Geometry of phase separation
Autor(a) principal: | |
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Data de Publicação: | 2009 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRGS |
Texto Completo: | http://hdl.handle.net/10183/101821 |
Resumo: | We study the domain geometry during spinodal decomposition of a 50:50 binary mixture in two dimensions. Extending arguments developed to treat nonconserved coarsening, we obtain approximate analytic results for the distribution of domain areas and perimeters during the dynamics. The main approximation is to regard the interfaces separating domains as moving independently. While this is true in the nonconserved case, it is not in the conserved one. Our results can therefore be considered as a “first-order” approximation for the distributions. In contrast to the celebrated Lifshitz-Slyozov-Wagner distribution of structures of the minority phase in the limit of very small concentration, the distribution of domain areas in the 50:50 case does not have a cutoff. Large structures areas or perimeters retain the morphology of a percolative or critical initial condition, for quenches from high temperatures or the critical point, respectively. The corresponding distributions are described by a cA− t ail, where c and t are exactly known. With increasing time, small structures tend to have a spherical shape with a smooth surface before evaporating by diffusion. In this regime, the number density of domains with area A scales as A1/2, as in the Lifshitz-Slyozov-Wagner theory. The threshold between the small and large regimes is determined by the characteristic area A~t2/3. Finally, we study the relation between perimeters and areas and the distribution of boundary lengths, finding results that are consistent with the ones summarized above. We test our predictions with Monte Carlo simulations of the two-dimensional Ising model. |
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Sicilia, AlbertoSarrazin, YoannArenzon, Jeferson JacobBray, Alan J.Cugliandolo, Leticia F.2014-08-26T09:26:13Z20091539-3755http://hdl.handle.net/10183/101821000725856We study the domain geometry during spinodal decomposition of a 50:50 binary mixture in two dimensions. Extending arguments developed to treat nonconserved coarsening, we obtain approximate analytic results for the distribution of domain areas and perimeters during the dynamics. The main approximation is to regard the interfaces separating domains as moving independently. While this is true in the nonconserved case, it is not in the conserved one. Our results can therefore be considered as a “first-order” approximation for the distributions. In contrast to the celebrated Lifshitz-Slyozov-Wagner distribution of structures of the minority phase in the limit of very small concentration, the distribution of domain areas in the 50:50 case does not have a cutoff. Large structures areas or perimeters retain the morphology of a percolative or critical initial condition, for quenches from high temperatures or the critical point, respectively. The corresponding distributions are described by a cA− t ail, where c and t are exactly known. With increasing time, small structures tend to have a spherical shape with a smooth surface before evaporating by diffusion. In this regime, the number density of domains with area A scales as A1/2, as in the Lifshitz-Slyozov-Wagner theory. The threshold between the small and large regimes is determined by the characteristic area A~t2/3. Finally, we study the relation between perimeters and areas and the distribution of boundary lengths, finding results that are consistent with the ones summarized above. We test our predictions with Monte Carlo simulations of the two-dimensional Ising model.application/pdfengPhysical review. E, Statistical, nonlinear and soft matter physics. Vol. 80, no. 3 (Sep. 2009), 031121, 9 p.Física estatísticaMétodo de Monte CarloModelo de isingPontos criticosEvaporaçãoDecomposicao spinodalSeparação de fasesGeometry of phase separationEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSTEXT000725856.pdf.txt000725856.pdf.txtExtracted Texttext/plain44051http://www.lume.ufrgs.br/bitstream/10183/101821/2/000725856.pdf.txt9f7190beed93ba09b13c5e325d627061MD52ORIGINAL000725856.pdf000725856.pdfTexto completo (inglês)application/pdf343044http://www.lume.ufrgs.br/bitstream/10183/101821/1/000725856.pdf2991c50c2dbbdbc1dce38b087c417ce8MD51THUMBNAIL000725856.pdf.jpg000725856.pdf.jpgGenerated Thumbnailimage/jpeg1949http://www.lume.ufrgs.br/bitstream/10183/101821/3/000725856.pdf.jpg06e75f275a2ba3342de1fef22fc244d2MD5310183/1018212024-03-28 06:24:32.509996oai:www.lume.ufrgs.br:10183/101821Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2024-03-28T09:24:32Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false |
dc.title.pt_BR.fl_str_mv |
Geometry of phase separation |
title |
Geometry of phase separation |
spellingShingle |
Geometry of phase separation Sicilia, Alberto Física estatística Método de Monte Carlo Modelo de ising Pontos criticos Evaporação Decomposicao spinodal Separação de fases |
title_short |
Geometry of phase separation |
title_full |
Geometry of phase separation |
title_fullStr |
Geometry of phase separation |
title_full_unstemmed |
Geometry of phase separation |
title_sort |
Geometry of phase separation |
author |
Sicilia, Alberto |
author_facet |
Sicilia, Alberto Sarrazin, Yoann Arenzon, Jeferson Jacob Bray, Alan J. Cugliandolo, Leticia F. |
author_role |
author |
author2 |
Sarrazin, Yoann Arenzon, Jeferson Jacob Bray, Alan J. Cugliandolo, Leticia F. |
author2_role |
author author author author |
dc.contributor.author.fl_str_mv |
Sicilia, Alberto Sarrazin, Yoann Arenzon, Jeferson Jacob Bray, Alan J. Cugliandolo, Leticia F. |
dc.subject.por.fl_str_mv |
Física estatística Método de Monte Carlo Modelo de ising Pontos criticos Evaporação Decomposicao spinodal Separação de fases |
topic |
Física estatística Método de Monte Carlo Modelo de ising Pontos criticos Evaporação Decomposicao spinodal Separação de fases |
description |
We study the domain geometry during spinodal decomposition of a 50:50 binary mixture in two dimensions. Extending arguments developed to treat nonconserved coarsening, we obtain approximate analytic results for the distribution of domain areas and perimeters during the dynamics. The main approximation is to regard the interfaces separating domains as moving independently. While this is true in the nonconserved case, it is not in the conserved one. Our results can therefore be considered as a “first-order” approximation for the distributions. In contrast to the celebrated Lifshitz-Slyozov-Wagner distribution of structures of the minority phase in the limit of very small concentration, the distribution of domain areas in the 50:50 case does not have a cutoff. Large structures areas or perimeters retain the morphology of a percolative or critical initial condition, for quenches from high temperatures or the critical point, respectively. The corresponding distributions are described by a cA− t ail, where c and t are exactly known. With increasing time, small structures tend to have a spherical shape with a smooth surface before evaporating by diffusion. In this regime, the number density of domains with area A scales as A1/2, as in the Lifshitz-Slyozov-Wagner theory. The threshold between the small and large regimes is determined by the characteristic area A~t2/3. Finally, we study the relation between perimeters and areas and the distribution of boundary lengths, finding results that are consistent with the ones summarized above. We test our predictions with Monte Carlo simulations of the two-dimensional Ising model. |
publishDate |
2009 |
dc.date.issued.fl_str_mv |
2009 |
dc.date.accessioned.fl_str_mv |
2014-08-26T09:26:13Z |
dc.type.driver.fl_str_mv |
Estrangeiro info:eu-repo/semantics/article |
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http://hdl.handle.net/10183/101821 |
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1539-3755 |
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000725856 |
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eng |
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eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Physical review. E, Statistical, nonlinear and soft matter physics. Vol. 80, no. 3 (Sep. 2009), 031121, 9 p. |
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info:eu-repo/semantics/openAccess |
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openAccess |
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