Dataset scaling

Parent Previous Next

Dataset scaling is a new feature in EosFit7c 7.6. It is only available in EosFit7c and it only affects the fitting of data. Therefore, EoS that are fitted to data using scales can still be used to give the same EoS results in other programs such as EosFit-Pinc or EosFit-GUI


Motivation: When combining data from different sources, such as PV datasets from two different published studies, their volumes may not be exactly on the same scale. This can often be seen if the two studies measured their samples at the same P and T. It arises from different calibrations of different instruments and it is quite normal; for example, many commercial software packages on laboratory Xray diffractometers use different values for the X-ray wavelengths and so give different volumes for the same material measured at the same conditions.  Such scaling can be performed in the Edit utility with the change command.


However, even if two datasets were measured at the same P,T conditions, scaling them together by the ratio of their volumes at these conditions is relying on those measurements being perfect and without uncertainties and errors. This is impossible, and biases the results when the combined scaled dataset is fitted. The alternative is to use scale factors for some and all of the datasets and to refine the scale factors so that all of the data in each dataset contributes to the scale factor, not just one or two data.


Scaling can also be useful if it is believed that one dataset has a systematic error in its values. See the analysis of the data for zircon as an example where RUS measurements of its bulk moduli were systematically too large. 


Scaling might also be used if you have bulk moduli data measured on polycrystalline samples, where the measured moduli will be somewhere between the Reuss and Voigt bounds on the bulk moduli. EosFit always works with the isothermal Reuss moduli, so for polycrystalline moduli data the scale factor allows the data to be used, and the scale factor should refine to slightly greater than 1. However, scale factors should not be used to allow for the isothermal to adiabatic conversion; that should be modeled with the thermal Grüneisen parameter and the thermal expansion from the EoS.



Method: 


You can use up to 10 scale factors. Each scale factor is assigned to the corresponding group of data...thus scale factor 3 applies to group 3.  It is used to multiply the V from the EoS to match the V in the data. That means:


V(data) = scale x V(EoS)


If the data in the group are moduli, the same applies:


K(data) = scale x K(EoS)


Default values of all scales are 1.000. So, if you do not change or refine the scale factors, you will get the same results from fitting to data as previous versions without scale factors. And the same results as in EosFit-GUI where scale factors are not used.


Scale factors are only used in least-squares and the list command. They are never applied to any other calculation.


When scale factors are in use, the list command lists the data values from the file as 'observed' values. The 'calculated' values listed are the values from the EoS multiplied by the scale factor for the group.



Usage in data fitting


For example, if you suspect that one subgroup of data (e.g. a dataset from another publication) has volumes that are all 1% bigger than your data, then you can assign that other dataset to group 2 (group command) and refine the Vo but not scale factor 1,  along with the other parameters and scale factor 2. It will come out as 1.01. The Vo will be the value that matches the data in group 1, and will be the value used in all EoS calculations.


If you only have one group of data, you cannot refine Vo and the scale factor at the same time. You can try, but the program should prevent you from doing that. Like any other parameter, if scale factors refine back to their implied value  (1.0) within their esd, you can change it back to 1.00000 exactly (input, then scale) and not refine it, and you will get as good a fit to the data.



Warnings


The scale factors are stored in .eos files so that you can save the results of a refinement to a particular dataset.