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G-cr -}- (6/23)Gc = G~c6,~3 - G~, - (6/23)G~ + RT ln(1 - YFe) + Y~,Ao
Carbon Activity (Graphite Standard) Sample XT1 XT2 XT3 XT4 BM
Temper Condition, ~ Hours 600, 5 650, 1.5 700, 50 700, 500 680, 21
Ref. 1 0.348 0.232 0.071 0.065 0.123
Re-calculated in This Discussion 0.720 0.480 0.147 0.133 0.253
where G-'s are the partial molar free energies. The thermodynamic parameters by Lundberg, et al. ,7 the same parameters as in Reference 1, are used, namely, G~ec6/23 -
G~e - (6/23)G gr = 5760 - 5.01T J / m o l
G~c6,23- G ~ r - (6/23)G g r = - 1 3 1 0 0 - 3.33T J / m o l G~-
G~ = -1247 J/mol G~r = G g r =
The re-calculated activity values for carbon seem more reasonable than the results in Reference 1. For instance, ac = 0.133 in XT4 gives a methane fugacity of 53 MPa in the 20 MPa hydrogen environment, which is greater than the 40 MPa sintering force of a 0.05 micron void. ~ The activity of carbon in Reference 1 for the same specimen gives only 26 MPa for the methane fugacity. In Reference 1, the carbon activities were adjusted so that the base metal obeyed the methane fugacity parameter K(T) for M3C carbides. We found difficulties in justifying such adjustment. The difference between the new ac values and those calculated with thermodynamics o n (Fe0.TCr0.3)23C6 is greater than the difference reported in Reference 1. However, there is a basic error in the thermodynamic calculation in Reference 1, and the calculated values are probably inaccurate. This will be explained as follows: When an Fe-Cr-C alloy consisting of a and carbide phases is in the equilibrium condition at certain temperature and pressure, two compositional variables determine the condition of the whole system. You may select any two compositional variables: for instance, the carbon and chromium contents in the carbide phase (Yc = 6 / 2 3 and Ycr = 0.3). Then, using known thermodynamic parameters, such as those reported by Lundberg, et al.,7 you can calculate the thermodynamic properties including the activity of carbon. You may not arbitrarily select the values of three variables, for instance Yc, Ycr (both in carbide) and the content of chromium in the a-phase. There is only one set of three variables corresponding to the equilibrium state, and if you select the values other than this set, they simply represent a nonequilibrium state. In Reference 1, the activity of carbon was calculated as a function of the atom fraction of chromium in the a-phase in presence of (Fe, Cr)23C6 carbides having known YF~ (Figure 5). Except for one set of YF~ (in carbide) and Xc, (in c~) on each line in Figure 5, all values are nonequilibrium. Therefore, Figure 5 should contain only one line instead of multiple lines to represent the equilibrium condition, and YF~ should vary along that line as a function of the carbon activity. A question may arise as to whether or not these lines in Figure 5 represent any acceptable approximation. Unfortunately, they do not seem very good approximations. This can be demonstrated by the following calculation. Equation [8] in Refere
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