Question

The Rhombohedral crystal structure has (where a, b, c are lattice parameters and \(\alpha, \beta, \gamma\) are their angles):

• A. \( a = b = c, \, \alpha = \beta = \gamma = 90^\circ \)
• B. \( a \ne b \ne c, \, \alpha \ne \beta \ne \gamma \ne 90^\circ \)
• C. \( a \ne b = c, \, \alpha \ne \beta = \gamma = 90^\circ \)
• D. \( a = b = c, \, \alpha = \beta = \gamma \ne 90^\circ \)

Hint:

In rhombohedral crystals, all edges are equal, and all angles are equal but not right angles. This distinguishes them from cubic structures where both sides and angles are equal and 90°.

Answer 1

The Correct Option is D

The rhombohedral (or trigonal) crystal system is one of the seven crystal systems in crystallography.
It is characterized by the following parameters: all three axes are of equal length (\( a = b = c \)), but the angles between them are equal and not 90 degrees (\( \alpha = \beta = \gamma \ne 90^\circ \)).
This leads to a unit cell shaped like a rhombohedron, where each face is a rhombus.
Such symmetry makes this system distinct from the cubic system, which has \( \alpha = \beta = \gamma = 90^\circ \).