How to determine the stoichiometric components

issues about thermodynamics and their coupling to MICRESS
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Posts: 1267
Joined: Mon Jun 23, 2008 9:29 pm

How to determine the stoichiometric components

Post by Bernd » Wed Oct 13, 2010 7:07 pm

Hi all,

I am more and more frequently asked by MICRESS users how to determine the stoichiometric components. Therefore I want to give something like a guide which relies on my personal experiences.

For such components which are really stoichiometric, i.e. which do not have any solubilty range, MICRESS does it automatically from Version 5.5 on, so the user needs not take care.

For ionic compounds, intermetallic phases, carbides, borides etc. I usually prefer to set them stoichiometric for all components, if there is no strong reason against. In most of those cases, the matrix element of the alloy is not identical to the matrix element in these phases, so their slopes are mostly not very meaningful and would probably just lead to numerical issues (e.g. MC-carbides in steels).

Much more complicated is the case when the stoichiometric condition has to be used to cure the consequences of "apparent demixing": As MICRESS uses a multi-binary extrapolation scheme for the isothermal redistribution between the phases, slopes with opposite sign for any of the elements in a phase interaction (more exactly: opposite sign of the product of m and the corresponding deltaS) may lead to demixing artefacts as if it were a binary alloy with miscibility gap. The only remedy available for that problem by now is to set this component stoichiometric in one of the two phases (preferentially the one with the higher absolute slope value) and to compensate the suboptimal redistribution by using more frequent relinearisation or a special redistribution scheme.

A typical problem for the latter case is solidification of gamma-prime forming Ni-base superalloys like CMSX-4. In principle it is easy to diagnose the situation of "apparent demixing": The latest MICRESS version gives a warning on screen if it occurs for any cell in any interface. Furthermore, one can check the linearisation parameter in the .TabLin output which is written for each output time step. But the situation is more weired due to the following reasons:

1.) It is not allowed to set the same component stoichiometric in two phases which interact. If e.g. W shows apparent demixing in both the liquid-gamma and the liquid-gamma_prime interface, one gets stuck! (I am working on a solution which is still not available...)

2.) Changing the stoichiometric condition of one element may change completely the behavior of the other elements!

3.) Apparent demixing may appear only in parts of a specific interface, and it may appear or disappear during the course of simulation. The .TabLin output shows only one linearisation parameter set for one of the interface cells of a complete interface, so this output does not necessarily show all problems!

4.) Opposite signs in the slopes of an element do not necessarily lead to numerical problems, as there is an internal strategy in the code which may prevent them.

5.) Once a simulation gets unstable, the linearisation outputs or warnings are no longer interpretable!

Therefore, the strategy for a complex simulation like the solidification of CMSX-4 should be the following:

- Reduce the size of the simulation domain as much as possible! Otherwise, the following procedure may take years...

- Start the first simulation run without setting any stoichiometric conditions

- Add them one by one in the order in which apparent demixing occurs

- Never use a stoichiometric condition for the liquid phase, because the high diffusivity will lead to serious problems!

- If necessary, go back and remove stoichiometric conditions, if you are not sure whether they are really needed.

- Make sure that instabilities are not caused by other numerical parameters like interface mobility etc.

- If you end up in a situation where it seems you are forced to use two stoichiometric conditions for the same element in two interactiong phases, go back and try other combinations - the problem may vanish after changing a condition for another element.

- Make sure that the apparent demixing is not caused by a strongly metastable situation, which can be identified by high values of the driving force.

- Make sure that the system does not exhibit a real miscibility gap - then the simulation cannot be performed at the given composition/temperature!

- Use exit strategies like excluding elements, phase interactions or try to use global linearisation which may reduce the probability or the negative consequences of apparent demixing (e.g. for interactions with gamma_prime in CMSX-4).

- Don't be frustrated, because this is really a difficult problem...

Hopefully, theses suggestions are helpful for you! Please give feedback about your experiences with this weired problem!


Posts: 1267
Joined: Mon Jun 23, 2008 9:29 pm

Re: How to determine the stoichiometric components

Post by Bernd » Fri Oct 15, 2010 4:47 pm

I forgot to mention that metastable situations may not only be caused by low interface mobilities but also if a phase is not allowed to nucleate. If e.g. a superalloy contains Carbon, and the relevant Carbides are not included in the simulation, strange behaviour including lots of "demixing" phenomena may be the consequence!


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