Using linearised phase diagrams

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WTMuser
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Using linearised phase diagrams

Post by WTMuser » Wed May 29, 2013 11:30 am

Dear Bernd,

Linearization parameter are stated in TabLin output file. What is the meaning of "k1", "k2" and "dcdT"?

Kind regards.
Martin

Bernd
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Re: Using linearised phase diagrams

Post by Bernd » Wed May 29, 2013 6:58 pm

Hi Martin,

in the .TabLin file, the linearisation parameters are given per interface. In case of global relinearisation ("database global"), this values are valid for the whole interface, otherwise only the parameters for the first interface cell are given exemplarily.
k1 and k2 are the grain numbers which form the interface. dcdt is the temperature dependency of the quasiequilibrium concentrations, which are used for better extrapolation, see PHYSICAL REVIEW E 73, 066122 (2006)

Bernd

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Re: Using linearised phase diagrams

Post by WTMuser » Thu Jun 06, 2013 5:50 pm

Hi Bernd,

I have one question and (maybe) one remark.

"m" in the TabLin file means the liquidus or solidus slope and results from binary phase diagrams? For Ni-based superalloys the slope for each alloying element is determined by the use of binary phase diagrams (Ni-Al, Ni-Co, Ni-Cr, ..., Ni-W)?

The import of .TabLin files into MATLAB causes some trouble due to the lack of delimiter (see Figure). Maybe you can fix this problem with the next MICRESS version?

Kind regards.
Martin
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Bernd
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Re: Using linearised phase diagrams

Post by Bernd » Mon Jun 10, 2013 9:03 am

Dear Martin,

yes, you are right: The slopes are obtained by local linearization of the thermodynamic data, and represent a multi-binary phase diagram description. They are derived by calculating derivatives of the driving force with respect to each component, as described in more detail in Phys Rev E73, 066122 (2006), equation 59.

The overlapping of the output in the .TabLin file is unfortunate, thank you for the hint! I will have a look on this..

Best regards

Bernd

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Re: Using linearised phase diagrams

Post by WTMuser » Fri Nov 15, 2013 6:31 pm

Hi Bernd,

I analysed the TabLin file with respect to the liquidus slope. I plotted the concentration of Ta (see Figure 1) and calculated the slope manually (dc/dT = -0.12). However, a comparison of the calculated value (my own calculation) with data from TabLin shows a difference. dc/dT(Ta)/ph1 from TabLin is about -2,65E-03. m(Ta)/ph1from TabLin is about -5,24. Of course, m(Ta)/ph1 is defined as dG/dc, but I expected a good agreement between dc/dT from TabLin and the calculated value in Figure 1.

Thanks for your support.
Martin
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Bernd
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Re: Using linearised phase diagrams

Post by Bernd » Mon Nov 18, 2013 11:09 am

Hi Martin,

while a phase diagram displays the interdependency of temperature and phase compositions, we separate the temperature and concentration dependency in MICRESS when we couple to thermodynamic data from database ("database", "linTQ"). The "phase diagram" slope m which is given in the .TabLin file is then recalculated from the concentration dependency and the temperature dependency of the driving force:

m^k_{\alpha\beta}=\frac {(\frac {\partial G_{\alpha\beta}} {\partial c_{\alpha}})_{T}} {(\frac {\partial G_{\alpha\beta}} {\partial T})_c}

This value should be comparable to the real phase diagram slope. But please keep in mind that (if "local" coupling to databases is used which is default), the .TabLin file gives only the thermodynamic description of one single cell of the corresponding interface, which may be not representative! Taking this into account, the difference between -8.3 and -5.24 is not too big...

On the other hand, dc/dT is something completely different, as it describes the pure temperature dependency of c0 (i.e. of the reference points of the linearised description).

Bernd

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