MiS Preprint Repository

The classical LSW-model describes the evolution of the radii of particles of one phase immersed in the other phase during the last stage of a phase transformation. Despite its simplicity, the LSW-model captures self-similar coarsening of the radii distribution. It is derived under the assumption of vanishing volume fraction $\varphi$ of the particles. Unfortunately, quantitative predictions of this model do not well agree with experiments. Hence there is a large interest in deriving first-order corrections of the LSW-model in $\varphi$.

In the first part of this paper, we present a new heuristic method to efficiently identify the first-order correction for a statistically homogeneous (and thus infinite) system. As was previously known, the first-order correction is of order ${\varphi }^{1/2}$. In the second part of this paper we consider finite systems (cluster). Numerical simulations have shown a cross-over in the scaling of the correction term from ${\varphi }^{1/3}$ to ${\varphi }^{1/2}$ when the cluster becomes larger than the screening length. We rigorously derive this cross-over for the time derivative of the energy. Our starting point for both parts is the monopole approximation.