3325.12

# 3325.12 - 5.12 An FCC iron-carbon alloy initially...

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5.12 An FCC iron-carbon alloy initially containing 0.35 wt% C is exposed to an oxygen-rich and virtually carbon-free atmosphere at 1400 K (1127 ° C). Under these circumstances the carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere; that is, the carbon concentration at the surface position is maintained essentially at 0 wt% C. (This process of carbon depletion is termed decarburization .) At what position will the carbon concentration be 0.15 wt% after a 10-h treatment? The value of D at 1400 K is 6.9 10 -11 m 2 /s. Solution This problem asks that we determine the position at which the carbon concentration is 0.15 wt% after a 10-h heat treatment at 1325 K when C 0 = 0.35 wt% C. From Equation 5.5 Cx ! C 0 Cs ! C 0 = 0.15 ! 0.35 0 ! 0.35 = 0.5714 = 1 ! erf x 2 Dt 2200 # 5 % 220d Thus, erf x 2 Dt ! 2200 # 5 % = 0.4286 Using data in Table 5.1 and linear interpolation z erf ( z ) 0.40 0.4284 z 0.4286 0.45 0.4755 z ! 0.40 0.45 ! 0.40 = 0.4286 ! 0.4284

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3325.12 - 5.12 An FCC iron-carbon alloy initially...

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