INTERFACE TRANSFER-COEFFICIENT IN 2ND-PHASE-GROWTH MODELS

In order to derive an atomistic expression for the transfer coefficient across an interface, we extend the Gibbs dividing-surface scheme to kinetic problems. In equilibrium thermodynamics, this scheme consists in replacing the continuous concentration profile between two coherent phases by a stepped profile with a discontinuity at the dividing surface: the Gibbsian excess free energy (interfacial energy) is the difference between the free energies associated with the true continuous profile and with the artificial stepped one. Close to equilibrium, the diffusion flux along the actual continuous concentration profile is equal to minus the gradient of the chemical potential multiplied by a mobility: the latter is a continuous function of the local equilibrium concentration, which can be evaluated in a mean-field approximation. Gibbs' dividing-surface scheme introduces a transfer coefficient across the (artificial) dividing interface. Equating the exact expression of the flux along the actual concentration profile to that predicted in Gibbs' scheme for the same difference in chemical potential across the system yields the expression for the transfer coefficient. In the simplest mean-field description of chemical diffusion, the transfer coefficient is found to be negative. The reason for that is that the mobility increases as the concentration goes to 1/2, at least in the simplest case. Assuming the concentration to be uniform up to the interface underestimates the flux and must be compensated by a negative ''contact resistance'' between the two phases. Neglecting the transfer coefficient results in underestimating the flux: the error can be large for small samples, in particular in the case of the nucleation and growth of a phase with low diffusivity, inside a high-diffusivity matrix. The range of validity of the model is shown to coincide with that of linear diffusion theory. In this range, the transfer coefficient at the interface does not depend on the velocity of the interface.