Ginzburg-Landau theory for the solid-liquid interface of bcc elements

We describe a simple order-parameter theory for the interfacial tension of body-centered-cubic solids. The principal order parameter is the amplitude of the density wave at the smallest nonzero reciprocal-lattice vector of the solid, but the density difference between solid and liquid is included to second order. The parameters entering the theory are fitted to the measured heat of fusion, melting temperature, and solid-liquid density difference, and to the liquid structure factor and its temperature derivative at freezing as calculated by a variational technique. Agreement with experiment is good for Na and Fe, and the calculated anisotropy of the surface tension among different crystal faces is of order 2%, in agreement with earlier calculations of Oxtoby and Haymet. With certain additional assumptions about universal behavior of bcc crystals at melting, the formalism predicts that the surface tension is proportional to the heat of fusion per surface atom, in agreement with the empirically derived relation of Turnbull [J. Appl. Phys. 24, 1022 (1950)].