Supercooling interface stability

Several authorshave conceptually related the transition from planar to cellular freezing of ice to the condition of constitutional supercooling Here the theoretical framework of morphological stability theory for a planar interface is combined with simple models of diffusion and free convection to derive the transition salinity in dependence on growth conditions. 

A simple constitutional supercooling (CS) criterion was developed by Rutter and Chalmers (1954) that predicts the ratio of the gradient required to stabilize the interface to the growth velocity for a given solidification system. Taking the derivative of Equation 13.4 at x = 0,... 

A quite different approach to the problem of interface breakdown i lliat of Mullins and Sekerka, who considered the stability of the mict race in the presence of shape fluctuations. This treatment has some advantages, particularly since it predicts some of the parameters, e.g. cell size, which were not treated in the original an ysts i>r constitutional supercooling. The treatment is mathematically complex and details can be obtained from the original paper. 

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