C) After 60 hours, the diffusion process of carbon reaches a
stead state condition at the distance of 1.0 mm to 1.5 mm below the
surface, determine the diffusion flux of the process given the
carbon concentration at the distance of 1.0 mm and 1.5 mm below the
surface are 2.04 kg/m3 and 1.78 kg/m3 , respectively.
(20 Points) (a) An FCC iron-carbon alloy initially containing 0.10 wt% C is processed to be a gear (shown in the following). To increase the wear resistance of the teeth of the gear, it is carburized at an
elevated temperature and in an atmosphere that gives a surface carbon concentration constant at 1.4 wt%. If after 50 h the concentration of carbon is 0.2 wt% at a position 2.0 mm below the surface of teeth, please determine the temperature at which the treatment was carried out. D, = 2.3 10- m2/s; Qd = 148,000 J/mol. (12 points)
erf(z 0
erf(z) 0.5633 0.6039 0.6420 0.6778 0.7112 0.7421 0.7707 0.7970 0.8209 0.8427 0.8802 0.9103
erf(z) 0.9340 0.9523 0.9661 0.9763 0.9838 0.9891 0.9928 0.9953 0.9981 0.9993 0.9998 0.9999
0 0.025 0.05 0.10 0.15 0.20 0.25 00 0.35 0.40 0.45 0.50
0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.0 1.1 1.2
1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.2 2.4 2.6 2.8
0.0282 0.0564 0.1125 0.1680 0.2227 0.2763 0.3286 0.3794 0.4284 0.4755 0.5205
b) With a sketch, name and explain the diffusion mechanism applied on the process. (4 points)