Domain coarsening in thin films (Q2710684)

The last stage of a first-order phase transition is characterized by coarsening of the morphology of the spatial distribution. An example is an initially spatially homogeneous two-component mixture that is suddenly cooled down to a temperature at which the phases want to segregate. Phase separation takes place by forming particles of one equilibrium volume fraction immersed into a matrix of the other equilibrium volume fraction. Now the system has reached equilibrium in the bulk. It is henceforth driven by interfacial energy and limited by diffusion. One observes that large particles grow at the expense of the small ones, which eventually vanish. This leads to a decrease in the number density of particles and an increase in the average size of particles. This form of coarsening is known as Ostwald ripening.NEWLINENEWLINENEWLINEIn the paper a mean-field model for Ostwald ripening in two-dimensional systems (that arise in the growth of thin metallic film) is derived rigorously. This is an extension of the Lifshitz-Slyozov-Wagner (LSW) theory to the two-dimensional case. It turns out that as opposed to the three-dimensional case, the mean field becomes singular at times when a particle disappears. The LSW-model is extended to the inhomogeneous case.NEWLINENEWLINENEWLINEIn the case of small volume fraction the evolution of all particle radii reduces to an evolution of the joint distribution of particle radii and particle center. A periodic arrangement of particles is considered with time dependent radii, which evolve according to a restricted Mullins-Sekerka evolution. A new result, compared to the results in three dimensions, is that this distribution has a certain uniform regularity at \(r=0\). A priori estimates concerning the particle growth and the distribution function are given.