CCP14
Methods, Problems and Solutions
Literature References relating to ESDs, Accuracy, Precision, Probable Error and Rietveld Analysis
The CCP14 Homepage is at http://www.ccp14.ac.uk
- "Background estimation using a robust Bayesian analysis",
W. I. F. David and D. S. Sivia,
J. Appl. Cryst. (2001). 34, 318-324
http://scripts.iucr.org/cgi-bin/paper?he0278
- "Robust Rietveld refinement in the presence of impurity phases",
W. I. F. David,
J. Appl. Cryst. (2001). 34, 691-698
http://scripts.iucr.org/cgi-bin/paper?he0280
- "A probabilistic approach to space-group determination from powder diffraction data",
A. J. Markvardsen, W. I. F. David, J. C. Johnson and K. Shankland,
Acta Cryst. (2001). A57, 47-54
http://scripts.iucr.org/cgi-bin/paper?gc0018
- Estimation of errors in the measurement of unit-cell parameters. I. Statistical uncertainties of peak positions of powder
diffraction lines determined by individual profile fitting
H. Toraya,
J. Appl. Cryst. (2001). 34, 558-565
http://scripts.iucr.org/cgi-bin/paper?hn0122
- Estimation of statistical uncertainties in quantitative phase analysis using the Rietveld method and the whole-powder-pattern
decomposition method
H. Toraya,
J. Appl. Cryst. (2000). 33, 1324-1328
http://scripts.iucr.org/cgi-bin/paper?hn0112
- Laboratory X-ray powder diffraction: a comparison of different
geometries with special attention to the usage of the CuK alpha doublet
M. Oetzel, G. Heger,
Journal of Applied Crystallography, 1999, Vol.32, No.Pt4, pp.799-807
http://www.iucr.org/cgi-bin/paper?zm0049
- Quantitative phase analysis of a- and b-silicon nitrides. I. Estimation of errors
H. Toraya,
J. Appl. Cryst. (1999). 32, 704-715
http://scripts.iucr.org/cgi-bin/paper?hn0112
- Quantitative phase analysis of a- and b-silicon nitrides. I. Estimation of errors
H. Toraya,
J. Appl. Cryst. (1999). 32, 704-715
http://scripts.iucr.org/cgi-bin/paper?hn0112
- Analysis of weighting schemes
R. Spagna and M. Camalli,
J. Appl. Cryst. (1999). 32, 934-942
http://scripts.iucr.org/cgi-bin/paper?he0236
- Rietveld refinement of site-occupancy parameters of Mg2-xMnxSiO4 using a new weight function in least-squares fitting
H. Toraya,
J. Appl. Cryst. (1999). 32, 51-59
http://www.iucr.org/cgi-bin/paper?hn0087
- "A practical approach to Rietveld analysis. Comparison of some programs running on personal computers".
L. Karanovic, I. PetrovicPrelevic, D. Poleti,
Powder Diffraction, 1999, Vol.14, No.3, pp.171-180
- "On the number of independent reflections in a powder diffraction pattern",
W. I. F. David,
J. Appl. Cryst. (1999). 32, 654-663
http://www.iucr.org/cgi-bin/paper?gl0589
- "Rietveld refinement guidelines",
L.B. McCusker, R.B. VonDreele, D.E. Cox, D. Louer, P. Scardi,
Journal of Applied Crystallography, 1999, Vol.32, No.Pt1, pp.36- 50
http://www.iucr.org/cgi-bin/paper?gl0561
- "Scale Factor in Powder Diffraction",
P. Riello, G. Fagherazzi and P. Canton,
Acta Cryst. (1998). A54, 219-224
http://www.iucr.org/cgi-bin/paper?gc0003
- "Accurate site occupancies for light atoms from powder X-ray data? Oxygen
vacancy ordering in 6H-BaFe0.67Ti0.33O3-delta (delta = 0.08 and 0.32)",
I.E. Grey, L.M.D. Cranswick, C. Li,
Journal of Applied Crystallography, 1998, Vol.31, No.Pt5, pp.692-699
- Rapid, accurate phase quantification of clay-bearing samples using a position-sensitive X-ray detector
M. Batchelder, G. Cressey,
Clays and Clay Minerals, 1998, Vol.46, No.2, pp.183-194
- "Effect of particle shape on the particle size distribution measured with commercial equipment",
M. Naito, O. Hayakawa, K. Nakahira, H. Mori, J. Tsubaki
Powder Technology, 1998, Vol.100, No.1, pp.52-60
- "Advances in powder diffraction analysis",
D. Louer,
Acta Crystallographica Section A, 1998, Vol.54, No.Pt6 SI1, pp.922-933
http://www.iucr.org/cgi-bin/paper?sc0008
- "Weighting Scheme for the Minimization Function in Rietveld Refinement",
H. Toraya,
J. Appl. Cryst. (1998). 31, 333-343
Synopsis: A new weighting scheme for the minimization function used in
the Rietveld method for structure refinement using powder diffraction data is
proposed. It significantly improved the accuracy of positional parameters of
test samples.
http://www.iucr.org/cgi-bin/paper?hn0067
- The influence of user-selected models on the results of the Rietveld refinement of the LaOCl structure
J. Holsa, M. Lastusaari, J. Valkonen,
Materials Science Forum, 1998, Vol.278-, pp.38-43
- "Standard uncertainty of angular positions and statistical quality of step-scan intensity data",
C. Rebmann, H. Ritter, J. Ihringer,
Acta Crystallographica Section A, 1998, Vol.54, No.Pt2, pp.225- 231
http://www.iucr.org/cgi-bin/paper?sh0098
- "A crystal structure model assembly program using a packing analysis method",
H. Miura,
Journal of the Ceramic Society of Japan, 1997, Vol.105, No.6, pp.536-540
- "Chemical accuracy and precision in Rietveld analysis: The crystal structure of cobalt(II) acetate tetrahydrate",
J.A. Kaduk, W. Partenheimer,
Powder Diffraction, 1997, Vol.12, No.1, pp.27-39
- "Symmetry Information Inherent in Powder Diffraction Data: a- and b-Quartz as Examples",
M. Ohmasa, K. Ohsumi, H. Toraya and H. Tokushima-Houki,
J. Appl. Cryst. (1997). 30, 254-258
http://www.iucr.org/cgi-bin/paper?hn0051
- "Redetermination of the crystal structure of Al2Br6. A comparison of three methods",
R.W. Berg, F.W. Poulsen, K. Nielsen,
Acta Chemica ScandinavicA, 1997, Vol.51, No.4, pp.442-448
- "Empirical texture correction for different diffraction geometries: Experimental tests",
R. Cerny, V. Valvoda,
Materials Science Forum, 1996, Vol.228, No.Pt1&2, pp.77-82
- "Powder diffraction",
J.I. Langford, D. Louer,
Reports on Progress in Physics, 1996, Vol.59, No.2, pp.131-234
- "Structure refinement with synchrotron data: R-factors, errors and significance tests",
D.E. Cox, R.J. Papoular,
Materials Science Forum, 1996, Vol.228, No.Pt1&2, pp.233-238
- "X-ray Rietveld analysis with a physically-based background",
P. Riello, G. Fagherazzi, D. Clemente, P. Canton,
journal of applied crystallography, 1995, Vol.28, No.Pt2, pp.115-120
http://www.iucr.org/cgi-bin/paper?hw0038
- "R-values in analysis of powder diffraction data using rietveld refinement",
E. Jansen, W. Schafer, G. Will,
Journal of Applied Crystallography, 1994, Vol.27, No.Pt4, pp.492-496
http://www.iucr.org/cgi-bin/paper?hn0019
- "International-Union-of-Crystallography - Commission on Powder Diffraction - Rietveld Refinement Round-Robin .2.
analysis of monoclinic ZrO2",
R.J. Hill, L.M.D. cranswick,
journal of applied crystallography, 1994, Vol.27, No.Pt5, pp.802-844
http://www.iucr.org/cgi-bin/paper?gl0318
- "Collection and analysis of powder diffraction data with near-constant counting statistics",
I. C. Madsen and R. J. Hill,
J. Appl. Cryst. (1994). 27, 385-392
http://www.iucr.org/cgi-bin/paper?hz0014
- "A Bayesian approach to extracting structure-factor amplitudes from powder diffraction data",
D. S. Sivia and W. I. F. David,
Acta Cryst. (1994). A50, 703-714
http://www.iucr.org/cgi-bin/paper?he0087
- "The use of the serial-correlations concept in the Figure-Of- Merit function for powder diffraction profile fitting",
Y.G. Andreev,
Journal of Applied Crystallography, 1994, Vol.27, No.Pt3, pp.288-297
http://www.iucr.org/cgi-bin/paper?la0059
- "Modeling of line-shape asymmetry in powder diffraction",
J.F. Berar, G. Baldinozzi,
Journal of Applied Crystallography, 1993, Vol.26, No.Pt1, pp.128-129
http://scripts.iucr.org/cgi-bin/paper?la0032
- "X-ray powder diffraction analysis of silver behenate, a possible low-angle diffraction standard",
T. C. Huang, H. Toraya, T. N. Blanton and Y. Wu,
J. Appl. Cryst. (1993). 26, 180-184
http://www.iucr.org/cgi-bin/paper?wi0112
- "Whole-pattern fitting in energy-dispersive powder diffraction",
V. Honkimaki, P. Suortti,
Journal of Applied Crystallography, 1992, Vol.25, No.Pt2, pp.97- 104
http://www.iucr.org/cgi-bin/paper?sr0127
- "On the determination of accurate intensities from powder diffraction data. I.
Whole-pattern fitting with a least-squares procedure",
J. Jansen, R. Peschar and H. Schenk,
J. Appl. Cryst. (1992). 25, 231-236
http://www.iucr.org/cgi-bin/paper?gl0222
- "On the determination of accurate intensities from powder diffraction data. II.
Estimation of intensities of overlapping reflections",
J. Jansen, R. Peschar and H. Schenk,
J. Appl. Cryst. (1992). 25, 237-243
http://www.iucr.org/cgi-bin/paper?gl0227
- (Original Hill and Madsen VCT (variable count time) Paper),
I. C. Madsen and R. J. Hill,
Adv. X-ray Anal. (1992), 35, 39-47
- (Bill David VCT (variable count time) reference),
W. I. F. David,
Accuracy in Powder Diffraction, Abstract P2.6 NIST Special
Publication No. 846, Page 210, (1992) National Institute of
Standards and Technology, Gaithersburg, MD, USA.
- "Structure refinement of mullite by the Rietveld method and a new method for estimation of chemical-composition",
T. Ban, K. Okada,
Journal of the American Ceramic Society, 1992, Vol.75, No.1, pp.227-230
- International-Union-of-Crystallography - Commission on Powder Diffraction - Rietveld Refinement Round-Robin .1.
analysis of standard X-ray and neutron data for PbSO4
R.J. Hill,
Journal of Applied Crystallography, 1992, Vol.25, No.Pt5, pp.589-610
http://www.iucr.org/cgi-bin/paper?gl0234
- "ESDs and estimated probable-error obtained in Rietveld refinements with local correlations",
J.F. Berar, P. Lelann,
Journal of Applied Crystallography, 1991, Vol.24, No.Pt1, pp.1-5
http://www.iucr.org/cgi-bin/paper?ms0319
- "Rietveld analysis using para-focusing and Debye-Scherrer geometry data collected with a Bragg-Brentano",
diffractometer
R.J. Hill, I.C. Madsen,
Zeitschrift fur Kristallographie, 1991, Vol.196, No.1-4, pp.73- 92
- "Profile agreement indexes in rietveld and pattern-fitting analysis",
R.J. Hill and R.X. Fischer,
Journal of Applied Crystallography, 1990, Vol.23, No.Pt6, pp.462-468
http://www.iucr.org/cgi-bin/paper?wi0047
- "Statistical descriptors in crystallography: Report of the IUCr Subcommittee on Statistical Descriptors",
D. Schwarzenbach, S. C. Abrahams, H. D. Flack, W. Gonschorek, Th. Hahn, K. Huml, R. E. Marsh, E. Prince, B. E.
Robertson, J. S. Rollett and A. J. C. Wilson,
Acta Cryst. (1989). A45, 63-75
http://www.iucr.org/cgi-bin/paper?er0097
- "Effect of divergence and receiving slit dimensions on peak profile parameters in Rietveld analysis of X-ray diffractometer data",
I. C. Madsen and R. J. Hill,
J. Appl. Cryst. (1988). 21, 398-405
http://www.iucr.org/cgi-bin/paper?pn0040
- "On the use of least-squares restraints for origin fixing in polar space groups",
H. D. Flack and D. Schwarzenbach,
Acta Cryst. (1988). A44, 499-506
http://www.iucr.org/cgi-bin/paper?bx0238
- "The use of the Durbin-Watson D-statistic in Rietveld analysis",
R.J. Hill, H.D. Flack,
Journal of Applied Crystallography, 1987, Vol.20, No.Pt5, pp.356-361
http://www.iucr.org/cgi-bin/paper?a27781
- "The probabilistic determination of intensities of completely overlapping reflections in powder diffraction patterns",
W. I. F. David,
J. Appl. Cryst. (1987). 20, 316-319
http://www.iucr.org/cgi-bin/paper?a27768
- "The effect of profile step width on the determination of crystal structure parameters and estimated standard deviations by
X-ray Rietveld analysis",
R. J. Hill and I. C. Madsen,
J. Appl. Cryst. (1986). 19, 10-18
http://scripts.iucr.org/cgi-bin/paper?a26304
- "Calculation of diffraction line-profiles in the case of coupled stacking-fault and size-effect broadening -
application to boehmite AlOOH",
D. Grebille, J.F. Berar,
Journal of Applied Crystallography, 1986, Vol.19, No.Pt4, pp.249-254
http://www.iucr.org/cgi-bin/paper?a26363
- "Calculation of diffraction line-profiles in the case of a major size effect - application to boehmite AlOOH",
D. Grebille, J.F. Berar,
Journal of Applied Crystallography, 1985, Vol.18, No.OCT, pp.301-307
http://www.iucr.org/cgi-bin/paper?a25249
- "Peak shape variation in fixed-wavelength neutron powder diffraction and its effect on structural parameters obtained by
Rietveld analysis",
R. J. Hill and I. C. Madsen,
J. Appl. Cryst. (1985). 18, 173-180
http://www.iucr.org/cgi-bin/paper?a25219
- "The effect of profile-step counting time on the determination of crystal structure parameters by X-ray Rietveld analysis",
R. J. Hill and I. C. Madsen,
J. Appl. Cryst. (1984). 17, 297-306
http://www.iucr.org/cgi-bin/paper?a24160
- "The analysis of powder diffraction data",
M. J. Cooper,
Acta Cryst. (1982). A38, 264-269
(SCRAP method for structure refinement from powder diffraction data)
Abstract: A comparison has been carried out between the results
of analysis of several sets of neutron powder diffraction
data using three different methods: the Rietveld
method [Rietveld (1967). Acta Cryst. 22, 151-152;
(1969) J. Appl. Cryst. 2, 65-711, a modification of the
Rietveld method to include off-diagonal terms in the
weight matrix [Clarke and Rollett (1982). Acta Cryst.
Submitted] and the SCRAP method, which involves the
estimation of observed Bragg intensities [Cooper,
Rouse and Sakata (1981) Z. Kristallogr. 157, 101-117]
Two simulations have also been carried out to
demonstrate the way in which the results can differ in
more extreme cases. This study has confirmed that the
values of the estimated standard deviations given by the
Rietveld method are not reliable and that, of the
methods considered, only the SCRAP method will in
general give reliable values for the estimated
standard deviations of the structural parameters.
http://www.iucr.org/cgi-bin/paper?a20636
- "The estimation of standard deviations in powder diffraction Rietveld refinements",
H. G. Scott,
J. Appl. Cryst. (1983). 16, 159-163
Abstract: It is shown that when the observed and calculated
intensities in a powder diffraction pattern differ
because of the model errors which affect the calculated
integrated intensities, in addition t the random
counting errors, Rietveld refinement with weights
determined solely by counting statistics yields estimated
standard deviations for the crystal structure
parameters which tend to be measures of the precision
rather than the accuracy of these parameters. Under
these conditions, e.s.d.'s calculated by Rietveld
refinement may be significantly smaller than those obtained
by integrated intensity refinement of the same data set.
A method of adjusting Rietveld e.s.d.'s, to provide
comparability with integrated intensity refinement,
is proposed.
Extract: It seems generally accepted that Rietveld refinement
yields unbiased estimates for the crystal structure parameters.
However, there is some ambiguity as to the
physical significance of the estimated standard
deviations calculated by current Rietveld refinement
programs. For example, Haywood and Shirley (1977)
found that is was necessary to multiply the e.s.d.'s for
the crystal structure parameters by factors of 2 to 3 to
reconcile the refinements of three sets of profile data
for tetraiodoethylene. Sakata and Cooper (1979) have
examined the problem analytically and concluded that
the correlation of errors in adjacent observations
could lead to the e.s.d.'s being underestimated in
Rietveld refinement: on the basis of some experimental
results they suggested that a factor of at least 2 could
be involved.
Subsequently, Hewat and Sabine (1981) and Prince (1981)
have challenged the analysis of Sakata and
Cooper and claimed that the usual Rietveld refinement
programs do provide correct e.s.d.'s. However,
they have demonstrated this only for hte case in which
counting statistics are the sole source of error, which
probably arises seldom.
Pawley (1980) has asserted that 'it is probable that
no published powder refinement has been limited by
counting statistics'.
http://www.iucr.org/cgi-bin/paper?a22890
- "Counting statistics and powder diffraction scan refinements",
E. Baharie and G. S. Pawley,
J. Appl. Cryst. (1983). 16, 404-406
http://www.iucr.org/cgi-bin/paper?a22940
- "Comparison of the fits of two models to the same data set",
E. Prince,
Acta Cryst. (1982). B38, 1099-1100
http://scripts.iucr.org/cgi-bin/paper?a21085
- "Suggested guidelines for the publication of Rietveld analyses and pattern decomposition studies",
R. A. Young, E. Prince and R. A. Sparks,
J. Appl. Cryst. (1982). 15, 357-359
http://www.iucr.org/cgi-bin/paper?a21793
- "Comparison of profile and integrated-intensity methods in powder refinement",
E. Prince,
J. Appl. Cryst. (1981). 14, 157-159
Abstract: If a powder pattern consists of well resolved peaks, and
if it is adequately described by a crystallographic model,
as determined by statistical tests, the estimates of the
parameters and their standard deviations will nto be
significantly different, in a statistical sense, whether the
method of refinement uses peak profiles or integrated
intensities. If the model does not fit adequately, the
standard deviations cannot be calculated by statistical
methods. If peaks overlap, there are correlations
between the intensities of the individual peaks that are
handled automatically in the profile method, but must be
included explicitly in the integrated-intensity
method. A background function should be included in
the model, and its parameters refined. The background
parameters have correlations with other parameters
that become important if the pattern is complex, and
therefore poorly resolved.
Extract: In a recent paper Sakata and Cooper (1979, hereafter
referred to as SC) have analyzed the technique of
refinement of powder data fitting the entire pattern
using adjustable parameters, as developed originally by
Rietveld (1969), and compared it with an alternative
procedure which fits the integrated intensities of
individual Bragg peaks. They assert that the profile
method calculates the estimated standard deviations of
the refined parameters incorrectly, leading to a
systematic underestimate of the uncertainties of the
crystallographic parameters. The purpose of this
communication is to show that, if the assumptions on
which the method of least squares is based are satisfied,
the two methods give similar results. If the fit of the
assumed model is not adequate, the precision and
accuracy of the parameter estimates cannot be validly
assessed by statistical methods.
http://www.iucr.org/cgi-bin/paper?a20490
- "The influence of systematic errors in crystal structure refinements using Guinier camera X-ray intensity data",
H. G. Scott,
Acta Cryst. (1981). A37, 456-459
http://www.iucr.org/cgi-bin/paper?a19696
- A. W. Hewatt and T. M. Sabine,
NSW Institute of Technology, Internal Report. (1981). NSWIT/PMN 24
- "Unit-cell refinement from powder diffraction scans",
G. S. Pawley,
J. Appl. Cryst. (1981). 14, 357-361
http://www.iucr.org/cgi-bin/paper?a20546
- "Unit-cell refinement from powder diffraction scans",
G. S. Pawley,
J. Appl. Cryst. (1981). 14, 357-361
Extract: The author wishes to thank Drs A. W. Hewat and R. Shirley,
with whom the experimental work was done and with whom attempts
to solve structures using no more than powder diffraction
data will continue.
http://www.iucr.org/cgi-bin/paper?a20546
- "EDINP, the Edinburgh powder profile refinement program",
G. S. Pawley,
J. Appl. Cryst. (1980). 13, 630-633
http://www.iucr.org/cgi-bin/paper?a19573
- "An analysis of the Rietveld refinement method",
M. Sakata and M. J. Cooper,
J. Appl. Cryst. (1979). 12, 554-563
Abstract: An analysis of the Rietveld profile refinement method
used in the interpretation of neutron or X-ray powder
diffraction patterns has been carried out. It is shown
that the values obtained for the structural parameters
are not exactly the same as those obtained from an
integrated intensity refinement of the same data and
that the standard deviations of the parameters are
determined incorrectly. Whilst the differences in the
values of the parameters may not be statistically
significant, the fact that their standard deviations are
estimated incorrectly severly limits their usefulness.
These conclusions are confirmed by refinement of a
number of data sets using both methods and in most of
these cases the standard deviations are found to be
underestimated by the profile refinement method by a
factor of at least two. Discussions based on the results of
profile refinement must therefore be reconsidered and
the relative value of powder diffraction techniques must
be reviewed.
http://www.iucr.org/cgi-bin/paper?a18236
- "A profile refinement method for nuclear and magnetic structures",
H. M. Rietveld,
J. Appl. Cryst. (1969). 2, 65-71
http://www.iucr.org/cgi-bin/paper?a07067
- "Line profiles of neutron powder-diffraction peaks for structure refinement",
H. M. Rietveld,
Acta Cryst. (1967). 22, 151-152
http://www.iucr.org/cgi-bin/paper?a05418
- "Precise and accurate lattice parameters by film powder methods. II. An exact eccentricity
correction for cylindrical film cameras",
K. E. Beu and D. L. Scott,
Acta Cryst. (1962). 15, 1301-1304
http://www.iucr.org/cgi-bin/paper?a03696
- M. J. Buerger,
Vector Space, (1959). pp. 198-217, New York: Wiley.