Homework 5 Solutions- EMS 164 Problems 3.1, 3.2, 3. 4 (only Part a) 3. 5 and 3.10 in textbook. 1. How much will copper grain growth rate change when temperature drops from 0.8 T_m to 0.5 T_m (delta G_a = 305 kJ/mol; T_m = 1356 K)?General Arrhenius equation: k= A * exp (-Ea/RT) ( 2 points) 0.8 Tm= 1356 *0.8 = 1084.8 K 0.5 Tm= 1356 * 0.5 = 678 K K1at 1084.8 K= A*exp ((-305000J/mol)/ (8.314 J/KMol*1084.8 K) = 2.057 * 10-15A ( 2 points) K2at 678 K= A*exp ((-305000J/mol)/ (8.314 J/KMol*678 K) = 3.234 * 10-24A (2 points) K1/K2= 6.34* 10-9The grain growth rate drops by 9 orders of magnitude. ( 1 point) (3 points for trying) 2. GRCop84 is a Cu-8at%Nb-4at%Cr alloy developed by NASA for combustion chamber liners. It is a high strength, high thermal conductivity material partly due to very stable Cr_2 Nb particles that pin the grain boundaries. Calculate the maximum grain size if the average particle diameter is 0.2 microns and particle volume fraction is 0.14. Hint: use Zener’s formula. If there is a volume fraction of particles all with a radius r, the mean number of particles intersecting unit area of a random plane is 3f/2∏r2. The restraining force per unit area of boundary is then:
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