homework3 - (a What does the concentration c α indicated...

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Matsc 503 Kinetics of Materials Processes - Spring 2002 Problem Set #3 - Due Feb. 6 1. The surface of a piece of pure iron is placed in contact with a carburizing gas at 800 ˚ C in which the activity of carbon is equivalent to a concentration of 0.8 wt % carbon in iron. Calculate the position of the austenite-ferrite phase boundary after 2 h. At 800 ˚ C the austenite and ferrite compositions in equilibrium with one another contain, respectively, 0.24 and 0.02 wt % carbon, the diffusion coefficient for carbon in ferrite is given by D α = 2 × 10 6 exp 84,100 J RT m 2 s and the diffusion coefficient for carbon in austenite is given by D γ = 7 × 10 6 exp 133, 900 J RT m 2 s 2. The attached concentration-distance curve is from a diffusion couple made up of a thick sample of uranium and a two-phase uranium-nickel alloy with an average nickel concentration c o = 1.3 wt. %, that had been annealed at constant temperature (~ 950 ˚ C) for 16 h. The origin on the abscissa corresponds to the position of the weld plane after diffusion
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Unformatted text preview: (a) What does the concentration c α indicated on the graph represent? (b) Determine the coordinate of the Matano interface; then calculate the diffusion coefficient by the Matano method for the concentration c = 0.2wt.%. (c) Assuming that the diffusion coefficient is constant, find the solution c(x) of Fick's second equation for the boundary conditions implied by the concentration-penetration curve. (d) Assume that the boundary of the two-phase region is displaced by a distance ξ during the time t, and that this process is diffusion-controlled, i.e. = 2 Dt , where is a constant. (i) Write the equation connecting the conservation of matter at the plane x = during the time dt to the displacement (d ) of the boundary of the two-phase region. (ii) From the equation obtained above, deduce the diffusion coefficient D. Compare this value with the one calculated by the Matano method....
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