Hi,

I am doing carbide precipitation/dissolution. I found that in MICRESS, Gibbs-Tompson effect cannot affect the thermodynamics e.g. the equilibrium concentration at the interface but affect the kinetics. So it is different from the classical theory if the interface is diffusion-controlled.

Do you guys agree?

## Gibbs-Tompson effect

### Re: Gibbs-Tompson effect

Hi zhubq,

no, I do not agree at all! Local curvature gives and additional contribution to the total driving force. If the interface is in local equilibrium (total driving force is 0), then the chemical driving force must compensate for thát, and that is only possible via a change in composition. In case of TC coupling, this means that, due to local curvature, local equilibrium is not characterized by a common tangent but by a parallel tangent. This automatically leads to different local compositions.

If the system is not diffusion limited but limited kinetically, then - of course - the compositions may not change due to curvature, because composition change is triggered by interface movement.

Please tell me under which conditions you found that curvature does not affect local composition!

Bernd

no, I do not agree at all! Local curvature gives and additional contribution to the total driving force. If the interface is in local equilibrium (total driving force is 0), then the chemical driving force must compensate for thát, and that is only possible via a change in composition. In case of TC coupling, this means that, due to local curvature, local equilibrium is not characterized by a common tangent but by a parallel tangent. This automatically leads to different local compositions.

If the system is not diffusion limited but limited kinetically, then - of course - the compositions may not change due to curvature, because composition change is triggered by interface movement.

Please tell me under which conditions you found that curvature does not affect local composition!

Bernd

### Re: Gibbs-Tompson effect

Hi, Bernd.

You are quite right. I made a mistake

You are quite right. I made a mistake

Bernd wrote:Hi zhubq,

no, I do not agree at all! Local curvature gives and additional contribution to the total driving force. If the interface is in local equilibrium (total driving force is 0), then the chemical driving force must compensate for thát, and that is only possible via a change in composition. In case of TC coupling, this means that, due to local curvature, local equilibrium is not characterized by a common tangent but by a parallel tangent. This automatically leads to different local compositions.

If the system is not diffusion limited but limited kinetically, then - of course - the compositions may not change due to curvature, because composition change is triggered by interface movement.

Please tell me under which conditions you found that curvature does not affect local composition!

Bernd

### Re: Gibbs-Tompson effect

Dear Expert,

I want to continue the discussion with this old but important thread.

Let us, for example, consider, that a single ferrite grain is growing in an austenite matrix.

Then, let us consider a hypothetical situation, where the local curvatures are different in different parts of the ferrite/austenite grain boundary. Then how this difference in local curvatures will effect the parallel tangent constructions, required for the quantification of chemical driving forces, in different parts of the ferrite/austenite grain boundary ?

The reason I wrote 'hypothetical situation' is that, as one might argue, if the ferrite grain is growing isotropically in the austenite matrix, then the local curvature will be the same throughout the ferrite/austenite grain boundary. In that case my question becomes void though.

I shall be grateful for your kind reply.

Thanking you,

Best regards,

Krishnendu

I want to continue the discussion with this old but important thread.

Let us, for example, consider, that a single ferrite grain is growing in an austenite matrix.

Then, let us consider a hypothetical situation, where the local curvatures are different in different parts of the ferrite/austenite grain boundary. Then how this difference in local curvatures will effect the parallel tangent constructions, required for the quantification of chemical driving forces, in different parts of the ferrite/austenite grain boundary ?

The reason I wrote 'hypothetical situation' is that, as one might argue, if the ferrite grain is growing isotropically in the austenite matrix, then the local curvature will be the same throughout the ferrite/austenite grain boundary. In that case my question becomes void though.

I shall be grateful for your kind reply.

Thanking you,

Best regards,

Krishnendu

### Re: Gibbs-Tompson effect

Dear Krishnendu,

In MICRESS (and also most other phase-field models) curvature is part of the phase-field equation, and thus separated from the chemical driving force. If we would assume that the interface cannot move (interface mobility is zero), then the curvature effect in the phase-field equation is blocked and thus has no effect at all: Concentrations and chemical driving force (and thus also all thermodynamic linearisation parameters) would be identical everywhere despite variation of curvature along the interface.

However, if there is a finite interface mobility, there will be at least a partial relaxation towards local equilibrium. Then, the front velocity depends on the sum of the chemical driving force and curvature, and thus the local composition will get different depending on curvature. If relaxation is complete (infinite mobility, diffusion control), then the chemical driving force will be equal to the negative curvature "force", so that the sum is zero and the front velocity is zero. This considerations are important for the interpretation of the .driv output, because in this case it indirectly reflects curvature.

A further aspect which your question might be directing to is that the calculation of thermodynamic linearisation parameters is done based on the interface compositions. That means, that depending on the interface kinetics, curvature effects might be included or not included in the linearisation data (as written e.g. to the .TabLin file). However, this normally does not make an important difference, because (within the accuracy of the multi-binary extrapolation) a shift of compositions (in case of moving interface) is equivalent to the corresponding shift of the distance of the parallel tangents (ΔG0) (in case of the immobile interface). The same argument also holds for average linearisation parameters (i.e. calculated from average interface compositions) in case of global relinearisation schemes.

Bernd

In MICRESS (and also most other phase-field models) curvature is part of the phase-field equation, and thus separated from the chemical driving force. If we would assume that the interface cannot move (interface mobility is zero), then the curvature effect in the phase-field equation is blocked and thus has no effect at all: Concentrations and chemical driving force (and thus also all thermodynamic linearisation parameters) would be identical everywhere despite variation of curvature along the interface.

However, if there is a finite interface mobility, there will be at least a partial relaxation towards local equilibrium. Then, the front velocity depends on the sum of the chemical driving force and curvature, and thus the local composition will get different depending on curvature. If relaxation is complete (infinite mobility, diffusion control), then the chemical driving force will be equal to the negative curvature "force", so that the sum is zero and the front velocity is zero. This considerations are important for the interpretation of the .driv output, because in this case it indirectly reflects curvature.

A further aspect which your question might be directing to is that the calculation of thermodynamic linearisation parameters is done based on the interface compositions. That means, that depending on the interface kinetics, curvature effects might be included or not included in the linearisation data (as written e.g. to the .TabLin file). However, this normally does not make an important difference, because (within the accuracy of the multi-binary extrapolation) a shift of compositions (in case of moving interface) is equivalent to the corresponding shift of the distance of the parallel tangents (ΔG0) (in case of the immobile interface). The same argument also holds for average linearisation parameters (i.e. calculated from average interface compositions) in case of global relinearisation schemes.

Bernd