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 +61 (0) 417 554 935 mobile FAX +61 3 9562 8919 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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