Computer‐aided evaluation of kossel patterns obtained from quasicrystals

Weber, Steffen; Schetelich, Ch.; Geist, V.

doi:10.1002/crat.2170290528

Cited by 15 publications

(9 citation statements)

References 8 publications

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“…Diffuse light originates by scattering from the impurities in thick crystals such as deviations in the polystyrene sphere diameter, dislocations, and vacancies in the lattice; for thin or dilute samples, a diverging source of light can be generated with an external diffuser [11]. Figure 1 depicts simulated Kossel lines [16] for an fcc crystal with a lattice parameter of 486 nm. In each case, the incident laser beam passes through the center of each frame; each circle or arc represents a band of attenuation arising from Bragg diffraction from a specific set of planes.…”

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Photonic Band Structure of fcc Colloidal Crystals

1996

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Polystyrene colloidal crystals form three dimensional periodic dielectric structures which can be used for photonic band structure measurements in the visible regime. From transmission measurements the photonic band structure of an fcc crystal has been obtained along the directions between the L point and the W point. Kossel line patterns were used for locating the symmetry points of the lattice for exact positioning and orientation of the crystals. In addition, these patterns reveal the underlying photonic band structure of the crystals in a qualitative way. PACS numbers: 78.20.Ci, 81.10.Aj, 82.70.Dd For the last eight years, the analogy between the propagation of electromagnetic waves in periodic dielectric structures, dubbed photonic band gap (PBG) or photonic crystals, and electron waves in atomic crystals has motivated scientists to explore new possibilities in this field [1][2][3][4][5]. On account of the periodic modulations in dielectric constant in PBG crystals, with spatial periods designed to be on the order of a desired wavelength, electromagnetic waves incident along a particular direction are diffracted for a certain range of frequencies, forming stop bands. When these stop bands are wide enough and overlap for both polarization states along all crystal directions, the material possesses a complete PBG. In such a crystal, propagation of electromagnetic waves within a certain frequency range is forbidden irrespective of their direction of propagation. This leads to interesting effects in quantum optics; for example, spontaneous emission of light can be controlled, where an excited atom embedded in a PBG crystal will not be able to make a transition to a lower energy state as readily if the frequency of the emitted photon lies within the band gap, hence increasing the lifetime of the excited state [1].Although PBG crystals will have novel applications in the optical regime, such as lowering thresholds in maintaining population inversions leading to very efficient solid state devices [1], the technological challenge of fabricating a 3D PBG crystal exhibiting a complete band gap in the optical regime has not yet been surmounted. Structures exhibiting full photonic band gaps in the microwave [6,7], millimeter [8], and submillimeter [9] regimes have already been fabricated, and a submicron length-scale photonic crystal has been proposed [10], but experimentally realizing these structures in the optical regime has remained a challenge. To carry out photonic band structure studies in the optical regime, polystyrene colloidal crystals with lattice spacings comparable to the wavelength of light have been used for this study [11,12]. These colloidal crystals consist of charged monodisperse polystyrene microspheres suspended in water, yielding a relative index of refraction of 1.20, which organize into face-centered-cubic (fcc) lattices under suitable conditions. Although such a crystal is not expected to exhibit large gaps because of the relatively low index contrast, it does permit study of photonic band s...

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“…Schetelich, and V. Greist [16] for providing us with their program for simulating Kossel line patterns. This work was supported by the National Science Foundation under Grant No.…”

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Photonic Band Structure of fcc Colloidal Crystals

1996

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“…Moreover, particularly the 001 11-reflection shows a transition from "L" to "D" with the "LD" contrast in between. A computer program called "KOQUA" is available, which allows not only the calculation of Kossel patterns but also the determination of diffraction geometry for every Kossel line segment [5]. The transition observed was interpreted employing "KOQUA" as a change from an asymmetric Bragg case to an asymmetric Laue case.…”

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confidence: 99%

“…Supplementary the parameters for Al,,Cu,,Co are given: Three-dimensional reciprocal and direct lattice parameters: uT = 2.656(2) nin-', i = 1 to 4, a: = 2.4107(3) nm-', a, = 0.3765(3) nm, i = 1 to 4; as = 0.41481(3) nm, five-dimensional unit cell parameters: di = 0.3368(1) nm, i = 1 to 4, d, = 0.41481(3) nm, clij = 60", i, j = 1 to 4, cli5 = 90", i = 1 to 4 [4]. The lattice constants of AI,,Cu,,Co,,Si, are close to those of Al,,Cu,,Co,, [5] (cf. Table 1).…”

Section: Methodsmentioning

confidence: 99%

Dynamical X-Ray Diffraction at Decagonal Quasicrystals Observed by the Kossel Technique

Schetelich

Weber

Geist

1994

Phys. Stat. Sol. (a)

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In all cases the dynamical "light-dark'' Kossel line contrast is observed. Moreover a characteristical change of the line profile, which depends on the emission depth as well as on the diffraction geometry, occurs. The fine structure of the Kossel lines is used for an estimation of the centric character of the decagonal phases. Furthermore it is shown that perpendicular to the dircctions of the Kossel cones puckered atomic layers exist, whose mean distances agree well with the measured d-values.

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“…However, only a few works deal with the topic of computerized analysis (such as SCOZIA 1990, WEBER 1994. Due to the problems of indexing reflections of the complex patterns and the photographic technique necessary for observation of these patterns up to now there is only a little interest in this analytical tool.…”

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confidence: 99%

KOPSKO: a Computer Program for Generation of Kossel and Pseudo Kossel Diffraction Patterns

Langer

Kurt²,

Däbritz

1999

Cryst. Res. Technol.

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Cryst. Res. Technol. 341999 7 801-816Diffraction techniques are widely used especially as additional tools for analytical microprobe analysis.A supplementary device to a scanning electron microscope (SEM) allows taking of X-ray lattice source and wide angle interference patterns, now termed Kossel and Pseudo Kossel patterns, respectively, in transmission and back reflection arrangement as reported by DÄBRITZ et al. (1986DÄBRITZ et al. ( , 1997a. The developed program KOPSKO simulates exactly the entire reflection system of Kossel and Pseudo Kossel diffraction patterns basing on the geometric diffraction theory. It permits phase, orientation, and structure determination. The present paper shows the wide range of possibilities using the computerized analysis in this field. Initially it deals with simulation of Kossel patterns, which are excellent suitable for a precise determination of lattice constants in the micro range for instance. A new way for simulation of Pseudo Kossel diffraction patterns using three dimensional vector algebra to calculate reflections in point by point procedure is presented in the second part. The attained precise coincidence of simulation and experimentally taken Pseudo Kossel patterns allows a relatively easy determination of crystallographic data of mono-and polycrystals. Particularly the program is designed to determine lattice constants precisely, for the complex divergent beam X-ray interferences, too. Through the three dimensional simulation it takes into account shade originated by the target holder. Moreover, the three dimensional point by point procedure enables the localization of lattice imperfections as well as the consideration of grain size effects in polycrystals, which lead to interruptions of Pseudo Kossel lines. By simulation of diffraction patterns of polycrystalline materials the study of such specimens is essentially simplified.

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Computer‐aided evaluation of kossel patterns obtained from quasicrystals

Cited by 15 publications

References 8 publications

Photonic Band Structure of fcc Colloidal Crystals

Photonic Band Structure of fcc Colloidal Crystals

Dynamical X-Ray Diffraction at Decagonal Quasicrystals Observed by the Kossel Technique

KOPSKO: a Computer Program for Generation of Kossel and Pseudo Kossel Diffraction Patterns

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