Dear Pietro, The n in Bragg's Law is indeed most interesting for teachers and a most delicate matter for those enquiring about it.
The diffraction grating equation, from which W L Bragg got the idea, a 'cheap accolade' he said to have it named after him in his Scientific American article, has each order at its own specific theta. n=1 at one angle, n=2 the next order of diffraction at higher angle, n=3 the next order at higher angle still and so on. This is how physicists usually first meet the effect and use monochromatic laser light and a periodically ruled, line, grating to see the laser diffraction pattern in the modern physics teaching labs. In crystal structure analysis the ruled line of the above is now the unit cell of the crystal and the contents are of chemical and biological interest, unlike the inside of a ruled line! Thus the switch to using lamba = 2d sin theta form of the equation and the n subsumed into the interplanar spacing. d=1 is the unit cell edge, d/2 half the unit cell and so on. Each has its own reflection intensity. The highest resolution molecular detail we get of the insides of the unit cell arising from the highest n diffraction reflection with a 'measurable' intensity. The use of polychromatic light, or white X-rays, we need not consider just now. Suffice to say at this point that, eg historically, the W H Bragg X-ray spectrometer provided monochromatic X-rays to illuminate a single crystal and so, as his son W L Bragg put it, immediately enabled a clear and more powerful analysis of crystal structure and thereby allowed the first detailed atomic X-ray crystal structure, sodium chloride, to be resolved. Several other Xray crystal structures immediately followed from the Braggs, using the Xray spectrometer, before 1914 ie when the Great War pretty much put all basic research and development 'on hold'. When one does come to the question of 'Laue diffraction' the so called multiplicity distribution of Bragg reflections in Laue pattern spots has been treated in detail by Cruickshank et al 1987 Acta Cryst A, as pointed out by Tim. Prime numbers are pivotal to the analysis, as James pointed out. Best wishes, John Prof John R Helliwell DSc FInstP CPhys FRSC CChem F Soc Biol. Chair School of Chemistry, University of Manchester, Athena Swan Team. http://www.chemistry.manchester.ac.uk/aboutus/athena/index.html On 20 Aug 2013, at 15:36, Pietro Roversi <pietro.rove...@bioch.ox.ac.uk> wrote: > 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
