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Bragg's Law in Crystallography 
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#1
Jan1013, 06:06 PM

P: 41

I took a course on protein crystallography last year and there's one thing I couldn't figure out then, and still can't figure out now. My understanding of Bragg's law hinges on the fact that inphase scattered waves constructively interfere, and the requirement to be inphase is met only when the extra distance traveled is an integral multiple of the photon's wavelength. With this premise and a diagram of two atoms scattering a photon, it becomes apparent that nλ = 2dsin(θ).
What I don't understand is why only maximalintensity waves are observed. Unless the two waves are π radians out of phase, there should still be some constructive interference that gives rise to amplitude at the detector plate. Therefore, there should be some intensity at almost any value of θ. The wikipedia page on Bragg's law acknowledges this fact: Thanks for any help! 


#2
Jan1113, 01:55 AM

Sci Advisor
P: 3,595

If there is a phase shift ##\phi## between rays reflected on adjacent planes (distance d) then there will be a phase difference ##n\phi## between planes with distance nd.
Hence if there are many planes you will observe constructive interference between all the reflected waves only if ##\phi< n/N## where N is the total number of planes in the crystal, i.e. D/d, where D is the diameter of the crystal (or better that of domains in the crystal). As D is many orders of magnitude larger than d, you get very sharp reflections. 


#3
Jan1413, 04:33 PM

P: 41

I might be extremely obtuse but I still don't get it. I drew a picture to visualize what you're saying:
Unfortunately, I don't see the relationship between Sorry again if I'm being stupid; I just don't see it clearly yet. 


#4
Jan1513, 01:59 AM

Sci Advisor
P: 3,595

Bragg's Law in Crystallography
First I wonder why you are asking this question in the biology forum and not in the general physics forum where you could calculate with much more answers.
Now to your question. The fields of the reflected waves sum up to the total field whose square is proportional to the intensity. Now this sum is something like ##E=E_0\sum_{j=N/2}^{N/2} \sin(2jd\sin(\theta)/\lambda)##. The latter sum can be calculated exactly. The point is that it will be nearly zero as long as ##2d\sin(\theta)/\lambda## is not a multiple of 2π because only for this value all ##\sin(2jd\sin(\theta)/\lambda)=1## and no two planes will interfere destructively. 


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