Conduction-limited crystallite melting

A Phase-Field Model for the Diffusive Melting of Isolated Dendritic Fragments

“…This is the identical definition to that used in [2,3]. The computational domain, Ω, is taken to be very large, relative to the semi-major axis,C, of the fragment.…”

“…The primary conclusions of this analysis were that for the majority of the melting phase the ratio C /A would either remain approximately constant [1] or would increase slowly with time [2] but that in the very final stages of melting C /A would collapse rapidly toward 1, such that at extinction the fragments were always spherical. This phenomenon was attributed to capillarity effects whereby the higher curvature, and consequentially slightly depressed melting temperature, at the tip of the elliptic fragment relative to its equator gave rise to a heat flow from the equator towards the tip which would accelerate melting near the tip, thereby reducing the C /A ratio towards unity [1,2]. However, due to the small length scales associated with capillary effects, this equalisation of C and A would naturally be restricted to the terminal stages of melting, as observed experimentally.…”

“…Following the recent publication of a series of papers [1,2,3] relating to the cyclic melting of material as part of the Isothermal Dendrite Growth Experiment (IDGE) there has been a resurgence of interest in the melting of dendritic crystal fragments. Three IDGE experiments were flown [4,5,6] in the cargo bay of the space shuttle in order to study the dendritic solidification of the plastic crystals succinonitrile (SCN) and pivalic anhydride (PVA) in the very stable, low gravity environment provided by this platform.…”

“…Despite this, during the final IDGE experiment video data of around 100 melting cycles in PVA was captured at 30 fps. It is the analysis [1,2,3] of these data that has stimulated the renewed interest in the melting of dendritic fragments.…”

“…The quantitative analysis of the melting of dendritic fragments conducted by [1,2,3] was generally restricted to the later stages of the melting cycle, wherein the complex interpenetrating array of side-branches can be reduced to a series of isolated crystals. Moreover, the almost complete melting back of secondary and tertiary arms gives rise to fragments, each of which can be approximated closely as a figure of revolution with an elliptic cross-section.…”