Beyond the Cahn-Hilliard Equation: a Vacancy-Based Kinetic Theory
A Self-Consistent Mean Field (SCMF) kinetic theory including an explicit description ofthe vacancy diffusion mechanism is developed. The present theory goes beyond the usual local equi-librium hypothesis. It is applied to the study of the early time spinodal decomposition in alloys. Theresulting analytical expression of the structure function highlights the contribution of the vacancydiffusion mechanism. Instead of the single amplification rate of the Cahn-Hillard linear theory, thelinearized SCMF kinetic equations involve three constant rates, first one describing the vacancy re-laxation kinetics, second one related to the kinetic coupling between local concentrations and paircorrelations and the third one representing the spinodal amplification rate. Starting from the same va-cancy diffusion model, we perform kineticMonte Carlo simulations of a Body Centered Cubic (BCC)demixting alloy. The resulting spherically averaged structure function is compared to the SCMF pre-dictions. Both qualitative and quantitative agreements are satisfying.
Yves Bréchet, Emmanuel Clouet, Alexis Deschamps, Alphonse Finel and Frédéric Soisson
M. Nastar "Beyond the Cahn-Hilliard Equation: a Vacancy-Based Kinetic Theory", Solid State Phenomena, Vols. 172-174, pp. 321-330, 2011