# ABC arrangement of FCC/CCP

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?

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

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.

• 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.

• 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 Jul 6 '18 at 10:39
• And how are B layers placed w.r.t A layer...if I can understand that then that will help a lot Jul 6 '18 at 11:21
• 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?
– MaxW
Jul 6 '18 at 14:59
• 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? Jul 6 '18 at 22:31
• And how come the number of B layer atoms is different in these two structures? Jul 6 '18 at 22:39