The mechanism of the impurity redistribution between phases of variable and constant compositions

The problem with describing the redistribution of impurities at the interface between phases of variable and constant composition is closely related to the impossibility of thermodynamically determining chemical potential for a phase of constant composition as a derivative by a variable of the impurity concentration. It is shown that the deviation of the chemical potential of a variable composition phase from its equilibrium value, determined by the common tangent to the Gibbs energies of the interacting phases, can be chosen as the thermodynamic force for the impurity transfer at interface between phases of constant and variable composition. The equations of the phase field dynamics and of the impurity redistribution is derived from non-equilibrium thermodynamics. The results of numerical modeling show qualitative compliance with the expected behavior and are presented in the form of graphs of the concentration distribution and the phase field.