Bill,
If I understand you correctly, the problem turns to be understanding
coordinate system.
The coordinate system in the plot in your original email is not a
complex one but a polar coordinate system [|F| and phase (polar
angle)]. In order to add the contribution of an atom with anomalous
scattering, a complex coordinate is borrowed and used regionally at
the tip region (why I say region not the tip) of Fp (Fp is subjected
to be added by Fa and iF"a), and the resultant F again is shown in the
polar coordinate system again. During the adduct, Fa and F"a are
perpendicular.
Lijun
Thanks for the overwhelming response. I think I probably didn't
phrase the question quite right, but I pieced together an answer to
the question I wanted to ask, which hopefully is right.
On Oct 13, 2010, at 1:14 PM, SHEPARD William wrote:
It is very simple, the structure factor for the anomalous scatterer
is
FA = FN + F'A + iF"A (vector addition)
The vector F"A is by definition always +i (90 degrees anti-
clockwise) with respect to the vector FN (normal scattering), and
it represents the phase lag in the scattered wave.
So I guess I should have started by saying I knew f'' was imaginary,
the absorption term, and always needs to be 90 degrees in phase
ahead of the f' (dispersive component).
So here is what I think the answer to my question is, if I
understood everyone correctly:
Starting with what everyone I guess thought I was asking,
FA = FN + F'A + iF"A (vector addition)
for an absorbing atom at the origin, FN (the standard atomic
scattering factor component) is purely real, and the f' dispersive
term is purely real, and the f" absorption term is purely imaginary
(and 90 degrees ahead).
Displacement from the origin rotates the resultant vector FA in the
complex plane. That implies each component in the vector summation
is rotated by that same phase angle, since their magnitudes aren't
changed from displacement from the origin, and F" must still be
perpendicular to F'. Hence the absorption term F" is no longer
pointed in the imaginary axis direction.
Put slightly differently, the fundamental requirement is that the
positive 90 degree angle between f' and f" must always be
maintained, but their absolute orientations are only enforced for
atoms at the origin.
Please correct me if this is wrong.
Also, since F" then has a projection upon the real axis, it now has
a real component (and I guess this is also an explanation for why
you don't get this with centrosymmetric structures).
Thanks again for everyone's help.
-- Bill
William G. Scott
Professor
Department of Chemistry and Biochemistry
and The Center for the Molecular Biology of RNA
228 Sinsheimer Laboratories
University of California at Santa Cruz
Santa Cruz, California 95064
USA
phone: +1-831-459-5367 (office)
+1-831-459-5292 (lab)
fax: +1-831-4593139 (fax)
Lijun Liu
Cardiovascular Research Institute
University of California, San Francisco
1700 4th Street, Box 2532
San Francisco, CA 94158
Phone: (415)514-2836