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

作者：Kim Woo Kyun; Tadmor Ellad B^*

来源：Journal of Statistical Physics, 2012, 148(5): 951-971.

DOI：10.1007/s10955-012-0559-x

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

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.

• 出版日期2012-9