Ho-Kei Chan & Ingo Dierking, Growth Models of Pure Supercooled Materials, Physical Review E, 77, 3, 2008, 031610-1 - 031610-6
Physical Review E 77 3
For a pure material, the dynamics of the growth of one phase in a supercooled other phase for the case of a
shallow temperature quench is traditionally understood via a kinetic thermal diffusion equation model or a
quasistatic Laplace equation model, if order-parameter details can be neglected. In the quasistatic model, the
interfacial boundary temperature TR is equal to the phase transition temperature Tm. In the kinetic model,
however, growth is driven by a nonzero interfacial undercooling Tm−TR. By assuming that the growth process
occurs at small but finite, identical spatial steps, the growth laws for the cases of shallow and deep temperature
quenches were derived analytically from the kinetic model in the limit of zero thermal diffusivity. For the case
of a shallow temperature quench, it is shown that the apparent difference between the assumed interfacial
boundary conditions of the quasistatic and the kinetic model does not exist.
PUBLISHED This paper presents an analytic derivation of two droplet growth laws which have been observed experimentally for a variety of condensed matter systems. The introduction of an additional length scale in the theoretical derivation solves the apparent contradiction between two conventional models for crystal growth.
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