196 research outputs found
Influence of uniaxial stress on the lamellar spacing of eutectics
Directional solidification of lamellar eutectic structures submitted to
uniaxial stress is investigated. In the spirit of an approximation first used
by Jackson and Hunt, we calculate the stress tensor for a two-dimensional
crystal with triangular surface, using a Fourier expansion of the Airy
function. crystal with triangular surface in contact with its melt, given that
a uniaxial external stress is applied. The effect of the resulting change in
chemical potential is introduced into the standard model for directional
solidification of a lamellar eutectic. This calculation is motivated by an
observation, made recently [I. Cantat, K. Kassner, C. Misbah, and H.
M\"uller-Krumbhaar, Phys. Rev. E, in press] that the thermal gradient produces
similar effects as a strong gravitational field in the case of dilute-alloy
solidification. Therefore, the coupling between the Grinfeld and the
Mullins-Sekerka instabilities becomes strong, as the critical wavelength of the
former instability gets reduced to a value close to that of the latter.
Analogously, in the case of eutectics, the characteristic length scale of the
Grinfeld instability should be reduced to a size not extremely far from typical
lamellar spacings. In a Jackson-Hunt like approach we average the undercooling,
including the stress term, over a pair of lamellae. Following Jackson and Hunt,
we assume the selected wavelength to be determined by the minimum undercooling
criterion and compute its shift due to the external stress. we realize the
shifting of the wavelength by the application of external stress. In addition,
we find that in general the volume fraction of the two solid phases is changed
by uniaxial stress. Implications for experiments on eutectics are discussed.Comment: 8 pages RevTex, 6 included ps-figures, accepted for Phys. Rev.
Phase-field-crystal model for liquid crystals
Based on static and dynamical density functional theory, a
phase-field-crystal model is derived which involves both the translational
density and the orientational degree of ordering as well as a local director
field. The model exhibits stable isotropic, nematic, smectic A, columnar,
plastic crystalline and orientationally ordered crystalline phases. As far as
the dynamics is concerned, the translational density is a conserved order
parameter while the orientational ordering is non-conserved. The derived
phase-field-crystal model can serve for efficient numerical investigations of
various nonequilibrium situations in liquid crystals
Anisotropy and Morphology of Strained III-V Heteroepitaxial Films
Strained coherent heteroepitaxy of III-V semiconductor films such as
InGaAs/GaAs has potential for electronic and optoelectronic
applications such as high density logic, quantum computing architectures, laser
diodes, and other optoelectronic devices. Crystal symmetry can have a large
effect on the morphology of these films and their spatial order. Often the
formation of group IV strained heterostructures such as Ge deposited on Si is
analyzed using analytic models based on the Asaro-Tiller-Grinfeld instability.
However, the governing dynamics of III-V 3D heterostructure formation has
different symmetry and is more anisotropic. The additional anisotropy appears
in both the surface energy and the diffusivity. Here, the resulting anisotropic
governing dynamics are studied to linear order. The resulting possible film
morphologies are compared with experimentally observed InGaAs/GaAs
films. Notably it is found that surface-energy anisotropy plays a role at least
as important as surface diffusion anisotropy if not more so, in contrast to
previous suppositions.Comment: 2 figures version includes one corrected inline equatio
Existence and stability of singular patterns in a GinzburgāLandau equation coupled with a mean field
We study singular patterns in a particular system of parabolic partial differential equations which consist of a GinzburgāLandau equation and a mean field equation. We prove the existence of the three simplest concentrated periodic stationary patterns (single spikes, double spikes, double transition layers) by composing them of more elementary patterns and solving the corresponding consistency conditions. In the case of spike patterns we prove stability for sufficiently large spatial periods by first showing that the eigenvalues do not tend to zero as the period goes to infinity and then passing in the limit to a nonlocal eigenvalue problem which can be studied explicitly. For the two other patterns we show instability by using the variational characterization of eigenvalues
Model of surface instabilities induced by stress
We propose a model based on a Ginzburg-Landau approach to study a strain
relief mechanism at a free interface of a non-hydrostatically stressed solid,
commonly observed in thin-film growth. The evolving instability, known as the
Grinfeld instability, is studied numerically in two and three dimensions.
Inherent in the description is the proper treatment of nonlinearities. We find
these nonlinearities can lead to competitive coarsening of interfacial
structures, corresponding to different wavenumbers, as strain is relieved. We
suggest ways to experimentally measure this coarsening.Comment: 4 pages (3 figures included
Finite to infinite steady state solutions, bifurcations of an integro-differential equation
We consider a bistable integral equation which governs the stationary
solutions of a convolution model of solid--solid phase transitions on a circle.
We study the bifurcations of the set of the stationary solutions as the
diffusion coefficient is varied to examine the transition from an infinite
number of steady states to three for the continuum limit of the
semi--discretised system. We show how the symmetry of the problem is
responsible for the generation and stabilisation of equilibria and comment on
the puzzling connection between continuity and stability that exists in this
problem
Stability of Solid State Reaction Fronts
We analyze the stability of a planar solid-solid interface at which a
chemical reaction occurs. Examples include oxidation, nitridation, or silicide
formation. Using a continuum model, including a general formula for the
stress-dependence of the reaction rate, we show that stress effects can render
a planar interface dynamically unstable with respect to perturbations of
intermediate wavelength
Amplitude equations for systems with long-range interactions
We derive amplitude equations for interface dynamics in pattern forming
systems with long-range interactions. The basic condition for the applicability
of the method developed here is that the bulk equations are linear and solvable
by integral transforms. We arrive at the interface equation via long-wave
asymptotics. As an example, we treat the Grinfeld instability, and we also give
a result for the Saffman-Taylor instability. It turns out that the long-range
interaction survives the long-wave limit and shows up in the final equation as
a nonlocal and nonlinear term, a feature that to our knowledge is not shared by
any other known long-wave equation. The form of this particular equation will
then allow us to draw conclusions regarding the universal dynamics of systems
in which nonlocal effects persist at the level of the amplitude description.Comment: LaTeX source, 12 pages, 4 figures, accepted for Physical Review
Prepyramid-to-pyramid transition of SiGe islands on Si(001)
The morphology of the first three-dimensional islands appearing during
strained growth of SiGe alloys on Si(001) was investigated by scanning
tunneling microscopy. High resolution images of individual islands and a
statistical analysis of island shapes were used to reconstruct the evolution of
the island shape as a function of size. As they grow, islands undergo a
transition from completely unfacetted rough mounds (prepyramids) to partially
{105} facetted islands and then they gradually evolve to {105} facetted
pyramids. The results are in good agreement with the predictions of a recently
proposed theoretical model
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