Spinodal decomposition of a crystal surface

Stewart, John Q.; Goldenfeld, Nigel

doi:10.1103/physreva.46.6505

Cited by 102 publications

(91 citation statements)

References 16 publications

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“…4,5 It must be noted that in contrast to liquids, the surface energy of solid surfaces is strongly anisotropic, leading to missing orientations in the dynamic or equilibrium surface shape [6][7][8][9][10] and faceting instability. [11][12][13][14][15][16][17][18] Anisotropy is certain to affect the dynamics of the pinhole. Moreover, it is possible that the nonlinear competition with the attractive wetting potential may even lead to the emergence of an equilibrium and thus to the suppression of the film dewetting and rupture.…”

Section: Recent Experimentsmentioning

confidence: 99%

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Morphologies and kinetics of a dewetting ultrathin solid film

Khenner

2008

Phys. Rev. B

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The surface evolution model based on a geometric partial differential equation is used to numerically study the kinetics of dewetting and the dynamic morphologies for the localized pinhole defect in the surface of an ultrathin solid film with the strongly anisotropic surface energy. Depending on the parameters such as the initial depth and width of the pinhole, the strength of the attractive substrate potential and the strength of the surface-energy anisotropy, the pinhole may either extend to the substrate and thus rupture the film, or evolve to the quasiequilibrium shape while the rest of the film surface undergoes a phase separation into a hill-and-valley structure followed by coarsening. Emergence of the quasiequilibrium shape and the termination of a dewetting are associated with the faceting of the pinhole tip. Overhanging ͑nongraph͒ morphologies are possible for deep, narrow ͑slitlike͒ pinholes.

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Section: Recent Experimentsmentioning

confidence: 99%

“…If the wetting potential is zero ͑z / ᐉ → ϱ͒, this reduces to the familiar strongly anisotropic form. 11,12,14 Finally,…”

Section: Problem Statementmentioning

confidence: 99%

Morphologies and kinetics of a dewetting ultrathin solid film

Khenner

2008

Phys. Rev. B

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“…The facetting transition in which a crystal surface is allowed to anneal in equilibrium with its vapor (or in vacuum), has also been modeled with equations of CH type [5,6], in which the orientation of the local tangent plane serves as a (vector) order parameter and the surface tension induces an effective free energy. Here, the surface tension is sufficiently anisotropic that certain crystal surfaces are thermodynamically unstable and hence missing in the crystal equilibrium state (Wulff shape [7]).…”

Section: Introductionmentioning

confidence: 99%

Coarsening dynamics of the convective Cahn-Hilliard equation

Watson

Otto

Rubinstein

et al. 2003

Physica D: Nonlinear Phenomena

104

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We characterize the coarsening dynamics associated with a convective Cahn-Hilliard equation in one space dimension. First, we derive a sharp-interface theory based on a quasi-static matched asymptotic analysis. Two distinct types of discontinuity (kink and anti-kink) arise due to the presence of convection, and their motions are governed to leading order by a nearest-neighbors interaction dynamical system. Numerical simulations of the kink/anti-kink dynamics display marked self-similarity in the coarsening process, and reveal a pinching mechanism, identified through a linear stability analysis, as the dominant coarsening event. A self-similar period-doubling pinching ansatz is proposed for the coarsening process, and an analytical coarsening law, valid over all length scales, is derived. Our theoretical predictions are in good agreement with numerical simulations that have been performed both on the sharp-interface model and the original PDE.

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“…The edge problem has the character to a phase transition of an interface and is governed by a steady Allen-Cahn equation where the double-well nature of the associated potential is related to the form of γ(θ). This analogy of the edge to a phase transition at an interface was first made by Cabrera (1963) and later by Stewart and Goldenfeld (1992) in the context of the sharp interface model. We go on to define and evaluate the edge energy associated with the presence of the edge region.…”

Section: Introductionmentioning

confidence: 99%

“…To date, the focus has been on the free boundary formulation which involves applying a regularisation by including higher terms to the surface energy, see Stewart & Goldenfeld (1992), Liu & Metiu (1993), Golovin et al (1998Golovin et al ( , 2001Golovin et al ( , 2003. This may involve adding surface diffusion or evaporation or more simply allowing the surface energy to depend also on curvature so that γ =γ(θ) + βK 2 , where K is the curvature of the interface and β is a constant.…”

Section: Introductionmentioning

confidence: 99%

Phase-field theory of edges in an anisotropic crystal

Wheeler

2006

Proc. R. Soc. A.

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In the presence of sufficiently strong surface energy anisotropy the equilibrium shape of an isothermal crystal may include corners or edges. Models of edges have, to date, involved the regularisation of the corresponding free boundary problem resulting in equilibrium shapes with smoothed out edges. In this paper we take a new approach and consider how a phase-field model, which provides a diffuse description of an interface, can be extended to the consideration of edges by an appropriate regularisation of the underlying mathematical model. Using the method of matched asymptotic expansions we develop an approximate solution which corresponds to a smoothed out edge from which we are able to determine the associated edge energy.

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Spinodal decomposition of a crystal surface

Cited by 102 publications

References 16 publications

Morphologies and kinetics of a dewetting ultrathin solid film

Morphologies and kinetics of a dewetting ultrathin solid film

Coarsening dynamics of the convective Cahn-Hilliard equation

Phase-field theory of edges in an anisotropic crystal

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