Question

The number of crystal systems in three dimensions is

• A. 5
• B. 7
• C. 10
• D. 14

Hint:

Remember the popular mnemonic device to keep the 7 crystal systems in order: Cub Touches Our Red Hen's Medical Toe \(\rightarrow\) Cubic, Tetragonal, Orthorhombic, Rhombohedral, Hexagonal, Monoclinic, Triclinic.

Answer 1

The Correct Option is B

Concept: To categorize all possible periodic crystal structures, crystallography defines basic unit cell shapes based on their essential geometric parameters. These parameters include the lengths of the three principal edges of the unit cell (\(a, b, c\)) and the angles between those edges (\(\alpha, \beta, \gamma\)). In three-dimensional space, all possible translational lattice configurations can be grouped into exactly 7 distinct crystal systems.

Step 1: The 7 Crystal Systems listed with their parameters.
The seven systems, ordered from highest to lowest geometric symmetry, are:
• Cubic: \(a = b = c\) and \(\alpha = \beta = \gamma = 90^\circ\)
• Tetragonal: \(a = b \neq c\) and \(\alpha = \beta = \gamma = 90^\circ\)
• Orthorhombic: \(a \neq b \neq c\) and \(\alpha = \beta = \gamma = 90^\circ\)
• Rhombohedral (Trigonal): \(a = b = c\) and \(\alpha = \beta = \gamma \neq 90^\circ\)
• Hexagonal: \(a = b \neq c\) and \(\alpha = \beta = 90^\circ, \gamma = 120^\circ\)
• Monoclinic: \(a \neq b \neq c\) and \(\alpha = \gamma = 90^\circ, \beta \neq 90^\circ\)
• Triclinic: \(a \neq b \neq c\) and \(\alpha \neq \beta \neq \gamma \neq 90^\circ\) (completely asymmetric)

Step 2: Addressing potential confusion with 14.
A common source of confusion is the number 14. There are 14 Bravais Lattices, which represent the total number of unique ways lattice points can be arranged in space. However, those 14 variations fit into the 7 broad geometric crystal systems listed above. The question explicitly asks for the number of crystal systems, which is 7. This matches Option (B).