Coarsening with an Anisotropic Surface Tension in the Dilute Limit

We consider the phase separation dynamics or coarsening of a

two-component system with a local conservation law and an anisotropic

surface tension, such as a quenched binary alloy. Our goal is to

understand whether the surface tension anisotropy has an impact on

either the coarsening power law growth exponent or the domain

structure. To address this, we work in the dilute limit, employing a

generalization of Lifshitz-Slyovoz theory to include an anisotropic

surface tension. We consider a weak anisotropy and solve the problem

explicitly within perturbation theory. We find the growth law to be

unaffected by the anisotropy, but also find, in contrast to the

expectations of Lifshitz and Slyozov, that the domains do not have the

equilibrium Wulff shapes but rather a new one-parameter family of

nonequilibrium shapes governed by the size of the drop relative to the

critical size. Further, we show that the drop size distribution is

dependent on the details and degree of the anisotropy.