Question

What is the total number of Bravais lattices present in seven types of crystal system?

• A. 12
• B. 7
• C. 10
• D. 14

Hint:

A useful mnemonic tool to remember the total counts is the phrase "3242111", which corresponds to the number of Bravais lattices within each of the seven systems from cubic down to hexagonal. Adding those digits together quickly brings you to 14.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We are required to identify the total number of unique three-dimensional space lattices (Bravais lattices) that can be constructed across the seven fundamental crystal systems.

Step 2: Detailed Explanation:
In solid-state chemistry, crystalline solids are categorized into 7 basic crystal systems based on their unit cell axial lengths ($a, b, c$) and interfacial angles ($\alpha, \beta, \gamma$): cubic, tetragonal, orthorhombic, monoclinic, triclinic, rhombohedral, and hexagonal.
When Auguste Bravais combined these 7 basic systems with the different possible lattice centerings (primitive, body-centered, face-centered, and end-centered), he mathematically demonstrated that only a specific set of arrangements can exist in three-dimensional space.
The distribution across the 7 systems is as follows:
Cubic system: 3 Bravais lattices (Primitive, BCC, FCC)
Tetragonal system: 2 Bravais lattices (Primitive, BCC)
Orthorhombic system: 4 Bravais lattices (Primitive, BCC, FCC, End-centered)
Monoclinic system: 2 Bravais lattices (Primitive, End-centered)
Triclinic system: 1 Bravais lattice (Primitive)
Rhombohedral system: 1 Bravais lattice (Primitive)
Hexagonal system: 1 Bravais lattice (Primitive)
Summing these up: $3 + 2 + 4 + 2 + 1 + 1 + 1 = 14$ distinct space arrangements.

Step 3: Final Answer:
The total number of Bravais lattices is 14, matching option (D).