402 research outputs found
Conformal Dynamics of Precursors to Fracture
An exact integro-differential equation for the conformal map from the unit
circle to the boundary of an evolving cavity in a stressed 2-dimensional solid
is derived. This equation provides an accurate description of the dynamics of
precursors to fracture when surface diffusion is important. The solution
predicts the creation of sharp grooves that eventually lead to material failure
via rapid fracture. Solutions of the new equation are demonstrated for the
dynamics of an elliptical cavity and the stability of a circular cavity under
biaxial stress, including the effects of surface stress.Comment: 4 pages, 3 figure
Phase Field Modeling of Fast Crack Propagation
We present a continuum theory which predicts the steady state propagation of
cracks. The theory overcomes the usual problem of a finite time cusp
singularity of the Grinfeld instability by the inclusion of elastodynamic
effects which restore selection of the steady state tip radius and velocity. We
developed a phase field model for elastically induced phase transitions; in the
limit of small or vanishing elastic coefficients in the new phase, fracture can
be studied. The simulations confirm analytical predictions for fast crack
propagation.Comment: 5 pages, 11 figure
Wetting layer thickness and early evolution of epitaxially strained thin films
We propose a physical model which explains the existence of finite thickness
wetting layers in epitaxially strained films. The finite wetting layer is shown
to be stable due to the variation of the non-linear elastic free energy with
film thickness. We show that anisotropic surface tension gives rise to a
metastable enlarged wetting layer. The perturbation amplitude needed to
destabilize this wetting layer decreases with increasing lattice mismatch. We
observe the development of faceted islands in unstable films.Comment: 4 pages, 3 eps figure
Modeling Elasticity in Crystal Growth
A new model of crystal growth is presented that describes the phenomena on
atomic length and diffusive time scales. The former incorporates elastic and
plastic deformation in a natural manner, and the latter enables access to times
scales much larger than conventional atomic methods. The model is shown to be
consistent with the predictions of Read and Shockley for grain boundary energy,
and Matthews and Blakeslee for misfit dislocations in epitaxial growth.Comment: 4 pages, 10 figure
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
A lattice model describing scale effects in nonlinear elasticity of nano-inhomogeneities
We present a procedure to map the constitutive laws of elasticity (both in
the linear and nonlinear regime) onto a discrete atomic lattice and we apply
the resulting elastic lattice model to investigate the strain field within an
embedded nano-inhomogeneity. We prove that its elastic behavior at the
nanoscale is governed by relevant atomistic effects. In particular, we
demonstrate that such effects on the linear and nonlinear elastic properties
are described by the same scaling exponent, in a large range of elastic
contrast between the matrix and the nano-inhomogeneity. This suggests that the
linear and nonlinear elastic behaviors of the composite system belong to the
same universality class (at least within the nanometer length scale here
investigated).Comment: Accepted on Phys.Rev.B (2010) (in press
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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