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

To solve the question of what fraction of one edge-centred octahedral void lies in one unit cell of an FCC (face-centered cubic) structure, we need to understand the geometry and arrangement of octahedral voids in this type of crystal lattice.

1. An FCC unit cell consists of a cubic arrangement where atoms occupy each of the eight corners and the centers of all six faces of the cube.
2. Octahedral voids are a type of vacant space that occurs in crystal lattices, specifically at the center and along the edges of the unit cells.
3. In an FCC unit cell:
   • There is one octahedral void at the center of the cube.
   • There is one octahedral void at the center of each edge of the cube. Since the cube has 12 edges, there are 12 edge-centered octahedral voids.
4. Each edge-centered octahedral void is shared between four unit cells because it lies at the intersection of four cells.
5. Therefore, the fraction of an edge-centered octahedral void within a single unit cell is given by: \(\frac{1}{4}\).

Therefore, the correct answer is \(\frac{1}{4}\), meaning one-fourth of an edge-centered octahedral void lies within one unit cell of an FCC lattice.