hw_07_sol (1) - MechEng 382 Winter 2009 Homework#7...

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MechEng 382 Winter 2009 Homework #7 Solutions 1. [ A&J-1 , Ex. 21.2] Explain what is meant by diffusion in materials. Solution Diffusion describes the tendency of various species (atoms, molecules), by virtue of random thermal fluctuations, to minimize their variation in quantity in space by moving from regions of high concentration to those of low concentration. (a) Account for the variation of diffusion rates with temperature, Solution The average kinetic energy of a species is proportional to the temperature. Since the ability of that species to jump to neighboring sites is positively related to the energy, a higher temperature leads to more jumps and more (greater) diffusion. (b) concentration gradient Solution The net movement of a chemical species across an arbitrary planar barrier to an adjacent region is proportional to the difference in quantity of that chemical species from one side of the barrier to the other, divided by the “length” of that barrier. In a limit sense, this quantity corresponds to dc/dx , the concentration gradient. (c) and grain size. Solution The amount (surface area) of grain boundaries in a material is inversely related to the grain size. Since grain boundaries act as fast diffusion paths in solids, the rate of diffusion is also inversely related to grain size. 1
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MechEng 382 Winter 2009 Homework #7 Solutions 2. [ A&J-1 , Ex. 21.3] Use your knowledge of diffusion to account for the following observations: (a) Carbon diffuses fairly rapidly through iron at 100 C, whereas chromium does not. Solution Since carbon atoms are significantly smaller than iron atoms, they follow an interstitial diffusion path. Chromium atoms are of similar size as that of iron, thus they follow vacancy diffusion. Since an adjacent vacancy must exist for an atom to move by the latter mechanism, the interstitial mode of diffusion is generally faster. As a result, carbon diffusion in Fe is more rapid than Cr. (b) Diffusion is more rapid in polycrystalline silver with a small grain size than in coarse- grained silver.
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