Question 1 a) Compute the radius r of an atom that will just fit into one of the tetrahedral interstitial sites in FCC crystal structure in terms of the atomic radius R of the host atom. MATE 302 b) Do the same computation for a octahedral site in BCC structure. Fall 2014 Homework # 2 Due: October 27th, 2014 (lecture time the latest) 1 Question 2: 2 Q estion 3: Question 3 A sheet of BCC iron 2 mm thick was exposed to a carburizing gas atmosphere on one side and a decarburizing deca bu g at atmosphere osp e e o on tthe e ot other e s side de at 6 675°C. 5C The preexponential (D0) and activation energy (Q) for the self-diffusion of nickel are 1.9x10-4 m2/s and 285 kJ/mole, respectively. Determine the mean time of stay of a nickel atom at a lattice site a) at 650°C and b) at 850°C. After having reached steady state, the iron was quickly cooled to room temperature. The carbon concentrations at the two surfaces of the sheet were determined to be 0.015 and d 0.0068 0 0068 wt%. t% Compute C t the th diffusion diff i coefficient ffi i t if the th diffusion flux is 9.36x10-9 kg/m2-s. Take density of graphite as 2.25 2 25 g/cm3 and that of iron as 7.87 7 87 g/cm3. 3 4 Question 5: Question 4: Nitrogen from a gaseous phase is to be diffused into pure iron at 675°C. If the surface concentration is maintained at 0.25 wt% N, what will be the concentration 1 mm from the surface f after ft 16 hours? h ? The Th diffusion diff i coefficient ffi i t for f nitrogen in iron at 675°C is 1.9x10-11 m2/s. •Below is a hypothetical phase diagram for the A-B system. •At temperature T1 B is practically i insoluble l bl in i A, A whereas h B can dissolve 15 atomic % A. α+ •A diffusion couple made by welding together pure A and pure B i annealed is l d att T1.  α t=0 L a) Show by a series of sketches how the concentration profiles and α/ interface position will vary with time. time b) If the overall composition of the couple is 65 atomic %B, what will be the maximum displacement of the α/ interface in terms of L? (Assume α and  have equal molar volumes.) Question 6: A diffusion couple including inert wires was made by plating pure copper on to a block of α-brass with a composition Cu-30 wt% Zn. After 56 days at 785 785°C C the marker velocity was determined as 2.6x10-8 mm/s. Microanalysis showed that the composition at the markers was XZn = 0.22, XCu =0.78, and that δXZn/δx was -0.089 mm-1. From an analysis of the complete penetration curve interdiffusion coeff (D”) at the markers was calculated as 4.5x10-13 m2/s. Use this data to calculate DαZn and DαCu in brass at 22 at% Zn. Zn Marker velocity is expressed as 7 6