Question

There is NO base-centered cubic lattice among the list of 14 Bravais lattices because of one or more of the following reasons:

• A. It does NOT have translational symmetry
• B. It is only compatible with the symmetry of orthorhombic crystal system
• C. It is only compatible with the symmetry of tetragonal crystal system
• D. It does NOT have 3-fold rotation axes along the body diagonals

Hint:

The 14 Bravais lattices are classified based on their symmetry properties. The BCC structure does not fit into the set due to its lack of certain rotational symmetries and incompatibility with specific crystal systems.

Answer 1

The Correct Option is C, D

The base-centered cubic (BCC) lattice is not one of the 14 Bravais lattices, and this is due to certain symmetry and rotational requirements. Let's analyze why:
1. Option (C): The base-centered cubic lattice is not compatible with the symmetry of the tetragonal crystal system. The tetragonal system requires a square base, which does not align with the asymmetric geometry of a base-centered cubic lattice. The BCC lattice does not possess the symmetry necessary to match the tetragonal system.
2. Option (D): The BCC lattice does not have 3-fold rotation axes along the body diagonals. This is a crucial requirement for some of the crystal systems, but the BCC structure lacks the required symmetry for these 3-fold rotation axes. In fact, the BCC lattice has only 2-fold symmetry along the body diagonals, which rules out the possibility of being a base-centered cubic lattice.
Thus, the correct answer is a combination of options (C) and (D). The absence of 3-fold symmetry and the incompatibility with the tetragonal crystal system prevent the existence of a base-centered cubic lattice.