Number of Nearest Neighbors in BCC Lattice for K

The BCC (Body-Centered Cubic) lattice is a common crystal structure in which atoms are arranged in a cubic lattice with an additional atom at the center of the cube. In this lattice, each atom is surrounded by eight nearest neighbors.

Explanation:

The BCC lattice consists of a simple cubic lattice with an additional atom at the center of the cube. This additional atom is called the body-centered atom.

Key Point:
In a BCC lattice, the unit cell contains two atoms - one at each corner of the cube and one at the center of the cube.

Step 1: Calculate the Number of Atoms per Unit Cell
To determine the number of nearest neighbors, we need to first calculate the number of atoms per unit cell in the BCC lattice.

In a BCC lattice, there is one atom at each corner of the cube and one atom at the center of the cube. Therefore, the total number of atoms per unit cell is:

Number of atoms per unit cell = 1 (corner atom) + 1 (body-centered atom) = 2

Key Point:
The number of atoms per unit cell in a BCC lattice is 2.

Step 2: Determine the Number of Nearest Neighbors
Next, we need to determine the number of nearest neighbors for each atom in the BCC lattice.

Since the BCC lattice contains two atoms per unit cell, we will consider the nearest neighbors for both the corner atom and the body-centered atom.

Key Point:
In a BCC lattice, each atom has 8 nearest neighbors.

Conclusion:
Therefore, each K atom in the BCC lattice has 8 nearest neighbors.