ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
We present an analysis of crystal growth of a pure material from its melt, using a phase field model. This model for a first-order phase transition couples nonconserved order parameter kinetics to thermal diffusion. It has been shown to give unique one-dimensional solutions, with velocity selection. We demonstrate that these steady-state solutions cease to exist for the thermal diffusivity above a critical value, which depends on the parameter coupling the kinetics to the temperature. We suggest a scaling which leads to agreement between numerical integration of the time-dependent equations and a perturbation analysis of the coupling. For small velocity, our model reduces to a standard model commonly applied to dendritic growth, which replaces the kinetic equation with one of interfacial equilibrium. Because the velocity vanishes at the critical point, the thermal diffusion length and dendritic wavelength diverge at this point. We relate this critical point to bifurcations in the phase space of a mechanical equivalent to the steady-state growth equations. We conclude that solutions cease because thermal diffusion drives the system to local kinetic equilibrium, and we discuss experimental accessibility and means of avoiding equilibrium.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.459889
