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)
