The prefix "para-" has several definitions, one of which is "abnormal, 
incorrect" or "resembling". I assumed this prefix was used because BB geometry 
uses the focusing condition but is not truly a focusing geometry: The 
diffractometer circle and focusing circle being different causes the focusing 
circle (the circle on which the source, sample and detector lie) to effectively 
become smaller as a function of increasing 2-theta.

I didn't think the sample flatness had so much to do with it, because even if 
you define the sample to be infinitely small (or curved) you will still change 
the radius of the focusing circle with changing 2-theta.


jools


From: rietveld_l-requ...@ill.fr [mailto:rietveld_l-requ...@ill.fr] On Behalf Of 
ian.mad...@csiro.au
Sent: 2. mai 2016 10:06
To: rietveld_l@ill.fr; rowle...@gmail.com
Subject: Re: Parafocussing definition?


Hi Matthew,



I've got some nice figures from an old XRD Basics presentation from decades ago 
- the problem is that all this stuff is in my CSIRO office and I'm at home!



However, I will do my best to recall the basic principles of parafocusing In a 
Bragg-Brentano instrument:-

  1.  The source (tube target) and receiving slit are both on the 
diffractometer circle (not to be confused with the focusing circle) and are 
equidistant from the diffractometer (rotation) axis.
  2.  The beam is divergent (strictly speaking, a parallel beam instrument is 
not Bragg-Brentano geometry).
  3.  The sample is an extended flat plate.
  4.  The centre line of the incident beam will strike the sample at the centre 
of the diffractometer rotation axis (assuming the instrument is well aligned 
and the sample properly presented - not always a given!) at some angle theta. 
This beam will diffract from crystal planes parallel to the surface to the 
receiving slit also at an angle theta (yippee - theta + theta = 2theta - I'm a 
maths wiz)
  5.  The lower extremity of the diverging incident beam will strike the sample 
on the tube side of the diffractometer rotation axis at some angle (theta + 
phi). Now (and this is where the magic comes in) this beam will diffract from 
planes rotated phi degrees to the surface - for the same reflection as in 4. 
above, this means that the diffracted beam now makes an angle of (theta - phi) 
to the surface. Now (theta + phi) + (theta - phi) = 2theta - still amazing.
  6.  The upper extremity of the diverging incident beam will strike the sample 
on the detector side of the diffractometer rotation axis ... follow reasoning 
above for planes rotated -phi with respect to the sample surface.
  7.  This works because (this is the important bit) within a circle equal arcs 
make equal angles - a simple ray tracing diagram will help here.
  8.  Part of the reason Bragg-Brentano instruments have good intensity is due 
to the fact that the diverging beam will diffract from a wider range of 
crystallite orientations than say a parallel beam instrument.
  9.  There is no true 'focusing' of the X-ray beam in this context - the 
apparent focusing is happening because of 4 - 6 above in the context of 
diverging beams.
  10. I don't think that flat vs curved sample needs to come into this 
explanation.

I hope this helps.

​


Cheers



o----------------------------oo0oo----------------------------o

     Ian Madsen
     Honorary Fellow
     CSIRO Mineral Resources Flagship
     Private Bag 10,  Clayton South 3169
     Victoria,   AUSTRALIA
     Phone +61 3 9545 8785 direct
                 +61 3 9545 8500 switch
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     Email ian.mad...@csiro.au<mailto:ian.mad...@csiro.au>

o----------------------------oo0oo----------------------------o
________________________________
From: rietveld_l-requ...@ill.fr<mailto:rietveld_l-requ...@ill.fr> 
<rietveld_l-requ...@ill.fr<mailto:rietveld_l-requ...@ill.fr>> on behalf of 
Matthew Rowles <rowle...@gmail.com<mailto:rowle...@gmail.com>>
Sent: Monday, May 2, 2016 3:52 PM
To: RIETVELD_L Distribution List
Subject: Parafocussing definition?

Hi all

I've been trying to find a good explanation of what parafocussing (wrt 
Bragg-Brentato geometry) actually is, but haven't been able to find one.

Klug and Alexander just reference Brentano's papers.

"The Basics of Crystallography and Diffraction" 2nd ed say that B-B geometry is 
"semi-focussing" because the sample is flat, and not curved to follow the 
focussing circle (this doesn't sound right to me)

Brentano, J Appl. Phys. 17, 420 (1946) says that a ray reflecting off the arc 
defined by ACB where A is the source, C is the centre of the gonio, and B is 
the detector (ie the focussing circle)  is automatically parafocussing, because 
you only can establish the location of the crystallites, not their orientation, 
but then goes on to say that you can actually find the orientation, as the 
lattice plane normal bisects the angle ACB.

I also haven't been able to find a use of the word "parafocus" outside of the 
diffraction literature, so I can't see how the word is used elsewhere.

Any ideas?


Matthew
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