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### PS#3 Solutions

Course: MSE 4100, Fall 2011
School: Cornell
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Word Count: 223

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comments This PS#3 PS had a wider range of scores than most. Some comments: Prob 1. The question asks for two processes with explanations and scaling laws. Some interpreted process as a treatment process, others interpreted it as a microstructural treatment. Both approaches got full credit if fully explained. Prob 2. This question asked for a logical argument, not a text description of constitutional supercooling,...

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comments This PS#3 PS had a wider range of scores than most. Some comments: Prob 1. The question asks for two processes with explanations and scaling laws. Some interpreted process as a treatment process, others interpreted it as a microstructural treatment. Both approaches got full credit if fully explained. Prob 2. This question asked for a logical argument, not a text description of constitutional supercooling, or a mathematical derivation. The important points of the logic are that the first and last assumption will result in a liquidus temperature, TL, profile ahead of the solidification front in which TL is increasing and TL(x) is concave down. Since the second assumption that is the actual temperature profile, T(x), ahead of the interface is linear, constitutional supercooling will occur when dTL(x)/dx > dT(x)/dx. It is likely that this will occur since dTL(x)/dx depends on the concentration gradient, which can be quite high (diffusion flux is limited), while dTL(x)/dx depends on the temperature gradient, which is normally limited (since metals are thermally conductive). Prob 3. Many people thought about a twin plane parallel to the film surface. While just fine in principle (and also awarded full credit), there are no shear stresses on this plane, so deformation twins like this will never form. The solutions show the twins that are seen.
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