Monday, October 10, 2011

Quasicrystals

I was going to do a post about quasicrystals and this year's chemistry Nobel, but Don Monroe has done such a good job in his Phys Rev Focus piece that there's not much more to say.  Read it!

The big conceptual change brought about by the discovery of quasicrystals was not so much the observation of five-fold and icosahedral symmetries via diffraction.  That was certainly surprising, since you can't tile a plane with pentagons; it was very hard to understand how you could end up with a periodic arrangement of atoms that could fill space and give diffraction patterns with those symmetries.  The real conceptual shift was realizing that it is possible to have nice, sharp diffraction patterns from nonperiodic (rather, quasiperiodic) arrangements of atoms.   The usual arguments about diffraction that are taught in undergrad classes emphasize that diffraction (of electrons or x-rays or neutrons) is very strong (giving 'spots') in particular directions because along those directions, the waves scattered by subsequent planes of atoms all interfere constructively.   Changing the direction leads to crests and troughs of waves adding with some complicated phase relationship, generally averaging to not much intensity.  In particular symmetry directions, though, the waves scattered by successive planes of atoms arrive in phase, as the distances traveled by the various scattered contributions all differ by integer numbers of wavelengths.  Without a periodic arrangement of atoms, it was hard to see how this could happen nicely.

It turns out that quasicrystals really do have a hidden sort of symmetry.  They are projections onto three dimensions of structures that would be periodic in a higher dimensional space.  The periodicity isn't there in the 3d projection (rather, the atoms are arranged "quasiperiodically" in space), but the 3d projection does contain information about the higher dimensional symmetry, and this comes out when diffraction is done in certain directions.  The discovery of these materials spurred scientists had to reevaluate their ideas about what crystallinity really means - that's why it's important.  For what it's worth, the best description of this that I've seen in a textbook is in Taylor and Heinonen.

5 comments:

Gautam Menon said...

I'm mildly thrilled that my comment on your earlier post re the Nobel prizes did predict Schectman, although in physics and not in chemistry.

Tahir said...

Personally, what I find most interesting about this prize is the story of how Schechthman was first received when he presented his results. His results seemed so bizarre and so against all known assumptions and logic, that he was blatantly ridiculed and insulted. He was asked to leave his research group. A fellow scientist gave him a basic textbook on crystallography and suggested he read it.

I guess this goes to show that quite often, the best science is also the most difficult to push through the community. So, persistence (but not stubbornness to the point of ignoring when one is definitely wrong) and belief in oneself are very important, particularly in the face of overwhelming opposition, even by so-called experts. A good lesson in the sociology of science, particular for graduate students, I think!

Doug Natelson said...

Gautam - you did, indeed, call it!

Tahir - I'd love to know the inside story on the social aspects of this. As described, it sounds nasty and unprofessional, two things I don't associate with NBS/NIST. Scientists are human, of course, and we all know that there can be personality conflicts at work sometimes that don't have a basis in rational judgment....

Behrang said...

Doug,

It seems like that the unprofessionalism and nastiness towards Shechtman didn't come from NIST colleagues; at least according to this story on our website:
http://www.nist.gov/public_affairs/releases/shechtman-100511.cfm

In the PRL publication of the results in 1984, John Cahn from NIST was a coauthor, and the article says he invited Shechtman to come back to NIST throughout the 80s to do more experiments.

(D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Metallic Phase with Long-Range Orientational Order and No Translational Symmetry. Physical Review Letters. Vol. 53, No. 20; Nov. 12, 1984.)

Tahir said...

So, I based my comments on what I read in the Nobel Committee's "Information for the Public" pamphlet. There on page 3, it said:

"When Shechtman told scientists about his discovery, he was faced with complete opposition, and some col- leagues even resorted to ridicule. Many claimed that what he had observed was in fact a twin crystal. The head of the laboratory gave him a textbook of crystallography and suggested he should read it. Shechtman, of course, already knew what it said but trusted his experiments more than the textbook. All the commo- tion finally led his boss to ask him to leave the research group, as Schechtman himself recalled later. The situation had become too embarrassing."