# [Ifeffit] schemes for delr and sigma2 for multiple scattering paths

Jatinkumar Rana jatinkumar.rana at helmholtz-berlin.de
Tue Oct 12 11:07:40 CDT 2010

Hi Matt,

Thank you very much. I have gone through the chapter in your Tutorial
and things are more convincing now.

With best regards,
Jatin Rana
HZB Berlin

On 09.10.2010 19:00, ifeffit-request at millenia.cars.aps.anl.gov wrote:
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> than "Re: Contents of Ifeffit digest..."
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>
> Today's Topics:
>
>     1. Re: schemes for delr and sigma2 for multiple scattering	paths
>        (Matt Newville)
>     2. Re: schemes for delr and sigma2 for multiple scattering	paths
>        (Jatinkumar Rana)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Fri, 8 Oct 2010 13:13:23 -0500
> From: Matt Newville<newville at cars.uchicago.edu>
> To: XAFS Analysis using Ifeffit<ifeffit at millenia.cars.aps.anl.gov>
> Subject: Re: [Ifeffit] schemes for delr and sigma2 for multiple
> 	scattering	paths
> Message-ID:
> 	<AANLkTimBJbC9EqyUs31kiHuU9F+fHSVv+ib5oXBKq5Kb at mail.gmail.com>
> Content-Type: text/plain; charset=ISO-8859-1
>
> Dear Jatin,
>
> I tried to answer both of these question in chapter 3 of
>      http://xafs.org/Tutorials?action=AttachFile&do=view&target=Newville_xas_fundamentals.pdf
>
> Does the explanation there help?   If not, do you have any suggestions
> for making it clearer?
>
> The basic physics is that an absorbed x-ray creates a photo-electron
> which will scatter from its neighbors.   A portion of the scattered
> portion (so, a small amount) of that photo-electron will return to the
> absorbing atom.  But Pauli's exclusion principle tells us that if an
> electron is at the absorbing atom, and has the same energy (and other
> quantum numbers) as the outgoing photo-electron, the outgoing
> photo-electron cannot be created in the first place.   Thus, the
> scattering of the photo-electron from the neighbors affects whether
> the photo-electron can be created, and so whether the x-ray will be
> absorbed.
>
> The effect can be either destructive or constructive, as with nearly
> any wave-like phenomenon.    It does seem a bit circular that the
> photo-electron scattering affects the existence of the photo-electron,
> but quantum mechanics leads to many much stranger behaviors.
>
> --Matt
>
>
> ------------------------------
>
> Message: 2
> Date: Sat, 09 Oct 2010 09:41:12 +0200
> From: Jatinkumar Rana<jatinkumar.rana at helmholtz-berlin.de>
> To: ifeffit at millenia.cars.aps.anl.gov
> Subject: Re: [Ifeffit] schemes for delr and sigma2 for multiple
> 	scattering	paths
> Message-ID:<4CB01C98.4020103 at helmholtz-berlin.de>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
>
> Hello Chris, Bruce,
>
> Thank you so very much for your detailed explanations.
>
> With best regards,
> Jatin Rana
> HZB Berlin
>
>
>
>
>
> On 08.10.2010 19:00, ifeffit-request at millenia.cars.aps.anl.gov wrote:
>
>> Send Ifeffit mailing list submissions to
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>> or, via email, send a message with subject or body 'help' to
>> 	ifeffit-request at millenia.cars.aps.anl.gov
>>
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>> 	ifeffit-owner at millenia.cars.aps.anl.gov
>>
>> than "Re: Contents of Ifeffit digest..."
>>
>>
>> Today's Topics:
>>
>>      1. Re: schemes for delr and sigma2 for multiple scattering	paths
>>         (Chris Patridge)
>>      2. Re: schemes for delr and sigma2 for multiple scattering	paths
>>         (Bruce Ravel)
>>      3. Re: schemes for delr and sigma2 for multiple scattering	paths
>>         (Bruce Ravel)
>>
>>
>> ----------------------------------------------------------------------
>>
>> Message: 1
>> Date: Fri, 8 Oct 2010 10:09:34 -0400
>> From: Chris Patridge<patridge at buffalo.edu>
>> To: XAFS Analysis using Ifeffit<ifeffit at millenia.cars.aps.anl.gov>
>> Subject: Re: [Ifeffit] schemes for delr and sigma2 for multiple
>> 	scattering	paths
>> Message-ID:<68FC92BB-B842-48F2-8596-7675D168EB16 at buffalo.edu>
>> Content-Type: text/plain;	charset=us-ascii;	format=flowed;	delsp=yes
>>
>> Hello Jatin,
>>
>> I don't confess expertise but i think the absorption coeff. relates to
>> the overlap between the initial and final wavefunction. Therefore the
>> interference between outgoing and backscattering modulates the final
>> wavefunction which manifests as the exafs fluctuations past the edge
>> which in turn changes the It signal so we can use the difference
>> between Io and It to measure exafs data.  Any additional comments are
>> welcomed if I am mistaken as I said I am not an expert.
>>
>> Buena salud,
>>
>> Chris Patridge
>>
>>
>> On Oct 8, 2010, at 9:30 AM, Jatinkumar Rana<jatinkumar.rana at helmholtz-berlin.de
>>    >   wrote:
>>
>>
>>
>>> Hi Scott,
>>>
>>> Nice to see you back-in-action from holidays. Thank you very much
>>>
>>> Since last few days i was trying to visualize the physical process
>>> going on inside an absorbing atom when we measure EXAFS, i met few
>>> really basic questions, which of course, could be due to lack of my
>>> understandings. Therefore, I tried to go through literatures and
>>> EXAFS books but i am not satisfied.
>>>
>>> Therefore, i decided to put them to mailing list
>>>
>>> My first question is :
>>>
>>> In EXAFS, the oscillations are due to the intereference between the
>>> outgoing photo electron from absorbing atom and incoming
>>> backscattered photoelectron from the scatterer. Depending upon, how
>>> much they are out of phase w.r.t each other we get oscillations in
>>> EXAFS curve. These oscillations are nothing but the variation in the
>>> absobtion coefficient of sample as the energy of incident photon is
>>> varied.
>>>
>>> I wonder, how, the intereference between the photo electrons is
>>> related to absorbtion coefficient of sample ??
>>>
>>> because, It = I0 * exp (-ut)
>>>
>>> My second question is :
>>>
>>> While measuring EXAFS at beamline, we only measure the intial
>>> intensity (Io) and the transmitted intenstiy from sample (It). In
>>> other words, we only measure the number of photons before and after
>>> the sample and variation in abs.coeffi.(u) is related to variation
>>> in It.
>>>
>>> How interference between photoelectrons will be reflected as
>>> variation in abs.coeffi. (u) of sample while we never measure photo
>>> electrons in EXAFS??
>>>
>>> We only measure Io and It.
>>>
>>> Also, whether the intereference between photo electrons is
>>> constructive or destructive, the incident photon will lose its
>>> energy once it knocks an electron from say K-shell of absorbing atom
>>> and hence photon is said to have absorbed.
>>>
>>> I will be really thankful to you for your valuable explanation.
>>>
>>> With Best regards,
>>> Jatin Rana
>>> HZB, Berlin
>>>
>>>
>>>
>>>
>>>
>>> On 07.10.2010 19:00, ifeffit-request at millenia.cars.aps.anl.gov wrote:
>>>
>>>
>>>> Send Ifeffit mailing list submissions to
>>>>      ifeffit at millenia.cars.aps.anl.gov
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>>>>      http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
>>>> or, via email, send a message with subject or body 'help' to
>>>>      ifeffit-request at millenia.cars.aps.anl.gov
>>>>
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>>>> than "Re: Contents of Ifeffit digest..."
>>>>
>>>>
>>>> Today's Topics:
>>>>
>>>>      1. Re: Multiple scattering paths in fitting (Frenkel, Anatoly)
>>>>      2. Re: schemes for delr and sigma2 for multiple scattering
>>>> paths
>>>>         (Scott Calvin)
>>>>
>>>>
>>>> ---
>>>> -------------------------------------------------------------------
>>>>
>>>> Message: 1
>>>> Date: Thu, 7 Oct 2010 09:38:26 -0400
>>>> From: "Frenkel, Anatoly"<frenkel at bnl.gov>
>>>> To: "XAFS Analysis using Ifeffit"<ifeffit at millenia.cars.aps.anl.gov>
>>>> Subject: Re: [Ifeffit] Multiple scattering paths in fitting
>>>> Message-ID:
>>>>      <CCBF39F82283424BBB90EA208CD9DE80014175C7 at exchangemb5.bnl.gov>
>>>> Content-Type: text/plain; charset="iso-8859-1"
>>>>
>>>> For relationships between sigma2 for MS and SS paths, some are
>>>>
>>>> P. Shanthakumar, et al, Physical Review B 74, 174103 (2006).
>>>>
>>>> Anatoly
>>>>
>>>>
>>>>
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>>>>
>>>>>
>>>>>
>>>> ------------------------------
>>>>
>>>> Message: 2
>>>> Date: Thu, 7 Oct 2010 06:58:04 -0700
>>>> From: Scott Calvin<dr.scott.calvin at gmail.com>
>>>> To: XAFS Analysis using Ifeffit<ifeffit at millenia.cars.aps.anl.gov>
>>>> Subject: Re: [Ifeffit] schemes for delr and sigma2 for multiple
>>>>      scattering    paths
>>>> Message-ID:<86AF0804-8418-4943-BBB3-163F7E63983D at gmail.edu>
>>>> Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes
>>>>
>>>> Jatin,
>>>>
>>>> IF the uniform expansion model is valid for single scattering paths,
>>>> then it is for multiple scattering paths as well. For some materials,
>>>> particularly those with cubic space groups, that's got a good chance
>>>> of being a useful model. Others tends to distort with changes in
>>>> temperature, doping, etc., and it may not work as well. But even in
>>>> those cases, if you've decided how to constrain the delr for single-
>>>> scattering paths, you'll do reasonably well by using some kind of
>>>> appropriate average of the delr's for related single-scattering
>>>> paths.
>>>>
>>>> --Scott Calvin
>>>> Sarah Lawrence College
>>>>
>>>> On Oct 7, 2010, at 3:05 AM, Jatinkumar Rana wrote:
>>>>
>>>>
>>>>
>>>>
>>>>> Dear all,
>>>>>
>>>>> It is reasonable to assign a constant fraction by which unit cell
>>>>> expands at a given temperature of XAFS measuremnt and so the
>>>>> variation
>>>>> in the path lengths for every single scattering paths could be
>>>>> assigned
>>>>> as delr = alpha * Reff. Similarly, one can assign  sigma2 value for
>>>>> each
>>>>> single scattering path depending on both type of scatterer and its
>>>>> distance from the absorbing atom.
>>>>>
>>>>> Now coming to multiple scattering paths, Sigma2 for multiple
>>>>> scattering
>>>>> paths can be constrained based on the sigma2 of related single
>>>>> scattering paths and a definite path-geometry-dependent scheme
>>>>> (Triangle, collinear, reversed etc.) could be applied.
>>>>>
>>>>> Is there any such scheme for delr of multiple scattering paths ?
>>>>> or we
>>>>> can simply assume that all paths (single scattering and multiple
>>>>> scattering) undergo uniform expansion by a factor alpha.
>>>>>
>>>>>
>>>>> With best regards,
>>>>> Jatin Rana
>>>>> _______________________________________________
>>>>> Ifeffit mailing list
>>>>> Ifeffit at millenia.cars.aps.anl.gov
>>>>> http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
>>>>>
>>>>>
>>>>>
>>>> ------------------------------
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>>>
>> ------------------------------
>>
>> Message: 2
>> Date: Fri, 8 Oct 2010 10:50:52 -0400
>> From: Bruce Ravel<bravel at bnl.gov>
>> To: XAFS Analysis using Ifeffit<ifeffit at millenia.cars.aps.anl.gov>
>> Subject: Re: [Ifeffit] schemes for delr and sigma2 for multiple
>> 	scattering	paths
>> Message-ID:<201010081050.52390.bravel at bnl.gov>
>> Content-Type: Text/Plain;  charset="iso-8859-1"
>>
>> On Friday 08 October 2010 09:30:14 am Jatinkumar Rana wrote:
>>
>>
>>> In EXAFS, the oscillations are due to the intereference between the
>>> outgoing photo electron from absorbing atom and incoming backscattered
>>> photoelectron from the scatterer. Depending upon, how much they are out
>>> of phase w.r.t each other we get oscillations in EXAFS curve. These
>>> oscillations are nothing but the variation in the absobtion coefficient
>>> of sample as the energy of incident photon is varied.
>>>
>>> I wonder, how, the intereference between the photo electrons is related
>>> to absorbtion coefficient of sample ??
>>>
>>> because, It = I0 * exp (-ut)
>>>
>>>
>> As always, it is important to consider the physical meaning of the
>> terms we use.  \mu is the absorption coefficient, i.e. the thing that
>> goes up at the edge and up and down throughout the EXAFS.
>>
>> Another way to say this is that \mu is some kind of measure of the
>> amplitude of the unoccupied (recall that electrons are fermions -- if
>> an electron already occupies a particular statem, the photoelectron
>> cannot transition into that state) portion of the density of states
>> projected onto the final state angular momentum.  That's a mouthful.
>> In short, for a K edge, we measure the unoccupied portion of the p
>> band.
>>
>> That portion of the density of states is not flat.  It has structure
>> -- peaks and troughs.  A peak is place where there is higher state
>> density and vice versa for a trough.  Consequently, if the incident
>> photon has the amount of energy needed to raise the photoelectron to
>> an energy at which there is a peak in the density of states, then it
>> is relatively more likely to be absorbed than for a photon with an
>> energy that takes the photoelectron to a trough.  The wiggles in the
>> XAS follow the ups and downs of the density of states.
>>
>> Now suppose that one were interested in calculating an XAS spectrum.
>> Well, there are many theoretical frameworks for making such a
>> calculation.  Feff (and, as a consequence, Ifeffit and Artemis) use an
>> approach called "real space multiple scattering".  In this approach we
>> need to know two things -- the function that describes how an electron
>> travels between points in space and the function that describes how an
>> electron scatters off of an atom.  Putting these two functions
>> together, we can now describe how an electon leaves the point in space
>> occupied by the absorbing atom, travels to a neighbor, scatters off
>> that neighbor, and continues traveling.
>>
>> We are interested in computing the absorption at a particular atom.
>> The photoelecton starts in the deep core of the absorber and is
>> promoted to a higher lying state OF THE ABSORBER.  Thus, the thing
>> that is relevant is to compute the density of states OF THE ABSORBER.
>> In the RSMS approach, the density of states is computed from the
>> overlap of the wavefunctions of the outwardly propagating
>> photoelectron with the functions of the various scattered waves.
>> The part of the overlap that is relevant to computing the density AT
>> THE ABSORBER is the bit that happens at the position OF THE ABSORBER.
>>
>> So, the interaction in question is "a deep core electron is promoted
>> to an occupied state of the absorber".  The computational tool used to
>> compute that interaction is RSMS.  Happily, the parameters of the RSMS
>> approach (R, sigma^2, N) map readily onto the things that we want to
>> know when we do an XAS experiment.
>>
>> Here are all the details, as implemented in Feff:
>>
>>     http://rmp.aps.org/abstract/RMP/v72/i3/p621_1
>>
>> It's a dense read but it's also an excellent and very rewarding paper.
>>
>> B
>>
>>
>>
>>
>>
>
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