Structure analysis of displacively modulated molecular crystals

Petřı́ček, V.; Coppens, Philip; Becker, Petra

doi:10.1107/s0108767385001027

Cited by 48 publications

(17 citation statements)

References 7 publications

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“…all atoms of the ring must be in phase. The final structural model can be described by the following three main features [61,64]: a torsion with an amplitude of 5:5 for each phenyl ring, i.e., the maximum deformation angle being f ¼ 11 , a rotation around the normal to the mean molecular plane, with an amplitude of w ¼ 1 and a translation along the long molecular axis with an amplitude of d ¼ 0:035 Å (Fig. 6).…”

Section: Even a H--h Distance Of D H--h ¼ 22 å Is Reportedmentioning

confidence: 99%

“…In some first publications [64,69] the "rigid-body approach" known from the treatment of thermal motion [70] was extended and applied to the displacive modulation of molecular crystal structures assuming a molecule or a part of it to be displaced as a rigid-unit. It is argued, that due to stiffness of the intramolecular linkages between the atoms -for example due to covalent bonds -translational and rotational displacement does not affect only individual atoms but the complete molecule or at least some of its segments.…”

Section: Modulated Moleculesmentioning

confidence: 99%

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Organic molecular compounds with modulated crystal structures

Schoenleber¹

2011

Zeitschrift Für Kristallographie

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Abstract. Even though the higher-dimensional superspace approach is an established method to describe aperiodic crystal structures, it is not yet fully considered and applied by a larger community of scientists. In this contribution the structural description of incommensurately and commensurately modulated molecular compounds is discussed and it is shown, that the higher-dimensional superspace approach is an elegant way for an exact structural description and an exact crystal-chemical analysis of such structures. While discussing several modulated molecular compounds, the idea behind the higher-dimensional superspace approach is shown. On the examples treated in the discussion it is explained, how to understand and how to interprete modulated molecular compounds. Also a short introduction is given to the higher-dimensional superspace approach itself, to the basic principles and to the applied nomenclature.

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Section: Even a H--h Distance Of D H--h ¼ 22 å Is Reportedmentioning

confidence: 99%

Section: Modulated Moleculesmentioning

confidence: 99%

Organic molecular compounds with modulated crystal structures

Schoenleber¹

2011

Zeitschrift Für Kristallographie

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“…The computer program COMPREF used in the refinements allows both displacive and occupational modulation. It incorporates the rigidbody displacement model of Petricek, Coppens & Becker (1985). Expression (9) differs from the expression given recently by Kato (1990) which requires a numerical integration over the modulation.…”

Section: H~=(hkl) H2:(hkm)mentioning

confidence: 88%

The description and analysis of composite crystals

Petřı́ček¹,

Malý²,

Coppens³

et al. 1991

Acta Cryst Sect A

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“…As discussed in Section 2.3 calculations within statistical method require slightly more advanced mathematics. The method allows, however, for fully analytical derivation of the structure factor formula with no need of complex expansion methods used in classical approach to the subject [39][40][41]. General formula (8) can be again reduced to 1D integration over distribution P(u) given in (4) in 3 intervals defined in (5).…”

Section: Structure Factor For Modulated Structuresmentioning

confidence: 99%

“…The complete diffraction pattern of Thue-Morse chain is presented in Figure 4c. expansion methods used in classical approach to the subject [39][40][41]. General formula (8) can be again reduced to 1D integration over distribution ( ) given in (4) in 3 intervals defined in (5).…”

Section: Structure Factor For Thue-morse Sequencementioning

confidence: 99%

Statistical Approach to Diffraction of Periodic and Non-Periodic Crystals—Review

2016

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Abstract:In this paper, we show the fundamentals of statistical method of structure analysis. Basic concept of a method is the average unit cell, which is a probability distribution of atomic positions with respect to some reference lattices. The distribution carries complete structural information required for structure determination via diffraction experiment regardless of the inner symmetry of diffracting medium. The shape of envelope function that connects all diffraction maxima can be derived as the Fourier transform of a distribution function. Moreover, distributions are sensitive to any disorder introduced to ideal structure-phonons and phasons. The latter are particularly important in case of quasicrystals. The statistical method deals very well with phason flips and may be used to redefine phasonic Debye-Waller correction factor. The statistical approach can be also successfully applied to the peak's profile interpretation. It will be shown that the average unit cell can be equally well applied to a description of Bragg peaks as well as other components of diffraction pattern, namely continuous and singular continuous components. Calculations performed within statistical method are equivalent to the ones from multidimensional analysis. The atomic surface, also called occupation domain, which is the basic concept behind multidimensional models, acquires physical interpretation if compared to average unit cell. The statistical method applied to diffraction analysis is now a complete theory, which deals equally well with periodic and non-periodic crystals, including quasicrystals. The method easily meets also any structural disorder.

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Structure analysis of displacively modulated molecular crystals

Cited by 48 publications

References 7 publications

Organic molecular compounds with modulated crystal structures

Organic molecular compounds with modulated crystal structures

The description and analysis of composite crystals

Statistical Approach to Diffraction of Periodic and Non-Periodic Crystals—Review

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