Consider an Al-Cu alloy with the Cu concentration Ccu=10at% (ie 10% of the atoms are Cu) which was processed such that Cu is in solid solution. The alloy is annealed to produce precipitation of the theta phase, which is a Al2Cu intermetallic. In Step 1, precipitates with diameter 20 nm are produced and 7at% of Cu is left in solid soltion. The annealing process is continued to Step 2, to produce precipitates with diameter of 30 nm, case in which only 5at% Cu is left in the solid solution.

a. Compute the volume fraction of precipitates in both steps 1 and 2. Consider that the density of the precipitates is the same with that of the solid solution and is independent of the Cu concentration, ie the volume fraction is the same with the mass fraction. THe mass of Al atoms is mAL=26.98 and that of Cu atoms is mCu=63.54 both in atomic units.

b. Compute by how much the strength increment due to precipitation increases from step 1 to step 2.