Directional solidification of Al-Si hypoeutectic alloy

dendritic solidification, eutectics, peritectics,....
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micress
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Directional solidification of Al-Si hypoeutectic alloy

Post by micress » Thu Oct 24, 2019 12:33 pm

Hello, I am new to MICRESS and have been trying to learn from your example programs and websites such as MICRESS Forum.
I am simulating the directional solidification of hypoeutectic Al-Si alloy especially at high cooling rate,
and I want to see unidirectionally solidified dendrite with eutectic structure in bulk.
However, I am puzzled by many problems, so here I'll pick some of them.
(I attempted .dri file.)

1. First of all, is it fine to apply GES5 file without mobility database?
If so I thought I would need to put info related to mobility in a section, but I can't find it.
So instead I am now using phase diagram data such as solidus slope etc.

2. Initial grains at the bottom somehow split and grow in both +/- 45 degree assuming 0 degree in z-direction although aluminum has FCC structure.
What is it caused by?

3. What is “substrate phase” in Data for further nucleation?
I am not sure about the difference between reference phase and substrate phase.
(I understand what reference phase means.)
I wonder what is another factor(phase) necessary for nucleation setting.

4. How should I set nucleation info to simulate the phenomenon mentioned above?
This is the biggest problem for me.

Best regards,
Yuta
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Bernd
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Re: Directional solidification of Al-Si hypoeutectic alloy

Post by Bernd » Thu Oct 24, 2019 8:21 pm

Hi Yuta,

Welcome to the MICRESS forum!

Let me try to give you answers along your questions. If you have follow-up questions, please don't hesitate to ask again in this topic!

1. Of course you can apply a .GES5 file which does not have mobility data inside. In this case, you must define diffusion data manually by using the selectors "d" or "f" (see here, or by using the old syntax as you did in your .dri file). Please note that "mobility" in this context means diffusion data.

2. Splitting of dendrites sometimes can be physically correct. However, if the branches grow in 45° direction, then either you have a 45° orientation (I have seen you use random orientation!), or the growth direction is dominated by grid anisotropy (as a consequence of crashing interfaces). To avoid the first, you should fix the orientation to 0° (it is easier to use "angle_2d" at the end of Phase Data input), for the latter it is essential to achieve numerical stability (see further remarks below).

3. The substrate phase is to be specified if you have chosen "interface" or "triple" as nucleation region. The reference phase is the phase in which nucleation undercooling is calculated, while the substrate phase is the phase "at" which the nucleus is growing. For example, when nucleating Si phase at a liquid/fcc interface, one would choose liquid as reference and fcc as substrate phase. By the way, local curvature of the substrate phase contributes to the critical nucleation undercooling.

4. If you want to simulate directional solidification, you would typically set initial grains of the primary phase (fcc) at the bottom of the domain, or nucleate them at the bottom using "region" as nucleation site. In many cases (if the simulation domain is rather small), you would put one seed only to the lower left corner and use periodic ("p") or symmetric ("s") boundary conditions at the right and left side of the domain (East and West). If you want to have dendrites growing parallel to the z-direction, orientation of the initial grains /nuclei should be 0° (in "angle_2d" specification).
For nucleation of silicon, a eutectic reaction is expected. Therefore you would nucleate using "interface" with fcc as substrate and liquid as reference phase. Please note that due to the relatively low Si-content of your alloy, and the resulting small eutectic structures, you will need to use a quite high grid resolution. Alternatively, if you are not so much interested in the eutectic morphology but rather in the primary dendrite structure, you could use the "unresolved" model (see e.g. here) at lower resolution, which results in diffuse phase mixtures instead of a discrete eutectic morphology.

Further remarks:

- given the high cooling rate of 1000K/s, your grid spacing is probably too big. This leads to wrong interface kinetics and other artefacts.
- You should definitively use "mob_corr" in order to achieve correct interface kinetics without calibration of the interface mobility (see here).

Bernd

micress
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Re: Directional solidification of Al-Si hypoeutectic alloy

Post by micress » Fri Oct 25, 2019 11:35 am

Hi Bernd,

Thank you for your quick response.
I am really impressed with your very kind and detailed answers!
I attempted the renewed drive file.

1. I am relieved to hear that because we have only DEMO ver. of Al-alloys mobility database on Thermo-calc which doesn’t support my study condition.
So my program works properly only in terms of diffusion data because using the old syntax(?) instead using the selectors?
Could you tell me what you mean by “the old syntax”?

2. “angle_2d” made dendrites not split but grow in z-direction!
By the way, the reason why grains grow with plus(+) shape is because the crystal symmetry for the phase is cubic?

3. The last time I took MICRESS lesson, I learned that reference phase means one where nuclei appear. Seeing from another point of view, it is correct too?

4. I am interested in the phenomenon with some grains at the bottom at high cooling rate and under high temperature gradient which often happens in Additive Manufacturing process, so I will try the simulation of one seed to the lower-left corner when I have time!
In the case where you set FCC_A1 as substrate and liquid as reference phase using “interface”, nuclei grow in liquid at FCC_A1 phase as starting point(phase), right?
When I want to simulate the nucleation of Al(FCC_A1) and Si(Diamond_A4), I need to prepare two seeds in Data for further nucleation, for both of which with FCC_A1 as substrate and liquid as reference phase?
Thank you for the alternative method, however I am interested in the eutectic morphology and want to compare it in simulation and experiment results.

Through your answer, I’ve got other questions.
In Data for further nucleation, I need to set nucleation model, maximum number of new nuclei, grain radius etc, and especially I wonder which value to set as maximum number of new nuclei. No papers I can refer to, I set negative value for unlimited number. Could you give me some advice?

Yuta
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Bernd
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Re: Directional solidification of Al-Si hypoeutectic alloy

Post by Bernd » Fri Oct 25, 2019 8:20 pm

Hi Yuta,

I will comment along your points:

1.) The issue with old and new syntax is just a formal thing and has nothing to do with functionality. Therefore, it is not important whether you use old or new syntax, as long as MICRESS still supports old syntax. The new syntax rules are indicated at the top of the diffusion data input (if you updated your .dri file with the .in output). Anyway, if you specify diffusion data manually (i.e. using old syntax “diff” or new syntax “diagonal d”), you do not request diffusion data from the .ges5 file. Therefore it doesn’t matter whether the .ges5 file contains mobility data or not.

2.) “angle_2D” means that you specify orientations of new grains or nuclei using just by one angle. Thus, if you request “random” orientations, the [001] direction always is inside the simulation plane (0° is in z-directions). All the other options for orientation input format will create 3D-orientations, which do not necessarily lie in the simulation plane in case of 2D simulation. Then, in 2D simulations, the anisotropy is “projected” into the 2D plane, leading to smaller anisotropies and increasing the chance of tip splitting. For your application, you want the fcc dendrites to grow in z-direction (i.e. [001] should point in z-direction). The easiest way to achieve that is to choose “angle_2d” and to set the orientations of nuclei or initial grains to “fix” 0.
The cross-shape of the dendrites you describe is indeed reflecting the 4-fold symmetry of the cubic anisotropy.

3.) The term “where nuclei appear” seems a bit undefined, but it is of course true in case of bulk nucleation. However, if you nucleate at interfaces or triple junctions, there are multiple phases present, and one needs a more sophisticated definition…

4.) No, only Si should nucleate at the fcc/liquid interfaces! It does not make sense to nucleate fcc here because it is already present. It is sufficient to have fcc as initial seed in the lower left corner. Only in case that you expect further fcc seeds to come from the melt (if you want to simulate columnar-equiaxed transition, I don’t expect that to be important for Additive Manufacturing) you would add an extra seed type for “bulk” nucleation (ideally using the seed density model for heterogeneous nucleation on virtual seeding particles).

For “number of new nuclei”, you should always use a negative number as you did in order to avoid strange effects. “grain radius” in most cases will be 0, as you typically want to set a “small” nucleus which starts from a small phase fraction. The nucleation model “seed_density” should be used only in case of heterogeneous nucleation from the melt and only is available in conjunction with “bulk” or “region”. Otherwise, you always should use the “seed_undercooling“ model where you specify a critical undercooling as nucleation criterion.

Bernd

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Re: Directional solidification of Al-Si hypoeutectic alloy

Post by micress » Sun Oct 27, 2019 3:45 am

Hi, Bernd,

Thank you for your reply.

1. I see. Considering MICRESS update in future, it is better to use new syntax, but it has no problem currently. I'll fix it in near future.

2. I understood what made the cross-shape. Thank you for your advice, I’ll apply it to my simulation.

3. I might translate into English wrongly. I will remember the meaning as you mentioned.

4. I suppose that the phenomenon such as the attempted Fig. 1 (dendrites with eutectic structure in bulk) can be seen in my simulation and am trying to simulate.
As you mentioned, it is one of methods to nucleate further seeds from the melt, but it doesn’t make sense so much? Just forcing to do so in order to simulate as I expected.
I ran the simulation with only Si nucleation at the fcc/liquid interfaces, however it looks that Si nucleated “in” fcc phase in the lower part of the domain(see Fig.2). Why can it happen?

I have got other problems. The output time is somehow weird. I set the output time as every 0.01s until 30s, but it gave 0.01, 0.02, 0.03, 0.0300041, 0.035033, 0.04, 0.040001, 0.045001, 0.05…(see Fig.3)
Could you give me some advice, please?
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Bernd
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Re: Directional solidification of Al-Si hypoeutectic alloy

Post by Bernd » Mon Oct 28, 2019 9:04 pm

Hi Yuta,

Si-particles nucleate at the liquid-fcc interface, but get rapidly overgrown. This is the reason you find them inside fcc. Possible causes are a too low undercooling, too high curvature undercooling, too low spatial resolution, or other numerical issues.
The outputs at irregular intervals are caused by the option "out_nucleation", which creates extra outputs each time when nucleation happens. Deactivating this option will otherwise not change the simulation results.

Further hints:
- If dendrite arms have "holes" or semisolid parts (see especially the long tertiary arm in the center of the displayed structure in figure 2, it reveals that the interfaces are unstable. You can try to use stabilisation (2nd optional parameter in the same line as the interfacial energy), which has the same units as interfacial energy and can be chosen up to ~10 times its value. If this is not sufficient, it will be necessary to increase spatial resolution...
- If the Si-phase has a solubility range for Al (even if very small), it is necessary to define this phase as stoichiometric (it won't hurt otherwise...) at the top of the phase diagram input data. Whether this phase has a solubility range or not depends on the exact version of your database. Stoichiometric phases without solubility range are automatically defined as such in MICRESS, however close to stoichiometric phases should be defined as stoichiometric manually for numerical reasons!
- When using different interface energy values for different phase interactions, the correct triple point angles will only be simulated if "multi_obstacle" is defined in the flags section of the input file. You definitively should do that!
- your relinearisation interval of thermodynamic data is 0.1s, which means once after 100K of cooling! It should be at least 10 times more often...
- You should increase the interface mobility values to be sure that they are not cutting down the diffusion-limited mobility which is provided by the mob_corr functionality. It does not hurt to make them too big, so you can use e.g. a value of 10/cm3 to be in the safe side...

Bernd

Bernd

micress
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Re: Directional solidification of Al-Si hypoeutectic alloy

Post by micress » Wed Nov 06, 2019 9:02 am

Hi Bernd,

I am so sorry for too late reply. I was so busy with some academic conferences.


I turned on the option “out_nucleation” by my mistake. Thank you.

I see, holes or semisolid parts are caused by unstable interfaces

Yes, Si phase has a solubility range for Al!
I’ll define Si phase as stoichiometric.

So in order to apply stabilization mode on interfacial energy, I only have to put 10 times value of the set interfacial energy after it in the same line? In my case, I should put “2.00000E-05 2.00000E-04” in the line?

Okay, I’ll use multi_obstacle function and change the value of relinearization interval!

10/cm3? Aren’t you talking about kinetic coefficient? I think the unit should be cm4/(Js). I might misunderstand something, though.

Bernd
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Re: Directional solidification of Al-Si hypoeutectic alloy

Post by Bernd » Wed Nov 06, 2019 11:36 pm

Hi Yuta,

Yes, interface stabilisation is correct like you say. Please try out whether it is helpful for you, it depends a bit on the circumstances...

You are also right with the units of the interface mobility :?

Bernd

micress
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Re: Directional solidification of Al-Si hypoeutectic alloy

Post by micress » Thu Nov 07, 2019 7:07 am

Hi Bernd,

Thank you for your advice. I'll try it!

By the way, I have been wondering why Si should nucleate at fcc/liquid interfaces as you mentioned on your 3rd latest posting.
I am thinking of following reasons.

1. Si gets rich in the front of interfaces, so it is natural to nucleate Si at interfaces
2. In eutectic reaction, two adjacent elements - Al, Si in this system - help each other to grow then build lamellar structure, so it is natural to nucleate Si near fcc.

They match what you think as the reason?

Yuta

Bernd
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Re: Directional solidification of Al-Si hypoeutectic alloy

Post by Bernd » Thu Nov 07, 2019 11:41 am

Hi Yuta,

I fully agree!

Bernd

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