Thermal evolution of crystal shapes: The fcc crystal

Abstract

The thermal evolution of the equilibrium shape of an fcc crystal with both first- and second-nearest-neighbor interatomic interactions is studied. Exact zero-temperature calculations are extended to nonzero temperatures by use of solid-on-solid models appropriate to and directions in the crystal, yielding a reasonably complete global description of the thermal evolution. Universal features of the shape associated with second-order phase transitions are described, as are first-order phase transitions which appear as sharp edges between facets. Some new results for the six-vertex model appear as by-products. Contact is made with experiment, including a discussion of practical limitations on measurements of universal features of crystal shapes.