Atomic diffusion theory challenging the Cahn-Hilliard method

International audienceOur development of the self-consistent mean-field (SCMF) kinetic theory for nonuniform alloys leads tothe statement that kinetic correlations induced by the vacancy diffusion mechanism have a dramatic effecton nanoscale diffusion phenomena, leading to nonlinear features of the interdiffusion coefficients. Lattice rateequations of alloys including nonuniform gradients of chemical potential are derived within the Bragg-Williamsstatistical approximation and the third shell kinetic approximation of the SCMF theory. General driving forcesincluding deviations of the free energy from a local equilibrium thermodynamic formulation are introduced. Thesedeviations are related to the variation of vacancy motion due to the spatial variation of the alloy composition.During the characteristic time of atomic diffusion, multiple exchanges of the vacancy with the same atoms mayhappen, inducing atomic kinetic correlations that depend as well on the spatial variation of the alloy composition.As long as the diffusion driving forces are uniform, the rate equations are shown to obey in this form theOnsager formalism of thermodynamics of irreversible processes (TIP) and the TIP-based Cahn-Hilliard diffusionequation. If now the chemical potential gradients are not uniform, the continuous limit of the present SCMFkinetic equations does not coincide with the Cahn-Hilliard (CH) equation. In particular, the composition gradientand higher derivative terms depending on kinetic parameters add to the CH thermodynamic-based compositiongradient term. Indeed, a diffusion equation written as a mobility multiplied by a thermodynamic formulationof the driving forces is shown to be inadequate. In the reciprocal space, the thermodynamic driving force hasto be multiplied by a nonlinear function of the wave vector accounting for the variation of kinetic correlationswith composition inhomogeneities. Analytical expressions of the effective interdiffusion coefficient are givenfor two limit behaviors of the vacancy, the latter treated as either a conservative species (fixed concentration) ora nonconservative species (time-dependent equilibrium concentration). Relying on the same vacancy diffusionmodel, we perform kinetic Monte Carlo simulations starting from a sinusoidal composition modulation in binarymodel alloys, with no interaction or nearest-neighbor interactions leading to clustering or ordering tendencies,along the [100] crystallographic direction of a body centered cubic (bcc) lattice. The resulting temporal variationof the modulation amplitude is compared to the corresponding SCMF equations. Qualitative and satisfyingquantitative agreements systematically strengthen our theoretical conclusions. The model alloys are shown to berepresentative enough of some real alloys, so that one may expect these new heterogeneous correlation effects tobe non-negligible in these alloys