The number of next nearest neighbours around each particle in face-centred cubic lattice is

Options

A. 4
B. 6
C. 8
D. 12

Answer

To determine the number of next nearest neighbors around each particle in a face-centered cubic (FCC) lattice, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the FCC Structure**:
- In a face-centered cubic lattice, atoms are located at each corner of the cube and at the center of each face of the cube.

2. **Identify the Nearest Neighbors**:
- The nearest neighbors of a given atom in an FCC structure are the atoms located at the face centers adjacent to it. Each atom has 4 nearest neighbors.

3. **Identify the Next Nearest Neighbors**:
- The next nearest neighbors are those located at the corners of the cube. For any given atom, the next nearest neighbors are those that are not directly adjacent but are still close enough to be considered.

4. **Count the Next Nearest Neighbors**:
- In an FCC lattice, each atom has 12 next nearest neighbors. These are the atoms located at the corners of the cube that are diagonally adjacent to the face-centered atom.

5. **Visualize the Unit Cell**:
- When visualizing the FCC unit cell, you can see that there are 8 corner atoms and 6 face-centered atoms. The next nearest neighbors for any atom can be visualized as connecting the corners of the cube.

6. **Final Count**:
- Therefore, the total number of next nearest neighbors around each particle in a face-centered cubic lattice is **12**.

### Final Answer:
The number of next nearest neighbors around each particle in a face-centered cubic lattice is **12**.

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