Talk:Close-packing of equal spheres

message: There are two regular lattices that achieve this highest average density.
There's actually a few other regular lattices that have just as high average density.
Let's start with a hexagonally-close-packed sheet of atoms (marbles, spheres, whatever): A.
(See http://www.kings.edu/~chemlab/vrml/clospack.html for some pretty illustrations).
Pack a second sheet B on top of the first.
The third layer is where something very interesting happens.
* We *could* line up the atoms in the 3rd sheet directly over the atoms in A --
and keep repeating A-B-A-B-A-B... . This gives us "hexagonal close packed" hcp.
* We *could* line up the atoms in the 3rd sheet in so they *don't* line up with the atoms in A. Then we could make the 4th sheet line up with A, and repeat: A-B-C-A-B-C-A-B-C. This is "cubic close packed" ccp.
Are these the *only* possibilities ?
I vaguely remember hearing that some real crystals form such a close-packed lattice, but one different from hcp or ccp. Perhaps it was something like
* A-B-C-B-A-B-C-B-A
* A-B-A-B-C-A-B-A-B-C.
Anyone remember exactly what it was that formed those crystals ?
If I knew its name, I could google for more information.
--DavidCary 05:10, 8 Jan 2005 (UTC)
replies: text: I added the 3D ray-tracings. I think they make it much easier to visualize what’s going on. Greg L (my talk) 14:11, 26 April 2007 (UTC)
thread_title: Only two regular lattices?

message: The hexagonal lattice linked from here is not the packing intended; in terms of this article's notation it is AAA, less dense.  --Tamfang 23:42, 15 January 2006 (UTC)
thread_title: Hexagonal lattice

message: I originally came to this site hoping to find an easy way to make a lattice for close packing spheres. So, on the chance someone else might want that I added  that section. It is somewhat unclear I realize and probably not in good wikipedia style. Thanks for the help. Mangledorf 18:37, 31 July 2007 (UTC)
thread_title:  Lattice Formation Section 

message: Hi
The animated gif (Fig.6) shows how the hcp structure is built up. First, plane A is constructed showing red triangles with a magenta height h=a*sqrt(3)/2. Plane B is now positioned at a delta-y of h/3 which should be h/2.
wolf  —Preceding unsigned comment added by 131.130.25.66 (talk) 10:42, 30 October 2007 (UTC)
replies: text:  I am changing the caption of the animated gif.  I am disappointed that such sloppy work has gone uncorrected for so long.  Two layers of spheres do NOT differentiate between fcc and hcp structure.  That is, the gif is wrong because it is incomplete.  Apparently, since it is animated it has been uncritically accepted as being useful.  My opinion is that it should be removed, it is mostly useless, especially without a third layer being added.  But I will just edit the caption to say that it is showing the first two layers of either a fcc or a hcp structure.  I also note here that not only are A-B-A-B... and A-B-C-A-B-C structures possible but so are structures with mixes of A-B-A and A-B-C ordering.216.96.79.169 (talk) 22:00, 1 May 2013 (UTC)
thread_title:  Animated gif is misleading 

message: I pruned the long list of graphics here.  Some of them were redundant, and the large number made it hard to clearly see the difference between FCC and HCP. -- Beland (talk) 19:11, 24 April 2008 (UTC)
thread_title:  Too many graphics 

message: This article should mention why random packing could never exceed the FCC close-packing limit. This article http://www.physorg.com/news131629886.html talks about how physicists have very recently derived mathematics to prove this as it has never properly been proven until now.H0dges (talk) 20:30, 2 June 2008 (UTC)
thread_title:  Random Packing 

message: Far from the current controversy, I would like to make a modest suggestion: could someone include a mention of the relation of this to the constant above?  Katzmik (talk) 16:07, 17 September 2008 (UTC)
thread_title:  [[Hermite constant]] 

message: Ran into a german mathmattician on the street in SF.  He said, pre-newton, there used to be an "Angel Theory", the basis of isaac disraeli's derision "lets not argue how many angels can fit on the head of a needle."  Debate came up because angels are "perfect" hence they are "spheres" (cf ptolemaic), and "invisible" hence "infinitesmal".  I can't find anything on the net or in history books.  Does anyone know if this really from a historic debate regarding a packing problem of spheres, or was he pulling my leg? Tautologist (talk) 20:43, 27 September 2008 (UTC)
thread_title:  Close Packing Spheres ("on the head of a needle") 

message: Can someone put up an additional section for simple fcc or ccp lattice??? They have included one for hcp but nor for fcc. So please add it up is someone can  —Preceding unsigned comment added by Nradam (talk • contribs) 02:03, 15 February 2009 (UTC)
thread_title:  FCC LATTICE 

message: Just been reading "Kepler's Conjecture" (Wiley 2003) by George G Szpiro. On page 18 he states "it turns out that the FCC and the HCP are the exact same packing, viewed from different angles!" citing an illustration in Barlow 1833.
I am not an expert in close packing but what do you say to this? The book was well received by all the major journals  --Nick Green (talk) 16:46, 19 February 2009 (UTC)
replies: text: If you consider only two adjacent layers, FCC and HCP look alike; so they have the same density, and if you're looking to prove or disprove the Kepler conjecture there may be no reason to distinguish them.  But if you crush FCC you get rhombic dodecahedra, while if you crush HCP you get trapezo-rhombic dodecahedra. —Tamfang (talk) 01:26, 20 February 2009 (UTC)
thread_title:  FCC and HCP are the same thing 

message: It probably doesn't fit in the article but this picture is nice.
JIMp talk·cont 01:00, 11 July 2009 (UTC)
thread_title:  Snowballs 

message: Doesn't function on a Mac running Mac OS 10.6.3 using Safari browser.  —Preceding unsigned comment added by 67.180.152.105 (talk) 07:36, 21 May 2010 (UTC)
replies: text: Neither it works on Windows with Firefox. There are constant problems with displaying animated gifs on wikipedia, and while changing image size options sometimes solve this, wikimedia updates change things from time to time. For myself, I decided to wait until the developers fix this problem for good. Materialscientist (talk) 07:50, 21 May 2010 (UTC)
thread_title:  Animated GIF Does Not Work 

message: To whomever keeps reverting the correction.
You either 
a) have to change your description of what the pitch parallel to z is ie.
"The distance between sphere centers parallel to the z axis"
or
b) the equation that says the distance is
\text{pitch}_Z = \sqrt{6} \cdot {d\over 3}\approx0.81649658 d,
Unless you can explain to me how the centers of two spheres can be a distance of less than 1 diameter apart from each other.  —Preceding unsigned comment added by 24.80.230.150 (talk) 02:04, 17 October 2010 (UTC)
replies: text: It is a projection on z axis, and thus is smaller than the diameter. Materialscientist (talk) 02:09, 17 October 2010 (UTC)
thread_title:  Pitch z  

message: The end of the second line of the caption for Figure 2 runs into the beginning of the second line of the caption for Figure 3; it looks like "stack shown in Figure 3 only in stack,". Someone please fix, I suppose by moving the "only in" down to start the third line. I don't know how to do it.HowardJWilk (talk) 16:10, 14 May 2016 (UTC)
thread_title:  Captions for figures 2 and 3 

message: In the section "Positioning and spacing" something's amiss. The sentence "Relative to a reference layer with positioning A, two more positionings B and C are possible" seems to have the implicit requirement on the reference layer to be hexagonal. It seems to me it should read "Relative to a hexagonal reference layer with positioning A, two more positionings B and C are possible." The way it is right now, it would allow the reference layer to be tetragonal, which leads to contradictions in various places. For instance, the picture labeled "FCC arrangement seen on 4-fold axis direction", as well as the rear snowball stack, both have a tetragonal base, if I use that as the reference layer, the the structure is clearly ABAB, hence HCP, and not FCC, as clearly labeled. If the reference layer is required to be hexagonal, then it would need to be one of the sides of the snowball stack, and then I can see the ABCABC, hence FCC.
The insertion of the word as mentioned is what I can see resolves the contradictions, but maybe they can (and should) be resolved in different way? Can some expert please clear this up, and modify the article accordingly?79.223.69.169 (talk) 12:30, 9 January 2022 (UTC)
thread_title:  Essential information only implicit?