Question B2 At low temperatures, a certain element has a hexagonal crystal structure with unit cell parameters a = 3.59 Å, c = 26.38 Å. The motif contains nine atoms at the fractional positions given in the following table: X y z 0 0 0 ○ 713 23 0 9 9 4959 23 79 13 23 13 23 0 23 ○ 23 0 23 13 23 -3 0 3 9 a) Calculate the angle 20 at which the first (lowest-angle) diffraction peak from this material will be observed using Cr Ka radiation of wavelength λ = 2.2896 Å. b) Crystallites (individual crystals) of this material have the form of flakes that are about 2 mm wide in the ab plane and about 2 μm thick in the c direction. Using a convolution argument, explain qualitatively what shape the diffraction peaks will have in 3D reciprocal space. c) Explaining your logic carefully, show that this is a close-packed structure. Give the layer sequence in ABC notation.

Question B2 At low temperatures, a certain element has a hexagonal crystal structure with unit cell parameters a = 3.59 Å, c = 26.38 Å. The motif contains nine atoms at the fractional positions given in the following table: X y z 0 0 0 ○ 713 23 0 9 9 4959 23 79 13 23 13 23 0 23 ○ 23 0 23 13 23 -3 0 3 9 a) Calculate the angle 20 at which the first (lowest-angle) diffraction peak from this material will be observed using Cr Ka radiation of wavelength λ = 2.2896 Å. b) Crystallites (individual crystals) of this material have the form of flakes that are about 2 mm wide in the ab plane and about 2 μm thick in the c direction. Using a convolution argument, explain qualitatively what shape the diffraction peaks will have in 3D reciprocal space. c) Explaining your logic carefully, show that this is a close-packed structure. Give the layer sequence in ABC notation.