What is a crystal?

You would have thought such a basic question would have been settled a very long time ago. Solid state physics textbooks written before 1980 certainly give that impression. But no, as recently as 1991, the International Union of Crystallography revised its definition.

After undergraduates learn about crystal structures it is good to teach them about Quasi-crystals. Several good reasons are:

• they are beautiful and fun
• it is a story which should encourage students to question conventional wisdom and not just believe everything in the textbook or that their lecturers tell them
• it illustrates the simple (but sometimes overlooked) truth that just because property A implies property B the converse does not necessarily apply

Here are the slides for my lecture.

The most useful website I found was Introduction to Quasicrystals produced by Steffen Weber. It includes software for producing different tiling patterns and making fourier transforms.

An aside: there is also an interesting 2007 article in Science by Peter Lu and Paul Steinhardt, Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture. The article generated some "lively" correspondence which you can read online.

I welcome suggestions of other online resources.