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Stephen H. Davis - One of the best experts on this subject based on the ideXlab platform.

  • The effect of surface stress and wetting layers on Morphological Instability in epitaxially strained films
    Journal of Applied Physics, 2004
    Co-Authors: T. V. Savina, Peter W. Voorhees, Stephen H. Davis
    Abstract:

    This paper investigates effects of surface stress and wetting layers on the Morphological Instability of a growing epitaxially strained dislocation-free solid film. Linear stability analysis of the planar film shows that the film, unstable due to lattice mismatch, is affected differently by surface stress for a film under compression than for one under tension and depends on whether the relative stiffness of the film to the substrate is less than or greater than (1−2ν)−1; here ν is Poisson’s ratio. The presence of a wetting layer has the capacity to substantially stabilize the planar film. The critical thickness of the film below which the film is stable depends on the bulk elastic properties of film and substrate and increases with increase of the wetting potential.

  • Morphological Instability of pores and tubules
    Interfaces and Free Boundaries, 2002
    Co-Authors: Dimitri J Kirill, Michael J Miksis, Stephen H. Davis, Peter W. Voorhees
    Abstract:

    We present a linear stability analysis of a uniaxially stressed, hollow cylindrical tubule, where the mass transport mechanism is surface diffusion driven by surface curvature- and elastic-energy. We find that there are always two distinct eigenmodes for any choice of wavenumbers, applied stress, and geometry. We also find that applied stress has a destabilizing effect, increasing the range of unstable wavenumbers. For any choice of applied stress and geometry, the most dangerous mode is axisymmetric, and can be either sinuous or varicose depending on choices of geometry and applied stress. The case of a cylindrical pore in a stressed infinite solid emerges as a limiting case.

  • Morphological Instability of a whisker
    Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 1999
    Co-Authors: D J Kirill, Stephen H. Davis, Michael J Miksis, Peter W. Voorhees
    Abstract:

    A thin stressed solid cylinder, a whisker, is subject to mass transport by curvature and elasticstressdriven surface diffusion. The stability of the cylindrical surface is examined using linear sta...

  • Effect of anisotropy on Morphological Instability in the freezing of a hypercooled melt
    Physica D: Nonlinear Phenomena, 1998
    Co-Authors: Alexander Golovin, Stephen H. Davis
    Abstract:

    Abstract Considered is the Morphological Instability of a rapid-solidification front propagating in a hypercooled melt when the solidification process is controlled by kinetics and there are cubic anisotropies of surface tension and attachment kinetics. It is shown that, due to anisotropy, the threshold of Morphological Instability depends on the direction of the crystal growth and generates, in the general case, traveling cells (waves) propagating on the solidification front in a preferred direction determined by the anisotropy coefficients. Weakly nonlinear analysis of the waves is carried out in the vicinity of the Instability threshold and it is shown that the evolution of the waves is usually governed by an anisotropic dissipation-modified Korteweg-de Vries equation. In special cases it is governed by an anisotropic Kuramoto-Sivashinsky equation that describes stationary cells. Regions in the parameter space are found where the stationary and traveling cells are stable and could be observed in experiment. The characteristics of the cells are studied as functions of the direction of the crystal growth.

  • Shear stabilization of Morphological Instability during directional solidification
    Journal of Crystal Growth, 1995
    Co-Authors: T. P. Schulze, Stephen H. Davis
    Abstract:

    Abstract A linear stability analysis is performed on the interface formed during the directional solidification of a dilute binary alloy in the presence of a time-periodic flow. In general, the flow is generated by translating the crystal relative to the far-field flow in elliptical orbits parallel to the interface. The presence of this complex, unsteady flow can either stabilize or destabilize the system relative to the case without flow, with the result depending on the frequency and amplitude of the oscillations as well as the properties of the material. We find, however, that proper selection of the frequency and amplitude of the modulation, both physically realizable, can eliminate the possibility of Morphological Instability for a significant range of solute concentrations.

Peter W. Voorhees - One of the best experts on this subject based on the ideXlab platform.

  • Morphological Instability of ferromagnetic thin films
    Journal of Applied Physics, 2009
    Co-Authors: Peter W. Voorhees
    Abstract:

    We investigate the Morphological Instability of ferromagnetic planar thin films using linear perturbation theory. We find that, for a uniformly magnetized ferromagnetic planar film with a nonzero component of the magnetization along the normal to the planar film, the planar surface is unstable with respect to perturbations having a wave number smaller than a critical value. In addition, the critical wave number changes with the direction of the surface perturbations, with the perturbations perpendicular to the in-plane component of the magnetization having the largest critical wave number. Such anisotropy could be important in controlling the evolution of the morphology of the film and nanoscale-island formation.

  • The effect of surface stress and wetting layers on Morphological Instability in epitaxially strained films
    Journal of Applied Physics, 2004
    Co-Authors: T. V. Savina, Peter W. Voorhees, Stephen H. Davis
    Abstract:

    This paper investigates effects of surface stress and wetting layers on the Morphological Instability of a growing epitaxially strained dislocation-free solid film. Linear stability analysis of the planar film shows that the film, unstable due to lattice mismatch, is affected differently by surface stress for a film under compression than for one under tension and depends on whether the relative stiffness of the film to the substrate is less than or greater than (1−2ν)−1; here ν is Poisson’s ratio. The presence of a wetting layer has the capacity to substantially stabilize the planar film. The critical thickness of the film below which the film is stable depends on the bulk elastic properties of film and substrate and increases with increase of the wetting potential.

  • Morphological Instability of pores and tubules
    Interfaces and Free Boundaries, 2002
    Co-Authors: Dimitri J Kirill, Michael J Miksis, Stephen H. Davis, Peter W. Voorhees
    Abstract:

    We present a linear stability analysis of a uniaxially stressed, hollow cylindrical tubule, where the mass transport mechanism is surface diffusion driven by surface curvature- and elastic-energy. We find that there are always two distinct eigenmodes for any choice of wavenumbers, applied stress, and geometry. We also find that applied stress has a destabilizing effect, increasing the range of unstable wavenumbers. For any choice of applied stress and geometry, the most dangerous mode is axisymmetric, and can be either sinuous or varicose depending on choices of geometry and applied stress. The case of a cylindrical pore in a stressed infinite solid emerges as a limiting case.

  • Ordered growth of nanocrystals via a Morphological Instability
    Applied Physics Letters, 2002
    Co-Authors: J. J. Eggleston, Peter W. Voorhees
    Abstract:

    Nanocrystal formation on patterned substrates during heteroepitaxy is studied. Deposition on a substrate with a mesa induces a qualitatively new Morphological Instability that is driven solely by capillarity. If the film possesses a lattice parameter misfit with the substrate, this Instability then propagates as a traveling wave along the substrate. This traveling wave yields large regions of highly ordered nanocrystals. Strongly anisotropic surface energy greatly increases the growth rate of the Instability of a planar film and, thus, decreases the distance over which the traveling wave propagates. Even in this case, however, deposition on a substrate with a periodic arrangement of mesas can yield highly ordered arrays of nanocrystals.

  • Morphological Instability of a whisker
    Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 1999
    Co-Authors: D J Kirill, Stephen H. Davis, Michael J Miksis, Peter W. Voorhees
    Abstract:

    A thin stressed solid cylinder, a whisker, is subject to mass transport by curvature and elasticstressdriven surface diffusion. The stability of the cylindrical surface is examined using linear sta...

L. Zhang - One of the best experts on this subject based on the ideXlab platform.

  • In situ TEM observations on Morphological Instability of ultrathin Pb films
    Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2004
    Co-Authors: Manling Sui, L. Zhang
    Abstract:

    Abstract An ultrathin bilayer Pb–Al film was made by cold rolling and ion beam thinning techniques. Morphological Instability of the Pb layer under electron beam irradiation was investigated by means of in situ transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM). Morphological Instability of the Pb layer was characterized by spheroidization of Pb film and coalescence of Pb particles. Under electron beam irradiation, the ultrathin Pb layer with an incoherent Pb–Al interface was unstable and sphericized into Pb particles with an initial size about 3 nm. The Pb particles were mobile on the Al substrate and the coalescence of Pb particles took place. The Pb particles grew up only in the way of coalescence and the mobility of the particles decreased with the particle size increasing. The growth rates of Pb particles in different stages of coalescence were measured, respectively. The mechanism of spheroidization and coalescence was discussed. Driving forces for the spheroidization and the coalescence were attributed to minimizing the total energy. The intensive motion of the surface atoms for the Pb films and particles under irradiation activated the Morphological Instability of the system.

J S Wettlaufer - One of the best experts on this subject based on the ideXlab platform.

  • Morphological Instability of a non equilibrium ice colloid interface
    Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2010
    Co-Authors: S S L Peppin, Apala Majumdar, J S Wettlaufer
    Abstract:

    We assess the Morphological stability of a non-equilibrium ice–colloidal suspension interface, and apply the theory to bentonite clay. An experimentally convenient scaling is employed that takes advantage of the vanishing segregation coefficient at low freezing velocities, and when anisotropic kinetic effects are included, the interface is shown to be unstable to travelling waves. The potential for travelling-wave modes reveals a possible mechanism for the polygonal and spiral ice lenses observed in frozen clays. A weakly nonlinear analysis yields a long-wave evolution equation for the interface shape containing a new parameter related to the highly nonlinear liquidus curve in colloidal systems. We discuss the implications of these results for the frost susceptibility of soils and the fabrication of microtailored porous materials.

  • experimental verification of Morphological Instability in freezing aqueous colloidal suspensions
    Physical Review Letters, 2008
    Co-Authors: S S L Peppin, J S Wettlaufer, M G Worster
    Abstract:

    We describe an experimental test of a new theory of the unidirectional freezing of aqueous colloidal suspensions. At low freezing speeds a planar ice lens completely rejects the particles, forming a steady-state compacted boundary layer in the liquid region. At higher speeds the planar interface becomes thermodynamically unstable and breaks down geometrically to trap bulk regions of colloid within. The theoretical stability threshold is determined experimentally, thereby demonstrating that colloidal suspensions can be treated analogously to atomic or molecular alloys.

  • Evaporatively driven Morphological Instability.
    Physical review. E Statistical nonlinear and soft matter physics, 2007
    Co-Authors: Robert W Style, J S Wettlaufer
    Abstract:

    Simple observations of evaporating solutions reveal a complex hierarchy of spatiotemporal instabilities. We analyze one such Instability suggested by the qualitative observations of Du and Stone and find that it is driven by a variant of the classical Morphological Instability in alloy solidification. In the latter case a moving solid-liquid interface is accompanied by a solutally enriched boundary layer that is thermodynamically metastable due to constitutional supercooling. Here, we consider the evaporation of an impure film adjacent to a solid composed of the nonvolatile species. In this case, constitutional supercooling within the film is created by evaporation at the solution-vapor interface and this drives the corrugation of the solid-solution interface across the thickness of the film. The principal points of this simple theoretical study are to suggest an Instability mechanism that is likely operative across a broad range of technological and natural systems and to focus future quantitative experimental searches.

  • Morphological Instability in freezing colloidal suspensions
    Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2007
    Co-Authors: S S L Peppin, Grae M Worster, J S Wettlaufer
    Abstract:

    We present a linear stability analysis of a planar ice interface during unidirectional solidification of a hard-sphere colloidal suspension. We find that the interface can become unstable due to constitutional supercooling, yielding a new mechanism for pattern formation in colloidal systems. The interfacial stability is shown to depend strongly on the size and concentration of the particles. Increasing the particle radius tends to stabilize the interface, while increasing the concentration has a destabilizing effect. Additional effects that may influence the stability and morphology of such a system are described.

Brian Spencer - One of the best experts on this subject based on the ideXlab platform.

  • Nonlinear evolution of the stress-driven Morphological Instability in a two-dimensional semi-infinite solid
    Acta Metallurgica et Materialia, 1994
    Co-Authors: Brian Spencer, D.i. Meiron
    Abstract:

    Abstract We consider the nonlinear evolution of the stress-driven Morphological Instability on the surface of a two dimensional semi-infinite solid. We track the branch of steady state solutions numerically and find that the solution branch terminates. The surface shape at the point of termination has a cusp singularity that points into the solid. We also consider the time-dependent evolution of the Instability from small disturbances as a function of disturbance wavenumber. We find that the formation of singular grooves in the solid is a general feature of the nonlinear evolution of the Instability. Various physical factors which may affect formation of the singularity are discussed.

  • Morphological Instability in epitaxially strained dislocation free solid films linear stability theory
    Journal of Applied Physics, 1993
    Co-Authors: Brian Spencer, Peter W. Voorhees, Stephen H. Davis
    Abstract:

    The Morphological Instability of a growing epitaxially strained dislocation‐free solid film is analyzed. An evolution equation for the film surface is derived in the dilute limit of vacancies based on surface diffusion driven by a stress‐dependent chemical potential. From the time‐dependent linear stability problem the conditions for which a growing film is unstable are determined. It is found that the Instability is driven by the lattice mismatch between the film and the substrate; however, low temperatures as well as elastically stiff substrates are stabilizing influences. The results also reveal that the critical film thickness for Instability depends on the growth rate of the film itself. Detailed comparison with experimental observations indicates that the Instability described exhibits many of the observed features of the onset of the ‘‘island Instability.’’

  • Morphological Instability in epitaxially strained dislocation-free solid films.
    Physical review letters, 1991
    Co-Authors: Brian Spencer, Peter W. Voorhees, Stephen H. Davis
    Abstract:

    We perform the first analysis of the Morphological Instability of a growing epitaxially strained dislocation-free olid film. We derive an evolution equation for the film surface based on surface diffusion driven by a stress-dependent chemical potential. From the time-dependent linear stability problem we determine the conditions for which a growing film is unstable. Our results reveal that the critical film thickness for Instability depends on the growth rate of the film itself, and that the Instability we describe exhibits many of the observed features of the onset of the ``island Instability.''