Growth model on (1 + 1) dimensions with local relaxation and discrete number of orientations

Abstract

We introduced in this work a simple model for studying the texture formation during the electrodeposition process. Monte Carlo simulations were used to describe the formation of the deposits, and scaling concepts were also employed to characterize their growth and roughness properties. Particles are randomly deposited on a substrate, and their main axis can be aligned in a discrete set of possible directions. The final orientation of the deposited particle is determined by the interaction energy with its first neighboring particles and substrate temperature. Particle interactions are chosen according to the q-state ferromagnetic Potts model hamiltonian. Simulations were performed on (1 + 1) dimensions, for different values of temperature and substrate size. We have found different behaviors at low and high temperatures. Only at zero temperature the system reaches an absorbing state with all the layers occupied by particles oriented in the same direction. At this temperature we found the dynamic, roughness and growth exponents of the model, which satisfies the well known Family–Vicsek scaling relation for the self-affine interfaces. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)