Appl. Phys. Lett., 2006, 88, 143501.Terraneo M., Peyrard M., Casati G. Controlling the Energy Flow in Nonlinear Lattices: A Model for a Thermal Rectifier. Phys. Rev. Lett., 2002, 88, P. 094302.Terraneo M., Peyrard M., Casati G. Controlling the Energy Flow in Nonlinear Lattices: A Model for a Thermal Rectifier. Phys. Rev. Lett., 2002, 88, P. 094302.Wang L., Li B. Thermal Memory: A Storage of Phononic Information. Phys. Rev. Lett., 2008, 101, P. 267203.Wang L., Li B. Thermal Memory: A Storage of Phononic Information. Phys. Rev. Lett., 2008, 101, P. 267203.Khalatnikov I. M. Heat Transfer Between Solids and Liquid Helium II. JETP, 1952, 22, P. 687Khalatnikov I. M. Heat Transfer Between Solids and Liquid Helium II. JETP, 1952, 22, P. 687Little W. A. The Transport Of Heat Between Dissimilar Solids At Low Temperatures. Can. J. Phys., 1959, 37, P. 334–349.Little W. A. The Transport Of Heat Between Dissimilar Solids At Low Temperatures. Can. J. Phys., 1959, 37, P. 334–349.Stoner R. J., Maris H. J. Kapitza conductance and heat flow between solids at temperatures from 50 to 300 K. Phys. Rev. B, 1993, 48, P. 16373.Stoner R. J., Maris H. J. Kapitza conductance and heat flow between solids at temperatures from 50 to 300 K. Phys. Rev. B, 1993, 48, P. 16373.Swartz T., Pohl R. O. Thermal resistance at interfaces. Rev. Mod. Phys., 1989, 61, P. 605–608.Swartz T., Pohl R. O. Thermal resistance at interfaces. Rev. Mod. Phys., 1989, 61, P. 605–608.Zhang L., Keblinski P., Wang J.-S., Li B. Interfacial thermal transport in atomic junctions. Phys. Rev. B, 2011, 83, P. 064303.Zhang L., Keblinski P., Wang J.-S., Li B. Interfacial thermal transport in atomic junctions. Phys. Rev. B, 2011, 83, P. 064303.Meilakhs A. P., Eidelman E. D. New Model of Heat Transport across the MetalInsulator Interface by the Example of Boundaries in a DiamondMetal Composite. JETP Letters, 2013, 97, P. 38–40.Meilakhs A. P., Eidelman E. D. New Model of Heat Transport across the MetalInsulator Interface by the Example of Boundaries in a DiamondMetal Composite. JETP Letters, 2013, 97, P. 38–40.Young D. A., Maris H. J. Lattice-dynamical calculation of the Kapitza resistance between fcc lattices. Phys. Rev. B, 1989, 40, P. 3685–3693.Young D. A., Maris H. J. Lattice-dynamical calculation of the Kapitza resistance between fcc lattices. Phys. Rev. B, 1989, 40, P. 3685–3693.Hu M., Keblinski P., Schelling P. K. Kapitza conductance of siliconamorphous polyethylene interfaces by molecular dynamics simulations. Phys. Rev. B, 2009, 79, P. 104305.Hu M., Keblinski P., Schelling P. K. Kapitza conductance of siliconamorphous polyethylene interfaces by molecular dynamics simulations. Phys. Rev. B, 2009, 79, P. 104305.Tian Z., Esfarjani K., Chen G. Enhancing phonon transmission across a Si/Ge interface by atomic roughness: First-principles study with the Greens function method. Phys. Rev. B, 2012, 86, P. 235304.Tian Z., Esfarjani K., Chen G. Enhancing phonon transmission across a Si/Ge interface by atomic roughness: First-principles study with the Greens function method. Phys. Rev. B, 2012, 86, P. 235304.Saaskilahti K., Oksanen J., Tulkki J., Volz S. Role of anharmonic phonon scattering in the spectrally decomposed thermal conductance at planar interfaces. Phys. Rev. B, 2014, 90, P. 134312.Saaskilahti K., Oksanen J., Tulkki J., Volz S. Role of anharmonic phonon scattering in the spectrally decomposed thermal conductance at planar interfaces. Phys. Rev. B, 2014, 90, P. 134312.Yang N., Luo T. et. al. Thermal Interface Conductance between Aluminum and Silicon by Molecular Dynamics Simulations. J. Comp. and Theor. Nanoscience, 2015, 12, P. 168.Yang N., Luo T. et. al. Thermal Interface Conductance between Aluminum and Silicon by Molecular Dynamics Simulations. J. Comp. and Theor. Nanoscience, 2015, 12, P. 168.Anselm A. I. Introduction to Semiconductor Theory. Englewood Cliffs.: Prentice-Hall, 1981.Anselm A. I. Introduction to Semiconductor Theory. Englewood Cliffs.: Prentice-Hall, 1981.Arnold V. I. Collected Works, Vol. 1, Springer, 2009, 253 p.Arnold V. I. Collected Works, Vol. 1, Springer, 2009, 253 p.Landau L. D., Lifshitz E. M. Course of Theoretical Physics, Vol. 7: Theory of Elasticity. New York.: Pergamon, 1986.Landau L. D., Lifshitz E. M. Course of Theoretical Physics, Vol. 7: Theory of Elasticity. New York.: Pergamon, 1986.Meilakhs A. P. Nonequilibrium Distribution Function in the Presence of a Heat Flux at the Interface between Two Crystals. Phys. Solid State, 2015, 57, P. 148–152.Meilakhs A. P. Nonequilibrium Distribution Function in the Presence of a Heat Flux at the Interface between Two Crystals. Phys. Solid State, 2015, 57, P. 148–152.

The authors declare that there are no conflicts of interest present.