Using a Computer as a Teaching Aid in Crystallography
There were two major goals to this project. The first was to create a
computer program that would be able to symbolically derive the
expressions for the Young's Modulus representation surface for each of
the 32 point groups. This was done in full tensor notation for
theoretical accuracy, with the idea that the computer could carry out
cumbersome tensor calculations not normally performed in the
classroom. The second goal was to graph the surfaces in order to
enable the user to see the effects of changing the values of the
elastic constants. In the classroom it is next to impossible to draw
the surfaces for anything other than cubic crystals, but with the aid
of a computer it becomes possible to view even triclinic surfaces.
The World Wide Web pages are designed to make the second goal
available to the public. The user can choose a crystal group and
elastic constant values and view the resulting surface. The user can
also animate the surface as one of its constant values varies over any
range. This is intended to help students understand how the values of
the constants affect the geometry of the surface.
Similar features are now available for
longitudinal piezoelectric surfaces.
The server scripts for the HTML forms were written in Scheme48, a
compact, portable version of Scheme. You can find out more about Scheme48, or about
Scheme in
general.
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astark@mit.edu