Bragg diffraction - How to make sense of it ?

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Bragg diffraction - How to make sense of it ??

Is there a way to make sense of Diffraction of X Rays without taking recourse to oversimplified concepts like "Reflection of X Rays by parallel planes" which is generally the explanation in most basic physics books. It's been a couple years since I first studied it and i continue to get confused by assertions like reflecting of Photons by atoms. Online sources are also full of it :

http://www-outreach.phy.cam.ac.uk/camphy/xraydiffraction/xraydiffraction7_1.htm
OR
http://chemwiki.ucdavis.edu/Analytical_Chemistry/Instrumental_Analysis/Diffraction/Bragg's_Law
 
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You can start with the Laue equations, which are derived from interference principles used in gratings, and derive the Bragg equation from them: http://www.phys.utk.edu/courses/Fall%202009/physics671/chapter1c.pdf

Or you can start with the fully quantum mechanical Bloch theorem and derive the Bragg equation:
http://www.uni-tuebingen.de/meso/ssscript/blochelectrons.pdf

But the Bragg equation is very simple, and very accurate, so I have used it extensively in my electron diffraction work.
 
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I get that. But, is there a way to explain things without relying on mathematical formalism. I mean a general discussion on the physical mechanism.
 
M Quack said:
This article by P. P. Ewald, one of the founding fathers of x-ray diffraction, give an excellent overview without excessive math.

http://rmp.aps.org/abstract/RMP/v37/i1/p46_1

Thanks for the link. If you have access, could you pls give me the pdf ?