Learn Space Groups

Test Your Understanding

This test will cover everything you’ll need to understand about symmetry elements and coordinates in orthorhombic space groups. Ensure you at least understand the answers to the questions before proceeding, even if you do not get them right first time. The answers are on the next page, with explanations.

1. A two-fold rotation axis parallel to \(a\) is located at \((a, 0, \frac{1}{4})\). What effect does this have on the coordinates \((x, y, z)\)?
2. A mirror plane perpendicular to \(b\) is located at \(b = 0\). What effect does this have on the coordinates \((x, y, z)\)?
3. An inversion centre is located at \((\frac{1}{2}, 0, \frac{1}{4})\). What effect does this have on the coordinates \((x, y, z)\)?
4. An \(a\) glide plane perpendicular to \(b\) is located at \(b = \frac{1}{4}\). What effect does this have on the coordinates \((x, y, z)\)?
5. An \(n\) glide plane perpendicular to \(c\) is located at \(c = 0\). What effect does this have on the coordinates \((x, y, z)\)?
6. A \(2_{1}\) screw axis parallel to \(c\) is located at \((\frac{1}{4}, 0, c)\). What effect does this have on the coordinates \((x, y, z)\)?
7. What effect does \(I\)-centring have on the coordinates \((x, y, z)\)?
8. What effect does \(B\)-centring have on the coordinates \((x, y, z)\)?
9. What symmetry elements are present in the space group \(Ccc2\)? Give unique axes of symmetry elements but not positions.
10. What symmetry elements are present in the space group \(Pca2_{1}\)? Give unique axes of symmetry elements but not positions.
11. What symmetry elements are present in the short space group symbol \(Pbca\)?
12. Derive the other symmetry elements present in \(Pbca\) that are not listed in the short space group symbol. What is the full space group symbol of \(Pbca\)?
13. What symmetry element is produced by the combination of \(A\)-centring and a \(2_{1}\) screw axis parallel to \(c\)?