Question

Find the distance and first, second, third and fourth nearest neighbor in B.C.C lattice.

Answer 1

In body centered cubic packing structure model we have an atom at the center and eight atoms at the 8 corners of the cube. These are the nearest neighbours for the atom at the center. SO there are EIGHT. The distance between them is $\frac{diagonal-of-cube}{2}=\frac{\surd 3a}{2}$ .
a = size of the cube in the lattice

If you repeat the cubes around, you will see there are 6 cubes, one at each face of our cube. There is one at the center of the adjacent cube to our cube. That will be the nearest neighbour at the next level. The distance would be 'a' = size of cube in the lattice.

Say you are sitting in the center of a cell. Then:

• Your first neighbours are at the corners of the same cell.
• Second neighbours are at the centers of the nearest adjacent cells.
• Third neighbours: centers of the next adjacent cells (those which share two corners with your cell).
• Fourth neighbours: far corners of the nearest adjacent cells.