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. Please 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, resp