Phase Diagram Input for Multi-component Systems with NPLE

solid-solid phase transformations, influence of stresses and strains
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markoklups
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Phase Diagram Input for Multi-component Systems with NPLE

Post by markoklups » Thu Jul 25, 2019 6:53 pm

Hi all,
I am running some MICRESS simulations for intercritical annealing (austenite formation) of a steel (0.039wt% C and 1.65 wt% Mn). I'd like to include both C and Mn as solutes and use either NPLE or paraequilibrium for Mn at the interface.

My question is: as the peak position of Mn at the interface under NPLE follows a specific tie line on the ternary phase diagram, what phase diagram should I put into the model? It seems that the input file asks me for two binary phase diagrams (Fe-C and Fe-Mn), which does not seem reasonable to me.

A side question as well:
NPLE introduces a sharp Mn peak (or valley) at the interface in analytical models, but to maintain solute conservation, should there also be a valley (peak) on the other side of the interface?

Thanks,
Marko

Bernd
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Re: Phase Diagram Input for Multi-component Systems with NPLE

Post by Bernd » Thu Jul 25, 2019 8:40 pm

Hi Marko,

Welcome to the MICRESS Forum!

If you have chosen to use a ternary linearized phase diagram description, you do not specify two binary phase diagrams: You rather select a ternary equilibrium point as reference, and describe the concentration dependence of the equilibrium temperature for both elements independently in a "multi-binary" approach. This is a huge difference, because close to this reference point you have a valid ternary description.

However, if you use the nple model, the operating tie-line typically is not close to the equilibrium (which you would get if Mn had a higher mobility). Therefore, it is important to place the reference point close to the operating tie-line. Otherwise, the linearized phase-diagram description can be very bad because of too far extrapolation. Unfortunately, you cannot always know the operating tie-line if the process is not stationary. E.g. in case of a heating-cooling cycle you would be in trouble.

In case of TQ-coupling, you need not worry about this problem, because MICRESS will always calculate the local linearisation parameters based on the current operating tie-line. Therefore, I would always prefer to do that!

Your side question: As nple still has "local equilibrium", a peak in one phase always is mirrored to the other phase. And if there is some slow diffusion of Mn which leads to a thin peak in Mn the mixture composition, there must be a corresponding valley directly behind (however, the nple model does not require any diffusion!).

Bernd

markoklups
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Re: Phase Diagram Input for Multi-component Systems with NPLE

Post by markoklups » Mon Jul 29, 2019 10:34 pm

Hi Bernd,
Thanks for your reply. My simulation will be a continuous heating scenario, so according to your suggestion I should go for TQ coupling. Unfortunately in my department ThermoCalc and MICRESS are not installed on the same computer so I cannot use the TQ coupling directly within MICRESS. Is there a remedy for this? (i.e. can I just use an output from ThermoCalc? I think the gamma-alpha example used a database but I do not have that database file so I cannot run it.)

I also wonder if MICRESS with TQ can calculate parameters such as "entropy for fusion". In the linearized phase diagram approach many paper did not calculate entropy directly from ThermoCalc, but used some formula derived from driving force and local equilibrium undercooling (fit ΔG vs ΔT assume ΔG is approximately "ΔS" times ΔT) and I'm not sure if the approximation is good.

Thanks,
Marko

Bernd
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Re: Phase Diagram Input for Multi-component Systems with NPLE

Post by Bernd » Tue Jul 30, 2019 12:00 am

Hi Marko,

It does not matter whether you have installed Thermo-Calc and MICRESS on the same computer. If you have installed a MICRESS version with TQ-coupling, the only things you need to do with Thermo-Calc is performing pretests and creating the binary .GES5 files from the database which you need to use with MICRESS. It does not matter whether you do that on another computer.

The "entropy of fusion" which typically is used in linearized phase diagram descriptions is not really the entropy of fusion but rather the derivative of the driving force ΔG with temperature. Thus, the described procedure appears reasonable. If you use MICRESS with TQ-coupling, you will automatically get all parameters like entropy of fusion, reference concentrations, phase diagram slopes, etc.

Bernd

billyzhangubc
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Re: Phase Diagram Input for Multi-component Systems with NPLE

Post by billyzhangubc » Tue Sep 10, 2019 3:11 am

Hi Bernd,
I have some further questions on a similar system, although not on phase diagrams. I am running (once again) 1D α-to-γ tests on Fe-C-Mn ternary systems with TQ coupling. Under diffusion control, kinetics is usually fast at the beginning (C-diffusion controlled and close to NPLE), reaching a "NPLE limit" (stasis) followed by much slower kinetics (Mn-diffusion controlled) and eventually reaching full equilibrium.

In a 110-μm system with 1% initial γ, my DICTRA simulation shows that NPLE limit is reached after ~10 seconds at 1100K (figure attached). My MICRESS simulation on a similar system gives much slower initial kinetics if I use "normal" for Mn. With "NPLE" for Mn the kinetics is even slower. I used a very high yet artificial α/γ interface mobility (1 cm4/J/s), trying to push the transformation towards diffusion control (my thermo-calc does not have the mobility database). This is simple and doable for binary Fe-C but doesn't seem working on my Fe-C-Mn system.

My questions are:
(1) Mathematically, what does the option "mob_corr" do (I will need to explain it to my supervisor :D )? I guess it will artificially increase interface mobilities to result in diffusion-controlled transformation...
(2) If I want to simulate the initial fast kinetics at least, on which component(s) (C or Mn) should I apply mob_corr?
(3) "mob_corr" cannot be used if NPLE or para is used for Mn. I could get fast kinetics with paratq for Mn, but not with NPLE for Mn (normal for C in both cases). I wonder if in this case, mob_corr is still necessary for C.

Thanks in advance,
Billy

Bernd
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Re: Phase Diagram Input for Multi-component Systems with NPLE

Post by Bernd » Wed Sep 11, 2019 7:18 pm

Hi Billy,

The problem of calculating γ-α or α-λ transformations using a phase-field method is that there is a fast and a slow diffusing component, and that the diffusion pile-up of both elements cannot be resolved at the same time. Contrarily, in Dictra this can be achieved in 1D by grid refinement towards the interface. Thus, if correctly performed, Dictra simulations can serve as benchmark case for phase-field simulations.

In MICRESS, the concentration pile-up of the controlling element (C for the initial fast kinetics in your case) should be properly resolved. Hereby, using "normal mob_corr" or "atc mob_corr" ensures that numerical artefacts which are due to the finite interface thickness are minimized. When using "mob_corr", the interface mobility, which is specified in the phase interaction data, should be assumed to be the physical value (i.e. a high value like 1.0 cm4/J/s for diffusion control). Then, an effective (corrected) interface mobility is calculated, which is always smaller than the physical value and which would correct for the mentioned numerical artefacts (see .mueS output).

If there are slow diffusing elements like Mn, which have a pile-up which is not properly resolved in MICRESS, "nple", "para" or "paraTQ" should be used without "mob_corr". "normal" would lead to undefined behaviour somewhere between "nple" and "para". The use of "mob_corr" would erroneously assume a very small effective interface mobility in order to prevent "overrunning" of the Mn pile-up, which however is the expected behaviour according to the nple growth mode.

Thus, at least for the initial fast kinetics, I would expect MICRESS to give similar results as DICTRA, provided that the grid resolution is fine enough for resolving the C-profile, and that you specify a high physical value of the interface thickness, and "normal mob_corr" or "atc mob_corr" for the redistribution behaviour of C, and "nple" for Mn. If there are still differences, please also check whether the diffusion data which are assumed in both simulations are identical.

For the much slower kinetics later, which is diffusion controlled by Mn, I would expect MICRESS to deliver only approximate results under these circumstances, given that the diffusion profile of Mn is probably still not well-resolved despite of the much smaller interface velocity. Of course, MICRESS would be correct again, if the resolution were chosen sufficient for Mn-difffusion. In such a simulation, one would assume infinite diffusion for Carbon in order to avoid huge calculation times.

Your questions:

(1) Please look up the theory in our publication

A.Carré, B.Böttger, M.Apel: "Implementation of an antitrapping current for a multicomponent multiphase-field approach",
Journal of Crystal Growth 380(2013)5–13.

If using the full diffusion matrix, effective diagonal terms are calculated for the given phase interface (unpublished up to now). If you don't have access to the paper, I can send it to you by e-mail.

(2) Please use "mob_corr" only for C, not for Mn

(3) yes, mob_corr is still necessary for C!

Bernd

billyzhangubc
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Re: Phase Diagram Input for Multi-component Systems with NPLE

Post by billyzhangubc » Fri Sep 13, 2019 12:52 am

Hi Bernd, thank you very much for your reply. With mob_corr my kinetics make more sense. Now under NPLE for Mn and "normal mob_corr" for C, I am able to replicate my DICTRA result (see the plot attached; red curve is the MICRESS result) even after the NPLE-PLE transition.
NPLE_PLE_transition_1075_overlaywithPFM.png
NPLE_PLE_transition_1075_overlaywithPFM.png (112.06 KiB) Viewed 226 times
Now I have a new question on PARA. For example, my Fe-0.039wt%C-1.65wt%Mn at 1075K has a full equilibrium γ fraction of ~48%. In my simulation with PARATQ for Mn, γ fraction keeps increasing after the PARA-PLE transition (~47%) and eventully goes towards ~55%, which doesn't make sense to me (see curves attached. Starting γ is 2% for all cases).
kINETICS_1075k_LOG.PNG
kINETICS_1075k_LOG.PNG (25.64 KiB) Viewed 226 times
I would anticipate that if PARA is used throughout my simulation, then upon reaching the PARA limit, the γ fraction should either level off (if Mn is configurationally frozenor if I assume a pseudo-binary system), or slowly go towards the full equilibrium fraction (if Mn diffuse), in this case, decrease gradually to 48%.

Therefore, I wonder how MICRESS deals with the PARA/PARATQ option with TQ coupling.

Thanks,
Billy

Bernd
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Re: Phase Diagram Input for Multi-component Systems with NPLE

Post by Bernd » Fri Sep 13, 2019 5:37 pm

Hi Billy,

Thank you for presenting your results here. I am astonished, that the NPLE model of MICRESS converges so well to PLE when the driving force is not sufficient for overrunning the MN pile-up. Great!

In contrary to the NPLE model, which essentially converts the interface region to an extended "sharp interface", but still assumes local equilibrium, PARA and PARATQ cannot be expected to converge to full equilibrium, although they work in different way:
PARA still assumes some local equilibrium, but with a shifted tie-line so that the effect of Mn on the driving force vanishes - i.e. it is not the correct equilibrium!
PARATQ, on the other hand, calculates the phase compositions of Mn using the Thermo-Calc paraequilibrium model, and thus does not provide any segregation of Mn. Thus, Mn should be equally distributed in the whole domain always, which also does not correspond to full equilibrium!

Thus, both paraequilibrium models in MICRESS should be only used during the paraequilibrium stage, they cannot converge to PLE automatically!

Bernd

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