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