RE: Mean vs. Median to reduce bias in grainy intensities (was Re: Level of Preferred Orientation)
Guys, This appeared in a Rietveld e-mail a bit ago needs a comment: While I can understand the general rationale for the idea (minimize the weight of the very strong reflections to the final integrated intensity for the reflection) The fact of the matter is that most least squares programs doing Rietveld refinement (GSAS included) use weights that are equal to 1/I. This is what one expects from pure Poisson counting statistics for reasonably large numbers of counts (i.e. 20). Because of this choice of weights, each observation in the refinement is equal in terms of impact on the refinement. So the above suggestion that the weights for strong reflections be reduced is already done in the standard form of Rietveld least squares refinement. The extra residual you may see in the vicinity of strong reflections is actually no larger when weighted (unless the model isn't right, of course) than the surrounding lower intensity values. In GSAS, the graphics routine POWPLOT has an option that clearly illustrates this. The W option scales each intensity difference by the weight. The resulting curve has no peaks(!) and is what the LS minimization engine actually sees for refinement. Bob Von Dreele R.B. Von Dreele IPNS Division Argonne National Laboratory Argonne, IL 60439-4814
Level of Preferred Orientation
Hi, I would like to discuss a couple of questions raised by a referee;-( I am not sure if it is ethical or not - I thought it is better to ask the way than . 1. I have used very (very very)small amount of sample to collect a powder pattern and I have corrected possible graininess with spherical harmonics to account for small discrepancies in some of the peaks (to give an idea - the Rwp decreased only 1% on correction - if the numbers mean anything). Is it possible to estimate the level of preferred orientation, if one uses a spherical harmonics correction? (I know preferred orientation is not the right term to use here, in the first place) 2. The data I have collected is on a image plate (only one frame). Also, I have used a z-matrix (rigid body) and allowing small meaningful changes in bond lengths, angles, and torsions, i.e., z-matrix of the type (in TOPAS): A1 X2 A1 1.855 min 1.8 max 1.9 X3 X2 1.649 min 1.6 max 1.7 A1 114.987 min 113 max 116 X4 X3 1.649 min 1.6 max 1.7 X2 x4x3x2 122.80 min 122 max 123 A1 169.5 min 160 max 175 In such a case, is it possible to give (any meaningful) Standard Uncertainties for the atom positions, (also) given the fact that the atoms are not refined independently? Thanks for any wise comments in advance, Bhuv N. Bhuvanesh Texas AM Univ. Coll. Stn., TX __ Do you Yahoo!? Make Yahoo! your home page http://www.yahoo.com/r/hs
Re: Level of Preferred Orientation
Dear Bhuv, yes it is possible to evaluate it. Normally it should be sufficient to compute the F2 index from the spherical harmonic coefficient. The problem may be is that TOPAS does not have such computation inside. So the other way is to export the coefficients, to hope they are some standard one and input them in a texture program that can compute F2 or texture strength index. There could be some problems: - if you have reduced the image to only one spectrum than using the harmonic apparatus what you get as F2 it could be it is not at all representative of the real texture strength as you are not fitting the real texture. - as the texture coverage you have is for sure very small and insufficient, the harmonic coefficient will be strongly correlated with other errors and as the harmonic is not robust at all in such cases you are likely to get big errors in F2. I would suggest one thing. If the Rwp decreases only 1%, why to use the harmonic texture correction at all? A texture correction should be used (and especially the harmonic one) having a high level of confidence on the method, its effect and knowledge of the real texture of your sample and geometry/texture connections. Otherwise is just a black box that may lead to more errors than corrections. Best regards, Luca Lutterotti On Apr 1, 2005, at 17:44, P. Bhuv wrote: Hi, I would like to discuss a couple of questions raised by a referee;-( I am not sure if it is ethical or not - I thought it is better to ask the way than . 1. I have used very (very very)small amount of sample to collect a powder pattern and I have corrected possible graininess with spherical harmonics to account for small discrepancies in some of the peaks (to give an idea - the Rwp decreased only 1% on correction - if the numbers mean anything). Is it possible to estimate the level of preferred orientation, if one uses a spherical harmonics correction? (I know preferred orientation is not the right term to use here, in the first place) 2. The data I have collected is on a image plate (only one frame). Also, I have used a z-matrix (rigid body) and allowing small meaningful changes in bond lengths, angles, and torsions, i.e., z-matrix of the type (in TOPAS): A1 X2 A1 1.855 min 1.8 max 1.9 X3 X2 1.649 min 1.6 max 1.7 A1 114.987 min 113 max 116 X4 X3 1.649 min 1.6 max 1.7 X2 x4x3x2 122.80 min 122 max 123 A1 169.5 min 160 max 175 In such a case, is it possible to give (any meaningful) Standard Uncertainties for the atom positions, (also) given the fact that the atoms are not refined independently? Thanks for any wise comments in advance, Bhuv N. Bhuvanesh Texas AM Univ. Coll. Stn., TX __ Do you Yahoo!? Make Yahoo! your home page http://www.yahoo.com/r/hs
Re: Level of Preferred Orientation
Dear Bhuv pattern and I have corrected possible graininess with spherical [...] The data I have collected is on a image plate (only one frame). Not sure I understand? If you have a 2D image showing powder rings then you should have some very good ideas about the level of granularity or texture in the sample. Just look for the variation in intensity versus azimuth? Did you mean a one dimensional image plate? One way to reduce graininess if you have a mixture of grains and fine powder: take the median when integrating around the rings instead of the mean. If you only have grains and no continuous rings then better to do the single crystal experiment... In such a case, is it possible to give (any meaningful) Standard Uncertainties for the atom positions, (also) given the fact that the atoms are not refined independently? Some comments: 1) Standard Uncertainty is a defined statistical quantity. Always theoretically possible to derive it from a least squares refinement. It should always represent what it is defined to represent. Rarely what you want to know ;-) 2) If the cell parameters a,b,c of a cubic crystal are constrained to be equal I assume the value and esd is the same for all three, and that they are 100% correlated. That they have not been refined independently would be a relief (equivalent feats are sometimes attempted via Rietveld). 3) For your constrained positions the esd from the refinement may reflect the esd on the position and orientation rather the individual atom position. It just means there are very high correlations being hidden by the constraints (Z-matrix or otherwise). 4) Replace Z-matrix constraint with symmetry operator constraint and then decide if you could bring yourself to list atomic positions and esds in a lower space group than the one you used for refinement. (eg: for comparing structures above and below a phase transition) So yes it seems possible to give meaningful standard uncertanties for the atomic positions, provided you mention the constraints and restraints used. Although they are not interesting, they are considerably more meaningful than Rwp in terms of evaluating the structure! Good luck, Jon
Re: Level of Preferred Orientation
Not sure I understand? If you have a 2D image showing powder rings then you should have some very good ideas about the level of granularity or texture in the sample. Just look for the variation in intensity versus azimuth? Did you mean a one dimensional image plate? One way to reduce graininess if you have a mixture of grains and fine powder: take the median when integrating around the rings instead of the mean. If you only have grains and no continuous rings then better to do the single crystal experiment... Dear Bhuv, I don't know your experimental setup. When working with single grains, you might consider to apply the Gandolfi method, i.e. turning the grain simultaneously around two axes instead of just one (as in the Debye-Scherrer setting) during exposure. If your grain is not a single crystal, this should give you a nearly perfect powder I vs 2th pattern, especially if you integrate around the rings as suggested by Jon, and you can forget about inadequate intensity corrections. BTW, graininess may also give you a peak displacement. Best Miguel -- Miguel Gregorkiewitz Dip Scienze della Terra, Università via Laterino 8, I-53100 Siena, Europe fon +39'0577'233810 fax 233938 email [EMAIL PROTECTED]
