Finite-size corrections to the free energy of crystalline solids
arXiv:cond-mat/9909162 · doi:10.1063/1.481102
Abstract
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 () corrections, the remaining free energy is found to depend linearly on 1/N. Extrapolating to the thermodynamic limit (), we estimate the free energy of a defect free crystal of particles interacting through an -potential. We also estimate the free energy of perfect hard-sphere crystal near coexistence: at =1.0409, the excess free energy of a defect-free hard-sphere crystal is 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.
4 pages, 2 figures
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