Pattern selection with anisotropy during aluminum electropolishing

Abstract

This paper investigates the effect of anisotropic interfacial energy on nanoscale pattern formation during the electropolishing of aluminum. We have derived the anisotropic evolution equation of the aluminum interface by including the effects of interfacial energy with cubic anisotropy. The special cases of [1 1 1], [1 1 0], and [1 0 0] directions are considered. A linear stability analysis was used to predict the growth rate at the maximum wave number, and a weakly nonlinear analysis was used to predict the type and stability of the patterns (i.e. hexagons or stripes). We find that increasing the interfacial energy can extend the stability range of hexagons. When the interfacial energy is high enough, only stable hexagons exist for the [1 1 1] and [1 0 0] directions. Previous studies have shown that electropolished [1 1 1] aluminum exhibits stable hexagons and stripes, depending on the alignment of the hexagonal array with respect to the crystal axes while [1 1 0] produces only striped patterns. For the [1 0 0] direction, anisotropy has no effect and an isotropic solution result. Our theoretical predictions agree qualitatively with the existing experiments.