IChO 2003 · Theory problem 19

Crystal structure of iron

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Which structure describes best the crystal system of iron in which the coordination number is 8?

a) simple cubic ( )
b) body-centered cubic ( )
c) cubic closest packed ( )
d) hexagonal closest packed ( )
e) none of the above ( )

Official English text of the problem.

Answers

  • 19. b) body-centered cubic.

Solution

19. The coordination number is the number of nearest-neighbor atoms surrounding an atom.

In a body-centered cubic (BCC) structure, the atom at the center of a cubic unit cell has eight nearest neighbors, one at each corner. If the cube edge length is \(a\), all eight neighbors lie at the same distance: \[ d=\sqrt{\left(\frac a2\right)^2+\left(\frac a2\right)^2+\left(\frac a2\right)^2} =\frac{\sqrt{3}}{2}a. \] Every atom has this equivalent environment, so the coordination number is 8.

For comparison, simple cubic has coordination number 6, while cubic closest packed and hexagonal closest packed both have coordination number 12. Therefore, mark b).

The answers were checked against the official answers published by the organisers.