Kinetic roughening and step free energy in the solid-on-solid model and on naphthalene crystals

Abstract

The authors describe a method to estimate the critical supersaturation sigma c above which a growing crystal face becomes kinetically rough. They discuss the relation of sigma c with the step free energy kT gamma . The method is tested with computer simulations of the growth of the (001) face of a simple cubic crystal in the solid-on-solid (SOS) model. Near TR, the roughening transition temperature, the results are in good agreement with other estimates of gamma . The method is then applied to growth of (110) faces of naphthalene for melt and solution. They find that gamma does not depend on the temperature, in contrast to gamma found for the SOS model. The (110) face of naphthalene hence does not behave according to the infinite-order roughening transition of Kosterlitz-Thouless type. The classical method to model crystal growth from solution with SOS models turns out to be fundamentally incapable to describe surface roughening in the naphthalene case.