problem1)Answer the following problems or computations relative to face centered (FCC) crystal structure.

a) On the cubic unit cell shown below, draw location of atoms for the FCC structure

b) How many atoms are per unit cell for the face centered cubic structure

c) Derive the equation for relationship between inter-atomic distance (2R) and lattice constant (a0) for the face centered cubic (FCC) structure. You must derive the equation to receive full credit. Only partial credit might be given for writing down the right equation)

d) Consider hard sphere approximation, volume of each atom is given by (V=4/3 ? R3), where 2R is the inter-atomic distance, derive the expression and compute the atomic packing factor (APF) for the FCC crystal structure.

problem2) Find out the ASTM grain size number if 30 grains per square inch are measured at a magnification of 250.