72 research outputs found
Defects and multistability in eutectic solidification patterns
We use three-dimensional phase-field simulations to investigate the dynamics
of the two-phase composite patterns formed upon during solidification of
eutectic alloys. Besides the spatially periodic lamellar and rod patterns that
have been widely studied, we find that there is a large number of additional
steady-state patterns which exhibit stable defects. The defect density can be
so high that the pattern is completely disordered, and that the distinction
between lamellar and rod patterns is blurred. As a consequence, the transition
from lamellae to rods is not sharp, but extends over a finite range of
compositions and exhibits strong hysteresis. Our findings are in good agreement
with experiments.Comment: 6 pages, 8 figure
Remarks on some open problems in phase-field modelling of solidification
International audienceThree different topics in phase-field modelling of solidification are discussed, with particular emphasis on the limitations of the currently available modelling approaches. First, thin-interface limits of two-sided phase-field models are examined, and it is shown that the antitrapping current is in general not sufficient to remove all thin-interface effects. Second, orientation-field models for polycrystalline solidification are analyzed, and it is shown that the standard relaxational equation of motion for the orientation field is incorrect in coherent polycrystalline matter. Third, it is pointed out that the standard procedure of incorporating fluctuations into the phase-field approach cannot be used in a straightforward way for a quantitative description of nucleation
Lattice Boltzmann simulations of 3D crystal growth: Numerical schemes for a phase-field model with anti-trapping current
A lattice-Boltzmann (LB) scheme, based on the Bhatnagar-Gross-Krook (BGK)
collision rules is developed for a phase-field model of alloy solidification in
order to simulate the growth of dendrites. The solidification of a binary alloy
is considered, taking into account diffusive transport of heat and solute, as
well as the anisotropy of the solid-liquid interfacial free energy. The
anisotropic terms in the phase-field evolution equation, the phenomenological
anti-trapping current (introduced in the solute evolution equation to avoid
spurious solute trapping), and the variation of the solute diffusion
coefficient between phases, make it necessary to modify the equilibrium
distribution functions of the LB scheme with respect to the one used in the
standard method for the solution of advection-diffusion equations. The effects
of grid anisotropy are removed by using the lattices D3Q15 and D3Q19 instead of
D3Q7. The method is validated by direct comparison of the simulation results
with a numerical code that uses the finite-difference method. Simulations are
also carried out for two different anisotropy functions in order to demonstrate
the capability of the method to generate various crystal shapes
Grain coarsening in two-dimensional phase-field models with an orientation field
In the literature, contradictory results have been published regarding the
form of the limiting (long-time) grain size distribution (LGSD) that
characterizes the late stage grain coarsening in two-dimensional and
quasi-two-dimensional polycrystalline systems. While experiments and the
phase-field crystal (PFC) model (a simple dynamical density functional theory)
indicate a lognormal distribution, other works including theoretical studies
based on conventional phase-field simulations that rely on coarse grained
fields, like the multi-phase-field (MPF) and orientation field (OF) models,
yield significantly different distributions. In a recent work, we have shown
that the coarse grained phase-field models (whether MPF or OF) yield very
similar limiting size distributions that seem to differ from the theoretical
predictions. Herein, we revisit this problem, and demonstrate in the case of OF
models [by R. Kobayashi et al., Physica D 140, 141 (2000) and H. Henry et al.
Phys. Rev. B 86, 054117 (2012)] that an insufficient resolution of the small
angle grain boundaries leads to a lognormal distribution close to those seen in
the experiments and the molecular scale PFC simulations. Our work indicates,
furthermore, that the LGSD is critically sensitive to the details of the
evaluation process, and raises the possibility that the differences among the
LGSD results from different sources may originate from differences in the
detection of small angle grain boundaries
Spinodal decomposition and domain coarsening in a multi-layer Cahn-Hilliard model for lithium intercalation in graphite
During the intercalation of lithium in layered host materials such as
graphite, lithium atoms can move within the plane between two neighboring
graphene sheets, but cannot cross the sheets. Repulsive interactions between
atoms in different layers lead to the existence of ordered phases called
"stages", with stage consisting of one filled layer out of , the others
being empty. Such systems can be conveniently described by a multi-layer
Cahn-Hilliard model, which can be seen as a mean-field approximation of a
lattice-gas model with intra- and interlayer interactions between lithium
atoms. In this paper, the dynamics of stage formation after a rapid quench to
lower temperature is analyzed, both by a linear stability analysis and by
numerical simulation of the full equations. In particular, the competition
between stages 2 and 3 is studied in detail. The linear stability analysis
predicts that stage 2 always grows the fastest, even in the composition range
where stage 3 is the stable equilibrium state. This is borne out by the
numerical simulations, which show that stage 3 emerges only during the
non-linear coarsening of stage 2. Some consequences of this finding for the
charge-discharge dynamics of electrodes in batteries are briefly discussed.Comment: 15 pages, 8 figures, submitted to Phys. Rev.
Phase-field crystal study of grain-boundary premelting
We study the phenomenon of grain-boundary premelting for temperatures below
the melting point in the phase-field crystal model of a pure material with
hexagonal ordering in two dimensions. We investigate the structures of
symmetric tilt boundaries as a function of misorientation for two different
inclinations and compute in the grand canonical ensemble the disjoining
potential V(w) that governs the fundamental interaction between crystal-melt
interfaces as a function of the premelted layer width w. The results reveal
qualitatively different behaviors for high-angle grain boundaries that are
uniformly wetted, with w diverging logarithmically as the melting point is
approached from below, and low-angle boundaries that are punctuated by liquid
pools surrounding dislocations, separated by solid bridges. This qualitative
difference between high and low angle boundaries is reflected in the
w-dependence of the disjoining potential that is purely repulsive (V'(w)<0 for
all w) above a critical misorientation, but switches from repulsive at small w
to attractive at large w for low angles. In the latter case, V(w) has a minimum
that corresponds to a premelted boundary of finite width at the melting point.
Furthermore, we find that the standard wetting condition (the grain boundary
energy is equal to twice the solid-liquid free energy) gives a much too low
estimate of the critical misorientation when a low-temperature value of the
grain boundary energy is used. In contrast, a reasonable estimate is obtained
if the grain boundary energy is extrapolated to the melting point, taking into
account both the elastic softening of the material at high temperature and
local melting around dislocations.Comment: 24 pages, 13 figures, some figure files with reduced resolution
because of submission size limitations. In the 2nd version, some parts (and
figures) have been modified, especially in Sec. V (discussion
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