1) a) Draw a schematic diagram of an X-ray diffractometer. [4 marks] 

b) The results of an X-ray diffraction experiment that used X-rays of wavelength 0.154 nm show the first 6 peaks at angles of 40.6°, 58.8°, 73.8°, 87.8°, 101.8°, and 116.4°. 

i) Use this information to determine the possible crystal structures of the sample. [10 marks] 

ii) An additional scan was performed on the sample and an additional peak was observed at an angle of 133.2°. Determine the crystal structure of the sample. [3 marks] 

iii) Calculate the Miller indices for each of the measured peaks. [7 marks] 

iv) Draw the orientation of the crystal plane within the unit cell corresponding to the peak at 101.8°. [3 marks] 

v) Calculate the lattice constant and identify the sample. [3 marks]