Consider a hypothetical crystalline metal. as the temperature is raised from 800 to 1000k, the lattice parameter increases 0.05% due to thermal expansion and -the density decreases by 0.16%. this density decrease is due to the combination of thermal expansion and vacancy creation a) what is the expected percentage decrease in density due to normal thermal expansion alone? thus you can calculate volume per unit cell increase by 3 times the lattice parameter increase) (2) (hint: for simplicity in calculation, the expansion of unit cell is relatively small in this case, b) evaluate the net density decrease due to vacancy production alone. (2) c) if the vacancy concentration at 800k is 106, estimate the activation energy for vacancy production.