Interaction of a Bulk and a Surface Energy with a Geometrical Constraint

Chambolle, Antonin; Solci, Margherita

doi:10.1137/060649173

Cited by 25 publications

(51 citation statements)

References 17 publications

(17 reference statements)

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“…2.38 and 2.39) to treat the presence of anisotropy in the surface term (we refer also to the recent works [3,6] for related relaxation results in higher dimension).…”

Section: − At the Points Of Its Reduced Boundary (Which Coincides Inmentioning

confidence: 99%

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Epitaxially strained elastic films: the case of anisotropic surface energies

Bonacini

2012

ESAIM: COCV

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Abstract.In the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer of the total energy. Following the approach of [N. Fusco and M. Morini, Equilibrium configurations of epitaxially strained elastic films: second order minimality conditions and qualitative properties of solutions. Preprint], we obtain these results by means of a minimality criterion based on the positivity of the second variation.Mathematics Subject Classification. 74G55, 74K35, 74G65, 49Q20, 49K10.

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“…2.38 and 2.39) to treat the presence of anisotropy in the surface term (we refer also to the recent works [3,6] for related relaxation results in higher dimension).…”

Section: − At the Points Of Its Reduced Boundary (Which Coincides Inmentioning

confidence: 99%

“…Changing variables in I 1 and using the equalityḢ 6) where the last equality follows by integration by parts, using the periodicity of ϕ.…”

Section: Then the Functionu Belongs To A(ω H ) And Satisfies The Equamentioning

confidence: 99%

Epitaxially strained elastic films: the case of anisotropic surface energies

Bonacini

2012

ESAIM: COCV

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“…Here we have chosen to present a self-contained proof based on somewhat different arguments. We should mention that the results contained in [4] have been extended and generalized in a higher dimensional setting in the two recent papers [6] and [8].…”

Section: Introductionmentioning

confidence: 99%

Equilibrium Configurations of Epitaxially Strained Crystalline Films: Existence and Regularity Results

Fonseca

Fusco

Leoni

et al. 2007

Arch Rational Mech Anal

150

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Strained epitaxial films grown on a relatively thick substrate are considered in the context of plane linear elasticity. The total free energy of the system is assumed to be the sum of the energy of the free surface of the film and the strain energy. Because of the lattice mismatch between film and substrate, flat configurations are in general energetically unfavourable and a corrugated or islanded morphology is the preferred growth mode of the strained film. After specifying the functional setup where the existence problem can be properly framed, a study of the qualitative properties of the solutions is undertaken. New regularity results for volume constrained local minimizers of the total free energy are established, leading, as a byproduct, to a rigorous proof of the zero contact-angle condition between islands and wetting layers.

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“…Finally, dividing (12) by |Ω|, raising it to the power 5/4, and multiplying it by e [33,15,13,29,2]). …”

Section: Scaling Law In Dimension Three For the Dirichlet Energymentioning

confidence: 99%

“…Even though our method seems to be quite flexible, the richness of the geometry makes the extension to more general energy functionals difficult (see [12] for some results). Let us finally notice that in higher dimension, the elastic part of the energy can be seen as a repulsive nonlocal term giving the problem a flavor of the Ohta-Kawasaki model which has recently received a lot of attention (see [33,15,13,29,2]).…”

Section: Introductionmentioning

confidence: 99%

Scaling Law and Reduced Models for Epitaxially Strained Crystalline Films

Goldman¹,

Zwicknagl²

2014

SIAM J. Math. Anal.

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A variational model for the epitaxial deposition of a film on a rigid substrate in the presence of a crystallographic misfit is studied. The scaling behavior of the minimal energy in terms of the volume of the film and the amplitude of the misfit is considered, and reduced models in the various regimes are derived by Γ-convergence methods. Depending on the relation between the thickness of the film and the amplitude of the misfit, the surface or the elastic energy contribution dominate, and in the critical case the two contributions balance. In particular, the formation of islands is proven if the amplitude of the misfit is large compared to the volume of the film.

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Interaction of a Bulk and a Surface Energy with a Geometrical Constraint

Cited by 25 publications

References 17 publications

Epitaxially strained elastic films: the case of anisotropic surface energies

Epitaxially strained elastic films: the case of anisotropic surface energies

Equilibrium Configurations of Epitaxially Strained Crystalline Films: Existence and Regularity Results

Scaling Law and Reduced Models for Epitaxially Strained Crystalline Films

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