Kossel Patterns Research Articles

Investigation of icosahedral quasicrystals by the kossel technique

X-ray Kossel patterns from icosahedral quasicrystals have been observed for the first time by exciting fluorescence radiation inside the i-Al70Pd20Mn10 and i-Zn50Mg45Y5 quasicrystals, using a 30 keV electron beam and white synchrotron radiation, respectively. The reflections detected allowed a determination of the lattice parameters and the crystal orientation. Some Kossel lines possess a “light-dark” or a “dark-light” fine structure, which depends on the intensity of absorption effects inside the crystal. This behaviour is due to dynamical X-ray diffraction.

Excitation of Kossel patterns by synchrotron radiation

In this article we will report on Kossel experiments by means of synchrotron radiation. To our knowledge this is the first demonstration that Kossel patterns can be observed using fluorescent radiation excited by synchrotron X-rays. Kossel patterns are characterized by the importance of a high degree of information in the determination of the crystal structure, e.g. the orientation matrix, lattice parameter, symmetry elements and the phase of scattering waves into the microstructure of the single crystal under consideration. In the first test experiment Cu and GaAs single crystals were investigated.

Appllied Crystallography in the Scanning Electron Microscope Using a CCD Detector*

Abstract The development of a new charge coupled device (CCD)-based detector for the scanning electron microscope (SEM) has allowed high quality backscattered electron Kikuchi patterns (BEKP) suitable for crystallographic analysis to be collected. These BEKPs can be used for crystallographic texture, phase and microstress analysis. This CCD detector system, can also be equipped with a special filter for removing backscattered electrons, which allows us to image low intensity, highly divergent x-ray diffraction (Kossel) patterns. The Kossel patterns are utilized for the accurate measurement of d-spacings suitable foe residual stress and lattice parameter measurements.

Computer‐aided evaluation of kossel patterns obtained from quasicrystals

AbstractFor the evaluation of Kossel experiments on quasicrystals such as the decagonal phase of AlCoNi or AlCoCuSi a computer program called KOQUA has been written, which allows to simulate Kossel patterns of two‐ and three‐dimensional quasicrystals as well as of every conventional crystal system. In some examples the application of the program is demonstrated.

Phase identification in Ti/TiN diffusion couples with the Kossel technique

A Ti/TiN diffusion couple, which had been prepared by isothermal annealing of a Ti sheet in nitrogen atmosphere at 1091 °C and quenched in water, was investigated by Kossel microdiffraction. Kossel patterns were obtained from all phases present in the diffusion couple (α-Ti(N), η-Ti3N2−x, ζ-Ti4N3−x and δ-TiN1-x)It could be shown that the Kossel technique has a superior lateral resolution (10 μm) compared to commercially used X-ray microdiffraction methods, especially in the case of weak X-ray radiation.

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?.

CdTe2O5 space group determination by Kossel patterns

On demontre que le compose du titre cristallise dans le systeme monoclinique, groupe d'espace C2/m

Crystallography using the diffraction of proton induced X-rays

Diffraction (Kossel) patterns are obtained by bombarding single crystals with a 700 keV proton beam and collecting the emitted characteristic X-rays on photographic film. The diffraction curves appear superimposed on the isotropic (in the case of K-lines) distribution typically obtained when non-single-crystal targets are bombarded. They are identified using stereographic projection. In contrast to previous uses of this technique, variable line intensities were observed. They were compared with calculation intensities using a geometrical model based on: proton energy loss, X-ray production cross section, and attenuation before and after being diffracted, as well as competition between reflection and deficiency. A good agreement was obtained. The calculations were carried out up to 5 MeV proton energy and also for a simulated microbeam.

Diffraction effect of x‐rays on the accuracy of quantitative analysis of crystals

AbstractIn order to understand an apparent discrepancy of concentration of constituent elements in the quantitative analysis of thin KCl crystals with an energy dispersive X‐ray analyzer, which has been partly explained by fluorescent X‐ray excitation, more detailed experiments were carried out on binary alkali halides and tricomponent amorphous material by changing the azimuthal angle. Intensity ratios of X‐rays from the constituent elements in KCl and KBr single crystals varied considerably according to the rotation of the specimens. The observed differences between maximum and minimum intensity ratios were 15% for a thin KCl crystal about 100 nm thick and 20% for a bulk KCl crystal, which corresponded to 4.1% and 4.5% differences in atomic concentration, respectively. It was ascertained that for amorphous materials such as Co87Zr5Nb8, such a variation of the intensity ratio of X‐rays was not observed. It is thus proved that the variations of the intensity ratios of X‐rays from the constituent elements with azimuthal angle for KCl and KBr are attributed to the diffraction effect of characteristic X‐rays generated in crystalline specimens. This effect, which is the same as that in the production of Kossel patterns, is one of the essential factors limiting the accuracy of the analysis.

Diffusion bonding of silver balls to a copper substrate and vice versa

Small balls of pure silver (copper) placed on a single crystal substrate of copper (silver), as well as pairs of silver and copper balls kept in contact by gravity, were annealed at temperatures close to the eutectic temperature. Some aspects of the Ag Cu interphase boundaries which form were examined and 105 relative orientations of both phases were measured from Laue back reflection or Kossel patterns. These orientations are classified conveniently in terms of disorientations of the silver lattice with respect to the copper lattice. The disorientations are treated firstly in terms of a random distribution of the relative orientations of both lattices, and secondly in terms of a model where the lattices are oriented in such a manner that they have non-primitive near-coincident cells. The model allows the computation of theoretical disorientations corresponding to such relative orientations and gives results in agreement with some of the experimental disorientations.

In-situ determination of lattice expansion in proton-bombarded GaP single crystals

Abstract The lattice expansion of GaP, irradiated by 0.3–1.4 MeV protons at 140–715 K was studied in situ by means of the proton- induced Kossel effect. The measurements characterize the surface layer of the crystal with a thickness of 1–2μm. The increase of interplanar spacing Δd{111} measured at T ≥ RT follows a “sublinear” dose-relation with saturation at higher doses. The different initial slopes of the curves obtained at various incidence energies can be described by the energy dependence of the elastic displacement cross section. Measurements performed at T < RT exhibit a more linear “expansion-dose” dependence with a higher expansion rate. As shown by channeling backscattering analysis at RT, the damage density increases with the proton dose in the same manner as the lattice expansion. The expansion was also investigated using X-ray topographs and electron-induced Kossel patterns, confirming the in-situ results.

ANOMOLOUS PATTERNS OF TUNGSTEN SAMPLES OBSERVED WITH SCANNING ELECTRON MICROSCOPE

On recording a number of SACP's of tungsten specimen successively tilted -to different orientations, some anomolous patterns superimposed on the general SACP's were observed at the exact positions of direction, direction, and direction. These anomolous patterns are similar to Kossel patterns observed with transmission electron microscope. Moreover, the present patterns have two additional important characteristics. First, the intensity distribution of patterns changes with the electron energy (the electron accelerating voltage). Second, the geometric feature of the patterns can be used to represent some characters of the internal structure of the crystal. Finally, from the view points of the anomolous scattering effect, and the parameter a, which represents the interaction strength between the crystal potential. and the incident electron, the origin of the contrast of these patterns was explained qualitatively.

Axial Channeling in Electron Diffraction

Abstract Kossel patterns from Silicon and Niobium were obtained with a convergent electron beam. An intensity maximum in the direction of the zone axes [001] and [111] of Nb was interpreted as axial channeling. The intensity distribution in Kossel patterns was calculated by means of the Bloch wave picture of the dynamical theory of electron diffraction. Particularly zone axis patterns were calculated for different substance-energy combinations and they were compared with experimental observations. The intensity distribution in the calculated Kossel patterns was very sensitive to the model of absorption and it was found that a treatment of the absorption close to the model of Humphreys and Hirsch [Phil. Mag. 18, 115 (1968)] gave the best agreement with the experimental observations. Furthermore it is shown which Bloch waves are important for the intensity distribution in the Kossel patterns, how they are absorbed and how they change with energy.

Aspects of intergranular fracture of CuBi studied in the scanning electron microscope

IntroductionKossel X-ray diffraction within the SEM can be used to obtain orientation relationships (to 0.2° routinely) and crystal perfection information from microvolumes (5μm)3, this being the principal feature of the technique1. A study of the cracking behaviour of CuBi alloys has been made in an attempt to understand the mechanism by which intergranular fracture occurs due to the addition of down to 0.001at.% Bi2. Orientation relationships (angle/axis pairs) were needed for cracked boundaries but can only be found from Kossel patterns from annealed materials. Thus orientation work was done on annealed material, which was then deformed in a 4-point bending machine. Observations of changes in crystal perfection were made at various strains, as cracks appeared, at positions within grains and at boundaries. Finally, optical study of slip lines at boundaries and fracture surfaces was made.A Cu0.02 wt.% Bi sample was given a maximum embrittlement heat treatment (1073K,10min,air-cooled; 773K, 4h, furnace-cooled) which caused a large percentage of the Bi to segregate to the boundaries.

GaxIn1-xSb Crystals Grown by Liquid Phase Epitaxy

Epitaxial layers of GaxIn1-xSb have been gown on GaSb and/or InSb substrates over the whole composition range. The influences of the growth conditions on the crystalline qualities of GaxIn1-xSb have been investigated by an optical microscope and the X-ray Kossel patterns. Single crystalline layers can be gown in the composition range, 0≤x≤0.93 on (111) InSb substrates and in the range, 0.70≤x≤1 on (100) GaSb substrates. The etch pit density in the grown layer was about 107 cm-2, independent on the substrates and composition x. A considerable increase in the etch pit density in the substrate was observed after epitaxial growth. Ga was detected in the InSb substrate after epitaxial growth.

Experimental studies of the crystallography of the precipitation of β vanadium hydride

The structure of the interface between β vanadium hydride plates and the parent b.c.c. solid solution of hydrogen in vanadium has been studied by transmission electron microscopy, and measurements have been made of the shape strain and orientation relationship. The results are generally in good agreement with the predictions of the phenomenological theory of martensitic transformations. The prediction that the interface dislocations generating the lattice invariant shear should be resolvable has been confirmed, and direct confirmation obtained of the hypothesis that the complementary shear system is {112} 〈 11 1〉. For the identity correspondence and specific shear system (112) B [ 11 1] R the predictions of the theory that the habit plane is near (2̄27) B and the displacement direction near [22̄7] B have been confirmed by the electron microscopy and the shape strain measurements. The measured magnitudes of both shape and complementary strains agree well with predicted values. Orientation determinations from Laue and Kossel patterns indicate that the [001] direction of the hydride is inclined to the (001) plane and are compatible with monoclinic hydride structures in which either χ or β is greater than 90°. However, measurements of the orientation relationship are generally in better agreement with predictions of the theory for structures with β 〉 90°.

Transmission Kossel Study of the Structure of Cold‐Rolled Iron and its Nucleation Behaviour

By examining thin sections and by use of the more strongly absorbed Ti Kα radiation rather than Fe Kα radiation it was found possible to obtain useful transmission Kossel patterns from iron that had been deformed 40% by rolling. Examination of the as–deformed material showed large misorientations in all the matrix grains (20–54°) and many of the grains showed deformation bands where the orientation changed rapidly (up to 15° over distances of 50 μm). On annealing the material recrystallized by strain‐induced boundary migration with all the invaded grains being those with (111) parallel to the rolling plane. Only one example was found of new grain formation by mutual invasion across a deformation band, the main nucleation mode previously observed in aluminum deformed 40% by compression. The difference between the two examples appears to arise from the smaller misorientations of the deformation bands in rolled iron.

On the unique solution of Kossel patterns

On the unique solution of Kossel patterns

Kossel patterns in research on diffusion in single crystals

Kossel patterns in research on diffusion in single crystals

Utilisation des diagrammes de Kossel pour la détermination précise des paramètres cristallins d'alliages dilués d'aluminium

A new method for the accurate determination of lattice parameters using Kossel patterns has been worked out in order to measure the small variations of lattice parameter in aluminum alloys. Experimental values of the size factors for vanadium and copper in aluminum obtained by this method have been compared with theoretical expectations and experimental results obtained from supersaturated alloys prepared by ultra-rapid quenching.