Question

Out of seven crystal systems, how many have face-centred unit cells?

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

Recall the seven crystal systems and the 14 Bravais lattices. Identify which crystal systems include a face-centred arrangement of lattice points in their unit cells. Remember that face-centred cubic (FCC) is a type of cubic lattice, and face-centred orthorhombic is a type of orthorhombic lattice.

Answer 1

The Correct Option is B

There are seven crystal systems, which can be further divided into 14 Bravais lattices based on the arrangement of lattice points in the unit cell.
The seven crystal systems and the types of unit cells they exhibit are: 1.
**Cubic:** Primitive (simple cubic), Face-centred cubic (FCC), Body-centred cubic (BCC) - 3 types 2.
**Tetragonal:** Primitive, Body-centred - 2 types 3.
**Orthorhombic:** Primitive, Face-centred, Body-centred, End-centred - 4 types 4.
**Rhombohedral (Trigonal):** Primitive - 1 type 5.
**Hexagonal:** Primitive - 1 type 6.
**Monoclinic:** Primitive, End-centred - 2 types 7.
**Triclinic:** Primitive - 1 type We are interested in the crystal systems that have face-centred unit cells.
From the list above, we can see that face-centred unit cells occur in the following crystal systems: - **Cubic:** Face-centred cubic (FCC) is one of the Bravais lattices within the cubic crystal system.
- **Orthorhombic:** Face-centred orthorhombic is one of the Bravais lattices within the orthorhombic crystal system.
Therefore, there are two crystal systems (Cubic and Orthorhombic) that have face-centred unit cells.