Dynamic scaling in polycrystalline growth

The dynamic scaling properties of a polycrystalline growth model proposed by Van der Drift are discussed. We present an analytic derivation of the dynamic exponent, describing the growth of monocrystalline surface domains, yielding p=1/2 and 1/4 for two and three dimensions, respectively. For specific, highly nonuniform, initial conditions in the two-dimensional model we find that initially the exponent p is equal to 1, but that after some time, crossover takes place to p=1/2. The results are confirmed by numerical simulations for the two-dimensional case. We investigate the relation between our model and the Huygens model for amorphous growth, formulated by Tang, Alexander, and Bruinsma and examine both models in the context of a differential equation for interface growth, analyzed by Kardar, Parisi, and Zhang.