marc.schi...@epfl.ch wrote:
The elastically scattered photons (which make up the Bragg peaks) also
do not not retain the momentum of the incident photon.
Although technically true to say that photons traveling in different
directions have different momenta, all elastically scattered photons
have the same wavelength (momentum) as the incident photon. Otherwise,
they would not interfere constructively to form Bragg peaks and they
would be called Compton-scattered photons. The small change in energy
required to preserve wavelength upon a change in direction during
elastic scattering is contributed by the entire crystal as a "recoil"
phonon. Arthur Compton wrote a paper about this:
http://www.pnas.org/cgi/reprint/9/11/359.pdf
which probably contributed to his Nobel four years later. This is a
classic example of the confusion that can arise from the particle-wave
duality.
Fluorescent x-rays have a VERY different wavelength from the incident
beam and therefore cannot interact coherently with Bragg-scattered
photons, so they contribute to nothing but background. Fluorescence is
also a true absorption-reemission process, and must occur from one atom
at a time. The "core hole lifetime" before emission occurs is small,
but there is still a "random delay" before the fluorescent photon is
emitted. This means there is essentially no interference between
fluorescence events from different atoms. Scattering, on the other
hand, occurs from every atom in the crystal simultaneously for each
incident photon, and this is why we see interference.
-James Holton
MAD Scientist
