Caesium chloride,

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction

Solid State Physics, Ch Symmetry and the classification of crystals

Problem

Caesium chloride, CsCl\mathrm{CsCl}, crystallises with space group Pm3ˉmPm\bar3m (a primitive cubic lattice, one lattice point per conventional cell). The Cs+\mathrm{Cs^+} ions occupy Wyckoff position 1a1a at (0,0,0)(0,0,0) with site symmetry m3ˉmm\bar3m (order 48), and the Cl−\mathrm{Cl^-} ions occupy Wyckoff position 1b1b at (12,12,12)(\tfrac12,\tfrac12,\tfrac12), also with site symmetry m3ˉmm\bar3m. ((a)) State the multiplicity (number of equivalent atoms per conventional cell) of each of the two sites. ((b)) Add these multiplicities and check the result against the number of atoms in one CsCl\mathrm{CsCl} formula unit, given that the primitive cell contains Z=1Z=1 formula unit.

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