[Ifeffit] the use of constraints

[Kellie Aldi]

Hi, I have a question on the use of constraints and restraints in EXAFS data
fitting.

I am using SixPack to build a model for the EXAFS of some synthetic layered
transition metal (TM) oxides with relatively large amounts of layer
vacancies. I am refining the occupancy of the layer TM site, from which I
can determine the amount of layer vacancies. I want to include a parameter
in this model that refines the number of these vacancies that are capped by
interlayer TM (something that can happen in these structures), but I am
having difficulty in deciding a responsible way to define the parameters of
this variable. I am modifying the intensity of the interlayer TM scattering
paths with a parameter

fcap = (1-focc)*percap

where focc is the refined occupancy of the layer TM site, and percap is the
percentage of vacancies, "1-focc", that are capped by interlayer TM.

However, just letting percap float, the value goes greater that 1... which,
as a percentage, does not make much sense physically in my model. So I want
to keep the value of this between 0 and 1. I have tried what was suggested
on the IFEFFIT frequently asked questions page regarding constraints and
restraints. I don't feel comfortable simply using a constraint and forcing
the value to be between 0 and 1 using the suggested min/max idiom.

I like better the idea of penalizing a fit when percap is outside of a
defined range and thus "encouraging" the fit to settle percap somewhere
inside this range. But in trying to use the restraint idea, including the
fix suggested by Matt Newville for only penalizing the fit outside of the
min/max range, percap still goes slightly above 1 (about 1.02) and in my
results I get a value for the "penalty" that I am unsure how to interpret.
Can this value be used to understand why the restraint still allows the
value of percap to be outside of the defined "ideal" range?

I am trying to understand how the restraint that Matt Newville defined in
the link in the restraints/constraints FAQ works, but I am relatively new to
EXAFS modeling and thus shaky on my skills at defining these parameters and
knowing how certain math functions can be used. Are there any other help
sections or guides that might address the use of such restraints? Or any
suggestions on how to re-define this restraint?

I would greatly appreciate any suggestions/input!

Thanks,

Kellie Aldi
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