EXAFS mean free path in small particles
I'm working on a couple of projects involving nanoparticles, and a collaborator pointed out an old paper by Zhao and Montano (PRB 40,3401(1989)) which claimed theoretical reasons why the electron mean free path in nanos should be smaller than in bulk. This would cause coordination numbers to be underestimated. The effect is supposedly due to a surface plasmon which grows in importance as particle size shrinks. I have reasons why I think this paper exaggerates the possible effects, but I'm posting this to see what other people think about this effect. The paper seems to have gone down into obscurity, but that doesn't mean it isn't right. Thanks. Matthew Marcus
[Ifeffit] EXAFS mean free path in small particlesMatthew, This is one of the references stating that surface plazmon intensity vanishes as the particle size gets smaller than 2nm: C.N.R.Rao et al, Size-Dependent Chemistry: Properties of Nanocrystals, Chem. Eur. J. 2002, 8, No. 1, p. 29. Here is the quote: "Gold nanocrystals of varying diameters between 2 and 4nm exhibit distinct bands around ~ 525 nm, the intensity of which increases with size (ref, ref). The intensity of this feature becomes rather small in the case of 1 nm diameter particles basically due to a reduced number of "itinerant" electrons in the electron cloud." There are other evidences that small particles have DOS similar to molecules, not typical metals. Most notable is the evidence that HOMO-LUMO band grows to more than 1 eV at sizes of 1 nm range. The point is, to my opinion, that since In the most interesting range, below 2nm, the plasmon activity decreases, therefore its effect on EXAFS interpretation, if any, should be negligible. Regards, Anatoly -----Original Message----- From: ifeffit-bounces@millenia.cars.aps.anl.gov [mailto:ifeffit-bounces@millenia.cars.aps.anl.gov]On Behalf Of matthew marcus Sent: Tuesday, June 14, 2005 11:09 AM To: ifeffit@millenia.cars.aps.anl.gov Subject: [Ifeffit] EXAFS mean free path in small particles I'm working on a couple of projects involving nanoparticles, and a collaborator pointed out an old paper by Zhao and Montano (PRB 40,3401(1989)) which claimed theoretical reasons why the electron mean free path in nanos should be smaller than in bulk. This would cause coordination numbers to be underestimated. The effect is supposedly due to a surface plasmon which grows in importance as particle size shrinks. I have reasons why I think this paper exaggerates the possible effects, but I'm posting this to see what other people think about this effect. The paper seems to have gone down into obscurity, but that doesn't mean it isn't right. Thanks. Matthew Marcus _______________________________________________ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
Anatoly,
The point is, to my opinion, that since In the most interesting range, below 2nm, the plasmon activity decreases, therefore its effect on EXAFS interpretation, if any, should be negligible.
I think I may not understand your point. The Zhao and Montano paper shows very pronounced changes in the plasmon spectra between each of 10,3,2, and 1 nm for Al. At 1 nm, the surface plasmon is definitely dominating -- not going away. So their conclusion, that lambda changes substantially below 10 nm due to the changing relative importance of surface-to-bulk plasmons seems well-argued to me (not to say its correct). I agree (I think) with Matthew that the Zhao and Montano work shouldn't be too easily dismissed, though it might not be completely correct. I don't know of any other work on how lambda might depend on particle size, and never really thought about this. The Rao paper seems broader in scope and not necessarily addressing plasmons and mean free path, but I only skimmed it, so maybe I missed something. Their fig 8 definitely shows a size dependence of O K-edge, though I didn't immediately see a clear interpretation for this -- it could have several explanations. Again, I only skimmed this paper, so maybe I missed something: perhaps the electron diffraction literature has more information??
... There are other evidences that small particles have DOS similar to molecules, not typical metals. Most notable is the evidence that HOMO-LUMO band grows to more than 1 eV at sizes of 1 nm range.
Hmm, I'm not sure I see that becoming more molecular and less metallic indicates that using the bulk mean-free-path is OK. . The 'universal mean free path' that Feff uses and the fact that S02 is still has to be a fitting parameter even for excellent data with Feff8 suggests to me that there may be many hidden sins in Feff's mean-free-path calculation. Sadly, we seem to be a little short on theorists these days. --Matt
The question of the appropriate self-energy to be used in EXAFS and XANES seems overdue for improvements on the conventional Hedin-Lundqvist plasmon-pole approximation. Within Hedin's GW approximation the self energy Sigma(E) is determined by poles in G and poles in W = epsilon**(-1) V_coul. The electron gas plasmon-pole approximation was derived for 3d metals, and is questionable in insulators and other systems such as small particles. Indeed, the GW PP often overestimates loss. Efforts to improve on this are in progress, however, e.g., using ab initio calculations of epsilon**(-1). See for example, ``Electron self-energy calculation using a general multi-pole approximation," J. A. Soininen, J. J. Rehr and E. L. Shirley, J. Phys.: Condens. Matter, {\bf 15}, 2572 (2003). In the meantime, the self-energy can be adjusted in fits, e.g. to the mean free path. I'd be interested in hearing experimental evidence for the need for such corrections. J. Rehr
Hi John,
In the meantime, the self-energy can be adjusted in fits, e.g. to the mean free path. I'd be interested in hearing experimental evidence for the need for such corrections.
Yeah, I don't know of a very good experimental test for loss terms other than analyzing the heck out of good data. Trying the 10K Cu data, it turns out that I do get a better fit to the first shell when adjusting all of {S02, Ei, ThetaD} than when adjusting only {S02, ThetaD} and leaving Ei=0 (ie, using only Feff's loss terms). I get these results (using feff calculations from Feff 8.20): |-----------------------------------------------------------------| |Fit S02 ThetaD Ei E0 dR chi_reduced| |-----------------------------------------------------------------| |#1 0.93(0.03) 271(12) 0.0( - ) 0.7(0.4) -0.003(0.002) 12.8 | |#2 0.78(0.09) 300(23) -1.5(0.9) 0.7(0.3) -0.003(0.001) 10.9 | |-----------------------------------------------------------------| By refining Ei, reduced chi-square (not just chi-square!!) is better and the refined Debye Temperature is closer to the "known" value (315 K). Ei is actually negative when refined, which makes S02 smaller. Curious, huh? Of course, S02 and Ei are very highly correlated (~0.97) but both best-fit values have definitely moved away from the result when Ei is set to 0. It's seems pretty hard to say that the "leave Ei=0" fit is better. More details of this, including figures and all fit data, feff files, and scripts are at http://cars9.uchicago.edu/~newville/Feff_MFP/ I have not done this with multiple temperatures, but that might be a slightly more robust test. Cheers, --Matt
Hi Matt, Thanks for the interesting Cu fits. Clearly the coorrelations between S02, ThetaD and Ei make any assessment of possible problems with Ei problematic. Also, I don't know what the experimental resolution Gamma_expt is - probably some fraction of an eV, so Ei=Gamma_expt+Im delta Sigma implies a comparable but negative correction delta Sigma to the self-energy, which is evidence of excessive loss in the HL plasmon-pole self-energy for Cu. Moreover, although your fits are in R-space, inspection of the k-space data shows that contributions from distant MS paths are suppressed by the theory, also suggesting that FEFF's PP self-energy overestimates loss. It will be interesting to see what Ei does if one forces S02=0.9 (based on Luke Campbell's theoretical estimate) and ThetaD=315 K. We'll also try to make an independent fit using the Bayesian/EXAFS+XANES scheme that we're working on here. J. Rehr
|-----------------------------------------------------------------| |Fit S02 ThetaD Ei E0 dR chi_reduced| |-----------------------------------------------------------------| |#1 0.93(0.03) 271(12) 0.0( - ) 0.7(0.4) -0.003(0.002) 12.8 | |#2 0.78(0.09) 300(23) -1.5(0.9) 0.7(0.3) -0.003(0.001) 10.9 | |-----------------------------------------------------------------|
Hi John, Thanks for looking at this!
Clearly the coorrelations between S02, ThetaD and Ei make any assessment of possible problems with Ei problematic. Also, I don't know what the experimental resolution Gamma_expt is - probably some fraction of an eV, so Ei=Gamma_expt+Im delta Sigma implies a comparable but negative correction delta Sigma to the self-energy, which is evidence of excessive loss in the HL plasmon-pole self-energy for Cu.
I'd guess the monochromator resolution was around 0.75 to 1eV for the Cu measurement. And I agree that testing the effect of Ei v. S02 is very challenging, especially with finite monochromator resolution and finite thermal vibrations.
Moreover, although your fits are in R-space, inspection of the k-space data shows that contributions from distant MS paths are suppressed by the theory, also suggesting that FEFF's PP self-energy overestimates loss.
Yep, it looks to me that in both k- and R-space the shapes of the amplitudes for the best-fit result are slightly, but perceptively different from the data. At first look this is an exampalry "great fit". But looking more closely you can really see that reduced chi-square should be ~10, as the best-fit really is off from the data in ways that can't be easily explained as a wrong value for S02, sigma2, or Ei. I don't have a good explanation for the discrepcancy (and don't want to guarantee it's not a systematic error in the data -- but it sure doesn't seem to be). This results seem very similar to those of Bud Bridges several years ago. I think it's fair to say that neither you nor I disagreed with Bud at the time: we've known that reduced chi-square for fits to very good data is much too big for some time. It would be very nice if we could nail down the pieces that go into the EXAFS amplitudes better. It will be interesting to see if you come up with anything different. I'd love to hear about it! --Matt
participants (4)
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Anatoly Frenkel -
John J. Rehr -
Matt Newville -
matthew marcus