The von Neumann relation generalized to coarsening of three-dimensional microstructures

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalNot applicablepeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)1053-1055
Journal / PublicationNature
Volume446
Issue number7139
Publication statusPublished - 26 Apr 2007
Externally publishedYes

Abstract

Cellular structures or tessellations are ubiquitous in nature. Metals and ceramics commonly consist of space-filling arrays of single-crystal grains separated by a network of grain boundaries, and foams (froths) are networks of gas-filled bubbles separated by liquid walls. Cellular structures also occur in biological tissue, and in magnetic, ferroelectric and complex fluid contexts. In many situations, the cell/grain/bubble walls move under the influence of their surface tension (capillarity), with a velocity proportional to their mean curvature. As a result, the cells evolve and the structure coarsens. Over 50 years ago, von Neumann derived an exact formula for the growth rate of a cell in a two-dimensional cellular structure (using the relation between wall velocity and mean curvature, the fact that three domain walls meet at 120° and basic topology). This forms the basis of modern grain growth theory. Here we present an exact and much-sought extension of this result into three (and higher) dimensions. The present results may lead to the development of predictive models for capillarity-driven microstructure evolution in a wide range of industrial and commercial processing scenarios - such as the heat treatment of metals, or even controlling the 'head' on a pint of beer.

Citation Format(s)

The von Neumann relation generalized to coarsening of three-dimensional microstructures. / MacPherson, Robert D.; Srolovitz, David J.

In: Nature, Vol. 446, No. 7139, 26.04.2007, p. 1053-1055.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalNot applicablepeer-review