Geometric effects on surface roughness in electrodeposition

^** Email: ranga{at}ufl.edu Our aim is to understand the early stages of roughness growthin electrodeposition. We present a study of the branching ofsteady planar electrode surfaces to steady non-planar electrodesurfaces as the voltage imposed at a cathode is decreased throughits critical value. We aim to discover the type of branchingand to learn whether or not the new branches can be detectedby measuring the current. The cross-sectional shape of the electrodemakes a difference. Circular electrodes lead to transcriticalbranching; ordinarily, rectangular electrodes lead to a pitchfork,sometimes forward and sometimes backward.