[Ifeffit] Anharmonic correction (Aaron Slowey)

Fri Mar 26 15:00:41 CDT 2010

When fitting the third cumulant, you should watch out for a couple of things.  

First, you should make sure in the fitting process that the third cumulant C3 doesn't get much more than twice C2^(3/2) (i.e. 2 sigma^3) - values much larger than that are probably unphysical, even if they happen to give you a better fit. 

Second,  the cumulant expansion loses its utility if it doesn't converge quickly enough.  It's essentially an expansion in terms of order k*sigma, and if that approaches 1 the higher order cumulants may be large enough that convergence is questionable.  If you are lucky and the effective distribution is Gaussian, or most of the variance is due to Gaussian broadening of a skewed distribution, it may converge OK, but that shouldn't be assumed a priori.

Grant Bunker

On Mar 26, 2010, at 1:41 PM, ifeffit-request at millenia.cars.aps.anl.gov wrote:

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> Today's Topics:
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>   1. Anharmonic correction (Aaron Slowey)
>   2. Re: Anharmonic correction (Scott Calvin)
>   3. Re: Anharmonic correction (Frenkel, Anatoly)
> 
> 
> ----------------------------------------------------------------------
> 
> Message: 1
> Date: Fri, 26 Mar 2010 10:13:56 -0700
> From: Aaron Slowey <aslowey at usgs.gov>
> To: ifeffit at millenia.cars.aps.anl.gov
> Subject: [Ifeffit] Anharmonic correction
> Message-ID: <9683660E-9ED8-4DBB-8E26-88586073B0F8 at usgs.gov>
> Content-Type: text/plain; charset="us-ascii"
> 
> Dear XAFS community:
> 
> I am fitting Hg L3-edge EXAFS of what I think are mercury sulfide nanoparticles.  I fit Fourier filtered 1st shell Hg-to-Sulfur pair correlations for 5 spectra and obtain interatomic distances (r) that are 0.2 angstroms shorter than a cubic HgS(s) (i.e., metacinnabar) and Hg-to-S coordination numbers (N) that range from 2.6 to 3.0 (compared to N = 4 for metacinnabar).  Delta_E0 values are less than a few eV, so I think the r's are not 'incorrect' as far as these preliminary fits are based on harmonic atomic vibrations/Gaussian pair-distribution functions.  
> 
> What intrigues me most about these data is that the fitted N's are consistent with the average 1st-shell Hg-S coordinations of 1 to 2 nm HgS clusters obtained by isotropically truncating the metacinnabar crystal lattice.  In one case, I can also fit first-nearest Hg neighbors in the first shell, and this N is also consistent with a 1 nm HgS cluster.
> 
> My objective is to scrutinize the tentative conclusion that the mercury sulfides in the samples consist of 1 to 2 nm subunits (within a larger aggregate, as determined by DLS).  For instance, while the fitted N's are consistent with nanoclusters, the assumption of a metacinnabar lattice to estimate N of nanoclusters is undermined by the shorter interatomic distances fitted to the data.  This got me reading the work of Manceau and Combes from the late 1980s and Frenkel et al. (2001) J. Phys. Chem. B.  In Frenkel's paper (p. 12691), they describe that they used a "third cumulant" to account for anharmonic corrections, but I'm not sure how exactly this is implemented. 
> 
> It is something that you request in a feff.inp file, or is it a path parameter for IFEFFIT to include in its calculations?  
> 
> I am using Artemis on Mac OS X 10.6 (thanks to iXAFS 2.1.1 beta!!) to execute FEFF 7 calculations and fit my data.  I noticed parameters called "3rd" and "4th" in the path dialog; is "3rd" the same parameter as, for example, the sigma_sub_i_superscript_(3) term in eqn (2) of Frenkel et al. (2001)?
> 
> Thanks for reading this lengthy note...
> 
> Aaron
> 
> Branch of Regional Research, Water Resources
> U.S. Geological Survey
> Office (650) 329-5474
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> 
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> ------------------------------
> 
> Message: 2
> Date: Fri, 26 Mar 2010 13:25:18 -0400
> From: Scott Calvin <SCalvin at slc.edu>
> To: XAFS Analysis using Ifeffit <ifeffit at millenia.cars.aps.anl.gov>
> Subject: Re: [Ifeffit] Anharmonic correction
> Message-ID: <E74A18A4-EFFC-40CE-BAEB-432469EA06B6 at slc.edu>
> Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes
> 
> Hi Aaron,
> 
> I find a nearest-neighbor third cumulant is frequently a useful  
> parameter for nanoscale materials. It's not just the anharmonicity of  
> individual bonds, it's also the anharmonicity of the distribution of  
> environments. In other words, in nanoscale materials there are core  
> atoms and surface atoms, atoms one monolayer below the surface, and so  
> on. (Or, in your case, read "interface" for "surface.") The atoms on  
> the surface may very well have interatomic distances a bit different  
> from those further in, and that distribution is often not symmetric,  
> for essentially the same reason that thermal vibrations are not  
> symmetric: it's energetically more favorable to stretch a bond from  
> equilibrium than to compress it by the same amount.
> 
> To use a third cumulant in Artemis, go to the Paths menu and check  
> "extended path parameters." The path dialogs will then include a blank  
> for "3rd," which is the third cumulant in the literature. It is then  
> used like any other path parameter. (Or, of course, you can access it  
> through IFEFFIT scripts, again using "3rd.")
> 
> --Scott Calvin
> Sarah Lawrence College
> 
> On Mar 26, 2010, at 1:13 PM, Aaron Slowey wrote:
> 
>> Dear XAFS community:
>> 
>> I am fitting Hg L3-edge EXAFS of what I think are mercury sulfide  
>> nanoparticles.  I fit Fourier filtered 1st shell Hg-to-Sulfur pair  
>> correlations for 5 spectra and obtain interatomic distances (r) that  
>> are 0.2 angstroms shorter than a cubic HgS(s) (i.e., metacinnabar)  
>> and Hg-to-S coordination numbers (N) that range from 2.6 to 3.0  
>> (compared to N = 4 for metacinnabar).  Delta_E0 values are less than  
>> a few eV, so I think the r's are not 'incorrect' as far as these  
>> preliminary fits are based on harmonic atomic vibrations/Gaussian  
>> pair-distribution functions.
>> 
>> What intrigues me most about these data is that the fitted N's are  
>> consistent with the average 1st-shell Hg-S coordinations of 1 to 2  
>> nm HgS clusters obtained by isotropically truncating the  
>> metacinnabar crystal lattice.  In one case, I can also fit first- 
>> nearest Hg neighbors in the first shell, and this N is also  
>> consistent with a 1 nm HgS cluster.
>> 
>> My objective is to scrutinize the tentative conclusion that the  
>> mercury sulfides in the samples consist of 1 to 2 nm subunits  
>> (within a larger aggregate, as determined by DLS).  For instance,  
>> while the fitted N's are consistent with nanoclusters, the  
>> assumption of a metacinnabar lattice to estimate N of nanoclusters  
>> is undermined by the shorter interatomic distances fitted to the  
>> data.  This got me reading the work of Manceau and Combes from the  
>> late 1980s and Frenkel et al. (2001) J. Phys. Chem. B.  In Frenkel's  
>> paper (p. 12691), they describe that they used a "third cumulant" to  
>> account for anharmonic corrections, but I'm not sure how exactly  
>> this is implemented.
>> 
>> It is something that you request in a feff.inp file, or is it a path  
>> parameter for IFEFFIT to include in its calculations?
>> 
>> I am using Artemis on Mac OS X 10.6 (thanks to iXAFS 2.1.1 beta!!)  
>> to execute FEFF 7 calculations and fit my data.  I noticed  
>> parameters called "3rd" and "4th" in the path dialog; is "3rd" the  
>> same parameter as, for example, the sigma_sub_i_superscript_(3) term  
>> in eqn (2) of Frenkel et al. (2001)?
>> 
>> Thanks for reading this lengthy note...
>> 
>> Aaron
> 
> 
> 
> ------------------------------
> 
> Message: 3
> Date: Fri, 26 Mar 2010 14:39:59 -0400
> From: "Frenkel, Anatoly" <frenkel at bnl.gov>
> To: "XAFS Analysis using Ifeffit" <ifeffit at millenia.cars.aps.anl.gov>,
> 	"XAFS Analysis using Ifeffit" <ifeffit at millenia.cars.aps.anl.gov>
> Subject: Re: [Ifeffit] Anharmonic correction
> Message-ID:
> 	<CCBF39F82283424BBB90EA208CD9DE800141691D at exchangemb5.bnl.gov>
> Content-Type: text/plain; charset="iso-8859-1"
> 
> In fact, an article (attached) about such surface-induced disorder and its effect on EXAFS analysis of nanoparticles just came out today, written by another Aaron...
> 
> Anatoly
> 
> 
> 
> ________________________________
> 
> From: ifeffit-bounces at millenia.cars.aps.anl.gov on behalf of Scott Calvin
> Sent: Fri 3/26/2010 1:25 PM
> To: XAFS Analysis using Ifeffit
> Subject: Re: [Ifeffit] Anharmonic correction
> 
> 
> 
> Hi Aaron,
> 
> I find a nearest-neighbor third cumulant is frequently a useful 
> parameter for nanoscale materials. It's not just the anharmonicity of 
> individual bonds, it's also the anharmonicity of the distribution of 
> environments. In other words, in nanoscale materials there are core 
> atoms and surface atoms, atoms one monolayer below the surface, and so 
> on. (Or, in your case, read "interface" for "surface.") The atoms on 
> the surface may very well have interatomic distances a bit different 
> from those further in, and that distribution is often not symmetric, 
> for essentially the same reason that thermal vibrations are not 
> symmetric: it's energetically more favorable to stretch a bond from 
> equilibrium than to compress it by the same amount.
> 
> To use a third cumulant in Artemis, go to the Paths menu and check 
> "extended path parameters." The path dialogs will then include a blank 
> for "3rd," which is the third cumulant in the literature. It is then 
> used like any other path parameter. (Or, of course, you can access it 
> through IFEFFIT scripts, again using "3rd.")
> 
> --Scott Calvin
> Sarah Lawrence College
> 
> On Mar 26, 2010, at 1:13 PM, Aaron Slowey wrote:
> 
>> Dear XAFS community:
>> 
>> I am fitting Hg L3-edge EXAFS of what I think are mercury sulfide 
>> nanoparticles.  I fit Fourier filtered 1st shell Hg-to-Sulfur pair 
>> correlations for 5 spectra and obtain interatomic distances (r) that 
>> are 0.2 angstroms shorter than a cubic HgS(s) (i.e., metacinnabar) 
>> and Hg-to-S coordination numbers (N) that range from 2.6 to 3.0 
>> (compared to N = 4 for metacinnabar).  Delta_E0 values are less than 
>> a few eV, so I think the r's are not 'incorrect' as far as these 
>> preliminary fits are based on harmonic atomic vibrations/Gaussian 
>> pair-distribution functions.
>> 
>> What intrigues me most about these data is that the fitted N's are 
>> consistent with the average 1st-shell Hg-S coordinations of 1 to 2 
>> nm HgS clusters obtained by isotropically truncating the 
>> metacinnabar crystal lattice.  In one case, I can also fit first-
>> nearest Hg neighbors in the first shell, and this N is also 
>> consistent with a 1 nm HgS cluster.
>> 
>> My objective is to scrutinize the tentative conclusion that the 
>> mercury sulfides in the samples consist of 1 to 2 nm subunits 
>> (within a larger aggregate, as determined by DLS).  For instance, 
>> while the fitted N's are consistent with nanoclusters, the 
>> assumption of a metacinnabar lattice to estimate N of nanoclusters 
>> is undermined by the shorter interatomic distances fitted to the 
>> data.  This got me reading the work of Manceau and Combes from the 
>> late 1980s and Frenkel et al. (2001) J. Phys. Chem. B.  In Frenkel's 
>> paper (p. 12691), they describe that they used a "third cumulant" to 
>> account for anharmonic corrections, but I'm not sure how exactly 
>> this is implemented.
>> 
>> It is something that you request in a feff.inp file, or is it a path 
>> parameter for IFEFFIT to include in its calculations?
>> 
>> I am using Artemis on Mac OS X 10.6 (thanks to iXAFS 2.1.1 beta!!) 
>> to execute FEFF 7 calculations and fit my data.  I noticed 
>> parameters called "3rd" and "4th" in the path dialog; is "3rd" the 
>> same parameter as, for example, the sigma_sub_i_superscript_(3) term 
>> in eqn (2) of Frenkel et al. (2001)?
>> 
>> Thanks for reading this lengthy note...
>> 
>> Aaron
> 
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