Dear Dr. Holton and CCP4BBers,
Are you saying that a resonant event is always accompanied by a fluorescence
event? If that were true, wouldn't the resonant event end up manifesting as
*negative* scattering component from the resonant atom, due to the
elimination of an otherwise-scattered photon, this making the resonant atom
"darker" than would be expected?
Also, in your selenium crystal example, I think there would still be an
anomalous signal, because there would always be regular scattering as well
as the anomalous effect. Isn't that true?
By the way, while we're on the topic of comparing uv-vis fluorescence to
x-ray fluorescence, does anybody know of an example of the use of FRET in
x-ray fluorescence? I cannot think, off hand, of an application for such,
but theoretically it could be done easily with two types of heavy atoms,
such as a Se-met and some appropriate acceptor.
Jacob
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Jacob Pearson Keller
Northwestern University
Medical Scientist Training Program
Dallos Laboratory
F. Searle 1-240
2240 Campus Drive
Evanston IL 60208
lab: 847.491.2438
cel: 773.608.9185
email: j-kell...@northwestern.edu
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----- Original Message -----
From: "James Holton" <jmhol...@lbl.gov>
To: <CCP4BB@JISCMAIL.AC.UK>
Sent: Thursday, April 23, 2009 8:59 PM
Subject: Re: [ccp4bb] Reason for Neglected X-ray Fluorescence
Dirk Kostrewa wrote:
yes, this is certainly true for real fluorescence effects. But the
anomalous scattering can be best thought of as a resonance phenomenon
without any frequency change, and as such, it has a distinct phase
relationship to the elastically scattered photon and does have an effect
on the intensities (which, I think, was the background of the original
question?). But for the lighter atoms in biological macromolecules, where
in a typical experiment the measurement frequency is far away from any
resonance frequency, this effect can be neglected.
This leads me to my follow-up question to the experts: why is the
resonance effect "anomalous scattering" measured by a fluorescence scan
that should have all the effects mentioned by James? Don't we get as a
result a mixture of signals from resonance (i.e. anomalous) and from
absorption-emission (i.e. fluorescence) effects?
Fluorescent photon emission happens well after the incident photon has
"passed", so anomalous scattering is only indirectly related to
fluorescence. The relationship is that absorption induces a phase shift
in scattering (this is the anomalous scattering effect), but it also
induces an electronic transition in the atom, leaving a "core hole" or
vacant orbital near the nucleus. The filling of this core hole will
generate a fluorescent photon (some fixed fraction of the time), and this
allows us to equate the intensity of observed fluorescence to the number
of core holes produced and therefore to the absorption cross section of
the atom. In actual fact, the "MAD scan" we do before a MAD/SAD
experiment is not a "fluorescence spectrum", but rather an absorption
spectrum using fluorescence as a tally. A fluorescence spectrum would
have the energy of the fluorescent photon on the x-axis. (Bob Sweet has
corrected me several times for getting that wrong).
As for the connection between absorption and anomalous scattering, I tend
to think of this in the classical picture. Scattering lags the incident
beam by 90 degrees because a simple harmonic oscillator driven at
frequencies much higher than resonance lags behind the force upon it. An
oscillator driven at resonance will move 180 degrees out-of-phase with the
driving force. You can verify this yourself by playing with a weight tied
to the end of a rubber band. Another way to think about it is that
absorption must create a wave that is 180 degrees out of phase with the
incident beam because it reduces the intensity of the incident beam. The
details of the physics are much more complicated than this, but this is
how I like to remember it.
So, as you approach a resonance, some of the electrons in the atom will
start "absorbing" (resonating) and therefore move out-of-phase with the
other electrons in the atom (and indeed the other electrons in the
crystal). It is this "out of sync" behavior that reduces the effective
occupancy of the atom and also creates an "imaginary" component to the
scattering. This "imaginary electron density" is hard to accept if you
have never taken complex algebra, but the easy way to think about it is to
remember than multiplying a complex number by sqrt(-1) changes its phase
by 90 degrees. So the "imaginary component" is really just a mathematical
way to represent electrons that are out-of-sync with the majority of
electrons in the crystal. Yes, the majority, because a pure selenium
crystal has no anomalous scattering (since no atoms lag any other atoms).
The "imaginary component" is what leads to the breakdown of Friedel's law
(which states that the Fourier transform of a real-valued function is
centrosymmetric). But all this is really just a fancy way of saying that
some of the electrons are out of phase with the rest.
Hope this makes sense.
-James Holton
MAD Scientist
Best regards,
Dirk.
*******************************************************
Dirk Kostrewa
Gene Center, A 5.07
Ludwig-Maximilians-University
Feodor-Lynen-Str. 25
81377 Munich
Germany
Phone: +49-89-2180-76845
Fax: +49-89-2180-76999
E-mail: kostr...@lmb.uni-muenchen.de
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