Maximum-likelihood methods in powder diffraction refinements

Antoniadis, Anestis; Berruyer, Jacques; Filhol, A.

doi:10.1107/s0108767390004500

Cited by 46 publications

(21 citation statements)

References 18 publications

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“…Using the program ABFfit, which uses the algorithm of maximum resemblance to compare observed and calculated profiles (Antoniadis, Berruyer and Filhol, 1990) the positions of 17 peaks were extracted. Using the program ABFfit, which uses the algorithm of maximum resemblance to compare observed and calculated profiles (Antoniadis, Berruyer and Filhol, 1990) the positions of 17 peaks were extracted.…”

Section: Resultsmentioning

confidence: 99%

The structure of solid carbon tetrafluoride

Fitch¹

1993

Zeitschrift Für Kristallographie - Crystalline Materials

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The structure of phase II of CF 4 has been refined in the monoclinic space group C2/n (No. 15) from high-resolution powder neutron diffraction data. At 1.5 Κ the lattice parameters are a = 8.4098(2) Â, b = 4.3022(1) A, c = 8.3506(2) Â, and β = 119.588(1)°, Ζ = 4. An error in the table of coordinates in the original report of the structure, which was improperly corrected in a subsequent paper, has been rectified. The refined structure of phase II is in excellent agreement with recent theoretical calculations of the crystal static energy and molecular dynamics simulations. The unit cell of the orientationally disordered phase I has been indexed as rhombohedral, a = 11.577(9) Â, α = 89.49(1)° at 80 K. It is likely that this phase is isostructural with phase lb of CC1 4 .

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Section: Resultsmentioning

confidence: 99%

The structure of solid carbon tetrafluoride

Fitch¹

1993

Zeitschrift Für Kristallographie - Crystalline Materials

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“…'s are critical to the correct interpretation of small differences (e.g. oxidation states, occupancy parameters or unusual bond lengths that might indicate unusual chemistry), the reader is referred to the papers by Prince (1981Prince ( , 1993, Scott (1983), Hill & Flack (1987), Hill & Madsen (1987), Antoniadis et al (1990), Be Â rar (1992) and Cox & Papoular (1996).…”

Section: Estimated Standard Deviationsmentioning

confidence: 99%

Rietveld refinement guidelines

et al. 1999

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A set of general guidelines for structure re®nement using the Rietveld (whole-pro®le) method has been formulated by the International Union of Crystallography Commission on Powder Diffraction. The practical rather than the theoretical aspects of each step in a typical Rietveld re®nement are discussed with a view to guiding newcomers in the ®eld. The focus is on X-ray powder diffraction data collected on a laboratory instrument, but features speci®c to data from neutron (both constant-wavelength and time-of-¯ight) and synchrotron radiation sources are also addressed. The topics covered include (i) data collection, (ii) background contribution, (iii) peak-shape function, (iv) re®nement of pro®le parameters, (v) Fourier analysis with powder diffraction data, (vi) re®nement of structural parameters, (vii) use of geometric restraints, (viii) calculation of e.s.d.'s, (ix) interpretation of R values and (x) some common problems and possible solutions.

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“…Although several methods have previously been proposed to overcome this issue (Antoniadis et al, 1990;David & Sivia, 2001), they are difficult to incorporate into existing Rietveld programs as they require changes to the refinement algorithm. This bias is particularly problematic in cases where the experimental data are typified by low background values.…”

Section: Discussionmentioning

confidence: 99%

“…In these programs, leastsquares refinement is performed using different weights or maximum-likelihood methods (Rietveld, 1969;Sakata & Cooper, 1979;Wiles & Young, 1981;Antoniadis et al, 1990;Hill & Fischer, 1990;Toraya, 1998;Altomare et al, 2001). In these programs, leastsquares refinement is performed using different weights or maximum-likelihood methods (Rietveld, 1969;Sakata & Cooper, 1979;Wiles & Young, 1981;Antoniadis et al, 1990;Hill & Fischer, 1990;Toraya, 1998;Altomare et al, 2001).…”

Section: Introductionmentioning

confidence: 99%

Bayesian approach to the Rietveld refinement of Poisson-distributed powder diffraction data

Bergmann¹,

Monecke

2010

J Appl Cryst

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The Rietveld method is based on a weighted least‐squares fit of a model diffraction pattern to the step‐scan data of a complete experimental X‐ray or neutron diffraction pattern. It is shown here that the weight most commonly used in Rietveld refinement of powder diffraction data leads to a biased background estimate. To overcome this bias, an alternative method for refinement of Poisson‐distributed experimental data is suggested that only involves changes of the input data and the weights of least‐squares refinement. Model calculations demonstrate that this novel method allows an improved refinement of the parameters describing the background and the Bragg reflections. The proposed method can be readily implemented in existing Rietveld programs.

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Maximum-likelihood methods in powder diffraction refinements

Cited by 46 publications

References 18 publications

The structure of solid carbon tetrafluoride

The structure of solid carbon tetrafluoride

Rietveld refinement guidelines

Bayesian approach to the Rietveld refinement of Poisson-distributed powder diffraction data

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