Dear Bernd,
First of all, apologies for the late reply. I come back to this project from time to time, so there can be quite a gap between my responses. Regarding homogeneous nucleation, I agree that the required undercooling should be high. However, I think such undercooling can theoretically be reached at the bottom of the melt pool. Based on the experimental data I have analysed across a broad range of materials, I believe that homogeneous nucleation of Al₃X from the liquid should be considered a plausible mechanism. Of course, I cannot exclude the possibility of nucleation on impurities, as has been reported for some alloy systems, or on surviving Al₃X particles. However, I do not think either mechanism is likely to be dominant. My reasoning is that the experimentally observed thickness of the fine-grained region varies considerably between different processing conditions. If surviving Al3X particles were the dominant mechanism, I would expect the thickness of this region to be governed primarily by the temperature range between the liquidus and solidus of Al3X. However, our process simulations suggest that the variation in this thickness is not particularly large, in contrast to the significant differences observed experimentally.
For this reason, I think it would be worth assuming homogeneous nucleation of Al3X or, more generally, the formation of nanoscale nucleation sites and systematically investigating the effect of undercooling on their stabilisation and subsequent grain refinement. My idea is to investigate five or six scenarios with progressively changing undercooling requirements for Al3X formation. For each scenario, I would then evaluate the thickness. However, I have already tried this approach, using the seed_undercooling option in combination with analytical_curvature and stabilisation, but I have not managed to obtain the trends I was looking for. The main difficulty is that seeds seem to form almost everywhere unless I reduce their maximum number when using analytical_curvature so I see fully equiaxed grains everywhere. For stabilisation option, Columnar grains start to form after some moment (e.g., columnar front overcomes seeds before fcc nucleates) but grain refinement is observed again at the top of the domain since seeds again forms everywhere.
In particular, I am not entirely sure how MICRESS determines whether a seed is activated at a given location and whether it subsequently becomes stabilised based on the local driving force and undercooling. With my current settings, the artificially stabilised seeds also cause grain refinement near the top of the simulation domain, which is physically inconsistent with the behaviour I am trying to reproduce. Given this, I would really appreciate your advice on how you would approach this problem. If your objective were to systematically investigate the influence of the minimum undercooling required for Al3X formation on grain refinement, would you follow a similar strategy, or would you recommend a different approach? In particular, are there specific settings or adjustments to the nucleation and stabilisation models that you would suggest to ensure that seeds are only activated and stabilised under the appropriate local conditions? I have mailed you the input files.
Thanks again for your time and help.
Best regards,
Ahmet