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I know that FCC shows ABC type but I am confused about it. For simple cubic and body centered, it is pretty easy to work out the packing arrangement but FCC is giving me a headache.

What is this Wikipedia article trying to tell in the diagram and how did choose A, B and C? What's up with the different orientations?

enter image description here

Can somebody tell me these in a simple way as I can't solve FCC problems based on structure.

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Perhaps the simple way to look at this is think of the sphere structures as three layers. Think of the (x,y) coordinates of the spheres, neglecting the z coordinate. The first (white balls) and second layers (black balls) are the same in HCP and FCC. So let's label the first layer the A layer and the second layer the B layer.

Now we add the third layer.

enter image description here

  • In HCP, which is shown on the left in the above image, the center of spheres in the third layer would be placed directly over the center of a sphere in the A (first) layer. So the third layer (white ball)is another A layer.

  • In FCC, which is shown on the right in the above image, the spheres in the third layer (green ball) would be offset by 1/2 the radius of the sphere, above a sphere in the first layer. (Note that the dashed circle denotes a position directly above the A level circle.) So the third layer is neither an A layer nor a B layer. Let's call it a C layer. Now the fourth layer would again have spheres whose center are directly above the center of the spheres in the first layer. So it would be another A layer.

So HCP has (AB)(AB)(AB)... layers but FCC has (ABC)(ABC)(ABC)... layers. Where A, B and C denote different sets of (x,y) coordinates. Again the z coordinate being the layer of the ball coming out of the 2D image.

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  • $\begingroup$ Sorry for the late activity.I am stuck at B layer......isn't the black sphere B placed like in three dimensional.I thought the B layer would be 2nd white layer from the bottom of your picture or is the entire white layer A $\endgroup$ – Hydrous Caperilla Jul 6 '18 at 10:39
  • $\begingroup$ And how are B layers placed w.r.t A layer...if I can understand that then that will help a lot $\endgroup$ – Hydrous Caperilla Jul 6 '18 at 11:21
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    $\begingroup$ I edited this a bit again. The (x,y) coordinates are in the plane of the paper (monitor). The z coordinated would be due to balls stacking. Does that help? $\endgroup$ – MaxW Jul 6 '18 at 14:59
  • $\begingroup$ Yeah I understand but I am confused about the arrangement of B layer....I know they fill the voids of layer A but isn't it physically impossible to cover all gaps with theme......does that mean we can't predict stacking of B? $\endgroup$ – Hydrous Caperilla Jul 6 '18 at 22:31
  • $\begingroup$ And how come the number of B layer atoms is different in these two structures? $\endgroup$ – Hydrous Caperilla Jul 6 '18 at 22:39

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