[Ifeffit] k range

[Matt Newville]

Hi Steven,

On Tue, 27 Apr 2004, Steven Sangyun Lim wrote:

> My question is how low can I set the k range? Is there any minimum
> range for reliable result? Please let me get out of this
> dilemma...

Scott answered the question of how small "delta k" can be.  It 
seems you might also be asking how low kmin can be.  I'll try to 
answer that one:

It depends on the details of the system, but using a kmin between 2
and 3Ang^-1 is a fairly safe value.  Many people tend to stay on the
conservative side of that (that is, kmin=3 or higher).  Below kmin=2
(which is only 15eV above E0), the spectra can be heavily influenced
by multiple-scattering, details of the background subtraction, and
the selection of E0.  In principle these XANES features could be
modelled as part of the EXAFS if you trust the background function
and either use enough paths or are very confident there are no
contributions from multiple-scattering in that range.

I believe some spectra for highly disordered metals really have
analyzable EXAFS starting at k=1Ang^-1, but that seems to be the
exception, not the rule.  In practice, the cost in complexity is
usually not worth the benefit in first shell information.

--Matt

PS: Scott's answer in a way that should be archived better:

Hi Steven,

I once published with k-ranges as small as 4-8.

I think there are two related criteria you can look at off the bat
to see if your k-range is definitely too small. One is, of course,
the Nyquist criterion comparing independent points to variables
being fit (automatically computed by IFEFFIT). This criterion
assumes that information is "ideally packed" in the EXAFS signal,
which it's not, so although fitting more variables than you have
"independent points" according to this criterion is definitely bad,
you really want to clear this criterion by a significant margin.

The second (related) criterion is the resolution of different
scatterers. A rule of thumb is that in order to resolve two
different absorber-scatterer distances, you need to satisfy:

kmax - kmin > pi/(2 x delta r)

where delta r is the difference in absorber-scatterer distances you
are hoping to resolve. You'll notice that with a k-range of 4-8,
that means I couldn't resolve distances less than 0.4 angstroms
apart...

--Scott Calvin
Sarah Lawrence College