(a) In the simple cubic structure if we alternately place Na and Cl atoms we would obtain...

(a) In the simple cubic structure if we alternately place Na and Cl atoms we would obtain the NaCl structure. Show that the Na atoms (and the Cl atoms) independently form FCC structures. The lattice constant associated with each FCC structure is 5.6402 Å. Corresponding to the X-ray wavelength 1.542 Å, show that the diffraction maxima will be observed at θ = 13.69°, 15.86°, 22.75°, 26.95°, 28.97°, 33.15°, 36.57°, 37.69°, 42.05°, 45.26°, 50.66°, 53.98°, 55.10°, 59.84°, 63.69°, 65.06°, 71.27°, 77.45° and 80.66°.

(b) Show that if we treat NaCl as a simple cubic structure with lattice parameter 2.82 Å then the maxima at θ = 13.69°, 26.95°, 36.57°, 45.26°, 53.98°, 63.69° and 77.45° will not be observed. Indeed in the X-ray diffraction pattern of NaCl, the maxima corresponding to these angles will be very weak.