Holes in a Hexagonal Closest-Packed Structure

What type of holes exist in a hexagonal closest-packed (hcp) structure? How many holes of each type are there?

There are many trigonal holes, but these holes are rarely occupied in ionic solids.

The display below shows a unit cell for the hexagonal closest-packed structure. The atoms making up the hcp structure are shown in a light blue color. The largest atoms that fit into tetrahedral holes are shown in red, and the largest atoms that fit into octahedral holes are shown in dark blue.

The controls for the display allow various combinations of atoms to be displayed in order to illustrate the positions of the various holes in the ccp structure. Carefully examine the structure from various perspectives for different display settings and answer the following questions.

1. How many lattice atoms (light blue) are contained in the unit cell?
2. How many tetrahedral holes exist in the unit cell?
3. If all tetrahedral holes are occupied by atoms (red), how many such atoms are contained in the unit cell?
4. How many octahedral holes exist in the unit cell?
5. If all octahedral holes are occupied by atoms (blue), how many such atoms are contained in the unit cell?
6. How many cubic holes exist in the unit cell?
7. The hcp structure has open channels that run straight through the structure. Do any of the holes lie in this channel? If so, what is the geometry of these holes?

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