Role of interfacial energy during pattern formation of electropolishing

Abstract

This paper investigates the effect of interfacial energy on nanoscale pattern formation during electropolishing of aluminum. We correct a small error in the existing theory of Yuzhakov et al. that unfortunately no longer predicts stable hexagonal patterns. Upon including the interfacial energy in the derivation, the stable hexagons are recovered. We have derived the evolution equation of the aluminum interface during electropolishing and performed a linear and weakly nonlinear stability analysis. The results give values that lead to stable striped or hexagonal patterns. Results of a full nonlinear simulation of the evolution equation agree qualitatively with the weakly nonlinear results. Experimental results also verify our model, which predicts the coexistence of striped and hexagonal patterns in one sample.