Past exam of the condensed matter physics course of the University of Oxford / 2016 / 1 / b

The two sites give phases one and $\exp [i\pi (h+k+l)]=(-1{)}^{h+k+l}$. ThusFor real nonresonant form factors, even $h+k+l$ gives the square of the sum and odd $h+k+l$ the square of the difference. The factor $K_{hkl}$ represents the remaining experimental corrections, not another basis-interference term. Since the two ions differ, a half-body-diagonal translation does not preserve the decorated crystal. Its Bravais lattice is therefore simple cubic, with a two-ion basis; CsCl is not a monatomic body-centered cubic Bravais lattice.

Replacing both sites by identical Fe atoms changes the amplitude toNow the body-centering translation does preserve the structure. It is a body-centered cubic lattice with one Fe atom per primitive cell, or two per conventional cubic cell.

For 111 the parity is odd: CsCl generally has a nonzero amplitude $f_{\mathrm{C}{\mathrm{s}}^{+}}-f_{\mathrm{C}{\mathrm{l}}^{-}}$, whereas the identical-Fe 111 reflection is systematically absent. A numerical absolute CsCl intensity requires the angle-dependent form factors and experimental normalization; no such values are supplied. Forward electron counts, 54 for Cs+ and 18 for Cl-, explain why their amplitudes are substantially unequal, but are not substituted for the actual finite-angle factors without an additional approximation.