Fitting moduli

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quartz_moduli dataset:


This file contains the bulk and linear adiabatic moduli recalculated from the cij values reported by Wang et al. (2015). This illustrates all of the features of an input data file with moduli for EosFit. For details of the file format for moduli, go here


For a description of the methods used in EosFit7 to fit moduli and volumes simultaneously please read Milani et al. (2017).


This example shows how to load the data and perform a combined refinement to the bulk moduli data and the volume data.


Before you start, read in the quartz PV data and fit it, as in the first example.







Dataset: 




Before you start: fit the PV data


Read in the quartz PV data and fit it, as in the first example.


After fitting, when you type list you should see a list of the P-V data like this one.





Read in the moduli data


Type read,  navigate to the quartz_moduli.dat file and read it in.


The program reports that it contains five sets of data at pressure, with 'data' for V, a, and c. This means it contains bulk moduli for V, and linear moduli for a and c axes.


Input A  to add this new data to the P-V data in the program. (The option O will delete the old data and you will only have the new data in the program).


The new data is added as data group 2. This makes it easy for you to use/omit the different datasets. 


Input V  to select the volume moduli (i.e. the bulk modulus).


All of the data is then listed. Note that the list has a type column which tells you which data is V and which data is Ks (adiabatic bulk moduli).


The column Value has the values of these data. 


Scroll down, and see that data point 23 has an observed value of Ks=37.44 GPa, but the calculated value is 37.13 GPa, the room-pressure value of the isothermal bulk modulus. This is because you have no Grunesien parameter loaded.



Input the Gruneisen parameter


See the section Adiabatic-Isothermal moduli to understand the relationship between these different moduli.


Start the Input utility to input the thermal parameters to input the Gruneisen and other needed parameters.



Type Thermal (or simply th) to input thermal parameters 


Input 1 to select the simplest Berman thermal expansion (this data is only at room temperature, so you can use any thermal expansion equation.


Input 3.45 as the volume thermal expansion coefficient of quartz.


Input 0.67 as the best estimate for γ0 of quartz. 


(for the other parameters just hit enter to not change the values.


Check the summary of the active EoS and make sure that you have typed in the correct parameters and then type exit to quit the INPUT EOS> subroutine



Type LIST to list the data again.


The output should now look like this.


Look at data point 23. Now it has a calculated value of 37.38 GPa, because the isothermal value of 37.13 GPa (see above) has now been converted to the adiabatic value, using the Gruneisen parameter and thermal expansion coefficient you just entered.



Now omit data point 27 because it was collected at pressures above the hydrostatic pressure limit of the pressure medium used (see Wang et all., 2015).



Fit the combined data


Start the least-squares fitting procedure by typing FIT.


The questions are just the same as for fitting P-V data!


And the output is just the same!


The screenshot shows the end of the least-squares fitting and the final listing of the observed and calculated data.



Comments


Be very careful when fitting combined data to assign realistic uncertainties to all of the data. The final refined parameters will be very sensitive to the relative weights of the different datasets.


Some refinements involving moduli data and phase transitions can be very slow because of some of the calculations involved have to be performed iteratively. Be patient!