An extension of the classical Cahn-Hilliard equation, including elastic interactions is presented. This generalized diffusion equation allows real time simulation of phase-transformations, such as GP-zone formation in a near-commercial ΔICu alloy. No a priori assumptions about kinetics, diffusion fields, as well as precipitate shape are necessary. Shape of precipitates and kinetic of simulated GP-zone formation are in qualitatively good agreement with experiments of Sato and Takahashi, and the concurrenltly derived interfacial energies are reasonable.
Two algorithms for a numerical solution of the Cahn-Hilliard equation are presented. While the simple finite difference scheme does not converge, a slightly more complicated Fourier spectral method behaves reasonable as tested for a synthetic chemical potential.