Question B1 The material rubidium antimony selenide, Rb3SbSe3, is known to have a cubic crystal structure. A diffraction experiment using Cu Ka radiation of wavelength X = 1.5406 Å showed peaks at 2012.319, 15.103°, 17.456°, 19.536°, 21.421°, and 24.784°. a) Index each of these peaks (that is, calculate possible h, k, and I values for each of them). Show that these data are consistent with a cubic unit cell, and calculate its unit cell parameter a. Which cubic Bravais lattice (i.e., simple cubic, body-centred cubic, or face-centred cubic) is most appropriate? On the other hand, the related compound rubidium manganese selenide, RbMnSe2, has a body-centred tetragonal structure with unit cell parameters a = 4.266 Å and c = 14.033 Å. Its motif consists of a Rb atom at (0, 0, 0), a Mn atom at (½, 0, 1), and Se atoms at (½, 1, 0.15) and (,,-0.15). b) Draw the unit cell of this structure in projection down the b axis, with the a axis vertical and the c axis horizontal. Draw the Mn atoms as small filled circles, the Rb atoms as large empty circles, and the Se atoms as small empty circles. Label each atom with its b fractional coordinate. c) Give the precise locations of an example of each of the following symmetry elements in this structure, or state that none exists. (i) A mirror plane (ii) A centre of symmetry (iii) A fourfold proper rotation axis (iv) A fourfold improper rotation axis (v) A twofold proper rotation axis d) Given that a material has a centre of symmetry at the origin, show that all of its structure factors F(hkl) will be real. You may assume that the atomic form factors f are real.

Question B1 The material rubidium antimony selenide, Rb3SbSe3, is known to have a cubic crystal structure. A diffraction experiment using Cu Ka radiation of wavelength X = 1.5406 Å showed peaks at 2012.319, 15.103°, 17.456°, 19.536°, 21.421°, and 24.784°. a) Index each of these peaks (that is, calculate possible h, k, and I values for each of them). Show that these data are consistent with a cubic unit cell, and calculate its unit cell parameter a. Which cubic Bravais lattice (i.e., simple cubic, body-centred cubic, or face-centred cubic) is most appropriate? On the other hand, the related compound rubidium manganese selenide, RbMnSe2, has a body-centred tetragonal structure with unit cell parameters a = 4.266 Å and c = 14.033 Å. Its motif consists of a Rb atom at (0, 0, 0), a Mn atom at (½, 0, 1), and Se atoms at (½, 1, 0.15) and (,,-0.15). b) Draw the unit cell of this structure in projection down the b axis, with the a axis vertical and the c axis horizontal. Draw the Mn atoms as small filled circles, the Rb atoms as large empty circles, and the Se atoms as small empty circles. Label each atom with its b fractional coordinate. c) Give the precise locations of an example of each of the following symmetry elements in this structure, or state that none exists. (i) A mirror plane (ii) A centre of symmetry (iii) A fourfold proper rotation axis (iv) A fourfold improper rotation axis (v) A twofold proper rotation axis d) Given that a material has a centre of symmetry at the origin, show that all of its structure factors F(hkl) will be real. You may assume that the atomic form factors f are real.