In order to achieve the relationship between the melt thermal history and the solidification structure so
as to explore new methods to effectively control the solidification process and the solidification structure of metal,
the effect of the melt thermal history of Ga on the nucleation undercooling has been studied by using DSC,
and some formulae among the atom cluster size in melt, the nucleation undercooling of melt, the melt temperature and
the concerned physical and chemical parameters of metal have been proposed. The experimental results
show that the nucleation undercooling increases with increasing the holding time at high temperature after a
heating process and decreases with increasing the holding time after cooling to low temperature, but the change
rates of the nucleation undercooling decrease with increasing the holding time. An equation between the atom
number in the largest cluster in the melt and the melt temperature has been obtained by studying the effect of the
liquid temperature on the cluster size thermodynamically and kinetically. Formulae between the homogenous
nucleation undercooling, the heterogeneous nucleation undercooling and the temperature of liquid metal have been
achieved. In terms of these formulae, the atom number in the largest cluster in the melt and the nucleation
undercooling of the melt can be predicted if the temperature at which liquid metal is heated and hold is known. A
method for predicting the hysteretic extent of nucleation temperature after changing the liquid temperature has
been developed. The predicted results of the hysteretic extent of the nucleation temperature are in agreement with
the experiential results. The predicted and experimental hysteretic extents of the nucleation temperature are -10.7
and -10.3 K for Ga heated from 303 K to 373 K, and 7.9 and 8.3 K for Ga cooled from 373 K to 313 K, respectively. The errors between the predicted hysteretic extent of the nucleation temperature and the experimental
result are only 3.9\% for Ga heated from 303 K to 373 K and 4.8\% for Ga cooled from 373 K to 313 K,
respectively.