Nucleation density and influence of shielding

dendritic solidification, eutectics, peritectics,....
Bernd
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Joined: Mon Jun 23, 2008 9:29 pm

Re: Nucleation density and influence of shielding

Post by Bernd » Tue Feb 22, 2022 7:31 pm

Dear Venkatesh,

Good news that after having corrected the Python error your measured distribution is less extreme!

I have two concerns about your extrapolation of the seed density distribution:
  • When fitting or extrapolating a density distribution function, you need to take care that each class has the same Δr. The integral over the density distribution must be equal to the total number N of particles! In your plot of the measured distribution, for example, the bending of the curve is probably not real, it is just because Δr is smaller for the class with radius 85 nm...
  • Your tabulated distributions cannot contain the same value of r twice (0.05). Furthermore, at least in the MICRESS input, the classes must be put in order with decreasing radius!
Furthermore, for extrapolation the important question is not the total number of the generated seeds but the number for each class. For the class with the highest extrapolated radius the number of seeds must be significantly smaller than the number of nucleation events you expect in order to get a reasonable grain size (otherwise if they would nucleate simultaneously, you still would get too fine grains...).

Bernd

Moritz
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Re: Nucleation density and influence of shielding

Post by Moritz » Fri Mar 04, 2022 10:06 am

Dear Bernd,

I would like to add one follow up question to this whole topic of seeds.

As you already described, seeds effect each other in regards to the formation of grains, because earlier acitivated seeds can lead to grain growth which "swallows" seeds that otherwise would have acted as nucleation sites. So double the volume fraction of seed particles should not result in double the number of activated or effective seeds.

Do you know of any established methods to determine these effects, when calculating seed numbers based on one composition of elements for another?

In MICRESS, there is obviously the possibility to set shielding times and distances. Is the determination of these parameters a fit, to reach the desired microstructure?

As always, thank you very much for the helpul insights.

Best regards,

Moritz

Bernd
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Joined: Mon Jun 23, 2008 9:29 pm

Re: Nucleation density and influence of shielding

Post by Bernd » Fri Mar 04, 2022 12:31 pm

Dear Moritz,

I would say that the "swallowing" you mention is just a minor effect, while the effect of latent heat in most cases is dominant for explaining the non-linearity between seed density and expected grain sizes. And the question, how much growth you have (and how much latent heat is released as consequence), primarily depends on the growth restriction factor (grf) which is essentially the derivative of the undercooling to the fraction of solid. Both effects can be taken into account in MICRESS, so I would name MICRESS first as "established method" to determine these effects ;)
Of course, in a not spatially resolved way, the same effects have been modeled e.g. by Greer et al. (Quested TE, Greer AL. Acta Mater 2004;52:3859 / Greer AL, Cooper PS, Meredith MW, Schneider W, Schuhmacher P, Spittle JA, et al. Adv Eng Mater 2003:81).

The use of shield time and distance in MICRESS is a different story because it is (at least in my opinion) not usable for predictive modelling. It is rather meant for cases when other effects are more dominant, e.g. for nucleation at interfaces. Then, these parameters allow for a pragmatic calibration of the simulation with respect to an expected or experimentally observed microstructure.

Bernd

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