In the lectures it was mentioned how one can mathematically define a structure to be a Bravais lattice if it admits a representation R = n1a1 + n2a2 + n3a3. Due to the periodic nature of crystal structures, I was curious if anyone has come across research in this field taken from a purely mathematical approach. It seems to me that there could be some interesting ideas in terms of crystal structure if one was to apply group theory and abstract algebra to the structures.
I'm sure it would have been done, however I was just interested if it was still a fairly active research area.
This comment has been removed by the author.
ReplyDeleteThere is a research area at UQ (in maths) called Topology Optimization, which can be applied (in physics) to designing crystal structures for use in optics, photonics etc.
ReplyDeleteThe group theory of crystal structures was worked out more than one hundred years ago and so does not attract much research interest these days.
ReplyDeleteHowever, more recent topic is quasi-periodic structures such as Penrose tiling and quasi-crystals
http://en.wikipedia.org/wiki/Aperiodic_tiling