A phonon heat bath approach for the atomistic and multiscale simulation of solids

E. G. Karpov*, Harold S. Park, Wing Kam Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

59 Scopus citations


We present a novel approach to numerical modelling of the crystalline solid as a heat bath. The approach allows bringing together a small and a large crystalline domain, and model accurately the resultant interface, using harmonic assumptions for the larger domain, which is excluded from the explicit model and viewed only as a hypothetic heat bath. Such an interface is non-reflective for the elastic waves, as well as providing thermostatting conditions for the small domain. The small domain can be modelled with a standard molecular dynamics approach, and its interior may accommodate arbitrary non-linearities. The formulation involves a normal decomposition for the random thermal motion term R(t) in the generalized Langevin equation for solid-solid interfaces. Heat bath temperature serves as a parameter for the distribution of the normal mode amplitudes found from the Gibbs canonical distribution for the phonon gas. Spectral properties of the normal modes (polarization vectors and normal frequencies) are derived from the interatomic potential. Approach results in a physically motivated random force term R(t) derived consistently to represent the correlated thermal motion of lattice atoms. We describe the method in detail, and demonstrate applications to one- and two-dimensional lattice structures.

Original languageEnglish (US)
Pages (from-to)351-378
Number of pages28
JournalInternational Journal for Numerical Methods in Engineering
Issue number3
StatePublished - Apr 16 2007


  • Crystal structure
  • Generalized Langevin equation
  • Heat bath
  • Molecular dynamics
  • Multiscale simulation
  • Normal modes

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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