Although your results cannot be accepted any more, it is still possible to download the original measurements. Some of the reasons for initiating the round robin can be found below, and more details about the material and analysis procedures are here.

The measurements (the so-called "representative" diffraction patterns) that are available for download were collected at participating laboratories with the intent to include a wide variety of experimental conditions (sealed and synchrotron x-ray, CW neutrons). All the measurements were done on two samples:

- CeO
_{2}powder that shows broadened diffraction lines was synthesized by Daniel Louër and Nathalie Audebrand at the University of Rennes. This is the sample for which we want to determine values of coherent domain size and (micro)strain. - Annealed CeO
_{2}powder with narrow diffraction lines. As it is well known, for the analysis of line broadening, instrumental response has to be accounted for. At first, I planned to use an NIST SRM as an instrumental standard, such as LaB_{6}. However, there are two drawbacks to this: (i) neutron-diffraction measurements (boron); (ii) some of the line-broadening methods that will be used in the first stage of the round robin require (or at least greatly simplify and minimize systematic errors) that lines of instrumental standard and broadened sample coincide in 2q positions. Therefore, I prepared an "instrumental standard" by annealing commercial-grade CeO_{2}powder at elevated temperature. When selecting the annealing temperature, I tried to strike a compromise between a narrow line width and not too large a grain size. Indeed, the annealed sample of CeO_{2}thus obtained shows only slightly broader lines than the NIST SRM LaB_{6}at lower angles and even less broadening than LaB_{6}at high angles. However, this difference is insignificant when correcting for instrumental effects at this level of CeO_{2}broadening. Moreover, at this stage of the round robin, we are more interested in systematic differences between the methods/instruments and less in the absolute value of calculated parameters.

Although the first sample selected for the Round Robin shows isotropic line broadening, future samples will exhibit anisotropic line broadening.

CeO_{2} belongs to the space group *Fm-*3*m* with the
approximate lattice
parameter of *a* = 5.41 Å. Atom (ion) positions are as follows:

Atom x y z

Ce+4 0 0 0

O-2 0.25 0.25 0.25

The suggested list of line-broadening methods of analysis is as follows:

- Stokes deconvolution + Warren-Averbach analysis
- Modified Williamson-Hall analysis (Lorentz function for the size-broadened profile + Gauss function for the strain-broadened profile)
- "Double-Voigt" analysis (Voigt function for both size-broadened and strain-broadened profiles)
- Rietveld-refinement analysis -- modified TCH line-broadening model (GSAS, DBWS, FullProf) and Fourier series profile synthesis (ARIT)
- "Fundamental-parameter" approach -- this way, the results
obtained by different methods that use annealed CeO
_{2}as an "instrumental standard" can be compared to this "standardless" method.

I put data files in three different formats (special thanks to Nita Dragoe who adapted Powder 2 to handle large number of data points – yes, the ESRF measurements):

- *.xy (Bragg angle, counts, and e.s.d. if available in ASCII format)
- *.gs (GSAS histogram)
- *.dbw (DBWS data file)

These three formats cover all the line-broadening methods that will be used. The
designation "sh" in file names stands for "sharp" and denotes the
"instrumental standard", and "br" denotes diffraction patterns with
broadened lines.
The recommended value of *P* for a
polarization factor for x-rays, 1 + *P*cos^{2}2q,
is given below for all the data sets.

The "representative" diffraction patterns can be downloaded by clicking on the links below.

Laboratory x-ray sources:

- "Common" instrumental setup: University of Le Mans (Amel Le Bail)

- "Instrumental standard" (lebailsh.xy, lebailsh.gs, lebailsh.dbw)
- "Broadened sample" (lebailbr.xy, lebailbr.gs, lebailbr.dbw)
- l (CuKa
_{1}) = 1.5406 Å, l (CuKa_{2}) = 1.5444 Å,I(CuKa_{2})/I((CuKa_{1}) = 0.48,P= 0.8

- Incident-beam monochromator: University of Birmingham (J. Ian Langford)

- "Instrumental standard" (langfsh1.xy, langfsh2.xy, langfsh3.xy, langfsh1.gs, langfsh2.gs, langfsh3.gs, langfsh1.dbw, langfsh2.dbw, langfsh3.dbw)
- "Broadened sample" (langfbr1.xy, langfbr2.xy, langfbr3.xy, langfbr1.gs, langfbr2.gs, langfbr3.gs, langfbr1.dbw, langfbr2.dbw, langfbr3.dbw)
- l (CuKa
_{1}) = 1.5406 Å, l (CuKa_{2}) = 1.5444 Å,I(CuKa_{2})/I((CuKa_{1}) = 0.016,P= 0.8

Synchrotron x-ray sources:

- 2nd-generation synchrotron, flat-plate geometry: NSLS X3B1 beamline, Brookhaven National Laboratory (Peter W. Stephens)

- "Instrumental standard" (stephsh.xy)
- "Broadened sample" (stephbr.xy)
- l = 0.6998 Å,
P= 0 (because of a highly polarized synchrotron beam,Pis small;P= 0 recommended as a satisfactory approximation)

- 3rd-generation synchrotron, capillary geometry: ESRF BM16 beamline, Grenoble (Olivier Masson and Andy Fitch)

- "Instrumental standard" (massonsh.xy)
- "Broadened sample" (massonbr.xy)
- l = 0.39982 Å,
P= 0 (because of a highly polarized synchrotron beam,Pis small;P= 0 recommended as a satisfactory approximation)

Neutron sources (constant wavelength):

- ILL D1A diffractometer, Grenoble (Alan Hewat)

- NCNR BT1 diffractometer, NIST-Gaithersburg (Brian Toby)

Neutron spallation source (time-of-flight data):

- ISIS HRPD, Rutherford-Appleton Laboratory, Oxford (Mark Daymond). Because of a specific profile shape from neutron TOF measurements, only a few Rietveld-refinement programs can be successfully used for the analysis of ISIS data.

- "Instrumental standard" (daymsh.gs)
- "Broadened sample" (daymbr.gs)
- HRPD Instrumental parameters file (isishrpd.ins)
- Use only Bank 1 (168°) for refinement and refine DIFC and DIFA only for the "instrumental standard" sample.

The Organizer,

Davor Balzar, University of Denver and NIST; balzar@boulder.nist.gov

The Commission on Powder Diffraction (CPD) of the International Union of Crystallography (IUCr) is sponsoring a round robin on size and strain effects in materials. The purpose is twofold: (i) Different methods of line-broadening analysis will be compared on the identical sets of measurements; (ii) Reliability of determination of coherent domain size and (micro)strain by different instruments will be tested on an identical set of samples. The results will be published in the open literature and reprints disseminated to the powder-diffraction community. The initiative to organize a Round Robin on Size/Strain goes back to 1998 and the ECM-18 and EPDIC-6 conferences. There is a vast literature on this subject. An insight into some of the problems and definition of basic terminology can be found in recent publications:

**Line-Profile Analysis and Standards**,*6th European Powder Diffraction International Conference (EPDIC-6)*, Budapest, Hungary, August 22-25, 1998 (plenary lecture). PRESENTATION SLIDES (PDF)

**Voigt-Function Model in Diffraction Line-Broadening Analysis**, in*Defect and Microstructure Analysis by Diffraction*,

Quantification of a specimen's size and strain values requires definition of the analysis method and correction for the instrumental-broadening effects. Even a casual user of some of the line-broadening techniques is aware of systematic and significant differences in results obtained through different approaches. There are literally dozens of different analysis methods that can yield much different or even physically impossible results. The approaches are broadly divided into two groups: model-independent and model-dependent. The former is mainly identified with the Fourier-deconvolution correction for instrumental broadening (Stokes method), which is followed by the Warren-Averbach approximation for the size/strain-effect separation. The latter mainly contains different integral-breadth methods among which some are more widely used and therefore proposed as a part of the Round Robin. Integral-breadth methods are to be preceded by the instrumental-broadening correction, which will depend on a particular method and will be defined accordingly. Furthermore, as Rietveld-refinement programs build in more and more sophisticated line-broadening approaches, they will be used more frequently as a tool for line-broadening analysis.

The list of methods to be used by Round-Robin participants is given above. It was planned that the "representative" diffraction patterns be sent to the Round-Robin participants. The "representative" designation has at least twofold connotation: First, diffraction patterns is collected with different radiation and geometry (sealed and synchrotron x-ray, CW neutrons). Second, it is of utmost importance for a successful Round Robin on methods of line-broadening analysis to have high-quality data without substantial systematic errors. The list of facilities where "representative" diffraction patterns were collected is given above.