Question

Which of the following is a Bravais lattice?

• A. Cubic
• B. Tetragonal
• C. Face-centered cubic
• D. Hexagonal

Hint:

Always distinguish between Crystal Systems (the 7 structural shapes) and Bravais Lattices (the 14 specific point arrangements). For example, "Cubic" is a system, but "Face-centered cubic" is a specific Bravais lattice.

Answer 1

The Correct Option is C

Concept: In crystallography, geometric configurations are categorized at two levels: Crystal Systems and Bravais Lattices.
• A *crystal system* represents a broad classification based on the axial relationships and interaxial angles of the unit cell geometry. There are exactly 7 distinct crystal systems in three dimensions.
• A *Bravais lattice* is an infinite array of discrete points generated by a set of discrete translation operations. When we combine the 7 crystal systems with the different possible lattice centering arrangements (Primitive \(P\), Body-centered \(I\), Face-centered \(F\), Base-centered \(C\)), we get exactly 14 unique spatial arrangements known as the 14 Bravais Lattices.

Step 1: Grouping the terminology.
Let us break down the options given in the problem statement:
• Cubic: This refers to a *crystal system* characterized by \(a = b = c\) and \(\alpha = \beta = \gamma = 90^\circ\). It is not a single specific Bravais lattice.
• Tetragonal: This refers to a *crystal system* defined by \(a = b \neq c\) and \(\alpha = \beta = \gamma = 90^\circ\).
• Hexagonal: This refers to a *crystal system* characterized by \(a = b \neq c\), \(\alpha = \beta = 90^\circ\), and \(\gamma = 120^\circ\).
• Face-centered cubic (FCC): This is a specific *Bravais lattice* (often denoted as Cubic \(F\)). It belongs to the cubic crystal system and features lattice points located at all eight corners as well as at the centers of all six faces of the unit cell cube.

Step 2: Conclusion.
Options (A), (B), and (D) describe crystal systems, whereas option (C) describes a precise, fully defined Bravais lattice geometry. Therefore, Option (C) is the correct answer.