Lithium crystallizes in a body centred cubic lattice. How many next-nearest neighbours does each Li have?

Options

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

Answer

To determine how many next-nearest neighbors each lithium atom has in a body-centered cubic (BCC) lattice, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the BCC Structure**: In a body-centered cubic lattice, there is one atom at each of the eight corners of the cube and one atom at the center of the cube.

2. **Identify Nearest Neighbors**: The nearest neighbors of a lithium atom located at the body center are the atoms located at the corners of the cube. In a BCC lattice, there are 8 corner atoms surrounding the central atom.

3. **Count the Next-Nearest Neighbors**: The next-nearest neighbors for the lithium atom at the center are the atoms located at the face centers of the cube. In a BCC structure, each face of the cube has one atom at its center. Since there are 6 faces in a cube, there are 6 face-centered atoms that are next-nearest neighbors to the central lithium atom.

4. **Conclusion**: Therefore, each lithium atom in a BCC lattice has 6 next-nearest neighbors.

### Final Answer:
Each lithium atom has **6 next-nearest neighbors**.

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