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From: "Hyatt, Neil" [NHyatt@lsm.co.uk] To: "'firstname.lastname@example.org'" [email@example.com] Subject: Resolution in powder diffraction Date: Fri, 11 May 2001 10:04:57 +0100 Dear All, The resolution of a diffractometer is often quoted in terms of "delta d / d" or as full-width-at-half-height (FWHM, on the two-theta scale). The concept of FWHM is fairly easy to understand and visualise - but I'm having trouble grasping the concept of what "delta d / d" means in physical terms. What I would like to know is: 1. How is "delta d / d" formally defined (an equation would help here!) - I guess it arsies somehow from differentiating Braggs Law? 2. When a value of "delta d / d" is quoted in the literature, is this conventionally taken to be the best achievable resolution for a given diffractometer set-up? 3. Is there an "accepted" way of measuring resolution? I guess the answer here is to use a suitable "standard" specimen with a known or "zero" reflection broadening component arising from crystallite stress / strain etc. Finally, am I right in thinking that talking about resolution in terms of "delta d / d" rather than FWHM is advantageous since it allows a relative comparison of the resolution afforded by different techniques, e.g. time-of-flight neutron vs. constant wavelength X-ray? I'd be really grateful to hear from anyone with thoughts on this issue. All the best, Neil Hyatt.
Date: Fri, 11 May 2001 13:11:47 -0400 From: "Brian H. Toby" [Brian.Toby@nist.gov] Organization: NIST Center for Neutron Research To: firstname.lastname@example.org Dear Neil & others, Instrumental resolution is best expressed (IMHO) as FWHM(Q) vs Q (see for example http://www.ncnr.nist.gov/xtal/bt1_for_physicists.html), where Q=2pi/d; not in 2theta because 2theta is dependent on wavelength and thus cannot be compared between techniques and not d-space because that overemphasizes the low Q (low angle) portion of the pattern which has minor leverage on most results and further is where one rarely needs to worry about optimizing instrumental resolution.
Date: Mon, 14 May 2001 11:57:28 +0200 To: email@example.com From: Jonathan WRIGHT (firstname.lastname@example.org) Subject: Re: Resolution in powder diffraction Brian H. Toby wrote: > ... <SOAPBOX}Besides, Q > is the Fourier conjugate of x (the coordinates); d-spaces have no > physical significance. D-spaces can mislead a novice into correlating > reciprocal space distances with real space distances.</SOAPBOX> D-spacings are distances between lattice planes and provide me at least with a nice physical picture of Bragg's law. In this way I guess I am correlating real space distances with reciprocal space distances, but I think I prefer remain a novice than give up what little understanding I have :) >and thus cannot be compared between techniques and not d-space because >that overemphasizes the low Q (low angle) portion of the pattern which >has minor leverage on most results and further is where one rarely needs >to worry about optimizing instrumental resolution. High resolution at low Q is handy for indexing, and is essential for tackling moderately complex magnetic structures with powder neutron data. ToF diffractometers which use slow neutrons (eg OSIRIS at ISIS) appear to be doing particularly well for resolution in the d=3-10 Angstrom region (I hope we eventually see such machines at SNS and ESS). Peak broadening effects and splittings can be easier to interpret where there is less peak overlap, so high resolution in this range can again be useful. It's a question of applying the right instrument or setup to the particular problem in mind. >In the plot on my web page, low angle asymmetry is subtracted out -- but it >should not be. For very short wavelength machines, the asymmetry can be >severe for the bulk of the pattern. There are a lot of different trade offs to take into account when choosing a wavelength, with x-rays at least. If low angle asymmetry is a problem for the experiment in question then you can use a small beam on sample and/or narrower receiving slits. My recent experience at ESRF is that a lot of the asymmetry can be removed without destroying the count rate even with a large unit cell and fairly hard x-rays. (nb. removed by slits, not deconvolution) For ToF neutrons the moderator asymmetry is less dominant as ToF increases, and this is where the resolution is maximised anyway. It can be fitted very well with the right programs and the advantages of going to very low d-spacings (high Q) also has to be taken into account. Comparing resolution functions only tells part of the story, the real question is how much information did you gain from the experiment. This can depend on a lot of other factors, not least background, Q-range and count rate which are rarely compared in quite the same way. Remember the sample can still ruin the background and the resolution regardless of the instrument :) Cheers, Jon