On the interaction between order and a moving interface: Dynamical disordering and anisotropic growth rates

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Abstract
The way in which the velocity of a propagating interface determines the degree of surface disorder and the anisotropy of such interfacial velocities due to a crystalline lattice are examined using steady state solutions of the time dependent Landau–Ginzburg or Cahn–Hilliard equations. In the case of an interface described by two weakly coupled order parameters a divergence of the thickness of the surface disorder at a critical interfacial velocity is described. It is demonstrated that even for two surfaces with the same surface tension the growth rates may differ significantly due to a geometric factor arising from the underlying crystal lattice.