Am 20:59, schrieb James Holton: ...
The loss of the 1/r^2 term arises because diffraction from a crystal is "compressed" into very sharp peaks. That is, as the crystal gets larger, the interference fringes (spots) get smaller, but the total number of scattered photons must remain constant. The photons/area at the tippy-top of this "transform-limited peak" is (theoretically) very large, but difficult to measure directly as it only exists over an exquisitely tiny solid angle at a very precise "still" crystal orientation. In real experiments, one does not see this transform-limited peak intensity because it is "blurred" by other effects, like the finite size of a pixel (usually very much larger than the peak), the detector point-spread function, the mosaicity of the crystal, unit cell inhomogeneity (Nave disorder) and the spread of angles in the incident beam (often called "divergence" or "crossfire"). It is this last effect that often tricks people into thinking that spot intensity falls off with 1/r. However, if you do the experiment of chopping down the beam to a very low divergence, choosing a wavelength where air absorption is negligible, and then measuring the same diffraction spot at several different detector distances you really do find that the pixel intensity is the same: independent of distance.
... Hi James, as always, I enjoy your explanations a lot.Just one minor point - I would not quite agree that the solid angle of a reflection is _that_ exquisitely small, even in the absence of finite pixel size, mosaicity, unit cell inhomogeneity and crossfire (wavelength dispersion could be added to the list of non-ideal conditions).
In fact a crystal is composed of mosaic blocks (size roughly 1 um, maybe bigger for some space-grown crystals), and the coherence length is (taking numbers from Bernhard) several 0.1 um to several 10 um.
Thus, if we assume a wavelength of 1A, then the angle arising from the finite size of the mosaic-block-and-coherence-length-combined is on the order of 1A/1um, which at 100mm distance means a width of about 0.1mm - the size of a typical detector pixel.
(It follows that if we build detectors with much smaller pixels than 0.1mm this won't help much in increasing the signal/noise ratio; in particular, it won't help to measure data from tiny crystals unless these are single mosaic blocks.)
best, Kay
smime.p7s
Description: S/MIME Cryptographic Signature
