Test01 - Test 1(due 24 February Problem 1 X-rays with =...

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Test # 1 (due 24 February) Problem # 1 X-rays with λ = 1.54 Å are scattered off a crystal which has the CsCl structure (see Kittel, Chapter 1, Fig.20) with cubic lattice constant a = 2.7 Å. Find all allowed scattering angles and the associated lattice planes {hkl} responsible for the diffraction. What happens if the atomic form-factors of the two non-equivalent atoms in a unit cell of the crystal are equal? Problem # 2 Assuming that binding in a monoatomic 3D solid is controlled by the Lennard-Jones potential acting only between nearest neighbors, predict which of the structures is energetically more favorable: sc , bcc or fcc . Problem # 3 n+ 2 n n+ 1 n 1 C 2 C 1 C 1 C 2 n 2 a Consider lattice vibrations in a one-dimensional monatomic crystal for which both first- and second-nearest-neighbor interactions are important. The equilibrium interatomic distance is a , and the atomic mass is M . The force constant between first nearest neighbors is C 1 and that between second nearest neighbors is
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