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Implementation of Q_broad instrumental parameter #29

@rjkoch

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@rjkoch

The current implementation of r-dependent peak broadening in the PDF due to Q-space resolution may contain a bug, if the literature is considered correct. This pertains to the Q_broad term.

Specifically, the peak width due to the ij atom pair is currently implemented as
image1
where sigma' is the peak width due to the Debye-Waller terms, and the deltas are the standard correlated motion terms.

This is problematic, as including Q_broad inside the root dictates that it multiplies the intrinsic FWHM.
According to this reference (last line of p 342-343), the Q_broad should modify the intrinsic FWHM in an additive manner.
Specifically, the above reference proposes the following:
image2

In practice, the current implementation mixes instrumental and thermal sources of PDF peak broadening. This will yield different values of Q_broad for different temperatures when fitting PDF data from a standard material temperature series. The values can vary by a factor of 2 or 3. This is an issue, as the instrument resolution should not be temperature dependent.

I would propose modifying the code to define the "JeongPeakWidth" as follows:
image3

This would preserve backwards compatibility for those already using the multiplicative term, and would facilitate the use of a proper additive term as proposed in the above reference.

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