โ Scribed by Daniel E. Rosner; Michael Epstein
No coin nor oath required. For personal study only.
To elucidate the rapid crystallization of highly supercooled materials, and to provide novel methods for data interpretation in terms of crystallization kinetic parameters, we treat here the directional solidification of a semi-infinite (one-dimensional) radiation-cooled opaque melt using a versatile and computationally efficient integral (profile) technique. Our attention is focused on the coupling of crystallization kinetics with heat transfer limitations in determining the experimentally observable outer surface temperature-time history of the sample. Representative results are displayed for the case of locally planar solidification 'fronts' which propagate at a rate dependent either exponentially or on a power of the instantaneous interfacial undercooling, using material property values and cooling rates representative of previously reported experiments on the solidification of ZrO,(r) droplets. In the particular case of constant wave front speed, our present computational method compares favorably in accuracy with an exact solution. Thus, the present model and computational method not only rationalizes the observed luminousity structure of recalescence ('spearpoints') in refractory metals and oxides but also appears to hold some promise for inferring phenomenological kinetic laws for the internal solidification of highly supercooled refractory substances, based on readily available luminosity-time records for solidifying opaque melts.
๐ SIMILAR VOLUMES
The effect of heat transfer and the role of the surface integration process in crystal growth are analysed quantitatively in terms of a non-isothermal effectiveness factor, defined as the ratio of actual growth rate to the rate that would be obtained if conditions of the supercooled or supersaturate