Nucleation density and influence of shielding

[Moritz]

Hello everyone,

Question 1 - Seed density based on Experimental Values
when setting up nucleation in MICRESS, the available seeds are an important input. Greatly influencing are also parameters like the shielding time or shielding distance.

If seeds sizes and density are known based on experimental values(TEM analysis of the ODS particle density and radius), the seeds are going to be effectively activated based on Greer et.al model implemented in MICRESS.



However, this activates more seeds and much finer grain sizes are seen than from the experiments. Hence, in the paper "Revealing the Mechanisms of Grain Nucleation and Formation During Additive Manufacturing" by Bermingham et al. from 2019, there are some insights formulated on how the shielding distance mechanism works and how it could be calculated. As MICRESS allows only for a constant shielding distance/time, changing conditions on the shielding distance (i.e. the liquid/solid ratio) can not be taken into account. Is it therefore reasonable to assume them to be fitting parameters, of course in the range of possible values?

Can it be a reasonable approach to try to derive the distances of nucleation events based on the distance of the center of different grains for different volume fractions of the ODS fractions?

Question 2 - Seed density based on fitting values

As seen from Janin Eiken's thesis, the seed density is a fitting parameter, hence can a benchmark model for the AM experiments be developed based on the fitted seed density with particle sizes from the TEM experiments using the formula below as from the thesis.



In order to further study the effect of the volume fraction of these heterogeneous nuclei, can a direct proportionality be assumed between the seed density and ODS particle fraction. (eg. doubling the volume fraction leads to doubling the seed density as seen from the paper'' https://www.researchgate.net/publicatio ... th_CALPHAD '')


As always, I am happy with your suggestions.

Best regards,

Moritz

[Bernd]

Dear Moritz,

Thank you for these interesting questions. To open discussion, let me ask back some points. The topic is quite complex and involves a number of different concepts.

• What do you mean by ODS? Is it Oxide Dispersion Strengthening? If so, does that mean that the alloy of your interest contains a high volume fraction of relatively large oxide particles?

• The seed density model as implemented in MICRESS is designed as a physically based model for heterogeneous nucleation. It is not identical to Greer's Model which does not treat explicitly located nucleants and which makes further assumptions like a homogeneous temperature and missing solutal interactions. Where do you take the information from that "this" model (Greer, seed-density model in MICRESS?) activates more and smaller nucleants than seen in experiments?

• The shield distance and time stem from the second major nucleation concept in MICRESS which is the "seed_undercooling" model. In contrary to the seed-density model, here we do not focus on the physical mechanisms behind nucleation but rather try to directly match the experimentally observed seeds by specifying typical distances (shield distance, nucleation distance). Thus, to conceptually link the shield distance with the seed-density model is not straight-forward (and was never intended in first place). Is your idea to do so based on the Bermingham paper and the "Interdependence Model"?

• Do you have reliable particle density distributions from experiments in your case, and did you try to implement them in MICRESS as seed-density distribution? Could you confirm your theory that this type of modelling does not fit to your experimental data?

• The measured particle radius distribution does not directly correspond to the distribution required for the seed density model in MICRESS, because the critical undercooling for nucleation on the particle also depends on the wetting conditions (i.e. the "effective" seed radius may be considerably smaller if no perfect wetting is expected). Is this the point you raise with the formula from Janin Eiken's thesis (I don't have it at hand at the moment...)

Bernd

[venkatesh.pandi97]

Dear Bernd,

I am Venkatesh, also working on the same topic with Moritz.

1. Yes, in our case TiN in ferritic steel is processed via AM. The alloy contains 0.8% of ODS particles and below is the number density from TEM experiments.
Radii (nm) Number density(cm-3)
10 3.69861E+15
20 7.92902E+15
30 7.20913E+15
40 7.95767E+15
50 2.75741E+15
60 9.68821E+14
70 6.21039E+14
80 2.73257E+14
85 8.58525E+14

2. I assumed that MICRESS seed density model activated more nucleants than from experiments because the grain size was much finer as obtained from the simulation than compared to the experiments when the above data is inputted in the seed density model.

3. Hence, I tried to control the grain size by playing with the shield distance as seen from Bermingham paper. But I now see this wouldn't be a scientifically right approach as in their case it is of a constitutional undercooling approach, but in my case, it should be based on the heterogeneous nucleation due to the TiN in the melt.

4. Yes, this didn't fit as much finer grain sizes were obtained.

5. Yes, I completely agree with you. Is there a reliable way to predict it? Or should I follow the approach as stated in Jannin thesis ''The distribution of the impurity particles is modeled by an exponential function (Eq. 5.1), based on an estimated mean particle radius r ̄nuc = 0.05 μm and a calibrated total nucleant density N = 4. · 106 cm−3 .'', in my case, I know already my mean particle radius and I can calculate the density function based on the formula stated below cited from Janin's thesis.

[Bernd]

Dear Venkatesh,

I think the problem of your ODS system is that the radii of the particles which you consider as nucleants are much bigger than what is normally assumed in a seed density model (and also the Greer model) for classical alloys where seed particles typically are smaller than 1 µm. The huge radii in ODS alloys lead to extremely small curvature contributions (<<1 K), so that effects of irregular shapes or no-wetting conditions between the metallic melt and the ceramic particles are certainly dominant.

Can you see in your experiments any correlation between the particle radius and the probability that it serves as nucleant (i.e. leads to the formation of an extra grain)?

I am wondering whether it would be an option to explicitly include the TiN particles in the simulation, and treat nucleation on the particles by the "seed_undercooling" model with nucleation at interfaces (instead of using the seed_density option).

Bernd

[venkatesh.pandi97]

Dear Bernd,

I think there might be a misunderstanding. In my case, the ODS particles are in the range of nanometers (ie. 10-80nm). Therefore, in my simulations, I could see curvature undercooling. So do you think still I need to include the seed density model?


Seed number 137 set at time t = 9.31000E-05 s
---------------------------------------------
in the bulk, zp = 40700
Phase: 1 (BCC_A2)
Seed type: 1 (7: 8/13)
Local temperature = 1772.0 K
Undercooling = 5.8595 K
Nucleus curvature undercooling = 5.8303 K
Grain number = 212

I haven't seen any correlation as far as now.

When I used a random seed-density distribution as seen below, I achieved a good match with the experiments on the CET and grain sizes.
# Specify radius [micrometers] and seed density [cm**-3] for class 1
0.23 500000000
# Specify radius [micrometers] and seed density [cm**-3] for class 2
0.18 1000000000
# Specify radius [micrometers] and seed density [cm**-3] for class 3
0.16 2500000000
# Specify radius [micrometers] and seed density [cm**-3] for class 4
0.14 5000000000
# Specify radius [micrometers] and seed density [cm**-3] for class 5
0.12 10000000000
# Specify radius [micrometers] and seed density [cm**-3] for class 6
0.10 25000000000
# Specify radius [micrometers] and seed density [cm**-3] for class 7
0.08 45000000000
# Specify radius [micrometers] and seed density [cm**-3] for class 8
0.05 70000000000
# Specify radius [micrometers] and seed density [cm**-3] for class 9
0.04 125000000000
# Specify radius [micrometers] and seed density [cm**-3] for class 10
0.01 250000000000

But on the other hand, when I assumed that the seed-density distribution to be equal to the titanium nitride distributed in the melt as obtained from TEM experiments seen below, I obtained much finer grain sizes.

# (Specify radius [micrometers], Seed density [cm**-3])
# Specify radius [micrometers] and seed density [cm**-3] for class 1
0.085 8.59E14
# Specify radius [micrometers] and seed density [cm**-3] for class 2
0.08 2.73E14
# Specify radius [micrometers] and seed density [cm**-3] for class 3
0.070 6.21E14
# Specify radius [micrometers] and seed density [cm**-3] for class 4
0.06 9.69E14
# Specify radius [micrometers] and seed density [cm**-3] for class 5
0.05 2.76E15
# Specify radius [micrometers] and seed density [cm**-3] for class 6
0.04 7.96E15
# Specify radius [micrometers] and seed density [cm**-3] for class 7
0.03 7.21E15
# Specify radius [micrometers] and seed density [cm**-3] for class 8
0.02 7.93E15
# Specify radius [micrometers] and seed density [cm**-3] for class 9
0.01 3.7E15

[Bernd]

Dear Venkatesh,

Oh yes, I have read your table wrongly, please forget what I wrote in my last post

So, if I understand you correctly now, the random distribution, which you used exemplarily, gives reasonable results, while the measured one produces much too fine grains. I think, there are two major differences between the two distributions:

• the distribution measured with TEM has a much higher seed density in every radius class (~3-5 orders of magnitude)

• the measured distribution function has a steep and abrupt end above the highest radius class

The efficiency of a grain refiner not only depends on the number density of seed particles, but also on the shape of the distribution, especially the slope (change of density with decreasing radius). The ideal grain refiner would consist of only one class of seeds with a sufficient high density, additional seed classes with smaller radius would not hurt but not play any role. But the existence of an even very small number of bigger seeds (e.g. as impurity) can easily destroy such an ideal refiner, because few grains would grow earlier and prevent the refiner from getting activated.
I think, your measured distribution is such an "ideal" refiner, because already the biggest class has such a high density that they already are sufficient to create extremely fine grains. Due to their equal radius they all come simultaneously, so that they cannot shield each other.

I could imagine, that you could get a much coarser grain structure if you would add some (few) bigger particles to your distribution. What you could try to do is e.g. to fit the measured distribution and extrapolate it to bigger radii. You should add these classes with bigger radii as far as their extrapolated density is still relevant (you can see in the .log-file output how many seed positions are actually created for each radius class). Probably, these bigger particles are really existing, they were just not found in TEM due to their much smaller number.


Bernd

[venkatesh.pandi97]

Dear Bernd,

Thanks a lot for your reply.

I completely agree with your reply that larger particles weren't included in TEM, as particles larger than 150nm were seen in the TEM experiments, but were quite hard to characterize the number density and hence were not included. So now I shall extrapolate the seed-density distribution for the measured values from TEM and try my new simulations and shall measure the activated nuclei for each seed class.

In addition, I performed some simulations where the number density was reduced by a factor of 10000 (30%) and I could obtain coarser grains matching the experiments. Could I argue here it is due to the potency of the nucleants, where the rest weren't activated due to the shape, wettability, etc. reaching an inoculation efficiency of 70%? I do observe a CET transition in my simulation and it wasn't affected and had a good match with experiments too.

Thanks

Venkatesh

[Bernd]

How do you match the factor of 10000 with 30%?

I think one could easily argue that a certain percentage of particles is poisoned or ill-shaped, but not 99.99%. Perhaps my first suggestion will help and you need maybe only a smaller factor...

Bernd

[venkatesh.pandi97]

Dear Bernd,

I miscalculated the factor and hence 30% is wrong. The image below shows by seed density plot and extrapolated values until 0.5µm, as I don't expect particles greater than this to be present.

Capture.JPG

I have snow several results below showing the activated seeds at different inputs.

1. Extrapolated
0.05 6.45E10
0.085 8.59E+14
0.08 2.73E+14
0.07 6.21E+14
0.06 9.69E+14
0.05 2.76E+15
0.04 7.96E+15
0.03 7.21E+15
0.02 7.93E+15
0.01 3.70E+15

For this seed type 80085 seed positions have been generated

2. Orginal
0.085 8.59E+14
0.08 2.73E+14
0.07 6.21E+14
0.06 9.69E+14
0.05 2.76E+15
0.04 7.96E+15
0.03 7.21E+15
0.02 7.93E+15
0.01 3.70E+15

For this seed type 80097 seed positions have been generated.

3. Calibrated
0.085 8.59E+10
0.08 2.73E+10
0.07 6.21E+10
0.06 9.69E+10
0.05 2.76E+10
0.04 7.96E+10
0.03 7.21E+10
0.02 7.93E+10
0.01 3.70E+10

For this seed type 421 seed positions have been generated

4. Extrapolated
0.05 6.45E10
0.15 1.7E13
0.3 1E12
0.4 1E11
0.085 8.59E+14
0.08 2.73E+14
0.07 6.21E+14
0.06 9.69E+14
0.05 2.76E+15
0.04 7.96E+15
0.03 7.21E+15
0.02 7.93E+15
0.01 3.70E+15
For this seed type 79608 seed positions have been generated

I see from the following literature that seed density was rather used as a fitting parameter rather based on the particles from the experiments, should I also go with it then as my target would be to study the CET transition for a heterogeneously nucleated Fe-based alloy in AM?

https://www.jstage.jst.go.jp/article/is ... 9/_article
https://www.researchgate.net/publicatio ... eld_Method
https://www.researchgate.net/publicatio ... Al4V_Alloy

[venkatesh.pandi97]

Dear Bernd,

There was a mistake in my python code to calculate the seed density and I have now solved it, which changed the SDD (seed density distribution) as shown in Figure below.

Capture.JPG

The MICRESS simulation for this seed density activated around 8600 seeds and lead to a finer grain. When I tried adding extrapolated data as you mentioned before, I could see some larger grains forming but they don't dominate and their sizes still don't fit my range. So I will try now adding more extrapolated data and will come back again with the grain size analysis.