Talk:Quasicrystal

Potential Uses of quasicrystals

I am currently reading a book on Atlantis which explains the use of quasicrystals as "libraries", storing massive amounts of information which is programmed into them telepathically. Does anyone have some information on this or telepathy in any state? Skeptics need not respond —Preceding unsigned comment added by Nonskeptic (talk • contribs)

As Wikipedia has aspirations of being taken seriously as a reliable source of information, I'm afraid only the skeptical viewpoint on questions such as this will be permitted to remain for any length of time represented on its pages. Quadibloc (talk) 09:36, 8 April 2013 (UTC)

No need to answer to the last comment, but quasicrystals have been used indeed for practical applications. Due to their low friction coefficient they have been used as coating in frying pans by a french firm. quasicrystals are also promissing materials for hydrogen storage especially the Zr-Ti-Ni alloy. —Preceding unsigned comment added by 69.138.202.161 (talk • contribs)

1D quasicrystals?

Are one dimensional quasicrystals possible? Can anyone give me an example(mathematical example is fine) of a 1D quasicrystal?

(Check the link to S.Weber's Introduction):

10110101101101011010110110101101101011010110... The Fibonacci sequence is a standard example of 1D quasicrystal: it is neither ordered ('crystal') nor disordered ('noise'). The Fourier transform of such nonperiodic systems with well defined long range order exhibits delta peaks with spacings which are fractions of some irrational number. The absence of this feature is taken as a sign of insufficient long range order and then the systems are taken to be closer to random ones. The Bombieri-Taylor argument allows eventually to identify the quasicrystals.195.96.229.95 07:44, 7 August 2006 (UTC)

This a quote from the Riemann hypothesis article: "The Riemann hypothesis implies that the zeros of the zeta function form a quasicrystal, meaning a distribution with discrete support whose Fourier transform also has discrete support. Dyson suggested trying to prove the Riemann hypothesis by classifying, or at least studying, 1-dimensional quasicrystals. Dyson, F., (2009), "Birds and frogs", Notices of the American Mathematical Society 56 (2): 212–223, MR2483565, ISSN 0002-9920 [1] 195.96.229.83 (talk) 12:03, 7 February 2011 (UTC)

The relation between R.H. and 1-dimensional quasicrystals appears on From Prime Numbers to Nuclear Physics and Beyond： http://www.ias.edu/about/publications/ias-letter/articles/2013-spring/primes-random-matrices This article contains some recent research on random matrics and R.H.. --Enyokoyama (talk) 01:08, 12 May 2013 (UTC)

addition of hyper-dimensional images

Just wondering if the article could benefit from the electron diffraction images related to the high dimensional structures from which they are projeced.

While, I would admit the connection to E8 is not discussed specifically, the fact that the 5-cube and 6-cube are within it as sub-groups and their patterns fit with the electron diffractions make it relavent. Jgmoxness (talk) 00:08, 31 December 2011 (UTC)

Please, upload an electron diffraction image without montage (I suppose that it has a compatible license since you already used it). BTW nothing in commons:File:Ho-Mg-Zn E8-5Cube.png worth such a high resolution with 2700 pixels image size. Incnis Mrsi (talk) 21:25, 31 December 2011 (UTC)

The electron diffraction image is already taken from the article. The geometry overlay is similar to those on the Penteract page (of my own creation). Are you suggesting this triad of images would be good for the article (if reduced in resolution)? Jgmoxness (talk) 21:49, 31 December 2011 (UTC)

Modified image set:

E8_(mathematics) and Quasicrystals
6-cube (Hexeract) orthographically projected to 3D using the Golden ratio. This is used to understand the aperiodic icosahedral structure of Quasicrystals.	240 E₈ polytope vertices with 1440 6-cube (6D) unit edges and Golden ratio basis vectors orthographically projected to 3D.	240 E8_(mathematics) vertices projected to 2D using 5-cube Petrie_polygon basis vectors	240 E₈ polytope vertices projected to 2D using 5-cube Petrie basis vectors overlaid on electron diffraction pattern of an icosahedral Zn-Mg-Ho Quasicrystal.

Jgmoxness (talk) 17:35, 1 January 2012 (UTC)

de Bruijn (1981) famously demonstrated that a Penrose tiling can obtained as a 2D projection from a 5D cubic lattice and it was rather obvious that a diffractogram can be obtained in the same way - the text says so. There is no need to drag in the E8 polytope and unless adequate scholarly references are provided its presence here qualifies as OR. It is the physics, not the maths, that needs understanding now. 195.96.229.83 (talk) 10:34, 9 January 2012 (UTC)

I understand. Unfortunately, the description of the picture that was shown is not precisely the 5-cube (it has more vertices included from E8 which happen to perfectly show more of the diffraction pattern detail. The proper picture is now included w/o E8 references. IMO, the triacontrahedron from 6-Cube using golden ratio projection as documented here [2] provides significant value in understanding the high dimensional structure (and should not have been removed w/the E8 references). How about this:

• High dimensional projections and Quasicrystals
• 
  6-cube (Hexeract) using 6D orthographic_projection to a 3D Perspective_(visual) object (the Rhombic_triacontahedron) using the Golden ratio in the basis_vectors (inner edges removed leaving their vertices).
• 
  6-cube (Hexeract) using 6D orthographic_projection to a 3D Perspective_(visual) object (the Rhombic_triacontahedron) using the Golden ratio in the basis_vectors. This is used to understand the aperiodic Icosahedron structure of Quasicrystals.
• 
  5-cube (Penteract) vertices using 5D orthographic_projection to 2D using Petrie_polygon basis_vectors.
• 
  5-cube (Penteract) vertices using 5D orthographic_projection to 2D using Petrie_polygon basis_vectors overlaid on electron diffraction pattern of an Icosahedron Zn-Mg-Ho Quasicrystal.

Jgmoxness (talk) 14:09, 9 January 2012 (UTC)

Perhaps we could keep the older figure with this new caption? As I get it 5D is necessary in order to have the interesting non-crystallographic symmetry, exhibited already by the more simple decagonal quasicrystals (stacks of Penrose tilings, i.e. 1D+2D); 6D is for the icosahedral, fully 3D, case. What people usually miss is that a forbidden symmetry is not necessary for the construction of a qcrystal : you can consider a simple 3D Fibonacci grid. As the Lifshitz paper [3] explains, an other 6D Fourier space allows to decompose the energy modes of any lattice into phonons and phasons, and that reveals an interesting aspect of the symmetries. Thus classical crystals remain invariant under translations while qcrystals would need an additional rearrangement which does not affect their diffractogram.91.92.179.172 (talk) 21:17, 9 January 2012 (UTC)

I guess my concern for accuracy could be waived on the electron diffraction overlay, but my concern is about providing both 2D and 3D visuals to provide the lay reader with something to connect with (not you or I who are comfortable with the abstract math). They provide further value in that the URLs to relevant WP articles (otherwise missing in pointing to the high dimensional pages). The 6-cube projected triacontehedron has factors of 2, 3 and 5 fold symmetries (including icosahedron). They are intimately related to the 5-cube (with different projection basis vectors). I just think these are far more interesting to more readers (with or w/o familiarity of QuasiCrystals) - so they should be included. The points you make about Fibonacci are relevant - and linked to the golden ratio and these projections. It's all good - but a (few) picture(s) are worth thousands of words! Can we keep the 3D 6-cube 5 fold perspective as well as the current Penteract overlay?

How about:

High dimensional projections and Quasicrystals
6-cube (Hexeract) using 6D orthographic_projection to a 3D Perspective_(visual) object (the Rhombic_triacontahedron) using the Golden ratio in the basis_vectors. This is used to understand the aperiodic Icosahedron structure of Quasicrystals.	5-cube (Penteract) vertices using 5D orthographic_projection to 2D using Petrie_polygon basis_vectors overlaid on electron diffraction pattern of an Icosahedron Zn-Mg-Ho Quasicrystal.

Jgmoxness (talk) 02:57, 10 January 2012 (UTC)

I have no further opinion on the matter and leave it for others to judge.91.92.179.172 (talk) 13:55, 10 January 2012 (UTC)

... but I can't resist to quote an expert, N. D. Mermin: "I argue that this ascent into superspace in search for periodicity leads to a crystallographic scheme which is excessively complicated and potentially misleading" (PhysRevLett 68(92)1172, the paper is called suggestively Copernican Crystallography, its argument being that adding new dimensions is like adding epicycles.) Next sentence is: "A simpler unified scheme for the classification... can be constructed without ever leaving three dimensions."91.92.179.172 (talk) 11:16, 7 February 2012 (UTC)

Right, but, the next paragraph has a kicker (if you follow to the endnote).

"...the single advantage of ascending to superspace in search of a classification scheme based on periodicity, is that it relieves one of having to take a radical new look at the foundations of ordinary crystallography [12].

[12] Superspace can, of course, be used advantageously for other purposes, such as building models that suggest where the atoms might be in real 3-space. See, for example, ..."

Jgmoxness (talk) —Preceding undated comment added 14:00, 7 February 2012 (UTC).

In the news -- from meteorites?

http://www.bbc.co.uk/news/science-environment-16393296 It may be worth adding to the article.P0M (talk) 17:50, 3 January 2012 (UTC)

Sounds interesting, although the link to the PNAS article is dead and the doi doesn't resolve. If anyone can find the original paper somewhere that would be nice. a13ean (talk) 18:57, 3 January 2012 (UTC)

I just checked. The link was:http://www.pnas.org/content/early/2012/01/03/1111115109 and clicking on it in the BBC article worked for me.P0M (talk) 07:20, 4 January 2012 (UTC)

Meteorite resource

"World's Only Known Natural Quasicrystal Traced to Ancient Meteorite A theoretical physicist searched for years to find the only known natural occurrence of an exotic type of structure, the discovery of which netted the 2011 Nobel Prize in Chemistry" by Richard Van Noorden Scientific American January 3, 2012

99.181.147.68 (talk) 06:38, 4 January 2012 (UTC)

I believe the edits and my decision to revert to them are justified as the new findings are related to things known earlier and alredy mentioned in the text. Much of the new addition - type of meteorite etc - is not pertinent. There was an unused ref at the botton which was suppressed. Please note that there is currently a separate article on icosahedrite .

The polytope pics should also be removed; something more about phasons and symmetry should be added; there is a recent article by R. Lifschitz in the arXiv.91.92.179.172 (talk) 17:05, 5 January 2012 (UTC)

E pluribus unum

                               432 deg 
                                / 
                                / 
                                / 
                                / 
                                / 
                                / 
            324 deg  /////////////////////// 108 deg 
                               / / 
                            /   /   /   36 deg   
                         /      /      / 
              288 deg /         / 72 deg   /  144 deg 
                                / 
                                / 
                            216 deg 

I apologize for the caveman graphics as that is about as good as I am with these things and feel free to clear up the lines.I need another graphic where the lines reflect the spokes of a hexagonal form based on 324 degrees minus 144 degrees and 288 degrees minus 108 degrees and the central line of 432/216 degrees remains unchanged.There is a purpose to all this and especially as the first 4 sequential geometric values reflect the angles of Penrose tiling and although the overall structure reflects a hexagonal form with pentagonal traits,it is much more interesting than this.Gkell1 (talk) 12:33, 19 February 2012 (UTC)

POV Dispute Tag

I just applied the POV tag to the History section of the article because it seems to be written in a way that "rewrites" the history of the actual discovery. The initial discovery was actually extremly controversal which has been well documented. Right now there is nothing about that which strikes me as whitewashing. I'll try to edit things in the near future a bit but since the changes might be controversial it seems like starting things off here might be a prudent course of action. Darkstar949 (talk) 13:01, 29 May 2013 (UTC)

Imho the additions made by Ilanbech should be discarded. 195.96.229.83 (talk) 11:19, 3 June 2013 (UTC)