Extreme Anisotropy of Diffuse Interfaces in Crystals
N D. Alikakos, P W. Bates, John W. Cahn, P C. Fife, G Fusco, G B. Tanoglu
We investigate a model of anisotropic diffuse interfaces in ordered FCC crystals introduced recently by Braun et al, focussing on parametric conditions which give extreme anisotropy. For a reduced model, we prove existence and stability of plane wave solutions connecting the disordered FCC stated with the ordered Cu(sub3)Au state described by solutions to a system of three equations. These plane wave solutions correspond to planar interfaces. Different orientations of these planes in relation to the crystal axes give rise to different surface energies. Guided by previous work based on numerics and formal asymptotics, we are able to reduce this problem in the six dimensional phase space of the system to a single equaiton approximation by taking advantage of the symmetries of the crystal. For this a standing wave solution is constructed that corresponds to a transition that in the extreme anisotropy limit is continuous but not differentiable. We also investigate the stability of the constructed solution by studying the eigenvalue problems for the linearized equation.