On 22 August 2013 07:54, James Holton <jmhol...@lbl.gov> wrote: > Well, yes, but that's something of an anachronism. Technically, a > "Miller index" of h,k,l can only be a triplet of prime numbers (Miller, W. > (1839). A treatise on crystallography. For J. & JJ Deighton.). This is > because Miller was trying to explain crystal facets, and facets don't have > "harmonics". This might be why Bragg decided to put an "n" in there. But > it seems that fairly rapidly after people starting diffracting x-rays off > of crystals, the "Miller Index" became generalized to h,k,l as integers, > and we never looked back. >
Yes but I think it would be a pity if we lost IMO the important distinction in meaning between "Miller indices" as defined above as co-prime integers and (for want of a better term) "reflection indices" as found in an MTZ file. For example, Stout & Jensen makes a careful distinction between them (as I recall they call "reflection indices" something like "general indices": sorry I don't have my copy of S & J to hand to check their exact terminology). The confusion that can arise by referring to "reflection indices" as "Miller indices" is well illustrated if you try to explain Bragg's equation to a novice, because the "d" in the equation (i.e. "n lambda = 2d sin[theta]") is the interplanar separation for planes as calculated from their Miller indices, whereas the "theta" is of course the theta angle as calculated from the corresponding reflection indices. If you say that Miller & reflection indices are the same thing you have a hard time explaining the equation! One obvious way out of the dilemma is to drop the "n" term (so now "lambda = 2d sin[theta]") and then redefine d as d/n so the new d is calculated from the same reflection indices as theta, and the Miller indices don't enter into it. But then you have to explain to your novice why you know better than a Nobel prizewinner! As you say Bragg no doubt had a good reason to include the "n" (i.e. to make the connection between the macroscopic properties of a crystal and its diffraction pattern). Sorry for coming into this discussion somewhat late! Cheers -- Ian
