High pressure and temperature dataset

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PVT Spessartine dataset:


Data are taken from Greaux & Yamada (2014). This is an example of an experiment where simultaneous high pressure and high temperature volume (PVT) data have been collected.


Two versions of this data are included as example datafiles. One has the volumes given as unit cell volumes, and the other has the volumes converted to molar volumes (cm3/mol). Only the file with molar volumes can be used to fit the MGD EoS, because the MGD requires molar volumes to calculate the thermal pressure correctly.


Both files  can be used to fit the Holland-Powell thermal pressure EoS and isothermal EoS. Fits of identical EoS to the two datasets should give you identical parameters, apart from the value of Vo.


See in the example datasets section  PVT_Spessartine.dat for further details about this dataset.


A macro file (spessartine.mcr) is available in the software distribution package together with the dataset files. If you run the macro, it will do all of the commands and calculations in the worked example for you!! Note: to ensure that the macro runs correctly, close EosFit7c and start it again immediately before running the macro.


Dataset:



Set the log file


It is always strongly recommended to open a log file where all of your calculations and results will be written and stored.


Type log to open the log and chose the appropriate directory using the file browser, then 


Type the log file name spessartine and the program will create the log file "spessartine.log"


The file name for the log file can be provided with or without extension. If no extension is provided the program will choose the default extension for log files (*.log, see file types).Instead of using the file browser is possible to directly type log followed by the filename. In this case all the file will be placed in the working directory lastly used.


Whenever you want you can change the log file.


For further information on log files handling please refer to EoS Calculations.


Read the dataset


Type read to read the dataset  spessartine_Vmolar.dat


The program will prompt the title of the dataset together with all the available input parameters, and will ask to make the choice of parameters to fit (i.e. V, a, b, c, d).


In this case the dataset contains only P, T, Volumes.  Because the system is cubic, the program can calculate any cell parameter, d-spacing or lattice spacing for you. 


For this example input V




All the calculations will be performed in terms of volume. You can always select other inputs. To select other input use the command select 




Fitting EoS: for the isotherm 295K




The first step is to fit the PV compression at room temperature


Type Omit to exclude the data that you don't want to use and keep only one isotherm (i.e. only data collected at 295K).


In this example all the data at 295K is data points 1 to 10. Therefore we want to omit (not use) all the data outside this range (i.e. all the data after 10).


Type 11, -25 to omit all the data included in the interval between data line 11 and 25.

Hit enter to exit



Check that all the data from data lines 11 to 25 are flagged with 0 at the beginning of the line.



For further information on omit command use please refer to the Fitting EoS.


Input the thermoelastic coefficients (perform the calculation for the isotherm 295K)


Type input then type reasonable parameters for a reasonable EoS parameters. In this case you are fitting a group of data containing isothermal PV data therefore: 


Type pr to chose the appropriate P-EoS parameters 


Input 2 to select the Birch-Murnaghan EoS (refer to Equations of State


Input 3 to select the second order truncation (i.e. BM3) 


Input 117.9 that correspond to the measured V0,300


Input 170 that is a reasonable guess for a garnet (or can be determined from an f-F plot of the data)


Input 4 for the value of Kp (K') as a good starting value





Check the summary of the active EoS and make sure that you have typed in the correct parameters. 

Then type exit to quit the INPUT EOS>



Fitting EoS 


Setup refinement (perform the calculation for the isotherm 300K)


Type fit to start performing the fitting of the dataset.


In order to select the parameters that you want to refine 


Type Y to refine V0,300


Type Y to refine K0,300


Type Y to refine K'0,300



Type Y three times to use the esd's in the dataset for V, P and T in weighting the least-squares fit.


The program will now start the refinement cycles until convergence.







For further information on fitting results use please refer to the Fitting EoS.





When convergence is reached the program will output the results together with the relevant statistical parameters from the fit (see Fitting EoS).



Note that the data points at high T that were not used in the refinement still have iuse = 0 in the second column of the output list, and 0.00000 in the last column which is a list of the weights applied to the data. This indicates that they were not used. But you can see that the P and V are calculated from the EoS for these data.


In this case the standard deviation, SHIFT and SHIFT/ERROR on V0,300 K0,300 and K'0,300  are reasonable and the CHI^2 and maximum delta-pressure are reasonable compared to the data uncertainties.



Therefore you could consider the resulting parameters as a good fitting result.

You can therefore update the EoS parameters:


Type Y to update the EoS parameters


Now you might want to try increase the truncation order to see if the fitting results benefit from an higher truncation order, therefore 


Type n to exit from fitting.


Type save to output the current EoS parameters into an *.eos file (spessartine_pv.eos'). N.B. the .eos file can also be read in Eosfit7 GUI.




Fitting EoS: for the whole PVT dataset



Select data to use (perform the calculation for the whole PVT dataset)


All the data points 11 to 25 were omitted because we only started with the PV data. Now we set all data to be used.


Type use all to set all data to be used.


In the data listing you will now see that all of the use flags (second column) are now 1



For further information on use command use please refer to Fitting EoS.


Input the thermoelastic coefficients (perform the calculation for the whole PVT dataset)



In this case you already have the pressure parameters from the previous fitting but now you are working with the whole dataset that contains temperature data as well therefore you need to input the thermal expansion parameters: 


Type input and then th to chose the appropriate T-EoS parameters (see chapter Equations of State).


Input 7 to select the MGD thermal pressure EoS. We use this EoS because it has the fewest parameters and still provides a good fit to most data. 


Leave the reference temperature as 298K 


You are now asked...

Do you want to use q-compromise version (Y/N) <N>?

answer Y

The q-compromise MGD EoS does not have a refineable q parameter and is therefore more stable than a full refinement of an MGD EoS. If the refinement of the q-compromise EoS is successful you can always switch over the full MGD EoS.


Hit return (<CR>) to leave the volume as the value from the previous fitting


Input 1 as starting coefficient for alpha0 


Input 500K as the Debye temperature. This is an initial guess, and most minerals have Debye temperatures above 400K


Input 20 for Natom, the number of atoms in the formula unit


Leave the value of 1 for gamma0


If you don't understand the meaning of Debye Temperature, gamma0 or q, read the section on thermal pressure EoS and the references and links given there.



Setting the Volume and Pressure scales


After typing in the parameters you will see two warnings:

*****WARNING: EoS must have a Pscale in kbar or GPa and a Vscale in cm3/mol set to get correct results.


Therefore you must use set the volume and pressure scales: This tells the program the units of your volume and pressure in your EoS. Obviously these must match the data!


type Pscale and then enter GPa 


type Vscale and then enter cm^3/mol




Check the summary of the active EoS and make sure that you have typed in the correct parameters. 

Then type exit to quit the INPUT EOS>



Fit the PVT EoSs




Type fit to start performing the fitting of the dataset.



Type Y to refine all five parameters. 


(These are the only free parameters in a q-compromise MGD  Thermal-Pressure EoS)



(If you look at the output from the macro file, you will see that the thermal parameters are first fitted alone, and then a second refinement including the Vo, bulk modulus and Kprime is performed. This is not necessary for this dataset, but is useful for some datasets if you do not know the expected range of parameter values)

 

Type Y three times to use the esd's in the dataset for V, P and T in weighting the least-squares fit.



The program will now start the refinement cycles until convergence, and you will get the final values that are shown here


Given the uncertainties in the dataset values this is a reasonable fit, as you will see when you hit enter, and compare the observed and calculated values in the list



Therefore you can consider the resulting parameters as a good fitting result and you can update the EoS parameters to perform other calculation (i.e. output data for plotting):


Type Y to update the EoS parameters


Type N to go back to the main menu


Now save the EoS parameters to a file by typing save and giving a filename, for example spessartine_MGD


For further information on fitting results use please refer to Fitting EoS.



Output for plotting:



You can now use the props command to list the properties of the EoS at any individual P and T (see the output from the macro)





And you can either use pvcal command or tvcal command if you need to plot properties of the EoS at varying P or T


In the macro we show both. Here we show tvcal to calculate the properties at fixed pressures over a range of temperature 


Type Tvcal


The program will now list the EoS parameters. 


Hit return (<CR>) to not change the parameters



A file browser will open. Type in the filename for the output file, for example spessartine_MGD_TV The extension *.cal will be used as default unless differently specified (see file types)


Input the temperature limits 0,1500,50 

This will calculate properties from 0 to 1500K in steps of 50K


Input the first pressure for the calculations, e.g. 0 (i.e. room pressure)


You can type several pressures  and all the calculated values for the specified T interval and step will be added in sequence at the bottom of the selected output file. The output file also contains all of the EoS parameters. You can read the file with a text editor, and the data values can be imported into spread sheets or data analysis and plotting software.



For further information on Pvcal and Tvcal commands and outputs please refer to Output for plotting.



EoS Calculations:



Calculate pressure at any volume and temperature


Type pcal


The program will now list the EoS parameters. 


Hit return (<CR>) to not change the parameters


To calculate pressures from V and not V/V0 input n


Input the volume and temperature at which the pressure needs to be calculated,  in this example 115.2, 900


For further information on pcal command please refer to EoS calculation.


Calculate elastic parameters at any pressure and temperature


Type props


The program will now list the EoS parameters. 


Hit return (<CR>) to not change the parameters



Input the pressure and temperature values at which the calculation will be performed 6.754, 900


After one calculation if done you can type other values or hit return (<CR>) to exit the calculation



For further information on Props command please refer to EoS calculation.