Measurement of individual structure-factor phases with tenth-degree accuracy: the 00.2 reflection in BeO studied by electron and X-ray diffraction

Zuo, Jian‐Min; Spence, J.C.H.; Downs, James W.

doi:10.1107/s0108767392010699

Cited by 18 publications

(5 citation statements)

References 12 publications

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“…Nevertheless, it may only be possible to obtain this with sufficient accuracy for simple structures -the only example we know of is BeO (Zuo, Spence, Downs & Mayer, 1993).…”

Section: Discussionmentioning

confidence: 99%

The Phase Problem in the Analysis of X-ray Diffraction Data in Terms of Electron-Density Distributions

Haouzi¹,

Hansen²,

Hénaff³

et al. 1996

Acta Crystallogr A Found Crystallogr

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The refinement of electron-density distributions for noncentrosymmetric crystals from X-ray diffraction data may lead to a very good fit between model and data but to totally meaningless electron densities. This is to a large extent because varying certain parameters, or combination of parameters, in the model mainly leads to a change in the phases of the structure factors. A formal analysis of why this happens, when using multipole models, is given as well as specific examples using real data: the contributions of odd-order multipoles, which are invariant under crystal-class symmetry operations, are poorly determined. The importance of applying constraints on the models is stressed. The conclusions of this analysis can be carried over to refinements of anharmonic atomic vibrations.

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“…Nevertheless, it may only be possible to obtain this with sufficient accuracy for simple structures -the only example we know of is BeO (Zuo, Spence, Downs & Mayer, 1993).…”

Section: Discussionmentioning

confidence: 99%

The Phase Problem in the Analysis of X-ray Diffraction Data in Terms of Electron-Density Distributions

Haouzi¹,

Hansen²,

Hénaff³

et al. 1996

Acta Crystallogr A Found Crystallogr

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show abstract

“…As a final example of structure-factor phase measurement, the 002 reflection in the noncentrosymmetric BeO crystal structure has been measured (Zuo, Spence, Downs & Mayer, 1993). BeO has the wurtzite structure, space group P63mc, with cell parameters a = 2.6979 (2) and c = 4.3772 (2) A (Downs, Ross & Gibbs, 1985).…”

Section: F/ Lmentioning

confidence: 99%

On the accurate measurement of structure-factor amplitudes and phases by electron diffraction

Spence¹

1993

Acta Cryst Sect A

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138

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A review is given of research into the measurement of crystal structure-factor amplitudes and phases by transmission electron diffraction. Accuracies for amplitudes are commonly a fraction of a percent (after conversion to X-ray structure factors) while phases may now be measured in favorable cases using three-beam electron diffraction to an accuracy of much better than 1 °. Following a brief review of theory, the main techniques are outlined. These include quantitative convergent-beam electron diffraction, the critical-voltage method, the intersecting K_ikuchi-and HOLZ-Iine methods and methods based on weak high-order reflections in wide-angle patterns. Enantiomorphs and polarity are discussed. Summaries are given of measurements of the mean inner potential and of structure factors generally. A brief review of the implications of this work for studies of crystal bonding and ordering in alloys is given, and its use to test ab initio computations of charge density. The mean inner potential is found to be the quantity most sensitive to the bonding distribution of valence electrons and sensitively constrains accurate X-ray structure-factor measurements. Electron diffraction techniques are to be preferred for studies of individual microcrystals or artificially formed structures and for the very accurate measurement of structure-factor phases in acentric crystals with small unit cells.

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“…We note that experimental determination of phases is an active area of research (see, for example, Shen & Colella, 1986;Hiimmer, Weckert & Bondza, 1990;Spence, 1993), although the only useful results (for the purposes of charge density analysis) appear to be measurements of the phase of the 002 reflection (with estimated error 0.07 °) in CdS (Zuo, Spence & Hoier, 1989) and the 002 reflection in BeO [with estimated error 0.52 ° (Zuo, Spence, Downs & Mayer, 1993)]; for organics, triplet phases can be determined with an accuracy of -,~45 ° (Htimmer et al, 1990).…”

Section: Introductionmentioning

confidence: 99%

Retrieval of Structure-Factor Phases in Non-centrosymmetric Space Groups. Model Studies Using Multipole Refinements

Spackman¹,

Byrom²

1997

Acta Crystallogr Sect B

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Structure factors with known magnitude and phase are constructed for seven different molecular crystals in non-centrosymmetric space groups and used to calibrate the retrieval of structure-factor phase information with several different scattering factor models. Monopole models are confirmed to be inadequate, yielding poor estimates of phases and underestimating the Fourier deformation electron density by as much as 50%. Multipole models are generally successful, with the conspicuous exception of hexamethylenetetramine (HMT). The results confirm the known difficulty of phasing structure-factor magnitudes for HMT, but reveal a broad spectrum of behaviour of phase retrieval in various non-centrosymmetric space groups, depending partly on the number of reflections with restricted phases. For several systems (urea, hydrogen peroxide, L-alanine and borazine) the results confirm that multipole refinements of scattering factor models against experimental data are capable of yielding highly accurate phases and hence reliable electron distributions. For the exceptional case of HMT a simple eigenvalue filtering technique enables retrieval of phases and electron densities with an accuracy comparable to the best of the other non-centrosymmetric systems studied.

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Measurement of individual structure-factor phases with tenth-degree accuracy: the 00.2 reflection in BeO studied by electron and X-ray diffraction

Cited by 18 publications

References 12 publications

The Phase Problem in the Analysis of X-ray Diffraction Data in Terms of Electron-Density Distributions

The Phase Problem in the Analysis of X-ray Diffraction Data in Terms of Electron-Density Distributions

On the accurate measurement of structure-factor amplitudes and phases by electron diffraction

Retrieval of Structure-Factor Phases in Non-centrosymmetric Space Groups. Model Studies Using Multipole Refinements

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