Which of the following characteristic features match(es) with the crystal systems: hexagonal and monoclinic?

Options

A. Both have the cell parameters a = b = c and `alpha=beta=gamma`
B. Both belong to different crystal systems
C. Both have only two crystallographic angles of `90^(@)`
D. Both belong to same crystal system

Answer

To determine the characteristic features that match the hexagonal and monoclinic crystal systems, we need to analyze the properties of each system step by step.

### Step 1: Understand the Hexagonal Crystal System
- In the hexagonal crystal system, there are four axes: three of equal length (a1, a2, a3) that are 120 degrees apart in the same plane, and one axis (c) that is perpendicular to this plane.
- The edge lengths are not equal: a1 = a2 = a3 ≠ c.
- The angles are: α = β = 90 degrees, and γ = 120 degrees.

### Step 2: Understand the Monoclinic Crystal System
- In the monoclinic crystal system, there are three axes of unequal lengths (a, b, c).
- Two angles are 90 degrees, and the third angle (γ) is not 90 degrees.
- The edge lengths are not equal: a ≠ b ≠ c.
- The angles are: α = γ = 90 degrees, and β ≠ 90 degrees.

### Step 3: Compare the Features
- **Edge Lengths**:
- Hexagonal: a1 = a2 = a3 ≠ c
- Monoclinic: a ≠ b ≠ c
- **Angles**:
- Hexagonal: α = β = 90°, γ = 120°
- Monoclinic: α = γ = 90°, β ≠ 90°

### Conclusion
- Both crystal systems have two angles equal to 90 degrees.
- The edge lengths are not equal in both systems.
- The third angle is different in both systems.

### Final Answer
The characteristic features that match with the hexagonal and monoclinic crystal systems are:
1. Both have two angles equal to 90 degrees.
2. Edge lengths are not equal.