A sharp interface model describing transient non-equilibrium solidification processes for planar interfaces is extended to describe early stages of nucleus growth in an undercooled melt. Interface velocity and interface concentrations are calculated until full equilibrium is reached. Curvature pressure and latent heat release are considered. Realistic Gibbs free energies and concentration gradients in both phases are included in the simulation calculations. The calculations bridge the gap between the length scales of Molecular Dynamics simulations and conventional continuum models that assume local equilibrium at the solid/liquid interface. (c) 2013 Elsevier B.V. All rights reserved.