Which the following is true about the size of tetrahedral and octahedral voids ?

Options

A. Size of tetrahedral void = Size of octahedral void
B. Size of tetrahedral void `gt` Size of octahedral void
C. Size of tetrahedral void `lt` Size of octahedral void
D. Size of voids depends on the size of atoms present in packing

Answer

To determine the relationship between the sizes of tetrahedral and octahedral voids, we can follow these steps:

### Step 1: Understand the Number of Voids
In a close-packed structure, the number of tetrahedral and octahedral voids can be determined based on the number of closely packed spheres (atoms).
- For every 'n' closely packed spheres, the number of tetrahedral voids is 2n, and the number of octahedral voids is n.

### Step 2: Example in FCC Structure
In a face-centered cubic (FCC) unit cell:
- There are 4 atoms (n = 4).
- Therefore, the number of tetrahedral voids = 2n = 2 × 4 = 8.
- The number of octahedral voids = n = 4.

### Step 3: Radius Ratio Concept
To compare the sizes of tetrahedral and octahedral voids, we need to consider the radius ratio (R/r):
- R = radius of the closely packed sphere.
- r = radius of the void.

### Step 4: Radius Ratio Values
- The radius ratio for tetrahedral voids (r/R) is approximately 0.225.
- The radius ratio for octahedral voids (r/R) is approximately 0.414.

### Step 5: Comparison of Sizes
Since the radius ratio for octahedral voids (0.414) is greater than that for tetrahedral voids (0.225), we can conclude that:
- The size of octahedral voids is larger than the size of tetrahedral voids.

### Conclusion
Thus, the correct statement regarding the sizes of tetrahedral and octahedral voids is that octahedral voids are larger than tetrahedral voids.