Faceted crystal growth in two dimensions

Abstract

CRYSTAL growth has attracted interest for centuries¹. Three-dimensional crystals are usually faceted, but equilibrium thermodynamics prohibits faceting in two dimensions²: the one-dimensional perimeter of a two-dimensional crystal cannot exhibit long-range order at any non-zero temperature³. This need not, however, prevent facets from being stable dynamically during the growth process. Computer simulations have indeed produced nearly faceted two-dimensional crystals^4,5. Here we describe the results of experiments on monolayers of a surfactant, sodium dodecyl sulphate (SDS), at the surface of an aqueous solution. Surface-tension measurements and fluorescence microscopy^6–8 reveal a solid–liquid transition in the surface monolayer at fixed SDS bulk concentration, as the temperature is decreased. At low SDS con-centration, faceted monolayer crystals appear, although increasing the concentration induces a change to smoother growth morpho-logies. The faceted crystals become unstable as growth proceeds, the corners emitting filaments of various shapes. Some of these growth processes seem not to have three-dimensional analogues.