Hi, Bernd.

I have a fundamental question about thermodymics.

Take Fe-C system as an example. How to calculate the driving pressure when the temperature is above the ferrite-to-austenite transition temperature (912C for pure iron)? The reference carbon concentration at the same temperature will be negative if using a linearized diagram though we always use a different reference temperature. But is it physically true? This may result in negative concentration at interface if it is a diffusion-control mode with enough high mobility.

Thank you.

Ben

## thermodymics problem

### Re: thermodymics problem

Hi Ben,

assuming that you use a linearized phase diagram for gamma-alpha in the Fe-C system, the way to get the driving force is the following:

1.) Take the local mixture composition c and go down in the phase diagram until you reach a point where

+

2.) Take the difference between the temperature where you find this condition and the actual temperature for calculation of the driving force:

This way to calculate the driving force (and the redistribution) should not lead to negative concentrations!

I am not sure whether I understood your question correctly - please tell me if not...

Bernd

assuming that you use a linearized phase diagram for gamma-alpha in the Fe-C system, the way to get the driving force is the following:

1.) Take the local mixture composition c and go down in the phase diagram until you reach a point where

+

2.) Take the difference between the temperature where you find this condition and the actual temperature for calculation of the driving force:

This way to calculate the driving force (and the redistribution) should not lead to negative concentrations!

I am not sure whether I understood your question correctly - please tell me if not...

Bernd

### Re: thermodymics problem

Bernd.

So far I have not seen any negative value in my simulation.

But what do you think about the interface concentration configuration if the temperature is in a single phase region when people talk about using an extremely high mobility such that the interface is diffusion controlled. Because if it is diffusion controlled, it means the phase concentration is the equilibrium value which is meaningless out of the intercritical region in the phase diagram.

Ben

So far I have not seen any negative value in my simulation.

But what do you think about the interface concentration configuration if the temperature is in a single phase region when people talk about using an extremely high mobility such that the interface is diffusion controlled. Because if it is diffusion controlled, it means the phase concentration is the equilibrium value which is meaningless out of the intercritical region in the phase diagram.

Ben

### Re: thermodymics problem

Hi Ben,

Now I see what you mean! It is possible to get negative compositions inside the interface if you are using an unphysical shape of a linear phase diagram (or possibly if you extrapolate too far from a trmporary linearisation in case of TQ coupling): this is the case if the two phase diagram lines which correspond to a phase transformation do not cross at the composition 0! Such situations are unphysical because this is always required!

Imagine an alpha-gamma transformation starting with composition c0 (see below). If the phase-diagram is physical (lines are crossing at c=0), then the minimum concentration is given like in the image below and never can be negative, even if the temperature is higher than T0.

By the way, if T>T*, the reaction cannot be diffusion limited because the driving force is too high for the maximum pile-up, it is massive!

Bernd

Now I see what you mean! It is possible to get negative compositions inside the interface if you are using an unphysical shape of a linear phase diagram (or possibly if you extrapolate too far from a trmporary linearisation in case of TQ coupling): this is the case if the two phase diagram lines which correspond to a phase transformation do not cross at the composition 0! Such situations are unphysical because this is always required!

Imagine an alpha-gamma transformation starting with composition c0 (see below). If the phase-diagram is physical (lines are crossing at c=0), then the minimum concentration is given like in the image below and never can be negative, even if the temperature is higher than T0.

By the way, if T>T*, the reaction cannot be diffusion limited because the driving force is too high for the maximum pile-up, it is massive!

Bernd