Finite-size corrections to the free energy of crystalline solids

Details Finite-size corrections to the free energy of crystalline solids Finite-size corrections to the free energy of crystalline solids

1999-09-10

arxiv.org/abs/cond-mat/9909162v1

J. Chem. Phys. 112, 5339 (2000).

Physics

Condensed Matter

Statistical Mechanics

4 pages, 2 figures

Scientific paper

10.1063/1.481102

We analyse the finite-size corrections to the free energy of crystals with a fixed center of mass. When we explicitly correct for the leading ($\ln N/N$) corrections, the remaining free energy is found to depend linearly on 1/N. Extrapolating to the thermodynamic limit ($N\to\infty$), we estimate the free energy of a defect free crystal of particles interacting through an $r^{-12}$-potential. We also estimate the free energy of perfect hard-sphere crystal near coexistence: at $\rho \sigma^{3}$=1.0409, the excess free energy of a defect-free hard-sphere crystal is $5.91889(4)kT$ per particle. This, however, is not the free energy of an equilibrium hard-sphere crystal. The presence of an finite concentration of vacancies results in a reduction of the free energy that is some two orders of magnitude larger than the present error estimate.

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