Nucleation energetics during homogeneous solidification in elemental metallic liquids

Abstract

The solidification of a liquid by nucleation is an important first order phase transition process. It is known that in order for elemental liquids to solidify homogeneously, it is necessary to supercool the liquid to a characteristic temperature (TUC) below the thermodynamic melting point (TMP). Approximately 60 years ago Turnbull [J. Appl. Phys. 21, 1022 (1950)] established the empirical rule that ΔT∗=|TUC−TMP| is approximately given by 0.18 TMP for several elemental metallic liquids. We show here that the magnitude of ΔT∗ and TUC for the metals can be accurately predicted from classical nucleation theory (CNT) provided the excess volume resulting from the density difference between liquid and solid be accounted for. Specifically, the density change accompanying the formation of a microscopic nucleus of the solid from the liquid results in a volume change in the surrounding liquid. When this is included in the free energy calculations within CNT, the resulting predictions for ΔT∗ and TUC for several metals with TMP ranging from ∼200 to 2900 K are in very good agreement with experimental measurements. This theory also shows that there is a universal character in the minimum nucleation barrier energy and the critical radius. The minimum barrier energy occurs at temperature TN∼0.27 TMP for all the elemental liquids investigated, while the temperature dependencies of the barrier energy and the critical radius appear identical when expressed as a function of the scaled temperature TUC/TMP.