1D CAHN–HILLIARD EQUATION: OSTWALD RIPENING AND MODULATED PHASE SYSTEMS

1D Cahn-Hilliard equation: Ostwald Ripening and Modulated Phase Systems

Using an approximate analytical solution of the Cahn-Hilliard equation describing the coalescence during a first order phase transition, we compute the characteristic time for one step of period doubling in Langer's self similar scenario for Ostwald ripening. As an application, we compute the thermodynamically stable period of a 1D modulated phase pattern.

1D Cahn-Hilliard equation for modulated phase systems

Formation of modulated phase patterns can be modelized by a modi…ed Cahn-Hilliard equation which includes a non local term preventing the formation of macroscopic domains. Using stationnary solutions of the original Cahn-Hilliard equation as analytical ansatzs, we compute the thermodynamically stable period of a 1D modulated phase pattern. We …nd that the period scales like the power -1/3 of th...

Ostwald ripening pdf

Homoepitaxial Ostwald ripening

This paper reports level set simulations of the Ostwald ripening of two-dimensional homoepitaxial islands. The simulation accurately accounts for both adatom diffusion between the islands and adatom attachment/detachment processes at the island edges. We compute the time evolution of the average island size and the full island size distribution function. The results provide support for a previo...

Part I: Ostwald ripening theories

The physical basis behind the Ostwald ripening process for two-phase mixture has been reviewed in detail, using the various theories developed to describe this process. The Ostwald ripening, also termed second phase coarsening, is generally thought to be slow, diffusion-controlled process which occurs subsequent to phase separation under extremely small under-saturation levels. The major advanc...