Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 5.7, Problem 20AAP
The surface of a steel gear made of 1020 steel (0.20 wt% C) is to be gas carburized at 927°C. Calculate the carbon content at 0.95 mm below the surface of the gear after an 8.0-h carburizing time. Assume the carbon content at the surface of the gear is 1.25 wt%. D (C in γ iron) at 927°C = 1.28 × 10−11 m2/s.
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Determine the carburizing time necessary to achieve a carbon concentration of 0.50 wt% at a position 3.1 mm into an iron-carbon
alloy that initially contains 0.12 wt% C. The surface concentration is to be maintained at 1.2 wt% C, and the treatment is to be
conducted at 1080°C. Assume that Do = 5.8 x 10-5 m²/s and Qd = 156 kJ/mol. The table Tabulation Error Function Values may be
useful.
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.
%3D
Table 5.1 Tabulation of Error Function Values
erf(z)
erf(z)
erf(z)
0.55
0.5633
1.3
0.9340
0.0282
0.0564
0.025
0.60
0.6039
1.4
0.9523
0.05
0.10
0.65
0.70
0.75
0.6420
1.5
0.9661
0.1125
0.6778
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
0.85
0.90
0.25
0.2763
0.7707
1.9
0.9928
0.9953
0.9981
0.30
0.3286
0.7970
2.0
0.35
0.3794
0.95
0.8209
2.2
0.8427
0.8802
0.40
0.4284
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
A 1020 steel contains 0.20% carbon is carburized by a source that maintains a surface carbon content 0f
2.0% C. It is desired to produce a 0.80 wt% C concentration 0.1 cm below the steel surface after a 4-hour
treatment. At what temperature should the carburization be carried out? R = 8.314 J/mol•K; DO =
2.3x10-5 m2 /s; Qd=148,000 J/mol
erf(z)
erf(z)
erf(z)
0.55
0.5633
1.3
0.9340
0.025
0.05
0.0282
0.60
0.6039
1.4
0.9523
0.0564
0.65
0.6420
1.5
0.9661
0.10
0.1125
0.70
0.6778
1.6
0.9763
0.15
0.1680
0.75
0.7112
1.7
0.9838
0.20
0.25
0.30
0.2227
0.80
0.7421
1.8
0.9891
0.2763
0.85
0.7707
1.9
0.9928
0.3286
0.90
0.7970
2.0
0.9953
0.35
0.3794
0.95
0.8209
2.2
0.9981
0.40
0.4284
1.0
0.8427
2.4
0.9993
0.45
0.4755
1.1
0.8802
2.6
0.9998
0.50
0.5205
1.2
0.9103
2.8
0.9999
Chapter 5 Solutions
Foundations of Materials Science and Engineering
Ch. 5.7 - Prob. 1KCPCh. 5.7 - Write an equation for the number of vacancies...Ch. 5.7 - Prob. 3KCPCh. 5.7 - Prob. 4KCPCh. 5.7 - Describe the substitutional and interstitial...Ch. 5.7 - Prob. 6KCPCh. 5.7 - What factors affect the diffusion rate in solid...Ch. 5.7 - Write the equation for Ficks second law of...Ch. 5.7 - Prob. 9KCPCh. 5.7 - Prob. 10KCP
Ch. 5.7 - (a) Calculate the equilibrium concentration of...Ch. 5.7 - Prob. 12AAPCh. 5.7 - Determine the diffusion flux of zinc atoms in a...Ch. 5.7 - The diffusion flux of copper solute atoms in...Ch. 5.7 - Prob. 15AAPCh. 5.7 - Prob. 16AAPCh. 5.7 - Prob. 17AAPCh. 5.7 - A gear made of 1020 steel (0.20 wt% C) is to be...Ch. 5.7 - Prob. 19AAPCh. 5.7 - The surface of a steel gear made of 1020 steel...Ch. 5.7 - Prob. 21AAPCh. 5.7 - If boron is diffused into a thick slice of silicon...Ch. 5.7 - Prob. 23AAPCh. 5.7 - Prob. 24AAPCh. 5.7 - Prob. 25AAPCh. 5.7 - Prob. 26AAPCh. 5.7 - Prob. 27AAPCh. 5.7 - Prob. 28AAPCh. 5.7 - Prob. 29AAPCh. 5.7 - Prob. 30AAPCh. 5.7 - The diffusivity of copper atoms in the aluminum...Ch. 5.7 - Prob. 32AAPCh. 5.7 - Prob. 33SEPCh. 5.7 - Prob. 34SEPCh. 5.7 - Prob. 37SEPCh. 5.7 - Prob. 38SEPCh. 5.7 - The activation energy of nickel atoms in FCC iron...Ch. 5.7 - Prob. 40SEPCh. 5.7 - The self-diffusion of iron atoms in BCC iron is...Ch. 5.7 - Would you expect the diffusion rate of copper...Ch. 5.7 - Would you expect the diffusion rate of copper...Ch. 5.7 - Prob. 44SEPCh. 5.7 - Prob. 45SEPCh. 5.7 - Prob. 46SEPCh. 5.7 - Prob. 47SEPCh. 5.7 - Prob. 48SEPCh. 5.7 - Prob. 49SEPCh. 5.7 - Prob. 50SEP
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