Electron microscopic studies of modulated structures in (Au, Ag) Te2: Part II. Sylvanite AgAuTe4

Tendeloo, Gustaaf Van; Gregoriades, P.; Amelinckx, S.

doi:10.1016/0022-4596(83)90204-9

Cited by 17 publications

(10 citation statements)

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“…Note that superspace embedding is necessary for a symmetry characterization in terms of Euclidean space groups, but not if that is not required. Indeed, in the present paper we will stick to the threedimensional description.In a previous paper on the morphology of calaverite (Dam, Janner & Donnay, 1985) a first partial reindexing of a number of crystal faces was given, taking advantage of the electron diffraction results of Van Tendeloo, Gregoriades & Amelinckx (1983) and Van Tendeloo, Amelinckx & Gregoriades (1984). Their diffraction patterns show the existence of extra socalled satellite spots around the main reflections of the basic reciprocal lattice, revealing that the crystal is modulated by a periodic lattice distortion, which is incommensurate with respect to a basic structure having C2/m symmetry.…”

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confidence: 99%

The morphology of calaverite (AuTe2) from data of 1931. Solution of an old problem of rational indices

Janner¹,

Dam²

1989

Acta Cryst Sect A

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The anomalous high-index faces (hkl) of the mineral calaverite (Au~_xAgxTe2) measured goniometrically in the year 1931 by Goldschmidt, Palache & Peacock [Neues Jahrb. Mineral (1931), 63, 1-58] are re-interpreted and related to the wave vector q of the displacive incommensurate modulation which was recently found in the crystal structure. All crystal * Present address: Philips Research Laboratories, PO Box 80.000, NL-5600 JA Eindhoven, The Netherlands.faces (including the high-index ones) can be given four low indices (hklm), using q as a fourth basis vector. From this an almost hundred-year-old anomaly in crystal morphology is in principle solved. I. IntroductionThe present investigation started from a non-applicability of the law of rational indices to crystal growth forms of calaverite Aul_pAgpTe2 (p < 0.15) (Smith, 1902;Goldschmidt, Palache & Peacock, 1931).Classically (Bravais-Friedel) the morphology of crystals is related to the existence of a crystal lattice. This crystal lattice is even implicitly suggested by Haiiy's law of rational indices. The latter can be extended to the use of four or more rational indices in order to describe the crystal forms of modulated crystals (Janner, Rasing, Bennema & van der Linden, 1980;Dam & Janner, 1983, 1986. The fact that the number of indices can be larger than three reflects the fact that the number of fundamental periodicities can also be larger than three, which is a key concept for the understanding of crystal faces. Hence, in the description of crystal morphology one is not necessarily restricted to the three periodicities generating a three-dimensional space lattice. In the onedimensional modulated case the modulation wave vector q = aa* + fib* + yc* has to be added as a fourth basic vector to the three ones of the undistorted reciprocal-lattice unit cell: a*, b*, c*. Any crystal face of a one-dimensionally modulated crystal is then labeled by the four indices (hklm) of the corresponding face normal given by k--ha*+kb*+lc*+ mq.The use of four indices is closely related to the superspace approach as introduced for incommensurately modulated crystals by de Wolff (1977) and Janner & Janssen (1977. Indeed, the presence of fundamental periodicities in a given crystal does not mean that the structure is periodic in space. One can eventually restore the familiar lattice periodicity by embedding the crystal in a larger space, the superspace, with as many dimensions as there are fundamental periodicities. In Dam & Janner (1986) the details of this approach are explained and applied to the morphology of the modulated phases of the crystal tetramethylammonium tetrachlorozincate [(CH3)aN]2ZnCI 4. The most recent experimental result of morphological research on that compound is the observation of a roughening of a satellite orientation (hklm) upon a change of the modulation wave vector q as a function of temperature (Dam, 1985). Note that superspace embedding is necessary for a symmetry characterization in terms of Euclidean space groups, but not if that is not req...

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The morphology of calaverite (AuTe2) from data of 1931. Solution of an old problem of rational indices

Janner¹,

Dam²

1989

Acta Cryst Sect A

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“…3. The coupling of the displacement wave with the ordering between Cu and Au could for instance occur in the same way as suggested for sylvanite (Van Tendeloo et al, 1983b).…”

Section: Discussionmentioning

confidence: 59%

“…This produces a modulated structure with wavevector q. The way in which coupling may be understood is described by Van Tendeloo et al (1983b).…”

Section: Discussionmentioning

confidence: 99%

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High-resolution electron-microscopic study of the modulated structure of kostovite (Cu_1−xAu_1+xTe₄)

Tendeloo¹,

Amelinckx²

1986

Acta Crystallogr Sect B

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The modulated structure of kostovite (AuCuTe4) is shown to be closely related to that of sylvanite (AuAgTe4). Well ordered stoichiometric kostovite has a commensurate superstructure of the idealized calaverite structure (AuTe2). A long-period antiphase-boundary modulated structure, which produces an apparently incommensurate diffraction pattern, is found in the non-stoichiometric samples. A detailed model is presented for this structure. Chemically disordered specimens exhibit a displacementmodulated structure related to that of calaverite. It is suggested that in the ternary compounds, displacements as well as antiphase-boundary modulations occur, the two modes being interrelated, whereas in calaverite only displacement modulations are present. These conclusions are based on the results of a study by means of electron diffraction and high-resolution electron microscopy and on in situ heating experiments.

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“…A labelling of the crystal faces by three low indices did not seem to be possible, although many attempts were made. At present, it is known that there is a one-dimensional incommensurate modulation in this crystal (Sueno, Kimata & Ohmasa, 1979;Van Tendeloo, Gregoriades & Amelinckx, 1983;Schutte & de Boer, 1988), so that the rank of the ~-module is four. The Fourier wave vectors, therefore, can be labelled by four integral indices.…”

Section: Introductionmentioning

confidence: 98%

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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Electron microscopic studies of modulated structures in (Au, Ag) Te2: Part II. Sylvanite AgAuTe4

Cited by 17 publications

References 4 publications

The morphology of calaverite (AuTe2) from data of 1931. Solution of an old problem of rational indices

The morphology of calaverite (AuTe2) from data of 1931. Solution of an old problem of rational indices

High-resolution electron-microscopic study of the modulated structure of kostovite (Cu_1−xAu_1+xTe₄)

Equilibrium morphology of incommensurately modulated crystals: a superspace description

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Electron microscopic studies of modulated structures in (Au, Ag) Te2: Part II. Sylvanite AgAuTe4

Cited by 17 publications

References 4 publications

The morphology of calaverite (AuTe2) from data of 1931. Solution of an old problem of rational indices

The morphology of calaverite (AuTe2) from data of 1931. Solution of an old problem of rational indices

High-resolution electron-microscopic study of the modulated structure of kostovite (Cu1−x Au1+x Te4)

Equilibrium morphology of incommensurately modulated crystals: a superspace description

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High-resolution electron-microscopic study of the modulated structure of kostovite (Cu_1−xAu_1+xTe₄)