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How is Cubic Closed Packing "cubic" and also how is hexagonal closed packing "hexagonal" ?

I have been thinking over this since a few hours but I am unable to visualise.

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I understand that when placing the third layer on top of the second layer ,2 situations arise:
If the third layer is placed on the tetrahedral voids it forms an A-B-A-B... type structure which is called hcp(why?)
and If the third layer is placed on the octahedral voids it forms an A-B-C-A-B-C... type structure which is called ccp(why?)

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Start with the hexagonal A-B-A-B structure. It is hexagonal because, choosing one atom in a layer, it is surrounded by 6 equivalent atoms. So, you have a 6-fold symmetry axis, hence the 'hex-'. The fact that it is close-packed can be gotten at mathematically (or at least shown that it is closer-packed than other crystal structures).

Cubic close packing is, at least in most materials science and metallurgy circles, much more commonly called face centered cubic. The 'standard' unit cell is a cube of atoms with additional atoms at the center of each face. It is somewhat harder to visualize how this is related to close-packed planes, although there are many pictures available on-line (one, chosen somewhat randomly, is from Florida State). The point is that the stacking direction of the close-packed planes are along the 111 body diagonal of the cube.

Rotate the cube so that it is standing on one point with the opposite point on the body diagonal pointing up. Your close packed planes are: (1) the bottom point, (2) the top point, (3) the three corner atoms closest to the bottom point as well as the face atoms closest to the bottom atom, (4) the three corner atoms closest to the top atom as well as the face atoms closest to the top atom. It may take some squinting...

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  • $\begingroup$ RE: "Cubic close packing is, at least in most materials science and metallurgy circles, much more commonly called face centered cubic." That just isn't right. There is simple cubic (SC), body centered cubic (BCC) and face center cubic (FCC). BCC and FCC are two different packing arrangements with the same packing fraction. BCC can't be called FCC. $\endgroup$ – MaxW Sep 4 '18 at 17:51
  • $\begingroup$ @MaxW - yes, there are different cubic systems. However, only one is close packed (fcc). $\endgroup$ – Jon Custer Sep 4 '18 at 18:06
  • $\begingroup$ HUH?!? BCC has the same packing fraction as FCC $\approx 74\%$ $\endgroup$ – MaxW Sep 4 '18 at 18:31
  • $\begingroup$ @MaxW - No, that is not correct. The packing fraction of fcc is about 0.74, bcc is only about 0.68, and simple cubic is about 0.52. This is a standard solid state physics homework problem (say, Ashcroft & Mermin chapter 4). $\endgroup$ – Jon Custer Sep 4 '18 at 18:37
  • $\begingroup$ Dah... I confused BCC with hexagonal close packing (HCP) which does have the same packing fraction as FCC. You are right too on the point that only FCC is called cubic close packing. // Thanks for keeping me honest... $\endgroup$ – MaxW Sep 4 '18 at 19:10

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