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Pawley Refinement and Background Fitting

As a follow on to a discussion on the Rietveld mailing list regarding how to determine the background in a Pawley Refinement with heavily overlapped peaks.

Often the background seems unreasonably low or just wrong. The reason is that there's a range of intensities+bkg that produce an equivalent fit. Jon Wright pointed to a paper of his that has a neat trick for “helping” the bkg set properly http://www.oldenbourg-link.com/doi/pdf/10.1524/zkri.219.12…. It consists of adding a penalty that comprise the sum of squares of the intensities. The effect this has is to reduce intensities and to equipartition the intensities such that two identically overlapping peaks would end up with the same intensity. To do this in TOPAS is as follows:

macro I_Penalty(c, v)
{
    #m_argu c
    c v 
    = c^2;
}
penalties_weighting_K1 .01
xdd...
   hkl_Is
      ...
      load hkl_m_d_th2 I penalty
      {
         0   0   1   2    8.57631       10.30615 I_Penalty(@, 1)
         ...

The value for penalties_weighting_K1 .01 is a little arbitrary. Basically anything that brings the high angle backgroud up to something that looks reasonable. The higher the value the smaller the intensites become and the higher the bkg.

Using the above approach on test_examples\Pawley1.inp (see the attached I-Penalty.inp) brings the background up a little at high angles. This is not a great example for testing I_Penalty but it does show the effect.

Note also that the bootstrap_errors can be used to determine the range in values for the intensities.

 bootstrap_errors 100

Alan


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