Size Dependent Surface Energy and Surface Tension

A model for size-dependent surface energy of nanocrystals, γ
sv
(D), has been established based on previous models for bulk surface energy γ
sv0
and the size-dependent cohesive energy E(D). Since the structure and energy differences between solid and liquid are small in comparison with those between solid and gas or between liquid and gas, this model can be extended to describe the size dependence of surface tension γ
1v
(D). It is found that γ
sv
(D) and γ
1v
(D) drop monotonically with size in the nanometer region while the surface energy ratio between different facets is size-independent and equals the corresponding bulk one. Moreover, size dependence of Tolman length is also discussed. Modeling predictions agree with the experimental and theoretical results of γ
sv
(D) for beryllium, magnesium, sodium, aluminum and gold, and the computer simulations of γ
1v
(D) for sodium, and aluminum droplets.