Dear Bernd,

I am working with additively manufactured (LPBF) MPEAs trying to simulate solidification microstructure under different thermal conditions in order to investigate microstructure evolution. Yet I have a quite big limitation; I don't have a mobility database for my alloy system. I assume even under fast solidification velocities, not having a proper input would deviate segregations and thus the morphology of solidified state (e.g. wrong eutectic morphologies and etc.)

I am mainly working with two different compositions, one solidifies in single phase FCC and other solidifies in FCC-B2 phases. I coupled my custom thermodynamic database with one of the MOBFE databases to use diffusion data for FCC. Besides, I thought that I can enter the diffusion constants for diffusion of individual elements in liquid (in the order of 10E-5) manually by using diagonal d, and also activation energies and pre-exponential factors for diffusion in B2-NiAl phase, so that it can calculate temperature dependent diffusion coefficients. In my case, however, the B2 phase is non stoichiometric NiAl (there is also solubility of other elements), but the activation energies and pre-exponential factors I entered is for diffusion in Ni48Al52 (stoichiometric) for 900 to 1200°C range , since it was the best I can find from literature;

# How shall diffusion of component CO in phase LIQUID be solved?

diagonal d

# Diff.-coefficient:

# Prefactor? (real) [cm**2/s]

2.00000E-05

# Activation energy? (real) [J/mol]

0.0000

# How shall diffusion of component CO in phase A1_FCC be solved?

multi ggg

# How shall diffusion of component CO in phase B2_BCC be solved?

diagonal d

# Diff.-coefficient:

# Prefactor? (real) [cm**2/s]

3500

# Activation energy? (real) [J/mol]

346610

# How shall diffusion of component NI in phase LIQUID be solved?

diagonal d

# Diff.-coefficient:

# Prefactor? (real) [cm**2/s]

2.0000E-05

# Activation energy? (real) [J/mol]

0.0000

# How shall diffusion of component NI in phase A1_FCC be solved?

multi ggg

# How shall diffusion of component NI in phase B2_BCC be solved?

diagonal d

# Diff.-coefficient:

# Prefactor? (real) [cm**2/s]

1400

# Activation energy? (real) [J/mol]

346630

# How shall diffusion of component AL in phase LIQUID be solved?

diagonal d

# Diff.-coefficient:

# Prefactor? (real) [cm**2/s]

2.00000E-05

# Activation energy? (real) [J/mol]

0.0000

# How shall diffusion of component AL in phase A1_FCC be solved?

multi ggg

# How shall diffusion of component AL in phase B2_BCC be solved?

diagonal d

# Diff.-coefficient:

# Prefactor? (real) [cm**2/s]

2300

# Activation energy? (real) [J/mol]

339710

# How shall the interval for updating diffusion coefficients

# data be set?

# Options: constant from_file

constant

# Interval for updating diffusion coefficients data? [s]

0.1

# Concentration solver

# --------------------

# Factor for diffusion time stepping? (0.0 < factor < 1.0)

0.95000

#

# List of phases and components which are stoichiometric:

# phase and component(s) numbers

# List of concentration limits (at%):

# <limits>, phase number and component number

# List of penalty conditions:

# <penalty>, phase 1, phase2, component number

# List for ternary extrapolation (2 elements + main comp.):

# <interaction>, component 1, component 2

# Switches: <stoich_enhanced_{on|off}> <solubility_{on|off}>

# List of relative criteria on phase composition

# <criterion_higher | criterion_lower>, phase No 1, phase No 2, component No

# List of sublattice order conditions:

# <ordered|disordered>, phase , sublattice 1, sublattice 2

# List of source changes for diffusion data

# <switch_diff_data>, Phase-No., reference phase

# Switch: Add composition sets for calculation of diffusion/volume/enthalpy data

# <diff_comp_sets | vol_comp_sets | enth_comp_sets>, phase list

# End with 'no_more_stoichio' or 'no_stoichio'

diagonal

no_stoichio

My question is, do you think this approach can somehow work? Do you have any recommendations on how to do a workaround?

Regards,

## Mixed input (manual, global) for diffusion data

### Re: Mixed input (manual, global) for diffusion data

Dear Atur,

Technically, this type of input should work. However, with MPEA's we typically think of "sluggish" diffusion, which should apply to all phases, and we cannot assume conventional mobility databases to predict correct diffusion coefficients.

Anyway, with fast cooling in LPBF, solid diffusion should not play any role during solidification. So, you need to focus on diffusion in liquid only, and eventually it will be necessary to calibrate the liquid diffusion coefficients (or interface energy, if you do not know it exactly) with respect to experiments to obtain correct morphologies.

I think you can assume all liquid diffusion coefficients to be equal. Alternatively, you could try to define some constant factors between them based on experimental data (or mobility databases).

Bernd

Technically, this type of input should work. However, with MPEA's we typically think of "sluggish" diffusion, which should apply to all phases, and we cannot assume conventional mobility databases to predict correct diffusion coefficients.

Anyway, with fast cooling in LPBF, solid diffusion should not play any role during solidification. So, you need to focus on diffusion in liquid only, and eventually it will be necessary to calibrate the liquid diffusion coefficients (or interface energy, if you do not know it exactly) with respect to experiments to obtain correct morphologies.

I think you can assume all liquid diffusion coefficients to be equal. Alternatively, you could try to define some constant factors between them based on experimental data (or mobility databases).

Bernd

### Re: Mixed input (manual, global) for diffusion data

Dear Bernd,

Thank you for your answer. I would also like to ask you a question about "Start compositions and limits in quasi equilibrium". I can see that when I couple a mobility databse, compositions differs significantly than each other, even though the initial compositions are set as I defined in my drive file. Does this mean that my composition limits and stoichiometry is set according to diffusion data of steels (I used mobfe5 for diffusion input)? If yes, does that mean I need to manually define the stoichiometry/limits of the phases in concentration solver? I am confused since as far as I understand, the solubility limit for each element in each phase is 0 to 100 percent, which means these limits should efect so much (if the brackets means solubility limits). In addition, I dont get any warning regarding the limits.

I also have a short question regarding the initial grains. I would like to predict the PDAS value from my simulations for different thermal conditions.

I read some of the topics but I could not find a clear answer or at least I did not understand. As mentioned in one of the topics, I would also like to simulate/assume (epitaxial) growth in fastest growth direction (Z direction) during my simulations. How can I assign a orientation to the initial grain so that it will grow faster in Z direction without making me wait until dendrites form? Can I do it from the option called "rotation angle"? I added lots of small random round grains as a starter (in order to introduce high number of interfaces) but I am not sure whether if this makes sense. When I start with a flat rectangle grain, I see kind of a flat front for some time and then derdites froms. I would be happy to hear your comments!

Start Composition and Limits for quasi-equilibrium (for coupling with mobility database for liquid and FCC phase)

--------------------------------------------------

FE in LIQUID: 97.0773 at% (>0 - 100.000at% )

CO in LIQUID: 0.971059 at% (>0 - 100.000at% )

NI in LIQUID: 0.990099 at% (>0 - 100.000at% )

AL in LIQUID: 0.961538 at% (>0 - 100.000at% )

FE in FCC_A1: 34.1017 at% (>0 - 100.000at% )

CO in FCC_A1: 0.317965 at% (>0 - 100.000at% )

NI in FCC_A1: 36.7250 at% (>0 - 100.000at% )

AL in FCC_A1: 28.8553 at% (>0 - 100.000at% )

FE in B2_BCC: 11.8638 at% (>0 - 100.000at% )

CO in B2_BCC: 11.1066 at% (>0 - 100.000at% )

NI in B2_BCC: 66.6801 at% (>0 - 100.000at% )

AL in B2_BCC: 10.3495 at% (>0 - 100.000at% )

Start Composition and Limits for quasi-equilibrium (no-coupling with mobility database at all)

--------------------------------------------------

FE in LIQUID: 25.1220 at% (>0 - 100.000at% )

CO in LIQUID: 24.8780 at% (>0 - 100.000at% )

NI in LIQUID: 25.3659 at% (>0 - 100.000at% )

AL in LIQUID: 24.6341 at% (>0 - 100.000at% )

FE in FCC_A1: 25.4545 at% (>0 - 100.000at% )

CO in FCC_A1: 24.5455 at% (>0 - 100.000at% )

NI in FCC_A1: 26.3636 at% (>0 - 100.000at% )

AL in FCC_A1: 23.6364 at% (>0 - 100.000at% )

FE in B2_BCC: 11.7755 at% (>0 - 100.000at% )

CO in B2_BCC: 11.4531 at% (>0 - 100.000at% )

NI in B2_BCC: 65.6406 at% (>0 - 100.000at% )

AL in B2_BCC: 11.1308 at% (>0 - 100.000at% )

# Concentration solver (common in both)

# --------------------

# Factor for diffusion time stepping? (0.0 < factor < 1.0)

0.95000

#

# List of phases and components which are stoichiometric:

# phase and component(s) numbers

# List of concentration limits (at%):

# <limits>, phase number and component number

# List of penalty conditions:

# <penalty>, phase 1, phase2, component number

# List for ternary extrapolation (2 elements + main comp.):

# <interaction>, component 1, component 2

# Switches: <stoich_enhanced_{on|off}> <solubility_{on|off}>

# List of relative criteria on phase composition

# <criterion_higher | criterion_lower>, phase No 1, phase No 2, component No

# List of sublattice order conditions:

# <ordered|disordered>, phase , sublattice 1, sublattice 2

# List of source changes for diffusion data

# <switch_diff_data>, Phase-No., reference phase

# Switch: Add composition sets for calculation of diffusion/volume/enthalpy data

# <diff_comp_sets | vol_comp_sets | enth_comp_sets>, phase list

# End with 'no_more_stoichio' or 'no_stoichio'

diagonal

no_stoichio

Regards,

Ahmet

Thank you for your answer. I would also like to ask you a question about "Start compositions and limits in quasi equilibrium". I can see that when I couple a mobility databse, compositions differs significantly than each other, even though the initial compositions are set as I defined in my drive file. Does this mean that my composition limits and stoichiometry is set according to diffusion data of steels (I used mobfe5 for diffusion input)? If yes, does that mean I need to manually define the stoichiometry/limits of the phases in concentration solver? I am confused since as far as I understand, the solubility limit for each element in each phase is 0 to 100 percent, which means these limits should efect so much (if the brackets means solubility limits). In addition, I dont get any warning regarding the limits.

I also have a short question regarding the initial grains. I would like to predict the PDAS value from my simulations for different thermal conditions.

I read some of the topics but I could not find a clear answer or at least I did not understand. As mentioned in one of the topics, I would also like to simulate/assume (epitaxial) growth in fastest growth direction (Z direction) during my simulations. How can I assign a orientation to the initial grain so that it will grow faster in Z direction without making me wait until dendrites form? Can I do it from the option called "rotation angle"? I added lots of small random round grains as a starter (in order to introduce high number of interfaces) but I am not sure whether if this makes sense. When I start with a flat rectangle grain, I see kind of a flat front for some time and then derdites froms. I would be happy to hear your comments!

Start Composition and Limits for quasi-equilibrium (for coupling with mobility database for liquid and FCC phase)

--------------------------------------------------

FE in LIQUID: 97.0773 at% (>0 - 100.000at% )

CO in LIQUID: 0.971059 at% (>0 - 100.000at% )

NI in LIQUID: 0.990099 at% (>0 - 100.000at% )

AL in LIQUID: 0.961538 at% (>0 - 100.000at% )

FE in FCC_A1: 34.1017 at% (>0 - 100.000at% )

CO in FCC_A1: 0.317965 at% (>0 - 100.000at% )

NI in FCC_A1: 36.7250 at% (>0 - 100.000at% )

AL in FCC_A1: 28.8553 at% (>0 - 100.000at% )

FE in B2_BCC: 11.8638 at% (>0 - 100.000at% )

CO in B2_BCC: 11.1066 at% (>0 - 100.000at% )

NI in B2_BCC: 66.6801 at% (>0 - 100.000at% )

AL in B2_BCC: 10.3495 at% (>0 - 100.000at% )

Start Composition and Limits for quasi-equilibrium (no-coupling with mobility database at all)

--------------------------------------------------

FE in LIQUID: 25.1220 at% (>0 - 100.000at% )

CO in LIQUID: 24.8780 at% (>0 - 100.000at% )

NI in LIQUID: 25.3659 at% (>0 - 100.000at% )

AL in LIQUID: 24.6341 at% (>0 - 100.000at% )

FE in FCC_A1: 25.4545 at% (>0 - 100.000at% )

CO in FCC_A1: 24.5455 at% (>0 - 100.000at% )

NI in FCC_A1: 26.3636 at% (>0 - 100.000at% )

AL in FCC_A1: 23.6364 at% (>0 - 100.000at% )

FE in B2_BCC: 11.7755 at% (>0 - 100.000at% )

CO in B2_BCC: 11.4531 at% (>0 - 100.000at% )

NI in B2_BCC: 65.6406 at% (>0 - 100.000at% )

AL in B2_BCC: 11.1308 at% (>0 - 100.000at% )

# Concentration solver (common in both)

# --------------------

# Factor for diffusion time stepping? (0.0 < factor < 1.0)

0.95000

#

# List of phases and components which are stoichiometric:

# phase and component(s) numbers

# List of concentration limits (at%):

# <limits>, phase number and component number

# List of penalty conditions:

# <penalty>, phase 1, phase2, component number

# List for ternary extrapolation (2 elements + main comp.):

# <interaction>, component 1, component 2

# Switches: <stoich_enhanced_{on|off}> <solubility_{on|off}>

# List of relative criteria on phase composition

# <criterion_higher | criterion_lower>, phase No 1, phase No 2, component No

# List of sublattice order conditions:

# <ordered|disordered>, phase , sublattice 1, sublattice 2

# List of source changes for diffusion data

# <switch_diff_data>, Phase-No., reference phase

# Switch: Add composition sets for calculation of diffusion/volume/enthalpy data

# <diff_comp_sets | vol_comp_sets | enth_comp_sets>, phase list

# End with 'no_more_stoichio' or 'no_stoichio'

diagonal

no_stoichio

Regards,

Ahmet

### Re: Mixed input (manual, global) for diffusion data

Dear Ahmed,

These are two very different and also very broad topics which you address. I am not sure whether I can give you a sufficiently comprehensive answer in this first attempt.

The output of "Start compositions and limits in quasi equilibrium", which MICRESS gives you on starting when you use a thermodynamic database, gives you information about the content of the .ges5 file as it has been created by Thermo-Calc.

The start compositions can be relevant in cases where calculation of a quasi-equilibrium in MICRESS can get more than one solution (i.e. you can find more than one parallel tangent construction if e.g. the second derivative of the Gibbs energy functions changes sign). Then, the starting point for iteration in the composition space can be important. This is often the case for phases which can form different composition sets, like e.g. for FCC_L12 or BCC_A2. The question which start compositions are stored in the .ges5 file is decided by the choice of so-called "major constituents" on each sublattice of the phase. When you create a .ges5 file, this is typically handled by the database itself (what you cannot see because it is often crypted). If you use Thermo-Calc to manually calculate start equilibria, and then store the workspace as .ges5 file, then you will get altered predefined composition sets and also altered start compositions. If the start compositions are really relevant for your simulation, I would suggest to define the mayor constituents explicitly when creating the .ges5 file (see e.g. here or here), but often this is not necessary.

The fact that the start compositions change when you add a mobility database probably comes from extra commands in that database which probably have a different method for automatically defining composition sets and major constituents.

The second column of the output gives you the solubility ranges for each element in each phase, how is is obtained from the number of sites for each element in each sublattice. As you have considered phases only where all elements can sit on all sublattices, you get a (theoretical) range of 0-100% for each element. This would be different if you would consider e.g. carbon in fcc, which can sit only on one of the sublattices. You can further restrict the allowed range of compositions by setting manually user-defined limits (which would also appear in this listing).

Predicting of the PDAS by simulation is a difficult task because there is a quite broad stability range, and the value which you will get after the dendrite growth gets stationary depends on the initial condition (i.e. whether you start from big or small initial distances. In any case, you need to define a temperature gradient in z-direction, as well as a cooling rate. Particles are typically set at the bottom of the domain, and the "moving_frame" option is used to be able to follow the dendritic front long enough until you have reached stationary growth.

One strategy is to start from a planar front and observe the break-up of this front into different primary trunks. Another one is to set one grain to one of the bottom corners of the domain and let it grow along the bottom (so that secondary arms form the new dendrite trunks). Finally, you can also start from a fixed distance by defining a row of seeds at the bottom of the domain.

Typically, you will simulate PDAS inside a single grain. This comes out automatically with the first two methods, and requires to chose identical crystal orientations ("rotation angle") for the initial grains in the third method. Otherwise, dendrites will grow in different directions, and you will observe rather grain selection than selection of the PDAS. Of course, you can do both at the same time, if your simulation domain is big enough...

Bernd

These are two very different and also very broad topics which you address. I am not sure whether I can give you a sufficiently comprehensive answer in this first attempt.

The output of "Start compositions and limits in quasi equilibrium", which MICRESS gives you on starting when you use a thermodynamic database, gives you information about the content of the .ges5 file as it has been created by Thermo-Calc.

The start compositions can be relevant in cases where calculation of a quasi-equilibrium in MICRESS can get more than one solution (i.e. you can find more than one parallel tangent construction if e.g. the second derivative of the Gibbs energy functions changes sign). Then, the starting point for iteration in the composition space can be important. This is often the case for phases which can form different composition sets, like e.g. for FCC_L12 or BCC_A2. The question which start compositions are stored in the .ges5 file is decided by the choice of so-called "major constituents" on each sublattice of the phase. When you create a .ges5 file, this is typically handled by the database itself (what you cannot see because it is often crypted). If you use Thermo-Calc to manually calculate start equilibria, and then store the workspace as .ges5 file, then you will get altered predefined composition sets and also altered start compositions. If the start compositions are really relevant for your simulation, I would suggest to define the mayor constituents explicitly when creating the .ges5 file (see e.g. here or here), but often this is not necessary.

The fact that the start compositions change when you add a mobility database probably comes from extra commands in that database which probably have a different method for automatically defining composition sets and major constituents.

The second column of the output gives you the solubility ranges for each element in each phase, how is is obtained from the number of sites for each element in each sublattice. As you have considered phases only where all elements can sit on all sublattices, you get a (theoretical) range of 0-100% for each element. This would be different if you would consider e.g. carbon in fcc, which can sit only on one of the sublattices. You can further restrict the allowed range of compositions by setting manually user-defined limits (which would also appear in this listing).

Predicting of the PDAS by simulation is a difficult task because there is a quite broad stability range, and the value which you will get after the dendrite growth gets stationary depends on the initial condition (i.e. whether you start from big or small initial distances. In any case, you need to define a temperature gradient in z-direction, as well as a cooling rate. Particles are typically set at the bottom of the domain, and the "moving_frame" option is used to be able to follow the dendritic front long enough until you have reached stationary growth.

One strategy is to start from a planar front and observe the break-up of this front into different primary trunks. Another one is to set one grain to one of the bottom corners of the domain and let it grow along the bottom (so that secondary arms form the new dendrite trunks). Finally, you can also start from a fixed distance by defining a row of seeds at the bottom of the domain.

Typically, you will simulate PDAS inside a single grain. This comes out automatically with the first two methods, and requires to chose identical crystal orientations ("rotation angle") for the initial grains in the third method. Otherwise, dendrites will grow in different directions, and you will observe rather grain selection than selection of the PDAS. Of course, you can do both at the same time, if your simulation domain is big enough...

Bernd