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Visualizing the Anisotropy of Crystals: Nye Plus 3-D Graphics

Darrell G. Schlom
Organization: The Pennsylvania State University
Journal / Anthology

submitted to Journal of Materials Education

A graduate-level course on crystal anisotropy based on J.F. Nye's classic text Physical Properties of Crystals: Their Representation by Tensors and Matrices has been enhanced to allow students to visualize tensor properties and variables in three dimensions (3-D). Using Mathematica, graduate students form a graphical link between equations and their physical significance both inside and outside the classroom. The availability of computerized classroom facilities for visual lectures and visual homework makes this possible. Examples include magnetic point groups, pyroelectricity, thermal expansion, piezoelectricity, elastic stiffness, and piezoresistivity. Such visualization is extremely helpful for comprehending the spatial variation of properties that occurs in important low-symmetry materials, e.g., quartz and orthoclase, and in identifying the directions in which a particular tensor quantity will be maximal or minimal. Use of Mathematica also aids with the extensive matrix manipulations used to deduce the form of the tensor property matrices for specific point group symmetries using Neumann's Law.

*Science > Physics > Crystallography