On Thursday, October 14, 2010 01:18:04 pm Bart Hazes wrote:
>
> On 10-10-14 01:34 PM, Ethan Merritt wrote:
>
>
> ...
>
> The contribution from normal scattering, f0, is strong at low resolution
> but becomes weaker as the scattering angle increases.
> The contribution from anomalous scattering, f' + f", is constant at
> all scattering angles.
>
> ...
> My simple/simplistic mental picture for this is that electrons form a cloud
> surrounding the atom's nucleus. The larger the diameter of the cloud the
> more strongly the atomic scattering factor decreases with resolution (just
> like increased B-factors spread out the electrons and reduce scattering).
>
> Anomalous scattering is based on the inner electron orbitals that are much
> closer to the nucleus and thus their scattering declines more slowly with
> resolution. By this reasoning f' and f" would still decline with resolution
> but perhaps the difference is so substantial that within the resolution
> ranges we work with they can be considered constant.
I don't trust my intuition as things start getting quantum mechanical.
A detailed theoretical treatment and summary of earlier results is given in
Acta Cryst. (1997). A53, 7-14 [ doi:10.1107/S0108767396009609 ]
Investigation of the Angle Dependence of the Photon-Atom Anomalous Scattering
Factors
P. M. Bergstrom Jnr, L. Kissel, R. H. Pratt and A. Costescu
To the extent that I dare attempt a summary, my understanding of this analysis
is:
At energies near the absortion edge in question the anomalous scattering is
essentially independent of angle. At much higher energies this breaks down,
but even at these higher energies the deviation is not substantial for
scattering angles less than ~60 degrees.
Ethan
> By the same reasoning you'd expect neutron diffraction to have scattering
> factors that are for all practical purposes independent of resolution,
> assuming b-factors of zero.
>
> In addition, the different fall-off in the scattering factors for f0 and f'
> or f" will be much less noticeable for anomalous scatters with high B-values
> where the latter dominates the 3D distribution of the electrons.
>
> Bart
>
--
Ethan A Merritt
Biomolecular Structure Center, K-428 Health Sciences Bldg
University of Washington, Seattle 98195-7742
