Why MC carbides sometimes are so difficult...

helpful tips or ideas for unconventional solutions
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Why MC carbides sometimes are so difficult...

Post by Bernd » Sun Dec 22, 2019 7:26 pm

Dear all,

When simulating intermetallic phase precipitation in steels or Ni-based alloys, MC carbides are often the precipitates which first form during solidification. Normally, they are not difficult to simulate if we follow the advice to set them fully stoichiometric. However, in cases of multicomponent alloys which contain several carbide forming elements, from a numerical point of view, they may represent one of the most difficult type of phases. The reasons are many-fold, and in order to navigate through the difficulties when addressing these phases with MICRESS it is helpful to know and understand the underlying problems. Four principal reasons can be identified:

1.) In Calphad, MC carbides usually are modeled as composition sets of the fcc phase FCC_A1 or FCC_L12. This means that an uncontrolled switching between the fcc and MC composition sets may occur. Furthermore, different MC-carbides can exist as different composition sets, and other phases like nitrides or borides also use the same phase description. In case of FCC_L12, moreover, there are two sublattices for the substitutional elements which can be ordered (different site fractions) or disordered (identical site fractions), so that ordered γ' can be described using the same phase model. The problems connected with composition sets and their solution have been described e.g. here.

2.) MC-carbides have a very low solubility for Ni and Fe. In MICRESS this means, given that these typically are the matrix components in steels and Ni-based alloys, respectively, that all other constituents of the MC phase should be defined as stoichiometric, because otherwise no redistribution could be calculated without having huge numerical errors.

3.) At the same time, typical carbide forming elements like Zr, Hf, Ta, Ti, W, V ,Nb often have a broad solubility range in MC, at least if more than one of them is present in the alloy. Given the necessity to define all the elements as stoichiometric as explained before, their content is fixed during redistribution, and the phase composition only can change due to updating of the thermodynamic linearisation data. This exhibits a fundametal problem not only because of the often limited update frequency, but also when using global relinearisation schemes (which are often indispensable in multicomponent systems for sake of calculation performance): Global relinearisation forces identical composition of the carbides in all regions where the linearisation data apply, even if the local mixture composition is varying (e.g. due to local segregation). A solution can be to use a sufficiently low globality like "globalF" or "globalGF" for linearisation data in order to allow at least every carbide particle to develop its own composition.
A further numerical issue is caused by this unfortunate combination of stoichiometric redistribution and high solubility range: If the composition changes considerably due to updating linearisation data (be it because of too seldom relinearisation, or due to numerical problems), suddenly high amounts of these elements are released into the matrix phase, leading to extreme local phase compositions which often are negative or above 100%, potentially leading to additional problems.

4.) In addition to the problems described under point 3, MC carbides often change composition with temperature, so that e.g. during solidification of Ni-base alloys they may start forming as TiC and then transform to TaC or HfC at lower temperatures, without undergoing explicit phase transformations. Given that is is difficult to have sufficiently high update rates in MICRESS simulations, especially large particles with large local phase fractions may behave unrealistically.

Unfortunately, we still do not have a comprehensive solution of these problems of multicomponent MC carbides. If problems with this phase occur, there are several possibilities how address them:

- Although not necessary in most cases, it always is better to control the major constituents when creating .GES5-files (see here).

- If different composition sets are relevant for a MICRESS simulation, always a separate phase should be defined in MICRESS for each of them. It may even be helpful to define separate phases if the MC carbides just form under different conditions in different places (and with different compositions).

- There are several commands which can be used to prevent switching of composition to composition ranges of other composition sets: "limits", "penalty", "ordered"/"disordered", "criterion_higher"/"criterion_lower"

- The choice of globality of relinearisation ("local", "global", "globalF", "globalG", "globalGF") can be of utmost importance, although it is difficult to say which choice is the best. While higher locality should in principle be better, the connected higher number of individual quasi-equilibrium calculations as well as local concentration deviations can also increase the risk of numerical problems

- Theoretically, it is also possible to chose one of the carbide forming elements as matrix component. Then, the other carbide formers with high solubility range need not be defined as stoichiometric which would in principle solve the problem. However, this can only be done if this alternative matrix element is abundantly present in the matrix phase in the whole temperature range, and also in all other phases.


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