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

Jatinkumar Rana jatinkumar.rana at helmholtz-berlin.de
Sat Oct 9 02:41:12 CDT 2010


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:
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> Today's Topics:
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>     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
>> for your suggestions.
>>
>> 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:
>>      
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>>> 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
>>> listed in the Appendix to this article:
>>>
>>> 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.
>>>>
>>>> Thank you so much in advance for your valuable time...
>>>>
>>>> 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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>>> End of Ifeffit Digest, Vol 92, Issue 6
>>> **************************************
>>>
>>>
>>>
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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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