## New publication on MICRESS phase-field model

### New publication on MICRESS phase-field model

Dear all,

there is a new publication from us, which explains exaxtly the multiphase-field approach which is used in the MICRESS software. Here is the reference:

PHYSICAL REVIEW E 73, 066122 (2006)

"Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application"

J. Eiken, B.Boettger, and I. Steinbach

Bernd

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original message from Bernd

there is a new publication from us, which explains exaxtly the multiphase-field approach which is used in the MICRESS software. Here is the reference:

PHYSICAL REVIEW E 73, 066122 (2006)

"Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application"

J. Eiken, B.Boettger, and I. Steinbach

Bernd

---

original message from Bernd

### Update: New publication on MICRESS phase-field model

Dear all,

I just want to update the list of relevant MICRESS publications:

This paper reviews important MICRESS applications in the field of steels including gamma-alpha transformation, stainless steel solidification, continuous casting, hot cracking prediction and graphite nucleation in grey iron.

This paper is still in press, but will be soon available online.

I just want to update the list of relevant MICRESS publications:

**1.) B. Böttger, M. Apel, J. Eiken, P. Schaffnit, I. Steinbach, Phase-field simulation of solidification and solid-state transformations in multicomponent steels. Steel Research Int. 79 (2008) No.8, 608-616.**This paper reviews important MICRESS applications in the field of steels including gamma-alpha transformation, stainless steel solidification, continuous casting, hot cracking prediction and graphite nucleation in grey iron.

**2.) B. Böttger et al., Phase-field simulation of microstructure formation in technical castings – A self-consistent**

homoenthalpic approach to the micro–macro problem, J. Comput. Phys. 228 (2009), doi:10.1016/j.jcp.2009.06.028homoenthalpic approach to the micro–macro problem, J. Comput. Phys. 228 (2009), doi:10.1016/j.jcp.2009.06.028

This paper is still in press, but will be soon available online.

### New publication on MICRESS phase-field model

Hi all,

The "homoenthalpic" paper is now ready:

I can send you a personal copy on request.

Bernd

The "homoenthalpic" paper is now ready:

**B. Böttger, J. Eiken, M.Apel, Phase-field simulation of microstructure formation in technical castings – A self-consistent homoenthalpic approach to the micro–macro problem, J. Comput. Phys. 228 (2009), 6784-6795.**I can send you a personal copy on request.

Bernd

### Re: New publication on MICRESS phase-field model

Hi, Bernd

Could you kindly send me a copy of your great paper (B. Böttger, J. Eiken, M.Apel, Phase-field simulation of microstructure formation in technical castings – A self-consistent homoenthalpic approach to the micro–macro problem, J. Comput. Phys. (2009), 6784-6795. ) to me? My e-mail is sunny22417@gmail.com.

Thank you very much in advance!

Sincerely yours,

Sunny

Could you kindly send me a copy of your great paper (B. Böttger, J. Eiken, M.Apel, Phase-field simulation of microstructure formation in technical castings – A self-consistent homoenthalpic approach to the micro–macro problem, J. Comput. Phys. (2009), 6784-6795. ) to me? My e-mail is sunny22417@gmail.com.

Thank you very much in advance!

Sincerely yours,

Sunny

### Re: New publication on MICRESS phase-field model

Hi, Bernd,

I got the paper, which will be for my personal use.

Thank you very much!

Best wishes!

Sincerely yours,

Sunny

I got the paper, which will be for my personal use.

Thank you very much!

Best wishes!

Sincerely yours,

Sunny

### Re: New publication on MICRESS phase-field model

Hi,

I am reading this paper "Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application".

It was said that the derivation of the formula is for the case of substitutional solute and

So does it mean that the formula for the driving force as Eq. (30)[difference in chemical potential] will be different?

By the way, is the kernal of current MICRESS based on the extropolation formula in this paper?

Thank you.

I am reading this paper "Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application".

It was said that the derivation of the formula is for the case of substitutional solute and

**"It can be done in the same way for interstitial systems,**

but with an adapted set of independent composition variables"but with an adapted set of independent composition variables"

So does it mean that the formula for the driving force as Eq. (30)[difference in chemical potential] will be different?

By the way, is the kernal of current MICRESS based on the extropolation formula in this paper?

Thank you.

### Re: New publication on MICRESS phase-field model

Hi,

for substitutional elements quasi-equilibrium is characterized by parallel tangent planes to the Gibbs energies of the two phases which are in contact. Quasi-equilibrium is a special form of deviation from equilibrium in which - according to eq (30) in our PhysRev paper - all substitutional elements exhibit the same difference in chemical potential between the two phases. As a consequence, there is a driving force for phase transformation (eq. 30), but no driving force for diffusion between the phases, because in case of substitutional elements the flux of one element has to be compensated by other elements, and the gain in free energy would thus be 0.

This is different for interstitial elements like carbon, which can diffuse without need of a counterflux. Therefore, in the quasi-equilibrium situation, the chemical potentials of the interstitials must be the same in both phases - otherwise there would be a diffusion flux between the phases. In so far, eq (30) holds only for substitutional elements.

In the framework of MICRESS, quasi-equilibrium is calculated with help of Thermo-Calc software: A "dormant" equilibrium corresponds here to a situation where the fraction of a phase is forced to be 0 (i.e. phase transformation is forbidden), but the phases are in diffusional equilibrium. We extend this in MICRESS to non-zero phase fractions by iteration of the mass balance.

To your second question: In MICRESS we use a multibinary extrapolation of the quasi-equilibrium like described in the Physical Review paper, especially according to eqns. (59)-(66).

Bernd

for substitutional elements quasi-equilibrium is characterized by parallel tangent planes to the Gibbs energies of the two phases which are in contact. Quasi-equilibrium is a special form of deviation from equilibrium in which - according to eq (30) in our PhysRev paper - all substitutional elements exhibit the same difference in chemical potential between the two phases. As a consequence, there is a driving force for phase transformation (eq. 30), but no driving force for diffusion between the phases, because in case of substitutional elements the flux of one element has to be compensated by other elements, and the gain in free energy would thus be 0.

This is different for interstitial elements like carbon, which can diffuse without need of a counterflux. Therefore, in the quasi-equilibrium situation, the chemical potentials of the interstitials must be the same in both phases - otherwise there would be a diffusion flux between the phases. In so far, eq (30) holds only for substitutional elements.

In the framework of MICRESS, quasi-equilibrium is calculated with help of Thermo-Calc software: A "dormant" equilibrium corresponds here to a situation where the fraction of a phase is forced to be 0 (i.e. phase transformation is forbidden), but the phases are in diffusional equilibrium. We extend this in MICRESS to non-zero phase fractions by iteration of the mass balance.

To your second question: In MICRESS we use a multibinary extrapolation of the quasi-equilibrium like described in the Physical Review paper, especially according to eqns. (59)-(66).

Bernd

### Re: New publication on MICRESS phase-field model

Hi, Bernd.

Thank you for your reply.

Eq. (59)-(66) cannot be applied to interstitial solute diffusion and partition?

How does MICRESS deal with this?

Thank you for your reply.

Eq. (59)-(66) cannot be applied to interstitial solute diffusion and partition?

How does MICRESS deal with this?

### Re: New publication on MICRESS phase-field model

MICRESS does not make any distinction between interstitial and substitutional elements, neither for partitioning nor for diffusion. Of course, this distintion is made in the sublattice models of the phases in the database, but MICRESS uses the outcome of the thermodynamic models only in terms of concentrations, not in terms of site fractions.

In most cases, it does not make a big difference, but there are examples where it does (for diffusion in MC carbides, for example).

In most cases, it does not make a big difference, but there are examples where it does (for diffusion in MC carbides, for example).

### Update: New publication on MICRESS phase-field model

Hi all,

there is a new publication on solidification simulation in steels and hot-cracking (online first) which may be of interest:

It is about microstructure simulation for continuous casting using MICRESS. It includes quantitative microstructure evaluation, prediction of hot-cracking using the Rappaz criterion, and discusses the effect of TiN precipitation.

It is available online for those who have access. Otherwise I can provide a personal copy.

Bernd

there is a new publication on solidification simulation in steels and hot-cracking (online first) which may be of interest:

**B. Böttger, M. Apel, B. Santillana, D. G. Eskin, "Relationship Between Solidification Microstructure and Hot Cracking Susceptibility for Continuous Casting of Low-Carbon and High-Strength Low-Alloyed Steels: A Phase-Field Study", Metall and Mat Trans A, DOI 10.1007/s11661-013-1732-9.**It is about microstructure simulation for continuous casting using MICRESS. It includes quantitative microstructure evaluation, prediction of hot-cracking using the Rappaz criterion, and discusses the effect of TiN precipitation.

It is available online for those who have access. Otherwise I can provide a personal copy.

Bernd