337 research outputs found
Percolation-dependent Reaction Rates in the Etching of Disordered Solids
A prototype statistical model for the etching of a random solid is
investigated in order to assess the influence of disorder and temperature on
the dissolution kinetics. At low temperature, the kinetics is dominated by
percolation phenomena, and the percolation threshold determines the global
reaction time. At high temperature, the fluctuations of the reaction rate are
Gaussian, whereas at low temperature they exhibit a power law tail due to
chemical avalanches. This is an example where microscopic disorder directly
induces non-classical chemical kinetics.Comment: Revtex, 4 pages, 5 figure
Diffuse-interface model for nanopatterning induced by self-sustained ion etch masking
We construct a simple phenomenological diffuse-interface model for
composition-induced nanopatterning during ion sputtering of alloys. In
simulations, this model reproduces without difficulties the high-aspect ratio
structures and tilted pillars observed in experiments. We investigate the time
evolution of the pillar height, both by simulations and by {\it in situ}
ellipsometry. The analysis of the simulation results yields a good
understanding of the transitions between different growth regimes and supports
the role of segregation in the pattern-formation process.Comment: 10 pages, 3 figures; minor revisions with respect to first version;
figures nicened; journal ref. adde
Stability of hexagonal solidification patterns
We investigate the dynamics of cellular solidification patterns using
three-dimensional phase-field simulations. The cells can organize into stable
hexagonal patterns or exhibit unsteady evolutions. We identify the relevant
secondary instabilities of regular hexagonal arrays and find that the stability
boundaries depend significantly on the strength of crystalline anisotropy. We
also find multiplet states that can be reached by applying well-defined
perturbations to a pre-existing hexagonal array.Comment: Minor changes, mainly in introduction and conclusion, one reference
adde
A mean-field kinetic lattice gas model of electrochemical cells
We develop Electrochemical Mean-Field Kinetic Equations (EMFKE) to simulate
electrochemical cells. We start from a microscopic lattice-gas model with
charged particles, and build mean-field kinetic equations following the lines
of earlier work for neutral particles. We include the Poisson equation to
account for the influence of the electric field on ion migration, and
oxido-reduction processes on the electrode surfaces to allow for growth and
dissolution. We confirm the viability of our approach by simulating (i) the
electrochemical equilibrium at flat electrodes, which displays the correct
charged double-layer, (ii) the growth kinetics of one-dimensional
electrochemical cells during growth and dissolution, and (iii) electrochemical
dendrites in two dimensions.Comment: 14 pages twocolumn, 17 figure
Eutectic colony formation: A phase field study
Eutectic two-phase cells, also known as eutectic colonies, are commonly
observed during the solidification of ternary alloys when the composition is
close to a binary eutectic valley. In analogy with the solidification cells
formed in dilute binary alloys, colony formation is triggered by a
morphological instability of a macroscopically planar eutectic solidification
front due to the rejection by both solid phases of a ternary impurity that
diffuses in the liquid. Here we develop a phase-field model of a binary
eutectic with a dilute ternary impurity and we investigate by dynamical
simulations both the initial linear regime of this instability, and the
subsequent highly nonlinear evolution of the interface that leads to fully
developed two-phase cells with a spacing much larger than the lamellar spacing.
We find a good overall agreement with our recent linear stability analysis [M.
Plapp and A. Karma, Phys. Rev. E 60, 6865 (1999)], which predicts a
destabilization of the front by long-wavelength modes that may be stationary or
oscillatory. A fine comparison, however, reveals that the assumption commonly
attributed to Cahn that lamella grow perpendicular to the envelope of the
solidification front is weakly violated in the phase-field simulations. We show
that, even though weak, this violation has an important quantitative effect on
the stability properties of the eutectic front. We also investigate the
dynamics of fully developed colonies and find that the large-scale envelope of
the composite eutectic front does not converge to a steady state, but exhibits
cell elimination and tip-splitting events up to the largest times simulated.Comment: 18 pages, 18 EPS figures, RevTeX twocolumn, submitted to Phys. Rev.
Phase field theory of polycrystalline solidification in three dimensions
A phase field theory of polycrystalline solidification is presented that is
able to describe the nucleation and growth of anisotropic particles with
different crystallographic orientation in three dimensions. As opposed with the
two-dimensional case, where a single orientation field suffices, in three
dimensions, minimum three fields are needed. The free energy of grain
boundaries is assumed to be proportional to the angular difference between the
adjacent crystals expressed here in terms of the differences of the four
symmetric Euler parameters. The equations of motion for these fields are
obtained from variational principles. Illustrative calculations are performed
for polycrystalline solidification with dendritic, needle and spherulitic
growth morphologies.Comment: 7 pages, 4 figures, submitted to Europhysics Letters on 14th
February, 200
Current Induced Fingering Instability in Magnetic Domain Walls
The shape instability of magnetic domain walls under current is investigated
in a ferromagnetic (Ga,Mn)(As,P) film with perpendicular anisotropy. Domain
wall motion is driven by the spin transfer torque mechanism. A current density
gradient is found either to stabilize domains with walls perpendicular to
current lines or to produce finger-like patterns, depending on the domain wall
motion direction. The instability mechanism is shown to result from the
non-adiabatic contribution of the spin transfer torque mechanism.Comment: 5 pages, 3 figures + supplementary material
Phase-Field Formulation for Quantitative Modeling of Alloy Solidification
A phase-field formulation is introduced to simulate quantitatively
microstructural pattern formation in alloys. The thin-interface limit of this
formulation yields a much less stringent restriction on the choice of interface
thickness than previous formulations and permits to eliminate non-equilibrium
effects at the interface. Dendrite growth simulations with vanishing solid
diffusivity show that both the interface evolution and the solute profile in
the solid are well resolved
Phase-Field Approach for Faceted Solidification
We extend the phase-field approach to model the solidification of faceted
materials. Our approach consists of using an approximate gamma-plot with
rounded cusps that can approach arbitrarily closely the true gamma-plot with
sharp cusps that correspond to faceted orientations. The phase-field equations
are solved in the thin-interface limit with local equilibrium at the
solid-liquid interface [A. Karma and W.-J. Rappel, Phys. Rev. E53, R3017
(1996)]. The convergence of our approach is first demonstrated for equilibrium
shapes. The growth of faceted needle crystals in an undercooled melt is then
studied as a function of undercooling and the cusp amplitude delta for a
gamma-plot of the form 1+delta(|sin(theta)|+|cos(theta)|). The phase-field
results are consistent with the scaling law "Lambda inversely proportional to
the square root of V" observed experimentally, where Lambda is the facet length
and V is the growth rate. In addition, the variation of V and Lambda with delta
is found to be reasonably well predicted by an approximate sharp-interface
analytical theory that includes capillary effects and assumes circular and
parabolic forms for the front and trailing rough parts of the needle crystal,
respectively.Comment: 1O pages, 2 tables, 17 figure
- …