Modeling of Electrochemical Machining Through a Monolayer Colloidal Crystal Mask for Metal Surfaces Nanostructuring

Through-mask electrochemical machining is widely used to produce micro- and nanostructured surfaces. Various types of masks are used to localize the areas of anodic dissolution or cathodic deposition. A possibility of producing nanostructured surfaces by using the anodic dissolution of substrate metal through a mask of regularly arranged spherical particles has been experimentally shown in several works. In contrast to the case of metal electrodeposition into spherical mask pores, when the deposit geometry is completely determined by the pore geometry, in the anodic dissolution, the geometry of substrate surface differs essentially from the geometry of mask pores.In this work, the problem of predicting the shape and dimensions of substrate surface as a function of the mask parameters and operation conditions was solved. A method of numerical simulation of electrochemical shaping for the anodic dissolution of substrate metal through a mask of a single-layer colloidal crystal (monodispersed spherical particles) was developed. The Laplace equation and the equation of evolution of workpiece surface, which was prescribed by an explicit function, were used as the mathematical model of the process. The geometry of computational region was determined with regard for the system's symmetry: the region with the regular-hexagonal cross-section was taken as a unit cell. The unit cell was limited above by the outer boundary of diffusion layer and, below, by the workpiece surface. The numerical solution of Laplace equation was performed by a fast multipole boundary element method. The numerical solution of equation of anode surface evolution was performed by the Level Set method. The results of the simulation are presented for various sphere package densities and treatment times.