New theory of undercooling during rapid solidification: application to pulsed laser heated silicon

A new theory of undercooling has been developed based on the Fickian form of heat flux expressed in terms of a gradient in enthalpy density. It is shown that heat diffusion is more fundamental than Fourier’s law of heat conduction. During the solid–liquid phase change, diffusion requires continuity of the enthalpy density across the phase-change boundary, which has two important consequences. First, the calculated melt-depth during rapid heating is reduced, and second, during cooling the rate of loss of heat is independent of both the rate of release of latent heat and the temperature of the interphase layer. The cause of undercooling is diffusive heat loss without recrystallisation, which simply causes the temperature of the liquid to drop. Both the nature of melting and classical nucleation have been examined and shown to support diffusion over conduction. In particular, it is established that the literature supports a model of melting in which phase fluctuations at the melting point occur, and that these phase fluctuations must inevitably lead to thermal transport at uniform temperature. Hitherto unrecognized inconsistencies in classical nucleation theory also support the diffusive framework. The model is applied to pulsed laser melting and amorphisation of (111) silicon. PACS  64.70.Dv; 66.30.Xj; 68.18.Jk