Microwave Bragg-scattering zone-axis-pattern analysis

Louis deBroglie's connection between momentum and spatial-frequency vectors is perhaps most viscerally-experienced via the real-time access that electron-diffraction provides to transverse slices of a nano-crystal's reciprocal-lattice. The classic introductory (and/or advanced) physics lab-experiment on microwave Bragg-scattering can with a bit of re-arrangement also give students access to "zone-axis-pattern" slices through the 3D spatial-frequency (i.e. reciprocal) lattice of a ball-bearing crystal, which may likewise contain only a few unit-cells. In this paper we show how data from the standard experimental set-up can be used to generate zone-axis-patterns oriented down the crystal rotation-axis. This may be used to give students direct experience with interpretation of lattice-fringe image power-spectra, and with nano-crystal electron-diffraction patterns, as well as with crystal shape-transforms that we use here to explain previously mis-identified peaks in the microwave data.