Halliday, Resnick & Walker — Diffraction: Problem 59

59 Consider a two-dimensional square crystal structure, such as one side of the structure shown in Fig. 36-28a. The largest interplanar spacing of reflecting planes is the unit cell size \(a_0\). Calculate and sketch the (a) second largest, (b) third largest, (c) fourth largest, (d) fifth largest, and (e) sixth largest interplanar spacing. (f) Show that your results in (a) through (e) are consistent with the general formula \(d = \frac{a_0}{\sqrt{h^2 + k^2}}\), where \(h\) and \(k\) are relatively prime integers (they have no common factor other than unity).