2. Experimental procedures

Our experimental system consisted of a 4×4×4 simple-cubic ball-bearing lattice with lattice spacing a ≈ b ≈ c ≈ 4.27 cm and angles α ≈ β ≈ γ ≈ 90o embedded into a styrofoam cube.  A Welch-system 10-GHz klystron (Marcley1960, Donnally1968, Bullen1969, Rossing1973) on one arm provides the microwave source, while a diode detector on the other arm measures the scattered microwave intensity.  A piece of aluminum foil is placed next to the styrofoam cube and between the source and detector arms to eliminate wavepaths not interior to the crystal.

The crystal orientation at an azimuthal angle φlattice is selected where φlattice = 0 corresponds to the (100) lattice direction symmetric between the two arms of the system, as shown in Fig. 2 (at right). The scattered microwave intensity I is measured at various grazing angles θBragg between the source arm and the (vertical) ball-bearing plane of interest. The (horizontal) angle between the detector-arm and that ball-bearing plane is set to the same θBragg, so that intensity at a scattering angle of 2θBragg is recorded. If the sample is a standard simple cubic ball bearing lattice, a quite complete data set can be obtained by recording such profiles for crystal orientations φlattice running from 0 to 45 degrees in 5 degree increments, as shown in Fig. 3 (at left).

The wavelength of the microwave radiation was determined by removing the Styrofoam cube, setting θBragg equal to 0 degrees, and varying the distance between the source and the detector in 1 mm steps. A sinusoidal variation in the intensity is observed due to creation of standing waves between the source and the detector. By fitting this data to a sinusoid term (and a linear term), a wavelength of 3.025 ± 0.013 cm was measured. This procedure is described in the Pasco manual (Ayars2012), and the result is consistent with the literature frequency.

Related references:

• • Robert G. Marcley (1960) ``Apparatus drawings project #6: Bragg diffraction apparatus" Amer. J. Phys. 28, 415-417.

  • Bailey L. Donnally and George Bradley and Jacob Dewitt (1968) ``Models for microwave analogs of Bragg scattering" Amer. J. Phys. 36, 920.

  •  T. G. Bullen (1969) ``An improved mounting for the Welch-Bragg diffraction apparatus" Amer. J. Phys. 37, 333.

  • Thomas D. Rossing and Rodney Stadum and Douglas Lang (1973) ``Bragg diffraction of microwaves" Amer. J. Phys. 41, 129-130.

  • Eric Ayars (2012) ``Teachers Guide" in Instruction Manual and Experiment Guide for the PASCO Scientific Model WA-9314B: Microwave Optics (PASCO Scientific).