Criterion for judging the homogeneous and heterogeneous nucleation

A criterion for judging the nucleation form in highly undercooled liquid has, respectively, been derived from the nucleation and structure of liquid. It is found that the nucleation form of a highly undercooled liquid can be judged by determining the S_v in the liquid (where S_v is the surface area of the supposed catalyst in a unit volume of the liquid). When the determined value of S_v is equal to 10^10±1 m^-1, the liquid has nucleated homogeneously; it has nucleated heterogeneously if the determined value of S_v is less than 10^10±1 m^-1. By calculating the values of S_v in highly undercooled aluminum, copper, and silver, it is found that only silver melted under a slag has been undercooled to its undercooling of homogeneous nucleation.