[Ifeffit] Double crystal monochromator

Matthew mamarcus at lbl.gov
Fri Dec 4 13:22:24 CST 2009

Following up on Matt's following up on my answer:
Let's pretend that the Darwin curve is a simple rectangle, reflectivity=1 within the Darwin band and 0 outside.  Now consider a 
given energy, with the source having a wide angular
distribution.  The first crystal will select a range of angles to reflect.  Now, if the second crystal is exactly parallel to the 
first, it will reflect all of the rays.  If it's off by the Darwin width, then it will reflect none.
In between, the range of angles the two crystals have in common will be linearly related to the angular offset, so that the rocking 
curve of the one with respect to the other will be a triangle.  Now, at other energies, the
same thing happens, so with a white incident beam, you still get a triangle.
A useful tool for visualizing this is the Dumand diagram, which is a plot of angle vs. wavelength or energy.  The passband of a 
single crystal is a curve with a width to it (Darwin width).  For the
non-dispersive case (common in monochromators) the curves for the two crystals are parallel and offset in the angle direction by the 
angular offset.  The transmission of the system is proportional to the overlap
area of the two curves.  Books on X-ray diffraction should have examples of these diagrams, which will make it clearer than I can do 
with words alone.
----- Original Message ----- 
From: "Matt Newville" <newville at cars.uchicago.edu>
To: "XAFS Analysis using Ifeffit" <ifeffit at millenia.cars.aps.anl.gov>
Sent: Friday, December 04, 2009 10:53 AM
Subject: Re: [Ifeffit] Double crystal monochromator

> Just to follow up a little on Matthew's answer:
> The Darwin width is the angular width over which a particular
> reflection will diffract.   A rocking curve measurement usually leaves
> one crystal at a fixed angle and rotates the second crystal.   For a
> perfectly collimated beam, the resulting intensity would be a
> convolution of the two Darwin widths.
> In addition, real x-ray sources have a finite angular spread of the
> incident beam, so that the rocking curve profile is further blurred.
> For bending magnet beamlines on older sources, the angular spread of
> the source can dominate the rocking curve.  Many such sources use a
> collimating mirror before the monochromator in order to reduce the
> angular spread of the beam on the monochromator.
> In most cases, both contributions (natural Darwin width of the
> reflection and angular spread of the source) need to be included to
> get an accurate rocking curve.
> --Matt
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