Hi Atur,
I think the mechanism of fcc nucleating on the Al3X-precipitates can make sense, although I am not sure why you think that solute trapping plays an important role here.
It is clear that formation of the Al3X-particles takes time, so that its formation and growth should happen preferentially during the initial stage where the front is moving slowly. When the front gets faster, there is less time, but the temperature gradient gets smaller, so that nucleation can happen farther away from the front. So, the question whether at all and at which stage the 2-step mechanism for fcc nucleation can happen, is an interesting question which can perfectly be addressed with MICRESS.
Before discussing your simulation results, which seem to contradict experimental findings, it is important to check and refine your simulation setup to make sure that the results can be trusted. I found several issues which require attention:
1.) As physical base for your problem, the counterbalance of local undercooling and curvature is essential to decide whether nucleation is possible. For the first step, the nucleation of Al3X, this is ensured by using the seed-density model, which takes the radius of the hypothetical seed particles as basis for calculating the corresponding curvature undercooling. Here, the assumed seed density/radius distrubution function is typically unknown and requires some type of calibration or reasonable assumptions.
But the second step, namely the nucleation of fcc on Al3X, is again strongly dependent on the size of the respective Al3X-particle, which is not reflected by a simple "interface" nucleation type. What is important is to include the curvature of the substrate by using the "
substrate_curvature" keyword in seed type 2 of your nucleation input. Otherwise, the intrinsic physical mechanism of nucleation on particles is not included!
2.) A second important physical quantity in this counterbalance is the undercooling of the growing dendrite front. Apart from the 2D/3D-problematic (dendrite tip undercooling is much too high in 2D; also, the CET is much easier in 2D because equiaxed grains can much easier block a columnar front), there exists a strong issue with grid resolution: Ensuring diffusion-limited growth of an interface using mobility correction ("mob_corr") necessarily leads to an artificial excess kinetic undercooling, which is the bigger the coarser the grid resolution is. Thus, this effect systematically favors nucleation if resolution is too low. On top, in case the Al3X-particles are still unresolved when fcc nucleates, other types of numerical effects may retard fcc growth, also leading to a biased counterbalance of local undercooling and curvature. I think you will need to refine your numerical grid at least
by a factor of 2-3 to largely avoid such effects.
3.) Running your input file I found large regions of negative composition, which emerge during solidification and which are also already present in the initial microstructure which is read from the .rest-file. For finding them it is necessary to write out the phase compositions of all elements in all phases and examine them in DP_MICRESS (best way is setting value range to -0.001 - +0.001, see also
here). It seems that in this case there exist several reasons why this negative compositions emerge which you should tackle in order to avoid a loss of performance and accuracy:
a) the Al3X-phase is a nasty one, because there is an independent sublattice for Sc and Zr. This means that of the 6 elements Al, Mg, Sc, Zr, Fe, and Mn there are only 4 for which a composition can be defined independently. Although c(Al) (the matrix component) is already defined as dependent composition, c(Sc) and c(Zr) add up to exactly 25 at%, so that one of the two is also not independent. If MICRESS is executed without any special assumption for this phase, then an "independent_sublattice" model will be automatically invoked, which arbitrarily uses Sc (the first in the list) as dependent and Zr as independent element of this common sublattice and tries to approximate the interdependent redistribution of these two elements in the best way. Alternatively, the user can define the two elements as "stoichiometric", which often provides higher stability, but also cannot avoid the emergence of negative compositions up to a certain level. I this case, it turns out that using the "independent_sublattice"-model, redefined for using Zr as dependent composition, is more favorable:
#Numerical Parameters
#Concentration Solver
independent_sublattice 2 3 2
b) Penalty terms can be very efficient in avoiding negative concentrations stemming from extrapolation problems. They should be defined for the problematic element and phase, further restricted to a specific phase interface by giving a second phase number. In this case, Zr and Fe show problems in the liquid and fcc phase. Thus you should define
#Numerical Parameters
#Concentration Solver
penalty 1 2 4
penalty 0 2 3
penalty 1 2 3
c) it is dangerous to use diagonal terms of diffusion only, if the system is not dilute. The reason is that cross-terms can be strong and the diagonal values can be even negative! This happens in your case fore fcc and the elements Zr and Mn in certain temperature ranges and can lead to catastrophic diffusion behaviour if the negative coefficients persists long enough. Therefore you should either use the full diffusion matrix (which may exhibit further complications) or choose effective diagonal terms which can be obtained by
# Diffusion
diagonal_dilute z
d) As if your system was not complicated enough: In your case you also get some problems with the antitrapping current for Fe in the 0/1-interface. This is probably due to the strong segregation of this element and is not correctly caught-up by our safety algorithm (negotiating safety vs. efficiency). Therefore, you should either use "normal mob_corr" instead of "atc mob_corr" for Fe in the 0/1-interaction, or set a prefactor x (0<x<1) on the atc for this interface, e.g.
#Numerical Parameters
#Concentration Solver
atc_prefactor 0 1 0.5
4.) The time intervals for updating of diffusion data and linearisation data from database have been chosen unsufficiently in the input file you sent by PM, which may lead to inaccuracies, numerical problems, and even negative compositions. While the updating interval for diffusion coefficients is unnecessarily small (1.E-5 s would be sufficient), the updating interval for thermodynamic data should be smaller. Given the non-linear cooling behavior of L-PBF, it makes much sense to use the "automatic" mode which ties the updating interval to a local temperature change. For linearisation data, typically, a value of 1-5 K is reasonable, while for diffusion data 10-20K is usualy sufficient (an "automatic" mode for diffusion data will come with the next version
). Please note that if updating of linearisation data is defined for each interface separately, defining an additional global updating interval (in section "database") would lead to additional updating and should therefore be avoided.
I expect that using the recommendations given above should significantly change the result of your simulations, giving new impulses for their discussion. Please note that the suggested parameter settings are preliminary and may vary with the simulation conditions. You should always check for negative compositions and make sure that the simulation results are independent of grid resolution (as far as possible with reasonable calculation effort).
Finally, I would like to remark that the behavior which you want to model by nucleation of fcc on Al3X, could perhaps also be explained (and simulated) considering a fragmentation mechanism (B. Böttger, M. Apel, Phase-field simulation of the formation of new grains by fragmentation during melting of an ABD900 superalloy, IOP Conference Series: Materials Science and Engineering. Vol. 1281. No. 1. IOP Publishing, 2023
https://doi.org/10.1088/1757-899X/1281/1/012008[/i]).
Bernd
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