If you have got no realistic guess for the relation between atomic distance(s) and sigma square(s) for your sample system you should fit these parameters independently from each other.

Gerhard Martens Thanks for your answer. Can you please provide any reference where this type of approach is employed?

A good start could be to start from the crystallographic structure of hydroxyapatite, then think where Sr will insert or which cation it will replace. You can then use this structure around Sr as a starting point, at least for distances and so on. And if the fit does not work: your structural guess is wrong, try another…

See for instance « Differentiation of biological hydroxyapatite compounds by infrared spectroscopy, x-ray diffraction and extended x-ray absorption fine

structure », Chassot et coll., 2001, Journal of Applied Physics, vol. 90 n° 12, p. 5851where this approach was used to study Zn in hydroxyapatites.

Emmanuel Curis Thanks for your answer.

Sr mostly likely substitutes for Ca in the hydroxyapatite structure. A realistic approach might be to edit a hydroxyapatite cif file by replacing both instances of Ca with Sr. FEFF can then construct a complete list of the scattering distances that your spectrum might detect. Terra et al. (https://pubs.rsc.org/en/content/articlehtml/2009/cp/b802841a) then fit the shell degeneracies and scattering distances with fixed sigma squared values. Alternatively, you could fix the degeneracies and fit the scattering distances and sigma squared separately.

A few remarks about Andrew's answer:

1) If I remember correctly, there are two distinct Ca2+ site in HAP, and unless Sr percentage is high it will substitute either one or the other, but it is unlikely that two close Ca2+ sites will be both occupied by Sr2+. So substituting all sites with Sr once may give some incorrect scattering paths involving a second Sr2+ cation instead of a Ca2+ cation

2) Unless new versions of FEFF have changed this, FEFF does not hangle crystallographic symmetries. So to prepare the FEFF input file from the CIF file, you'll have to contruct several adjacent cells. This is especially important if the Ca atoms you substitute by Sr are on the edge of the unit cell.

3) Quite often with crystallographic data, equivalent distances are not exactly equal. This means that if Ca2+ is surrounded by 6 O at almost the same distance, for instance, then FEFF will find 6 paths of degeneracy 1 instead of a single path of degeneracy 6. Variations of such kind should be instead handled through the Debye-Waller factor. So you may have to manually select some equivalent paths, using for instance an average distance and a lower bound estimate of the Debye-Waller factor. It's easy for single scattering paths, it may be more tricky for multiple scattering paths, and becomes quickly tedious. What to do with amplitudes and phases computed by FEFF for all this single pathes is debatable, but using one of them arbitrary or doing the average should be OK as a first approximation.

The LASE software I wrote handles this post-FEFF fit preparation, by setting bounds of what are considered degenerate paths in terms of distance and angles difference... See http://xlase.free.fr for more details on getting this software (for unix) if you're interested in this point.