Kossel Pattern Research Articles

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.

Ion Beam Preparation Procedures for Three-dimensional SEM Resolved Kikuchi (EBSD) and Kossel Microdiffraction Analysis of Deformed Metals

The SEM provides information not only on the sample surface and near-surface regions concerning topography, composition, crystal orientation etc. With special preparation techniques the full 3D microstructure can be detected. The deformation-free revealing of the internal structure is not possible with mechanical cutting and grinding. Chemical and electrolytic methods allow only selected material-specific solutions. Ion beam preparation has essential advantages compared with conventional techniques. Especially for mechanically deformed metal samples with small dimensions special ion beam processing steps are required. The well established FIB technology is only useful for very small selected regions with micrometer dimensions. Here the problem will be solved to cut and to investigate samples with cross sections of typically 20 μm x 400 μm and 4 mm length after well defined deformation by microscopy and microdiffraction in the SEM over the full sample volume. The sample shape and size are shown in Fig. 1. After defined tensile tests these samples have been cut longitudinally (cut 1) and transverse (cut 2) by ion beam slope cutting and the macroarea was etched chemically (region 3). The ion beam cutting method [1] was carried out with the Gatan Precision Etching Coating System (PECS) acc. to Fig. 2. The broad ion beam is directed onto the sample mounted under a blind with a sharp edge. The ion gun allows to produce a beam of inert gas or reactive ions with energies up to 10 keV and densities up to 40 μA/mm. The processes can be observed by optical microscopy. A new stage allows sample positioning, tilting and rotation, blind mounting and adjustment with accurate sample transfer into the SEM for the final inspection. Fig. 3 shows a detail of the longitudinal ion beam cut area. In Fig. 4 the ion beam cut area of the full cross section (transversal cut) is shown. The cutting steps were carried out with 7 keV Krypton ions. The texture analysis by EBSD is shown in Fig. 5 for the cuts corresponding to Fig. 1 by Orientation Imaging Microscopy (OIM) maps of a 20 μm thin rolled Cu foil after a tensile test. More detailed discussion of the texture modified by deformation will be given in [2]. Also X-ray Kossel microdiffraction pattern have been detected of a tensile deformed Ni crystal [3]. The Kossel pattern in Fig. 6 shows an example of strong broadening and anisotropic intensity change of reflections due to the deformation process. EBSD provides information on crystallographic orientations, whereas X-ray Kossel microdiffraction pattern allow profound statements of the real microstructure. For both techniques the ion beam procedures are excellent tools to produce cut areas with high accuracy and to combine it very well with additional analysing methods.

Computer Color Mapping Analyses of Deformation Bands and Recrystallized Grains inside Elongated Grains near Surface of Hot-rolled Silicon Steel Sheet

Computer color mapping of elongated grains near the surface of hot-rolled silicon steel sheet was performed with an image analyzer, using the data of crystallographic orientation and strain obtained from a Kossel pattern examination. Matrix bands having two equivalent orientations of near (210) [123] and (210) [123] elongated grains formed alternately near the surface of hot-rolled silicon steel sheet. The characteristic morphology comprised transverse deformation bands across a grain elongated in the rolling direction. The misorientation between the matrix bands separating the deformation bands was 40° (max.), whereas that inside each matrix band was 3-12°. Most deformation bands are bordered by high angle grain boundaries with a width of 3 pixels, and are of complicated and highly curved form inside the elongated grain. The elongated grains which were of near {111} orientation had a large amount of strain and formed small recrystallized grains by strain induced boundary migration from the high energy area at the grain boundaries or from the deformation bands within the elongated grains. The type and formation mechanism of the recrystallized grains can easily be observed by color mapping.

A possible new route to precise lattice-parameter measurement of perfect crystals using the divergent-X-ray beam method

Newly observed diffraction phenomena that appear in the transmitted divergent-beam (pseudo-Kossel) patterns given by perfect or nearly perfect crystals are reported. They are seen within the areas of overlapping intensity distributions where two or more Kossel lines cross. The pseudo-Kossel patterns were generated using a scanning electron microscope to produce a small X-ray source (diameter < 10 μm) within a 2 μm-thick copper film coating single surfaces of polished, plate-shaped, nearly perfect diamond specimens. Experimental conditions determined that the observed width of Kossel lines was dominated by Cu Kα1 wavelength spread. Imposed upon the overall area of crossing of these dispersion-broadened lines, there appear fine streaks of enhanced transmitted intensity that delineate loci along which, as the wavelength changes, coherent multiple diffraction occurs, accompanied by enhanced Borrmann transmission. These fine-scale features, only a few arcseconds in angular width, add markers to the broad-line Kossel pattern that should be exploitable in lattice-parameter measurements.

Convergent beam electron diffraction zone axis pattern maps from a copper single crystal

Two zone axis pattern (ZAP) maps were obtained from a copper single crystal, using convergent beam electron diffraction in a transmission electron microscope: the Kossel pattern (KP) and the convergent beam electron diffraction (CBED) pattern ZAP map. A computer simulation of the KP map was used to aid its interpretation. The CBED ZAP map of copper consists of zero layer disks showing an intersecting set of higher-order Laue zone (HOLZ) deficiency lines. From the computer simulations of these disks, an operating high voltage of 84kV was determined. Both kinds of map are useful for subsequent “fingerprint” identification of copper in precipitates, alloy crystalline phases, and crystallographic direction determination.

Computer simulation of Kossel pattern maps from crystals

Computer simulation of Kossel pattern maps from crystals

AN IMPROVEMENT OF KOSSEL RATIO METHOD

An improvement of revised Kossel ratio method is put forward in this paper, at the same time a Kossel orientation method of crystal is developed. It can analyse more Kossel patterns than generally used ratio method. It is applied to a arbitrarily orientation Kossel pattern of a Fe-0.76wt%V-0.08wt%N alloy. The accuracy of the lattice parameter determination reaches 5×10-5?.

Contrast of Kossel Patterns in Electron Diffraction

Electron diffraction patterns from a Si crystal taken with a convergent beam of large angular aperture (Kossel pattern) are compared with the diffraction pattern taken with a hollow cone convergent electron beam. For thin crystals the patterns are complementary. This behaviour is discussed.

Correction for the effect of electron beam heating on Kossel pattern lattice spacing results

Correction for the effect of electron beam heating on Kossel pattern lattice spacing results

A note on the reading of Kossel patterns

A Kossel pattern, as recorded on a flat photographic plate, is best regarded as a gnomonic projection of a “spherical Kossel pattern”, recorded on a sphere centred at the source point. The spherical Kossel pattern is identical (at arbitrary scale) with the circles of intersection of the “X-ray Fermi sphere” (a sphere of radius 1 λ centred at the origin of reciprocal space) with the Brillouin planes, which form the boundaries of Brillouin zones. By this visualization one readily identifies the characteristic features in a Kossel pattern which are of value for revealing crystal orientation and lattice structure, for simple and sometimes sensitive measurement of lattice parameters, and for sensitive detection of strain. Two Kossel conies, one well observed ( i.e., a complete or nearly complete ellipse, or a hyperbola with both branches visible) will suffice to determine the orientation for a known crystal. Two well observed will give the lattice parameter as well if the characteristic X-ray wave-length is known, and three suffice to determine the lattice structure. However, special features such as Kossel-line intersections provide superior information which should be exploited as far as possible.

A single-exposure method for the determination of lattice spacings and crystal orientation from Kossel diffraction patterns

A single exposure method is described for the calculation of lattice spacings and crystal orientation, from Kossel diffraction patterns. This method is extremely simple from an experimental viewpoint since the only data required are the coordinates of five or more points on each Kossel diffraction curve in an arbitrary orthogonal system and the wavelength of the characteristic X-ray radiation forming the pattern. The method requires the analysis of at least two diffraction curves which can be either elliptical or hyperbolic. The equation of each curve is first derived in the arbitrary system. It is then transformed to a coordinate system in which the coefficients may be equated with those of an equation of the same curve derived in terms of the lattice spacing, the orientation of the crystal planes responsible for the diffraction cone and the X-ray wavelength. The lattice spacings and the directions of the crystal plane normals are calculated. A computer program has been written to handle the lengthy arithmetical operations required for the analysis, and application of the method to a Kossel pattern from a single grain of Swedish iron is described.

The influence of temperature on the MgO zone-axis pattern

Measurements made on convergent-beam patterns from MgO taken near the [001] zone-axis at two fixed temperatures have been studied in detail. Two types of patterns, namely the symmetrical excitation of a single 200 reflexion and the simultaneous excitation of the 200, 020, 220, reflexions were studied, using up to 129 beams in the dynamical calculations. The absorption function, Vih exp (−BiS2), was found to be well defined at the zone axis, allowing separate determination of Vih and Bi. For the pattern for single excitation, Vi0 = 0.6 volt, Vih = 0.14 volt, Bi = B = 0.3, was determined at room temperature. In comparing the two types of pattern at high temperature an increase in Vih of between two and three times was found for the 3-reflexion pattern. This increase, and the more normal value found for the single excitation pattern, seems to accord with other experience that the dynamical increase in Vih, as predicted by Yoshioka and Kainuma, possibly occurs in the vicinity of a many-line intersection of the Kossel pattern but not at the zone axis.

A computer program for the calculation of lattice spacings from Kossel diffraction patterns

A computer program, written in Whetstone Algol, is described for handling the arithmetical operations involved in a precision method of determining lattice spacings from Kossel diffraction patterns. The interpretation treats the Kossel pattern as a three-dimensional array of intersecting cones with a common vertex and depends on the fact that when three or more positions of a cone generator are established, its axis and semivertex angle are defined. The theory and experimental requirements of the method are outlined and the functions of the steps in the computer program are described. The full program, together with data sheets and print-out of results for a typical calculation is available on request. A subsidiary program is also available to provide a graphical display of relevant parts of the results.

Crystal Orientation and Lattice Parameters from Kossel Lines

A Kossel x-ray diffraction pattern of a single crystal contains information concerning crystal orientation, structure, and lattice parameters. Procedures have been developed for determining orientations to within ±0.5°, identifying conics and calculating d spacings to within ±0.5%, and determining lattice parameters in any crystal system with errors as small as 10 ppm. Orientation and structure calculations can be made starting with position measurements taken directly from a Kossel pattern. Precision parameter determinations require that suitable intersections of conics appear in the Kossel pattern. This can be assured by selection of appropriate conics and wavelengths and the aid of a stereographic projection of the pattern. Computer programs handle the bulk of the calculations.

Measurement of the Lattice Parameter of Silicon, using a Double-diffraction Effect

PRECISION measurements of the lattice parameters of single crystals have been made both by measuring directly the angles of Bragg reflexion1, and by analysing the Kossel, or divergent beam, patterns produced by a point source of X-rays2. The angles between the Bragg cones or their intersections are determined by the ratio . Lonsdale3 has shown that when these angles are very small, as for example when a number of Bragg cones almost intersect at a point, high precision can be achieved using relatively modest apparatus. By recording part of the Kossel pattern of diamond at a distance of 1 metre she obtained a very accurate value of the lattice parameter.

細管X線管球による類似Kossel線の出現とその応用について

細管X線管球による類似Kossel線の出現とその応用について