Literature References relating to ESDs, Accuracy, Precision, Probable Error and Rietveld Analysis

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[Problems and Solutions]
[Rietveld R and fit factors] | [Errors and Rietveld R Factors] | [ESDs, Probable Error and Rietveld Analysis]
[Calibration standards for Powder Diffraction] | [Diffconv - INEL PSD Spline based Data Calibration]

"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.

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