(a) In the general position has multiplicity 192 per conventional cell. Wyckoff…
PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Crystal structure, bonding and diffraction
Solid State Physics, Ch Symmetry and the classification of crystals
Problem
(a) In Fm3ˉm the general position has multiplicity 192 per conventional cell. Wyckoff position 24d, at (0,41,41), has a site symmetry of order 8, and 32f, at (x,x,x), has a site symmetry of order 6. How many symmetry-equivalent sites per conventional cell does each of these Wyckoff positions contain? (A lone impurity would break the symmetry; the count is of the sites a symmetry-preserving arrangement would have to fill.) (b) Magnesium oxide crystallises in the rock-salt structure, space group Fm3ˉm, with Mg2+ on Wyckoff position 4a (multiplicity 4) and O2− on Wyckoff position 4b (multiplicity 4) of the conventional cell. How many atoms does the conventional cell contain in total, and how many formula units of MgO is that? (c) MgO's Bravais lattice is face-centred cubic, with conventional lattice constant a=4.212A˚. Give the coordinates of the L point of its first Brillouin zone in units of 2π/a, and compute ∣ΓL∣ in A˚−1.