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Metallic Crystals - The Structures of Pure Metals

Face-Centered Cubic Lattice: Tetrahedral Holes

Wireframe modelShow tetrahedral holesHide
1 2 3 4 5 6 7 8 x

The figure depicts a face-centered cubic unit cell. The unit cell contains 4 atoms in total. Because the corner sites are shared by the 8 unit cells that meet there, each only counts as ⅛ of a sphere. On the faces of the cube, each sphere is shared by two unit cells so each only counts as ½:

  • 8 · ⅛ : Atom sites at the corners of the cube
  • 6 · ½ : Atom sites on the faces of the cube

In the closest-packed structures, N atoms are coordinating 2N tetrahedral holes and N octahedral holes. The unit cell depicted here contains a total of 4 atoms. Accordingly, the unit cell also contains 8 tetrahedral holes, which you can highlight by clicking on the numbers in the table. All of the tetrahedral holes are fully contained in the unit cell shown here.

Please think about how it would be possible to geometrically calculate the size of the tetrahedral holes.

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