Basic Structure, Plane Orientation, and Facetting in the Face-Centered and Body-Centered Cubic Crystal Structures

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This simple Demonstration is used in our course "Foundations of Materials Science" to help students visualize the orientation and structure of various low index planes for the face-centered cubic and body-centered cubic crystal structures. This Demonstration has a simple interface but hopefully provides enough flexibility to explore the cubic crystal structure in detail. The interface also allows for simulating basic facetting structures that are observed during the growth of "kitchen crystals" such as alum.

Contributed by: Sean G. Corcoran (Virginia Tech) (March 2011)
Open content licensed under CC BY-NC-SA



I have used many excellent programs [1] in my courses at Virginia Tech while teaching basic crystal structures in our undergraduate foundational materials science class [2]. However, I often needed to tailor the output of the visual on the fly to accommodate student questions. The result of trying to answer similar questions over the past several years prompted me to write this simple Demonstration in Mathematica. This current version only gives options for the FCC and BCC crystal systems but can be easily extended as needed. The clipping options, although simple, surprisingly allow for a number of different visualization options that I have found able to answer most questions asked of students at this introductory level.

Applications and Control Settings (shown in the snapshots):

Snapshot 1: facetted crystal structure showing the octahedral structure observed by students as they grow alum crystals in their own kitchen for homework

Snapshot 2: using the "remove lattice" option, angular relationships between planes can be easily shown

Snapshot 3: another example of generating a multiple-facetted structure

Snapshot 4: another example using the "remove lattice" option to show the entire family of {111} planes

Snapshot 5: a simple example showing the structure and orientation of a (110) family of planes in the body centered cubic crystal lattice

Snapshot 6: clipping at plane "0" allows for the displaying of single planes within the overall structure; the (111) plane is shown here


[1] For example, the freeware by Stephen Michael Schimpf, "Crystalline Solids," version 2.0.1, copyright 1997–2005, The Regents of the University of California.

[2] MSE2044 Fundamentals of Materials Science, Virginia Tech. Text book: W. D. Callister, Materials Science and Engineering An Introduction, New York: John Wiley & Sons, 2007.

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