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Gold (Au) is a very important precious metal used for many technical applications as well as being one of the most important commodity metals used in trade and financial markets. The figure below shows an X-ray diffraction pattern for pure gold obtained using a powder X-ray diffractometer equipped with Cuka monochromatic radiation having an average wavelength (n) of 0.1542 nm. The diffraction peaks have been indexed to determine their corresponding (hkl) values. The diffraction angles and relative integrated intensities of the diffraction peaks are listed in the pattern. 6000- 5000 Peak (111) (200) (220) (311) (222) 20 38.18 44.36 64.52 77.53 81.67 100 27 11 11 3 4000 Intensity (arb. unit) 3000 - 2000 - 1000 O 20 40 60 80 100 2e (in deg.) 1) Gold is known to belong to the cubic crystal system. From consideration of the sequence of hkl values of the diffraction peaks in the above diffraction pattern, state the Bravais lattice of the gold. Explain briefly the reason for your answer. (5 marks) 2) Using the Bravais lattice given in your answer to Part 1), specify a motif that could be used to build the crystal structure of the gold. Sketch the crystal structure indicating the lattice parameter(s). (5 marks) 3) Based on your answer in Part 2) and using the diffraction data, determine the values of the lattice parameter(s) of the gold (10 marks) 4 Using your answer in Parts 2) and 3), determine the theoretical density of the gold (atomic mass of gold is 196.97 g/mol). (5 marks) 5) Based on your answer in Part 2), derive the structure factor expression specific to the gold from the generalised structure factor equation (given left) and use it to confirm the (nkl) indices of the peaks that appear in the above XRD pattern (10 marks) 6) Using your structure factor expression derived in Part 5) and any other relevant data, calculate the theoretical relative intensities of the diffraction peaks (refer to the lecture example). Compare your calculated intensities with those stated in the diffraction pattern and explain any significant differences. (20 marks) N 2- RVw)