1,089 research outputs found
Phase field modeling of electrochemistry II: Kinetics
The kinetic behavior of a phase field model of electrochemistry is explored
for advancing (electrodeposition) and receding (electrodissolution) conditions
in one dimension. We described the equilibrium behavior of this model in [J. E.
Guyer, W. J. Boettinger, J.A. Warren, and G. B. McFadden, ``Phase field
modeling of electrochemistry I: Equilibrium'', cond-mat/0308173]. We examine
the relationship between the parameters of the phase field method and the more
typical parameters of electrochemistry. We demonstrate ohmic conduction in the
electrode and ionic conduction in the electrolyte. We find that, despite making
simple, linear dynamic postulates, we obtain the nonlinear relationship between
current and overpotential predicted by the classical ``Butler-Volmer'' equation
and observed in electrochemical experiments. The charge distribution in the
interfacial double layer changes with the passage of current and, at
sufficiently high currents, we find that the diffusion limited deposition of a
more noble cation leads to alloy deposition with less noble species.Comment: v3: To be published in Phys. Rev. E v2: Attempt to work around
turnpage bug. Replaced color Fig. 4a with grayscale 13 pages, 7 figures in 10
files, REVTeX 4, SIunits.sty, follows cond-mat/030817
Phase field modeling of electrochemistry I: Equilibrium
A diffuse interface (phase field) model for an electrochemical system is
developed. We describe the minimal set of components needed to model an
electrochemical interface and present a variational derivation of the governing
equations. With a simple set of assumptions: mass and volume constraints,
Poisson's equation, ideal solution thermodynamics in the bulk, and a simple
description of the competing energies in the interface, the model captures the
charge separation associated with the equilibrium double layer at the
electrochemical interface. The decay of the electrostatic potential in the
electrolyte agrees with the classical Gouy-Chapman and Debye-H\"uckel theories.
We calculate the surface energy, surface charge, and differential capacitance
as functions of potential and find qualitative agreement between the model and
existing theories and experiments. In particular, the differential capacitance
curves exhibit complex shapes with multiple extrema, as exhibited in many
electrochemical systems.Comment: v3: To be published in Phys. Rev. E v2: Added link to
cond-mat/0308179 in References 13 pages, 6 figures in 15 files, REVTeX 4,
SIUnits.sty. Precedes cond-mat/030817
Epitaxial growth in dislocation-free strained alloy films: Morphological and compositional instabilities
The mechanisms of stability or instability in the strained alloy film growth
are of intense current interest to both theorists and experimentalists. We
consider dislocation-free, coherent, growing alloy films which could exhibit a
morphological instability without nucleation. We investigate such strained
films by developing a nonequilibrium, continuum model and by performing a
linear stability analysis. The couplings of film-substrate misfit strain,
compositional stress, deposition rate, and growth temperature determine the
stability of film morphology as well as the surface spinodal decomposition. We
consider some realistic factors of epitaxial growth, in particular the
composition dependence of elastic moduli and the coupling between top surface
and underlying bulk of the film. The interplay of these factors leads to new
stability results. In addition to the stability diagrams both above and below
the coherent spinodal temperature, we also calculate the kinetic critical
thickness for the onset of instability as well as its scaling behavior with
respect to misfit strain and deposition rate. We apply our results to some real
growth systems and discuss the implications related to some recent experimental
observations.Comment: 26 pages, 13 eps figure
A Model for Solid He: II
We propose a simple Ginzburg-Landau free energy to describe the magnetic
phase transition in solid He. The free energy is analyzed with due
consideration of the hard first order transitions at low magnetic fields. The
resulting phase diagram contains all of the important features of the
experimentally observed ph ase diagram. The free energy also yields a critical
field at which the transition from the disordered state to the high field state
changes from a first order to a second order one.Comment: This paper has been accepted for publication in Journal of Low
Temperature Physics. Use regular Tex, with the D. Eardley version of Macros
called jnl.tex. 10 pages, 4 figs available from [email protected]
Thermodynamics of non-local materials: extra fluxes and internal powers
The most usual formulation of the Laws of Thermodynamics turns out to be
suitable for local or simple materials, while for non-local systems there are
two different ways: either modify this usual formulation by introducing
suitable extra fluxes or express the Laws of Thermodynamics in terms of
internal powers directly, as we propose in this paper. The first choice is
subject to the criticism that the vector fluxes must be introduced a posteriori
in order to obtain the compatibility with the Laws of Thermodynamics. On the
contrary, the formulation in terms of internal powers is more general, because
it is a priori defined on the basis of the constitutive equations. Besides it
allows to highlight, without ambiguity, the contribution of the internal powers
in the variation of the thermodynamic potentials. Finally, in this paper, we
consider some examples of non-local materials and derive the proper expressions
of their internal powers from the power balance laws.Comment: 16 pages, in press on Continuum Mechanics and Thermodynamic
Stress-driven instability in growing multilayer films
We investigate the stress-driven morphological instability of epitaxially
growing multilayer films, which are coherent and dislocation-free. We construct
a direct elastic analysis, from which we determine the elastic state of the
system recursively in terms of that of the old states of the buried layers. In
turn, we use the result for the elastic state to derive the morphological
evolution equation of surface profile to first order of perturbations, with the
solution explicitly expressed by the growth conditions and material parameters
of all the deposited layers. We apply these results to two kinds of multilayer
structures. One is the alternating tensile/compressive multilayer structure,
for which we determine the effective stability properties, including the effect
of varying surface mobility in different layers, its interplay with the global
misfit of the multilayer film, and the influence of asymmetric structure of
compressive and tensile layers on the system stability. The nature of the
asymmetry properties found in stability diagrams is in agreement with
experimental observations. The other multilayer structure that we study is one
composed of stacked strained/spacer layers. We also calculate the kinetic
critical thickness for the onset of morphological instability and obtain its
reduction and saturation as number of deposited layers increases, which is
consistent with recent experimental results. Compared to the single-layer film
growth, the behavior of kinetic critical thickness shows deviations for upper
strained layers.Comment: 27 pages, 11 figures; Phys. Rev. B, in pres
A new echocardiographic model for quantifying three-dimensional endocardial surface area
A new technique for quantitatively mapping the three-dimensional left ventricular endocardial surface was developed, using measurements from standard cross-sectional echocardiographic images. To validate the accuracy of this echocardiographic mapping technique in an animal model, the endocardial areas of 15 excised canine ventricles were calculated using measurements made from echocardiographic studies of the hearts and compared with areas determined with latex casts of the same ventricles. Close correlation (r = 0.87, p < 0.001) between these two measures of endocardial area provided preliminary confirmation of the accuracy of the maps.To further characterize the mapping algorithm, it was translated into computer format and used to map the surfaces of idealized hemiellipsoids. Areas measured with this mapping technique closely approximated the actual areas of idealized surfaces with a wide spectrum of shapes; maps were particularly accurate for ellipsoids with shapes similar to those of undistorted human ventricles. Also, the accuracies of area calculations were relatively insensitive to deviation from the assumed positions of the echocardiographic short-axis planes. Finally, although the accuracy of the mapping technique improved as data from more transverse planes were added, the procedure proved reliable for estimating surface areas when data from only three planes were used. These studies confirm the accuracy of the echocardiographic mapping technique, and they suggest that the resulting planar plots might be useful as templates for localizing and quantifying the overall extent of abnormal wall motion
Critical dimensions for random walks on random-walk chains
The probability distribution of random walks on linear structures generated
by random walks in -dimensional space, , is analytically studied
for the case . It is shown to obey the scaling form
, where is
the density of the chain. Expanding in powers of , we find that
there exists an infinite hierarchy of critical dimensions, ,
each one characterized by a logarithmic correction in . Namely, for
, ; for ,
; for , ; for , ; for , , {\it etc.\/} In particular, for
, this implies that the temporal dependence of the probability density of
being close to the origin .Comment: LATeX, 10 pages, no figures submitted for publication in PR
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