Replacement Partition Function for Small Crystals in Homogeneous Nucleation Theory

Abstract

The replacement partition function was calculated for small fcc crystals by numerical normal mode analysis using exactly the same model, which considers nearest-neighbor interactions only and neglects the surface relaxation and thermal expansion, to compute all the necessary quantities. A method of calculating the surface free energy of a small crystal from data on the macroscopic surface was introduced. The numerical value of the replacement partition function thus computed was, for example, 108 at T=2θ and for n=87. This is considerably larger than the value estimated for a crystal so far, which is 102-−04 at T=2θ and for n ≅ 100. This result suggests the need of further work both in numerical calculation and in theoretical studies.