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Metallic Crystals - The Structures of Pure Metals

Face-Centered Cubic Lattice: Octahedral Holes

Wireframe modelShow octahedral holeShow entire octahedral holeHide
1 2 3 4 5 6 7 8 9 10 11 12 x x

The figure shows 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 counts as only 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 4 octahedral holes, which you can show or hide by clicking the numbers in the table. One of the octahedral holes is completely contained in the unit cell represented; 12 are only ¼ present.

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

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