Typical values for minimal mobility

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Moritz
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Typical values for minimal mobility

Post by Moritz » Mon Jan 31, 2022 9:59 am

Hello everyone,

I recetly added Zener pinning to one of my simulations. As you know, there are two values required: The Zener pinning pressure and the minimal mobility.

For the Zener pinning pressure, there are many literature sources and also suggestions on how to calculate it, so I am fairly certain that I use a correct or nearly correct value.

Unfortunately, that is not the case for the minimal mobility, as this is a MICRESS parameter. I conducted a parameter study with the same value for the Zener pinning pressure and altered the minimal mobility. I did not see any significant difference, even when the minimal mobility changed by the factor of 10 oder 100.

Does anyone has suggestions about a "correct" or often used value for the minimal mobility? Does it only matter in certain cases?

Best regards,

Moritz

Bernd
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Re: Typical values for minimal mobility

Post by Bernd » Mon Jan 31, 2022 10:38 am

Dear Moritz,

The minimal mobility is a parameter which should be 0 in a "pure" Zener pinning model, but which allows for taking into account that the pinning particles may exhibit Ostwald ripening by themselves (i.e. they grow with time and such loose part of their pinning activity). Therefore the minimal mobility must be chosen with suitable relation to the interface mobility itself: If you e.g. would chose it 100 times smaller than the interface mobilily, then particle pinning would not completely stop interfaces with insufficient driving force but only slow them down by this factor of 100. Of course, this is only a first order accounting for Ostwald ripening...

Bernd

Moritz
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Re: Typical values for minimal mobility

Post by Moritz » Fri Feb 18, 2022 12:42 pm

Hello Bernd,

as always, thank your for your answer. I suspected something like that. As I am in the process of confirming more and more parameters for my simulation, this is really reassuring.

I would like to ask a follow-up question regarding the mobility or more specific the Zener pinning. I only found one other relatively old forum discussion about it. There you wrote to another user: "The question how this critical pinning force is related to the size, shape and density of the pinning particles is not part of our mesoscopic pinning model. The user may apply analytical approaches like the Zener model in order to obtain a value for the critical pinning force, alternatively one may apply microscopic simulations like the one shown above in this thread."

What confuses me a little bit are the different terms used here. In MICRESS, is the Zener pinning force, which I can calculate based on more or less equal equations (with volume fraction, particle surface energy, particle radius) the critical pinning force? Or is this something different? Or put in other words: If I calculate a Zener pinning force, can I enter this value for the critical pinning force?

Best regards,

Moritz

Bernd
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Re: Typical values for minimal mobility

Post by Bernd » Fri Feb 18, 2022 1:31 pm

Hi Moritz,

Maybe, my answer at that time was unnecessarily confusing. I just wanted to say that the Zener model equation is not used in the MICRESS implementation of the pinning effect. We use the concept of "Zener particle pinning" and the quantity of the "Zener pinning force" (translated to a critical driving force), but not the Zener model equation which predicts the pinning force based on size, shape and density of the pinning particles. You may instead want to use other model equations or approaches to estimate the critical pinning force, including spatially resolved MICRESS simulations...

Bernd

Moritz
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Re: Typical values for minimal mobility

Post by Moritz » Fri Feb 18, 2022 3:44 pm

Hi Bernd,

thanks for the fast reply.

In your paper "Grain Growth Simulations Including Particle Pinning Using the Multiphase-field Concept" in figure 3, you show the interaction of a NbC particle with a grain boundary. It is something like this, when you think of a spatial resolved simulation?

Image

If I set-up this simulation, I think that the approach would be to calibrate it, until the movement of the grain boundary when passing the particle matches with the real behaviour. What I don't completely understand is, how I would compare the real condition to the simulation, as it is not possible to observe or rather measure this.

Do you think it is an scientificly acceptable approach to fit the critcal pinning force/pressure on a bigger scale by matching a solidification simulation with experimentally achieved microstructures? It would be more or less like the other approach, but on a slightly bigger scale.

And one last question: As the Zener pinning force and therefore the value for the critical pinning force in MICRESS depends on the volume fraction of the pinning particles, when one optained a value for this force, it is reasonable to change this value for different volume fractions by assuming a propotional relationship?

Best regards,

Moritz

Bernd
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Re: Typical values for minimal mobility

Post by Bernd » Fri Feb 18, 2022 5:16 pm

Dear Moritz,

Yes, it is such a type of simulation which I meant. However it must be in 3D and also big enough (or specifically arranged) to be representative. Essentially, as explained in our paper you are referring to, an interesting outcome of such simulations is not only the critical pinning force, but also the interface movement in case of partial pinning (Figure 2 in this paper). The results of such a study is the basis of the current MICRESS pinning model.

In practice, when applying the MICRESS pinning model, the main problem is that the number density and size distribution of the pinning particles is typically unknown. Therefore it is reasonable (and scientifically justified) to calibrate the critical pinning force on the meso-scale by comparison with experiments. Then, if you know or assume that in a given sample the pinning particle number density would be higher (with same sizes) than in one you already have calibrated, it would also be justified to multiply the critical pinning force with the corresponding density factor in accordance with the Zener model equation.

Bernd

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