Diffusion modeling of the carburization process
- PDF / 199,317 Bytes
- 2 Pages / 594 x 774 pts Page_size
- 94 Downloads / 243 Views
The values of e*! and e?~ are available from thermodynamic measurements. The following values m a y be derived from published data. 3 e~c = 0.15,
T. W A D A
e~cr = -0.052
[5]
Then, Goldstein and Moren published a fine work ~on diffusion modeling of the carburizing process of steel. Unfortunately, there was implicit misuse of concentration units, and Figs. 9 through 14 in their paper (Ref. 1) are open to question. The purpose of this communication is to propose a correction of some of the parameters used in Ref. 1. Figure 9 in Ref. 1 shows the carbon profile in the carburized case of an Fe-2.0 wt pct Cr-0.15 wt pct C alloy under a carbon potential of 1 pct in pure iron. There was a chromium-depleted zone near the surface, but if the carbon concentration in the inner region is extrapolated to the surface, it reaches to 1.69 pct (Fig. 10 in Ref. 1). This surface carbon concentration is far higher than expected from thermodynamics. Using thermodynamic parameters reported by Brown and Kirkaldy, 2 which were used in Ref. 1, the surface carbon concentration in the 2 pct Cr steel is estimated as 1.18 pct. A similar value, 1.19 pct C, is obtained using parameters reported by Wada, Wada, Elliott and Chipman. 3,4 The discrepancies seem to be caused by mixed use of concentration units in Ref. 1. The authors used wt pct for diffusion calculation and mole fraction for evaluating D~fD?!. It should be noticed that the value of D~2/D~I depends on the unit of concentration, although it is a nondimensional quantity. The original form of Eq. [13] in Ref. 1 is 3
3
8# I / r N 2
DI2/DI! = -81~]/rNl
n CCr Fe*/n F~*-- _ 0.0889. ~*'~ CC This value would be used for the diffusion calculation on the weight percent basis. There is an alternative way to calculate r~3,/r~3, 12" ~ I I approximately. Since 5
3
3 =
el2Nl
-1 + e]lN !
MF~ • 100
eI,
[71
MFe etz e*2 "" 2.30 • 100 • M 2
[8]
e*~ --2.30
M~
•
where MF~, M!, and M 2 are atomic weights of iron, components 1 and 2, respectively, one obtains D31~
M 1
M! D32
el2N I
D~'~ - - M :
1 + ellN l
[9]
M 2 D3!
9 F~ 0.343, Eq. [9] gives Using D cF ~c / D cc = D CV**/r~ F~, = _ 0.0792, a reasonably close value to C r ' ~ CC Eq. [6]. The calculations may be cross-checked using an equation derived by Brown and Kirkaldy. 2 Equation [13] in Ref. 2 may be applied to the surface concen-
0
0.02 !
I
I
!
0.04 I
I
I
!
I
0.06 I
I
!
!
INCH !
I
I
927 c (t7oo F)
[1]
1.5
k
[2]
Fe-2.0Cr-O.15C Fe-2.5Si-~. 15C 2.99 x I0~ sec (8.31 hr)
\
where F! is the partial free energy of component 1. The quantities 6~ I / r N 2 and so forth are obviously dependent of the unit for concentrations N~ and N 2. Taking mole fraction as the unit, Eq. [1] gives Eq. [13] in Ref. 1, namely,
DI2/D"
[6]
\ \
Fe 43 ~Cr, REF. 1 CoFe CCr/DCC :-0.3 )
\~ ~
- 1.0 'X
~
Cr, THIS STUDY
A unit for concentration should be used consistently throughout the calculation. If one chooses weight percent, an interaction parameter based on weight percent may be useful. This parameter, written as e* in this
Data Loading...
