On the double structure of the crystal-melt transition layer: Density functional analysis of a (111) fcc crystal-melt interface

Abstract A density functional theory for a (111) fcc crystal-melt interface is proposed. Two order parameters, η ⊥ and η ∥ , characterizing the ordering in directions normal and parallel to the interface are used to describe the density wave oscillations. The density waves are parameterized in three different ways: in the crystalline region they are approximated by a superposition of Gaussians, in the liquid-like region a wave representation is used and in the intermediate region, where η ∥ is small compared to η ⊥ , a mixed Gaussian-wave representation is chosen. As a result of the minimization of the free energy with respect to the order parameters, the double-soliton structure of the interface is revealed. The profiles of the order parameters clearly demonstrate that the lateral ordering decreases much faster than the decay of the density oscillations normal to the interface. Using the calculated surface free energy values, γ ⊥ and γ∥, 0.609 T and 0.433 T respectively, we estimated that the crystal-melt interface is rough. The present results are in good agreement with the Lennard-Jones computer simulation data.