Diffuse Scattering and Phason Elasticity in the AlPdMn Icosahedral Phase

Boissieu, M. de; Boudard, Michel; Hennion, B.; Bellissent, R.; Kycia, S.; Goldman, A. I.; Janot, Chr.; Audier, M.

doi:10.1103/physrevlett.75.89

Cited by 141 publications

(74 citation statements)

References 28 publications

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“…It should be emphasized that all these artifacts are not speci®c to the phasing method and will exist in any reconstructed quasicrystalline density map. They should not be confused with the phason disorder in real quasicrystals (Lyonnard et al, 1996;de Arau Â jo et al, 1996;de Boissieu et al, 1995), which manifests itself in the occurrence of true partially occupied sites at the same positions.…”

Section: Quasicrystals and Incommensurate Structuresmentioning

confidence: 99%

A new phasing method based on the principle of minimum charge

Kalugin

2001

Acta Cryst Sect A

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A new method for phase determination in X‐ray crystallography is proposed. The method is based on the so‐called `minimum‐charge' principle, recently suggested by Elser [Acta Cryst. (1999), A55, 489–499]. The electron‐density function is sought in the form = , where is an ‐component real function. The norm is minimized under the constraint imposed by the measured data on the amplitudes of Fourier harmonics of . Compared with the straightforward implementation of the `minimum‐charge' scheme, the method attenuates the Gibbs phenomenon and is also capable of extrapolation of the diffraction data beyond the set of measured amplitudes. The method is applicable to quasicrystals under the condition that the number of components of the function is bigger than the dimensionality of the `atomic surface'. It has been successfully tested on synthetic data for a Fibonacci chain and octagonal tiling. In the latter case, the reconstructed density map shows the shape of the atomic surface, despite relatively low resolution data.

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Section: Quasicrystals and Incommensurate Structuresmentioning

confidence: 99%

A new phasing method based on the principle of minimum charge

Kalugin

2001

Acta Cryst Sect A

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“…This is because most of the papers reporting the evaluation of K 1 and K 2 by diffuse scattering measurements (e.g., [6][7][8][9]) follow the definition by Widom [15]. We note that the phonon displacement part in Eq.…”

Section: Introductionmentioning

confidence: 99%

“…So far, experimental evaluations of the phason elastic constants have been done exclusively by diffuse scattering measurements of neutron or X-ray; the measurements have been reported for icosahedral quasicrystals of Al--Pd--Mn [6,7], Al--Cu--Fe [8] and Zn--Mg--Sc [9] systems. In this paper, we propose and formulate another method for the evaluation of the phason elastic constants (more precisely their ratio K 2 /K 1 ), in which we use a high-resolution transmission electron microscopy (HRTEM) image of a dislocation.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of phason elastic constants from HRTEM image of a dislocation in icosahedral quasicrystal

Edagawa¹,

Kamimura²,

So³

2009

Zeitschrift Für Kristallographie - Crystalline Materials

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Abstract. A method is proposed for quantitative evaluation of the ratio of the two phason elastic constants K 2 /K 1 in icosahedral quasicrystals from a high-resolution transmission electron microscopy (HRTEM) image of a dislocation. Here, the Hytch's method originally proposed for quantitative evaluation of displacement fields in crystals is generalized to quasicrystals. The generalized Hytch's method gives phason displacement fields around a dislocation in icosahedral quasicrystals, from which K 2 /K 1 can be evaluated. This method is demonstrated using a simulated HRTEM image of a dislocation in an icosahedral quasicrystal.

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“…The most usual technique for studying diffuse scattering, these days, is to make use of a four-circle diffractometer and count pulses with an appropriate detector suitably aligned so as to receive radiation within a small solid angle centred along the direction of the scattered beam. This is the technique used, for example, by de Boissieu et al (1995), who measured neutron diffuse scattering from a single grain of the Al±Pd±Mn icosahedral phase in order to obtain information on phason disorder. While this technique provides a very precise mapping of limited regions of reciprocal space with high resolution, a photographic technique usually called`monochromatic Laue', or`mono-Laue' for short, gives a global view of a wide region of reciprocal space in a very short time.…”

Section: Introductionmentioning

confidence: 99%

Exploring reciprocal space of a quasicrystal by means of an imaging plate

Kopecký

Colella

1999

J Appl Cryst

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A monochromatic Laue technique is used to extract information about the reciprocal lattice of a quasicrystal. A synchrotron beamline, normally available for protein crystallography, was used in this study. Each photograph is a planar projection of a spherical cap, a portion of the Ewald sphere, in reciprocal space. The algorithms needed to relate the images to reciprocal space are described in detail. It is found that many weak, but readily detectable, Bragg re¯ections are found in unexpected positions in reciprocal space, as predicted from theory. Some very weak Bragg re¯ections are clearly visible on the imaging plate, but could not be detected by photon counting using a four-circle diffractometer. Some images show characteristic`rings' or`arcs' of diffuse scattering, as previously observed in other icosahedral quasicrystals. In view of the`extreme perfection' of the quasicrystalline specimen used in this study, it is proposed to view these rings (or arcs) as intrinsic features of the icosahedral quasicrystalline structure.

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Diffuse Scattering and Phason Elasticity in the AlPdMn Icosahedral Phase

Cited by 141 publications

References 28 publications

A new phasing method based on the principle of minimum charge

A new phasing method based on the principle of minimum charge

Evaluation of phason elastic constants from HRTEM image of a dislocation in icosahedral quasicrystal

Exploring reciprocal space of a quasicrystal by means of an imaging plate

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