The Roughening Transition on Surfaces

Abstract

The concept of a roughening transition on surfaces has been introduced in 1951 by Burton,Cabrera and Frank¹ in order to explain why the growth of crystals was observed to proceed in two very different regimes: layer by layer or tridimensional. They have shown that a surface layer of a simple cubic crystal in which every site can be either occupied or empty, is formally equivalent to an assembly of up and down spins known as the 2-d Ising model. From the Onsager solution of this model² they have predicted a transition from a smooth phase at low temperature to a rough phase at higher temperature. However there is no reason to restrict the roughening to the outermost layer (empty or occupied) and it was recognized later that the removal of this restriction shifts the transition in an other universality class first described by Kosterlitz and Thouless³. The first experimental evidence of the existence of the roughening transition, given in 1974 by Pawlowska and Nenow⁴, has strongly stimulated researches in this field: theory,simulation and experiment. The nature of the roughening transition is now well understood and realistic models have been solved either analytically or by simulation. They can be compared to an increasing number of accurate experimental data.