In article <email@example.com>, "Tim Golden BandTech.com" <firstname.lastname@example.org> wrote:
> On Jul 21, 11:29 am, John Stafford <n...@droffats.net> wrote:
> > > > There is a strange outlier in crystal formation. Perhaps it is best to > > call it a quasi-crystalline structure that has a tiling pattern that > > cannot possibly be built in the traditional atom-to-atom, linear manner > > (symmetric translation). See the work of Dany Shechtman, 1984. > > > > The point illustrated by this quasi-crystal is that in order to form its > > five-fold symmetry, all the atoms in the solution would have to > > simultaneously organize. It's a non-local action. Spooky stuff, as the > > man said. > > I found a SIAM article covering Shechtman's discovery. Pretty neat. > I've got a copy of Kittel's solid state physics which specifically > rules out the 5-fold symmetry. I do have a hard time with the Bravais > breakdown because it seems so cartesian based. I do have an > alternative lattice style in polysign: > http://bandtechnology.com/PolySigned/Lattice/Lattice.html . > > How much of a space can we actually have? Some work that I've done > exposes that we can have more or less than tradition will allow: > http://bandtechnology.com/ConicalStudy/conic.html > Perhaps there is a way around the simultaneous organization > requirement here. > > I've never fully followed the crystallographic X-ray patterning, which > is supposed to be the boon of analysis, even under the Shechtman > discovery, but am happy to consider that there could be some > electromagnetics in diffraction that is being overlooked too > conveniently. We don't see any photograph of the aluminum and > manganese alloy, which I suppose does not look very impressive. Should > there be some attempt to grow one of these and see if there is some > growth pattern? I couldn't find any photos of the material, or even a > name for it. Didn't work too hard at it though. > > - Tim
I found a photo in Roger Penrose's _ Emperor's New Mind_, page 564 in our library copy. It is early, and different from the later representations. If you surf for "penrose aluminum-manganese alloy" (sans quotes), you should come up with some good information.
I struggle to follow Penrose, but that's my shortcoming. He's a very good instructor and writer.