Modeling of Gamma-Alpha transformation

[deepumaj1]

Hi,
I was trying to model a gamma-alpha transformation, starting from the standard micress example for the same. The simulation runs properly, but the following message shows up in the screen output(*_scr.txt) at the beginning of the simulation:

Intermediate output for t = 1.0000 s
CPU-time: 319 s
Current phase-field solver time step = 6.27E-02 s
Average conc. of comp. 1 = 0.1800000, Variation = +0.0000000 wt%
Average conc. of comp. 2 = 0.7500000, Variation = +0.0000000 wt%
Average conc. of comp. 3 = 0.3500000, Variation = -0.0000000 wt%
Average conc. of comp. 4 = 0.5000000, Variation = +0.0000000 wt%
Average conc. of comp. 5 = 0.4000000, Variation = -0.0000000 wt%
Temperature at the bottom = 1143.1 K
Temperature gradient = 0.00000 K/cm
Forcing automatic start values
Automatic start values will be set


--> Force automatic start values
# Minimum undercooling for stable growth, seed type 1: 63.67842 K [r=0.1000000 mic.]
# Minimum undercooling for stable growth, seed type 2: 63.67842 K [r=0.1000000 mic.]
# Minimum undercooling for stable growth, seed type 3: 63.67842 K [r=0.1000000 mic.]
complete relinearisation!

Questions:

1. What is this parameter 'Minimum undercooling for stable growth'. How is it related to '# min. undercooling [K] (>0)' that we give in the input file?
2. Why does it take these automatic start values?
3. Does the 'automatic value' decrease the accuracy of the simulation?

Thanks,
Deepu

[Bernd]

Hi Deepu,

thank you for your questions.

1. The output 'Minimum undercooling for stable growth' is written when nucleation for a seed type is checked for the first time. The value is calculated from the interface energy between the new phase and the matrix phase, the corresponding ΔS value and a critical radius which corresponds to one grid cell. The meaning of this value is the numerical undercooling which is needed to overcome the stage of a small grain. As you may know, there is a "small grain" model in MICRESS which helps new nuclei to overcome the single-grid stage and to get the size where the normal phase-field equation can take over. If the "stabilisation" model is used, the grain is stabilized until it reaches a fraction of 1 in the central cell. At this stage, stabilisation ends, and the grain is subject to a curvature undercooling which has a value close to the 'Minimum undercooling for stable growth' value.
For practice, the value means that the '# min. undercooling [K] (>0)' value should be higher than 'Minimum undercooling for stable growth' value to assure that growth is not hindered by the numerical grid. This is a quite good criterion for nucleation in the bulk, for nucleation at interfaces or triple junctions growth may be possible also with somewhat smaller undercoolings. One possibility to work around this numerical restriction is to use the "analytical curvature" model.

2,3. This means that for initialisation of the Thermo-Calc workspace, automatic start values are used for the phase compositions. MICRESS uses an extra workspace for each phase interaction. As you may know, Thermo-Calc always uses start compositions from the previous calculation. So, for the first one, an initialisation procedure is necessary. This has nothing to do with the accuracy of the calculations.

Bernd

[deepumaj1]

Hi Bernd,
Thank you for the explanation.

I had been doing trials with different grid sizes. When I deceased the grid size(increase the grid resolution), the value of 'Minimum undercooling for stable growth' kept on increasing. Now I understand the reason.

But I have a problem. In my simulation, I have to do holding at 790 degrees and according to the experimental CCT, the phase transformation starts only at 800 degrees. In Micress scr file, I see that the seeds are set around 800 degrees. Now the problem is that the 'Minimum undercooling for stable growth' is 64 degree(at the current grid resolution) and if I set '# min. undercooling [K] (>0)' greater than this value, I'm not getting nucleation at all. I would like to achieve the following in the simulation:
1. The nucleation has to start at 800 degrees.
2. At a cooling rate of 4 degrees per minute, the volume fraction of alpha phase at 790 degrees should be at least 7%.
3. Nucleation should happen at all three sites, in the order: triple junction first and bulk at last. (I hope giving different values of '# min. undercooling [K] (>0)' for different seed types helps here. But, how much is the difference in temperature that I can give(a typical value) to achieve this aim?)
4. The number of nuclei at each site has to be controlled. For example, out of all the triple junctions, I want nucleation at only 10 sites. The problem is, if I define '# maximum number of new nuclei 1?' as 10, I don't really get 10 stable nuclei in my simulation, with the current conditions.

Please suggest, how and what parameters have to be tuned to achieve the above. Will 'analytical curvature' option help(I'm currently using 'stabilisation')?

Thanks and Regards,
Deepu

[Bernd]

Dear Deepu,

The effect you describe is typical if working at high resolution. The problem is that the critical seed radius which corresponds to the experimentally observed nucleation undercooling is bigger than one grid cell.

1. Using the "analytical curvature" model allows you to define an initial grain size of 0 ("small grain"), but at the same time to specify a critical radius which may be bigger than the grid size. At the small grain stage (fraction of central cell >1) the curvature undercooling is calculated analytically by assuming a virtual seed particle with critical radius and a layer of the nucleating phase on top of it, in agreement with the real phase fraction. The radius of this assembly (in 3D) defines the local curvature. After reaching full size (and this is the important detail for you), still all local curvatures which are higher than the critical radius are truncated, which helps the particle grow further until reaching the critical radius.
You can reach your goal by chosing the critical radius such that it corresponds to an undercooling which is reached at 800°C.

2. This is a question of growth kinetics and nucleation sites. I would propose to stick to the nple model like it is done in the standard MICRESS example.

3. If you work at constant temperature, different values of critical undercooling for different nucleation sites do not give the desired effect because they will either appear instantaneously or never. The solution is to switch to a frequency/probability based distinction of site preferences (see 4.)

4. Instead of defining a maximum number of nuclei you should chose a big shield distance and short shield time or use the "nucleation distance" to allow only 1 or few seeds per checking time. Then, by selecting a proper checking interval, you can define a nucleation rate which can be chosen differently for the different nucleation sites. Take care that the shield time is smaller than the checking interval, otherwise your nucleation rate will be affected and interdepend between the different sites. (If you wish to be more tricky, you could even define different "shield groups" for the different sites to prevent shielding between them).

Bernd

[deepumaj1]

Dear Bernd,
Thanks for the suggestions.

I have a doubt in point number 4 you told. Does the 'shield distance' and 'shield time' of one seed type affect the other?

Deepu

[Bernd]

Dear Deepu,

By default, they affect each other if the same phase is nucleated (which physically makes sense). You can change this default behaviour by defining a "shield group" for each shield type: Same number means they affect each other.

Bernd

[deepumaj1]

Dear Bernd,
Thanks for the reply. If I understand you correctly, the nuclei of same phase should be shielded from each other. But in my simulation, I'm getting twins as shown in the attached image(The shield distance for all seed types is 5 micrometer). Initially I thought it was a shielding problem and that two nuclei types come very close to each other. But now I understand it is not the reason. What could be the reason for this behaviour?

I want to also address a couple of other problems.
1. After a certain number of time steps, the nuclei seem to lose its energy for growth and the boundary shape becomes 'loose'. Is this normal? Is is a sign that the nuclei has obtained 'stable' state and there is no longer a driving force for further growth, or is it a problem with the numerical parameters?
2. I have labelled 'metastable seeds' in the image attached. I wanted to confirm whether they are metastable seed itself and whether I would be able to remove them with the 'kill metastable' option.

I'm sending the input file, the phase output and the driving force output by email. Please use this to further analyse the problem.

Deepu

[Bernd]

Dear Deepu,

I think, the reason why you get nuclei close together is that the shield expires after 50 s (shield time), and your simulation time is much longer that 50 s. If you want to prevent nucleation close to previous nuclei completely you should increase the shield time.

Your other questions:

1. I don't know what you mean with "loose". To detect numerical problems in an interface, the .phas output is not very helpful. The best one is the .driv output - unfortunately I cannot open it without .geoF file...

2. I think the undercooling of these seeds is not high enough to overcome the 'Minimum undercooling for stable growth'. What you can do is either to lower temperature, to increase grid spacing, or to use the analytical_curvature model. With the "kill_metastable" option, they would probably disappear after a while (after the shield time + some time to dissolve).

Bernd

[Bernd]

Dear Deepu,

I finally did a simulation run with your input files which you sent me by e-mail. I did it without parallelization, and it took quite long .

In principle the results confirmed what I have written above. There is one contribution which I did not consider in first place which is the nple redistribution mode. There are two major consequences:
1. There is an additional driving force threshold for overrunning the solutal pile up of the substitutional elements which adds to the 'Minimum undercooling for stable growth'
2. The simulation (on the time scale of interstitial diffusion) does not run to equilibrium but only to the point where the driving force is too low to overcome the additional threshold mentioned in 1. I think, this explains why 'the nuclei seem to lose its energy for growth'.

Apart from that, during the simulation run, a lot of CPU time was simply lost by the high diffusivity of C in bcc. Given the fact that this diffusivity is more than 100 times higher compared to fcc, the C concentration is practically flat in bcc. By using restricted infinite diffusion (i.e. infinite diffusion inside each grain, keyword 'diagonal I') for C in bcc, the simulation time in serial mode is reduced drastically.
Another source of performance loss is the diffusion of C in fcc before first nucleation of bcc. You could use a trick (infinite_limit, available in terse input mode for diffusion coefficients) to switch from infinite diffusion to finite diffusion at a temperature just before bcc nucleation.


Bernd

[deepumaj1]

Dear Bernd,

Thank you so much for trying out the simulation . I have tried adjusting the shield parameters and now I'm not getting the close nucleation problem. I have some doubts:

1. How do we identify that the simulation hasn't reached the equilibrium? Is it by analysing the .driv file or with the help of some other data?
2. Is there a problem, if the simulation doesn't reach equilibrium?
3. The ferrite volume fraction in this simulation is far different from what we get in experiments. I tried changing the mobility and nucleation conditions. The problem I'm having is that the volume fraction in the simulation, instead of gradually increasing, shoots up very quickly to high values, during holding . I tried lowering the mobility(only the 1/2 mobility ), but when I do so, the volume fraction at higher temperature is going down. Is there any other values I can adjust, to tune my volume fraction to experiments? Should I go for adjusting the diffusion data and try out some options under this?

Deepu