Planar Solidification from Undercooled Melt: An Approximation of a   Dilute Binary Alloy for a Phase-field Model
  Planar solidification from an undercooled melt has been considered using the phase-field model. The solute and the phase fields have been found in the limit of small impurity concentration. These solutions in the limit of vanishing velocity of the interface motion give the equilibrium partition coefficient and the liquidus slope. Asymptotic expansions for the solute and for the phase fields, and the relation between the diffusive speed and the parameters of the phase field model have been found at high growth velocity. A comparison with numerical calculations is presented. 
Denis Danilov