Question

Coordination number in BCC crystals is

• A. 6
• B. 4
• C. 8
• D. 12

Hint:

Remember: BCC = 8, FCC = 12, Simple Cubic = 6 (coordination numbers).

Answer 1

The Correct Option is C

Take the BCC unit cell with edge length \( a \) and place an atom at the body center, at coordinates \( \left(\frac{a}{2}, \frac{a}{2}, \frac{a}{2}\right) \).

1. Step 1: The distance from the body-center atom to any corner atom (say at the origin) is \[ d = \sqrt{\left(\frac{a}{2}\right)^2+\left(\frac{a}{2}\right)^2+\left(\frac{a}{2}\right)^2} = \frac{\sqrt{3}}{2}a \]
2. Step 2: All eight corners of the cube are the same distance \( \frac{\sqrt{3}}{2}a \) from the body center, by the symmetry of the cube.
3. Step 3: No other atom in the structure is closer than this distance to the body-center atom, so these eight are its true nearest neighbours.

\[ \boxed{\text{Coordination number} = 8} \]

Answer 2

Coordination number and atomic packing factor (APF) are closely linked, since more efficient packing generally means more nearest neighbours. Checking each option against BCC's known packing factor of about 0.68 helps confirm the answer.

1. 6: a coordination number of 6 (simple cubic) corresponds to a much lower packing factor of about 0.52, less efficient than BCC's actual packing, so it does not match.
2. 4: a coordination number of 4 corresponds to the very open diamond cubic structure with a packing factor around 0.34, far looser than BCC, so this does not match either.
3. 8: BCC's packing factor of 0.68 is consistent with each atom touching along the body diagonal and having eight equidistant nearest neighbours at the cube corners (for the body-center atom) or cube centers (for a corner atom).
4. 12: a coordination number of 12 corresponds to the close-packed FCC or HCP structures, which have a higher packing factor of about 0.74, denser than BCC.

Since BCC's packing efficiency sits between simple cubic and the close-packed structures, its coordination number of 8 fits consistently in between their values of 6 and 12.

Therefore, the correct answer is 8.