Letter abstract
Nature Materials 3, 385 - 388 (2004)
Published online: 23 May 2004 | doi:10.1038/nmat1138
Subject Categories: Design synthesis and processing | Computation, modelling and theory
Topological complexity and the dynamics of coarsening
R. Mendoza1, I. Savin1, K. Thornton1 & P. W. Voorhees1
Coarsening or Ostwald ripening occurs in a vast array of two-phase systems. Coarsening results in a decrease in the interfacial area per unit volume and a concomitant increase in the size scale of the interfacial morphology. Much is known about the coarsening process in two-phase mixtures consisting of a polydisperse array of spherical particles1, 2. In contrast, in many two-phase mixtures, such as those found in two-phase polymers3, ceramics4, dendritic solid–liquid mixtures5, 6 and order–disorder transformations7, the interfaces are both interconnected and have a spatially varying mean curvature. Here we show that the morphological evolution of these topologically complex systems during coarsening can be quantified by measuring the probability of finding a patch of interface with a given curvature tensor. We find that the morphological evolution is described by the flow of probability density in this curvature space that is induced by the coarsening process. The hallmark of our approach is a close coupling between experiment and theory; we use the experimentally measured three-dimensional microstructure as an input to a phase-field calculation that then determines the flow in curvature space. The methodology is general, and applicable to many systems undergoing coarsening, regardless of their topology.
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208-3108, USA
Correspondence to: P. W. Voorhees1 e-mail: p-voorhees@northwestern.edu
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