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MSE Nürnberg, Sep. 1-4, 2008
Thermodynamic modelling of bcc interstitial solutions
Bengt Hallstedt and Dejan Djurovic
Materials Chemistry, RWTH Aachen University,
Aachen, Germany
MSE Nürnberg, Sep. 1-4, 2008
Contents
• Motivation
• The standard model for bcc interstitial solutions
• Current state
• Suggestion of a new model
• Fe-C
• Nb-N
• Conclusion
MSE Nürnberg, Sep. 1-4, 2008
The (stable) Fe-C binary phase diagram
All diagrams are
calculated from TCFE4
(using Thermo-Calc).
The thermodynamic
descriptions are
published in the open
literature and used
almost universally.
MSE Nürnberg, Sep. 1-4, 2008
The Nb-N phase diagram
The gas phase is not
included!
MSE Nürnberg, Sep. 1-4, 2008
Nb-N with isobars
MSE Nürnberg, Sep. 1-4, 2008
The bcc crystal structure
Octahedral sites which
are distorted in different
directions have different
colours.
In Fe-C martensite one
set of sites is occupied,
and the lattice symmetry
becomes tetragonal.
MSE Nürnberg, Sep. 1-4, 2008
bcc sublattice model(the “standard” model)
The sublattice model: M1(Va,X)3
The Gibbs energy:
G = yVaGM + yXGMX3 + 3RT(yValnyVa+yXlnyX) + yVayXL
(yVa is the fraction of Va on the second sublattice)
MSE Nürnberg, Sep. 1-4, 2008
Mo-C
MSE Nürnberg, Sep. 1-4, 2008
Nb-C
MSE Nürnberg, Sep. 1-4, 2008
Ni-C
MSE Nürnberg, Sep. 1-4, 2008
Cr-N
MSE Nürnberg, Sep. 1-4, 2008
Mo-N
MSE Nürnberg, Sep. 1-4, 2008
W-N
MSE Nürnberg, Sep. 1-4, 2008
No problem with bcc in:
Co-C
Cr-CTi-C
V-C
W-C
Co-N
Fe-NNi-N
Ti-N
V-N !
MSE Nürnberg, Sep. 1-4, 2008
New model for bcc
Change number of sites on the second sublattice from 3 to 1. This is the same as for fcc.
The sublattice model: M1(Va,X)1
The Gibbs energy:
G = yVaGM + yXGMX + RT(yValnyVa+yXlnyX) + yVayXL
MSE Nürnberg, Sep. 1-4, 2008
Fe-C
MSE Nürnberg, Sep. 1-4, 2008
Fe-C peritectic region
Black (and red) lines:
new model.
Green dashed lines:
old model.
Difference in peritectic
temperature is about
0.1 K.
MSE Nürnberg, Sep. 1-4, 2008
Fe-C: bcc-fcc T0 line
Black (and red) lines:
new model.
Green dashed lines:
old model.
MSE Nürnberg, Sep. 1-4, 2008
Nb-N
MSE Nürnberg, Sep. 1-4, 2008
The Nb-N phase diagram
Black (and red) lines:
new model.
Green dashed lines:
old model.
The bcc parameters
were reoptimised using
the actual experimental
data.
MSE Nürnberg, Sep. 1-4, 2008
N solubility in bcc-Nb
Black line: new model.
Green dashed line:
old model.
MSE Nürnberg, Sep. 1-4, 2008
N chemical potential in bcc-Nb
Black lines: new model.
Green dashed lines:
old model.
MSE Nürnberg, Sep. 1-4, 2008
N chemical potential in bcc-Nb
Black lines: new model.
Green dashed lines:
old model.
MSE Nürnberg, Sep. 1-4, 2008
Conversion of parameters(dilute solutions)
∆G(MX)new = 1/3 ∆G(MX3)old – RTln3
Lnew = 1/3 Lold
MSE Nürnberg, Sep. 1-4, 2008
Conclusions
• The “standard” bcc interstitial model Me1(Va,X)3 is rather
tricky to handle
• The model Me1(Va,X)1 is much easier to handle
• The parameter values can be directly compared to those of the fcc phase
• Experimental data for Me-C and Me-N systems can be described equally well with both models
• Conversion is easy in most cases
• Me-H systems can probably not be described
MSE Nürnberg, Sep. 1-4, 2008
We want to thank DFG for financial support through the
collaborative research centre SFB 761 “Steel - ab initio; quantum mechanics guided design of new Fe based
materials"
Acknowledgement