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Tutorials and Examples

Peak Fitting using Xfit-Koalariet (Coelho and Cheary) for Win95/NT

Fitting Lab XRD data using Fundamental Parameters Approach - Y2O3

The CCP14 Homepage is at http://www.ccp14.ac.uk

[Tutorials page] | [XFIT Tutorial Index]

[The reference to use for XFIT or FOURYA in any resulting publications is: Cheary, R. W. & Coelho, A. A. (1996). Programs XFIT and FOURYA, deposited in CCP14 Powder Diffraction Library, Engineering and Physical Sciences Research Council, Daresbury Laboratory, Warrington, England. (http://www.ccp14.ac.uk/tutorial/xfit-95/xfit.htm)]

Why Bother?

In the following example, we are going to go through what it takes to fit parts of a laboratory diffractometer using the fundamental parameters approach. This uses the geometry of the diffractometer as well as other information to model the contribution to the peak profiles, leaving the size and strain to be refined. This is very stable and requires less refinable parameters.

Other annoyances with other methods are such things as low and high angle peak asymmetry (the low angle peak asymmetry being primarily due to axial divergence of the X-ray beam; and the high angle peak asymmetry being due to penetration depth of the X-ray beam). XFIT handles this as part of the machine geometry without the need for releasing extra parameters.

However, the geometry, slit system, and tube type have to be defined correctly. This Y2O3 data was collected with a Philips 1050 goniometer (173mm goniometer radius) with Cu LFF X-ray tube, incident and diffracted beam Sollers slits with 5.1 degree acceptance angles, 1 degree fixed divergence slit, 0.1mm receiving slit, 1 degree scatter slit, diffracted beam curved graphite monochromator and proportional counter.

Download Data

Click here to download a zip file of the Y2O3 data

Warning: When doing the following, you have to remember that it is not enough to just set the value of a parameter in the Value area, but you must also tell the program that you wish to Use this parameter in the Use menu area.

Obtaining a better fit by better defining the Physics

The main point of the fundamental parameters approach is that any misfit on the peaks is due to a lack of understanding of the problem or incorrectly defining the physics. Modelling of the peaks is constrained by the physics we have modelled in this situation, not by arbitrary mathematics. For instance, the characteristic Copper K radiation lines are not two peaks but five. Thus if we more accurately describe the radiation, we would expect a better fit.

Letting all the peaks have Separate Crystallite and Strain Sizes

To let the peaks refine crystallite size and strain separately, via Options, go to File Details, Peaks, Fundamental Parameters Peaks, Codes. Highlight the crystallite size refinement flags.

  • Then click on the Set to Unique Codes

  • Repeat the above on the Strain Codewords

  • Before you refined this, under Options, Ins/Del Peaks, put the labels on to Cry Size - which will now label the peaks with the crystallite size instead of 2-theta labels. When you refine this, the fit only goes down to from 4.26 to 4.20. Implying there is not much in the way of peak anistoropy.

  • Fitting of the Low Angle Peaks and Peak Asymmtry

    To fit low angle peaks, the procedure is the same as above. The point to note is that the low angle peak asymmetry is automatically refined without the need for separate parameters. You will note that the XFIT peak position seems to be offset. This is not an error but is the 2-theta peak position calculated from the d-spacing of the emission profile that had the largest intensity. At low angles, the 2-theta position does not generally coincide with the peak maximum. This is due to the instrument and specimen aberations that move the peak maximum. XFIT gives you a peak position of the peak maximum as if the data was collected on a perfect instrument with monochromatic radiation.

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