Statistical descriptors in crystallography: Report of the IUCr Subcommittee on Statistical Descriptors

Schwarzenbach, D.; Abrahams, S. C.; Flack, H. D.; Gonschorek, W.; Hahn, Th.; Huml, K.; Marsh, Richard E.; Prince, E.; Robertson, B. E.; Rollett, J. S.; Wilson, A. J. C.

doi:10.1107/s0108767388009596

Cited by 75 publications

(36 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If the data are oversampled, not only is no new information introduced, the points in the PDF are not statistically independent, [9,10] which leads to improper estimates of uncertainties in refinement parameters and slowing down the refinement. [11] We have systematically studied the optimal PDF sampling interval for PDF data and demonstrate that it is consistent with the value predicted by the Nyquist-Shannon sampling theorem. [12] This gives the minimum amount of information we need to completely specify a PDF from a given F (Q).…”

Section: Introductionsupporting

confidence: 64%

See 1 more Smart Citation

Nyquist-Shannon sampling theorem applied to refinements of the atomic pair distribution function

et al. 2011

View full text Add to dashboard Cite

We have systematically studied the optimal realspace sampling of atomic pair distribution data by comparing refinement results from oversampled and resampled data. Based on nickel and a complex perovskite system, we demonstrate that the optimal sampling is bounded by the Nyquist interval described by the Nyquist-Shannon sampling theorem. Near this sampling interval, the data points in the PDF are minimally correlated, which results in more reliable uncertainty prediction. Furthermore, refinements using sparsely sampled data may run many times faster than using oversampled data. This investigation establishes a theoretically sound limit on the amount of information contained in the PDF, which has ramifications towards how PDF data are modeled.

show abstract

Section: Introductionsupporting

confidence: 64%

“…The algorithm also provides estimates of uncertainties on those parameters upon convergence, though strictly the estimates are only accurate if the data are independent and the statistical errors are Gaussian distributed and properly determined. [11] 3 The Nyquist-Shannon sampling theorem…”

Section: The Pdf Methodsmentioning

confidence: 99%

Nyquist-Shannon sampling theorem applied to refinements of the atomic pair distribution function

et al. 2011

View full text Add to dashboard Cite

show abstract

“…Many aspects are summarized in the Reports of IUCr subcommittees on Statistical Descriptors in Crystallography (Schwarzenbach et al, 1989(Schwarzenbach et al, , 1995. In their second Report, inter alia they emphasize the terms uncertainty and standard uncertainty (s.u.).…”

Section: A4 Statistical Descriptors and Goodness Of ®Tmentioning

confidence: 99%

Remarks about protein structure precision

Cruickshank

1999

Acta Crystallogr D Biol Crystallogr

513

482

View full text Add to dashboard Cite

Full‐matrix least squares is taken as the basis for an examination of protein structure precision. A two‐atom protein model is used to compare the precisions of unrestrained and restrained refinements. In this model, restrained refinement determines a bond length which is the weighted mean of the unrestrained diffraction‐only length and the geometric dictionary length. Data of 0.94 Å resolution for the 237‐residue protein concanavalin A are used in unrestrained and restrained full‐matrix inversions to provide standard uncertainties σ(r) for positions and σ(l) for bond lengths. σ(r) is as small as 0.01 Å for atoms with low Debye B values but increases strongly with B. The results emphasize the distinction between unrestrained and restrained refinements and between σ(r) and σ(l). Other full‐matrix inversions are reported. Such inversions require massive calculations. Several approximate methods are examined and compared critically. These include a Fourier map formula [Cruickshank (1949). Acta Cryst.2, 65–82], Luzzati plots [Luzzati (1952). Acta Cryst.5, 802–810] and a new diffraction‐component precision index (DPI). The DPI estimate of σ(r, Bavg) is given by a simple formula. It uses R or Rfree and is based on a very rough approximation to the least‐squares method. Many examples show its usefulness as a precision comparator for high‐ and low‐resolution structures. The effect of restraints as resolution varies is examined. More regular use of full‐matrix inversion is urged to establish positional precision and hence the precision of non‐dictionary distances in both high‐ and low‐resolution structures. Failing this, parameter blocks for representative residues and their neighbours should be inverted to gain a general idea of σ(r) as a function of B. The whole discussion is subject to some caveats about the effects of disordered regions in the crystal.

show abstract

“…For SA the largest difference is observed for the lattice parameter c with a value of 0.0014 Å after water-based processing (SAH2O). However, it has to be taken into account that deviations in the range of ≈ 0.001 Å have to be interpreted carefully since they are in the range of measurement inaccuracy [28][29][30][31]. This applies in particular in the present case, as no systematic tendency in the change of lattice parameters can be For the neutron data, 7 h acquisition time was used and a comparable 8 h time was used for the first two XRD measurements of cathodes.…”

Section: Resultsmentioning

confidence: 99%

Influence of Particle Morphologies of LiFePO4 on Water- and Solvent-Based Processing and Electrochemical Properties

et al. 2017

View full text Add to dashboard Cite

LiFePO 4 (LFP) primary particles and secondary agglomerates have been processed into water-and solvent-based cathodes. By means of neutron and X-ray diffraction it was found that no structural changes of LiFePO 4 occurred upon water-and solvent-based slurry preparation. Electrochemical characterization was carried out with full-cells and a distinct influence of particle morphology was observable. Water-based processing of primary particles leads to deficits in electrochemical performance while secondary agglomerates are non-sensitive to water during processing. In the presence of water, high mechanical stress during slurry preparation causes a partial detachment of carbon coating. However, this effect is negligible for secondary agglomerates since only surface particles are exposed to mechanical stress. Due to longer diffusion paths and the fact that secondary agglomerates represent a micro-heterogeneity in the cathode, the C-rate capability of secondary agglomerates is slightly lower than that of primary particles. This paper demonstrates that for any high energy application with moderate C-rates, secondary agglomerates hold a great potential for environmentally friendly and cost-efficient water-based cathode production.

show abstract

Statistical descriptors in crystallography: Report of the IUCr Subcommittee on Statistical Descriptors

Cited by 75 publications

References 31 publications

Nyquist-Shannon sampling theorem applied to refinements of the atomic pair distribution function

Nyquist-Shannon sampling theorem applied to refinements of the atomic pair distribution function

Remarks about protein structure precision

Influence of Particle Morphologies of LiFePO4 on Water- and Solvent-Based Processing and Electrochemical Properties

Contact Info

Product

Resources

About