Dendrite Cleaving Simulation
- Bruce T. Murray, ACMD
- Adam A. Wheeler, University of Southampton
- M. E. Glicksman, Rensselaer Polytechnic Institute
- The development and application of phase-field models for studying phase
transitions under a variety of conditions has been the focus of a successful
collaborative effort between researchers in CAML, MSEL, and some external to NIST.
One component of this effort has been the investigation of first-order phase transitions, such as solidification of a pure material under conditions where
the solid crystal grows in the form of a dendrite.
The classical free boundary approach models solidification by treating the solid
and liquid phases individually and by explicitly determining the moving interface between the two bulk phases. In contrast, the phase-field method introduces a continuous transition between the two phases across a thin layer
of finite thickness. A phase-field variable (and corresponding field
equation) is introduced and its value at a point identifies the phase. This
additional field equation must be solved along with the equation that governs
conservation of energy. The advantage of this approach is that the
location of the interface does not have to be explicitly determined as part
of the solution. Thus, the method is well suited for calculating the
evolution of complicated solidification morphology (e.g., dendritic growth).
- Computations of dendritic growth using the phase-field method have provided
some of the most realistic simulations of this complicated
phenomenon which involves an interplay between diffusion in the bulk phases
and surface energy and kinetic effects at the solid/liquid interface.
Simulations performed using numerical algorithms developed in the ACMD
have provided a better understanding of the nature of the interaction between
the various physical mechanisms and have allowed material scientists and
physicists to test and modify existing simplified theories. Currently,
it has been proposed to use the micro-scale study of dendritic growth via the
phase-field computations to guide the development of meso-scale models which
can then be employed in large-scale computations for the solidification of castings;
casting simulations can reduce the development costs and improve the quality of
cast parts.
- As an example of the utility of the phase-field simulations, an attempt
to understand a phenomenon observed in dendritic growth experiments under
certain conditions has been the focus of a recent series of phase-field
computations. The figure shows an experimental photograph of a
succinonitrile dendrite on the left. At an earlier time, the primary dendrite branch
split into two main branches. After a short period of parallel growth,
one of the branches becomes dominant and the growth of the other branch
is suppressed. At the time shown, the suppressed branch appears as though
it has been ``cleaved'' from the primary branch, and this phenomenon has
been referred to as a cleaving event. Also included in the figure
is a phase-field computation which is an attempt to simulate
this cleaving behavior. While the growth conditions and the scale of the
dendrite in the computations differ from those of the experiment, the simulation
qualitatively represents the behavior observed in the experiment and will provide better understanding into the nature of such complex physical phenomena.