Invent a simple cubic lattice with a three-atom basis of identical atoms at

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Crystal structure, bonding and diffraction

Condensed Matter Physics, Ch Diffraction: how a structure is actually measured

Problem

Invent a simple cubic lattice with a three-atom basis of identical atoms at d1=(0,0,0)\mathbf{d}_1=(0,0,0), d2=(13,13,13)\mathbf{d}_2=(\tfrac13,\tfrac13,\tfrac13) and d3=(23,23,23)\mathbf{d}_3=(\tfrac23,\tfrac23,\tfrac23), all fractions of the cube edge. Derive SGS_{\mathbf{G}} for a general reflection (hkl)(hkl), and show that it is 3f3f when h+k+lh+k+l is a multiple of 33 and exactly 00 otherwise.

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