The wear resistance of a steel gear is to be improved by hardening its surface. This is to be accomplished by increasing the carbon content within an outer surface layer as a result of case-hardening. The carbon is to be supplied from an external carbon-rich gaseous atmosphere at an elevated and constant temperature. The initial carbon content of the steel is kept as a constant and is 0.20 wt%. The surface concentration is to be maintained at 1.00 wt%. For this treatment to be effective, (a) What diffusion process can be assumed in this situation? (b) What type of solid solution is it for the steel after diffusion?(c) What is the diffusion coefficient of carbon in steel if the heat treatment is conducted at 800 ℃?(d) How long will it take to achieve a carbon content of 0.60wt% at a position 0.75 mm below the surface at 1050 ℃? DiffusingSpeciesHost MetalDy(m'/s)QAJ/mol)Interstitial DiffusionFe (a or BCC)1.1 x 10-687,400Fe (y or FCC)23 x 10148,000N°Fe (a or BCC)"5.0 x 1077,000NFe (y or FCC)9.1 x 10-5168,000Self-Diffusion2.8 X 105.0 x 10FeFe (a or BCC)251,000FeFe (y or FCC)"284,000CuCи (FCC)2.5 x 10200,000AFAl (FCC)2.3 x 10-144,000MgZnMg (HCP)1.5 x 10+136,000Zn (HCP)1.5 x 1094,000MoМо (ВСС)Ni (FCC)1.8 X 10-4461,000Ni1.9 x 10285,000Interdiffusion (Vacancy)ZnСи (FCC)2.4 X 10189,000Zn (HCP)2.1 x 106.5 x 10-51.2 x 10Cu124,000CuAl (FCC)136,000MgAl (FCC)130,000CuNi (FCC)2.7 x 10256,000NiСи (FCC)1.9 x 104230,000erf(z)erf(z)erf(z)0.550.56331.30.93400.0250.02820.600.60391.40.95230.050.05640.650.64201.50.96610.100.11250.700.67781.60.97630.150.16800.750.71121.70.98380.200.22270.800.74211.80.98910.250.27630.850.77071.90.99280.300.32860.900.79702.00.99530.350.37940.950.82092.20.99810.400.42841.00.84272.40.99930.450.47551.10.88022.60.99980.500.52051.20.91032.80.9999

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Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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The wear resistance of a steel gear is to be improved by hardening its surface. This is to be accomplished by increasing the carbon content within an outer surface layer as a result of case-hardening. The carbon is to be supplied from an external carbon-rich gaseous atmosphere at an elevated and constant temperature. The initial carbon content of the steel is kept as a constant and is 0.20 wt%. The surface concentration is to be maintained at 1.00 wt%. For this treatment to be effective,

(a) What diffusion process can be assumed in this situation?

(b) What type of solid solution is it for the steel after diffusion?

(d) How long will it take to achieve a carbon content of 0.60wt% at a position 0.75 mm below the surface at 1050 ℃?

Diffusing
Species
Host Metal
Dy(m'/s)
QAJ/mol)
Interstitial Diffusion
Fe (a or BCC)
1.1 x 10-6
87,400
Fe (y or FCC)
23 x 10
148,000
N°
Fe (a or BCC)"
5.0 x 10
77,000
N
Fe (y or FCC)
9.1 x 10-5
168,000
Self-Diffusion
2.8 X 10
5.0 x 10
Fe
Fe (a or BCC)
251,000
Fe
Fe (y or FCC)"
284,000
Cu
Cи (FCC)
2.5 x 10
200,000
AF
Al (FCC)
2.3 x 10-
144,000
Mg
Zn
Mg (HCP)
1.5 x 10+
136,000
Zn (HCP)
1.5 x 10
94,000
Mo
Мо (ВСС)
Ni (FCC)
1.8 X 10-4
461,000
Ni
1.9 x 10
285,000
Interdiffusion (Vacancy)
Zn
Си (FCC)
2.4 X 10
189,000
Zn (HCP)
2.1 x 10
6.5 x 10-5
1.2 x 10
Cu
124,000
Cu
Al (FCC)
136,000
Mg
Al (FCC)
130,000
Cu
Ni (FCC)
2.7 x 10
256,000
Ni
Си (FCC)
1.9 x 104
230,000
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
0.05
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
0.2227
0.80
0.7421
1.8
0.9891
0.25
0.2763
0.85
0.7707
1.9
0.9928
0.30
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

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