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Recent progress in the concurrent atomistic-continuum method and its application in phonon transport

Published online by Cambridge University Press:  24 October 2017

Xiang Chen ,
Weixuan Li ,
Adrian Diaz ,
Yang Li ,
Youping Chen  and
David L. McDowell
Xiang Chen*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, Florida 32611, USA
Weixuan Li
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, Florida 32611, USA
Adrian Diaz
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, Florida 32611, USA
Yang Li
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, Florida 32611, USA
Youping Chen
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, Florida 32611, USA
David L. McDowell
Affiliation:
Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
*
Address all correspondence to Xiang Chen at xiangchen@ufl.edu
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Abstract

This work presents the recent progress in the development of the concurrent atomistic-continuum (CAC) method for coarse-grained space- and time-resolved atomistic simulations of phonon transport. Application examples, including heat pulses propagating across grain boundaries and phase interfaces, as well as the interactions between phonons and moving dislocations, are provided to demonstrate the capabilities of CAC. The simulation results provide visual evidence and reveal the underlying physics of a variety of phenomena, including phonon focusing, wave interference, dislocation drag, interfacial Kapitza resistance caused by quasi-ballistic phonon transport, etc. A new method to quantify fluxes in transient transport processes is also introduced.

Type
Prospective Articles
Information
MRS Communications , Volume 7 , Issue 4 , December 2017 , pp. 785 - 797
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Copyright
Copyright © Materials Research Society 2017 

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References

1. U.S.D.o.E. Office of Science: Computational Materials Science and Chemistry – Accelerating Discovery and Innovation through Simulation-Based Engineering and Science (2010).Google Scholar
2. Narumanchi, S.V.J., Murthy, J.Y., and Amon, C.H.: Boltzmann transport equation-based thermal modeling approaches for hotspots in microelectronics. Heat Mass Transf. 42, 478 (2006).CrossRefGoogle Scholar
3. Minnich, A.J.: Advances in the measurement and computation of thermal phonon transport properties. J. Phys. Condens. Matter 27, 053202 (2015).CrossRefGoogle ScholarPubMed
4. Chen, G.: Multiscale simulation of phonon and electron thermal transport. Annu. Rev. Heat Transf. 17, 1 (2014).CrossRefGoogle Scholar
5. Mingo, N. and Yang, L.: Phonon transport in nanowires coated with an amorphous material: an atomistic Green's function approach. Phys. Rev. B 68, 245406 (2003).CrossRefGoogle Scholar
6. Sadasivam, S., Che, Y., Huang, Z., Chen, L., Kumar, S., and Fisher, T.S.: The atomistic Green's function method for interfacial phonon transport. Annu. Rev. Heat Transf. 17, 89 (2014).CrossRefGoogle Scholar
7. Cahill, D.G., Ford, W.K., Goodson, K.E., Mahan, G.D., Majumdar, A., Maris, H.J., Merlin, R., and Phillpot, S.R.: Nanoscale thermal transport. J. Appl. Phys. 93, 793 (2003).CrossRefGoogle Scholar
8. Chernatynskiy, A., Clarke, D. R., and Phillpot, S. R.: Thermal transport in nanostructured materials, in Handbook of Nanoscience, Engineering, and Technology, 3rd ed., edited by Goddard, W.A. III, Brenner, D.W., Lyshevski, S.E. and Iafrate, G.J. (CRC Press, Boca Raton, 2012), p. 545.Google Scholar
9. Chalopin, Y., Rajabpour, A., Han, H., Ni, Y., and Volz, S.: Modeling heat conduction from first principles. Annu. Rev. Heat Transf. 17, 147 (2014).CrossRefGoogle Scholar
10. Chen, Y. and Diaz, A.: Local momentum and heat fluxes in transient transport processes and inhomogeneous systems. Phys. Rev. E: Stat. Phys. Plasmas Fluids 94, 053309 (2016).CrossRefGoogle ScholarPubMed
11. Jund, P. and Jullien, R.: Molecular-dynamics calculation of the thermal conductivity of vitreous silica. Phys. Rev. B 59, 13707 (1999).CrossRefGoogle Scholar
12. Bagri, A., Kim, S.-P., Ruoff, R.S., and Shenoy, V.B.: Thermal transport across twin grain boundaries in polycrystalline graphene from nonequilibrium molecular dynamics simulations. Nano Lett. 11, 3917 (2011).CrossRefGoogle ScholarPubMed
13. Hu, M. and Poulikakos, D.: Si/Ge superlattice nanowires with ultralow thermal conductivity. Nano Lett. 12, 5487 (2012).CrossRefGoogle ScholarPubMed
14. Koh, Y.K., Cao, Y., Cahill, D.G., and Jena, D.: Heat-transport mechanisms in superlattices. Adv. Funct. Mater. 19, 610 (2009).CrossRefGoogle Scholar
15. Regner, K.T., Sellan, D.P., Su, Z., Amon, C.H., McGaughey, A.J.H., and Malen, J.A.: Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance. Nat. Commun. 4, 1640 (2013).CrossRefGoogle ScholarPubMed
16. Chen, Y., Zimmerman, J., Krivtsov, A., and McDowell, D.L.: Assessment of atomistic coarse-graining methods. Int. J. Eng. Sci. 49, 1337 (2011).CrossRefGoogle Scholar
17. Dove, M.T.: Introduction to Lattice Dynamics (Cambridge University Press, Cambridge; New York, 1993).CrossRefGoogle Scholar
18. B.E.S.A. Committee: From Quanta to the Continuum: Opportunities for Mesoscale Science, edited by U. S. D. o. Energy (2012).Google Scholar
19. Kittel, C.: Introduction to Solid State Physics (Wiley, New York, 1966).Google Scholar
20. Irving, J.H. and Kirkwood, J.G.: The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics. J. Chem. Phys. 18, 817 (1950).CrossRefGoogle Scholar
21. Kirkwood, J.G.: The statistical mechanical theory of transport processes I. General theory. J. Chem. Phys. 14, 180 (1946).CrossRefGoogle Scholar
22. Eringen, A.C.: Mechanics of Micromorphic Continua (Defense Technical Information Center, Ft. Belvoir, 1967).Google Scholar
23. Eringen, A.C.: Microcontinuum Field Theories: I. Foundations and Solids (Springer, New York, 2012).Google Scholar
24. Chen, Y. and Lee, J.D.: Connecting molecular dynamics to micromorphic theory. (I). Instantaneous and averaged mechanical variables. Phys. A: Stat. Mech. Appl. 322, 359 (2003).CrossRefGoogle Scholar
25. Chen, Y. and Lee, J.D.: Connecting molecular dynamics to micromorphic theory. (II). Balance laws. Phys. A: Stat. Mech. Appl. 322, 377 (2003).CrossRefGoogle Scholar
26. Chen, Y., Lee, J.D., and Eskandarian, A.: Atomistic counterpart of micromorphic theory. Acta Mech. 161, 81 (2003).CrossRefGoogle Scholar
27. Chen, Y. and Lee, J.D.: Determining material constants in micromorphic theory through phonon dispersion relations. Int. J. Eng. Sci. 41, 871 (2003).CrossRefGoogle Scholar
28. Chen, Y.: Reformulation of microscopic balance equations for multiscale materials modeling. J. Chem. Phys. 130, 134706 (2009).CrossRefGoogle ScholarPubMed
29. Chen, Y. and Lee, J.: Atomistic formulation of a multiscale theory for nano/micro physics. Philos. Mag. A 85, 4095 (2005).CrossRefGoogle Scholar
30. Chen, Y.: Local stress and heat flux in atomistic systems involving three-body forces. J. Chem. Phys. 124, 054113 (2006).CrossRefGoogle ScholarPubMed
31. Chen, Y., Lee, J.D., and Eskandarian, A.: Atomistic viewpoint of the applicability of microcontinuum theories. Int. J. Solids Struct. 41, 2085 (2004).CrossRefGoogle Scholar
32. Chen, Y., Lee, J.D., and Eskandarian, A.: Examining the physical foundation of continuum theories from the viewpoint of phonon dispersion relation. Int. J. Eng. Sci. 41, 61 (2003).CrossRefGoogle Scholar
33. Deng, Q., Xiong, L., and Chen, Y.: Coarse-graining atomistic dynamics of brittle fracture by finite element method. Int. J. Plast. 26, 1402 (2010).CrossRefGoogle Scholar
34. Deng, Q. and Chen, Y.: A coarse-grained atomistic method for 3D dynamic fracture simulation. Int. J. Multiscale Comput. Eng. 11, 227 (2013).CrossRefGoogle Scholar
35. Deng, Q.: Coarse-graining Atomistic Dynamics of Fracture by Finite Element Method: Formulation, Parallelization and Applications (University of Florida, Gainesville, Florida, 2011), p. 124.Google Scholar
36. Xiong, L. and Chen, Y.: Coarse-grained simulations of single-crystal silicon. Model. Simul. Mater. Sci. Eng. 17, 035002 (2009).CrossRefGoogle Scholar
37. Xiong, L., Xu, S., McDowell, D.L., and Chen, Y.: Concurrent atomistic–continuum simulations of dislocation–void interactions in fcc crystals. Int. J. Plast. 65, 33 (2015).CrossRefGoogle Scholar
38. Yang, S., Xiong, L., Deng, Q., and Chen, Y.: Concurrent atomistic and continuum simulation of strontium titanate. Acta Mater. 61, 89 (2013).CrossRefGoogle Scholar
39. Xiong, L., McDowell, D.L., and Chen, Y.: Nucleation and growth of dislocation loops in Cu, Al and Si by a concurrent atomistic-continuum method. Scr. Mater. 67, 633 (2012).CrossRefGoogle Scholar
40. Xiong, L., Tucker, G., McDowell, D.L., and Chen, Y.: Coarse-grained atomistic simulation of dislocations. J. Mech. Phys. Solids 59, 160 (2011).CrossRefGoogle Scholar
41. Xiong, L., Deng, Q., Tucker, G.J., McDowell, D.L., and Chen, Y.: Coarse-grained atomistic simulations of dislocations in Al, Ni and Cu crystals. Int. J. Plast. 38, 86 (2012).CrossRefGoogle Scholar
42. Xiong, L., Deng, Q., Tucker, G., McDowell, D.L., and Chen, Y.: A concurrent scheme for passing dislocations from atomistic to continuum domains. Acta Mater. 60, 899 (2012).CrossRefGoogle Scholar
43. Xiong, L. and Chen, Y.: Coarse-grained atomistic modeling and simulation of inelastic material behavior. Acta Mech. Solida Sinica 25, 244 (2012).CrossRefGoogle Scholar
44. Yang, S., Zhang, N., and Chen, Y.: Concurrent atomistic–continuum simulation of polycrystalline strontium titanate. Philos. Mag. 95, 2697 (2015).CrossRefGoogle Scholar
45. Wolfe, J.P.: Imaging Phonons: Acoustic Wave Propagation in Solids (Cambridge University Press, Cambridge, U.K.; New York, 1998).CrossRefGoogle Scholar
46. Schmidt, A.J.: Optical Characterization of Thermal Transport from the Nanoscale to the Macroscale, in Mechanical Engineering (Massachusetts Institute of Technology, Cambridge, Massachusetts, 2008).Google Scholar
47. Stoner, R.J. and Maris, H.J.: Picosecond optical study of the Kapitza Conductance between metals and dielectrics at high temperature, in Phonon Scattering in Condensed Matter VII, edited by Meissner, M. and Pohl, R. (Springer, Berlin Heidelberg, 1993), p. 401.CrossRefGoogle Scholar
48. Hopkins, P.E., Stevens, R.J., and Norris, P.M.: Influence of inelastic scattering at metal-dielectric interfaces. J. Heat Transf. 130, 022401 (2008).CrossRefGoogle Scholar
49. Smith, A.N., Hostetler, J.L., and Norris, P.M.: Thermal boundary resistance measurements using a transient thermoreflectance technique. Microscale Thermophys. Eng. 4, 51 (2000).Google Scholar
50. Hurley, D.H., Shinde, S.L., and Gusev, V.E.: Lateral-looking time-resolved thermal wave microscopy. J. Korean Phys. Soc. 57, 384 (2010).CrossRefGoogle Scholar
51. Hurley, D., Shindé, S.L., and Piekos, E.S.: Interaction of thermal phonons with interfaces, in Length-Scale Dependent Phonon Interactions, edited by Shindé, L.S. and Srivastava, P.G. (Springer, New York, 2014), p. 175.CrossRefGoogle Scholar
52. Luckyanova, M.N., Garg, J., Esfarjani, K., Jandl, A., Bulsara, M.T., Schmidt, A.J., Minnich, A.J., Chen, S., Dresselhaus, M.S., Ren, Z., Fitzgerald, E.A., and Chen, G.: Coherent phonon heat conduction in superlattices. Science 338, 936 (2012).CrossRefGoogle ScholarPubMed
53. Chen, X., Chernatynskiy, A., Xiong, L., and Chen, Y.: A coherent phonon pulse model for transient phonon thermal transport. Comput. Phys. Commun. 195, 112 (2015).CrossRefGoogle Scholar
54. Kogure, Y., Tsuchiya, T., and Hiki, Y.: Simulation of dislocation configuration in rare gas crystals. J. Phys. Soc. Jpn. 56, 989 (1987).CrossRefGoogle Scholar
55. Chen, G.: Ballistic-diffusive equations for transient heat conduction from nano to macroscales. J. Heat Transf. 124, 320 (2001).CrossRefGoogle Scholar
56. Chen, X., Li, W., Xiong, L., Li, Y., Yang, S., Zheng, Z., McDowell, D.L., and Chen, Y.: Ballistic-diffusive phonon heat transport across grain boundaries. Acta Mater. 136, 355 (2017).CrossRefGoogle Scholar
57. Ravichandran, J., Yadav, A.K., Cheaito, R., Rossen, P.B., Soukiassian, A., Suresha, S.J., Duda, J.C., Foley, B.M., Lee, C.-H., Zhu, Y., Lichtenberger, A.W., Moore, J.E., Muller, D.A., Schlom, D.G., Hopkins, P.E., Majumdar, A., Ramesh, R., and Zurbuchen, M.A.: Crossover from incoherent to coherent phonon scattering in epitaxial oxide superlattices. Nat. Mater. 13, 168 (2014).CrossRefGoogle ScholarPubMed
58. Chernatynskiy, A., Grimes, R.W., Zurbuchen, M.A., Clarke, D.R., and Phillpot, S.R.: Crossover in thermal transport properties of natural, perovskite-structured superlattices. Appl. Phys. Lett. 95, 161906 (2009).CrossRefGoogle Scholar
59. Garg, J. and Chen, G.: Minimum thermal conductivity in superlattices: a first-principles formalism. Phys. Rev. B 87, 140302 (2013).CrossRefGoogle Scholar
60. Churochkin, D., Barra, F., Lund, F., Maurel, A., and Pagneux, V.: Multiple scattering of elastic waves by pinned dislocation segments in a continuum. Wave Motion 60, 220 (2016).CrossRefGoogle Scholar
61. Simkin, M.V. and Mahan, G.D.: Minimum thermal conductivity of superlattices. Phys. Rev. Lett. 84, 927 (2000).CrossRefGoogle Scholar
62. Lukes, J.R. and Zhong, H.: Thermal conductivity of individual single-wall carbon nanotubes. J. Heat Transf. 129, 705 (2006).CrossRefGoogle Scholar
63. Eshelby, J.D.: Dislocations as a cause of mechanical damping in metals. Proc. R. Soc. London, Ser. A 197, 396 (1949).Google Scholar
64. Nabarro, F.R.N.: The interaction of screw dislocations and sound waves. Proc. R. Soc. London, Ser. A 209, 278 (1951).Google Scholar
65. Klemens, P.G.: The scattering of low-frequency lattice waves by static imperfections. Proc. Phys. Soc. 68, 1113 (1955).CrossRefGoogle Scholar
66. Granato, A. and Lücke, K.: Theory of mechanical damping due to dislocations. J. Appl. Phys. 27, 583 (1956).CrossRefGoogle Scholar
67. Peach, M. and Koehler, J.S.: The forces exerted on dislocations and the stress fields produced by them. Phys. Rev. 80, 436 (1950).CrossRefGoogle Scholar
68. Maurel, A., Pagneux, V., Barra, F., and Lund, F.: Wave propagation through a random array of pinned dislocations: velocity change and attenuation in a generalized Granato and Lucke theory. Phys. Rev. B 72, 174111 (2005).CrossRefGoogle Scholar
69. Maurel, A., Mercier, J.-F., and Lund, F.: Elastic wave propagation through a random array of dislocations. Phys. Rev. B 70, 024303 (2004).CrossRefGoogle Scholar
70. Xiong, L., Rigelesaiyin, J., Chen, X., Xu, S., McDowell, D.L., and Chen, Y.: Coarse-grained elastodynamics of fast moving dislocations. Acta Mater. 104, 143 (2016).CrossRefGoogle Scholar
71. Chen, X., Xiong, L., McDowell, D.L., and Chen, Y.: Effects of phonons on mobility of dislocations and dislocation arrays. Scr. Mater. 137, 22 (2017).CrossRefGoogle Scholar
72. Koizumi, H., Kirchner, H.O.K., and Suzuki, T.: Lattice wave emission from a moving dislocation. Phys. Rev. B 65, 214104 (2002).CrossRefGoogle Scholar
73. Volz, S.G. and Chen, G.: Molecular-dynamics simulation of thermal conductivity of silicon crystals. Phys. Rev. B 61, 2651 (2000).CrossRefGoogle Scholar
74. Zhou, X.W., Jones, R.E., and Aubry, S.: Molecular dynamics prediction of thermal conductivity of GaN films and wires at realistic length scales. Phys. Rev. B 81, 155321 (2010).CrossRefGoogle Scholar
75. Hoover, W.G.: Computational Statistical Mechanics (Elsevier Science, Burlington, 2012).Google Scholar
76. Hoover, W.G.: Molecular Dynamics (Springer Berlin, Berlin, 2013).Google Scholar
77. Hardy, R.J.: Formulas for determining local properties in molecular dynamics simulations: shock waves. J. Chem. Phys. 76, 622 (1982).CrossRefGoogle Scholar
78. Youping, C.: The origin of the distinction between microscopic formulas for stress and Cauchy stress. Europhys. Lett. 116, 34003 (2016).Google Scholar
79. Todd, B.D., Daivis, P.J., and Evans, D.J.: Heat flux vector in highly inhomogeneous nonequilibrium fluids. Phys. Rev. E 51, 4362 (1995).CrossRefGoogle ScholarPubMed
80. Zimmerman, J.A., WebbIII, E.B., Hoyt, J.J., Jones, R.E., Klein, P.A., and Bammann, D.J.: Calculation of stress in atomistic simulation. Model. Simul. Mater. Sci. Eng. 12, S319 (2004).CrossRefGoogle Scholar
81. Edmund, I., Webb, B., Zimmerman, J.A., and Seel, S.C.: Reconsideration of continuum thermomechanical quantities in atomic scale simulations. Math. Mech. Solids 13, 221 (2008).Google Scholar
82. Esfarjani, K., Garg, J., and Chen, G.: Modeling Heat Conduction from First Principles (Annual Review of Heat Transfer, 2014), p. 9.Google Scholar
83. Cahill, D.G., Braun, P.V., Chen, G., Clarke, D.R., Fan, S., Goodson, K.E., Keblinski, P., King, W.P., Mahan, G.D., Majumdar, A., Maris, H.J., Phillpot, S.R., Pop, E., and Shi, L.: Nanoscale thermal transport. II. 2003–2012. Appl. Phys. Rev. 1, 011305 (2014).CrossRefGoogle Scholar