Dear Efi Dwi Indari ,

with respect to the evaluation of the EXAFS via parameter fitting or via Fouriertransform it is advised to have a net EXAFS spectrum as large as possible in kinetic energy of the photoelectron or for its wavenumber k.

Fortunately there is a decrease of EXAFS amplitude with increasing k due to the factors involving the EXAFS description such as a) 1/k and b) the Debye-Waller factor exp(-2sigma2k2).

The magnitude of the backscatter function |f(pi,k)| also decreases for quite large k. The experience shows that about 400eV ( k~ 10/ Å ) the EXAFS amplitudes are already quite low, that high expenditures to enlarge the k-space*) further on are not really necessary.

But also down to 300eV kinetic energy ( k~9/ Å ) the EXAFS evaluation is ok , also for quite high atomic number scatterers.

For low atomic numner scatterers such as C, N or O, which have a strong decreasing backscatter function you may go down to about 200eV (k~7/ Å ), if the experimental conditions demand this restriction.

*) the k scale is proportional to the square root of the energy scale: k~ sqrt(E); so around 400eV (and higher) a bit of increase in E only affects the k-scale very little.

Dear Artur Braun ,

thanks for the kind words.

Dear Efi Dwi Indari ,

I think you have got a lot of EXAFS data.

So in order to have a pragmatical approach to an answer of your question please take some of your EXAFS spectra and perform your data evaluation with respect to R (atomic distance), sigma and N (coordination number/ number of neighbours) and perform a series of evaluations while shortening step by step the available k-scale.

You will see that these numbers (R, sigma*) and N) are quite insensitive to the lengths of the k-scale in the range down to 8 or even to 7/Å. I expect that N and sigma will be the parameters which first will significantly deviate from the values that were derived from a 10/Å range in k.

For R I guess you can even go down to 5/Å range (~100eV) or even a bit lower.

You should figure out these limits for eg. C, N or O shell (low atomic numbers) and for e.g. a Fe, Ni, or Cu shell of medium or even a high atomic numbers.

I do not remember that I have seen such a systematic empiric investigation.

I only remember that we had done these principle tests the very beginning of our EXAFS investigations (very long time ago); but I have no documentation yet, sorry.

Artur Braun have you seen such investigations in a paper somewhere?

*) sigma is only available when the temperature dependence is measured.

Thanks for your response Artur Braun ,

you are completely right.

Best regards

G.M.

Dear Mr. Gerhard Martens and Mr. Artur Braun .. thank you very much for your comments. I would be working on the 'photon energy range hunting' then.

So Efi Dwi Indari , go on and good luck.

In the meantime I found a simple derivation of the absolute minimum energy range.

At least for the extraction of R from the EXAFS one has to have at least one complete cycle of the EXAFS oscillations for the data evaluation.

The EXAFS are commonly described by sin(2*k*R+phi(k))*) with R being the distance of the atoms, k the wave vector of the photo electron wave and phi(k) the scatter phase.

The above condition ('at least one cycle') leads to the following relation between the span or range delta_k of k and R:

2*pi= 2*delta_k*R; so we have delta_k= pi/R**).

The minimum atomic distances are around 1,8Å; so we have:

delta_k~pi/1,8Å~ 1,75/Å ( = minimum length of net k-range).

From here let us sweep to the energy scale.

It is well known that the XANES structures will go up to about 30eV above the edge energy. So EXAFS evaluation should start above 30 eV.

30eV is about 2,8/Å***) in k-space;

so additing delta_k to this 2,8/Å we will have a kmin value of the k-range for the EXAFS measurement of:

kmin ~ 2.8/Å + 1,75/Å~ 4,6/Å.

This k-value is equivalent to 80eV.

So you should extend your measurements at least to about 80eV above the edge energy in order to have a quite reliable result in the R evaluation.

.

*) the '2' in the argument of the sine function shows up due to the fact that the electron wave travels from the central atom the scatter atom and the same way back.

**) please do not interchange this relation with the definition of the k-vector known from x-ray scatter, x-ray diffraction and crystallography in which are k= 2pi/lambda or k=1/lambda.

***) k =(sqrt(2me*Ekin)/ħ; k[1/Å] =0,513*sqrt(Ekin[eV]) with me as the electron mass, Ekin as the kinetic energy of the photo electron, and

ħ=h/(2pi) with h as Planck's constant.

In addition to what is already posted in particular by Gerhard Martens , one should always keep in mind that the number of "statistically sound" parameters in an EXAFS fitting procedure is given by the number of independent data point N_idp, which can be calculated by the ranges in k used (for the Fourier transform and the detailed fitting) as well as the R-range in the FT that is to be modeled. N_idp is usually calculated by common EXAFS software packages such as Athena/Artemis or WinXas etc., but it can be calculated manually by

N_idp = Delta_R x Delta_k *2/Pi, Delta_k the range used in k-space for the Fourier-transform (i.e. k_max - k_min), and Delta_R the range in R to be described

(R_max-R_min). It is quite important that N_idp should always be substantially larger that the number of fit parameters used, typically for a single shell this is the bond distance R, the number of coordinated atoms N, the Debye-Waller factor (or the disorder parameter sigma), and the inner potential shift Delta_E0, i.e. 4 parameters. Thus N_idp should be substantially larger than 4!

Assuming that only first shell data is needed, then typically, an R-range from e.g. 1 to 2 (i.e. Delta_R = 1 Angström) is used for oxide materials, thus, the k-range can easily be calculated requiring e.g. that N_idp should be at least 5 to make the fit physically (and statistically) reasonable, justified and sound.

Using the numbers quoted above, therefore, the range in k should at least be about 7.85 inverse Angström, which is substantially larger than assumed above ... If N_idp = 4, then this would break down to about 6.3 inverse Angstroem...

Having in mind that EXAFS data should not be used for say k

And a second thing - a correct background calculation and subtraction, as well as normalization, and thereby a correct calculation of the X-ray absorption fine structure chi(k) will be extremely difficult if only an extremely short energy interval is available. You may easily find out using real data ...

However, if you do a literature search, you will find out that there are studies performing a Fourier-transform analysis of a very restricted energy range above the edge, e.g. Bugaev and Coworkers, Phys. Rev. B 65 (2001) 024105, DOI: 10.1103/PhysRevB.65.024105 , getting coordination numbers and bond distances under some additional assumptions.

Dear Dirk Luetzenkirchen-Hecht ,

you are completely right and thanks for that hint.

Background estimation, - subtraction and normalization is a very critical issue having only one EXAFS cycle. So my approach mentioned above should be regarded as a limit, which in reality cannot be reached when a quite reliable distance estimation is envisaged.

Thanks for the link, but I havn't access to PRB; can you send me this paper if you have full text?

In parallel I have request the full text here:

Article Fourier filtration of XANES as a source of quantitative info...

But to my experience there is unfortunately only a very poor response to full-text requests here on RG.

Thanks in advance and

best regards

G.M.

Gerhard Martens - I will send you the PRB paper privately ... Enjoy the week-end

Dirk

I totally agree with you

I totally agree with you