activity boundary condition

[tatalemon]

Hi,

I am simulating a case by setting different activity of the component as boundary condition,

for example setting it both in top and bottom of the simulation region.

However, I am quite confused about how to set the activity boundary condition in MICRESS ??

Would you please give me some example or guidance ?

Hopefully for your reply soon !

regards,
tatalemon

[Bernd]

Hi tatalemon,

I am sorry, but there is no way of setting an activity boundary condition in MICRESS! There are only indirect ways like e.g. introducing a gas phase region to fix the oxygen activity at the interface...
Of course, you can set a fixed composition (=molar or weight fraction) boundary condition, but I fear this is not what you want...

Bernd

[tatalemon]

Hi Bernd,

I have tried according to your suggestion, but I can not find where to include a gas phase region in the drive file,

the phase data and grain input only allow to input solid phase.
in addition, I have tried the 1D far field, but it can only input the concentration of diffusion component.
While in my case, I want to input the oxygen activity, and the oxygen component is input as component 0.

I am really confused and wondering about the indirect ways you have mentioned.
Could you please tell me how to introduce a gas phase region to fix the oxygen activity at the interface, and if possible,
can you give me an example or illustration ??

Looking forward to your reply soon.
kind regards,
tatalemon

[Bernd]

Hi tatalemon,

when you are asked for "solid" phases in MICRESS, this is for historical reasons only! The question whether the phase is solid, liquid or gas does not matter as long as you are not using fluid flow, it just depends on the thermodynamic data which you provide for this phases.
What you need of course for using a gas phase as activity boundary condition is a thermodynamic description of your system which includes a gas phase. I can image three possible ways:

1.) In the simplest case you need only one such boundary condition, i.e. one gas phase. You then can just set the gas as initial rectangular grain at one side of the domain. You define it as pure oxygen phase, and adjust the total pressure such that you get the correct activity. Pressure can be set using the hidden option "volume" in the line after the .ges file input, then a pressure is requested at the beginning of the "Boundary Conditions" section of the input file.

2.) If you want to apply two different activities at both sides of the domain, or you do not want to change the total pressure, then you could try to use a gas mixture (e.g. O2 and N2) instead, and fix the activity by a corresponding gas concentration and a "f" (fixed) concentration boundary condition on each sides. In this way you can apply different activities on both sides. The disadvantage is that you need to include an extra element (e.g. N2) which should not have any solubility in your alloy system.

3.) If your database does not include a gas phase, you could try to add one using a linearized phase diagram description in addition to your TQ-coupled simulation. This should do the same trick as 2).

I have tried only method 1) up to now, it was for reactive air brazing with a al-cu alloy.
It would be easier to help you if I had more information about your system and your aims with this simulation.

Bernd

[tatalemon]

Hi Bernd,

I have made several tries as your method, but I failed.

My case to be simulated is shown as follows,
[img]

Picture1.jpg (16.17 KiB) Viewed 12146 times

[/img]

This is an oxide system, with different gas environment on both sides, the gas phase only acts as an atmosphere, there is no phase transformation between ABO and gas, in other Words, the gas phase just plays a role of reference state for the component oxygen in the oxide, the system evolves with the effect of oxygen Chemical potential gradient.

Based on your last reply and my attempts, I have 3 confusions,

1.In the first way, you have mentioned about "adjust the total pressure" , I am quite confused about the concept of total pressure, we usually calculate the oxygen activity according to the formular,
[img]

picture2.jpg (13.69 KiB) Viewed 12146 times

[/img]

So here, if we adjust the total pressure, what does it mean ? and the reference state for gas phase is default to be 1e5 in MICRESS ? How can we obtain the oxygen activity according to the value of total pressure ? any formular or relationships available ?

2. (1) The oxide system is quite different from the alloy system, where the oxygen component is the matrix component, in MICRESS, "concentration data" only asks to input the diffusion component, so I set oxygen as main component 0, and choose A and B ,the alloy components, to input their diffusion data. Does this mean that the diffusion of oxygen component is not considered here, only its chemical potential gradient influence the diffusion of A and B ??? If it does, Is there any method to include the diffusion of oxygen component in the simulation ?

(2) I set the gas phase as initial rectangular grain in both side of the region, and use the above "concentration data" setting, while which lead to an undesirable result that the final average concentration of A and B is calculated based on the Whole region including ABO and gas region, which means the final concentration of A and B is reduced, this will make the simulation evolve into this concentration, it is totally wrong. The concentration of A and B should be conserved in the ABO, the phase fraction of gas region should not affect the simulation result.
Any solution to avoid this problem ??

(3) Besides, the above setting leads to another problem, i.e., all of the subsequent input only asks for concentration of A and B. So Where should I set the concentration for gas phase and oxygen activity ?

3. The last question is how to treat the phase interaction between gas phase and ABO oxide ?
What I want is just described at the beginning. The gas region should not affect the simulation, it is just an atmosphere to change the Chemical potential gradient of oxygen component.
(1) If I set "no phase interaction" ,then the gas phase is set as inert phase, there is no TC coupling data and concentration data input in the drive file. There is no place to set the gas concentration and oxygen activity ??? In addition, even the gas phase is set as inert phase, the problem in previous 2. (2) still exist. Then ......
(2) If I set "phase interaction" , a surface energy and interfacial mobility is input, TC coupling data and concentration data is input in the drive file. Does this mean there will be phase transformation between gas and ABO ?? it is undesirable.
I am really paralyzed which one can achieve the result I want.

That are all my questions, it is a bit wordy.
Thanks for your patience in advance!

Hopefully for your answers.
kind regards,
tatalemon

[Bernd]

Dear tatalemon,

The problem you want to treat with MICRESS is quite complicated, but I think it can be done. Let me try to answer your questions one by one:

1.) As the gas phase would be pure oxygen in case of my "method 1", the total pressure would be just P_O2. The reference pressure P^ref is not relevant and can be chosen arbitrarily, it would anyway cancel out because you need only the activity difference.
Of course, this equation you show is only an approximation for small pressures. You could get exact activity values using Thermo-Calc software (according to the reference state they have chosen in the database...).
But as for your application you need two different gas phases with different O₂ activity, let's forget method 1 in the following !

2.1) Thus now we focus on method 2 with a gas mixture with different compositions on both sides. The question which element is chosen as matrix component in MICRESS is crucial: This component is implicitly moving if other elements are diffusing, so it should have a solubility range in ABO.
On the other hand, as you need diffusion in all phases, the matrix component should be present in all phases. So, oxygen probably is the best choice. The other elements/species are N₂, A and B. While N₂ is stoichiometric (with composition 0) in the oxide, A and B are 0 and stoichiometric in the gas phase.
Now, you can specify the composition of the three "dissolved" species as N₂¹,0,0 and N₂²,0,0 in the two gas phases and 0 A B in the oxide phase. Diffusion of oxygen in ABO is implicitly defined by the diffusion of A and B.
If oxygen is filling a complete sublattice in ABO and thus is stoichiometric, this makes things more complicated because oxygen cannot diffuse - then only A can diffuse against B or vice versa. Let us assume this is not the case...

2.2) In the setup of 2.1), the average compositions of A and B do not depend on the size of the gas phase, because they cannot go to the gas phase. I am not sure whether I completely understand your concerns, but there should be no problem with the mixture compositions!

2.3) The oxygen activities in the case of an O₂/N₂ mixture depends on the partial pressure of oxygen which is proportional to the mole fraction ("concentration") of oxygen and the total pressure (1 atm standard pressure in MICRESS if not changed according to 1)). You define them by setting the mole fractions of nitrogen in the gas phases. A trick to be able to input them directly (and not wait for the fixed boundary condition to achieve it, or to read in concentration fields from file) is to define two different gas phases which are linked to the same thermodynamic phase in the database (i.e. using three different phases in MICRESS).

3.) There must be a phase transformation between gas and ABO, because otherwise only a diffusional exchange between the phases is possible. And diffusion means one component against another one, which requires two common elements in gas and ABO which you do not have! Anyway, the movement of the interface will be small because probably the concentration differences of O in ABO are very small. The question whether this lateral movement of ABO is real or an artifact of the modelling depends on which of the components is building up the lattice which serves as frame of reference. I know a bit the example of CoO ceramics where this effect is real!


Bernd

[tatalemon]

Dear Bernd,

I come back again , you have actually provided me very detailed answers, and I made a try but failed Again.
My simulation domain is as follows:

1.jpg (23.81 KiB) Viewed 12137 times

The boundary condition "ppii " has been used, "pp " for the top and bottom, " ii " for the right and left.

To be summary, I think the problems mainly concentrate on the following several aspects:
1) The problem last time still exists, the average composition of A,B and N is calculated accross the Whole region including two gas phase.??? I have set the composition of the phase as you suggest, component 1 and 2 represent A and B, component 3 is N, phase 1 is ABO, phase 2 and 3 are two gas phase, so what is the problem ???

# 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 for ternary extrapolation (2 elements + main comp.):
# <interaction>, component 1, component 2
# Switches: <stoich_enhanced_{on|off}> <solubility_{on|off}>
# End with 'no_more_stoichio' or 'no_stoichio'
1 3
2 1 2
3 1 2
no_more_stoichio
# In phase 1 component 3 is defined stoichiometric.
# In phase 2 components 1 and 2 are defined stoichiometric.
# In phase 3 components 1 and 2 are defined stoichiometric.
......

# Initial concentrations
# ======================
# How shall initial concentrations be set?
# Options: input equilibrium from_file [phase number]
input
# Initial concentration of component 1 in phase 0 ?at%]
0.0000
# Initial concentration of component 1 in phase 1 ?at%]
20.000
# Initial concentration of component 1 in phase 2 ?at%]
0.0000
# Initial concentration of component 1 in phase 3 ?at%]
0.0000
# Initial concentration of component 2 in phase 0 ?at%]
0.0000
# Initial concentration of component 2 in phase 1 ?at%]
20.000
# Initial concentration of component 2 in phase 2 ?at%]
0.0000
# Initial concentration of component 2 in phase 3 ?at%]
0.0000
# Initial concentration of component 3 in phase 0 ?at%]
0.0000
# Initial concentration of component 3 in phase 1 ?at%]
0.0000
# Initial concentration of component 3 in phase 2 ?at%]
79.000
# Initial concentration of component 3 in phase 3 ?at%]
99.9999


2) My system ABO is very closed to stoichiometric phase, where the oxygen is filling a complete sublattice:
: A^+Z1,VA : B^+Z1,B^+Z2,VA : O^-2,VA :
When the diffusion starts, the ABO will gradually decompose into new phase, but for the first step, I do not consider them.
Besides, the oxygen diffusion much faster than the cations A and B (3 or 4 order magnitude), and it is the main component, so the diffusion of oxygen should be considered or not ???. How should I treat it ?
ps: I do not have much data about this oxide system so far , so I use the constant diffusion data for A and B,will it have an effect on the diffusion of oxygen component combined with previous sublattice model ?

# How shall diffusion of component 1 in phase 0 be solved?
no_diff
# How shall diffusion of component 1 in phase 1 be solved?
diff
# Diff.-coefficient:
# Prefactor? (real) [cm**2/s]
3.02000E-12
# Activation energy? (real) [J/mol]
0.0000
# How shall diffusion of component 1 in phase 2 be solved?
no_diff
# How shall diffusion of component 1 in phase 3 be solved?
no_diff
# How shall diffusion of component 2 in phase 0 be solved?
no_diff
# How shall diffusion of component 2 in phase 1 be solved?
diff
# Diff.-coefficient:
# Prefactor? (real) [cm**2/s]
1.74000E-16
# Activation energy? (real) [J/mol]
0.0000
# How shall diffusion of component 2 in phase 2 be solved?
no_diff
# How shall diffusion of component 2 in phase 3 be solved?
no_diff
# How shall diffusion of component 3 in phase 0 be solved?
no_diff
# How shall diffusion of component 3 in phase 1 be solved?
no_diff
# How shall diffusion of component 3 in phase 2 be solved?
no_diff
# How shall diffusion of component 3 in phase 3 be solved?
no_diff

3) I have defined gas mixture phase as you suggested, there are two kinds of definition , which one is right or better ??
Definition 1:
PHASE O2GAS % 1 1.0 !
CONSTITUENT O2GAS :O2,N2 : !
PARAMETER G(O2GAS,N2;0) 2.98150E+02 +2GHSERNN#+RTLNP#; 6.00000E+03 N !
PARAMETER G(O2GAS,O2;0) 2.98150E+02 +2GHSEROO#+RTLNP#; 6.00000E+03 N !

Definition 2:
PHASE O2GAS % 1 1.0 !
CONSTITUENT O2GAS :O,N : !
PARAMETER G(O2GAS,N;0) 2.98150E+02 +GHSERNN#+RTLNP#; 6.00000E+03 N !
PARAMETER G(O2GAS,O;0) 2.98150E+02 +GHSEROO#+RTLNP#; 6.00000E+03 N !

4) When my test simulation starts, there is always error repeat "Force Automatic start value interface gas/ABO"
I set the phase interaction between gas phase and ABO phase as follows, is there something wrong with it ??

# Data for phase interaction 1 / 2:
# ---------------------------------
# Simulation of interaction between phase 1 and 2?
# Options: phase_interaction no_phase_interaction identical phases nb
# [standard|particle_pinning[_temperature]|solute_drag]
# | [redistribution_control]
phase_interaction
# 'DeltaG' options: default
# avg ... [] max ... [J/cm**3] smooth ... [degrees] noise ... [J/cm**3]
avg 0.9 max 100.
# I.e.: avg +0.90 smooth +45.0 max +1.00000E+02
# Type of surface energy definition between phases 1 and 2?
# Options: constant temp_dependent
constant
# Surface energy between phases 1 and 2? [J/cm**2]
# [max. value for num. interface stabilisation [J/cm**2]]
1.9000E-04
# Type of mobility definition between phases 1 and 2?
# Options: constant temp_dependent dg_dependent
constant
# Kinetic coefficient mu between phases 1 and 2? [cm**4/(Js)]
4.00000E-08


5) You have mentioned that there must be a phase transformation between ABO and gas phase , does it mean that the oxygen component will transport into or out of the ABO system ??? If it is the fact, the ABO system is not a closed system, it is so complicated... Could it be said that we have to consider the diffusion of oxygen atom in gas phase ???
I do not want to consider the diffusion flux of oxygen J(O2), and simply want to treat the gas as atmosphere, which can provide a constant potential gradient on both sides, in other word, the oxygen activity in the ABO on both boundary sides is fixed by the gas atmosphere, then the diffusion activated. Is it possible ??

It is really grateful for your patience.
Looking forward to your reply !

Best regards,
tatalemon

[Bernd]

Hi tatalemon,

The system seems to be more complex than I hoped

But let me go point by point:

1.) The problem with getting the average composition of your oxide system is the least problem of all. Of course, if you include gas phases, the average composition of the domain which is written on screen output will include the gas phases. But recalculating the average composition of your system of oxides (once other phases are involved) from the phase fractions (.TabF) and the average compositions per phases (.TabC) is easy!

2.) As you tell me, each element has its own sublattice, together with VA. So, in principle, each element could diffuse independently against VA. But in reality, charge must be conserved, so that none of the elements can diffuse independently from the others. So, it is also not possible that oxygen diffuses orders of magnitude faster than A and B (perhaps you mean self-diffusion, but this is another story...)!
So, my feeling is that one has to redefine the system such that diffusion of the three species is reduced to two combined diffusion fluxes where charge is conserved for each. And one has to take into account that MICRESS cannot treat VA as an element, and that diffusion in different sublattices cannot be explicitly distinguished...

3.) I must admit that I am not a Calphad expert, and I cannot see whether the two descriptions are completely equivalent. MICRESS should be able to handle both descriptions. There is only one detail, namely that MICRESS cannot checkout the solubility ranges for the elements if non-element species like O2 are involved. That means that, if needed, composition limits of this phase need to be set manually.
Thus, I would prefer description 2 if there are no other arguments against...

4.) This means that MICRESS has problems when calculating the initial equilibrium for this interface. I would prefer to address this point after the fundamental setup of the problem is clear.

5.) It is not possible to have an influence of the O2 activity on ABO without transporting some oxygen to the system. If there is no redox reaction which would require metallic charge transport (like in the case of Co oxides which contain Co²⁺ and Co³⁺), the total amount of oxygen (and also of A and B) would not be changed.

So, for me the crucial point is how this system can be described thermodynamically and in terms of diffusion so that charge is conserved! Also the question of metallic conductivity seems important. Do you have a correct thermodynamic description of the system, or are you working on it?

Bernd

[tatalemon]

Hi Bernd,

1) This oxide is actually an electronic conductor, in which the electron conduction is much faster than component diffusion,
so the charge does not need to be included, we just simply treat the component as non-charged components instead of ions during diffusion process. In addition, I have a correct thermodynamic description of this system with cations and anions as components, but we only have self-diffusivity available for the components in this oxide, no mobility database is available.
2) The real process should have redox reaction between the oxide and gas, 1/2 O₂+2e --> O^-2. However,
there is no electron effects included when CALPHAD database is developed, only the cations and anions are included.
so in this case, maybe the process is just simplified as O₂-->2O^-2. So the problem is how to realize the transference of atom oxygen O in gas into anion oxygen O^-2 in oxide without considering electrons????

I hope the above further information can be helpful.
Hopefully for your answers soon.

kind regards,
tatalemon

[Bernd]

Hi tatalemon,

If you consider O^2- to be fast, we must expect a fast flux of O^2- through the oxide system once an activity gradient is present. Assuming electronic conductivity, different O^2- concentrations can easily be compensated by the redox reaction
B⁺-->B²⁺ + e^-
everywhere inside the oxide, so we need not worry about the charge balance. On the other hand, there is no reason for A or B to move, so the only thing which will happen is the flux of O^2-, right?

Is there really no further interaction between the sublattices?

Bernd