[nigel433]

The picture in my text-book "explaining" the pattern of light and dark
at the receptor surface, as being the result of interference shows a
SINGLE wave-front impinging on the plane of scatterers IN PHASE.

But surely there are a large number of photons in a beam of X-rays,
which are never going to be in phase with each other. Why don't
they all simply overlap each other with no observable differentiation?

[Grundalizer]

I'm guessing the machine they use goes out of it's way to keep the photons in-phase.

[cth]

But surely there are a large number of photons in a beam of X-rays,
which are never going to be in phase with each other.

Why do you say that? The X-ray bean is monochromatic, or else there would be diffraction peaks from different wavelengths all over the place making data analysis impossible.

X-rays are generated by a beam of electrons that hit a piece of metal (usually copper or molybdenum). The resulting X-rays have the following profile (see http://www.gly.uga.edu/schroeder/geol3010/3010lecture09.html for more details):
 

The beam passes through a filter made from a metal with just lower atomic number than the one used to produce the X-rays (for example, nickel filter when the generator is copper). It absorbs most of the blank and K_β radiations while letting through enough K_α radiations to be useful.

[Grundalizer]

Well then I think that page has the answer.  If most of the electrons basically die out and give a weak signal because they hit the outer electrons and slow down, then you are only left with those really strong repulsed electrons that "bounce off" the crystal structure at certain angles. 

Mind you, I know absolutely nothing about X-ray crystalography accept the pictures I have seen in the textbooks, but I can draw a picture in my mind that may explain it. 

Say you have a door that is tilted at an angle in front of you, 45 degrees.  If you have a bucket of baseballs and start throwing them at the door, they will mostly all bounce off and go in the same direction.  Yes, many will slow down, some will go slightly higher or lower than others, but they will all have the same trajectory leaving that door, basically like the angle of incidence = angle of reflection.  If you have trillions of electrons bouncing off in the same direction with about the same amount of energy, I'd think you get those really bright bands we see so often in X-ray crystal pics. 

I don't think you get the crystal structure from where electron waves had constructive or destructive interference like in the double slit experiment, I think you get them because that is where the most electrons are accumulating and bouncing too. 

I view electrons as particles in this particular case, although an in depth discussion about how x-ray crystalography reveals the wave-particle nature of matter would be of interest if there is anything out there about that.  My school has poor inorganic labs, as I think most others do....ive never heard of an inorganic lab class

[nigel433]

Thank you.

I did not know about the filter to remove the bremsstrahlung radiation.

That makes it monochromatic, all right.

But still not a point source, or in phase, eh? X-ray diffraction
was in use before Lasers were invented.

It may be that one CAN talk about a single photon being scattered
by many electrons and interering with itself, but that certainly raises
many questions.

[cth]

Yes, the X-ray beam is monochromatic enough to be useful. The little blank and K_β radiations remaining can be accounted for by doing a background measurement without any crystal and subtracting it from the diffraction patterns. It limits as well the effects from local and interstellar radiations that could lower the quality of data collected.

The X-ray beam is made parallel by using a collimator. Although it is not perfect, you can consider it as a point source. Afterwards, crystallographic softwares try to attenuate that problem by taking into account the divergence and width of the beam, the crystal size and crystal content (heavy elements absorb more X-rays than light ones) by doing different corrections.

But still not a point source, or in phase, eh? X-ray diffraction
was in use before Lasers were invented.

It may be that one CAN talk about a single photon being scattered
by many electrons and interering with itself, but that certainly raises
many questions.

The question about the phase is very interesting. There is nothing to make the X-ray beam in phase, as it is something we can't do with nowadays technologies. So logically the beam is not in phase.
The simplest way to understand the diffraction phenomenon is by considering photons as a wave (which they are as well as particles), so each photon is widespread in space and it interacts with both atoms. You can picture it as a wave formed when a rock hits a water surface: it forms circles over large surface area. When the photon interacts with both atoms, it is diffracted in all directions. It then interferes with itself to form diffraction patterns.
Diffraction is a wavelike phenomenon that can't happen with particles. So when photons or electrons form diffraction patterns, it is because they have a wave nature as well as a particle one.

[nigel433]

cth, I think, is basically agreeing with me.

Of course this means the textbooks are WRONG to
talk about waves or rays being in phase with each
other if there is only one wave at a time, to discuss.

If we can say that each photon acts AS IF it is a wave
interering with itself, and the effects of many photons
accumulate to produce a pattern on a macroscopic scale...
then that is just barely acceptable as a PRELIMINARY step
to true understanding. Of course we have been stuck at this
stage of pseudo-explanation/waffle  for a hundred years now!
As Richard Feynman said :

 "Don't imagine for a second that anybody understands anything
 about quantum mechanics. I certainly don't."

The photon seems a bit like the cartoon cat Jerry who is chopped
to pieces by Tom, falls in a heap on the ground, and then
immediately reassembles. Only there are quadsquillions of them!

[nigel433]

Whoops... Tom is the cat and Jerry is the mouse...or perhaps this
is also turned around in the quantum world?

[nigel433]

I thinl Laue diffraction uses white X-rays?

[cth]

I thinl Laue diffraction uses white X-rays?

White X-rays are not used in daily crystallography, and in crystallographic labs you don't find tunable polychromatic X-ray sources.
The wavelength is determined by the energy of K_α of the metal used in the X-ray generator, and you can't change it easily.

The standard setup is such that it is the crystal that rotate while the X-ray wavelength stays fixed, by opposition to a possible setup where a crystal doesn't move and it is the X-ray beam wavelength that changes continuously.