general Phase field equation for multi-obstacle potential

Exchange about the physics background, diffuse interface theory, etc..
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khajezade
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general Phase field equation for multi-obstacle potential

Post by khajezade » Mon Jan 21, 2019 4:19 am

Hi there;

If I want to use the multi-phase-field model with the multi-obstacle potential option, what will be the final form of phase evolution? Is it the eq. 25 in the following paper? "Multiphase-Field approach for multicomponent alloys with extrapolation scheme for numerical application" in Phys. Rev. E 73 066122 (2006)

How can the relationship of the following topic be derived from it?: "http://board.micress.de/viewtopic.php?f ... p=461#p461"

Kindest Regards,

Ali

janin
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Re: general Phase field equation for multi-obstacle potential

Post by janin » Mon Jan 21, 2019 3:33 pm

Hi Ali,
the MPF equation currently implemented in Micress is essentially still the same as in the 2006 paper, apart from some small changes in the definition of the prefactors.

The major difference bewtween the two formuations you cited is that
in 1) gamma runs over all phases including alpha and beta
in 2) pairwise alpha and beta contributions have been separated from junction contributions.
(Note that sigma_alpha-beta = sigma_beta-alpha and sigma_alpha-alpha = 0.)

Both formulations can be converted into each other by:
Bild1.png
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Regards,
Janin

khajezade
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Re: general Phase field equation for multi-obstacle potential

Post by khajezade » Mon Jan 21, 2019 8:59 pm

Hi Janin;

Thanks for your explanation. I have three more questions regarding these equations.

1) In these relationships, Is M_{\alpha \beta }^{\phi } the physical interface mobility? Is it equal to the user's input or it is modified in this relationship?
2) What does \nu mean in term of physical interpretation? If I factor \nu from the equation I can put it under Mobility term which means that mobility is scaled by the local number of grains!
3) Do I need to worry about spreading of phi parameter in this model? Do I need to normalize the phase parameter after each iteration?

Kindest Regards,

Ali

janin
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Joined: Thu Oct 23, 2008 3:06 pm

Re: general Phase field equation for multi-obstacle potential

Post by janin » Wed Jan 23, 2019 10:16 pm

1.) In this formulation, the mobility M_{\alpha \beta }^{\phi } denotes the physical mobility of an interface between two phases alpha and beta. We have writen the PF equation in a way that the parameters can easily be identified by matching to the Gibbs-Thomson equation. In the case of uncoupled growth the mobility in the PF equation directly equals the kinetic coefficent. In case of concentration coupling, it still has to be corrected in the thin-intreface limit. Note that the mobility in the PF equation differs from the mobility in the relaxation approach by a constant factor.
Bild1.png
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2.) \nu is the number of local grains and used to consider the unit sum constraint of the phase-field parameters. Physically the unit sum constraint accounts for the local mass or volume balance. Of course, you could put the factor \nu explicitely or implicitely into the mobility. This will not change the results, but is just a different way to write it. We did that in former times mainly for sake of consistency with mobility definition in other MPF-models based on the assumption of equal mobility for all interfaces. But this mobility will no longer equal the kinetic coefficent.
Bild2.PNG
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3.) No spreading. Theorectically no normalization required, but maybe numerically. Depends on your numerical solver. Do you intend to implement your own MPF-program from scratch?
What is your motivation?

Regards,
Janin

khajezade
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Re: general Phase field equation for multi-obstacle potential

Post by khajezade » Thu Jan 24, 2019 11:51 pm

Hi Janin;

Thanks for the explanation.
I am writing the code from scratch for different phase-field models for grain growth and texture predictions. For my Ph.D. project, we are thinking to scale up our simulation domains (around a million grains). I asked you before about feasibility of doing these sort of simulations with the current version of MICRESS. I don't want to use categorization. We are using MPI standards to use as much as resources possible on our clusters.

Actually, I coded the model. I have checked my isotropic grain growth simulations with the results simulated by MICRESS for a small 2D microstructure(as a verification). I have noticed that while my code can reproduce the results, there are some differences e.g. shrinking grains disappeared faster while the big grains are Identical. Having said this, in my code, I need to sum up all the phase parameters in a grid point again and normalize them by summation. I always have phase parameters between 0 and 1 even if I don't normalize it, but it doesn't make a stable interface at the end I do not normalize.
I should mention, I loop over all phase parameters at a grid point and I do not skip the differences for very small numbers.

I appreciate any ideas on this and it is very kind of you if you do.

Thanks,

Kindest Regards,
Ali

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