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Holes in a Cubic Closest-Packed Structure

What type of holes exist in a cubic closest-packed (ccp) 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 a cubic closest-packed structure. The atoms making up the ccp 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 ccp structure. Use the virtual reality depiction to answer the following questions.

  1. What type of unit cell describes the cubic 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. Suppose all tetrahedral holes are occupied by atoms (red). What is the coordination number for a lattice atom (light blue) that is surrounded by atoms in tetrahedral holes? Do the atoms in tetrahedral holes always surround a lattice atom?
  5. How many octahedral holes exist in the unit cell?
  6. Suppose all octahedral holes are occupied by atoms (blue). What is the coordination number for a lattice atom (light blue) that is surrounded by atoms in octahedral holes? Do the atoms in octahedral holes always surround a lattice atom?
  7. How many cubic holes exist in the unit cell?
Unit Cell
 

Atoms in Unit Cell




 

View Along


Atoms in Tetrahedral Holes




 

Atoms in Octahedral Holes



 

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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