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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 virtual reality 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 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 hcp structure. Use the virtual reality depiction to answer the following questions.

  1. What type of unit cell describes the hexagonal closest-packed structure?
  2. How many lattice atoms (light blue) lie, either completely or partially, in the unit cell?
  3. How many tetrahedral holes exist in the unit cell?
  4. How many octahedral holes exist in the unit cell?
  5. How many cubic holes exist in the unit cell?
  6. 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?
Unit Cell

Atoms in Unit Cell


Atoms in Tetrahedral Holes

Atoms in Octahedral Holes

View Along

This virtual reality display requires Java3D. If the display is not visible, consult the Java3D FAQ. Dragging with the left mouse button rotates the display. Dragging with the center mouse buttons expands the display, and dragging with the right mouse button moves the display.

Holes in the Cubic Closest-Packed Structure                 Holes in the Hexagonal Closest-Packed Structure

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