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Article: Stable equilibria of anisotropic particles on substrates: A generalized Winterbottom construction

TitleStable equilibria of anisotropic particles on substrates: A generalized Winterbottom construction
Authors
KeywordsMultiple stable equilibrium
Anisotropic surface energy
Solid-state dewetting
Thermodynamic variation
Surface diffusion
Generalized Winterbottom construction
Issue Date2017
Citation
SIAM Journal on Applied Mathematics, 2017, v. 77, n. 6, p. 2093-2118 How to Cite?
AbstractWe present a new approach for predicting stable equilibrium shapes of two-dimensional crystalline islands on at substrates, as commonly occur through solid-state dewetting of thin films. The new theory is a generalization of the widely used Winterbottom construction (i.e., an extension of the Wulff construction for particles on substrates). This approach is equally applicable to cases where the crystal surface energy is isotropic, weakly anisotropic, strongly anisotropic, and "cusped". We demonstrate that, unlike in the classical Winterbottom approach, multiple equilibrium island shapes may be possible when the surface energy is strongly anisotropic. We analyze these shapes through perturbation analysis, by calculating the first and second variations of the total free energy functional with respect to contact locations and island shape. Based on this analysis, we find the necessary conditions for the equilibria to be stable to two-dimensional perturbations and exploit this through a generalization of the Winterbottom construction to identify all possible stable equilibrium shapes. Finally, we propose a dynamical evolution method based on surface diffusion mass transport to determine whether all of the stable equilibrium shapes are dynamically accessible. Applying this approach, we demonstrate that islands with Different initial shapes may evolve into Different stationary shapes and show that these dynamically determined stationary states correspond to the predicted stable equilibrium shapes, as obtained from the generalized Winterbottom construction.
Persistent Identifierhttp://hdl.handle.net/10722/303552
ISSN
2023 Impact Factor: 1.9
2023 SCImago Journal Rankings: 0.939
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorBao, Weizhu-
dc.contributor.authorJiang, Wei-
dc.contributor.authorSrolovitz, David J.-
dc.contributor.authorWang, Yan-
dc.date.accessioned2021-09-15T08:25:33Z-
dc.date.available2021-09-15T08:25:33Z-
dc.date.issued2017-
dc.identifier.citationSIAM Journal on Applied Mathematics, 2017, v. 77, n. 6, p. 2093-2118-
dc.identifier.issn0036-1399-
dc.identifier.urihttp://hdl.handle.net/10722/303552-
dc.description.abstractWe present a new approach for predicting stable equilibrium shapes of two-dimensional crystalline islands on at substrates, as commonly occur through solid-state dewetting of thin films. The new theory is a generalization of the widely used Winterbottom construction (i.e., an extension of the Wulff construction for particles on substrates). This approach is equally applicable to cases where the crystal surface energy is isotropic, weakly anisotropic, strongly anisotropic, and "cusped". We demonstrate that, unlike in the classical Winterbottom approach, multiple equilibrium island shapes may be possible when the surface energy is strongly anisotropic. We analyze these shapes through perturbation analysis, by calculating the first and second variations of the total free energy functional with respect to contact locations and island shape. Based on this analysis, we find the necessary conditions for the equilibria to be stable to two-dimensional perturbations and exploit this through a generalization of the Winterbottom construction to identify all possible stable equilibrium shapes. Finally, we propose a dynamical evolution method based on surface diffusion mass transport to determine whether all of the stable equilibrium shapes are dynamically accessible. Applying this approach, we demonstrate that islands with Different initial shapes may evolve into Different stationary shapes and show that these dynamically determined stationary states correspond to the predicted stable equilibrium shapes, as obtained from the generalized Winterbottom construction.-
dc.languageeng-
dc.relation.ispartofSIAM Journal on Applied Mathematics-
dc.subjectMultiple stable equilibrium-
dc.subjectAnisotropic surface energy-
dc.subjectSolid-state dewetting-
dc.subjectThermodynamic variation-
dc.subjectSurface diffusion-
dc.subjectGeneralized Winterbottom construction-
dc.titleStable equilibria of anisotropic particles on substrates: A generalized Winterbottom construction-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1137/16M1091599-
dc.identifier.scopuseid_2-s2.0-85042396916-
dc.identifier.volume77-
dc.identifier.issue6-
dc.identifier.spage2093-
dc.identifier.epage2118-
dc.identifier.isiWOS:000418681600011-

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