entropy difference between two phases

issues about thermodynamics and their coupling to MICRESS
zhubq
Posts: 84
Joined: Mon Jun 22, 2009 7:33 pm

entropy difference between two phases

Post by zhubq » Thu Jun 30, 2011 11:39 pm

Hi, Bernd
How do we get the entropy difference between two phase e.g. austenite and ferrite from Thermo-calc?
What I did is :
input the steel chemistry, get the equilibrium compositions of the two phases at a specific temperature, and the volumetric entropy of each phase.
Then get the difference of the entropy.
But the problem is that when I get the entropies of the ferrite and cementite, the former is smaller than the latter which is not true because ferrite is more stable than cementite at high temperature. (i think this is due to the difference of molar volume of phases)
So I thick what I did is not valid.

Ben

Bernd
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Joined: Mon Jun 23, 2008 9:29 pm

Re: entropy difference between two phases

Post by Bernd » Sun Jul 03, 2011 10:41 pm

Dear Ben,

I guess the reason why you want to calculate the entropy difference is that you intend to use a linearised phase diagram description with MICRESS, and you need it for the phase diagram input data, right?

The entropy difference is needed for calculating the driving force which results from a certain undercooling, i.e. it is the derivative

d\Delta G/dT
Even if the driving force is defined per volume, there is no reason to calculate the difference of entropy per volume, because the volume does not play any role as long as no stresses are involved. So, you rather should calculate the difference of the entropy per mole!

Alternatively, you could directly use Thermo-Calc to calculate the derivative of the driving force. But then you have to decide the composition of which phase should be kept constant when changing temperature. You can do this by setting one phase "ENTERED" with N=1 and the other "DORMANT", then the composition of the "ENTERED" phase will be kept konstant.
Doing so, you get two values of the entropy difference:

dS_{\alpha\beta}=[d\Delta G/dT]_{c_\alpha}, dS_{\alpha\beta}=[d\Delta G/dT]_{c_\beta}
In this case, you would have to use the "linearTQ" keyword in the phase diagram input which allows you to input both values.

Of course, you could also use MICRESS with TQ-coupling to get the initial linearisation data with these two values of the entropy difference, and just copy and paste the linearisation data (from the .log file) into the driving file for using a linearised phase diagram description of the "linearTQ" type...

Bernd

zhubq
Posts: 84
Joined: Mon Jun 22, 2009 7:33 pm

Re: entropy difference between two phases

Post by zhubq » Thu Jul 14, 2011 8:14 pm

Hi, Bernd.

the unit of entropy in MICRESS is J/m^3/K.
So if we get J/mol/k, we have to transit the unit with molar volume.
when I derive the entropy difference from Thermo-Calc, I divided it by the molar volume of the "ENTERED" phase.
I think that is also why we have to input the molar volume of each phase when coupled with Thermo-Calc.

Bernd
Posts: 1088
Joined: Mon Jun 23, 2008 9:29 pm

Re: entropy difference between two phases

Post by Bernd » Sun Jul 17, 2011 11:24 am

Sorry,

I was not clear enough in this point. What I meant is that you have to calculate the entropy difference in units per mole, because what we need is not really the entropy difference but rather the derivative of the driving force with temperature. And then, afterwards, it has to be changed to the MICRESS units (J/(cm**3 K)) by using the average molar volume of the two phases.
This should give roughly the same as if you would use coupling to TQ. In this case, as we assume that most databases still do not have volumes inside, the average of the user-defined molar volumes is used to change to the MICRESS units.

Bernd

zhubq
Posts: 84
Joined: Mon Jun 22, 2009 7:33 pm

Re: entropy difference between two phases

Post by zhubq » Mon Jul 18, 2011 9:04 pm

Ok. Now I see. you use the average molar volume.

zhubq
Posts: 84
Joined: Mon Jun 22, 2009 7:33 pm

Re: entropy difference between two phases

Post by zhubq » Tue Apr 24, 2012 12:43 am

Hi, Bernd.

If I want to use Thermo-Calc to get the entropy between two phases for linearized para phase diagram, what should I do?
As you mentioned, I should fix the composition of one phase and change the temperature to find out the driving force at various temperatures. But how do I find out the composition of the other phase that have the same tangent-line slope (Sorry, this is a question related to how to operate Thermo-Calc. )?

Another way to get the entropy is that I can change the composition of one phase at a specific temperature to find out the driving force as a function of composition and get the entropy as S=dG/dT=[dG/dc]/[dT/dc] where dT/dc is the slope of lines in the phase diagram.

But I am not sure which method is better: for the one you mentioned, maybe the calculated S changes with the composition we choose; for the way I mentioned, S may change with the selected temperature.

Thank you.


Bernd wrote:Dear Ben,

I guess the reason why you want to calculate the entropy difference is that you intend to use a linearised phase diagram description with MICRESS, and you need it for the phase diagram input data, right?

The entropy difference is needed for calculating the driving force which results from a certain undercooling, i.e. it is the derivative

d\Delta G/dT
Even if the driving force is defined per volume, there is no reason to calculate the difference of entropy per volume, because the volume does not play any role as long as no stresses are involved. So, you rather should calculate the difference of the entropy per mole!

Alternatively, you could directly use Thermo-Calc to calculate the derivative of the driving force. But then you have to decide the composition of which phase should be kept constant when changing temperature. You can do this by setting one phase "ENTERED" with N=1 and the other "DORMANT", then the composition of the "ENTERED" phase will be kept konstant.
Doing so, you get two values of the entropy difference:

dS_{\alpha\beta}=[d\Delta G/dT]_{c_\alpha}, dS_{\alpha\beta}=[d\Delta G/dT]_{c_\beta}
In this case, you would have to use the "linearTQ" keyword in the phase diagram input which allows you to input both values.

Of course, you could also use MICRESS with TQ-coupling to get the initial linearisation data with these two values of the entropy difference, and just copy and paste the linearisation data (from the .log file) into the driving file for using a linearised phase diagram description of the "linearTQ" type...

Bernd

Bernd
Posts: 1088
Joined: Mon Jun 23, 2008 9:29 pm

Re: entropy difference between two phases

Post by Bernd » Tue Apr 24, 2012 12:38 pm

Hi Ben,

whether you see the compositions of the dormant phases or not is just a question of the exact options for the list_equilibrium command in Thermo-Calc: It looks like

list_equilibrium
...
Options /VWCS/: <option(s)>

You can specify 4 characters, default is VWCS. They mean:
Fraction order: V means VALUE ORDER, A means ALPHABETICAL ORDER
Fraction type: W means MASS FRACTION, X means MOLE FRACTION
Composition: C means only COMPOSITION, N means CONSTITUTION and COMPOSITION
Phase: S means including only STABLE PHASES, P means including ALL NON-SUSPENDED PHASES

If you select P as last character, you will get the composition of the dormant phases!


The second way to calculate the entropy is imho equivalent to the first, but you need to evaluate also dT/dc. So, the first method should be more direct...
Of course, the value of dS will depend on the conditions, i.e. composition and temperature. But the composition which you use should always be on the phase diagram line - then the temperature is automatically determined, and the two methods are again completely equivalent!

Bernd

zhubq
Posts: 84
Joined: Mon Jun 22, 2009 7:33 pm

Re: entropy difference between two phases

Post by zhubq » Sat Aug 10, 2013 1:35 am

Hi Bernd,

I want to compare effect of transformation mode e.g. para and nple on kinetics. Then I need the linearization parameters by coupling ThermoCalc with Micress.
How can I get them when para-equilibrium is assumed? So far, I found the linearization parameters are the same for para and nple, i.e. both output the parameters for ortho-equilibrium.
So How can I get those parameters for para-equilibrium with MICRESS_TQ, i.e. reference concentration and entropy?

Thank you.

Ben

zhubq
Posts: 84
Joined: Mon Jun 22, 2009 7:33 pm

Re: entropy difference between two phases

Post by zhubq » Sat Aug 10, 2013 2:08 am

OK. I got it.

I need using ParaTQ with TQS version.

Bernd
Posts: 1088
Joined: Mon Jun 23, 2008 9:29 pm

Re: entropy difference between two phases

Post by Bernd » Sat Aug 10, 2013 9:46 pm

Hi Ben,

yes, that's it! Did you try already?

Bernd

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