Anisotropy of an Alloy on an FCC Lattice

Richard J. Braun
Geoffrey B. McFadden
Adam A. Wheeler, Bristol University, UK
Holly Rushmeier, Scientific Computing Environments Division
John W. Cahn, Materials Science and Engineering Laboratory
William J. Boettinger, Metallurgy Division

One instance of phase change that everyone knows by experience is solidification or freezing. Other types of phase change occur; heat treating metal alloys causes phase change, but these changes occur entirely within the solid phase. Some results for solid-solid phase change modeling are presented in the following images and descriptions. We have considered an alloy with species A and B on a face-centered-cubic (FCC) lattice; this lattice has four distinct sites which may be repeated periodically to make up a crystal. Like all crystalline materials, the properties change with direction; that is, they are anisotropic. One of our main purposes of this modeling was to determine the magnitude of the anisotropy of some of the properties of the interface between the different solid phases; the properties of interest to us are the surface energy and the attachment kinetics (or mobility) of the interfaces.

The surface energy is not very anisotropic, as is shown on by the contours on a sphere. We believe that the equilibrium shapes from this model will not exhibit missing orientations.

The kinetic anisotropy, on the other hand, is strongly anisotropic. A reference, isotropic configuration is shown here, where the distance from the (111) orientation (the line x=y=z) on the surface of the sphere is color coded from red to blue (the x, y and z axes are blue). The color of each orientation is retained in subsequent figures.

[image of fcc corner]

As the anisotropy increases, the growth shapes develop missing orientations, first by developing edges underneath the protruding "ears", then by the edges (and ears) splitting at their ends, then the split ends merge. The growth shape sequence for increasing anisotropy of kinetics is illustrated in the figures below. The kinetic shapes are what is left upon removing the "ears" or "swallowtails".

[image of fcc corner]
[image of fcc corner]
[image of fcc corner]

An animation of the sequence for increasing anisotropy may be seen (750 Kb).

We also have an animation of a sequence of sections illustrating how a larger ear splits into two smaller ones (578 Kb).