5. Derive simple expressions for F for both Si and GaAs, including the rules 6. 7. governing observed reflections. Compare the powder diffraction patterns. 444 444 444 444 4-5 A certain tetragonal crystal has four atoms of the same kind per unit cell, located at 00.00 (Do not change axes.) a) Derive simplified expressions for F. b) What is the Bravais lattice of this crystal? c) What are the values of F for the 100, 002, 111, and 011 reflections? *4-7 A Debye-Scherrer pattern of tungsten (BCC) is made with Cu Ka radiation. The first four lines on this pattern were observed to have the following values: Line 1 2 3 4 0 20.3 29.2 36.7 43.6 Calculate the relative integrated intensities of the first four lines of the Hull/Debye Scherrer pattern of tungsten, made with Cuka radiation. 8. Fluorite (CaF2) is face-centered cubic (a = 5.45 ) with 4 CaF2 per unit cell at Ca 000; F 4 4 4 4 4 4 with the other positions given by the face-centering translations. Derive simplified expressions for the structure factor F in terms of h. k, 1. (hint: =-4-4-4)