113 research outputs found
Eutectic Growth in Two-Phase Multicomponent Alloys
A theory of two-phase eutectic growth for a multicomponent alloy is
presented. This theory employs the thermodynamic equilibrium at the
solid/liquid interface and thus makes it possible to use standard CALPHAD
databases to determine the effects of multicomponent phase equilibrium on
eutectic growth. Using the same hypotheses as the Jackson Hunt theory, we find
that the growth law determined for binary alloys in the Jackson Hunt theory can
be generalized to systems with N elements. In particular, a new model is
derived from this theory for ternary two-phase eutectics. The use of this model
to predict the eutectic microstructure of systems is discussed
A quantitative variational phase field framework
The finite solid-liquid interface width in phase field models results in
non-equilibrium effects, including solute trapping. Prior phase field modeling
has shown that this extra degree of freedom, when compared to sharp-interface
models, results in solute trapping that is well captured when realistic
parameters, such as interface width, are employed. However, increasing the
interface width, which is desirable for computational reasons, leads to
artificially enhanced trapping thus making it difficult to model departure from
equilibrium quantitatively. In the present work, we develop a variational phase
field model with independent kinetic equations for the solid and liquid phases.
Separate kinetic equations for the phase concentrations obviate the assumption
of point wise equality of diffusion potentials, as is done in previous works.
Non-equilibrium effects such as solute trapping, drag and interface kinetics
can be introduced in a controlled manner in the present model. In addition, the
model parameters can be tuned to obtain ``experimentally-relevant" trapping
while using significantly larger interface widths than prior efforts. A
comparison with these other phase field models suggests that interface width of
about three to twenty-five times larger than current best-in-class models can
be employed depending upon the material system at hand leading to a speed-up by
a factor of , where and denote the interface width and
spatial dimension, respectively. Finally the capacity to model non-equilibrium
phenomena is demonstrated by simulating oscillatory instability leading to the
formation of solute bands.Comment: 51 pages, 9 figures, supplemental material
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