Be 1300 basic engineering ii: materials science for engineering applications q1. (20 points). for a pure cu crystal at 500°c, the activation energy for the formation of a vacancy is 0.80 ev. find the equilibrium fraction of crystal sites that are vacant. q2. (20 points). note that idea gas constant can be estimated by using r = k na , where na is avogadro’s number and k is the boltzmann constant. calculated the r in the unite of j/(mol k). q3. (20 points). for a given material, would you expect the surface energy to be greater than, the same as, or less than the grain boundary energy? why? da deng- wayne state university 2 q4. (20 points) the grain boundary energy of a small-angle grain boundary is less than for a high-angle one. why is this so? q5. (20 points). calculate the activation energy for vacancy formation in aluminum, given that the equilibrium number of vacancies at 500°c (773 k) is 7.57 × 1023 m-3. the atomic weight and density (at 500°c) for aluminum are, respectively, 26.98 g/mol and 2.62 g/cm3.