Revisiting the phenomenological model for effect of chemical ordering on diffusion

• The model for describing effect of chemical ordering on diffusion was revisited.
• The phenomenological model in 2SL was extended into a more physical one in 4SL.
• Different ordered states can be simultaneously described by the 4SL model.
• Endmember in 4SL model was first approximated by introducing pair activation energy.
• The proposed 4SL model was successfully applied to the ordered Ni–Al L12 phase.

The recently developed phenomenological model (Helander T, Ågren J. 1999.) in two-sublattice (2SL) formalism for describing the effect of chemical ordering on diffusion in bcc-B2 ordered alloys was carefully re-analyzed and validated to be applicable in ordered bcc-B2, fcc-L10 and fcc-L12 phases. The model was then extended into one in four-sublattice (4SL) formalism in a thermodynamically consistent way. With the more physically based 4SL model, different ordered structures (e.g., fcc-L10 and fcc-L12) with respect to the same disordered phase (e.g., fcc-A1) can be simultaneously described. In order to evaluate the reasonable “endmembers” in 4SL model when the first-principles calculations and/or sufficient experimental diffusivities are not available, the “pair activation energy” was proposed in the present work to a first approximation. The suggested phenomenological model in 4SL formalism together with the concept of “pair activation energy” was finally applied to describe diffusion in the ordered fcc-L12 phase of the binary Ni–Al system. Several advantages of using the 4SL model over the 2SL model were also demonstrated.