Which of following unit cell does not exist in cubic system?

Options

A. primitive
B. body centered
C. face centered
D. end centered

Explanation

To determine which of the following unit cells does not exist in the cubic system, we will analyze the options provided.

### Step-by-Step Solution:

1. **Understanding the Cubic System**:
- The cubic crystal system is characterized by unit cells that are in the shape of a cube. All sides of the cube are equal in length, width, and height.

2. **Identifying Unit Cells in the Cubic System**:
- **Primitive Cubic Unit Cell**: This unit cell has atoms only at the corners of the cube. It does exist in the cubic system.
- **Body-Centered Cubic (BCC) Unit Cell**: This unit cell has atoms at the corners and one atom at the center of the cube. It also exists in the cubic system.
- **Face-Centered Cubic (FCC) Unit Cell**: This unit cell has atoms at the corners and at the centers of each face of the cube. It exists in the cubic system as well.

3. **Analyzing the End-Centered Unit Cell**:
- The end-centered unit cell has atoms at the corners and at the center of two opposite faces (ends) of the cube. However, this type of unit cell is not possible in a cubic system. It typically exists in the tetragonal system, where the dimensions are unequal.

4. **Conclusion**:
- Among the options provided, the end-centered unit cell does not exist in the cubic system. Therefore, the correct answer is **D. End-Centered Unit Cell**.