Directional crystallization from a binary mixture was performed by pseudo-NpT ensemble molecular dynamics. The initial crystal phase having a face-centered-cubic (fcc) structure grew toward the whole cell according to the temperature gradient in the universal cell. The growing crystal phase was not planar even though the solute molecules grew in two-dimensional coordinates because the solvent molecules disturbed the crystallization of the solute molecules at the diffusive crystal-solution interface. This represented the essential phenomenon of solute distribution during crystallization. Consequently, the growing crystal phase still contained solvent molecules having a liquid structure. The time change of the solute composition in the early phase of crystal growth showed an increase in solute composition as the time step proceeded. The resulting solute composition in this early phase was considered at different temperature gradients in the universal cell and it increased as the temperature of the initial crystal-solution interface increased. A new distribution coefficient model was proposed as a function of the difference between the local solute composition and bulk solute composition in the solution around the crystal-solution interface. The impurity-solvent distribution coefficient could be represented by the new model for faster growth of the lower temperature's initial interface. As regards a better distribution coefficient, there was found to be a very dilute solution phase over the crystal phase. The new variable "distribution rate" instead of the ambiguous variable "growth rate" was considered as a function of temperature gradient in the universal cell.