e45_hw_5 - E45 HW05 Due October 1, 2010 References: J.F....

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E45 HW05 Due October 1, 2010 References: J.F. Shackelford, Introduction to Materials Science for Engineers, 6 th Edition, Prentice Hall, New Jersey (2005) Rensselaer Polytechnic Institute. “Concepts: Error function.” (1998). <http://www.ibiblio.org/links/devmodules/probstat/concepts/html/gauss_cdf.html> Problem 1 5.6 What type of crystal direction corresponds to the movement of interstitial carbon in an α-Fe between equivalent (½ 0 ½ – type) interstitial positions? Illustrate your answer with a sketch. SOLUTION α-Fe is BCC. Point-defects occur due to thermal-induced vibration. For an interstitial carbon moving between equivalent interstitial positions of the ½ 0 ½ – type, the carbon will move in generally the same direction, but curve around the Fe atoms. The equivalent position will be in the [110] direction, along the diagonal face. Problem 2 5.10 Carburization was described in Sample Problem 5.3. The decarburization of a steel can also be described by using the error function. Starting with Eq. 5.11 and taking c s =0, derive an expression to describe the concentration profile of carbon as it diffuses out of a steel with initial concentration, c 0 . (This situation can
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e45_hw_5 - E45 HW05 Due October 1, 2010 References: J.F....

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