Talk:Miller index

Wrong Diagram
The plane [111] is wrong in the first diagram. —Preceding unsigned comment added by Pcflet01 (talk • contribs) 20:33, 12 September 2008 (UTC)

Lowest terms?
In the introduction is stated "The integers are usually written in lowest terms, i.e. their greatest common divisor should be 1.", but isn't that wrong? i.e., (111) isn't the same as (222). 137.122.14.20 (talk) 18:59, 14 August 2008 (UTC)

HKL / LMN
The notation "lmn" is new for me. What is the difference to "hkl"? SietskeEN 13:35, 19 July 2007 (UTC)


 * Um, isn't that like asking the difference between "x" and "y"? They are just variable names, representing integers.  The choice of letters is pretty irrelevant &mdash; Miller indices are a positional notation, so only the position of the letters and the surrounding brackets matter.  —Steven G. Johnson 15:15, 19 July 2007 (UTC)


 * Ok, thanks! SietskeEN 20:20, 19 July 2007 (UTC)


 * There is a certain relevance in that if one convention is widely dominant that one should prevail. This is the first time I have seen 'lmn' used. Obviously I am a fairly small sample, but you might want to look at other sites. —Preceding unsigned comment added by Special:Contributions/ (talk)


 * Have just done a test on google, the entry: hkl miller indices returns 85 500 results, lmn miller indices returns 23 600 results.


 * First time I see lmn too, for the record. 137.122.14.20 (talk) 18:56, 14 August 2008 (UTC)


 * lmn was also surprising to me (89.77.158.160 (talk) 20:10, 8 December 2008 (UTC))


 * Yep same here hkl is what I have been taught at Uni, could it be changed to hkl? —Preceding unsigned comment added by 86.156.193.168 (talk) 21:46, 17 January 2009 (UTC)


 * ...So if you don't know it it is not true? ... maybe you should read in the Encyclopedia of Physics, VII "Crystal Physics Part I". @Steven: hkl is NOT a positional measure. It is a measure of room frequency. hkl are "coordinates" (in a mathematical sense) with reference to the so called "reciprocal axes". If one means coordinates with reference to the "direct axes" (i.e. axes of the crystal elementary cell) then the symbolic notation is "uvw". The notation "lmn" refers to reciprokal axes, as "hkl" does, bur "lmn" apparently means another set of reciprocal coordinate values than "hkl" but with one coordinate value being identical. — Preceding unsigned comment added by 129.13.72.198 (talk) 11:44, 24 August 2013 (UTC)

https://en.wikipedia.org/wiki/Crystal_structure

Hopefully this page will help?

If in doubt, I find the best recourse to visit a university or academia repository, and follow the course notes, as sometimes Wikipedia (and all related websites that use the metadata contained within this site) will use two incompatible notations side-by-side on the same page. Also reviewing past edits can often track down the cause for one notation, say the plane, being replaced with the coordinates, or similar. — Preceding unsigned comment added by 49.183.10.84 (talk) 15:29, 25 May 2022 (UTC)

Simplification
I am planning to restructure this article further. I think the reciprocal lattice should get less attention, certainly in the lead and in the beginning of the article. (I had a student who tried to understand Miller indices and looked it up here on wikipedia, and did not find it helpful at all.) /Pieter Kuiper 07:56, 9 October 2007 (UTC)

Ambiguous 3D Coordinate System
Given the ambiguity of left-handed vs right-handed 3D coordinate systems, I think image depicting miller planes should be altered to reflect which is the y and which is the x-axis. Anybody want to take this on? In my mineralogy class and textbook, only the right-handed system is used so the unlabeled left-hand coordinates on the illustration were really confusing at first. It's important to realize that people from multiple disciplines (not just engineering) could be looking at this article, so a little clarification could go a long way in making this article more accessible.

--ThinkGreen (talk) 12:03, 16 February 2008 (UTC)


 * Which image are you looking at? As far as I can tell, all of them are right-handed, and all of them are labelled sufficiently to determine this fact.  (However, one of them misspells "plane" as "plan", which should be fixed.)  —Steven G. Johnson (talk) 16:53, 16 February 2008 (UTC)

I agree with Thinkgreen as a first year MSE student those planes nearly killed me. Also an effective discussion of how reciprocal infinity is used would be appreciated by many. The image i was looking at is the one in the upper right containing all of the 100 110 001 etc. indices. —Preceding unsigned comment added by 72.66.107.174 (talk) 22:35, 17 July 2008 (UTC)

Rationale for four miller indices in hexagonal cell
can anyone tell me why four indices are used in hexagonal systems? —Preceding unsigned comment added by Sry19206 (talk • contribs) 16:35, 13 February 2009 (UTC)


 * In a haxagonal system hkl miller indices are enough to define a plane or a direction, however, You will prefer to use four hkil indices, because this way equivalent planes/directions will have similar indices. E.g. the unit cell defines 3 lattice unit vectors a, b, and c. Between a and b there is a 120° angle. With miller indices You would write a=[100], b=[010] and a+b=[110]. If You look carefully a+b is just the same as a or b, only rotated by 60°. So it is convenient to have a notation where this similarity is apparent. in the hkil notation a is 2,-1,-1, 0 while a+b is 1,1,-2,0. They look similar, that is why we use this notation. 2001:4C4D:2B06:D800:CCEA:9A42:B1D1:8D0 (talk) 11:24, 1 May 2024 (UTC)

Way too complex
this article needs to be simplified...currently it is mystifying to anyone without a background in crystallography...im a 3rd year biochemistry student, and i found the page almost entirely useless in terms of building my understanding of the subject 24.141.7.36 (talk)

Typo
Figure 3 has a typo: "plan", which should be "plane". Also figures 2 and 3 are not neat. We should upload new and clear figures. It will be difficult for new students to learn anything from these figures. Drajput (talk) 14:42, 14 October 2009 (UTC)
 * Fixed typo. Please be more clear on "not neat". Materialscientist (talk) 23:30, 14 October 2009 (UTC)

wrong indices
The right diagram in third picture from top has the wrong plane indices: it's 112 and not 221 — Preceding unsigned comment added by 129.94.216.91 (talk) 04:19, 10 August 2012 (UTC)
 * They follow the definition given left to the figure, and thus can't be wrong :-). Materialscientist (talk) 04:27, 10 August 2012 (UTC)

Which ⟨angled⟩ brackets to use?
I think we should harmonize the type of brackets used throughout the article. Different brackets have or could have been used to display the "same" shape, especially the angled brackets. There are:
 * 1) $$\left\langle 111 \right\rangle$$ TeX/math-mode \left\langle and \right\rangle
 * + Can be rendered as graphics.
 * - Maybe not displayed on text-only readers?


 * 1) less-than/greater-than signs (Unicode U+003c, U+003e)
 * + Is available as ASCII character.
 * - Wrong semantic meaning, not quite correct rendering.


 * 1) 〈111〉 Technical left/right-pointing angle brackets (Unicode U+2329, U+232a)
 * + Nice rendering. (On my screen.)
 * - Upon preview, it gets automatically converted into 〈111〉 Chinese, Japanese and Korean punctuation mark: left/right angle brackets ??!!


 * 1) ❬111❭ Dingbats: left/right-pointing angle bracket ornament (Unicode U+267c, U+267d)
 * + Common on MS Windows machines.
 * - Wrong semantic meaning, not quite correct rendering.


 * 1) ⟨111⟩ mathematical left/right brackets (Unicode U+27e8, U+27e9)
 * + Nice rendering. (On my screen.)
 * - Nothing?


 * 1) 〈111〉 Chinese, Japanese and Korean punctuation mark: left/right angle brackets (Unicode U+3008, U+3009)
 * + Nice rendering. (On my screen.)
 * - Wrong semantic meaning.

From the above, my first choice would be the ⟨111⟩ mathematical left/right brackets (Unicode U+27e8, U+27e9), since the indices are a mathematical representation of the crystal planes or directions. My second choice could be the 〈111〉 Technical left/right-pointing angle brackets (Unicode U+2329, U+232a), but I have the problem that they get converted into 〈111〉 Chinese, Japanese and Korean punctuation marks every time I preview my edits! Do you have any comments on this? Zeptomoon chat/chase 13:05, 15 December 2014 (UTC)
 * 1) Anything else?
 * No comments within a week... I'll go for the ⟨111⟩ mathematical left/right brackets (Unicode U+27e8, U+27e9). Zeptomoon chat/chase 18:20, 24 December 2014 (UTC)

Hexagonal
(u v t w)--->(u' v' w') u=1/3(2u'-v') v=1/3(2v'-u') w=w' t=-(u+v) Saleh Tabatabaei (talk) 12:16, 20 April 2016 (UTC)

Error in 'Definitions'?
Following the reciprocal definition:

"Then, given the three Miller indices h, k, ℓ, (hkℓ) denotes planes orthogonal to the reciprocal lattice vector:", Ghkl.

We then talk about '(hkℓ)' as vector :

"That is, (hkℓ) simply indicates a normal to the planes in the basis of the primitive reciprocal lattice vectors. Because the coordinates are integers, this normal is itself always a reciprocal lattice vector."

When it was just defined as a plane orthogonal to the vector, Ghkl, is this sentence not instead describing the vector Ghkl itself? Or have I misunderstood the definition? Grand Admiral Archduke (talk) 17:48, 30 December 2016 (UTC)

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