PS#3 Solutions - T x ahead of the interface is linear...

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PS#3 comments This 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, T L , profile ahead of the solidification front in which T L is increasing and T L (x) is concave down. Since the second assumption is that the actual temperature profile,
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Unformatted text preview: T ( x ), ahead of the interface is linear, constitutional supercooling will occur when dT L ( x )/ dx > dT ( x )/ dx . It is likely that this will occur since dT L ( x )/ dx depends on the concentration gradient, which can be quite high (diffusion flux is limited), while dT L ( 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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