Incommensurate Morphology of Calaverite (Au<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Te</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>) Crystals

Dam, B.; Janner, A.; Donnay, J. D. H.

doi:10.1103/physrevlett.55.2301

Cited by 55 publications

(25 citation statements)

References 10 publications

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“…The faces that determine the morphology of incommensurately modulated crystals are perpendicular to Fourier wave vectors of the ~-module. It was shown that the faces of Aul_xAgxTe2 could be labelled, very satisfactorily, with four low integral indices (Dam, Janner & Donnay, 1985;Janner & Dam, 1989). The same behaviour has been found for many other incommensurately modulated crystals (see Bennema et al, 1991).…”

Section: Introductionsupporting

confidence: 48%

“…It has been shown experimentally (Janner, Rasing, Bennema & van der Linden, 1980;Dam, Janner, Bennema, van der Linden & Rasing, 1983;Dam et al, 1985;Janner & Dam, 1989;Bennema et al, 1991) that the orientation of faces on incommensurately modulated crystals can be described very accurately with four integral indices hi, h 2, h 3 and h 4. These indices defme a vector H(hlhEhah4) perpendicular to the face.…”

Section: The Intersection Of Bonds By Crystallographic Planesmentioning

confidence: 99%

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Equilibrium morphology of incommensurately modulated crystals: a superspace description

Kremers¹,

Meekes²,

Bennema³

et al. 1995

Acta Cryst Sect A

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The theory for the explanation of equilibrium morphologies of incommensurately modulated one-dimensional crystals, presented in a previous paper, is extended to the case of incommensurately modulated three-dimensional crystals. It is shown that, concerning the morphology, there exists a one-to-one correspondence between faces on the physical crystal and crystallographic hyperplanes of the embedded crystal in superspace. This holds for both main faces and satellite faces. The occurrence of the latter, however, is unique for incommensurately modulated crystals. It is shown that the stability of satellite faces, as well as main faces, can be attributed to a principle of selective cuts. The superspace approach that is developed leads to a calculation method for surface free energies that, in principle, can be applied to incommensurately modulated structures of arbitrary complexity. Equilibrium morphologies are constructed ©1995 Intemational Union of Crystallography Printed in Great Britain -all fights reserved from the calculated surface free energies by means of a standard Wulff plot. The dependence of the equilibrium morphology on several structural parameters is studied for an incommensurately modulated simple cubic model crystal. This study allows for a basic understanding of the differences in morphology of AuTe 2 crystals and [(CH3)4N]2ZnC14 crystals.

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Section: Introductionsupporting

confidence: 48%

Section: The Intersection Of Bonds By Crystallographic Planesmentioning

confidence: 99%

Equilibrium morphology of incommensurately modulated crystals: a superspace description

Kremers¹,

Meekes²,

Bennema³

et al. 1995

Acta Cryst Sect A

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“…. ) the classical law of rational indices still holds for incommensurate crystals, provided the correct number of indices is used (four in the case of calaverite)' (Dam et al, 1985).…”

Section: Historical Perspectivementioning

confidence: 99%

A non-mathematical introduction to the superspace description of modulated structures

Wagner

Schönleber

2009

Acta Crystallogr Sect B

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The X-ray analysis of (6R,7aS)-6-(tert-butyl-dimethylsilanyloxy)-1-hydroxy-2-phenyl-5,6,7,7a-tetrahydropyrrolizin-3-one, C 19 H 27 NO 3 Si, revealed a diffraction pattern which is typical for modulated structures: strong Bragg peaks surrounded by weaker reflections which cannot be indexed with the same three reciprocal lattice vectors that are used to describe the strong peaks. For this class of crystal structures the concept of superspace has been developed which, however, for many crystallographers still constitutes a Gordian Knot. As a possible tool to cut this knot the crystal structure of the above-mentioned tetrahydropyrrolizinone derivative is presented as an illustrative example for handling and describing the modulated structure of a typical pharmaceutical (i.e. molecular) compound. Having established a working knowledge of the concepts and terminology of the superspace approach a concise and detailed description of the complete process of peak indexing, data processing, structure solution and structure interpretation is presented for the incommensurately modulated crystal structure of the above-mentioned compound. The superspace symmetry applied is P2 1 (0)0; the (incommensurate) q vector components at 100 K are = 0.1422 (2) and = 0.3839 (8).

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“…In 1931 the international commission of Goldschmidt (Germany), Palache (US) and Peacock (Canada) charged to repeat very carefully the measurements on a fairly large number of crystals, could also not solve the enigma in a proper way [32]. Eventually this mineral was found to be incommensurate modulated [2][3][4] and in 1985 a four-dimensional indexing fitted very nicely with the experimental data of 1931 [33,34].…”

Section: Symmetrymentioning

confidence: 79%

Incommensurate Morphology of Calaverite (AuTe2) Crystals

Cited by 55 publications

References 10 publications

Equilibrium morphology of incommensurately modulated crystals: a superspace description

Equilibrium morphology of incommensurately modulated crystals: a superspace description

A non-mathematical introduction to the superspace description of modulated structures

Personal reflections on the history of aperiodic crystals from early days to the state of the art

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