On Oct 13, 2010, at 3:09 PM, Tim Gruene wrote: > Dear Bill, > > The discussion is becoming complicated because of the mixing of notations. > There is a theory or model which describes the atomic scattering factor as > f = f0 + f' +if" > from which the structure factor is calculated. That right angle that you see > in > the picture you sent us with that link is a consequence of that factor i in > if", > therefore I would not call it a fundamental requirement.
Dear Tim: Sorry, I mean that it was a fundamental requirement (restriction) that the absorption term must remain 90 degrees out of phase with the dispersive term, regardless of the absolute phase angle of their resultant. (And it must be retarded, due to absorption and conservation of energy, as Bernhard pointed out). > Now as you displace that particular atom from the origin, all three components > receive the same phase which leaves Fa and Fa" in the same relative > orientation. That is what I was trying to say. (But on the drive home from work, I was plagued by renewed doubt, for why then would there be a relative angle between f0 and f' that was anything but 0 degrees or 180 degrees?) > That sounds pretty much like your explanation, but I have the impression that > we > have different notions of the sources of effects. I started to reply to emails in the inverse order I received them, realized I had forgotten to go to a boring meeting that in the end never went down anyway, and mixed notation from that email and the figure (or my false memory of the figure). > This could be, though, like a discussion about whether the chicken or the egg > came first, meaning that neither > is more or less correct than the other. Maybe to better understand your > question > you could explain what you think the origin ior source of that image actually > is (technically, not in terms of "copyright"). Google image search. Someone pointed out it was Bernhard's originally. (Sorry!) My understanding of the origin of the effect illustrated in the figure is roughly as follows: 1. We treat X-ray scattering using the assumptions inherent in the First-Order Born Approximation to elastic scattering (the photon interacts with an electron described by a spherically symmetric potential that is purely real). The photon scatters once, and elastically, so the atomic scattering factor is simply the Fourier Transform of the spherically symmetric (real) potential, or, using a couple of algebra steps and Poisson's equation, it is the Fourier Transform of the (real) electron density. The reality and symmetry of the potential ultimately are manifested in Friedel symmetry. The scattering from a spherically symmetric potential (not an electron per se) at the origin has a purely real amplitude and a phase of 1 (phase angle of zero) and nonzero phase angles result from displacement of the real scattering potential from the origin, so for elastic (non-absorptive) scattering, the resultant phase is a consequence purely of spatial displacement. Hopefully I am right so far ... 2. Within the confines of the approximation we use (or, equivalently, Fraunhofer Diffraction, if you want to stick to a purely classical treatment), absorption is modeled with a complex potential. The imaginary term added to the potential could account for both emission and absorption, but conservation of energy dictates it be the latter (hence the absolute value of the orientation of f"). There is a good treatment of this in James; Blundell and Johnson glosses over the some of the essential steps in the derivation. But the main point is that the F" (the imaginary component) arises as a consequence of absorption, which we model as a complex potential. This is distinct from what arises from path length displacement. > > In a centrosymmetric structure, all phase angles are either 0degree or > 180degree > whyfore - as you already point out - the additional anomalous term does not > affect the validity of Friedel's law. For basically the same reason you would > not detect an anomalous signal from a crystal containing only one element, > irrespective of the values of f' and f". > > The link you sent, by the way, rises the impression that in the absence of > anomalous scattering phi(F) = phi(-F), but this should read > phi(F) = -phi(-F). > Furthermore the abbreviation "-F" instead of "F(-h-k-l)" is also misleading > because F(-h-k-l) is not the same as -F(hkl). Here's the figures I made that I actually used in my lecture. I realize now the way I made the first one set me up for this confusion: <http://sage.ucsc.edu/~chem200a/2009/slides/diffraction_004/diffraction_004.html_files/diffraction_004.022-001.jpg> <http://sage.ucsc.edu/~chem200a/2009/slides/diffraction_004/diffraction_004.html_files/diffraction_004.023-009.jpg> These are actually composite images of several-step slides, and for some reason a couple of labels didn't appear when I exported from Keynote, so I looked for something else with Google, which I guess only made things needlessly complex. (I also geared it to my previous presentation on MIR, hence the "Native" data, but I explained the equivalent remote dataset(s), and then showed a specific example.) <http://sage.ucsc.edu/~chem200a/2009/slides/diffraction_004/diffraction_004.html_files/diffraction_004.025-002.jpg> > > Cheers, Tim Thanks. Bill > > On Wed, Oct 13, 2010 at 01:58:56PM -0700, William Scott wrote:
