Further considerations on the thermodynamics of the proeutectoid ferrite reaction in Fe-C alloys
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in their determination of a~. Leitnaker5 has privately suggested to us that the results of SBA should be reexamined on the basis of the more accurate values of this constant presently available. 4'6'7Accordingly, new values of a~ have been computed from the BEC CO/CO2 data 2'3 using the activity coefficient expression developed by BLH (their Eq. [4]). SBA showed that the most sophisticated statistical thermodynamic expression for the composition dependence of
a~ used in a previous study by Aaronson, Domian, and Pound (ADP), 8 that of Lacher, 9 Fowler and Guggenheim ]~ (LFG) is numerically equivalent to a more recent, further improved relationship, due to McLellan and Dunn (MD), ]1 in the range of interaction energies between nearest neighboring carbon atoms in austenite, w~, likely to be operative in Fe-C alloys. Employing the corrected a~ data of BEC 2'3 and the earlier, more limited but highly reliable data of R. P. Smith, 6 the LFG/MD treatments have been used to reevaluate w~. The values thus obtained are given in Figure 1, together with those of ADP and SBA. At higher temperatures the interaction energies calculated from the corrected data of BEC are seen to be as much as 400 cal/mole (1670 J/mole) less than those reported by SBA. The values of w~ obtained from the BEC and the R. P. Smith data are now seen to be in good agreement; Smith used the presently accepted4 CO/CO2 equilibrium constant. Employing the Smith ac~ data, ADP found the same wv values as were secured during this study at 1200~ and 1000 ~ at 800 ~ however, their wr value appears to be in error. The good agreement now obtained for w~ from the BEC and the Smith data makes clear that w~ increases with decreasing temperature (Figure 1). Hence, use of an average w~ is inappropriate, particularly since this quantity is required for calculations made at temperatures well below those at which a~ data are available. As a first approximation, a straight line extrapolation of w~ to lower temperatures may be made, as shown by the dashed line in Figure 1, yielding the following expression: wv = - 4 . 4 0 ( T -
273) + 11550 J/mole; T --< 1173 K
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11000 .~
~ , / w 3 j = -4.4 (T-273) + 11550 (J/mole)
10000
9000 o
"
E 8000
9 - ADP Calculations Ref. 8 (R. P. S
Ref 1 (BEC D . ~ I 9 -" CorrectedSBA O CalculatiOnSvaluesPresent Investigation
7000
6000
5000 300
I 400
I 500
I 600
I I 700 800 Temperature (~
I 900
I 1000
I 1100
1200
Fig. 1--Temperature dependence of interaction energy between nearest neighboring carbon atoms in austenite, wv
G. J. SHIFLET is Assistant Professor, Department of Materials Science, University of Virginia, Charlottesville, VA 22901; J.R. BRADLEY is associated with the Physics Department, General Motors Research Laboratories, Warren, MI 48090; and H. I. AARONSON is R. F. Mehl Professor, Department of Metallurgical Engineering and Materials Science, CarnegieMellon University, Pittsburgh, PA 15213. Manuscript submitted November 10, 1983. METALLURGICALTRANSACTIONS A
The conclusion that wv is temperature-dependent
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