(3+1)-Dimensional Patterson and Fourier methods for the determination of one-dimensionally modulated structures

Steurer, Walter

doi:10.1107/s010876738709994x

Cited by 26 publications

(8 citation statements)

References 9 publications

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“…For example, it allows the interpretation of Patterson and Fourier maps in superspace (Fig. 5) [15,16], and it allows the visualization of structural properties, like bond distances, as a function of the incommensurate coordinate (see below). Fig.…”

Section: The Atomic Structure and Direct Superspacementioning

confidence: 99%

An elementary introduction to superspace crystallography

Smaalen¹

2004

Zeitschrift Für Kristallographie - Crystalline Materials

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Abstract. Aperiodic crystals are defined as a crystalline state of matter, that has atomic structures with long-range order but without translational symmetry. Experimentally, they are characterized by sharp Bragg reflections in the Xray diffraction, that can be indexed by integers, if four or more reciprocal basis vectors are used. An introduction is given to the basic concepts of the superspace theory for structural analysis of incommensurately modulated crystals and incommensurate composite crystals [De Wolff, Janner and Janssen, Acta Crystallogr. 37 (1981) 625-636]. It is concluded that major challenges of the crystallography of incommensurate phases lie in the determination of the precise shapes of modulation functions, and in finding the relations between physical properties of incommensurate crystals and their atomic structures.

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Section: The Atomic Structure and Direct Superspacementioning

confidence: 99%

An elementary introduction to superspace crystallography

Smaalen¹

2004

Zeitschrift Für Kristallographie - Crystalline Materials

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“…attempts (Fu et al, 1993). Higher-dimensional Patterson methods (Steurer, 1987(Steurer, , 1989 work quite well, especially in combination with the symmetry-minimum function and image-seeking functions . Maximumentropy methods may be used in the final stages of phase determination and particularly for the improvement of electron-density maps (Haibach et al, 2000, and references therein).…”

Section: Structure Analysismentioning

confidence: 99%

Fascinating quasicrystals

2007

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It took Dan Shechtman more than two years to get his discovery of an Al-Mn phase with icosahedral diffraction symmetry and sharp Bragg reflections published. A paradigm shift had to take place before this novel ordering state of matter -seemingly contradicting crystallographic laws -could be accepted. Today, more than 25 years later, the existence of quasicrystals is beyond doubt. However, not everything is settled yet. All the factors governing formation, growth, stability and structure of quasicrystals are still not fully understood, nor is it resolved whether their structures are strictly or only on average quasiperiodic, and it is still an open question why only quasicrystals with 5-, 8-, 10-and 12-fold rotational symmetry have been experimentally observed so far. These points will be addressed in this review article.

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“…As there is no lattice in physical space, there is also no reciprocal lattice in the Fourier space. For some class of aperiodic structures, like modulated structures or quasicrystals, one can try to recover periodicity by going to higher dimensions [1][2][3][4][5][6][7][8][9][10]. Such higher-dimensional periodic structure can be cut in the so called perp-space (inner space) and then projected into physical space.…”

Section: Introductionmentioning

confidence: 99%