What is the number of octahedral voids per constituent particle in fcc?

In a cubic close packed structure, there are four octahedral voids in total. Aside from the body centre, each of the twelve edges has one octahedral vacancy in its centre. It is surrounded by six atoms, two of which belong to two neighbouring unit cells and four of which belong to the same unit cell (two on the corners and two on the face centres). Because each edge of the cube is shared by four neighbouring unit cells, the octahedral void on it is also shared.

Only one-fourth of each void belongs to a particular unit cell. Thus, in a cubic close packed structure, the octahedral void at the body centre of the cube will be one.

Twelve octahedral voids are located at each edge and are shared by four-unit cells; thus, the number of octahedral voids will be 12×14=3.

So, the total number of octahedral voids in cubic closed packed is four. We know, in CCP structure each unit cell has four atoms. Thus, the number of octahedral voids will be 44=1. Thus, the total number of octahedral void(s) per atom present in a cubic close packed structure is one.

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