Question

Among the 14 Bravais lattices, there is no base-centred cubic unit cell. Which of the following statement(s) is/are true?

• A. The base-centred cubic unit cell is same as the simple tetragonal unit cell
• B. The base-centred cubic unit cell is same as the body-centred tetragonal unit cell
• C. The base-centred cubic unit cell is same as the simple orthorhombic unit cell
• D. The base-centred cubic unit cell does not have any 3-fold rotation axis

Hint:

- There are 14 Bravais lattices only — not 15. - The so-called base-centred cubic is not unique; it is equivalent to body-centred tetragonal.

Answer 1

The Correct Option is A, D

Step 1: Recall Bravais lattices.
There are 14 distinct Bravais lattices, classified into 7 crystal systems. - Cubic system: simple cubic, body-centred cubic (BCC), and face-centred cubic (FCC). - Base-centred cubic does not exist as an independent Bravais lattice.
Step 2: Why base-centred cubic is not distinct.
- A base-centred cubic arrangement can be reinterpreted by choosing a different unit cell. - This transformation shows equivalence to another lattice.
Step 3: Equivalence proof.
- The base-centred cubic structure can be transformed into a **body-centred tetragonal** cell. - Hence, it is not considered a separate Bravais lattice.
Step 4: Analyze options.
(A) Wrong — base-centred cubic is not equivalent to simple tetragonal.
(B) Correct — it is equivalent to body-centred tetragonal.
(C) Wrong — it is not equivalent to orthorhombic.
(D) Wrong — cubic cells retain 3-fold rotation symmetry, contradiction here. Final Answer: \[ \boxed{\text{(B)}} \]