Thermodynamics of interfacial segregation in solute drag

The solute drag was discovered in connection with grain boundary migration during recrystallization, and it was suggested that the effect is caused by segregation of impurities to grain boundaries. This idea was later extended to the migration of phase interfaces during phase transformations. However, in a phase transformation, the phases often have different compositions. In order to maintain steady state conditions at the phase interface, a concentration profile must exist inside the moving interface if it has a finite width. This is realized by diffusion inside the phase interface, which consumes a part of the driving force. This concept does not necessarily involve the segregation to the boundary explicitly but is nevertheless often referred to as a solute drag effect. However, a complete solute drag model for phase transformations should of course also include the effect of phase-boundary segregation. Furthermore, the gradient energy may also need to be considered. In the present work, thermodynamics of interfacial adsorption will be discussed in conjunction with a solute drag model for phase transformations, recently modified to take into account the interfacial segregation of alloying elements. It will be shown that the classical interfacial adsorption treatment can be consistently included in the new modified solute-drag model. The gradient energy will be discussed, and an expression to evaluate its value from the Gibbs energy function will be presented.