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1. a) The unit cell parameter (a) for cubic nickel and copper are 350.7 pm and 362 pm respectively. Assuming Vergard's law is applicable, calculate the two theta diffraction angles for the (220) plane for alloys of composition (in at. %) 75Ni- 25Cu, 50Ni-50Cu and 20Ni-80Cu. (10) b) Ni – 50 at. % Al alloys exist as body centred cubic intermetallics in which Ni and Al atoms can be arranged randomly or in an ordered manner. Given the relationships for structure factor (Faki) below eq. 1 and solutions of exp[nai] below(eq. 2), predict which planes of the crystal structure yield reflections for the situations where atoms are randomly arranged and when they are ordered. You should investigate the following planes (100), (110), (111), (200), (210), (220) Fhkl = fn exp[2ni(hun + kvn + lwn)] Eq. 1 exp[nai] = (-1)" Eq. 2 where, h,k,l are the Miller indices of the plane under consideration and u, v, w fractional coordinates of atom n and f" is the structure factor for the atom position (10)