 Solution

ID: past-exam-of-the-condensed-matter-physics-major-option-course-of-the-university-of-oxford/2018/1/b/ii/solution

To obtain a crystal's point group, discard the translation parts of its space-group operations. A screw becomes a rotation and a glide becomes a mirror. Thus the tetragonal group's

4/ n

2_{1} / m

and

2/ m

operations give

4/ mmm \equiv D_{4 h} .

For the orthorhombic structure the three perpendicular twofold/glide or screw/mirror directions give

mmm \equiv D_{2 h} .

The primitive Bravais lattice symbol does not itself add a point operation; the fractional translations matter for the space group but disappear from this point-group reduction.

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