Homogeneous nucleation and crystallization model of aluminum droplet based on isothermal DSC analysis

Abstract

The aluminum (Al) sample was studied using differential scanning calorimetry (DSC) at non-isothermal and isothermal conditions. The first non-isothermal measurements were performed by melting the Al sample and then cooling it down at rates 2 to $-20\,^{\circ }\hbox {C}$ $\hbox {min}^{-1}$ to detect the crystallization temperature $\hbox {T}_{\text{C}}$ $\approx$ $642\,^{\circ }\hbox {C}$ (corresponding to undercooling $\Delta$ $\hbox {T}_{\text{C}}$ $\approx$ $18.3\,^{\circ }\hbox {C}$). On the contrary, the crystallization event was repeatedly detected by the isothermal DSC after several tens of minutes at the temperature T $\approx$ 653 to $-654\,^{\circ }\hbox {C}$. Overall crystallization of the Al droplet (at $\Delta$ T $\approx$ 6.3 to $-7.3\,^{\circ }\hbox {C}$) was analyzed utilizing Johnson–Mehl–Avrami–Kolmogorov (JMAK) model. However, the Avrami coefficient $n=d+1$, where d is the dimensionality of the growth, was less than 1, and thus, the JMAK model is not appropriate in some cases. In our model, we were focused predominantly on the nucleation kinetics under the assumption that crystallization of the Al droplet occurred by the homogeneous nucleation followed by the growth of nuclei. The surface energy of Al nuclei was estimated, and the kinetic equations of Al crystal nucleation were solved numerically, to determine the size distribution of nuclei and the nucleation rate. Numerical solution of kinetic nucleation equations showed that a decrease in Al atoms in the liquid droplet was predominantly a consequence of the formation of the subcritical clusters. The number of nuclei reached a quasi-stationary size distribution at a sufficiently long time, for which an analytical approach for the number of critical nuclei was determined.