Statics and Dynamics of the Roughening Transition: A Self-Consistent Calculation

Abstract

Crystal growth is strongly influenced by the configuration of the interface between the crystal and the vapour phases. The relation between the growth rate and the interfacial configuration was investigated Chui and Weeks^1,2 by means of linear-response theory and by using the Kosterlitz renormalization-group (RG) method. Above the roughening temperature T, where the interface is rough, the growth rate R is found to be proportional to the chemical potential difference Ay, whereas below T, where the interface is flat, the crystal is found not to grow. A puzzling feature of their results is that the ratio R/Ay for ∆µ → 0 is finite on approaching T_R from above, whereas it remains zero on approaching T_R from below. Interesting unanswered questions concern the extent of the non-growing region (in Ay) below T, and the nature of the growth for larger ∆µ.