Re: [RE: Combined neutron/x-ray refinements]
If we have an atom that is seen by one radiation and not by the other there will be a degradation in the quality of the parameters by combining the refinement in the current fashion. Do you mean for example that we might degrade the parameters of a V atom by introducing neutron data ? I don't think this is true, but it is an interesting question. If we were to extrapolate this argument "ad absurdum" we could say that because some reflections (for a given radiation) do not give any information about some parameters (easy to demonstrate) then we would obtain better estimates for those parameters by removing those reflections from the least squares process. (Surely untrue :-) What is true is that if we introduce systematic errors by combining radiations, we may indeed degrade the result. For example if we have serious preferred orientation with a very small X-ray sample, it is probably unwise to introduce this biased information into the refinement of the neutron data, where there may be less bias because of the average over a much larger volume. But if the data is not biased, you must always (?) do better by including more data, with for example combined X-ray and neutron refinements. Surely, it would be better to use a new weighting function for the atomic parameters, that is dependent on the scattering lengths for each radiation. Playing around with weighting schemes is to enter dangerous territory. Alan H. Alan Hewat, ILL Grenoble, FRANCE [EMAIL PROTECTED] tel (33) 4.76.20.72.13 ftp://ftp.ill.fr/pub/dif fax (33) 4.76.48.39.06 http://www.ill.fr/dif/
Re: [Re: [RE: Combined neutron/x-ray refinements]]
Alan, I am not suggesting removing reflections. But, I think that we should make sure that we are combining the data in the best possible way. If we know have strong information on a vanadium position from X-rays and (extrapolate again) have only noise from neutrons, then stastically introducing the neutron data whilst no changing the best fit will degrade the least - squares approach to it. The final structure should fit all data, but are we approaching it optimally? I know that this is a can of worms, but it is good to think about what we are doing as combined refinements will continue to become less exotic. -Andrew -- Andrew Wills Centre D'Études Nucléaires de Grenoble "Alan Hewat, ILL Grenoble" [EMAIL PROTECTED] wrote: If we have an atom that is seen by one radiation and not by the other there will be a degradation in the quality of the parameters by combining the refinement in the current fashion. Do you mean for example that we might degrade the parameters of a V atom by introducing neutron data ? I don't think this is true, but it is an interesting question. If we were to extrapolate this argument "ad absurdum" we could say that because some reflections (for a given radiation) do not give any information about some parameters (easy to demonstrate) then we would obtain better estimates for those parameters by removing those reflections from the least squares process. (Surely untrue :-) What is true is that if we introduce systematic errors by combining radiations, we may indeed degrade the result. For example if we have serious preferred orientation with a very small X-ray sample, it is probably unwise to introduce this biased information into the refinement of the neutron data, where there may be less bias because of the average over a much larger volume. But if the data is not biased, you must always (?) do better by including more data, with for example combined X-ray and neutron refinements. Surely, it would be better to use a new weighting function for the atomic parameters, that is dependent on the scattering lengths for each radiation. Playing around with weighting schemes is to enter dangerous territory. Alan H. Alan Hewat, ILL Grenoble, FRANCE [EMAIL PROTECTED] tel (33) 4.76.20.72.13 ftp://ftp.ill.fr/pub/dif fax (33) 4.76.48.39.06 http://www.ill.fr/dif/ Get your own FREE, personal Netscape WebMail account today at http://webmail.netscape.com.
Re: Stress
Hi all, ..following a bit the last posting on the topic... I start to be a little bit concerned about all those people claiming and pointing out that diffraction don't measure a residual stress but a residual strain. .. So, my own idea is that people who don't know how to transform strain in stress will measure only strain and the other are measuring stresses. Let me stress the audience about that; may be is that I am an engineer and not a physicist or chemist. Well, there is nothing wrong being an engineer but I cannot share your concerns. Not to bore the audience, I just claim that you are just short of a few quantities to measure stress directly from a diffraction experiment i.e. of the elastic constants (which one hopes to find conveniently tabulated somewhere and prays that they apply to the material under investigation). in any case it is in principle possible to measure some "elastic constants" using diffraction: it's just a matter of performing an in-situ 3 point bending or tensile or whatever kind of mechanical test on your sample and evaluate the response of the material itself. Since this is rarely possible, tabulated values as you say are the next choice... but they're useful only if you know what kind of grain interaction model is applicable to your particular case. I mean: you find tabulated the single-crystal elastic constants or the macroscopic mechanical elastic constants, but you need the X-ray elastic constants for the polycrystalline under study... you're not measuring all crystallites... you're just sampling some of them. Sometimes (eg the case of thin films, especially if they're textured), having the tabulated values for the single crystal elastic constants and getting a "physically reasonable" stress value are not synonyms! For measuring strain, on the other hand, the diffraction experiment provides all the quantities necessary, you don't even have to know the material. are you really sure?? If you care about relative values I agree, otherwise you need the unstressed lattice spacing I agree on the fact that what you measure is something "easily" related to the interplanar spacing; from that you can "easily" get the integrated relative displacement in the laboratory system (with no "personal assumptions"). What follows is then just a matter of ASSUMING a behavior for the material and modelling. From my point of view it's a huge integral problem, so the solution is not unique... we just need better models As for the fact that someone is able to measure strain and some others are able to measure stresses, well, even if it is impossible to demonstrate that someone knows THE residual stress present in a sample, it's rather easy to prove that different values can be obtained from THE SAME set of measured points. Moreover, if variations of the sin2(psi) method are used, it can be shown even without recurring to Shannon's theorem, that in most cases the result depends also on the sampling in the (psi - 2theta/theta space) Ok ok... this is supposed to be the Rietveld mailing list ;o) oops.. Alan is gonna kill me... well.. but there are some analogies with the Rietveld method... and stress models have already implemented inside it... and well.. at least here neutron and X-ray fans cannot fight ;o) The two techniques are "more complementary each other" than for structure determination... to get more info (surface and bulk)... you need both! Now I'll get a lot of ... ehm on me.. but in this case really X-rays become a "surface" technique and neutrons a "bulk" one... otherwise I'd give anyone a thin film and a 30cm-thick "heavy" sample and ask to get reasonable strain values for both using only one technique! Have fun... Mat PS. In any case better to know the material.. and the instrument: residual macrostrain is not the only source for peak shift! w g( o 0 )g --oOO--(_)---OOo---oOO-w-OOo--- MPI fuer Metallforschung Seestrasse, 92 74170 - Stuttgart (D) Matteo leoni, PhD Department of Materials Engineering University of Trento 38050 Mesiano (TN, Italy) .ooo0 0ooo.Tel +39 461 882417 ( ) ( )Fax +39 461 881977E-mail: [EMAIL PROTECTED] \ (---) /-- \_) (_/ | | | | .ooo0 0ooo. ( ) ( ) \ ( ) /
RE: Combined neutron/x-ray refinements
Jon Wright wrote: I guess the degradation which is found would come from parameters which are determined by both datasets and come out with different values in each separate refinement. Not necessarily. In order to get the ESD, the variance-covariance matrix is multiplied by chi^2, and the roots of the diagonal elements are taken. Therefore, if the chi^2 of the combined refinement is worse than that of the individual ones, the ESD will automatically be worsened. I think this is by far the commonest case. Also, by adding reflections that are insensitive to a given parameter my feeling is that you increase the esd on that parameter even if chi^2=1, but the proof of this is too tedious. Paolo
RE: Combined neutron/x-ray refinements
As chi^2 is a function of the number of data points included in the refinement, combined refinements have considerably improved values for a total chi^2 when compared with refinements carried out against individual data sets. Correspondingly the ESDs in the combined refinement output should be significantly lower than those obtained from a single data set refinement unless there is something drastically wrong with the application of combined refinement to the particular problem (e.g. preferred orientation, surface vs bulk etc). It is my experience that the combined refinement chi^2 is always lower than that obtained from using just (say) the neutron data. We have frequently collected data sets at both room temperature and 5 K using D2b. The room temperature data are refined simultaneously with lab X-ray data to give a chi^2 of 2.02 whilst the D2b data collected at 5 K refined as a single data set gives chi^2 of 4.53 (published in JACS, 1999, 121, 3958-3967). In my experience this improvement in chi^2 is typical. Eddie Cussen Inorganic Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford, OX1 3QR United Kingdom E-mail: [EMAIL PROTECTED] tel: (..44)(0)1865-272602 Fax: (..44)(0)1865-272690 On Tue, 25 May 1999 [EMAIL PROTECTED] wrote: Jon Wright wrote: I guess the degradation which is found would come from parameters which are determined by both datasets and come out with different values in each separate refinement. Not necessarily. In order to get the ESD, the variance-covariance matrix is multiplied by chi^2, and the roots of the diagonal elements are taken. Therefore, if the chi^2 of the combined refinement is worse than that of the individual ones, the ESD will automatically be worsened. I think this is by far the commonest case. Also, by adding reflections that are insensitive to a given parameter my feeling is that you increase the esd on that parameter even if chi^2=1, but the proof of this is too tedious. Paolo
RE: Combined neutron/x-ray refinements
I guess the degradation which is found would come from parameters which are determined by both datasets and come out with different values in each separate refinement. If they come out differently it is because they are differently biased by different systematic errors in the data not described by the model. Not necessarily. In order to get the ESD, the variance-covariance matrix is multiplied by chi^2, and the roots of the diagonal elements are taken. Therefore, if the chi^2 of the combined refinement is worse than that of the individual ones, the ESD will automatically be worsened. You may also get a higher chi^2 with higher resolution data, so does that mean that the structure will be less well determined with hi res data ? I think not, because the correlation between structural parameters should then be smaller - even if you have more points to fit with the same number of parameters, and the peak shapes are less well described by the model. You should similarly do better if you have both X-ray and neutron data (in the absence of bias). Also, by adding reflections that are insensitive to a given parameter my feeling is that you increase the esd on that parameter even if chi^2=1, but the proof of this is too tedious. Tedious and also impossible ? (This sounds like a contradiction in terms) There is no case you can make based on pure statistics or the mathematics of refinement. The only way combined refinement can be worse is if you introduce bias through systematic error (which unfortunately may happen). ... in most cases that the ESD's are underestimated. Mainly because the ESD's are only correctly calculated if the model is CAPABLE of fitting the data. This is not usually true when systematic errors are important compared to statistical errors, since the model is usually not capable of describing these systematic errors fully - background, texture etc... The conclusion is that you should use combined refinements provided that one set of data does not contain important uncorrected systematic errors. Alan Hewat, ILL Grenoble, FRANCE [EMAIL PROTECTED] tel (33) 4.76.20.72.13 ftp://ftp.ill.fr/pub/dif fax (33) 4.76.48.39.06 http://www.ill.fr/dif/
RE: Combined neutron/x-ray refinements
On Tue, 25 May 1999 [EMAIL PROTECTED] wrote: Not necessarily. In order to get the ESD, the variance-covariance matrix is multiplied by chi^2, and the roots of the diagonal elements are taken. The justification for multiplying by chi^2 is to assume that the systematic errors are really just due to overestimated counting statistics and you can rescale the weight of each data point accordingly. A question arises as to whether you should rescale each pattern's esds according to the individual patterns chi^2 or do you have to use the overall chi^2 for both together? Thinking of an (over-determined) D20 data and an (under-determined) lab x-ray data set then it makes sense to rescale errors for the D20 data but not the x-ray (common sense?!). It seems as if the method for calculating the esd's is nonsense - surely one can only justify rescaling the weights on a per dataset basis. The systematic errors which are being accounted for in each dataset are different. Fullprof (multipattern) does give a chi^2 per pattern although I don't know how it gets the esd's, GSAS doesn't so I assume it degrades the esd's. (I read that the multiplication by chi^2 has no basis in statistics anyway :) So is it compulsory to multiply by the overall chi^2? If not then I see no reason for a degradation unless the individual fits get worse due to a disagreement over a parameter. Therefore, if the chi^2 of the combined refinement is worse than that of the individual ones, the ESD will automatically be worsened. I think this is by far the commonest case. Agreed although I'm interpreting it as an odd method for estimating an error. Is it set in stone? Also, by adding reflections that are insensitive to a given parameter my feeling is that you increase the esd on that parameter even if chi^2=1, but the proof of this is too tedious. Can you direct me to a text with this tedious proof? My feeling is that if the derivative of a data point w.r.t a parameter is small or zero then it does not affect the LSQ calculation unless it alters the chi^2. If the chi^2 is 1 then how do an extra bunch of zero derivatives affect an esd??? For example adding or excluding background regions shouldn't alter the esd's on positions provided the chi^2 is unchanged. Is there anything other than GSAS for doing combined fits anyway? Apologies to the list if I am displaying my ignorance, sometimes it's the quickest way to learn. Jon Wright PS: Sorry to pick at your comments Paolo, it's a shame I'm not at RAL at the moment. Could have discussed it out over a coffee...
RE: Combined neutron/x-ray refinements
On Tue, 25 May 1999, Alan Hewat, ILL Grenoble wrote: I guess the degradation which is found would come from parameters which are determined by both datasets and come out with different values in each separate refinement. If they come out differently it is because they are differently biased by different systematic errors in the data not described by the model. I was thinking of C-H (D) bondlengths from x-ray and neutron data. Don't they come out differently if you use spherical form factors for the x-ray data? I guess a neutron expert might look on this as an systematic error in the x-ray model :) Maybe not if one looks on the x-ray refinement as fitting of the electron density function, rather than the nuclear positions. For bonding studies it is the differences which are of interest! Jon Wright. PS: Any offers other than GSAS and multipattern fullprof for actually doing these fits?
RE: Combined neutron/x-ray refinements
On Tue, 25 May 1999, Alan Hewat, ILL Grenoble wrote: Mainly because the ESD's are only correctly calculated if the model is CAPABLE of fitting the data. This is not usually true when systematic errors are important compared to statistical errors, since the model is usually not capable of describing these systematic errors fully - background, texture etc... ...and weights. Lubo
