Talk:Diamond cubic

Greater clarity

The article describes the positions of atoms in a unit cell as follows:

Atomic placement in unit cell of side length a is given by the following placement vectors.

$\mathbf {r} _{0}={\vec {0}}$

$\mathbf {r} _{1}=(a/4)({\hat {x}}+{\hat {y}}+{\hat {z}})$

$\mathbf {r} _{2}=(a/4)(2{\hat {x}}+2{\hat {y}})$

$\mathbf {r} _{3}=(a/4)(3{\hat {x}}+3{\hat {y}}+{\hat {z}})$

$\mathbf {r} _{4}=(a/4)(2{\hat {x}}+2{\hat {z}})$

$\mathbf {r} _{5}=(a/4)(2{\hat {y}}+2{\hat {z}})$

$\mathbf {r} _{6}=(a/4)(3{\hat {x}}+{\hat {y}}+3{\hat {z}})$

$\mathbf {r} _{7}=(a/4)({\hat {x}}+3{\hat {y}}+3{\hat {z}})$

No explanation is given for what the ${\hat {x}}$, ${\hat {y}}$, or ${\hat {z}}$ mean.

Just in case they represent standard unit basis vectors, wouldn't it be a lot clearer if the article presented the coordinates of the atoms in a unit cell of side length = 1, without inventing mysterious symbols for the unit basis vectors? Also, they could be ordered in an organized manner. The list of points would then be as follows:

( 0, 0, 0),

(1/4, 1/4, 1/4),

(1/2, 1/2, 0),

(1/2, 0, 1/2),

( 0, 1/2, 1/2),

(3/4, 3/4, 1/4),

(3/4, 1/4, 3/4),

(1/4, 3/4, 3/4).

Daqu (talk) 06:23, 2 April 2008 (UTC)

Citations

This article has a good information and it is well written, but it should have some citations. A text book would probably be ideal for this material, although a web source or online publication would do as well.128.97.68.15 (talk) 17:14, 18 July 2008 (UTC)

It's too self-serving for me to add myself, but:

• Eppstein, David (2008), "Isometric diamond subgraphs", Proc. 16th International Symposium on Graph Drawing, arXiv:0807.2218

uses this structure. I also have some talk slides for this paper, including a description of the diamond cubic, here. I searched for other descriptions of this structure to cite both here and in my paper without much success. —David Eppstein (talk) 23:59, 26 September 2008 (UTC)

To be more specific, this paper gives the structure mathematical coordinates in four dimensions that are nicer than the three-dimensional coordinates (they are just the integer points whose coordinates add to zero or one, with two points adjacent when they are at unit distance apart) and describes how to project these four-dimensional points down to 3d to get the more familiar form of the diamond structure. It also shows that, because of this 4d structure, the diamond cubic forms an infinite partial cube. —David Eppstein (talk) 23:19, 15 March 2011 (UTC)

Incorrect information

In the first paragraph, it says that "silicon/germanium alloys in any proportion" follow the diamond structure. That's not accurate. The overall positions of atoms may be the same as in the diamond structure, but if the atoms are not all the same, the structure is different. For example, with a 50-50 ratio, the material could be the zinc-blende structure. Diamond and zinc-blende do not share the same space group, as this article would imply. — Preceding unsigned comment added by Johncolton (talk • contribs) 00:11, 31 December 2010 (UTC)

Rotating figures

I think the rotating figures would be much more useful if the rotation could be stopped at any frame by clicking. (Even more useful might be if they could be rotated by the user, but that is secondary.) — Preceding unsigned comment added by 71.191.142.176 (talk) 14:19, 6 August 2016 (UTC)

I agree. Having two nearly identical rotating figures is just plain stupid. The article NEEDS a drawing of the unit cell. Not something that moves around in random directions. It took me several minutes to even count the number of atoms in the videos: ridiculous!!!98.21.210.4 (talk) 15:25, 10 June 2017 (UTC)

Giant molecule

• As the diamond structure looks like a polycyclic cage-type hydrocarbon taken to extremes, can it be said that a diamond crystal is a single giant covalent molecule? Anthony Appleyard (talk) 22:45, 6 August 2017 (UTC)

There is nothing in the definition of a molecule that rules out network solids, but people who study these solids don't tend to call them molecules. It seems there is nothing to be gained or lost either way, so go nuts. Student298 (talk) 21:19, 9 August 2020 (UTC)

Lattice

I have moved the following discussion from the user talk page I started it at, because it more appropriately belongs here.Student298 (talk) 18:26, 9 August 2020 (UTC)

Maybe this is the definition of lattice which we should consider relevant to the Diamond Cubic page: https://en.wikipedia.org/wiki/Bravais_lattice Student298 (talk) 03:45, 9 August 2020 (UTC)

It's still not a lattice in the usual mathematical meaning of the term. Yes, you can find meanings of "lattice" that include the diamond lattice, for instance by defining a lattice to be "one of these things called lattices" regardless of whether there is a natural mathematical definition that they all fit. But people familiar with the mathematical term of lattice, a set of repeating points with certain very specific properties (most importantly, adding the coordinates of any two of them produces another) are going to be confused by seeing the diamond lattice called a lattice when it resembles the mathematical lattices but is not one. We need to head off the confusion by letting them know that it really is not one. I don't understand why you think this useful and relevant information should be censored from the article. —David Eppstein (talk) 04:51, 9 August 2020 (UTC)

The article is not a mathematics article, so I don’t see why the failure to fit with a mathematical use of the word ‘lattice’ is relevant, when the diamond lattice is a perfectly fine example of a lattice in the sense of crystal structure: https://www.chemicool.com/definition/lattice_crystal.html

People familiar with that mathematical definition can fairly easily determine that the diamond lattice doesn't correspond to the points of a discrete subgroup of R^3. I think it's enough to clear up that potential confusion in the mathematical section for anyone who is trying to figure out what's going on with alternative meanings of the word. Also, maybe it's worth mentioning that the diamond lattice is an orbit of a mathy lattice in E(3). Student298 (talk) 18:14, 9 August 2020 (UTC)

It is not solely a mathematics article; about half of it is mathematics. So your statement that it is completely not a mathematics article is far from correct. The lead section is supposed to summarize the content of the article; see MOS:LEAD. That sentence in the lead both summarizes part of the mathematics section, and explains some of the naming of the article (why it might be called something other than a lattice in mathematical contexts); it should stay in the lead. Again, I don't see why you think its removal improves the article. —David Eppstein (talk) 19:29, 9 August 2020 (UTC)

I'll grant that a clarification does improve the lead. However, I don't like the way it is currently phrased because it implies that 'diamond lattice' is a misnomer, when in fact it just doesn't fit with this particular definition.Student298 (talk) 21:23, 9 August 2020 (UTC)

It is also not a lattice in the (more or less equivalent) sense used at the start of Bravais lattice, because its unit cell is not primitive. —David Eppstein (talk) 22:17, 9 August 2020 (UTC)

There is no requirement that the cell be primitive. It also states further down, when describing "the expanded Bravais lattice concept": "A crystal is made up of a periodic arrangement of one or more atoms". One of the sources used on the page for Crystal, by the way, is a database of crystal lattices, including the diamond lattice: https://homepage.univie.ac.at/michael.leitner/lattice/struk/a4.htmlStudent298 (talk) 19:59, 11 August 2020 (UTC)

There is also no disagreement that some people call it the diamond lattice. So I don't see what another link to another person calling it a diamond lattice is supposed to prove. —David Eppstein (talk) 20:30, 11 August 2020 (UTC)

My main point was that the Bravais lattice definition was more relevant to this article than the group theory one, and that the Bravais lattice definition does not require, as you claim, that there be only one atom in its basis.Student298 (talk) 02:33, 13 August 2020 (UTC)

"Mathematical Structure" section does not match diagrams

This page gives the following list of points for locations in a single lattice unit, scaled up to a side length of 4:

(0,0,0), (0,2,2), (2,0,2), (2,2,0), (3,3,3), (3,1,1), (1,3,1), (1,1,3)

However, the exploded lattice diagram shows a lattice unit comprising eight sub-units, where four of these sub-units are empty and the other four consist of a tetrahedron with a captured point in the center. That corresponds to a point list of:

(0,0,0), (0,2,2), (2,0,2), (2,2,0), (1,1,1), (1,3,3), (3,1,3), (3,3,1)

The first four points could be thought of as the four corners of the tetrahedron anchored at the origin, or alternately the anchor points of the four non-vacant sub-units; the last four points correspond to the captured point within each sub-unit tetrahedron, each offset by (1,1,1) from its anchor point.

The points as listed, however—along with the equation that produces them—require the "captured" points to be at the centers of the VACANT sub-units, rather than at the centers of the tetrahedrons.

Which of these is correct?

Cirne (talk) 14:10, 2 May 2022 (UTC)

The diagrams are not labeled by their coordinate axes. Isn't it just a question of relabeling? —David Eppstein (talk) 15:56, 2 May 2022 (UTC)