Aluminum gallium arsenide (Al,Ga-xAs, where 0x1) is an important opto-electronic alloy. The crystal structure consists of a face-centered cubic lattice with As atoms at 0 0 0 and Al or Ga atoms at 141414. The atomic numbers of these elements are ZAI= 13; ZGa = 31; ZAS = 33. Assume that the position is randomly occupied by Al or Ga with a fractional probability that depends on x. a) Derive the structure factor rules for this structure. b) Determine the Miller indices of the first five allowed diffraction reflections. c) Determine whether the relative intensity of each of these reflections increases or decreases as the compositional parameter x increases from 0 to 1.