Question

What fraction of one edge centred octahedral void lies in one unit cell of fcc?

• A. \(\frac 13\)
• B. \(\frac 14\)
• C. \(\frac {1}{12}\)
• D. \(\frac 12\)

Answer 1

The Correct Option is B

In a face-centered cubic (fcc) unit cell, there are several types of voids or interstitial sites where smaller atoms or ions can fit. One of these voids is the octahedral void, which in the context of an fcc lattice, is found at specific locations including the edge centers and the center of the cubic unit cell. 

For an octahedral void located at the edge center of a cube, its geometry involves sharing the void among multiple neighboring unit cells. Specifically, an edge center octahedral void is shared by four unit cells.

Given this sharing distribution, the fraction of the void associated with each individual unit cell can be calculated. Since each edge is shared by four cells, the fraction of an edge-centered octahedral void that belongs to one unit cell is \(\frac{1}{4}\).

Thus, the correct answer to the question is the fraction \(\frac{1}{4}\) of the octahedral void at the edge center that lies within one unit cell of the fcc lattice.

Answer 2

In a face-centered cubic unit cell, each edge is shared by 4 adjacent unit cells. Therefore, if you consider the edge-centered octahedral void, only \(\frac 14^{th}\) of the void is contained within one unit cell. This is because each unit cell contributes \(\frac 14^{th}\) of the void, and when you sum up the contributions from all adjacent cells, you get the complete void.

So, the correct option is (B): \(\frac 14\)