Caesium chloride crystallises as a simple cubic lattice with a two-ion basis, Cs 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

Caesium chloride crystallises as a simple cubic lattice with a two-ion basis, Cs

^+

(0,0,0)

and Cl

^-

(\tfrac12,\tfrac12,\tfrac12)

. Unlike bcc, the two basis positions are occupied by different ions, so the lattice itself is simple cubic, not body-centred. Using form factors

f_{\rm Cs}

and

f_{\rm Cl}

, derive

S_{\mathbf{G}}

and show that, unlike bcc, no reflection is ever exactly extinguished. Then find the intensity ratio

I_{100}/I_{110}

, taking

f_{\rm Cs}=55

and

f_{\rm Cl}=17

at zero angle, their electron counts.

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