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Adding to what James wrote: I see this as follows:

Bragg's law is only a necessary but not a sufficient criterion for
occurrence of a diffraction peak if viewed as a reflection. The problem imho
comes from not considering the structure factor as the actual quantifier of
(single photon) diffraction. Take for example the reflection condition rules
for I centered cells: Sum of  the three reflection indices all even. 111 333
missing but 222 is there...

The problem does not arise if you treat the diffraction pattern as a
probability distribution where the intensities are proportional to the
(Square of) the structure factors which includes the hkls and thus
automatically and necessarily the Bragg ns. Taking the simple 2-wave Bragg
reflection picture verbatim does not do justice to the diffraction process
(e.g. the non-coherence between incoming photons and necessity for a single
photon process have been discussed here before). James has already suggested
a few historic reasons.

Best, BR

-----Original Message-----
From: CCP4 bulletin board [mailto:[log in to unmask]] On Behalf Of Dom
Bellini
Sent: Dienstag, 20. August 2013 16:49
To: [log in to unmask]
Subject: Re: [ccp4bb] Dependency of theta on n/d in Bragg's law

Dear Pietro,

Ladd & Palmer book does explain it, just first example that springs to mind.

HTH

D

-----Original Message-----
From: CCP4 bulletin board [mailto:[log in to unmask]] On Behalf Of Pietro
Roversi
Sent: 20 August 2013 15:37
To: ccp4bb
Subject: [ccp4bb] Dependency of theta on n/d in Bragg's law

Dear all,

I am shocked by my own ignorance, and you feel free to do the same, but do
you agree with me that according to Bragg's Law a diffraction maximum at an
angle theta has contributions to its intensity from planes at a spacing d
for order 1, planes of spacing 2*d for order n=2, etc. etc.?

In other words as the diffraction angle is a function of n/d:

theta=arcsin(lambda/2 * n/d)

several indices are associated with diffraction at the same angle?

(I guess one could also prove the same result by a number of Ewald
constructions using Ewald spheres of radius (1/n*lambda with n=1,2,3 ...)

All textbooks I know on the argument neglect to mention this and in fact
only n=1 is ever considered.

Does anybody know a book where this trivial issue is discussed?

Thanks!

Ciao

Pietro



Sent from my Desktop

Dr. Pietro Roversi
Oxford University Biochemistry Department - Glycobiology Division South
Parks Road Oxford OX1 3QU England - UK Tel. 0044 1865 275339



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