The growth of roughness during electrodeposition

Measurements of the growth rate of roughness on a cathode surface can be used to study the physics of cathodic processes. But these growth rates are cell wide variables and they ordinarily depend on what is taking place at the anode as well as at the cathode. Our aim is to derive a simple condition under which the anode makes no contribution to the interpretation of growth rate measurements at the cathode.Our condition stems from the contribution of ion diffusion to the growth rate and it is satisfied for all non-small values of the wave number of a growing disturbance. This, together with the fact that surface tension is the only stabilizing factor and the fact that the surface tension coefficient multiplying the wave number is small, means that the anode ought not to be important for the fastest growing wave numbers.Once the effect of the anode is eliminated, the growth rate at the cathode can be expressed in a formula so simple that pencil and paper calculations are possible and this makes important questions in cell design easy to answer, e.g., is the growth rate diffusion controlled?