What is the coordination number of a sphere in s hexagonal closest packed struct

Question

What is the coordination number of a sphere in s hexagonal closest packed structure? In a cubic dose packed (or face-centered cubic) structure? How do the coordination numbers in these two structures compare? How do the fractions of space occupied by the spheres compare for the hexagonal closest packed arm the cubic closest packed structures? Is it possible to pack spheres more densely than in these two structures? Explain in terms of your observations on the models you built corresponding to Figures 7 and 8.

Explanation / Answer

E-1. Coordination number is 12 for both Hexagonal Closest Packed structure and Face-centered Cubic.

In a hexagonal closes packed structure, the structure repeats itself after every two layers and the stacking is described as "a-b-a-b-a-b type". The arrangement in a cubic closes packing is also similar to hcp, however, the structure does not repeat until a fourth layer is added. The second layer of spheres is placed on top of half of the depressions of the first layer. And so on. This type of arrangement of layers is termed "a-b-c-a-b-c type"

E-2. The fraction of space occupied by HCP is 74.04% and CCP is also 74.04% i.e., they are equally efficient in packing.

E-3. No. The most efficient way to put sphere around is each is HCP and CCP as described in E-1.

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