Which of the following is not a Bravais lattice ?

Options

A. End centred cubic
B. Body centred orthorhombic
C. Body centred tetragonal
D. End centred monoclinic

Answer

To determine which of the given options is not a Bravais lattice, we will analyze each option based on the characteristics of Bravais lattices.

### Step-by-Step Solution:

1. **Understanding Bravais Lattices**:
- Bravais lattices are distinct arrangements of points in space that describe the periodic structure of a crystal. There are 14 unique Bravais lattices in three-dimensional space.

2. **Analyzing Each Option**:
- **Option A: N-Centered Cubic**:
- The N-centered cubic lattice does not exist. The only cubic lattices that exist are:
- Face-Centered Cubic (FCC)
- Body-Centered Cubic (BCC)
- Primitive Cubic
- Therefore, N-centered cubic is not a valid Bravais lattice.

- **Option B: Body-Centered Orthorhombic**:
- This lattice exists. In this structure, there are two atoms per unit cell, and the axes are unequal in length but all angles are 90 degrees.

- **Option C: Body-Centered Tetragonal**:
- This lattice also exists. In this structure, two axes are equal (A = B) while the third axis (C) is different, and all angles are 90 degrees.

- **Option D: End-Centered Monoclinic**:
- This lattice exists as well. In this structure, all sides are unequal, and two angles (alpha and gamma) are 90 degrees, while the third angle (beta) is not 90 degrees.

3. **Conclusion**:
- After analyzing all the options, we conclude that the only option that does not represent a valid Bravais lattice is **Option A: N-Centered Cubic**.

### Final Answer:
**The option that is not a Bravais lattice is Option A: N-Centered Cubic.**

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