Effect Of Surface Energy Anisotropy Research Articles

Effect of surface energy anisotropy on hole growth in a single-crystalline thin film: A phase-field study

Prediction of the temporal evolution of a pre-existing hole on a solid-state thin film has important implications for self-organized nanoscale pattern formation. In this work, we employ a three-dimensional phase-field model to elucidate the mechanism of corner instability during capillary-driven hole growth in a single-crystalline free-standing thin film. We perform a systematic study to demonstrate the effect of crystalline anisotropy in surface energy, surface diffusivity, and film thickness on hole growth. Our simulations reveal that the instability during hole growth arises due to saturation of the rim height at the corner of the hole that is directly related to the arc length of the corner, specified by the anisotropy in surface energy. Our investigation further reveals the presence of a time-invariant shape of the corner with the onset of corner instability.

The role of surface energy anisotropy in the formation of a stepped relief of polycrystalline W under sputtering with Ar ions

This paper is devoted to the study of the effect of surface energy anisotropy on the tungsten surface relief modification under ion sputtering. In our experiments, the sputtering of textured polycrystalline tungsten with Ar ions resulted in a stepped surface relief formation. The surface after sputtering was analyzed using the electron backscatter diffraction and confocal laser scanning microscopy techniques. The formation of the stepped relief is explained by different surface energies of differently oriented grains (surface energy anisotropy). The surface energies of the three low-index W planes were calculated in the model of broken bonds. It is shown for the first time that the ratio of the sputtering depth of differently oriented grains of W is equal to the ratio of the differences of the surface energies of these grains. In that way, the ratio of the sputtering yields of differently oriented grains of tungsten can be quantified by knowing the surface energy, which depended on the reticular grain density and the number of broken bonds with nearest and next-nearest neighboring atoms on the surface using the broken bond model. It is shown that ion sputtering can be used as an instrument for studying the surface energy of solids.

Equilibrium and dynamics of strained islands.

We focus in this work on the effect of the surface energy anisotropy on an elastically strained semiconductor film and in particular on its role on the coarsening dynamics of elastically strained islands. To study the dynamics of a strained film, we establish a one-dimensional nonlinear and nonlocal partial differential equation which takes into account the elastic, capillary, wetting, and anisotropic effects. We first construct an approximate stationary solution of our model using a variational method and an appropriate ansatz. This stationary solution is used to compute the chemical potential dependence on the island height. In particular, we find that the surface energy anisotropy increases the convexity of the chemical potential and this is shown to have an effect on the driving force for the coarsening. Second, we study the coarsening dynamics of an islands pair by means of numerical simulations. We find that the presence of the surface energy anisotropy may increase or decrease the coarsening time of the system. We show that this phenomenon depends on the initial heights of island pairs. We thus highlight that the driving force for the coarsening is due to the variation of the chemical potential with respect to the islands height and that two different regimes are possible.

On the strain-induced stabilization of microstructural features formed along dislocations

Capillarity-driven mass transport limits the stability of microstructures with a high surface-to-volume ratio. Fiber reinforcements, dendritic structures, and other wire-like morphologies may be susceptible to Rayleigh instabilities and to concurrent or subsequent coarsening. Decreases in the characteristic length scales of microstructures to the nanoscale make such forms of evolution and instability evident at lower values of homologous temperature, consistent with expectations based on size scaling. Herein, we present a simple continuum theory that predicts that sufficiently small second-phase wires exhibiting dislocation character are stable to both Rayleigh instabilities and coarsening. Thus, defects such as hollow-core dislocations will tend to be stabilized while a freestanding nanowire will tend to be unstable. More generally, the effects of surface-energy anisotropy and strain energy on morphological stability are evaluated in a manner that allows their individual and combined effects on stability to be assessed and mapped.

Effects of surface energy anisotropy on void evolution during irradiation: A phase-field model

A phase-field model is employed to investigate the effects of surface energy anisotropy on void evolution during irradiation. By incorporating a simple orientation dependent surface energy with sharp cusps on given crystallographic orientations, experimentally observed void shape with facets and rounded corners is captured. When applied to polycrystalline materials, grain dependent void morphologies are predicted, and the simulation results are qualitatively similar to reported void morphologies in irradiated copper. In addition, the formation of void denuded zones and vacancy depleted zones adjacent to the grain boundaries (GBs) in bicrystalline and polycrystalline structures are studied.

Effect of Surface Energy Anisotropy on the Stability of Growth Fronts in Multiphase Alloys

Eutectic growth offers a variety of examples for pattern formation which are interesting both for theoreticians as well as experimentalists. One such example of patterns is ternary eutectic colonies which arise as a result of instabilities during growth of two solid phases. Here, in addition to the two major components being exchanged between the solid phases during eutectic growth, there is an impurity component which is rejected by both solid phases. During progress of solidification, there develops a boundary layer of the third impurity component ahead of the solidification front of the two solid phases. Similar to Mullins–Sekerka type instabilities, such a boundary layer tends to make the global solidification envelope unstable to morphological perturbations giving rise to two-phase cells. This phenomenon has been studied numerically in two dimensions for the conditions of directional solidification, by Plapp and Karma (Phys Rev E 66:061608, 2002) using phase-field simulations. While, in the work by Plapp and Karma (Phys Rev E 66:061608, 2002) all interfaces are isotropic, in our presentation, we extend the phase-field model by considering interfacial anisotropy in the solid–solid and solid–liquid interfaces and characterize the role of interfacial anisotropy on the stability of the growth front through phase-field simulations in two dimensions.

Effect of surface energy anisotropy on Rayleigh-like solid-state dewetting and nanowire stability

Nanowires and narrow wires patterned from thin films are usually subject to a Rayleigh-like instability and, when heated, will undergo evolution to particles with a characteristic size and spacing. This process can occur while the wires remain in the solid state. For materials with isotropic surface energies, the characteristic sizes and spacings of the resulting particles or islands are expected to depend only on the initial cross-sectional area of the wires. However, crystalline solids rarely have isotropic surface energy. We show that when wires are patterned from single-crystal films, the rate of particle formation and the characteristic size and spacing of the resulting particles depend strongly on the epitaxial orientation of the film and on the in-plane orientation of the patterned wires, even for wires with the same cross-sectional areas. Wires patterned with in-plane orientations that evolve to be bound by equilibrium facets that extend along the wire axis are found to be highly resistant to dewetting. These wires very slowly dewet into widely spaced particles.

Solid-State Dewetting of Thin Films

Solid films are usually metastable or unstable in the as-deposited state, and they will dewet or agglomerate to form islands when heated to sufficiently high temperatures. This process is driven by surface energy minimization and can occur via surface diffusion well below a film's melting temperature, especially when the film is very thin. Dewetting during processing of films for use in micro- and nanosystems is often undesirable, and means of avoiding dewetting are important in this context. However, dewetting can also be useful in making arrays of nanoscale particles for electronic and photonic devices and for catalyzing growth of nanotubes and nanowires. Templating of dewetting using patterned surface topography or prepatterning of films can be used to create ordered arrays of particles and complex patterns of partially dewetted structures. Studies of dewetting can also provide fundamental new insight into the effects of surface energy anisotropy and facets on shape evolution.

Anisotropy Driven Interrupted Coarsening of the Asaro-Tiller-Grinfeld Instability

We investigate the effects of surface energy anisotropy on the coarsening dynamics of the Asaro-Tiller-Grinfeld instability at stake in thin semiconductor films. We consider a continuum model which accounts for wetting interactions between the film and its substrate, elasticity driven mass currents and surface energy anisotropy. We derive an explicit non-linear, non-local evolution equation for the film height that we solve numerically. Anisotropy, which dictates the island shapes, impacts the growth kinetics by weakening the possible elastic relaxation, which can lead during annealing to an interruption of Ostwald ripening. The resulting stationary state is characterized by square-based pyramids separated by a wetting layer. It is found that the instability onset is delayed when the film thickness decreases above the critical thickness for the instability to occur. We characterize the influence of the growing flux used for the film deposition on the stationary state reached during subsequent annealing, and find that the density of the resulting self-organized islands increases with the flux.

Equilibrium Shape of Internal Cavities in Ruby and the Effect of Surface Energy Anisotropy on the Equilibrium Shape

Cavities formed in ruby (99.46Al2O3·0.54Cr2O3) by the healing and annealing of indentation cracks at 1600°C are more equiaxed than similar cavities in sapphire. Surface energies for the observed facet planes (R, S, and A) relative to the surface energy of the basal plane, C, were γA/C= 1.00 ± 0.03, γR/C= 1.05 ± 0.07, and γS/C= 1.02 ± 0.04, with the uncertainty representing 95% confidence limits. Thus, the surface energies of all observed facets were statistically indistinguishable. Unlike sapphire, P‐plane facets were not observed. The substantial rounding of the cavities in ruby indicated that portions of the Wulff shape were above the roughening transition temperature. Thus, even though Cr2O3 and Al2O3 form ideal solutions, Cr3+ ions are sufficiently surface active to modify the relative free energy of the surfaces.

Effect of surface-energy anisotropy on the kinetics of quantum dot formation

Dynamic continuum simulations of self-organized InAs quantum dot (QD) growth due to competing elastic and surface energetics are presented. The effect of varying the orientational dependence of the surface energy is investigated. It is found that the growth process is very sensitive to the detailed form of this relationship. Smoothly varying anisotropic surface energy functions can be chosen to produce equilibrum QDs of the correct size, shape and, distribution, but the kinetics of the growth process does not agree well with experimental observation. Surface-energy functions with sharp, cusped minima, however, reproduce many of the features of observed growth kinetics and also lead to the development of expected QD morphologies.

Model Studies of Rayleigh Instabilities via Microdesigned Interfaces

The energetic and kinetic properties of surfaces play a critical role in defining the microstructural changes that occur during sintering and high-temperature use of ceramics. Characterization of surface diffusion in ceramics is particularly difficult, and significant variations in reported values of surface diffusivities arise even in well-studied systems. Effects of impurities, surface energy anisotropy, and the onset of surface attachment limited kinetics (SALK) are believed to contribute to this variability. An overview of the use of Rayleigh instabilities as a means of characterizing surface diffusivities is presented. The development of models of morphological evolution that account for effects of surface energy anisotropy is reviewed, and the potential interplay between impurities and surface energy anisotropy is addressed. The status of experimental studies of Rayleigh instabilities in sapphire utilizing lithographically introduced pore channels of controlled geometry and crystallography is summarized. Results of model studies indicate that impurities can significantly influence both the spatial and temporal characteristics of Rayleigh instabilities; this is attributed at least in part to impurity effects on the surface energy anisotropy. Related model experiments indicate that the onset of SALK may also contribute significantly to apparent variations in surface diffusion coefficients.

Equilibrium geometry of a fluid phase in a polycrystalline aggregate with anisotropic surface energies: Dry grain boundaries

The equilibrium distribution of a fluid phase in a rock is controlled by the ratio of grain boundary energy to solid‐fluid interfacial energy (“surface energy”). A strong dependence of interfacial energy on interface orientation (anisotropy) is the rule for solid‐fluid surfaces of geological interest. We investigated the effects of surface energy anisotropy on the equilibrium interface configuration at the junction of two crystals with a fluid in a two‐dimensional solid‐fluid system. The two major effects are to promote the development of planar solid‐fluid interfaces parallel to crystallographic planes of minimum energy and to lead to large variations of the dihedral angle from one triple junction to the other (as a function of the orientation of crystalline lattices relative to the grain boundary). Despite these large variations, the frequency distributions of equilibrium dihedral angles remain unimodal; also the relationship between the mean fluid dihedral angle and the ratio of grain boundary to surface energy is very close to the isotropic law. Even in the most anisotropic systems, the fluid dihedral angle is therefore a parameter of primary importance for predicting the grain‐scale geometry of a low‐volume fraction of fluid and its mobility.

Surface and interface properties of alumina via model studies of microdesigned interfaces

The ability to produce controlled-geometry, controlled-crystallography internal voids in ceramics has made possible several new model experiments for studying the high-temperature properties of surfaces and interfaces in ceramics. Recent advances have enabled the production of more complex microdesigned internal defect structures, and have exploited new means of examining them, thus, broadening the range of problems that can be addressed. A particular topic of concern is the effect of surface energy anisotropy on both the driving force for and the mechanism of shape changes. This paper reviews and previews recent research focussing on improving our understanding of surface diffusion in ceramics. Rayleigh instabilities provide one means of examining morphological evolution. The modelling of Rayleigh instabilities in materials with surface energy anisotropy is reviewed, and the results of experiments utilizing microdesigned pore arrays in sapphire are summarized. In a material with anisotropic surface energy and a facetted Wulff shape, the driving force for shape changes hinges on both the absolute and relative surface energies. Microdesigned pore structures have been used to determine the stable surfaces in both undoped and doped sapphire and to provide the relative values of the energies of these stable surfaces. Nonequilibrium shape, controlled-crystallography cavities have been introduced into undoped sapphire, and the effect of crystallographic orientation on their morphological evolution has been studied. Comparisons of the results with predictions of models of surface-diffusion-controlled evolution indicate that surface-attachment-limited kinetics (SALK) play an important role.

Computer Simulations of the Self-Organized 3-D Islanding in Epitaxial Thin Film Systems

Abstract3-D computer simulations were carried out to investigate the effects of surface energy anisotropy and initial surface roughness on the self-organization of 3-D islands in epitaxial thin film systems. Under the present scheme, the driving force for surface diffusion is the gradient of surface chemical potential, which includes strain energy and surface energy. The simulations demonstrate that the typical sequence of surface evolution is from an initial random surface to a rippled surface, then to irregular islands and then to self-organized islands. Whether the final islands are regular or not depends on both the form of surface energy anisotropy and initial surface roughness. However, the stability and shape transition of the epitaxially strained islands are associated with the form of surface energy anisotropy. The comparisons between the simulations and various experiments were also discussed.

Grain-boundary energy of copper at 1030� C

The grain-boundary energies of individual boundaries have been determined by the analysis of the shapes of grain-boundary grooves. The effects of surface-energy anisotropy are fully taken into account. The results indicate that only boundaries associated with high-coincidence orientations (∑3 and ∑11) have significantly lower energies than average high-angle grain boundaries.