  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.
