A dendrite is a crystal with a tree-like branching structure. In the current context, we are interested in metallic dendrites formed when a metal, or an alloy of multiple metals, in liquid form freezes. Other materials when frozen form crystals consisting of dendritic (tree-like) branches, the most familiar example being snowflakes. The study of the formation of metallic dendrites through simulation is the subject of this research.
The micro-structures which form during the solidification (freezing) of a material play an enormous role in the properties of the solid material. In particular, during the solidification of an alloy, the micro-segregation patterns (i.e. the distribution of one alloy component in the other at a microscopic level) which result during dendritic and/or cellular solidification of an alloy are of substantial interest to the materials engineer. The goal of this research is to advance the theory of solidification through the development of portable high-performance parallel simulation and visualization software using the phase-field model.
The success of these simulations is judged by the degree to which these visualizations correctly reflect the growth of actual dendrites. In order to produce simulated dendrites of sufficient size, and with the level of detail required, our goal is to produce simulations on 3-dimensional grids of at least 1000^3 points.
For interactive use, we are also developing a system in which simulations over smaller grids can be interactively steered in order to more quickly explore, at a lower level of detail, the parameter space of this simulation.
We simulate, in three dimensions, the freezing of a binary alloy, such as an alloy consisting of nickel and copper. Each simulation produce a series of regularly spaced (in time) snapshots of the dendrites as they grow within a bounded volume. This volume is divided into a number of discrete grid points for computational purposes. Each snapshot consists of a pair of files, one containing the current phase of the material, from 0.0 (liquid) to 1.0 (solid), at each grid point and the other containing the relative concentrations of the two metals in the alloy at each grid point.
To visualize each snapshot, the phase value of 0.5 is taken as the surface of the dendrite and an isosurface of the phase data is computed. For images of the dendrite, each point on the computed isosurface is colored according to the corresponding value in a 3D array containing relative concentration of the metals. Two dimensional slices through the volume are also produced to show the internal structure of the dendrites. Once these images are generated they are saved individually and then used together to produce animations
As our simulations are expanded to grids of 500^3 to 1000^3 points, the increased computation time and memory requirements for computing the isosurfaces becomes a problem. At this writing, no available visualization software has been found that is able to perform these larger isosurface computations. As a result, we are developing an alternate technique for visualizing these dendrites. The first step in this new technique is to convert each point in the phase data with a value of 0.5 or higher into a 3-dimensional gylph. Each 3-dimensional glyph consists of 3 orthogonal planar quadrilaterals (squares). All three planes for each grid point are colored the same, according to the corresponding grid point in the relative concentration data. For display, the transparency of these planes can be varied to allow the internal structure of the dendrite to also be visible. One of the benefits of this approach is the ability to take advantage of advanced visualization hardware that is designed to process such polygonal data efficiently.
W. L. George and J. A. Warren, A Parallel 3D Dendritic Growth Simulator Using the Phase-field Method, Journal of Computational Physics, 177, 2002, pp. 264-283