RE: UVW - how to avoid negative widths?
Hi, I sent this to Jon this afternoon and thought that I'd pass the e-mail on. Here goes ... > You'll probably find a pre-PRODD CCSL subroutine that I wrote that > goes along the lines of > > width^2 = u^2 * ( tan(theta)-tan(theta_m) )^2 + w^2 > > Two neat things about this equation is that it doesn't go negative and > also theta_m should refine to close to half the monochromator take-off > angle. Bill P.S. I also sent him a slightly longer note later ... Because of the quadrature properties of Gaussians, we get strain terms like width^2 = e^2 * tan(theta)^2 size terms go like width^2 = s^2 / cos(theta)^2 = s^2 * (1 + tan(theta)^2) so if the monochromator half angle is theta_m so that the pure instrument term looks like width^2 = u^2 * ( tan(theta)-tan(theta_m) )^2 + w^2 then instrument & size & strain go like width^2 = u^2 * ( tan(theta)-tan(theta_m) )^2 + w^2 + e^2 * tan(theta)^2 + s^2 * (1 + tan(theta)^2) Obviously you get u, tan(theta_m) and w from a calibration like LaB6 - you can then plug in (certainly into TOPAS) - then with u0, v0 and w0 fixed at the LaB6 values we get width^2 = (u0 + f^2) * tan(theta)^2 + v0 *tan(theta) + (w0 + s^2) where e^2 = f^2-s^2 - and we've got the Gaussian component of the size and strain directly from the Cagliotti relationship. -Original Message- From: Jon Wright [mailto:wri...@esrf.fr] Sent: 19 March 2009 20:49 To: alan.he...@neutronoptics.com Cc: Rietveld Method Subject: Re: UVW - how to avoid negative widths? Alan Hewat wrote: > Jon Wright said: >> Quick question - does anyone have a trick to stop the Cagliotti formula >> going negative? > > This can happen if the resolution is relatively flat, so that there is no > well defined minimum. Seems to be the problem - also rather close to zero anyway. > if you have access to the refinement code. Here I am lucky! As suggested off list - simply return the function to the form it was in before I edited the code :-) Thanks a lot for the help Jon -- Scanned by iCritical.
2 post-doctoral positions in the structural characterisation of novel hydrogen storage materials at ISIS/Oxford
Dear Colleagues, We are advertising two postdoctoral positions in Hydrogen Storage Research at the ISIS Spallation Neutron Source in conjunction with Oxford University, Johnson Matthey and Ilika Technologies Ltd. The positions are for 2 years fixed-term and are available from April 2009. I would be grateful if you could pass the information on to interested colleagues. Bill _ Professor W I F David, STFC Senior Fellow, ISIS Facility, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, UK _ Tel. +44 1235 445179 Sec +44 1235 445604 _ 2 postdoctoral research assistants Novel Hydrogen Storage Materials Discovery and Characterisation ISIS Facility, Rutherford Appleton Laboratory, Chilton, Oxfordshire, UK (2 years, Fixed Term) Applications are invited for two Postdoctoral Research Assistants to work with Professor Bill David on the structural characterisation of novel hydrogen storage materials. The 2-year PDRA positions are part of a major Technology Strategy Board research grant entitled "HyStorM - tuning promising hydrogen storage materials towards automotive applications" that involves Johnson Matthey, Ilika Technologies Ltd., the University of Oxford and the Science and Technologies Facilities Council. The main project aim is to enable whole ternary and quaternary materials phase diagrams to be rapidly synthesised and assessed in terms of their hydrogen storage potential - this rapid throughput capability will accelerate the identification and development of compositions of high hydrogen storage promise. The successful candidates will be expected to play a major role in advancing the structural analysis of high throughput and in-situ characterisation of novel hydrogen storage materials using both high resolution X-ray and neutron powder diffraction techniques. The positions will both be based at the ISIS Facility, SFTC Rutherford Appleton Laboratory, Oxfordshire but will also involve frequent visits to the Inorganic Chemistry Laboratory, University of Oxford to liaise closely with the synthesis component of the project in collaboration with Professor Peter Edwards. The majority of the experimental work will be undertaken at central facilities including ISIS and Diamond at the Rutherford Appleton Laboratory and the ESRF in Grenoble. Applicants should have a doctorate, or have submitted their thesis, in inorganic chemistry, crystallography or a related subject. Experience in the analysis of X-ray and neutron powder diffraction data is desirable. For more information, contact Bill David (bill.da...@stfc.ac.uk). Closing date: Friday 13th March 2009 Interviews during the week commencing: 30th March 2009. -- Scanned by iCritical.
RE: About zero counts etc.
Title: RE: About zero counts etc. Hi Alan, The short answer is that the question of zero counts can indeed be answered in a simple and practical manner. There's a lot of apparent mystique about probability theory especially when one invokes the term Bayesian probability theory. However, Bayesian probability theory is really just common sense about what's likely and what's unlikely converted into mathematics. It may seem tautologous but the most probable answer is the answer with the highest probability value – i.e. the maximum of the probability distribution function (pdf). This is quite obvious – the subtle bit is “what is the probability distribution function”. Normally with enough counts, we move over to a Gaussian pdf along the lines of Gaussian pdf = const * exp(-0.5*(yobs-ycalc)/esd^2) This is a maximum when the negative log pdf is a minimum. The negative log pdf is simply negative log pdf = const2 * (yobs-ycalc)/esd^2 In other words, least squares. The corollary is that least squares is associated with (and only associated with) a Gaussian pdf which happily is the case almost all of the time in Rietveld analysis. However, when there are zeroes and ones around in the observed counts or when the model is incomplete or uncertain then we have to move away from a Gaussian pdf and by implication least squares. With zeroes and ones around, we have to move from a Gaussian pdf to a Poisson pdf and work with the negative log pdf of that. With incomplete models, we have to move over to the maximum likelihood methods that the macromolecular people have been using for years. So the bottom line is that fundamental statistics is as basic as fundamental parameters. You can fudge your way with a Pearson VII or a pseudo-Voigt function to fit an X-ray emission profile but the physics says that there are better functions. Similarly you can fudge your way with tweaking the Gaussian pdf when there are zero and one counts around but you’d be better to move over to the correct probability functions. Antoniadis et al. have been through all of this back in the early 90s. I’ve got code (and it’s only a few lines) that is precisely Poisson and moves seamlessly over to the chi-squared metric. I’ll send it to you offline – it would be great to have the ability to program our own algebraic minimisation function in a TOPAS input file. I’d love to be able to do that for robust statistics and also maximum likelihood! All the best, Bill -Original Message- From: AlanCoelho [mailto:[EMAIL PROTECTED] Sent: 13 October 2006 22:30 To: rietveld_l@ill.fr Subject: RE: About zero counts etc. Hi Bill and others Why cant this question of zero counts be answered in a simple and practical manner. I hope to read Devinder Sivia's excellent book one day but for the time being it would be useful if the statistical heavy weights were to advise on what weighting is appropriate without everyone havng to understand the details. The original question was how to get XFIT to load data files with zero counts; obviously setting the values to 1 is incorrect. Joerg Bergmann seems to indicate that the weihgting should be: weighting = 1 / (Yobs+1); as the esd is sqrt(n+1). Again without reading the book should the weighting be: weighting = 1 / If(Yobs, Yobs, Ycalc); Hopefully these spread sheet type formulas are understandable. This last equation is not liked by computers due to a possible zero divide when Ycalc is zero. Any ideas Bill and others Alan ________ From: David, WIF (Bill) [mailto:[EMAIL PROTECTED] Sent: Thursday, 12 October 2006 4:48 PM To: rietveld_l@ill.fr Subject: RE: About zero counts etc. Dear all, Jon's right - when the counts are very low - i.e. zeroes and ones around - then the correct Bayesian approach is to use Poisson statistics. This, as Jon said, has been tackled by Antoniadis et al. (Acta Cryst. (1990). A46, 692-711 Maximum-likelihood methods in powder diffraction refinements, A. Antoniadis, J. Berruyer and A. Filhol) in the context of the Rietveld method some years ago. This paper is very informative for those who are intrigued about the fact that you can do anything when diffraction patterns have lots of zeroes and ones around. Curiously, the weighting ends up having as much to do with the model value (which can, of course, be non-integer) as the data. Devinder Sivia's excellent OUP monograph, "Data Analysis: a Bayesian Tutorial" (http://www.oup.co.uk/isbn/0-19-856832-0) discusses all of this in a very readable way. Bill -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]] Sent: 12 October 2006 00:37 To: rietveld_l@ill.fr Subject: Re: About zero counts etc. Hello Joerg, > -Having measured n counts, the estimated value is n+1 You might have a hard time convincing me on that one. > -Having measured n counts, the esd is also sqrt(n+1)! If
RE: About zero counts etc.
Title: RE: About zero counts etc. Dear all, Jon's right - when the counts are very low - i.e. zeroes and ones around - then the correct Bayesian approach is to use Poisson statistics. This, as Jon said, has been tackled by Antoniadis et al. (Acta Cryst. (1990). A46, 692-711 Maximum-likelihood methods in powder diffraction refinements, A. Antoniadis, J. Berruyer and A. Filhol) in the context of the Rietveld method some years ago. This paper is very informative for those who are intrigued about the fact that you can do anything when diffraction patterns have lots of zeroes and ones around. Curiously, the weighting ends up having as much to do with the model value (which can, of course, be non-integer) as the data. Devinder Sivia's excellent OUP monograph, "Data Analysis: a Bayesian Tutorial" (http://www.oup.co.uk/isbn/0-19-856832-0) discusses all of this in a very readable way. Bill -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]] Sent: 12 October 2006 00:37 To: rietveld_l@ill.fr Subject: Re: About zero counts etc. Hello Joerg, > -Having measured n counts, the estimated value is n+1 You might have a hard time convincing me on that one. > -Having measured n counts, the esd is also sqrt(n+1)! If n is zero then spending more time on the data collection might be better than more time on the analysis. > Things change with variable counting times. id31sum uses counts=counts and esd=sqrt(counts+alp) where alp=0.5 is the default and can be overridden on the command line. Perhaps there aren't many people who use that option. Should we change the default? The 0.5 came from the literature but it was some time ago and I can't remember where. In any case it then gets convoluted with the monitor error. Sqrt(n+1) gives a very low chi^2 if the actual background is 0.1 (eg: 1 count every 10 datapoints). Might be better to just use the Poisson itself, as in abfit [1]. > the above correction for the estimated > values gave significant better R values. Are you using background subtracted R-values? If only R-values were significant. Jon [1] Acta Cryst. (1990). A46, 692-711 Maximum-likelihood methods in powder diffraction refinements A. Antoniadis, J. Berruyer and A. Filhol - This mail sent through IMP: http://horde.org/imp/
PDRA in powder diffraction studies of hydrogen storage materials
Title: PDRA in powder diffraction studies of hydrogen storage materials I have a postdoc position available immediately for powder diffraction research in the area of hydrogen storage materials. Details below. Bill Professor W I F David, CCLRC Senior Fellow, Associate Director, CCLRC Research Networks, ISIS Facility, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, UK Professor in Inorganic Chemistry, Inorganic Chemistry Laboratory, South Parks Road, University of Oxford, Oxford, OX1 3QR, UK Tel. +44 1235 445179 Fax +44 1235 445642 P.A. +44 1235 445610 Tel. +44 1865 272681 FBU029 Postdoctoral research assistant Novel Hydrogen Storage Materials Discovery and Characterisation ISIS Facility, Rutherford Appleton Laboratory, Chilton, Oxfordshire, UK (3 years, Fixed Term) Applications are invited for a Postdoctoral Research Assistant to work with Professor Bill David on the structural characterisation of novel hydrogen storage materials. The 3-year PDRA position is part of a major DTI/EPSRC research grant entitled “High Throughput Synthesis and Screening of Novel Hydrogen Storage Materials” which involves Ilika Technologies Ltd., Johnson Matthey, the University of Oxford and CCLRC. The main project aim is to enable whole ternary and quaternary materials phase diagrams to be rapidly synthesised and assessed in terms of their hydrogen storage potential – this rapid throughput capability will accelerate the identification and development of compositions of high hydrogen storage promise. The successful candidate will be expected to play a major role in advancing the structural analysis of high throughput and in-situ characterisation of novel hydrogen storage materials using both high resolution X-ray and neutron powder diffraction techniques. The position will be based at the ISIS Facility, Rutherford Appleton Laboratory, Oxfordshire but will also involve frequent visits to the Inorganic Chemistry Laboratory, University of Oxford to liaise closely with the synthesis and modelling components of the project. The majority of the experimental work will be undertaken at central facilities including the ESRF in Grenoble and the ISIS Facility at the Rutherford Appleton Laboratory. Applicants should have a doctorate, or have submitted their thesis, in inorganic chemistry, crystallography or a related subject. Experience in the analysis of X-ray and neutron powder diffraction data is desirable. Salary is in the range £24,638 to £27,998 per annum, dependent on experience. An excellent index linked pension scheme and generous leave allowance are also offered. For an informal discussion about the post, please contact Bill David on 01235 445179 or email [EMAIL PROTECTED] Application forms can be obtained from our website at www.cclrc.ac.uk following the links to the vacancies page. Alternatively, you may wish to contact us by email at [EMAIL PROTECTED] or phoning +44(0)1235 446677 (24 hour answer phone) quoting reference number FBU029. For more detailed information about CCLRC please visit www.cclrc.ac.uk . Closing date for applications is 25 August 2006 Interviews will be held on 8 September 2006
Re: Choosing origins
Apologies for sending the personal note to Jon to the whole mailing list - at least it didn't have gigabytes of attachments - and for the English and American members of the mailing list, 'en' is not a spelling mistake! Bill -Original Message- From: Jonathan Wright [mailto:[EMAIL PROTECTED] Sent: 31 March 2004 23:05 To: [EMAIL PROTECTED] Bill, Thanks! Exactly what I was after and I'd never have guessed it from the title... Jon On Wed, 31 Mar 2004, David, WIF (Bill) wrote: > Hi Jon, > > A lot of what you'll need is in the back of the International Tables Vol. A > in Chapter 15 which goes under the snappy title of "Euclidean and affine > normalisers of space groups and their use in crystallography". From memory, > earlier incarnations of Vol. A do not have this chapter. > > Bill
Re: Choosing origins
I'm just good at guessing! See you end of April en France. Bill -Original Message- From: Jonathan Wright [mailto:[EMAIL PROTECTED] Sent: 31 March 2004 23:05 To: [EMAIL PROTECTED] Bill, Thanks! Exactly what I was after and I'd never have guessed it from the title... Jon On Wed, 31 Mar 2004, David, WIF (Bill) wrote: > Hi Jon, > > A lot of what you'll need is in the back of the International Tables Vol. A > in Chapter 15 which goes under the snappy title of "Euclidean and affine > normalisers of space groups and their use in crystallography". From memory, > earlier incarnations of Vol. A do not have this chapter. > > Bill
Choosing origins
Hi Jon, A lot of what you'll need is in the back of the International Tables Vol. A in Chapter 15 which goes under the snappy title of "Euclidean and affine normalisers of space groups and their use in crystallography". From memory, earlier incarnations of Vol. A do not have this chapter. Bill -Original Message- From: Jon Wright [mailto:[EMAIL PROTECTED] Sent: 31 March 2004 21:14 To: [EMAIL PROTECTED] > > > >I am amazed by the flow of miss information that flows on this list whenever an >apparent problem with a space group comes up. > I asked a related question on sci.techniques.xtallography a few weeks ago, but have yet to hear anything, misinformation or otherwise. If anyone here can give me some pointers, I'd be very grateful. I just want to find all the allowed equivalent origin choices for comparing structures, and I'm wondering if there is a way to choose a specific one (for example in terms of the phases of certain reflections?). Thanks, Jon Forwarded from sci.techniques.xtallography, with my apologies if you have seen it before. >I was looking at models coming back from a molecular replacement >program being run using various datasets and then trying to decide if >the models are "good" or "bad", and therefore if the data were "good" >or "bad". In a specific example with space group P212121, frequently >the resulting model was found displaced by <1/2,0,0> from the ideal >position (and invariably moved still further away by one of 21 axes). >[All programs are using x,y,z; 1/2-x,-y,1/2+z; -x,1/2+y,1/2-z; >1/2+x,1/2-y,-z for P212121.] > >From looking at the space group diagrams in Int Tables, this seems to >be a perfectly good origin shift, as the symmetry operators are >arranged around [1/2,0,0] in the same way as [0,0,0]. So I wrote a >little script which applies all the origin shifts and symmetry >operators to a test model and tells me which origin shift and symmetry >operator gives the closest fit a target model. All well and good for >P212121, but now I was thinking that one day I might want to do this >for another space group... > >The first attempt to generalise was to apply the space group symmetry >to the point [0,0,0], which gives me three face centers, but misses >the body center and points <1/2,0,0>. Then it occurred to look at the >Patterson symmetry (apparently Pmmm here) and from that I could >probably have gotten a list of possible origin shifts, with a concern >about sometimes flipping enantiomers. Now I'm scared that one day I'll >meet a trigonal thing which has hexagonal Patterson symmetry and could >come back rotated by 60 degrees, but still be the same structure! > >So the question is: "How can the full list coordinate transformations >be generated which leave a structure invarient?" > >For P212121 it seems that "add [0.5,0,0]" is allowed, but I didn't see >how I should figure that out from the info in Int tables, or >algorithmically. > >There's a followup: "How should the transformation be chosen in order >to end up at a unique and reproducible representation of the >structure?" > >Would something like platon just do all this? At least one pair of >structures in the PDB database seem to represent different choices >about this origin shifting, but they represent the same packing and >structure... realising that was not as straightforward as it would >have been had both structures been recorded in a standardised way. > >Thanks in advance, > >Jon >
