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Question 58

The coordination number of an atom in a body-centered cubic structure is ______
[Assume that the lattice is made up of atoms.]


Correct Answer: 8

We need to find the coordination number of an atom in a body-centered cubic (BCC) structure.

In a BCC unit cell, there is one atom at the centre of the cube and one atom at each of the 8 corners. The central atom is the nearest neighbour to all 8 corner atoms.

The nearest neighbour distance in BCC is along the body diagonal. The body diagonal has length $$\sqrt{3}a$$, where $$a$$ is the edge length. The distance between the central atom and a corner atom is $$\frac{\sqrt{3}a}{2}$$.

The distance between two adjacent corner atoms is $$a$$ (along the edge), which is larger than $$\frac{\sqrt{3}a}{2} \approx 0.866a$$. So the nearest neighbours of any atom are the 8 atoms connected along the body diagonal directions.

For the corner atom, the 8 nearest neighbours are the body-centre atoms of the 8 unit cells that share that corner. For the body-centre atom, the 8 nearest neighbours are the 8 corner atoms of its unit cell.

So the coordination number in BCC is 8.

So, the answer is $$8$$.

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