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René Van Roij - One of the best experts on this subject based on the ideXlab platform.
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The Equilibrium Shape of fluid-fluid interfaces: Derivation and a new numerical method for Young’s and Young-Laplace equations
Journal of Chemical Physics, 2014Co-Authors: Giuseppe Soligno, Marjolein Dijkstra, René Van RoijAbstract:Many physical problems require explicit knowledge of the Equilibrium Shape of the interface between two fluid phases. Here, we present a new numerical method which is simply implementable and easily adaptable for a wide range of problems involving capillary deformations of fluid-fluid interfaces. We apply a simulated annealing algorithm to find the interface Shape that minimizes the thermodynamic potential of the system. First, for completeness, we provide an analytical proof that minimizing this potential is equivalent to solving the Young-Laplace equation and the Young law. Then, we illustrate our numerical method showing two-dimensional results for fluid-fluid menisci between vertical or inclined walls and curved surfaces, capillary interactions between vertical walls, Equilibrium Shapes of sessile heavy droplets on a flat horizontal solid surface, and of droplets pending from flat or curved solid surfaces. Finally, we show illustrative three-dimensional results to point out the applicability of the method to micro- or nano-particles adsorbed at a fluid-fluid interface.
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the Equilibrium Shape of fluid fluid interfaces derivation and a new numerical method for young s and young laplace equations
Journal of Chemical Physics, 2014Co-Authors: Giuseppe Soligno, Marjolein Dijkstra, René Van RoijAbstract:Many physical problems require explicit knowledge of the Equilibrium Shape of the interface between two fluid phases. Here, we present a new numerical method which is simply implementable and easily adaptable for a wide range of problems involving capillary deformations of fluid-fluid interfaces. We apply a simulated annealing algorithm to find the interface Shape that minimizes the thermodynamic potential of the system. First, for completeness, we provide an analytical proof that minimizing this potential is equivalent to solving the Young-Laplace equation and the Young law. Then, we illustrate our numerical method showing two-dimensional results for fluid-fluid menisci between vertical or inclined walls and curved surfaces, capillary interactions between vertical walls, Equilibrium Shapes of sessile heavy droplets on a flat horizontal solid surface, and of droplets pending from flat or curved solid surfaces. Finally, we show illustrative three-dimensional results to point out the applicability of the method to micro- or nano-particles adsorbed at a fluid-fluid interface.
Eckard Pehlke - One of the best experts on this subject based on the ideXlab platform.
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Influence of surface stress on the Equilibrium Shape of strained quantum dots
Physical Review B, 1998Co-Authors: Nikolaj Moll, Matthias Scheffler, Eckard PehlkeAbstract:The Equilibrium Shapes of InAs quantum dots ~i.e., dislocation-free, strained islands with sizes >10 000 atoms! grown on a GaAs ~001! substrate are studied using a hybrid approach that combines density functional theory ~DFT! calculations of microscopic parameters, surface energies, and surface stresses with elasticity theory for the long-range strain fields and strain relaxations. In particular we report DFT calculations of the surface stresses and analyze the influence of the strain on the surface energies of the various facets of the quantum dot. The surface stresses have been neglected in previous studies. Furthermore, the influence of edge energies on the island Shapes is briefly discussed. From the knowledge of the Equilibrium Shape of these islands, we address the question whether experimentally observed quantum dots correspond to thermal Equilibrium structures or if they are a result of growth kinetics. @S0163-1829~98!06132-3#
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The Equilibrium Shape of Quantum Dots
arXiv: Materials Science, 1996Co-Authors: Eckard Pehlke, Nikolaj Moll, Matthias SchefflerAbstract:The formation of dislocation-free three-dimensional islands during the heteroepitaxial growth of lattice-mismatched materials has been observed experimentally for several material systems. The Equilibrium Shape of the islands is governed by the competition between the surface energy and the elastic relaxation energy of the islands as compared to the uniform strained film. As an exemplification we consider the experimentally intensively investigated growth of InAs quantum dots on a GaAs(001) substrate, deriving the Equilibrium Shape as a function of island volume. For this purpose InAs surface energies have been calculated within density-functional theory, and a continuum approach has been applied to compute the elastic relaxation energies.
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The Equilibrium Shape of InAs quantum dots grown on a GaAs(001) substrate
arXiv: Materials Science, 1996Co-Authors: Eckard Pehlke, Nikolaj Moll, Matthias SchefflerAbstract:The Equilibrium Shape of strained InAs quantum dots grown epitaxially on a GaAs(001) substrate is derived as a function of volume. InAs surface energies are calculated within density-functional theory, and a continuum approach is applied for the elastic relaxation energies.
Giuseppe Soligno - One of the best experts on this subject based on the ideXlab platform.
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The Equilibrium Shape of fluid-fluid interfaces: Derivation and a new numerical method for Young’s and Young-Laplace equations
Journal of Chemical Physics, 2014Co-Authors: Giuseppe Soligno, Marjolein Dijkstra, René Van RoijAbstract:Many physical problems require explicit knowledge of the Equilibrium Shape of the interface between two fluid phases. Here, we present a new numerical method which is simply implementable and easily adaptable for a wide range of problems involving capillary deformations of fluid-fluid interfaces. We apply a simulated annealing algorithm to find the interface Shape that minimizes the thermodynamic potential of the system. First, for completeness, we provide an analytical proof that minimizing this potential is equivalent to solving the Young-Laplace equation and the Young law. Then, we illustrate our numerical method showing two-dimensional results for fluid-fluid menisci between vertical or inclined walls and curved surfaces, capillary interactions between vertical walls, Equilibrium Shapes of sessile heavy droplets on a flat horizontal solid surface, and of droplets pending from flat or curved solid surfaces. Finally, we show illustrative three-dimensional results to point out the applicability of the method to micro- or nano-particles adsorbed at a fluid-fluid interface.
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the Equilibrium Shape of fluid fluid interfaces derivation and a new numerical method for young s and young laplace equations
Journal of Chemical Physics, 2014Co-Authors: Giuseppe Soligno, Marjolein Dijkstra, René Van RoijAbstract:Many physical problems require explicit knowledge of the Equilibrium Shape of the interface between two fluid phases. Here, we present a new numerical method which is simply implementable and easily adaptable for a wide range of problems involving capillary deformations of fluid-fluid interfaces. We apply a simulated annealing algorithm to find the interface Shape that minimizes the thermodynamic potential of the system. First, for completeness, we provide an analytical proof that minimizing this potential is equivalent to solving the Young-Laplace equation and the Young law. Then, we illustrate our numerical method showing two-dimensional results for fluid-fluid menisci between vertical or inclined walls and curved surfaces, capillary interactions between vertical walls, Equilibrium Shapes of sessile heavy droplets on a flat horizontal solid surface, and of droplets pending from flat or curved solid surfaces. Finally, we show illustrative three-dimensional results to point out the applicability of the method to micro- or nano-particles adsorbed at a fluid-fluid interface.
Magali Benoit - One of the best experts on this subject based on the ideXlab platform.
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Equilibrium Shape of core(Fe)–shell(Au) nanoparticles as a function of the metals volume ratio
Journal of Applied Physics, 2020Co-Authors: Anne Ponchet, Segolene Combettes, Patrizio Benzo, Nathalie Tarrat, Marie-josé Casanove, Magali BenoitAbstract:The Equilibrium Shape of nanoparticles is investigated to elucidate the various core–shell morphologies observed in a bimetallic system associating two immiscible metals, iron and gold, that crystallize in the bcc and fcc lattices, respectively. Fe–Au core–shell nanoparticles present a crystalline Fe core embedded in a polycrystalline Au shell, with core and shell morphologies both depending on the Au/Fe volume ratio. A model is proposed to calculate the energy of these nanoparticles as a function of the Fe volume, Au/Fe volume ratio, and the core and shell Shape, using the density functional theory-computed energy densities of the metal surfaces and of the two possible Au/Fe interfaces. Three driving forces leading to Equilibrium Shapes were identified: the strong adhesion of Au on Fe, the minimization of the Au/Fe interface energy that promotes one of the two possible interface types, and the Au surface energy minimization that promotes a 2D–3D Stranski–Krastanov-like transition of the shell. For a low Au/Fe volume ratio, the wetting is the dominant driving force and leads to the same polyhedral Shape for the core and the shell, with an octagonal section. For a large Au/Fe ratio, the surface and interface energy minimizations can act independently to form an almost cube-Shaped Fe core surrounded by six Au pyramids. The experimental nanoparticle Shapes are well reproduced by the model, for both low and large Au/Fe volume ratios.
U Dahmen - One of the best experts on this subject based on the ideXlab platform.
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Equilibrium Shape and interface roughening of small liquid pb inclusions in solid al
Acta Materialia, 2001Co-Authors: H Gabrisch, L Kjeldgaard, E Johnson, U DahmenAbstract:Abstract The Shape of liquid Pb inclusions embedded in a solid Al matrix was investigated at temperatures between 300 and 500°C using in-situ electron microscopy. Inclusion Shapes in the size range from a few nanometers to about 150 nm were found to depend on size, temperature and thermal history. During isothermal annealing after melting, small inclusions rounded off while larger inclusions remained faceted until the temperature was raised to about 500°C. During subsequent cooling, inclusions refaceted, although less strongly than during heating. The Shape hysteresis between heating and cooling cycles was found to be due to the barrier of ledge nucleation necessary to advance the faceted interfaces. It is shown that this kinetic barrier can explain the observed dependence on size and temperature, and that the {1 1 1} interface undergoes a roughening transition at about 550°C. Even under conditions of kinetic limitation it was possible to measure local Equilibrium by modeling kinetically limited inclusions as a droplet in a crevice. For this type of measurement, the hysteresis between heating and cooling cycles disappeared, and the true Equilibrium Shape could be derived. The anisotropy of interfacial energy was shown to be significantly smaller than previously reported, and at about 2%, similar to the anisotropy of the surface energy for fcc metals. From the width of facets on the Equilibrium Shape, the step energy was determined to be e=1.9·10−11 J/m at 350°C.
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Size-Dependent Equilibrium Shapes of Solid Pb Inclusions in Al
Microscopy and Microanalysis, 1997Co-Authors: U Dahmen, E Johnson, S.q. Xiao, Sidnei Paciornik, A. JohansenAbstract:Small Pb inclusions in Al have been studied by a number of investigators because the alloy system offers the possibility of observing the processes of melting and solidification directly. Both solids are fee, and the mutual solubility of solid Pb and Al is negligible. Despite a large difference in lattice parameter, it has been found that inclusions follow a parallel-cube orientation relationship and their Equilibrium Shape is a cuboctahedron, bounded by ﹛111﹜ and ﹛100﹜ facets [1]. Following Herring, the relative extent of the two types of facet directly indicates a ratio of interfacial energies γl00/γ111- However, recent investigations have shown that for inclusions in the range of a few to a few tens of nanometers the Equilibrium Shape becomes a function of size [2].In the present work, this size dependence of the Equilibrium Shape has been investigated further. Al alloys with about lat.% Pb were prepared by rapid solidification or by ion implantation, and equilibrated by annealing at about 300°C.