Liquid diffusivity from database - pros and cons

dendritic solidification, eutectics, peritectics,....
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Liquid diffusivity from database - pros and cons

Post by Bernd » Thu Oct 24, 2019 1:01 pm

Hi all,

Lately I have been asked several times about whether in solidification simulations one should use diffusion data for the liquid phase from database or not. More and more commercial mobility databases now contain meaningful data for this phase, like e.g. MOBNI5 or MOBFE4.

The most important influence of the diffusivity of the liquid phase is on the length scale of the solidification microstructure: Increasing diffusivity will increase the value of the primary and secondary arm spacing of dendrites, and also will have effects on the size of cells or on lamellar spacing in eutectic systems, etc. However, the interface energy or stiffness is another typically unknown quantity which has similar effects. Thus, in practice, one needs to use calibration anyway, and the question is whether, in this light, using precise diffusion coefficients is helpful anyway…

Specifically, our application example A006_CMSX4_dri has been source for this discussion, as we decided still to use identical values for all elements, although more detailed information is available in MOBNI4/5. While in older versions the database just revealed an identical estimated diffusion coefficient of 1.E-5 cm2/s for all elements, now when reading diffusivities with MICRESS it appears that detailed information is available for each element including off-diagonal terms and temperature dependency. However, a closer look reveals that the mobility is still estimated to be identical for groups of elements (Cr, Co, Ta, Al, Ti, Hf/W, Mo, Re), i.e. no element-specific measurements have been used. However, the thermodynamic factor matrix is applied, so that they all look different.

Another important issue is that in high alloyed systems like CMSX-4, or generally in Ni-based superalloys, the off-diagonal terms of the diffusion matrix are strong, so that it is not allowed to use diagonal terms only. The diagonal terms then also cannot be interpreted in the sense that there are faster and slower elements!

In the following, I want to summarize arguments for or against using diffusion data from database:

- Computational performance: The main issue here is less the computational effort for retrieving thediffusion data from database, but the fact that having a range of different diffusivities in the liquid phase leads to smaller numerical time-steps for the fastest elements, which may not be the limiting elements for interface movement. In our case of CMSX-4, there is a factor of ~7 between the highest and lowest diagonal term, and off-diagonal term may add to the performance loss!
- In case there is only one primary phase like for CMSX-4, for calculating the interface kinetics (here of liquid/γ-interface) the flux equations can be diagonalized, i.e. the diffusion matrix can be transformed to a diagonal matrix without any loss of information. Furthermore, a reduction to a pseudo-binary system is possible, leading to a single effective diffusion coefficient which has the same growth restriction factor as the multicomponent system. Thus, if calibration of the interface energy is needed anyway (see above), there is no argument why using different diffusion coefficients for the different elements should be more exact. And when the γ' phase appears at lower temperature, solidification is already close to Scheil conditions, and diffusivities do not matter anymore. In fact, a further performance gain is therefore possible by artificially reducing the diffusion coefficient at lower temperatures, like it has been done in the application example A006_CMSX4_dri.

- Using diffusion data from database assures that one always is using the most complete information available
- In case of multiple primary phases like in eutectic systems, using different diffusivities for different elements may have a strong impact on morphology, as the relative kinetics of those phases may be different. In such cases, the diffusion matrix cannot be reduced. Information from the thermodynamic factor matrix may be helpful, even if the mobility of each element is still a crude estimation.

You are welcome to add you knowledge and experiences to this summary!


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