In which of the following systeams interfacial angles `alpha = gamma = 90^(@)` but `beta != 90^(@)`?

Options

A. Monoclinic
B. Rhombohedral
C. Triclinic
D. Hexagonal

Answer

To solve the question, we need to analyze the interfacial angles of different crystal systems and identify which one satisfies the conditions given: α = γ = 90° and β ≠ 90°.

### Step-by-Step Solution:

1. **Understanding Crystal Systems**:
We need to recall the definitions of the interfacial angles in different crystal systems. The main systems to consider are monoclinic, rhombohedral, triclinic, and hexagonal.

2. **Monoclinic System**:
- In the monoclinic system, the interfacial angles are defined as:
- α = 90°
- β ≠ 90°
- γ = 90°
- This satisfies the condition α = γ = 90° and β ≠ 90°.

3. **Rhombohedral System**:
- In the rhombohedral system, the interfacial angles are:
- α = β = γ ≠ 90°
- This does not satisfy the condition since all angles are equal and not equal to 90°.

4. **Triclinic System**:
- In the triclinic system, the interfacial angles are:
- α ≠ β ≠ γ
- None of the angles are equal to 90°, which does not satisfy the condition.

5. **Hexagonal System**:
- In the hexagonal system, the interfacial angles are:
- α = β = 90°
- γ = 120°
- This does not satisfy the condition since γ is not equal to 90°.

6. **Conclusion**:
- After analyzing all the systems, the only one that satisfies the condition α = γ = 90° and β ≠ 90° is the **monoclinic system**.

### Final Answer:
The correct answer is **monoclinic**.