An FCC iron-carbon alloy has an initial uniform carbon concentration of 0.25 wt% C. The alloy...

 

 

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An FCC iron-carbon alloy has an initial uniform carbon concentration of 0.25 wt% C. The alloy is carburized at 950 °C and in an atmosphere that gives a constant surface carbon concentration constant of 1.2 wt.% a) How much time is needed to get a carbon concentration of 0.8 wt% at a position 0.4 mm below the surface? (5 marks) b) How much time is needed to get the same carbon concentration if the carburization takes place at 750 °C? How does it compare to the time needed at 950 °C? (3 marks) Interpolate the error function to obtain your solution. Assume that the diffusivity (D) is a function of temperature and follows this relation D=Doe^-(QRT) where, D. is the standard diffusivity of 2.3 x 10^-5 m, R is the gas constant, T is the temperature, and Q is the activation energy of 148 kJ/mol. TABLE 5.1 The Error Function z 0.00 0.01 0.02 0.03 0.04 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 erf(z) 0.0000 0.0113 0.0226 0.0338 0.0451 0.0564 0.1125 0.1680 0.2227 0.2763 0.3286 0.3794 0.4284 0.4755 0.5205 0.5633 0.6039 0.6420 z 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 erf(z) 0.6778 0.7112 0.7421 0.7707 0.7969 0.8209 0.8427 0.8802 0.9103 0.9340 0.9523 0.9661 0.9763 0.9838 0.9891 0.9928 0.9953 Source: Handbook of Mathematical Functions, M. Abramowitz and I. A. Stegun, Eds., National Bureau of Standards. Applied Mathematics Series 55, Washington, DC, 1972. An FCC iron-carbon alloy has an initial uniform carbon concentration of 0.25 wt% C. The alloy is carburized at 950 °C and in an atmosphere that gives a constant surface carbon concentration constant of 1.2 wt.% a) How much time is needed to get a carbon concentration of 0.8 wt% at a position 0.4 mm below the surface? (5 marks) b) How much time is needed to get the same carbon concentration if the carburization takes place at 750 °C? How does it compare to the time needed at 950 °C? (3 marks) Interpolate the error function to obtain your solution. Assume that the diffusivity (D) is a function of temperature and follows this relation D=Doe^-(QRT) where, D. is the standard diffusivity of 2.3 x 10^-5 m, R is the gas constant, T is the temperature, and Q is the activation energy of 148 kJ/mol. TABLE 5.1 The Error Function z 0.00 0.01 0.02 0.03 0.04 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 erf(z) 0.0000 0.0113 0.0226 0.0338 0.0451 0.0564 0.1125 0.1680 0.2227 0.2763 0.3286 0.3794 0.4284 0.4755 0.5205 0.5633 0.6039 0.6420 z 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 erf(z) 0.6778 0.7112 0.7421 0.7707 0.7969 0.8209 0.8427 0.8802 0.9103 0.9340 0.9523 0.9661 0.9763 0.9838 0.9891 0.9928 0.9953 Source: Handbook of Mathematical Functions, M. Abramowitz and I. A. Stegun, Eds., National Bureau of Standards. Applied Mathematics Series 55, Washington, DC, 1972.

Answer rating: 100% (QA)

Answer The problem can be solved by using Ficks second law of diffusion which describes the movement of mass over time due to a concentration gradient ... View the full answer