driving force with linearized phase diagrams

issues about thermodynamics and their coupling to MICRESS
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Bernd
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driving force with linearized phase diagrams

Post by Bernd » Tue Oct 13, 2009 10:05 pm

How the driving force delta G is calculated in MICRESS using linearized phase diagrams?

Using the keyword "linear" in the phase diagram input, one can define a linear phase diagram like the one shown below, where the two phase lines may (but need not) intersect for c=0 (note that the temperature T_0 for which the linearisation parameter are specified in the input file and the corresponding equilibrium compositions are not shown here).
Lin_Phasdia.jpg
Lin_Phasdia.jpg (19.19 KiB) Viewed 1273 times
At the applied temperature T, the interface most probably is not in equilibrium, because the local phase fractions (phase-field parameter) inside the interface (i.e. for each interface cell) are not in accordance with the mixture composition c and the equilibrium compositions cL*/cS* for this given temperature T. Instead, accordance can be found for another temperature T_eq, which can be easily determined for a binary phase diagram, but which can also be calculated straightforward for multicomponent systems. Thus, the effective equilibrium compositions are taken rather at the temperature T_eq than at the real temperature T. The difference between T and T_eq is used to calculate the chemical driving force:

deltaG =deltaS * deltaT = deltaS (T - Teq)

In the multiphase case, T_eq is determined independently for each pairwise phase interaction. In triple junctions therefore, each pairwise interface can be more or less far from local equilibrium.


In the case of Thermo-Calc coupling as well as for "linearTQ", the construction of the (extrapolated) linear phase diagram is slightly different: The diagram is rather in terms of deltaG than of T, the slopes m' of the phase lines are derived from the driving force deltaG and related to the "real" slopes m:

m'_1/2 =d(deltaG)/dc1 = deltaS_1/2 * m_1/2
m'_2/1 =d(deltaG)/dc2 = seltaS_2/1 * m_2/1

Furthermore, a driving force offset and a temperature dependence of the equilibrium concentrations dc/dt is calculated or can be specified.

Bernd

kmukherj
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Re: driving force with linearized phase diagrams

Post by kmukherj » Tue Feb 09, 2010 2:43 pm

Dear Dr. Böttger,

I am simulating austenitization of two micro-alloyed steels. They are low Carbon steels. They have varying contents of Cr, Mo and Si. For both steels the initial microstructure is approximately 90% ferrite and 10% martensite.

I want to use linearized para-equilibrium diagram to simulate austenitization (austenitization temperatures 900 to 1350 degree centigrade).

At what temperature I should linearize the para-equilibrium diagrams of both steel so that I can compare their austenitization kinetics?

Thanking you,

Best regards,

Krishnendu Mukherjee

Bernd
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Re: driving force with linearized phase diagrams

Post by Bernd » Thu Feb 11, 2010 3:22 pm

Dear Krishnendu,

I am not an expert in austenitisation of steels, but generally linearisation of phase diagrams should be made in the middle of the transformation range, if the complete transformation is to be considered in the simulation.

If the actual (paraequilibrium) phase diagram is far from being linear, using a linearized description in MICRESS may be not very accurate. A not convenient but nevertheless possible solution would be to make several restarts with phase diagrams linearised at different temperatures. This way it is possible to follow more correctly the non-linear thermodynamic data.

A MICRESS paraequilibrium simulation with full coupling to TQ is presently not possible - this will be a viable alternative as soon as we get MICRESS running correctly with the newest version of TQ_S...

Bernd

kmukherj
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Re: driving force with linearized phase diagrams

Post by kmukherj » Thu Feb 11, 2010 4:12 pm

Dear Dr. Böttger,

From the dilatometer experiments I found Austenitization starts around 750 degree centigrade and finishes around 850 degree centigrade for these steels.

Fortunately, in this temperature range the para-equilibrium diagram is quite close to linear. :D

Thanking you,

Yours sincerely,

Krishnendu

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