Hi all, I've been pondering how much R dependence we should expect to see in S02; that is, how much R dependence is shown by intrinsic losses. I've looked at quite a bit of the literature, not to mention old threads from this mailing list. One recent (2002) reference is this one by Campbell et al.: http://prb.aps.org/pdf/PRB/v65/i6/e064107 My understanding is that S02 is intended to account for intrinsic losses; that is, those that are determined when the core hole forms. Extrinsic losses, such as inelastic scattering of the photoelectron and the effect of the core-hole lifetime, are accounted for by a mean free path term. The mathematics of how ifeffit implements this are here: http://cars9.uchicago.edu/~newville/feffit/feffit.ps Intrinsic losses are dependent on k for at least two reasons. One is that the cross-section of the intrinsic effects themselves depends on the energy of the incident x-ray. This is evident if one thinks in terms of shake-up and shake-off events. But another reason is that shake-up and shake-off events rob some energy from the primary photoelectron. At low k, ten or twenty electron volts can alter the phase of the primary photoelectron significantly, and thus shake-up and shake-off events will tend to cancel each other out. But at high k, the energy robbed from the photoelectron is less significant, because the EXAFS oscillations are more spread out in energy. Thus, shake-up and shake-off events, while still occurring, will not suppress the EXAFS amplitude as much at high k. S02 therefore gradually rises through most of the EXAFS region to reach a limiting value of 1 well above the top of the EXAFS region. The latter effect--the fact that removing a specified amount of energy from the primary photoelectron has less of an effect at high k than at low--also implies an R dependence. Low R oscillations are further apart in energy than high R oscillations, and thus over a specified k range low R oscillations should be less affected. In other words, S02 should show a modest decrease with increasing R over typical EXAFS ranges. Some papers, in particular those with John Rehr as an author, confirm that S02 should have an R dependence, but don't discuss the implications much. While ifeffit allows for floating ei, a parameter related to the mean free path, as I understand it that will still give a damping of the amplitude that is exponential in R. It seems to me that the S02 dependence on R, in contrast, is likely to be more gentle. Why is this important? Several authors, including myself, have analyzed crystallite size and/ or morphology by comparing the coordination number of successive scattering shells. This is potentially much more accurate than just finding the first-shell coordination number, because it is independent of any amplitude effects that are independent of R, such as normalization errors and many experimental effects. Errors in the mean free path are a bit more significant, but the exponential dependence of the mean free path gives it a very different shape than effects from size and morphology. But an R-dependence of S02 would be troubling, as the functional form might look a bit more like a size effect. So one question is this: does anyone have an order-of-magnitude estimate of how much R dependence to expect in S02 over the EXAFS range? If over a range of 2 to 6 angstroms S02 changed by even a few percent, that could have a significant effect on the kind of size analyses I mentioned in the preceding paragraph. Of course, another question is if I've completely blown it anywhere in my discussion above; I've just been puzzling this out over the last few days! --Scott Calvin Faculty at Sarah Lawrence College Currently on sabbatical at Stanford Synchrotron Radiation Laboratory
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Scott Calvin