Which of the following unit cells is the most unsymmetrical ?

Options

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

Explanation

To determine which of the following unit cells is the most unsymmetrical, we will analyze the characteristics of each unit cell type: triclinic, orthorhombic, monoclinic, and hexagonal.

### Step-by-Step Solution:

1. **Understanding Unit Cells**:
- A unit cell is the smallest repeating unit in a crystal lattice that reflects the symmetry and structure of the entire crystal.
- The symmetry of a unit cell is determined by its edge lengths and angles.

2. **Triclinic Unit Cell**:
- In a triclinic unit cell, the edge lengths are all unequal: \(a \neq b \neq c\).
- The interaxial angles are also unequal and not equal to 90 degrees: \(\alpha \neq \beta \neq \gamma\) and \(\alpha, \beta, \gamma \neq 90^\circ\).
- This lack of equality in both edge lengths and angles indicates a high degree of asymmetry.

3. **Orthorhombic Unit Cell**:
- In an orthorhombic unit cell, the edge lengths are unequal: \(a \neq b \neq c\).
- However, all angles are equal to 90 degrees: \(\alpha = \beta = \gamma = 90^\circ\).
- This symmetry in angles reduces the overall asymmetry compared to the triclinic unit cell.

4. **Monoclinic Unit Cell**:
- In a monoclinic unit cell, two edge lengths are unequal: \(a \neq b\) and \(a \neq c\) and \(b \neq c\).
- The angles are such that \(\alpha = \gamma = 90^\circ\) and \(\beta \neq 90^\circ\).
- While there is some asymmetry, it is less than that of the triclinic unit cell.

5. **Hexagonal Unit Cell**:
- In a hexagonal unit cell, two edge lengths are equal: \(a = b\) but \(a \neq c\).
- The angles are \(\alpha = \beta = 90^\circ\) and \(\gamma = 120^\circ\).
- This structure has a significant degree of symmetry due to equal angles.

6. **Conclusion**:
- Among the four types of unit cells, the triclinic unit cell is the most unsymmetrical due to its unequal edge lengths and angles that are not equal to 90 degrees.
- Therefore, the answer is **Option A: Triclinic**.