Talk:Quasicrystal/Archive 1

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Archive 1 | Archive 2


A couple of other sources ([[1]], [[2]]) state that Schechtman observed quasicrystals in 1984, but this article says 1982. Which is correct?

Crust 15:04, 1 Feb 2005 (UTC)

Shechtman et al. discovered the quasicrystalline phase in 1982 and published their results in 1984 (Phys. Rev. Lett. 53 (1984) 1951). —Preceding unsigned comment added by (talkcontribs)

See also Paracrystallinity, for instance in J. Appl. Cryst. (1980). 13, 521-523: The limiting size of natural paracrystals by F. J. Baltá-Calleja and R. Hosemann and other articles back to the sixties. F. Schmidt,15Dec2008 —Preceding unsigned comment added by (talk) 16:16, 15 December 2008 (UTC)

This article is frankly bad

It's an example of Wikipedia at its worst. Over-edited by experts or near experts in the field to the point of unintelligibility to anyone with who just wants to know why a topic might matter to them. Would someone be kind enough to put at least a summary paragraph at the front of the article? As I understand it, quasicrystals are both naturally occurring and synthetic materials that have some potentially interesting properties. The opening sentence should say something like that, not launch into a discussion of mathematical qualities of the atomic structure. That can come further down the page. — Preceding unsigned comment added by David Colver (talkcontribs) 18:49, 7 February 2011 (UTC)

Hardly constructive criticism. Neither the origin nor properties of quasicrystals are essential (at least currently). It is their "puzzling" atomic structure which is the key - sort of curiosity for scientists. Materialscientist (talk) 23:31, 7 February 2011 (UTC)

"bent" linear subspaces?

In a quasicrystal, flaws are locations where the 3D "subspace" is bent, or wrinkled, or broken as it passes through the higher-dimensional space.

seems to contradict the earlier description of non-periodic tilings (in that definition, the subspace was linear!). Can anyone clarify?

RandomP 01:24, 28 April 2006 (UTC)

Needs Revision?

I think that this article should be thoroughly revised. Since Shechtman's discovery many new experimental results have been reported. In physics 'Quasicrystals' has been a fashionable topic during the last 20 years, with lots of popular examples. Mathematicians have also taken some interest in this recent development. And now there is a pile of books with 'quasicrystal' in the title. None of this is apparent in the article. (I have added a few lines, but an expert is needed to rewrite all.)15:32, 28 June 2006 (UTC)After some reading, did some more rewriting but it is still far from being acceptable .al 14:34, 28 January 2007 (UTC)


It is a nice picture but not exactly a quasicrystal; relevant material can be seen at the external 17:51, 18 September 2006 (UTC)

Examples of quasicrystals

Maybe we can link to examples of quasicrystals that have their own page in wikipedia? One family of quasicrystals is the high temperature superconductors Bi-2201, Bi-2212, Bi-2223. They have a crystal unit cell that's modulated by a displacment function whose wavevector has irrational components. --spiralhighway 07:41, 14 August 2006 (UTC)

PS: By the way there's a great review article about all this stuff by Akiji Yamamoto: Acta Cryst. A52, 509-560 (1996)

I added a link to a story about medieval architectural tiling in the middle east. I know this is a link to an artistic use of a math concept, but then that's an interest of mine, and I hadn't heard of quasicrystals before. Listening to the story, I kept expecting them to mention fractals. [MDR 22 February 2007]

Needs improvement

The grammar and spelling need improvement in the main article.

—The preceding unsigned comment was added by (talk) 10:22, 6 February 2007 (UTC).

This article is not very informative

This article contains a lot of information about the discovery and publication in this field, but does not do a good job in describing quasicrystals. —The preceding unsigned comment was added by (talk) 22:30, 22 February 2007 (UTC).

Quasicrystalline designs in medieval Islamic architecture?

The article at: suggests there is basis for concluding that Medieval Muslims had some knowledge of quasicrystalline patterns over 500 years ago. Should the main encyclopedia article on Quasicrystals make some reference to these theories? —The preceding unsigned comment was added by Brad Bridgewater (talkcontribs) 05:31, 23 February 2007 (UTC).

Interesting. I was just reading the same thing on Reuters. Yes, I believe it merits a line or two in the article. 13:22, 23 February 2007 (UTC)

I added a short reference to the Lu and Steinhardt article in Science at the end of the "Brief History" section. That doesn't flow with the chronology (since it refers to a possible usage of quasi-crystalline patterns over 500 years before their "discovery" by Penrose et al.) but seemed less disruptive of the main discussion.Bridgewater 23:07, 23 February 2007 (UTC)

It is a pitty that no mention of this interesting finding is made in the body of the article. The readers deserve to know the fact that the quasicrystal-style tilings were used in decorations in the Middle East about 500 years ago. Some people would like to play down this fact by saying that most likely they were not aware of the implications of such a thing. My question is what better implication does one need other than actually trying to use it to tessellate a plane successfully in a real world application? (talk) 23:32, 9 February 2008 (UTC)Ur

Quasicrystals are a natural (i.e. physical) phenomenon. In natural history physical phenomena precede biological and cultural ones, so quasicrystals precede artisanal artefacts. Removed two passages which begin by stating:

  • "The earliest quasicrystal patterns date back to the girih tiles found in medieval Islamic architecture...
  • "Recently discoveries have shown that quasicrystal patterns were first employed in the girih tiles found in medieval Islamic architecture..

They are obviously incorrect or at least badly worded and also they are out of context. Please read the old comments in the section below and provide some answers before reverting once again. Item 6 is rephrased here: the article pertains to physics where tilings, mathematical or artisanal, are just (talk) 18:58, 4 March 2008 (UTC)


I believe that all of this is a misunderstanding and have reverted to a previous version. Here is why:

0.In these recent writings 'quasicrystalline' is used as a synonym for aperiodic.

1.'Quasicrystalline' means aperiodic and diffracting. Islamic decorators were interested in elegant and complicated designs but there is no ground to think they knew or cared about aperiodicity and diffraction. And even less that they understood quasicrystals which require both.

2. Aperiodic is not necessarily complicated in an obvious way: a square grid of lines with spacing following the binary fibonacci sequence is aperiodic (and diffracting). Any finite structure may be repeated so the term 'aperiodic' implies infinity and needs a conceptual proof. Obviously these points are outside artisanal interest. Drawing a straight segment is not the same as having the concept of a line.

3. Unusual or exotic symmetry is not mandatory for a qc. But without it the diffractive picture would not reveal aperiodicity and some other method is needed. The diffractive property is of interest as it implies indefinitely extended long-range order.

4. In the Reuter's hype the first reference to qc ('quasicrystalline') is rightly in quotes. And for a finish they quote Socolar, an undisputed authority, who attempts to avoid some misnomers and misunderstandings.

5. Speaking of discoveries is tricky if one does not want to credit plants with the discovering of the Fibonacci sequence; obviously the AlMn alloy did not discover the quasicrystals. There is a difference between mathematics and other natural phenomena or simple practices.

6 The link from decorations to quasicrystals goes through [[aperiodic tiling]] and a 'shortcut' here is out of place. The new additions were inaccurate and incorrect.

My hope is that readers and contributors to Wikipedia should be able to distinguish facts from 13:17, 3 March 2007 (UTC)

Steinhardt and Lu published some 'Further notes on quasi-crystal tilings' in Science, Vol. 316. no. 5827, pp. 981 - 982 (May 18, 2007) downplaying their previous claims. There are no hints that the possibility of aperiodicity has been considered, so they state: "Our conclusions were guarded, concurring with the remarks by Socolar and Levine in the accompanying news article, suggesting that evidence beyond a single large fragment is needed to prove that the designers understood this possibility. "al (talk) 19:51, 4 March 2008 (UTC)

Reversion Was Excessive

The reference to P. J. Lu and P. J. Steinhardt, Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture, Science Vol. 315 no. 5815, 1106-1110 (2007) that you deleted, al, was not hype. You seem to have a disagreement with Lu and Steinhardt, but that is no reason for deleting a reference to their work. I note that P.J. Steinhardt is the very same Steinhardt that the article still cites as an author of the first paper to use the term "quasicrystal." I would concur, however, in the deletion of the more florid text from the popular press.Bridgewater 23:00, 7 March 2007 (UTC)

Please explain what these decorations have to do, not with aperiodic tilings, but with quasicrystals per se. Quoting the name of Steinhardt does not answer any of the objection made above.
Any adman would agree that 'aperiodic' obviously bears negative connotations while 'quasicrystalline' sounds decidedly more positive. And his advice probably would be to use the second even if it is inaccurate. Called this 'hype' for short.
My disagreement is not with Steinhardt and Lu but with the mention of their work 22:28, 16 March 2007 (UTC)
Completely concur. —Preceding unsigned comment added by (talk) 14:28, 28 September 2007 (UTC)
Removed again some irrelevant history; please read the preceding comments. (talk) 10:24, 17 November 2008 (UTC)

The french WP page -

about quasi cristal looks like it were more complete, giving history, references and all. IANACrystallographist myself, but it may be interesting to take a look. Thanks. -- DLL .. T 20:00, 8 April 2007 (UTC)


Illustrating articles with works of art, related by name only, does not seem to be an acceptable option here: it would be ok in a magazine, but not in an encyclopedia. Removed 'a quasicrystal artwork', Painting 2006-7( Image:Tony Robbin artwork.JPG) by Tony Robbin. I will be looking for something 22:07, 14 August 2007 (UTC)

Aperiodic tilings are not the same as quasicrystals

The article is starting to shape up, but there could be more clarification of the distinction between the physical materials -- quasicrystals-- and the mathematical topic of aperiodic tiling.

In particular, the discussion of Wang's & Berger's, and to a much lesser extent Penrose's contributions to the study of Aperiodic Tilings, seems over-emphasized here. To this day no one knows why or how quasicrystalline materials form. One thing is absolutely known: defect-free, reliably non-periodic tilings cannot be assembled from local rules. In other words, quasicrystals are not perfect aperiodic tilings created by atoms coming together one by one by local interactions. Any one of these clauses might possibly be deleted, though, for a working model.

The point is, the structures formed by aperiodic sets of tiles and the structure of quasicrystals have some of the same gross features-- but that might be about it.

As far as Lu and Steinhardt's paper, again, it is not really clear that that deserves much attention in this article. They were not claiming-- quite obviously not!-- that islamic architects were interested in unusual Al-Mn alloys. Rather they noted very interesting 5-fold self-similar structures. Perhaps a discussion under substitution tiling would be more appropriate. As for hype, well, they did choose the term "quasicrystalline tiling", and had they not, the article would not have made nearly the splash it did (regardless of its merit). Predictably, this was distorted in the press, and here we are.

Aperiodic v/s nonperiodic

As the mathematicians would have it, a set of tiles is aperiodic if all the tilings which it admits are nonperiodic. So 'aperiodic tiling' appears to be a misnomer and use of 'aperiodic' as synonymous to nonperiodic may be a malaproprism. However the physicists' interest is in tilings (and not in tiles) and the context allows to disregard the distinction.

There seems to be a clash between correctness and usage which would not be easily resolved. Perhaps a note should mention 08:58, 1 October 2007 (UTC)

Mistake in Brief History?

It says "In 1961 Hao Wang proved that the tiling of the plane is an algorithmically unsolvable problem, which implied that there should be aperiodic tilings." However, I've been reading about Hao Wang's 1961 paper on Wikipedia itself, and it was mentioned that Hao Wang actually showed that if the domino problem was unsolvable, then there would have to be aperiodic tilings. However, this caused Wang to surmise that the problem must actually be algorithmically solvable, because he thought that aperiodic tilings were actually impossible. Later, he was shown to be wrong when the set of 20,000 aperiodic tiles were found. Since this information was also on wikipedia and might have been incorrect, someone should look into this and find reputable sources. —Preceding unsigned comment added by (talk) 06:44, 3 August 2008 (UTC)

physics is physics

Not materials science or history or general waffle. The Trouble with Physics - (Lee Smolin, Houghton Mifflin 2006) is that it gets overtaken by theory divorced from experiment. Quasiscrystals are quasicrystals. —Preceding unsigned comment added by (talk) 07:03, 24 September 2008 (UTC)

Removed some Original Research as it is outside the scope of Wikipedia. (talk) 10:26, 17 November 2008 (UTC)
I bet that this is the same as what I just removed. The web page presents itself as voice battling the universal consensus of the "quasicrystal industry", and urges us not to trust them. (talk) 03:52, 26 November 2008 (UTC)

If the misrepresentation had been deliberate, it must have been put in to catch out vandals. —Preceding unsigned comment added by Bourdillona (talkcontribs) 14:37, 26 November 2008 (UTC)

The web page shows that the pattern is not icosahedral as a matter of fact. For twenty five years this has not been noticed. When reviewers deny the fact to support their prejudices, they become disingenuous and the issue rightly becomes a matter of trust. But Wikipedia needs to keep to the facts. What the web page says is irrelevant except where evidence is concerned. The same goes for diffraction. In quasicrystals the order is fundamentally different from Bragg diffraction in crystals and this is obvious to any decent electron microscopist. —Preceding unsigned comment added by Bourdillona (talkcontribs) 04:50, 26 November 2008 (UTC)

Pick up an icosahedron, and then notice that the a side having the two fold symmetry at its centre is normal to the line, through it, joining the axes 53235. When you compare this fact with the data of Schechtman et al., you can see there is an anomaly. For symmetry, the 2-fold patterns are misoriented. This is only contentious for people who want to be.

  • I am not a crystallographer or an electron microscopist, and I don't have a handy icosahedron lying around, so I don't find your assertions obvious at all. The same will be true of almost all Wikipedians who come to this article wanting to learn something. I do know that claims that the scientific literature is wrong are usually contentious and likely to be challenged, and if that's the case then it needs a citation to a reliable secondary source. I am removing it, and please don't put it back until you can provide a citation to a reliable source that makes the same claim. Our policies on reliable sources and original research are quite clear on stuff like this. Reyk YO! 19:46, 16 December 2008 (UTC)

Actually, you have got an icosahedron: on appendix D. The policy of Wikipedia is "objectivism" and "doing the right thing" (Jim Wales' blog). Your "claims that the scientific literature is wrong...." may be true in general; but the claims are not contentious in this particular case of simple, verifiable fact. Further sources will be provided in due time. The sociological problems attached to reviewing are intractable and subsist in power squabbles (Smolin, as above), but Wikipedia has the best - perhaps the only - solution. —Preceding unsigned comment added by Bourdillona (talkcontribs) 15:11, 28 January 2009 (UTC)

Where ignorance is bliss.... It's in the literature now isn't it? You'll come round to it.

??? Besides, Wikipedia is uncensored. Unqualified - by their own admission - vandals should not be contentious. If everyone were without arguments, there would be no science, only wikiwacky. Please undo this vandalism.

Statement of fact is not outside the scope of Wikipedia. Nor is reference to research. What was removed is not original research. —Preceding unsigned comment added by Bourdillona (talkcontribs) 11:56, 17 November 2008 (UTC)

Meyer and Delone sets?

This article refers to "Meyer and Delone sets" without attempting to say what those are or to link to articles that define them. I've made "Delone" link to Boris Delone for now.

Can someone fix this? Michael Hardy (talk) 18:07, 18 April 2009 (UTC)

changed to Delaunay triangulation, cant find anything on Meyer sets to link to (talk) 09:45, 30 April 2009 (UTC)

Bragg diffraction

Is it Bragg difrraction? Quasicrystal diffraction does not follow Bragg's law because the lines are not in linear series, but in geometric series. This was previously explained in a link to a page on modified Bragg diffraction in quasicrystals. But the page has been redirected. Now there is a hole in the general description of quasicrystals because the modification to the Bragg diffraction is nowhere described. Why not direct back again? Bourdillona (talk) 13:22, 29 September 2009 (UTC)

Hi, I took the freedom to move your comment here -usually new comments go to the bottom. My opinion is that you should put the content of that page here in the article, in its own paragraph. --Cyclopia - talk 14:08, 29 September 2009 (UTC)

Thanks for this comment and for moving the discussion to the correct place. I am glad it got your attention. However, the person that redirected the page twice, did not give a reason the first time and on the second occasion wrote that the link is 'unnecessary.' I don't think I want to get involved in a section to be mangled. A link is the better solution and has been established for over one year. Anyway I don't have access to the page any more. Wikipedia needs to find resolution. The article still has a hole. —Preceding unsigned comment added by Bourdillona (talkcontribs) 14:50, 4 October 2009 (UTC)

Hi. I don't understand what you mean by "don't want to get involved in a section to be mangled". I personally think that a separate page was not the better solution, especially because it mostly dealed with research from a single researcher (you) and as such is at risk of being interpreted as a WP:POVFORK (I am not saying it is, but it becomes debatable). I would encourage you again to be bold and re-add the content, in a more concise way, to the quasicrystal page. --Cyclopia - talk 17:59, 4 October 2009 (UTC)

Source suggestions

OTRS received an email from Dr. Ben-Abraham at the Department of Physics at Ben-Gurion University [3] that I am posting here per his request. The book he refers to was the second entry in this bibliography, which may still appear on Wikipedia mirrors, but which is no longer in this article.

His contact information is at the link above.--Chaser (talk) 21:54, 21 November 2010 (UTC)

Good suggestions, thanks. I can confirm that Janot's book is excellent. -- Marie Poise (talk)

I posted this to the wrong page (see here). Ah well, should be helpful here, too.--Chaser (talk) 01:18, 23 November 2010 (UTC)

Quasicrystal stoichiometry

Do quasicrystalline alloys follow a definite stoichiometry like crystalline phases? If so, are the ratios always simple integers like with crystalline phases, or can they be irrational? It'd be interesting to have a compound like LiAlsqrt(2), for instance. Stonemason89 (talk) 04:12, 28 December 2010 (UTC)

In experiment, most binary, ternary, etc., crystals are non-stoichiometric, and the measurement accuracy is not that high, so the question whether the atomic ratio is an integer, rational, or irrational number has no answer. As to theory, I have no answer either :-). It is easy to have rather odd rational numbers: consider a crystal of C60 fullerene. C60 molecules in it can be substituted with various C-N-O-H derivatives, like C59N, etc., and there is no problem with the overall symmetry as we can make the molecules rotate. I don't know what will happen if we place such molecules instead of certain individual atoms here, i.e. whether this can give irrational numbers. Materialscientist (talk) 05:17, 28 December 2010 (UTC)

Colloidal Quasicrystals

Hello everybody does someone read the Pnas article last week (11.01.11)? —Preceding unsigned comment added by (talk) 12:38, 21 January 2011 (UTC)

The history section opening

The history section is opened with:

Although 20th-century physicists were surprised by the discovery of quasicrystals, their mathematical descriptions were already well established. For example, tiles in a medieval Islamic mosque in Isfahan, Iran, are arranged in a quasicrystalline pattern, suggesting that their designers achieved a mathematical breakthrough 500 years earlier than Western scholars.[1]

With this exceptional argument (which still remain more than doubtful IMO) being supported by Science journal article/letter to the editor. Never the less, still more sources are need to be provided IMO to justify this argument in the opening. Science is a great source, but this is only one article for an highly exceptional argument (that Islamic knowledge in Mathematics preceded the western one in 500 years) and though Science published this argument, it's still not clear at all whether this is the mainstream opinion or if there was an response to this article on Science itself.

Additionaly, today Dan Shechtman won the Nobel prize for the discovery of quasicrystals -he's not mentioned once in the aritcle.

The illustration of Penrose tiling

The second illustration (Penrose tiling) in this article is not very helpful, due to the coloring. It appears that the elements are of several shapes: star, half star, pentagram, and rhombus. The yellow rhombus is one of Penrose's shapes, but the other one is a fatter rhombus; of which there are none evident in this illustration. A much better illustration is found at Penrose tiling. — Preceding unsigned comment added by MathMan64 (talkcontribs) 23:44, 5 October 2011 (UTC)

Geometry of quasicrystals

The lead paragraph should probably be more specific about the dimensionality of quasicrystals, and how a quasicrystal divides a plane or higher-dimensional space:

"A quasicrystalline pattern fills all available space, but lacks translational symmetry."

In space, an ordered, gapless division is called a honeycomb. Is a three-dimensional quasicrystal a honeycomb? (If so, is it irregular or quasiregular?) If the sentence referred to a plane and not to space, then I might suppose that a quasicrystal tessellates. But is translational symmetry a necessary condition of tessellation? The lead paragraph uses the word space, but the first two illustrations are of planes. Ringbang (talk) 21:28, 6 October 2011 (UTC)


The alloy in the picture on the right is in doubt. Ag-Al and Al-Pd-Mn are both mentioned. — Preceding unsigned comment added by (talk) 09:30, 8 October 2011 (UTC)

See the top right. — Preceding unsigned comment added by (talk) 14:31, 20 October 2011 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Quasicrystal/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Rating the importance of this article is problematic for me.

Within physics quasicrystals are really important just for crystallographers or, more generally, just for solid state physics.

Outside physics they are, I believe, of a higher importance because they offer a clear example that the world is different from what is assumed as evident. The pair order/disorder is taken to be roughly equivalent with the pair periodic/aperiodic. A disordered system could not be periodic. Quasicrystals show that the obverse is not true: they are both odrered and aperiodic. So the arrangement of these conceptual (or linguistic) categories is not what it was taken to 18:59, 17 March 2007 (UTC)

Last edited at 18:59, 17 March 2007 (UTC).

Substituted at 15:37, 1 May 2016 (UTC)

  1. ^ Lu, P. J.; Steinhardt, P. J. (2007). "Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture". Science. 315 (5815): 1106–1110. Bibcode:2007Sci...315.1106L. PMID 17322056. doi:10.1126/science.1135491.