Forming condition of single crystal for highly undercooled metal melt

The effect of nucleation rate and crystal growth rate on the grain number n ucleated in undercooled metals has been systematically studied in considera tion of undercooling, and a theoretical expression representing the depende nce of the grain number nucleated in undercooled metal on thermodynamic und ercooling has been established. The results show that the grain numbers nuc leated in undercooled metal melt decrease with the increasing thermodynamic undercooling; when thermodynamic undercooling increases beyond a critical value, the grain number nucleated in undercooled metal melt will decrease t o one; the obtained theoretical criterion for forming single crystal agrees well with the experimental results reported.