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Visualization of Dendritic Growth



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 determined by the degree to which these snapshots and animations 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 3 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. Color is added to the image based on the relative concentration of the metals. For images of the dendrite, each point on the computed isosurface is colored according to the corresponding value in the 3D array of relative concentration data. 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. 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.



(bullet) Collaborating Scientist: James Warren
(bullet) Parallel computing: William L. George
(bullet) Visualization: William L. George & Steven G. Satterfield
(bullet) Group Leader: Judith E. Terrill


A dendrite of copper-nickel alloy as it grows (1356° C) and melts (1441° C)

Grows
1356° C
(bullet) AVI (15 MB)
(bullet) QuickTime (15 MB)
Melts
1441° C
(bullet) AVI (2.1 MB)
(bullet) QuickTime (2.1 MB)

Slice through the dendrite showing the relative concentration of the nickel and copper.

slice
1356° C
(bullet) AVI (15 MB)
(bullet) QuickTime (15 MB)
slice
1441° C
(bullet) AVI (36 MB)
(bullet) QuickTime (36 MB)

Slice through the dendrite showing the phase of the copper-nickel alloy.

slice
1356° C
(bullet) AVI (15 MB)
(bullet) QuickTime (15 MB)
slice
1441° C
(bullet) AVI (15 MB)
(bullet) QuickTime (15 MB)

Both the dendrite and several slices through the dendrite colored to show the relative concentrations.

slice
1356° C
(bullet) AVI (22 MB)
(bullet) QuickTime (22 MB)
slice
1441° C
(bullet) AVI (22 MB)
(bullet) QuickTime (22 MB)
Cover ofThe Journal of Research
of the National Institute of Standards and Technology, Volume 105
Number 3 (May-June 2000)
Cover ofThe Journal of Research of the National Institute of Standards and Technology, Volume 105 Number 3 (May-June 2000)

This image shows a simulated dendrite of a copper-nickel alloy as it is growing. The surface coloring represents the relative concentration of each of the two metals at the surface of the dendrite. This simulation uses the phase-field method for modeling this process and is implemented as a parallel program using MPI (Message Passing Interface).



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Date created: 2001-10-31, Last updated: 2011-01-12.
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