Metallic Crystals - The Structures of Pure Metals
Face-Centered Cubic Lattice: Octahedral Holes
|Wireframe model||Show octahedral hole||Show entire octahedral hole||Hide|
|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.