Effect of finite system size on thermal fluctuations: Implications for melting

Lattice-dynamics calculations and molecular-dynamics simulations are used to study the variation with particle number N in the mean squared displacement (u)2 N for systems with Lennard-Jones and repulsive Yukawa and r-n interactions. In the low-temperature harmonic regime, the leading correction to the N limit is found to have the known form (u)2 N/(u)2=1+ N-1/3. However, the sign of is not always negative as is indicated by simple arguments. For fcc crystals, -1 for all potentials. Thus finite-size errors are 10% for N=1000. In the bcc phase, errors may be more than 5 times larger and of either sign. We show that positive values of result from large anisotropies in the sound velocities. Anharmonic effects at higher temperatures change the value of , but not the scaling with N. For both structures becomes more negative, but the changes are much more pronounced in the bcc phase where may change sign. These results indicate that one must be careful in using (u)2 N for typical values of N in calculations of the Debye-Waller factor or a Lindemann criterion for melting. The variation with N of the temperature where melting is observed indicates that low-frequency shear modes are important in destabilizing the solid phase. © 1990 The American Physical Society.