Kossel Patterns Research Articles

Photopatterned Anchoring Stabilizing Monodomain Blue Phases.

Blue phase liquid crystals (BPLCs) are chiral self-assembled three-dimensional (3D) periodic structures which have attracted a lot of attention due to their electro-optical properties, relevant for tunable soft photonic crystals and fast-response displays. However, to realize this application potential, controlling the BPLC alignment at the surfaces is crucial, and one way to obtain the desired alignment is by photoalignment patterning. In this article, monodomain BPLC samples with controlled orientation are achieved by imposing different alignment patterns that have a periodicity that is compatible with the size of the BPLC unit cell, using two-step photoalignment with polarized ultraviolet (UV) light. Experiments are complemented by numerical simulations to design striped surface alignment patterns, which induce specific director orientations on the boundary layer of the confined BPLC. By designing the patterns and matching the periodicity to a specific BP material, we can control the orientation of the blue phase unit cell lattice in the sample, including the azimuthal angle. The orientation is measured by the Kossel patterns and matches the optimal configuration predicted by stability analysis using Landau-de Gennes free energy modeling. The detailed structure and reduced symmetry of the BP near the surface are investigated, and the corresponding (meta)stable structures are demonstrated. Overall, we demonstrate that two-step photoalignment patterning is a reliable, relatively simple, and reconfigurable method to achieve a high-quality monodomain BP with controlled and tunable crystalline orientation.

On the possibility of ultrafast Kossel diffraction

We discuss the possibility of realizing time-resolved Kossel diffraction experiments for providing indications on the crystalline order or the periodic structure of a material. We make use of the interaction of short, ultra-intense laser pulses with a solid target, which generates short bursts of hot electrons. Penetrating inside a layered sample (i.e., a crystal or an artificial multilayer material), these electrons ionize inner-shell electrons so that the subsequent radiative filling of K-shell vacancies results in a strong Kα emission that is enhanced in the Bragg directions corresponding to the period of the material. We present simulations of angle-resolved Kα emission, which displays so-called Kossel patterns around the Bragg angles. We then discuss possible experiments appropriate for laser facilities delivering short and intense pulses.

Two‐Step Photoalignment with High Resolution for the Alignment of Blue Phase Liquid Crystal

AbstractThe self‐assembling properties of liquid crystal (LC) are ideal for realizing switchable optical components. The director organization is strongly determined by the alignment at the substrate interfaces and photoalignment is a versatile method based on linearly polarized UV light. In this work, a two‐step photoalignment procedure is proposed to pattern the alignment at the surface. Illumination with uniform polarization or with an interference pattern is combined to obtain stripe patterns or square patterns of photoalignment. It can indeed be confirmed that the nematic director follows the varying azimuthal orientation. By increasing the angle between the two interfering beams, photoalignment with sub‐micrometer resolution is obtained, compatible with the dimensions of blue phase (BP) LC unit cell. Homogeneous domains of BP II with (100) or (110) crystal orientation are obtained and their Kossel patterns are recorded. The two‐step photoalignment technique allows to create patterns with high resolution and to control the orientation of BP LC, which is promising for photonic applications that require single domains.

Kossel lines in optics of defect spiral media

ABSTRACT We propose a general analytical way to describe the fluorescence peculiarities in photonic liquid crystals defect structure based at the localised optical defect modes existing in perfect photonic liquid crystal with a plane defect layer. The proposed approach allows us to predict theoretically the properties of optical Kossel lines in photonic liquid crystal with a plane defect layer (fluorescence polarisation, spectral and angular fluorescence distribution, appearance of Kossel line inside the stop band, influence of the light absorption in liquid crystal). Comparison of the theoretical results and the known experimental data shows that the theory reproduces sufficiently well the observation results on the fluorescence in photonic liquid crystals with a plane defect layer. Possible applications of the obtained results to the Kossel patterns in defect structures for another types of radiation (X-rays, electrons, neutrons) are briefly discussed.

Indexing of diffraction patterns for determination of crystal orientations.

The task of determining the orientations of crystals is usually performed by indexing reflections detected on diffraction patterns. The well known underlying principle of indexing methods is universal: they are based on matching experimental scattering vectors to some vectors of the reciprocal lattice. Despite this, the standard attitude has been to devise algorithms applicable to patterns of a particular type. This paper provides a broader perspective. A general approach to indexing of diffraction patterns of various types is presented. References are made to formally similar problems in other research fields, e.g. in computational geometry, computer science, computer vision or star identification. Besides a general description of available methods, concrete algorithms are presented in detail and their applicability to patterns of various types is demonstrated; a program based on these algorithms is shown to index Kikuchi patterns, Kossel patterns and Laue patterns, among others.

A program for refinement of lattice parameters and strain determination using Kossel diffraction patterns

The Kossel diffraction technique is well suited for investigating crystal lattices. Progress in digital recording of images opens the opportunity for simplification and improvement of the examination of Kossel patterns. Such patterns can be processed immediately after recording if appropriate computer programs are available. To provide such a tool, a new Windows-based software for computer-assisted analysis of Kossel patterns has been developed. With its easy-to-operate user interface, the program is intended to facilitate refinement of lattice parameters and determination of elastic strains. The refinement is based on matching experimental and geometrically simulated patterns, whereas the strain is obtained by matching Kossel line profiles in similar experimental patterns. The software is capable of simultaneous handling of multiple patterns.

Measurement of synchrotron-radiation-excited Kossel patterns.

Kossel line patterns contain information on the crystalline structure, such as the magnitude and the phase of Bragg reflections. For technical reasons, most of these patterns are obtained using electron beam excitation, which leads to surface sensitivity that limits the spatial extent of the structural information. To obtain the atomic structure in bulk volumes, X-rays should be used as the excitation radiation. However, there are technical problems, such as the need for high resolution, low noise, large dynamic range, photon counting, two-dimensional pixel detectors and the small spot size of the exciting beam, which have prevented the widespread use of Kossel pattern analysis. Here, an experimental setup is described, which can be used for the measurement of Kossel patterns in a reasonable time and with high resolution to recover structural information.

Strain resolution of scanning electron microscopy based Kossel microdiffraction

Kossel microdiffraction in a scanning electron microscope enables determination of local elastic strains. With Kossel patterns recorded by a CCD camera and some automation of the strain determination process, this technique may become a convenient tool for analysis of strains. As for all strain determination methods, critical for the applicability of the Kossel technique is its strain resolution. The resolution was estimated in a number of ways: from the simplest tests based on simulated patterns (of an Ni alloy), through analysis of sharp experimental patterns of Ge, to estimates obtained byin situtensile straining of single crystals of the Ni-based superalloy. In the latter case, the results were compared with those of conventional X-ray diffraction and synchrotron-based Kossel diffraction. In the case of high-quality Ge patterns, a resolution of 1 × 10−4was reached for all strain tensor components; this corresponds to a stress of about 10 MPa. With relatively diffuse patterns from the strained Ni-based superalloy, under the assumption of plane stress, the strain and stress resolutions were 3 × 10−4and 60 MPa, respectively. Experimental and computational conditions for achieving these resolutions are described. The study shows potential perspectives and limits of the applicability of semiautomatic Kossel microdiffraction as a method of local strain determination.

Zone Axis STEM Defect Imaging Based on Electron Kossel Patterns

Zone Axis STEM Defect Imaging Based on Electron Kossel Patterns

A Profile-Based Method of Determining Intragranular Strains Using Kossel Diffraction Patterns

Kossel microdiffraction is one of a few experimental methods of investigating heterogeneities of elastic stresses within crystallites. With digitally recorded back-reflection Kossel patterns, one can determine absolute lattice parameters, and hence lattice strains and stresses, based on geometry of Kossel lines, but the strain resolution of this approach is limited by finite widths of the lines. A new method is proposed which considerably improves the resolution in cases when the patterns originate from areas with similar lattice orientations. The method is based on determination of differences between pattern geometries: lattice strains are calculated from mutual shifts of intensity profiles of Kossel lines. The strain accuracy of this profile-based approach was estimated. It is demonstrated that the limit of strain resolution reaches a few parts per hundred thousand, i.e., it is nearly one order of magnitude better than that of the conventional Kossel-based lattice parameter refinement. This improvement concerns the critical range of lattice strain, and it constitutes a qualitative leap in resolution. The paper describes main aspects of the new approach and strain resolution tests.

Zone axis STEM defect imaging based on electron Kossel patterns

Extended abstract of a paper presented at Microscopy and Microanalysis 2012 in Phoenix, Arizona, USA, July 29 – August 2, 2012.

75 years of Kossel patterns – past and future

The year 2009 marks the 75th anniversary of the discovery of X-ray interferences from lattice sources by Walther Kossel in the city of Gdansk. The X-ray source is located within the crystal itself and interferences (lattice source interferences) appear, whose evaluation provides information on a significant number of physical material parameters. For example lattice constants with a precision of 10−5 can be determined non-destructively in the micro-range. Moreover, both, the local lattice parameter and the local crystal structure, can be ascertained at low and high temperatures, which is important for the investigation of crystallographic lattice transformations and especially for the characterisation of superconductors (V3Si). Beginning with the first Kossel investigations on copper single crystals in Gdansk up to computer simulated results on metals, intermetallic compounds as well as on complex materials, such as Cu-Sn phases (e.g., Cu41Sn11), with correspondingly running diffusion processes in microelectronical contacts, the Kossel technique provides comprehensive answers to current research questions. The article gives selected application examples from different fields. Moreover, the most important steps in the development of the Kossel interferences are briefly reviewed.

A 3D Hough transform for indexing EBSD and Kossel patterns

A three-dimensional Hough transform is designed for the detection of conic curves (hyperbolae and ellipses) formed by the gnomonic projection of diffraction Kossel cones. This new procedure is applied to a high-angular-accuracy analysis of electron backscatter diffraction (EBSD) patterns and to a fully automatic indexing of X-ray Kossel patterns in the SEM. The high-accuracy analysis of EBSD patterns allows for the determination of local elastic strains, without any reference pattern, and with a spatial resolution of a few tens of nanometres. An accuracy of 2 x 10(-4) is achieved on geometrically calculated diagrams. This paper presents also the first fully automatic indexing of Kossel patterns. This automatic indexing procedure can be applied to local texture analysis, as well as to local elastic strain measurements. Although the spatial resolution of Kossel is about 1 microm, the accuracy of strain measurement is in this case much higher than that presently obtained on EBSD.

First X-ray fluorescence excited Kossel diffraction in SEM

We present, for the first time, X-ray fluorescence excited Kossel patterns in the scanning electron microscope by way of a compact X-ray tube and a focusing polycapillary lens. Both the diffraction geometry in transmission and in back reflection can be carried out. The way is paved for the advantageous combination of micro-X-ray fluorescence analysis, the Laue method, and the X-ray fluorescence excited Kossel micro-diffraction with the high lateral resolution of the electron microscopy.

Crystallization of charged colloidal particles: an experimental study

Colloidal crystals are fabricated through a self-assembly process of monodispersed polystyrene particles. Evolution of colloidal crystal structures is analyzed by Kossel diffraction technique and UV-Vis spectrophotometer. According to the changes in the Kossel patterns we find the crystal structures change with passage of time and experience successively the following stages: liquid state-random layer structure-stacking disorder structure-fcc with (111) twin-normal fcc structure. The plane distances of different crystal planes and the lattice constants are also determined in this study. The 111 plane distances and the lattice constants evaluated according to the measurement of transmission spectrum are in accordance with the results by the analysis of Kossel line. In addition, it was found that the peaks of the transmission spectrum become sharper and shift considerably toward shorter wavelength during the crystal evolution, showing the lattice constants become smaller.

Advances in X-ray excitation of Kossel patterns by a focusing polycapillary lens

In this paper, the polychromatic X-ray excitation of Kossel patterns by an X-ray tube and a focusing polycapillary lens will be presented. Additionally, it will be shown that the lateral resolution of the Kossel technique under X-ray tube excitation can be improved and the exposure times can be strongly reduced by using a polycapillary lens. The advantageous combination of X-ray fluorescence and crystal structure analysis by means of Kossel microdiffraction will be demonstrated.

Lattice constant determination from Kossel patterns observed by CCD camera

The Kossel technique is known due to its precision for lattice constant determination in micro ranges by use of X-ray films. Recently we observed the Kossel interferences also by a CCD camera in a good quality. Thus, the diffraction interferences could be immediately processed and evaluated by computer permitting considerable time saving. In order to obtain the similar accuracy as for measurements with X-ray films further technical and experimental improvements were necessary, especially for a better contrast to observe intersection points of several weak reflections, for evaluating digital patterns, for optimizing of the shortest focus-screen distance and for considering the image field curvature of the objective. As a result, a precision in lattice constant determination could be achieved at a Fe-crystal coming relatively close to the one of comparable X-ray film patterns, which is still about one order of magnitude better for the time being.

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

Diffraction 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 DABRITZ et al. (1986, 1997a,b). 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.

Automatic orientation determination from Kikuchi patterns

Some formal aspects of crystal orientation determination from Kikuchi patterns are discussed, with respect to writing general and fast algorithms for automatic indexing of the patterns and orientation determination. The geometry of the problem is presented in a general form which is also suitable for channeling patterns or X-ray Kossel patterns. Moreover, geometrical ambiguities and other reliability issues are considered. Some strategies designed to handle artifacts of automatic pattern analysis are presented. Finally, the reliability and the accuracy of the described procedures and the sensitivity of the results to the errors of the basic measurement parameters were tested on computer-generated patterns.

Investigation of the Rhabdite/Kamacite Law of Intergrowth in iron meteorites with the aid of the Kossel technique

Abstract— X‐ray microdiffraction measurements based on the Kossel effect have been used for orientation determinations of rhabdite (i.e., small prismatic schreibersite crystals) with respect to the kamacite matrix. For that purpose, polished specimens of the Toluca meteorite have been analyzed after surface etching. Kossel patterns of kamacite and rhabdite have been recorded and simulated. As the law of intergrowth for idiomorphic rhabdite crystals, we confirmed the relations:In comparison with typical line widths, the Kossel lines of kamacite are distinctly broadened. This is found for the meteorite Toluca and a for a second sample, the meteorite Morasko. This behaviour is probably connected with a high dislocation density, as shown by transmission electron microscope investigations.