Metastable phase

dendritic solidification, eutectics, peritectics,....
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mogeritsch
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Metastable phase

Post by mogeritsch » Mon Sep 14, 2015 8:47 am

Dear Bernd

We try to simulate a peritectic reaction where stable and metastable form of the phase can occur. This happens if the solidification velocity is below the critical velocity and both phases solidify in a planar manner. There is no database available, therefore, we like to use “from file” or “linear” for the PHASE DIAGRAM-INPUT DATA: Is the simulation of solidification with stable and metastable phases are possible with MICRESS? In case of yes, which reference points for the phase diagram we have to use?

Best regards,

Johann
Attachments
peritectic region_metastable phases.pdf
The first diagram shows the pericetic region. The second files shows the same diagram and the metastable region of the solidus and liquidus line in blue and red. The main objects for our silulation are the concentrations between 0.48 and 0.54.
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Peritectic region.pdf
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Bernd
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Re: Metastable phase

Post by Bernd » Mon Sep 14, 2015 12:53 pm

Dear Johann,

As long as a system is binary and the phase-diagram looks quite linear as in the case you show, it makes sense and is very easy to use linearized phase diagrams.
MICRESS automatically includes the metastable regions, irrespective of the way how you define the phase diagram. The question, whether a phase (pair) grows in the metastable regions of the phase diagram or not, only depends on whether the third phase is present or not (i.e. on the nucleation parameters), on the growth kinetics (interface mobility), and on curvature undercooling (interface energy). Thus, MICRESS will always "use" the metastable prolongations, because the linearisation of each phase pair will always consider the complete line without taking into account the intersections with other lines, like shown in the peritectic phase diagram. The peritectic 3-phase reaction can only happen through interaction between the three types of interfaces (by solute diffusion, or directly at triple junctions).
The easiest way to define a peritectic phase diagram in MICRESS is to take the peritectic temperature as reference temperature and define the slopes of all three interfaces (solidus and liquidus/solvus for each, all but one negative in your case, units should be K/at%) at this temperature.
One condition which should be always considered in multi-phase systems is that the sum of the "entropy of fusion" values ΔS should always be 0 for a closed circular reaction, otherwise you could produce a perpetuum mobile:

ΔS(L/α) + ΔS(α/β) - ΔS (L/β) = 0.

Unfortunately, in your case, there is an extra complication: The reaction α/β is "demixing", i.e. the solidus and solvus slopes have opposite sign, and redistribution of elements between the two phases would diverge. There are two options how to handle this in case of a linearized phase diagram:
1.) You assume that the α/β-reaction is slow. Then you can use "no_phase_interaction" for this phase pair, and the problem would not appear. But then, the peritectic reaction cannot happen...
2.) You define the linearized phase diagram using the "linearTQ" option for the α/β-interaction. That means that you define the phase diagram in the same format as if it would have been obtained from database. This allows you to define a dS+ and dS- value for the solidus and solvus slope independently. If you specify them with different sign, then demixing is avoided. To fulfil the sum rule explained above, you could use ΔS(L/α)=1, ΔS(L/β)=1, dS+=0.1, dS-=-0.1. Furthermore, you need to specify a dummy value for dH (any value, is just for having the "copy/paste experience" from the .log file) and values for the temperature dependence of the reference concentrations (0, otherwise the phase-diagram would no longer be linear).

Option 2.) should work for you...

Bernd

mogeritsch
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Re: Metastable phase

Post by mogeritsch » Tue Sep 22, 2015 2:27 pm

Dear Bernd,
your answer helps me because we assume that there is no really a peritectic reaction.

Best regard,

Johann

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