1,739 research outputs found
Nonlinear Two-Dimensional Green's Function in Smectics
The problem of the strain of smectics subjected to a force distributed over a
line in the basal plane has been solved
Comment on ``Solidification of a Supercooled Liquid in a Narrow Channel''
Comment on PRL v. 86, p. 5084 (2001) [cond-mat/0101016]. We point out that
the authors' simulations are consistent with the known theory of steady-state
solutions in this system
Influence of Strain on the Kinetics of Phase Transitions in Solids
We consider a sharp interface kinetic model of phase transitions accompanied
by elastic strain, together with its phase-field realization. Quantitative
results for the steady-state growth of a new phase in a strip geometry are
obtained and different pattern formation processes in this system are
investigated
The influence of short range forces on melting along grain boundaries
We investigate a model which couples diffusional melting and nanoscale
structural forces via a combined nano-mesoscale description. Specifically, we
obtain analytic and numerical solutions for melting processes at grain
boundaries influenced by structural disjoining forces in the experimentally
relevant regime of small deviations from the melting temperature. Though
spatially limited to the close vicinity of the tip of the propagating melt
finger, the influence of the disjoining forces is remarkable and leads to a
strong modification of the penetration velocity. The problem is represented in
terms of a sharp interface model to capture the wide range of relevant length
scales, predicting the growth velocity and the length scale describing the
pattern, depending on temperature, grain boundary energy, strength and length
scale of the exponential decay of the disjoining potential. Close to
equilibrium the short-range effects near the triple junctions can be expressed
through a contact angle renormalisation in a mesoscale formulation. For higher
driving forces strong deviations are found, leading to a significantly higher
melting velocity than predicted from a purely mesoscopic description.Comment: 10 page
Elastic and plastic effects on heterogeneous nucleation and nanowire formation
We investigate theoretically the effects of elastic and plastic deformations
on heterogeneous nucleation and nanowire formation. In the first case, the
influence of the confinement of the critical nucleus between two parallel
misfitting substrates is investigated using scaling arguments. We present phase
diagrams giving the nature of the nucleation regime as a function of the
driving force and the degree of confinement. We complement this analytical
study by amplitude equations simulations. In the second case, the influence of
a screw dislocation inside a nanowire on the development of the morphological
surface stability of the wire, related to the Rayleigh-Plateau instability, is
examined. Here the screw dislocation provokes a torsion of the wire known as
Eshelby twist. Numerical calculations using the finite element method and the
amplitude equations are performed to support analytical investigations. It is
shown that the screw dislocation promotes the Rayleigh-Plateau instability.Comment: 16 page
Pattern formation during diffusion limited transformations in solids
We develop a description of diffusion limited growth in solid-solid
transformations, which are strongly influenced by elastic effects. Density
differences and structural transformations provoke stresses at interfaces,
which affect the phase equilibrium conditions. We formulate equations for the
interface kinetics similar to dendritic growth and study the growth of a stable
phase from a metastable solid in both a channel geometry and in free space. We
perform sharp interface calculations based on Green's function methods and
phase field simulations, supplemented by analytical investigations. For pure
dilatational transformations we find a single growing finger with symmetry
breaking at higher driving forces, whereas for shear transformations the
emergence of twin structures can be favorable. We predict the steady state
shapes and propagation velocities, which can be higher than in conventional
dendritic growth.Comment: submitted to Philosophical Magazin
Velocity selection problem for combined motion of melting and solidification fronts
We discuss a free boundary problem for two moving solid-liquid interfaces
that strongly interact via the diffusion field in the liquid layer between
them. This problem arises in the context of liquid film migration (LFM) during
the partial melting of solid alloys. In the LFM mechanism the system chooses a
more efficient kinetic path which is controlled by diffusion in the liquid
film, whereas the process with only one melting front would be controlled by
the very slow diffusion in the mother solid phase. The relatively weak
coherency strain energy is the effective driving force for LFM. As in the
classical dendritic growth problems, also in this case an exact family of
steady-state solutions with two parabolic fronts and an arbitrary velocity
exists if capillary effects are neglected. We develop a velocity selection
theory for this problem, including anisotropic surface tension effects. The
strong diffusion interaction and coherency strain effects in the solid near the
melting front lead to substantial changes compared to classical dendritic
growth.Comment: submitted to PR
Phase Field Modeling of Fracture and Stress Induced Phase Transitions
We present a continuum theory to describe elastically induced phase
transitions between coherent solid phases. In the limit of vanishing elastic
constants in one of the phases, the model can be used to describe fracture on
the basis of the late stage of the Asaro-Tiller-Grinfeld instability. Starting
from a sharp interface formulation we derive the elastic equations and the
dissipative interface kinetics. We develop a phase field model to simulate
these processes numerically; in the sharp interface limit, it reproduces the
desired equations of motion and boundary conditions. We perform large scale
simulations of fracture processes to eliminate finite-size effects and compare
the results to a recently developed sharp interface method. Details of the
numerical simulations are explained, and the generalization to multiphase
simulations is presented
Onsager approach to 1D solidification problem and its relation to phase field description
We give a general phenomenological description of the steady state 1D front
propagation problem in two cases: the solidification of a pure material and the
isothermal solidification of two component dilute alloys.
The solidification of a pure material is controlled by the heat transport in
the bulk and the interface kinetics.
The isothermal solidification of two component alloys is controlled by the
diffusion in the bulk and the interface kinetics.
We find that the condition of positive-definiteness of the symmetric Onsager
matrix of interface kinetic coefficients still allows an arbitrary sign of the
slope of the velocity-concentration line near the solidus in the alloy problem
or of the velocity-temperature line in the case of solidification of a pure
material. This result offers a very simple and elegant way to describe the
interesting phenomenon of a possible non-single-value behavior of velocity
versus concentration which has previously been discussed by different
approaches. We also discuss the relation of this Onsager approach to the thin
interface limit of the phase field description.Comment: 5 pages, 1 figure, submitted to Physical Review
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