Prob.set.2 - Physics 361 Problem set 2 due P2.1 scattering...

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Physics 361 Problem set 2 due October 14, 2009 P2.1 scattering from a honeycomb lattice The nearest neighbor distance of the honey- comb lattice of Fig. 4.17 is denoted b . For the calculations below use the primitive cell and atomic positions shown in that figure. a) Express the horizontal primitive vector ~a 1 in terms of the unit vector ˆ x and the length b . Express the other primitive vector ~a 2 in terms of ˆ x , ˆ y and b . b) Find the reciprocal lattice vectors ~ b 1 and ~ b 2 associated with ~a 1 and ~a 2 . c) Draw the reciprocal lattice out to the 4th smallest reciprocal lattice vector. d) Indicate the relative intensities of waves diffracted for each of the reciprocal lattice points in c). e) We send an x-ray beam with wavelength b/ 2 onto figure 4.17 from the bottom of the page. We then rotate the lattice through a complete revolution. In some orientations the x- rays will be diffracted. Using the methods of Chapter 6, find the angles at which the diffracted rays will be emitted relative to the incident beam direction?
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