Which of the following unit cell is not possible for monoclinic crystals ?

Options

A. Primitive
B. End centre
C. face centre
D. All of these

Answer

To determine which unit cell is not possible for monoclinic crystals, we need to understand the characteristics of monoclinic crystals and the types of unit cells.

### Step-by-Step Solution:

1. **Understand Monoclinic Crystal System**:
- In a monoclinic crystal system, there are three axes of unequal lengths (a, b, c) and two angles are 90 degrees (α = 90°, γ = 90°) while the third angle (β) is not equal to 90 degrees.

2. **Identify Types of Unit Cells**:
- **Primitive Unit Cell**: Atoms are located only at the corners of the unit cell.
- **End-Centered Unit Cell**: Atoms are located at the corners and at the center of two opposite faces.
- **Face-Centered Unit Cell**: Atoms are located at the corners and at the center of each face of the unit cell.

3. **Analyze Each Unit Cell Type for Monoclinic**:
- **Primitive Unit Cell**: This can exist in a monoclinic system since it only requires atoms at the corners, which is permissible.
- **End-Centered Unit Cell**: This can also exist in a monoclinic system because it allows for atoms at the corners and at the center of two opposite faces, which fits the monoclinic structure.
- **Face-Centered Unit Cell**: This cannot exist in a monoclinic system because it requires atoms at the center of all faces, which contradicts the monoclinic structure where only two angles are 90 degrees.

4. **Conclusion**:
- The only unit cell type that is not possible for monoclinic crystals is the **Face-Centered Unit Cell**.

### Final Answer:
**Face-Centered Unit Cell is not possible for monoclinic crystals.**