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Prediction of phonon properties of 1D polyatomic systems using concurrent atomistic–continuum simulation


In this work, we present the simulation results of phonon properties, including phonon dispersion relations, group velocities, phonon relaxation time and mode-specific thermal conductivity, of low-dimensional crystals using the newly developed concurrent atomistic–continuum (CAC) method. With significantly less number of degrees of freedoms than all-atom molecular dynamics, the CAC method predicts the phonon properties of one-dimensional (1D) polyatomic crystals at finite temperatures with the full anharmonicity of the atomic interactions being incorporated. Complete phonon branches of polyatomic crystals are obtained by CAC through the phonon spectral energy density analysis. It is shown that CAC allows medium to long-wavelength phonon transport from atomic to coarsely meshed finite element region without the need of special numerical treatment. The frequency-dependent phonon group velocities are explicitly measured in the simulation. Sub-THz phonon lifetimes in 100 -mm-long polyatomic chains containing 400 million of atoms are predicted. Analysis of the phonon mode-specific thermal conductivity shows that the medium to long-wavelength acoustic phonons are contributing to the majority of the heat transport in 1D crystal, suggesting that the long-wavelength phonons effectively act as thermal carriers in 1D system. This work provides a possible explanation for the anomalous heat transport observed in low-dimensional materials.

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  1. Born M., Huang K.: Dynamical Theory of Crystal Lattices. Oxford University Press, Oxford (1956)

    Google Scholar 

  2. Carborg C.F., Shiomi J., Maruyama S.: Thermal boundary resistance between single-walled carbon nanotubes and surrounding matrices. Phys. Rev. B 78, 205406 (2008)

    Article  Google Scholar 

  3. Chen Y., Lee J.D.: Connecting molecular dynamics to micromorphic theory. Part I: instantaneous mechanical variables. Physica A 322, 359–376 (2003)

    Article  MATH  Google Scholar 

  4. Chen Y., Lee J.D.: Connecting molecular dynamics to micromorphic theory. Part II: balance laws. Physica A 322, 359–376 (2003)

    Article  MATH  Google Scholar 

  5. Chen Y., Lee J.D., Eskandarian A.: Examining physical foundation of continuum theories from viewpoint of phonon dispersion relations. Int. J. Eng. Sci. 41, 61–83 (2003)

    MathSciNet  Article  MATH  Google Scholar 

  6. Chen Y., Lee J.D., Eskandarian A.: Atomistic viewpoint of the applicability of microcontinuum theories. Int. J. Solids Struct. 41, 2085–2097 (2004)

    Article  MATH  Google Scholar 

  7. Chen Y., Lee J.D.: Atomistic formulation of a multiscale theory for nano/micro physics. Philos. Mag. 85, 4095–4126 (2005)

    Article  Google Scholar 

  8. Chen Y.: Local stress and heat flux in atomistic systems involving three-body forces. J. Chem. Phys. 124, 054113 (2006)

    Article  Google Scholar 

  9. Chen Y.: Reformulation of microscopic balance equations for multiscale materials modeling. J. Chem. Phys. 130, 134706 (2009)

    Article  Google Scholar 

  10. Chen Y., Zimmerman J., Krivtsov A., McDowell D.L.: Assessment of atomistic coarse-graining methods. Int. J. Eng. Sci. 49, 1337–1349 (2011)

    Article  Google Scholar 

  11. Dove M.T.: Introduction to Lattice Dynamics. Cambridge University Press, Cambridge (1993)

    Book  Google Scholar 

  12. Eringen A.C., Suhubi E.S.: Nonlinear theory of simple micro-elastic solids-I. Int. J. Eng. Sci. 2, 189–203 (1964)

    MathSciNet  Article  MATH  Google Scholar 

  13. Eringen A.C.: Microcontinuum Field Theories I: Foundations and Solids. Springer, New York (1999)

    Book  MATH  Google Scholar 

  14. Gale J.D., Rohl A.L.: The general utility lattice program. Mol. Simul. 29, 291–341 (2003)

    Article  MATH  Google Scholar 

  15. Hardy R.: Formulas for determining local properties in molecular-dynamics simulations: shock waves. J. Chem. Phys. 76, 622–628 (1982)

    Article  Google Scholar 

  16. Heino P.: Dispersion and thermal resistivity in silicon nanofilms by molecular dynamics. Eur. Phys. J. B 60, 171–179 (2007)

    Article  Google Scholar 

  17. Henry A.S., Chen G.: Spectral phonon transport properties of silicon based on molecular dynamics simulations and lattice dynamics. J. Comput. Theor. Nanosci. 5, 1–12 (2008)

    Article  Google Scholar 

  18. Irving J., Kirkwood J.: The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics. J. Chem. Phys. 8, 817–829 (1950)

    MathSciNet  Article  Google Scholar 

  19. Jund P., Julien R.: Molecular dynamics calculation of the thermal conductivity of Vitreous Silica. Phys. Rev. B 59, 13707–13711 (1999)

    Article  Google Scholar 

  20. Kirkwood J.: The statistical mechanical theory of transport processes. I. General theory. J. Chem. Phys. 14, 180–201 (1946)

    Article  Google Scholar 

  21. Kogure Y., Tsuchiya T., Hiki Y.: Simulations of dislocation configuration in rare gas crystals. J. Phys. Soc. Jpn. 56, 989 (1987)

    Article  Google Scholar 

  22. Kong L.: Phonon dispersion measured directly from molecular dynamics simulations. Comput. Phys. Commun. 182, 2201–2207 (2011)

    Article  Google Scholar 

  23. Ladd A.J.C., Moran B., Hoover W.G.: Lattice thermal conductivity: a comparison of molecular dynamics and anharmonic lattice dynamics. Phys. Rev. B. 34, 5058 (1986)

    Article  Google Scholar 

  24. McGaughey A.J.H., Kaviany M.: Quantitative validation of the Boltzmann transport equation phonon thermal conductivity model under the single-model relaxation time approximation. Phys. Rev. B 69, 094303 (2004)

    Article  Google Scholar 

  25. Placidi, L., Rosi, G., Giorgio, I., Madeo, A.: Reflection and transmission of plane waves at surfaces carrying material properties and embedded in second-gradient materials. Math. Mech. Solids (2014). doi:10.1177/1081286512474016

  26. Rutledge G.C., Lacks D.J., Martonak R., Binder K.: A comparison of quasiharmonic lattice dynamics and Monte Carlo simulation of polymeric crystals using orthorhombic polyethylene. J. Chem. Phys. 108, 10274 (1998)

    Article  Google Scholar 

  27. Schelling P.K., Phillpot S.R., Keblinski P.: Phonon wave-packet dynamics at semiconductor interfaces by molecular-dynamics simulation. Appl. Phys. Lett. 80, 2484 (2002)

    Article  Google Scholar 

  28. Thomas J.A., Iutzi R.M., McGaughey A.J.H.: Thermal conductivity and phonon transport in empty and water-filled carbon nanotubes. Phys. Rev. B 81, 045413 (2010)

    Article  Google Scholar 

  29. Xiong L., Tucker G., McDowell D.L., Chen Y.: Coarse-grained atomistic simulation of dislocations. J. Mech. Phys. Solids 59, 160–177 (2011)

    Article  MATH  Google Scholar 

  30. Xiong L., Deng Q., Tucker G., McDowell D.L., Chen Y.: A concurrent scheme for passing dislocations from atomistic to continuum regions. Acta Materialia 60, 899–913 (2012)

    Article  Google Scholar 

  31. Xiong, L., Deng, Q., Tucker, G., McDowell, D.L., Chen, Y.: Coarse-grained atomistic simulations of dislocations in Al, Ni and Cu crystals. Int. J. Plast. 86–101 (2012)

  32. Xiong L., McDowell D.L., Chen Y.: Nucleation and growth of dislocation loops in Cu, Al and Si by a concurrent atomistic–continuum method. Script Materialia 67, 633–636 (2012)

    Article  Google Scholar 

  33. Xiong, L., Xu, S., McDowell, D.L., Chen, Y.: Concurrent atomistic–continuum simulations of dislocation-void interactions in fcc crystals. Int. J. Plast. (under review) (2014)

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Correspondence to Youping Chen.

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Xiong, L., Chen, X., Zhang, N. et al. Prediction of phonon properties of 1D polyatomic systems using concurrent atomistic–continuum simulation. Arch Appl Mech 84, 1665–1675 (2014).

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  • CAC simulation
  • Phonon properties
  • Polyatomic systems
  • Thermal transport