lab6_bragg_scattering - PHY 252 Lab 6 Bragg Scattering of...

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PHY 252 Lab 6: Bragg Scattering of Microwaves Fall 2009, version 2 1 Purpose In this experiment, we will study the scattering of microwaves from a “crystal” made up of ball bearings embedded in styrofoam. We will find diffraction maxima that are similar in form to those encountered in Bragg scattering of X-rays from crystal lattices (see Fig. 1), except that of course our “crystal” is in 3D (see Fig. 2). In the case when all atoms are in a simple cubic form with lattice constant a , the distance between planes becomes d = a 2 + m 2 + n 2 (1) where the Miller indices for the crystal are ( ℓmn ) . 2D Bragg planes 1 1 1 1 2 <12> <11> <10> Figure 1: Bragg planes in a 2D crystal lattice. The coherent superposition of scattering from individual atoms leads to the appearance of scattering planes within a crystal. These planes are indexed by the number of atomic steps one has to go to get to the next lattice plane. In this diagram, the 2D steps are ( 10 ) , ( 11 ) , and ( 12 ) . The extension to 3D is straightforward.
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