Thermodynamic modelling of bcc interstitial...

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!

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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

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Nb-C

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Ni-C

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Cr-N

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Mo-N

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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