The relation `a!=b!=c` and `alpha!=beta!=gamma!=90^(@)` represents which crystal system ?

Options

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

Answer

To determine which crystal system is represented by the relations \( a \neq b \neq c \) and \( \alpha \neq \beta \neq \gamma \neq 90^\circ \), we can follow these steps:

### Step 1: Understand the Notation
The notation \( a \), \( b \), and \( c \) represents the lengths of the edges of a unit cell in a crystal lattice, while \( \alpha \), \( \beta \), and \( \gamma \) represent the angles between these edges.

### Step 2: Analyze the Conditions
The conditions given are:
- \( a \neq b \neq c \): This means that the lengths of the edges are all different from each other.
- \( \alpha \neq \beta \neq \gamma \neq 90^\circ \): This indicates that all angles are different and none of them is equal to 90 degrees.

### Step 3: Identify the Crystal System
In crystallography, different combinations of edge lengths and angles define different crystal systems. The specific conditions provided:
- All edge lengths are different.
- All angles are different and not equal to 90 degrees.

These conditions are characteristic of the **triclinic crystal system**, which is the least symmetric of all crystal systems. In the triclinic system, there are no equal lengths or angles, and it does not have any right angles.

### Conclusion
Thus, the crystal system represented by the relations \( a \neq b \neq c \) and \( \alpha \neq \beta \neq \gamma \neq 90^\circ \) is the **triclinic crystal system**.