141 research outputs found
Relation Between Bulk and Interface Descriptions of Alloy Solidification
From a simple bulk model for the one-dimensional steady-state solidification
of a dilute binary alloy we derive an interface description, allowing arbitrary
values of the growth velocity. Our derivation leads to exact expressions for
the fluxes and forces at the interface and for the set of Onsager coefficients.
We, moreover, discover a continuous symmetry, which appears in the low-velocity
regime, and there deletes the Onsager sign and symmetry properties. An example
is the generation of the sometimes negative friction coefficient in the
crystallization flux-force relation
Diffusion-Induced Oscillations of Extended Defects
From a simple model for the driven motion of a planar interface under the
influence of a diffusion field we derive a damped nonlinear oscillator equation
for the interface position. Inside an unstable regime, where the damping term
is negative, we find limit-cycle solutions, describing an oscillatory
propagation of the interface. In case of a growing solidification front this
offers a transparent scenario for the formation of solute bands in binary
alloys, and, taking into account the Mullins-Sekerka instability, of banded
structures
Capillary-Wave Description of Rapid Directional Solidification
A recently introduced capillary-wave description of binary-alloy
solidification is generalized to include the procedure of directional
solidification. For a class of model systems a universal dispersion relation of
the unstable eigenmodes of a planar steady-state solidification front is
derived, which readjusts previously known stability considerations. We,
moreover, establish a differential equation for oscillatory motions of a planar
interface that offers a limit-cycle scenario for the formation of solute bands,
and, taking into account the Mullins-Sekerka instability, of banded structures
Capillary-Wave Model for the Solidification of Dilute Binary Alloys
Starting from a phase-field description of the isothermal solidification of a
dilute binary alloy, we establish a model where capillary waves of the
solidification front interact with the diffusive concentration field of the
solute. The model does not rely on the sharp-interface assumption, and includes
non-equilibrium effects, relevant in the rapid-growth regime. In many
applications it can be evaluated analytically, culminating in the appearance of
an instability which, interfering with the Mullins-Sekerka instability, is
similar to that, found by Cahn in grain-boundary motion.Comment: 17 pages, 12 figure
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