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-nu in the liquid (where S-nu, is the surface area of the supposed catalyst in a unit volume of the liquid). When the determined value of S-nu, is equal to 10(10+/-1) m(-1), the liquid has nucleated homogeneously; it has nucleated heterogeneously if the determined value of S-nu is less than 10(10+/-1) m(-1). By calculating the values of S-nu 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.