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Soft matter Quasicrystals[edit]

Soft matter systems such as block co-polymers, dendrimers, nanoparticles and mesophorous silica all exhibit self-assembly into quasicrystalline arrangements. Does information on this belong in this page as a section? Or as a separate page linked to this page? WpLila (talk) 16:41, 3 March 2020 (UTC)

Potential Uses of quasicrystals[edit]

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 (talkcontribs)

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 (talkcontribs)

please note the quasi crystal reflectivity characteristics used to 'cloak' stealth aircraft ... etc
also note the quasi crystal 'compounds' allows for surface coatings that can be used to 'surf' gravity waves and so
ride gravity or other energy waves in Red October fashion / magneto hydra dynamic fashion, squidding along (talk) 07:45, 27 May 2017 (UTC)I am shiva sr lads ! (talk) 07:45, 27 May 2017 (UTC)

1D quasicrystals?[edit]

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. 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] (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: 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[edit]

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

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
Ho-Mg-Zn E8-5Cube.jpg

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. (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:

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. (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. (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." (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).
I think Penrose tiling can occur in any number of dimensions, including four or more. Obviously, it is easier to see it in two dimensions.
Quasicrystals can occur in 0 and -1 dimensions, but they are not interesting. — Preceding unsigned comment added by MissouriOzark1947 (talkcontribs) 09:55, 1 September 2014 (UTC)

In the news -- from meteorites?[edit] 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: and clicking on it in the BBC article worked for me.P0M (talk) 07:20, 4 January 2012 (UTC)

Meteorite resource[edit]

"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 (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. (talk) 17:05, 5 January 2012 (UTC)

E pluribus unum[edit]

                               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[edit]

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 Ilanblech should be discarded. (talk) 11:19, 3 June 2013 (UTC)
What do you have in mind? In the end of the history section it says "Other puzzling cases have been reported,[18] but until the concept of quasicrystal came to be established, they were explained away or denied.[19][20] However, at the end of the 1980s, the idea became acceptable". I think this is appropriate. Maybe a further mentioning of this fact in the paragraph before? Or mention explicitly that Shechtman's findings also were explained away or denied? I've been working on quasicrystals only since the mid 90s, but the consensus of the scientific community at this time was (1.) quasicrystals do exist, and (2.) Linus Pauling did damage to both the discipline and himself in denying (1.). The links you cite are newspapers: in newspapers, the headlines tend to exaggerate. I tend to rate them as not to be taken too seriuosly. (The first link even repeats this bullshit on quasicrystalline patterns in medieval architecture.) --Frettloe (talk) 14:39, 13 November 2013 (UTC)
I think that mentioning that Dan Shechtman's findings were met with hostility from Linus Pauling since most people outside of that field of study have at least a passing knowledge that there was some controversy directed at Shechtman and the Shechtman and Pauling pages mention it. There doesn't necessarily have to be much, but after listening to an extended podcast about the history of quasicrystals and then seeing this Wikipedia page it struck (and still does) me of whitewashing the history. Plus, so what if they are newspapers? Most people don't get their scientific news from "Physical Review Letters" and to ignore the popular media is folly. (PS. I rarely check talk pages so tagging my user talk is the best way to get my attention) Darkstar949 (talk) 18:13, 30 April 2014 (UTC)
No new arguments yet. I will remove the POV Dispute Tag, in particular since I've asked around and several colleagues assured me that after 1984 several scientists (Tsai, Nissen, Beeli, Kuo...) started to discover more and more quasicrystals, while Linus Pauling still was claiming that there are no quasicrystals (to a rapidly shrinking audience). — Preceding unsigned comment added by Frettloe (talkcontribs) 14:53, 20 February 2014 (UTC)

Adding a distinguishing hatnote[edit]

The reasons I added a hatnote are: This article is about completely separate definition of the term Quasi-crystals. It is earlier and completely unrelated use of the term. It is neither sub-type of quasi periodic quasicrystal nor a more general - it is the original, independent, unrelated and standalone earlier dicovery. Thus should be a completely separate and unrelated Wikipedia article. Platanium (talk) 16:21, 30 April 2014 (UTC)

The hatnote is not very helpful: to a layperson, the distinction is unclear, and hence disambiguation fails. A better hatnote would be in the form: {{For|OTHER TOPIC|PAGE1}}, i.e. This article is about (clearly defined topic). For (clearly different topic), see Quasi-crystals (supramolecular). The distinctions should be clear in the hatnote to aid in locating the correct article(s).--Animalparty-- (talk) 02:31, 1 May 2014 (UTC)

Why Alan Mackay not shared the 2011 Nobel?[edit]

The 2010's O. E. Buckley Prize was shared with Alan Mackay, for "pioneering contributions to the theory of quasicrystals, including the prediction of their diffraction pattern", so there are a wide acception of Mackay's articles on Quasicrystal prediction, and was before 2011.

The Mackay's prediction was easy? Shechtman's work was not "easy"? What is easy? de Broglie wins the Nobel by the "prediction of the wave mater", that have been proposed in 1924 (before your thesis) in an a half-page article.

There are a good explanation?

There is far too much emphasis on stupid prizes here, instead of science. The article of 1924 should be specified in detail. — Preceding unsigned comment added by MissouriOzark1947 (talkcontribs) 14:33, 15 December 2014 (UTC)
The remark about 2011 seems to refer the the Nobel Prize for Chemistry, awarded to Shechtman in 2011. — Preceding unsigned comment added by MissouriOzark1947 (talkcontribs) 16:58, 20 January 2015 (UTC)

Broken English in lede[edit]

The lede has awkward or broken phrasings: "Alan Lindsay Mackay found to apply to"; "The ability to diffract comes from the existence of an indefinitely large number of elements" (diffract light? "comes from", indefinitely? chemical elements?); "this kind of experiment" (which kind?); "Next (yet in 1982)". -84user (talk) 22:57, 20 March 2015 (UTC)

Restored the lede, thanks. Materialscientist (talk) 23:22, 20 March 2015 (UTC)

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Is Pentagonite, a rare natural mineral which has five-fold symmetry, a quasicrystal? If so, perhaps this should be mentioned in this article. Isambard Kingdom (talk) 01:51, 20 August 2016 (UTC)