Re: Explaining for broadening of peaks due to a shift of theta in theta-two theta scanning?
Besides Joerg's suggestion of mis-cut substrates (which may be too expensive for use for thin film growth experiments) you could use Si wafers cut to (100). The first allowed peak in that direction is (400), which is at about 70 degrees 2theta for Cu K-alpha. That will still reflect any bremsstrahlung radiation from your x-ray tube, which can make a significant background. If you have a monochromator in your optics, that will cut it down, but you can still get artifacts, such as lambda/2 radiation reflecting from the (400) appearing to be a peak at the (forbidden) Si (200) position. Or, maybe you can find a compromise between the Si substrate peak and defocusing with a smaller value of omega (theta - 2theta/2) than 3 degrees. Another possibility, if you are ready to rearrange your diffractometer, is to make the source-sample and sample-detector distances different, so that source, sample, and detector are on the focusing circle with theta not half of 2theta. I wonder if any of the manufacturers provide this geometry? ^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~ Peter W. Stephens Professor, Department of Physics and Astronomy Stony Brook University Stony Brook, NY 11794-3800 fax 631-632-8176
Re: More Caglioti U V W parameters
In my opinion, the short answer (regarding use of Caglioti parameters) is
that their use is historic and somewhat convenient, but their usual
application is based on no theory whatsoever, and they can be quite
troublesome to apply.
They came from a paper (Nuc. Instrum. Methods, 1958) on the resolution
of a neutron powder diffractometer using mosaic crystals and S\{o}ller
(that's an umlaut over the o; please, not solar) collimators, which gives
precise expressions for U, V, and W in terms the various geometric
parameters of the diffractometer. If (as was true of most samples on
neutron powder diffractometers at the time) the instrument dominated the
peak shape, they give a good representation of the observed linewidth.
Maybe you could tweak them up a bit to account for sample broadening.
Accordingly, they were ideally suited to Rietveld's method which was first
developed for CW neutron powder diffractometers. Historically, they seem
to have overstayed their welcome, I mean their theoretical justification.
This is especially so for high resolution x-ray powder diffractometers at
synchrotrons and elsewhere where the peak width is almost entirely from
the sample, not the instrument.
One problem with them is that for inappropriate choices of U, V, and W,
the linewidth can become an imaginary number over a certain range of
diffraction angles. This leads to some unpleasant instabilities in
refinement programs that use them.
The fundamental parameters approach would have you model the instrument
and the sample separately, and for any other kind of diffractometer, U, V,
and W are probably not a very good model of either. You can learn about
fundamental parameters e.g., from the Bruker Topas documentation, or from
Klug and Alexander, chapter 6.
If you are not going to try to separately model instrument and sample, you
can get a pretty good line through your data points and relative
intensities suitable for Rietveld analysis with U, V, and W (and some of
their extensions, such as Lorentzian X and Y in, e.g., GSAS) Toward that
end note that if you forget V, the (Gaussian) FWHM is $(U \tan^2 \theta +
W)^{1/2}$, which suggests that U is kind of like strain broadening and W
is kind of like size broadening, coming together in quadrature. I have
had generally OK luck leaving V set to zero and refining U and W. That
has the advantage of being more robust than refining the three (or more)
parameters. I guess once your refinement is pretty much under control,
you could let V vary to see if the fit improves. Just be careful not to
believe that the refined values of U, V, and W have any meaning in such a
refinement.
^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~
Peter W. Stephens
Professor, Department of Physics and Astronomy
Stony Brook University
Stony Brook, NY 11794-3800
fax 631-632-8176
Powder Diffraction at NSLS-II
Friends and colleagues, You may be aware that plans are afoot to build a new synchrotron light source, dubbed NSLS-II, at Brookhaven Lab. This will be a medium energy (3 GeV) storage ring of extremely high brightness, proposed to start operations in 2013. I am writing to ask you to attend the NSLS-2 User Workshop coming up at BNL on 17-18 July. This meeting will provide an opportunity to hear details about the proposed machine and to participate in a breakout session which will define the next generation of powder diffraction x-ray scattering instruments for NSLS-2. Current plans are for a powder diffraction line to be one of the instruments built by the facility and operating on day 1. (Specifically, on a damping wiggler line, a very hot source having critical energy of 10.8 keV, brightness 10^18 photons / sec / 0.1% bw / mm^2 / mrad^2 at 50 keV, flux 5 x 10^14 photons / sec / 0.1% bw @ 50 keV. See the conceptual design report on the nsls2 website for more details.) This is extremely fortunate for our community, but it should not be taken for granted. First, we need to mobilize a clear message of enthusiastic support for such an enterprise. Second, we should start to work to define exactly what we want. This is the time to consider integrating beamline design with sample environments with the hope of defining a facility that is not just one more powder diffraction beamline, but rather a significant step forward in research capability. As a community, we must meet at this early stage to discuss: - next generation powder diffraction - related techniques such as pair distribution function - new detection modes and detector capabilities (e.g., not-quite-powder samples: 10-1000 crystals in a sample measured with an area detector) - new scientific opportunities and the scientific case - proposed organizational structure to fund and run the beamline for maximum scientific productivity and best access. We will be bringing one or two invited speakers to share their experiences and insights with other recent powder diffraction beamlines at major facilities. Go to https://www.bnl.gov/nsls2meeting/ (note that https:// is required) and register, including for the powder breakout session. If you want, please plan to give a short talk on your research interests or specific ideas about future instrumentation for powder diffraction. Note that the workshop deadline is 12 July. Best regards, Peter PS - if you have any comments that are not intended for the entire Rietveld discussion list, please make sure to direct them to me - [EMAIL PROTECTED] ^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~ Peter W. Stephens Professor, Department of Physics and Astronomy Stony Brook University Stony Brook, NY 11794-3800 fax 631-632-8176
Re: Powder Diffraction In Q-Space
Simon, You left a couple of jackets at my house - they're on their way back to you. Did you see anything interesting with the realtor? Do let us know if you'll be coming back for another visit with your wife. Best, Peter ^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~ Peter W. Stephens Professor, Department of Physics and Astronomy Stony Brook University Stony Brook, NY 11794-3800 fax 631-632-8176
OOPS.
Sorry about that. ^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~ Peter W. Stephens Professor, Department of Physics and Astronomy Stony Brook University Stony Brook, NY 11794-3800 fax 631-632-8176
Re: Strange peaks from grainy Si
I'll mail you some fine Si powder if you send me your address. My best guess is that you have a relatively big lump of Si in your sample that happens to be lined up to make a bright spot from the bremstrahlung part of the spectrum. It happens to meet some Si Bragg reflection condition for some wavelength in the brems. spectrum. ^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~ Peter W. Stephens Professor, Department of Physics and Astronomy Stony Brook University Stony Brook, NY 11794-3800 fax 631-632-8176
Re: Synchrotron Powder Diffraction Course
Thanks, nice to hear from you. Actually, Silvia Cuffini has invited me as an instructor in a crystallography workshop next November; I'm not completely clear on the exact venue or schedule. Best, Peter ~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~ Peter W. Stephens, Professor Department of Physics Astronomy State University of New York Stony Brook, NY 11794-3800
Re: Synchrotron Powder Diffraction Course
Sorry to blast you all with that correspondence. Once again, we are reminded that the reply key is a dangerous part of email! -Peter
Synchrotron Powder Diffraction Course
Dear Colleagues, I am writing to call your attention to a three-day course, High Resolution Powder Diffraction Data Collection and Analysis to be held at the National Synchrotron Light Source, January 25-27, 2005. This will be a blend of instruction, practical experience at synchrotron beamlines, and analysis of real data. Participants will have the opportunity to bring and measure their own samples, with appropriate prior arrangement. For details and registration, please follow the link http://www.nsls.bnl.gov/newsroom/events/workshops/powderdiff/. If you are interested, please act promptly. The application deadline, December 10th, is quite close; it can take 45 days for new visitors to obtain access to Brookhaven National Laboratory. ~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~ Peter W. Stephens, Professor Department of Physics Astronomy State University of New York Stony Brook, NY 11794-3800
RE: Anisotropic line broadening in cubic material
Jens, Your effect might be more related to strain than size broadening. You would have to check widths at various diffraction orders in a given direction (i.e., 111, 222, 333, etc., vs 200, 400, 600, etc. for an fcc material). If the widths increase roughly in proportion to diffraction order, but with a different slope for the two directions, you have anisotropic strain broadening. This was noted by Stokes and Wilson (Proc. Phys. Soc. London 56, 174-181 (1944)) in cold-worked fcc metals, who had a model as a random distribution of stresses. N. Popa and I have independently considered the effect more recently from a phenomenological viewpoint (J. Appl. Cryst. 31, 176 (1998) and ibid 32, 281 (1999), respectively). And there is a growing literature, especially from the group of Tamas Ungar, on the effect of specific lattice defects on strain-broadening in diffraction patterns. Regarding your use of the anisotropic size broadening model in GSAS, as you point out, broadening axis for a cubic material is a rather iffy concept. If my understanding is correct, GSAS does not do the full symmetry equivalents in that calculation, and so it's a matter of luck how the calculation will be done. That is, if you list a (111) broadening axis, and the reflection list contains (111), you'll get one answer, but if you list (-1 1 1) broadening axis, the (111) reflection will be calculated differently. -Peter ~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~ Peter W. Stephens, Professor Department of Physics Astronomy State University of New York Stony Brook, NY 11794-3800
Re: space group of NaxCoO2
I just recalled a more directly relevant paper for your question: M.L. Foo et al., Phys. Rev. Letters 92, 247001 (2004), published about six weeks ago. That paper is much more about electronic properties through the phase diagram as a function of x, but it will help get you oriented, and has some electron diffraction results, and pointers to other recent literature. There is also a nice discussion of the issues involved, perhaps a bit more readable than the PRL, by Ong and Cava in the July 2, 2004 issue of Science, page 52. ~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~ Peter W. Stephens, Professor Department of Physics Astronomy State University of New York Stony Brook, NY 11794-3800
Re: space group of NaxCoO2
You should start with the paper by J.D. Jorgensen et al., Phys. Rev. B 68, 214517 (2003). I don't have that paper in front of me, and so I don't know if it completely addresses the space group issue of both phases, but it will get you in touch with the recent literature. ~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~ Peter W. Stephens, Professor Department of Physics Astronomy State University of New York Stony Brook, NY 11794-3800
Re: indexing problem
Topas software is very good at solving such short axis problems. The advantage is that it will look at all of the peaks you feed it, instead of using just the first twenty or so to generate candidate solutions (the way that ITO and TREOR work). If you don't have access to Topas, I suggest the following, which has been quite successful for me in the past. Use the two axes you have to completely index the zone that contains the first reflections, and run a profile (Le Bail) fit using, e.g., fullprof. Put in a dummy b axis of 1 angstrom, so it doesn't generate any reflection markers in the range of your data. Refine the lattice parameters, so you get a clear indication of which peaks belong to your first zone and which do not. The next step is to pray that your sample is monoclinic, so you can leave alpha and gamma = 90, and you only have to determine the lattice parameter b. The first peak not indexed by your zone is probably the (010), (110), (011), (111), or (-111), and you can quickly calculate what the b parameter would have to be to fit each of those cases. Type it in, run another profile, and see which one works best. If that doesn't work, and you think your material is triclinic, it is still possible, but you have to identify three (h 1 ell) peaks and suggest indexations for them. That needs at least half a dozen good peaks outside of the first zone, and a little computer program to search the candidates. I don't know of any public domain software for that, but it's a good project to give a student to help them learn about reciprocal space geometry. Good luck, Peter ~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~ Peter W. Stephens, Professor Department of Physics Astronomy State University of New York Stony Brook, NY 11794-3800
