Random deposition model of particles with discrete orientations

We studied a simple model that describes the texture formation during the deposition of particles with a discrete set of orientations. The particles are randomly deposited on a surface, obeying the solid on solid condition. The orientation of the particle when it sticks to the surface depends on the orientation of its neighbors as well as on the temperature of the sample. A q-state ferromagnetic Potts model is used to determine the energy of interaction with the neighbors and the local equilibrium is found by the application of the Metropolis algorithm. We recorded the orientations along each vertical column i, and a variable S(i,t) was defined as a function of time t, representing the algebraic sum of the orientations. We also calculated the fluctuations around the mean value of S as a function of time and the linear size of the lattice. These fluctuations exhibit a self-affine behavior, and we determined the dynamical exponents related to the growth of the deposit as a function of temperature and number of possible orientations q of the axis of the particle. We have shown that the layer by layer growth shows a defined texture at long times and at low temperatures. On the other hand, at high temperatures the fluctuations of S do not saturate, and the system does not exhibit a texture with a well-defined orientation of the deposited particles.