A2: Structure-and Orientation Determination(Chapter 2) 9.5 points a Derive an expression for the diffraction of X-rays with wave length A in a crystal lattice as function of the incidence angle 0.Explain the derivation with a diagram. Indicate all symbols.(3 points) b) What is the extinction rule for fcc-lattice?(1 point) c Calculate the theoretical diffraction angle 0 for the first three lattice planes,which you can obtain from an X-ray diffractogram (see below),for the Nickel (aN=3,524 A). The wave length of the X-radiation is Aco=1.7902 A.(4 points) d) Assign the corresponding diffracting crystallographic planes to the peaks in an X-ray diffractogram of Ni powder according to your results from part c).Consider that the 0- angles obtained from an X-ray diffractogram can vary from the theoretically calculated ones by up to 0.1.(1.5 points) 3000 2000- 1000- 0- 20 30 40 50 Theta [ 22 A2: Structure- and Orientation Determination (Chapter 2) 9.5 points a) Derive an expression for the diffraction of X-rays with wave length λ in a crystal lattice as function of the incidence angle θ . Explain the derivation with a diagram. Indicate all symbols. (3 points) b) What is the extinction rule for fcc-lattice? (1 point) c) Calculate the theoretical diffraction angle θ for the first three lattice planes, which you can obtain from an X-ray diffractogram (see below), for the Nickel (aΝι = 3,524 Å). The wave length of the X-radiation is λCo = 1.7902 Å. (4 points) d) Assign the corresponding diffracting crystallographic planes to the peaks in an X-ray diffractogram of Ni powder according to your results from part c). Consider that the θ- angles obtained from an X-ray diffractogram can vary from the theoretically calculated ones by up to 0.1°. (1.5 points)