Question

The parameters of the unit cell of a substance are a = 2.5, b = 3.0, c = 4.0, $\alpha=90^\circ, \beta=120^\circ, \gamma=90^\circ$. The crystal system of the substance is :

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

Hint:

Never assume typos in crystallography questions. Always classify crystal systems strictly using {both axial lengths and interaxial angles}.

Answer 1

The Correct Option is D

To determine the crystal system of a substance from its unit cell parameters, we need to understand how the values of lattice constants and angles correspond to different crystal systems.

1. Given parameters: a = 2.5, b = 3.0, c = 4.0, \alpha=90^\circ, \beta=120^\circ, \gamma=90^\circ.
2. Identify the rules for different crystal systems based on lattice parameters:
   • Triclinic: a ≠ b ≠ c, \alpha \neq \beta \neq \gamma \neq 90^\circ
   • Hexagonal: a = b ≠ c, \alpha = \beta = 90^\circ, \gamma = 120^\circ
   • Orthorhombic: a ≠ b ≠ c, \alpha = \beta = \gamma = 90^\circ
   • Monoclinic: a ≠ b ≠ c, \alpha = \gamma = 90^\circ, \beta \neq 90^\circ
3. Comparing the given values:
   • Note that \alpha = \gamma = 90^\circ and \beta = 120^\circ. This implies that one angle is greater than 90°, which matches the monoclinic system.
   • The sides are all different (a ≠ b ≠ c).
4. None of the conditions match triclinic, hexagonal, or orthorhombic systems as they have different angle requirements than the given parameters.

Conclusion: The unit cell parameters correspond to a monoclinic crystal system.