Physics 361Problem set 2due October 14, 2009P2.1 scattering from a honeycomb latticeThe nearest neighbordistance of the honey-comb lattice of Fig. 4.17 is denotedb. For the calculations belowuse the primitive cell and atomic positions shown in that figure.a) Express the horizontal primitive vector~a1in terms of the unitvector ˆxand the lengthb. Express the other primitive vector~a2in terms of ˆx, ˆyandb.b) Find the reciprocal lattice vectors~b1and~b2associated with~a1and~a2.c) Draw the reciprocal lattice out to the 4th smallest reciprocallattice vector.d) Indicate the relative intensities of waves diffracted for each ofthe reciprocal lattice points in c).e) We send an x-ray beam with wavelengthb/2 onto figure 4.17from the bottom of the page.We then rotate the latticethrough a complete revolution.In some orientations the x-rays will be diffracted. Using the methods of Chapter 6, findthe angles at which the diffracted rays will be emitted relativeto the incident beam direction?
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