Determine the carburizing time necessary to achieve a carbon concentration of 0.50 wt% at a position 1.2 mm into an iron-carbon alloy that initially contains 0.18 wt% C. The surface concentration is to be maintained at 1.1 wt% C, and the treatment is to be conducted at 1200°C. Assume that Do = 6.5 x 10-5 m2/s and Qd = 168 kJ/mol. The following table may be useful. Table 5.1 Tabulation of Error Function Values erf(z) erf(z) erf(z) 0.55 0.5633 1.3 0.9340 0.025 0.0282 0.60 0.6039 1.4 0.9523 0.0564 0.1125 0.6420 0.6778 0.05 0.65 0.70 0.75 1.5 0.9661 0.10 1.6 0.9763 0.15 0.1680 0.7112 1.7 0.9838 0.20 0.2227 0.80 0.7421 1.8 0.9891 0.25 0.2763 0.85 0.7707 1.9 0.9928 0.30 0.35 0.3286 0.90 0.7970 2.0 0.9953 0.3794 0.4284 0.95 0.8209 2.2 0.9981 0.8427 0.8802 0.40 1.0 2.4 0.9993 0.45 0.4755 1.1 2.6 0.9998 0.50 0.5205 1.2 0.9103 2.8 0.9999 Part 1 From Equation 5.5 calculate the Gaussian error function: erf =

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Chapter1: Atomic Structure
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Determine the carburizing time necessary to achieve a carbon concentration of 0.50 wt% at a position 1.2 mm into an iron-carbon alloy that initially contains 0.18 wt% C. The surface concentration is to be maintained at 1.1 wt% C, and
the treatment is to be conducted at 1200°C. Assume that Do = 6.5 x 10-5 m2/s and Qd = 168 kJ/mol. The following table may be useful.
Table 5.1 Tabulation of Error Function Values
erf(z)
erf(z)
erf(z)
0.55
0.5633
1.3
0.9340
0.025
0.0282
0.60
0.6039
1.4
0.9523
0.0564
0.1125
0.6420
0.6778
0.05
0.65
0.70
0.75
1.5
0.9661
0.10
1.6
0.9763
0.15
0.1680
0.7112
1.7
0.9838
0.20
0.2227
0.80
0.7421
1.8
0.9891
0.25
0.2763
0.85
0.7707
1.9
0.9928
0.30
0.35
0.3286
0.90
0.7970
2.0
0.9953
0.3794
0.4284
0.95
0.8209
2.2
0.9981
0.8427
0.8802
0.40
1.0
2.4
0.9993
0.45
0.4755
1.1
2.6
0.9998
0.50
0.5205
1.2
0.9103
2.8
0.9999
Part 1
From Equation 5.5 calculate the Gaussian error function:
erf
=
Transcribed Image Text:Determine the carburizing time necessary to achieve a carbon concentration of 0.50 wt% at a position 1.2 mm into an iron-carbon alloy that initially contains 0.18 wt% C. The surface concentration is to be maintained at 1.1 wt% C, and the treatment is to be conducted at 1200°C. Assume that Do = 6.5 x 10-5 m2/s and Qd = 168 kJ/mol. The following table may be useful. Table 5.1 Tabulation of Error Function Values erf(z) erf(z) erf(z) 0.55 0.5633 1.3 0.9340 0.025 0.0282 0.60 0.6039 1.4 0.9523 0.0564 0.1125 0.6420 0.6778 0.05 0.65 0.70 0.75 1.5 0.9661 0.10 1.6 0.9763 0.15 0.1680 0.7112 1.7 0.9838 0.20 0.2227 0.80 0.7421 1.8 0.9891 0.25 0.2763 0.85 0.7707 1.9 0.9928 0.30 0.35 0.3286 0.90 0.7970 2.0 0.9953 0.3794 0.4284 0.95 0.8209 2.2 0.9981 0.8427 0.8802 0.40 1.0 2.4 0.9993 0.45 0.4755 1.1 2.6 0.9998 0.50 0.5205 1.2 0.9103 2.8 0.9999 Part 1 From Equation 5.5 calculate the Gaussian error function: erf =
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