An Analytical Self-consistent Solution for the Free Energy of a 1-D Chain of Atoms Including Anharmonic Effects

Woo Kyun Kim, Ellad B. Tadmor

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

The self-consistent method of lattice dynamics (SCLD) is used to obtain an analytical solution for the free energy of a periodic, one-dimensional, mono-atomic chain accounting for fourth-order anharmonic effects. For nearest-neighbor interactions, a closed-form analytical solution is obtained. In the case where more distant interactions are considered, a system of coupled nonlinear algebraic equations is obtained (as in the standard SCLD method) however with the number of equations dramatically reduced. The analytical SCLD solutions are compared with a numerical evaluation of the exact solution for simple cases and with molecular dynamics simulation results for a large system. The advantages of SCLD over methods based on the harmonic approximation are discussed as well as some limitations of the approach.

Original languageEnglish (US)
Pages (from-to)951-971
Number of pages21
JournalJournal of Statistical Physics
Volume148
Issue number5
DOIs
StatePublished - Sep 1 2012

Keywords

  • Anharmonic effects
  • Free energy
  • Lattice dynamics
  • One-dimensional chain
  • Self-consistent method
  • Statistical mechanics

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