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Article: The von Neumann relation generalized to coarsening of three-dimensional microstructures
Title | The von Neumann relation generalized to coarsening of three-dimensional microstructures |
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Authors | |
Issue Date | 2007 |
Citation | Nature, 2007, v. 446, n. 7139, p. 1053-1055 How to Cite? |
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. ©2007 Nature Publishing Group. |
Persistent Identifier | http://hdl.handle.net/10722/303300 |
ISSN | 2023 Impact Factor: 50.5 2023 SCImago Journal Rankings: 18.509 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | MacPherson, Robert D. | - |
dc.contributor.author | Srolovitz, David J. | - |
dc.date.accessioned | 2021-09-15T08:25:02Z | - |
dc.date.available | 2021-09-15T08:25:02Z | - |
dc.date.issued | 2007 | - |
dc.identifier.citation | Nature, 2007, v. 446, n. 7139, p. 1053-1055 | - |
dc.identifier.issn | 0028-0836 | - |
dc.identifier.uri | http://hdl.handle.net/10722/303300 | - |
dc.description.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. ©2007 Nature Publishing Group. | - |
dc.language | eng | - |
dc.relation.ispartof | Nature | - |
dc.title | The von Neumann relation generalized to coarsening of three-dimensional microstructures | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1038/nature05745 | - |
dc.identifier.scopus | eid_2-s2.0-34247641637 | - |
dc.identifier.volume | 446 | - |
dc.identifier.issue | 7139 | - |
dc.identifier.spage | 1053 | - |
dc.identifier.epage | 1055 | - |
dc.identifier.eissn | 1476-4687 | - |
dc.identifier.isi | WOS:000245950400043 | - |