A unit cell is obtained by closed packing layers of atoms in ABAB …… pattern. The total number of tetrahedral and octahedral voids in the unit cell are respectively

Options

A. 6, 12
B. 8, 4
C. 4, 8
D. 12, 6

Answer

To solve the problem of finding the total number of tetrahedral and octahedral voids in a unit cell with an ABAB... closed packing pattern, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Type of Packing**:
- The given packing pattern is ABAB..., which corresponds to hexagonal close packing (HCP).

2. **Determine the Number of Atoms per Unit Cell (Z)**:
- In hexagonal close packing, the number of atoms per unit cell (Z) is 6.

3. **Use the Formulas for Voids**:
- The number of tetrahedral voids (T) and octahedral voids (O) can be calculated using the following formulas:
- Tetrahedral voids = 2n (where n is the number of atoms in the unit cell)
- Octahedral voids = n

4. **Calculate the Number of Tetrahedral Voids**:
- Since Z = 6 (n = 6), the number of tetrahedral voids is:
\[ T = 2n = 2 \times 6 = 12 \]

5. **Calculate the Number of Octahedral Voids**:
- The number of octahedral voids is:
\[ O = n = 6 \]

6. **Final Result**:
- Therefore, the total number of tetrahedral voids is 12 and the total number of octahedral voids is 6.

### Summary:
- Tetrahedral voids = 12
- Octahedral voids = 6