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Growth model with a finite number of orientations on a linear substrate
Phys. Rev. E 69, 021608 – Published 27 February, 2004
DOI: https://doi.org/10.1103/PhysRevE.69.021608
Abstract
The aim of this work is to present a simple model for studying the texture formation during the electrodeposition process. Monte Carlo simulations are used to describe the formation of the deposits, and the scaling concepts are employed to characterize their growth and roughness properties. In this model particles are randomly deposited with an orientation chosen from a discrete set of possible directions. The final orientation of the deposited particle is determined by its interaction with the first neighboring particles and by the temperature of the substrate. Particle interactions are chosen according to the q-state ferromagnetic Potts model Hamiltonian. Simulations were performed on dimensions, and for several values of temperature and substrate size. The results of the simulations lead to different behaviors for the model at low and high temperatures. At high temperatures, the scaling exponent was found, which characterizes a pure random deposition model. However, at low temperatures, we observed that after a given time interval, particles start orienting in a fixed direction and the interface width saturates just during a time window. Suddenly, a fluctuation makes the interface width increase again, that is, we never observed a full saturation. On the other hand, at zero temperature, the system reaches an absorbing state with all the layers occupied by particles oriented in the same direction. At zero temperature we found and for the dynamic, roughness, and growth exponents, respectively. The scaling exponents are consistent with a self-affine behavior of the model and they are in agreement with the well known Family-Vicsek scaling relation.
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