Talk:Reciprocal lattice

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There a request for reciprocal lattice primitive cell from Wikipedia:ACF Regionals 2000 answers

If this is another name for a page that already exists could someone more knowledgeable than me make a redirect. Or if not could some make an article.--BirgitteSB 16:29, July 12, 2005 (UTC)

Why are the definitions repeated? I'm not sure if I'm qualified, but I think that the introduction could be made clearer. Hithisishal (talk) 03:22, 16 February 2008 (UTC)

What is the point of the redirect-sentence at the top? It suggests that there is some other article about general dual lattices, but it redirects to itself! --AasmundE 06:52, March 8, 2009 (UTC) —Preceding unsigned comment added by 129.241.133.230 (talk)

Formula incorrect?[edit]

Aren't the reciprocal lattice vector equations on this page incorrect? I thought (and I have checked some other sources such as http://www.chemsoc.org/ExemplarChem/entries/2003/bristol_cook/reciprocallattice.htm which verify this) that the bottom line didn't change, unlike what is presented on the current page. 212.2.167.48 10:11, 12 November 2007 (UTC)

The formulae are correct. The three expressions in the denominators are equivalent (a scalar triple product). You can check this by writing out the result component-wise. The result equals the (signed) volume of the reciprocal lattice primitive cell. WilliamDParker 13:15, 14 November 2007 (UTC)

Lattice means: discrete set of points[edit]

Is the extension to arbitrary arrangements of atoms justified? I have not seen this in the literature so far. In my view, a lattice is a discrete set of points, see Lattice (group). This would mean that a nonperiodic arrangement has no reciprocal lattice; also the animated C60 example does not fit here. --Anastasius zwerg (talk) 20:31, 18 August 2008 (UTC)

I agree that this should be limited to lattices whaich spatially periodic (in normal Euclidean space). Perhaps a new article could be started that linked to some broader view that some wish to take. The c60 image, while beautiful, should go. Hess88 (talk) —Preceding undated comment added 14:56, 14 September 2009 (UTC).

Somewhat tangentially related to the idea of a lattice being a discrete, periodic structure, I had a question about the formal definition of the reciprocal lattice. Given that the mathematical definition, e^(ik.r)=1, will always be true when the dot product of k and r is zero (ie. they are orthogonal), doesn't any given r vector have an entire, continuous plane of orthogonal k vectors (given that the magnitude doesn't affect the dot product in this case)? The mapping, then would be from a discrete space to a continuous one. It seems to me that, for the formal definition to be rigorous, a further restriction is needed on the definition of the k vectors, similar to what is said later in the article about "discrete mathematics" (that the product of magnitudes of k and r be an integer or something like that). I am relatively new to the topic, so forgive me if I am not explaining myself properly or am completely off the mark. --Chris —Preceding unsigned comment added by 68.195.78.160 (talk) 08:47, 22 November 2009 (UTC)

That is correct, and there is a restriction. The restriction is the periodicity of the lattice basis electron clouds which is used to derive the definition. IMO that's a good question. See Kittel, Intro to solid state physics, 8th ed, beginning of chap 2. --129.6.130.22 (talk) 12:35, 21 June 2010 (UTC)

Another point regarding the line "curiously the scalar triple product definition dominates most intro texts" line in the introductory paragraph. It probably follows from the usual derivation procedure used to introduce the interaction between the incident wave and electron clouds, which usually begins by stressing the independence of the primitive lattice vectors and 3D nature of the lattice. So a combined form is mathematically/geometrically astute, but not very intuitive upon a comparison with the original independent primitives presentation. Just an opinion. --129.6.130.22 (talk) 12:35, 21 June 2010 (UTC)

Diagrams[edit]

It would be beneficial to people new to the concept to have some diagrams of lattices in normal space alongside the reciprocal versions. e.g., in 2d square and hexagonal lattices and some simple 3d, e.g., bcc fcc lattices.Pondermotive (talk) 02:56, 10 March 2011 (UTC)

I agree, it would be very helpful to see an example! I'm particularly interested in an example for a finite discrete lattice. 10:57, 26 January 2012 (EST) — Preceding unsigned comment added by 130.207.197.185 (talk)

Article is misconceived and poorly written[edit]

The subject of lattices (the kind that are discrete subgroups of Euclidean space Rn) is a part of mathematics. That should be the way this article is introduced and basically slanted.

This subject has ample application to chemistry and physics, and naturally these ought to be given significant discussion in the article.

This article gets off to an extremely poor start. In the sentence that begins: "Consider a set of points R constituting a Bravais lattice, and a plane wave defined by:", there appear the letters K and r whose meaning is not stated. This certainly is not a "mathematical" description of anything, since a mathematical description doesn't leave letters undefined!!! This is simply an issue of clarity.

In the section "Generalization of a dual lattice" -- a very strange title for an article whose name is "Reciprocal lattice" -- at least two definitions of "dual" lattice are given, with no mention of how they are connected to one another.

Further, the identification of a (finite dimensional real) vector space V with its dual V* is *not* a question of a choice of "Haar measure" but rather the choice of an inner product on V.

If it is felt necessary for there to be a separate article on the applications of reciprocal lattices to physicis -- fine. But reciprocal or dual lattices is a mathematical subject and the underlying narrative, and above all the definitions, should be stated in a careful mathematical way -- completely unlike this article.Daqu (talk) 13:15, 26 August 2011 (UTC)

Then fix it. — Preceding unsigned comment added by 134.226.252.160 (talk) 15:58, 27 August 2011 (UTC)