Guten Morgen!
Dose selection of "database_*" options for the Concentration Data section in driving file lead automatically the diffusion calculation to solving complete Fick-Onsager equation ?
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original message from Sukeharu Nomoto
Today's question about diffusivity input
Re: Today's question about diffusivity input
Hi!
Well, again that's something that could do with a little bit more documentation...
Actually, for backward compatibility reasons, by default MICRESS only uses the diagonal terms of the diffusion matrix (looking back on it, it might not be the most obvious choice, but there you are...), so "database_*" only causes the diagonal term to be calculated from a database by TQ. To get the complete Fick-Onsager's equation you need to specify "multi".
This part is a bit convoluted, so it's perhaps better if I go over the whole thing:
- "diff" -> only diagonal term, user defined.
- "database_global" -> only one "global" diagonal term, from the database.
- "database_local" -> only diagonal term, from the database, with linear dependency on the local composition.
- "multi" -> full Fick-Onsager's equation with "global" coefficitents from the database.
- it is also possible to be more specific, and add (after "multi") a string made of "n", "d", "g" and "l" for each component. "n" meaning "no diffusion" (i.e.: do not take into account the influence of the gradient of this component on the flux), "d" for "user defined" diffusion coefficient (which should then be input), "g": "global" (i.e.: one only per phase and pair of components) diffusion coefficient from the database, and "l": diffusion coefficients taking (linearly) into account the influence of local composition.
The influence of local composition on the diffusion coefficients within one phase is taken into account via linear interpolation. This approach was suggested by John Agren and Lars Hoglund who considered it an appropriate estimate "in most cases".
Well... I think it sums it up, if I missed something or went too fast over it, please let me know.
Philippe
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original message from Philippe
Re: Today's question about diffusivity input
Thank you very much for your detailed information about controlling diffusion calculation. My another question of the difference between "database_local and "database_globa" was also resolved by this information.
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original message from Sukeharu Nomoto
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original message from Sukeharu Nomoto
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Re: Today's question about diffusivity input
Hi,
I have questions about treatment of diffusion coefficient in MICRESS.
1. How do we decide the mode which “database_” or “multi”? It depends on composition?
2. Which does MICRESS use a self-diffusion or inter-diffusion coefficient in the evolution equation of the concentration field?
I will appreciate your fruitful advice.
Regards,
Taka
I have questions about treatment of diffusion coefficient in MICRESS.
1. How do we decide the mode which “database_” or “multi”? It depends on composition?
2. Which does MICRESS use a self-diffusion or inter-diffusion coefficient in the evolution equation of the concentration field?
I will appreciate your fruitful advice.
Regards,
Taka
Re: Today's question about diffusivity input
Hi Taka,
I interpret your first question such that you want to know, under which circumstances it is better to use the "database_globel" or "database_local" keyword on one side, and the "multi" keyword on the other side.
The difference is that you use only the diagonal terms in case of the "database_" keyword and the complete matrix including off-diagonal terms on the other side. There are mainly three issues which may be important and help you to decide this question:
1.) accuracy vs. performance: The use of "multi" gives more exact results if the cross-terms of diffusion are not negligible. This depends on the alloy: it is known that cross diffuion of interstitial elements in steels or superalloys can be important, but also for substitutional elements the off-diagonal terms can be critical if the alloy is no "ideal mixture" but shows strong interactions between the elements.
The performance loss associated with "multi" consists of the extra diffusion terms which have to be solved and the access/update of the diffusion data from the database. The first contribution would automatically be negligible if the cross terms are small, because diffusion of this term would be rarely solved. The second contribution depends on the updating frequency and could hurt in some cases.
2.) availability of data: If no data on cross terms are available in the database, "database_" should be used. In case of the liquid phases in some mobility databases, it would be even wrong to use "multi" if no cross terms have been accessed!
3.) numerical stability: In rare cases, diffusion with off-diagonal terms may get instable, e.g. if the system is close to a miscibility gap. Often, this problem can be healed by increasing the frequency of updating diffusion coefficients, but sometimes it may be more appropriate to neglect one single critical off-diagonal term which causes the trouble (or replace it with a manually input).
The "multi" input also allows the explicite selection of diffusion terms. In a 5-component system e.g., the definition multi ngnn for component 2 would be equivalent to database_global, while multi nggn would additionally include the flux of component 2 due to the gradient of component 3. This flexible input allows you, if wished, to "manually" remove all the negligible terms from the diffusion matrix in order to reduce the performance loss due to updating of the diffusion coefficients.
Now to your second question: MICRESS calculates diffusion using a reduced diffusion matrix, i.e. by solving diffusion of all dissolved elements in the matrix. The flux of the matrix component is implicit. Iguess, this is what you mean with "inter-diffusion".
Bernd
I interpret your first question such that you want to know, under which circumstances it is better to use the "database_globel" or "database_local" keyword on one side, and the "multi" keyword on the other side.
The difference is that you use only the diagonal terms in case of the "database_" keyword and the complete matrix including off-diagonal terms on the other side. There are mainly three issues which may be important and help you to decide this question:
1.) accuracy vs. performance: The use of "multi" gives more exact results if the cross-terms of diffusion are not negligible. This depends on the alloy: it is known that cross diffuion of interstitial elements in steels or superalloys can be important, but also for substitutional elements the off-diagonal terms can be critical if the alloy is no "ideal mixture" but shows strong interactions between the elements.
The performance loss associated with "multi" consists of the extra diffusion terms which have to be solved and the access/update of the diffusion data from the database. The first contribution would automatically be negligible if the cross terms are small, because diffusion of this term would be rarely solved. The second contribution depends on the updating frequency and could hurt in some cases.
2.) availability of data: If no data on cross terms are available in the database, "database_" should be used. In case of the liquid phases in some mobility databases, it would be even wrong to use "multi" if no cross terms have been accessed!
3.) numerical stability: In rare cases, diffusion with off-diagonal terms may get instable, e.g. if the system is close to a miscibility gap. Often, this problem can be healed by increasing the frequency of updating diffusion coefficients, but sometimes it may be more appropriate to neglect one single critical off-diagonal term which causes the trouble (or replace it with a manually input).
The "multi" input also allows the explicite selection of diffusion terms. In a 5-component system e.g., the definition multi ngnn for component 2 would be equivalent to database_global, while multi nggn would additionally include the flux of component 2 due to the gradient of component 3. This flexible input allows you, if wished, to "manually" remove all the negligible terms from the diffusion matrix in order to reduce the performance loss due to updating of the diffusion coefficients.
Now to your second question: MICRESS calculates diffusion using a reduced diffusion matrix, i.e. by solving diffusion of all dissolved elements in the matrix. The flux of the matrix component is implicit. Iguess, this is what you mean with "inter-diffusion".
Bernd