Forming condition of single crystal for highly undercooled metal melt

The effect of nucleation rate and crystal growth rate on the grain number nucleated in undercooled metals has been systematically studied in consideration of undercooling, and a theoretical expression representing the de-pendence of the grain number nucleated in undercooled metal on thennodynamic undercooling has been established. The results show that the grain numbers nucleated in undercooled metal melt decrease with the increasing thermodynamic undercooling; when thermodynamic undercooling increases beyond a critical value, the grain number nucleated in under-cooled metal melt will decrease to one; the obtained theoretical criterion for forming single crystal agrees well with the experimental results reported.