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.
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 sounds pretty much like your explanation, but I have the impression that we
have different notions of the sources of effects. 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").
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).
Cheers, Tim
On Wed, Oct 13, 2010 at 01:58:56PM -0700, William Scott wrote:
> 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)
--
--
Tim Gruene
Institut fuer anorganische Chemie
Tammannstr. 4
D-37077 Goettingen
phone: +49 (0)551 39 22149
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