Thermodynamic properties of the Fe-Mn-V-C system
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I.
INTRODUCTION
THE
Fe-Mn-V-C system is a system of interest to the high-strength low-alloy (HSLA) steels, which are essentially carbon-manganese steels microalloyed with V, Nb, or Ti. [11 Though there is a large amount of literature on the thermal processing, phase transformation, and mechanical properties of the microalloyed steels, the experimental information on the thermodynamics and phase equilibria, which is very important for an understanding of the microalloyed steels, is very sparse. The CALPHAD (CALculation of PHAse Diagram) method ]2] is based on the use of thermodynamic models for the Gibbs energy of the various phases in the alloy system. The models are phenomenological and involve parameters to be defined from experimental information or estimated. When investigating into higher-order systems, the experimental information is usually scarce. In these cases, the assessment becomes a kind of prediction. The CALPHAD method can provide rather reliable predictions when the assessed descriptions of lower-order systems are available. The thermodynamic properties of the lower-order systems of the Fe-Mn-V-C system, i.e., Fe-Mn-C, I31 Fe-V-C, t41 Fe-Mn-V, tSj and Mn-V-C, t6] have already been evaluated. They can now be combined by the use of thermodynamic models to describe the thermodynamic properties of the Fe-Mn-V-C system. A variety of calculations can be made, which can, for example, give valuable information in applications of microalloyed steels.
II.
THERMODYNAMIC MODELS
The Fe-Mn-V-C system presented here contains 15 different phases: liquid (L), a-Mn ( a ) , / 3 - M n ( i l l facecentered cubic (fcc) (3/), hexagonal close-packed (hcp) (e), body-centered cubic (bcc) (6), and VC, V2C, VaC2, Mn23C6, Mn~C2, Mn7C3, cementite, graphite, and an intermetallic phase sigma (0-). The Gibbs energy of individual phases was described by sublattice models, tTj A special magnetic term, which is described in detail elsewhere, tS] was included when there is a magnetic contribution to the Gibbs energy.
A. Liquid The Gibbs energy of the liquid phase was described by the following expression of a one-sublattice model (Fe, Mn, V, C) for one mole of atoms: G~q =
o~liq o/"71iq ., o/'71iq .~_ y c O G ~ q YF~ O r e + YMn '--'Mn + . r v "-'V
+ RT(yFr In YF~ + YMn In YM. + Yv In Yv + Yc In Yc) + EG"mq [1] EGUmq = . . . .
lliq .... lliq .YFe.YMnZ..,Fe,Mn "~- .YFe.YVX.,Fe,V nL
rliq
-~- YFeYCLFe,C +
--liq
YMnYVLMn,V
~, ~, l l i q ~, ., l l i q YMn.YCL.,Mn,C -}- yV.YCz.,V,C
liq
liq
T liq
liq
+ YFeYM, ycLF~,Mn,C + YFeYvYcLF,,V,C + YMnYVYcLM,,V,C + YF~YM,yvLF,,Mn,V liq
+ YF, YMnYVYcLFe,Mn,V,C
[2] All of the lower-order interaction parameters have been evaluated in the relevant lower-order systems. The quaternary parameter lliq ~,F~.M~.V,C is simply set to be zero due to the lack of experimental data.
B. Solid Solution Phases [~-Mn, fl-Mn, Bcc, Fcc ( y or VC), and Hcp (e or V2C)] The solid-solution phases include a-Mn, /3-Mn, bcc, fcc, and hcp. The VC carbide, which is of the NaC1 type, and V2C, which is an hcp ph
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