-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Hi Ed,
your explanation E = rho(r)exp(2pi i (wt - r.S)) is nearly correct, as Blundell and Johnson are nearly correct. In Physics any function f(x,y,z,t) depending on three coordinates and time that can be expressed such that f(x,y,z,t) = f(\vec k.\vec x - \omega t) is a wave. In books on electrodynamics I often find the time dependency \omega t dropped, which you had to put back in. The reason for its dropping is probably that the time variation of the wave is only a mathematical concept in order to explain interference, but not a physical one: the intensity is the mean over time, i.e. an idealised light source does not flicker. So in your above equation you must replace S with k to get a spherical wave. Once you take the Laue equations into account, i.e. you realise your single scatterer is member of a crystal, you do not need to measure the scattered wave in all directions around the crystal but only in the directions governed by the Laue equations. Then you can replace k with S and find spots on your detector. Regards, Tim P.S.: complex numbers together with the operation '+' defined in the canonical way fulfill the axioms of a vector space, hence complex number are vectors. If you also take the operation '*' into account, defined in the canonical way, (C, +, *) fulfills the axioms of a field, which is an algebra, but not a vector space. So it depends on your point of you, just like with photons and their interpretation as waves or as particles: pick what suits you best depending on what you want to describe. On 04/02/2014 04:39 AM, Edward A. Berry wrote: > Encouraged by recent help from the BB in filling in gaps in my > understanding, maybe I can get help with another question: > > At the top of page 121 in Blundell and Johnson, it is written: > > "The total wave scattered by a small unit of volume dv at a > position r relative to the wave scattered from the origin will > therefore have an amplitude proportional to Rho(r)dv and phase 2Pi > i(r.S)dv" (OK so far) "i.e. wave scattered = Rho(r)exp(2Pi i > r.S)dv" > > How is that a wave? r and S are constant vectors. > > My best explanation so far is to say this is a complex coefficient > that will adjust the weight and phase of the wave scattered by > this point. > > Say the wave scattered from one electron at the origin will result > in a temporal cosine wave at the surface of the detector: > > E = exp(2Pi i wt) = cos(2Pi wt) > > (not sure if 2Pi is needed when w is radians/sec) > > Then the wave at the same point, scattered by dv at r, would be the > same multiplied by the quantity in question: > > E = rho(r)exp(2Pi i r.s)dv * exp(2pi i wt) = rho(r)exp(2pi i (wt - > r.S)) > > i.e. phase-shifted by 2Pi (r.S), and multiplied by Rho(r)dv > > Is that more or less it? > > (since these quantities add up to the Structure Factor F(s), I > guess I'm really asking what a structure factor is. Rupp says a > structure fator is a vector "representing" the diffracted X-rays", > which i take to be consistent with this if vector is in the > complex plane) > - -- - -- Dr Tim Gruene Institut fuer anorganische Chemie Tammannstr. 4 D-37077 Goettingen GPG Key ID = A46BEE1A -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.12 (GNU/Linux) Comment: Using GnuPG with Icedove - http://www.enigmail.net/ iD8DBQFTO/kvUxlJ7aRr7hoRAv0qAJ9Krez739lar2pPjqH+TU7bc2dTUwCfVKuy r9tLusH4fWiUSpwzczaavEU= =Uq/X -----END PGP SIGNATURE-----
