A summary of focusing X ray polycapillary optics is presented including history, theory, modeling, and applications development. The focusing effects of polycapillary optics come from the overlap of the beams from thousands of small hollow glass tubes. Modeling efforts accurately describe optics performance to allow for system development in a wide variety of geometries. The focusing of X ray beams with polycapillary optics yields high gains in intensity and increased spatial resolution for a variety of clinical, lab-based, synchrotron or in situ analysis applications.

https://downloads.hindawi.com/archive/2010/867049.pdf

Focusing Polycapillary Optics and Their Applications

The application of the electron backscatter diffraction technique to the investigation of phase transformations is reviewed. The wide variety of results obtained using this technique is illustrated and discussed, focusing on thermodynamics and kinetics of phase transformations, solidification, solid state phase transformations, environmentally assisted reactions and thin film deposition. Emphasis is also placed on two rapidly growing developments: coupling electron backscatter diffraction with advanced experimental techniques and with more and more complex modelling of phase transformations and of resulting material properties.

Application of electron backscatter diffraction to the study of phase transformations

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.

A 3D Hough transform for indexing EBSD and Kossel patterns.

The analysis of thin layers of thickness ∼100 nm has become a new field of application for glow discharge optical emission spectroscopy (GDOES). In this paper an overview is given of the experiences and possibilities gained by the authors in later years at their research, development and application of GDOES. During GDOES analysis of a multilayer system the depth resolution was determined using the inverse maximal slope method. Under optimized discharge conditions a depth resolution of ∼25 nm at 100 nm depth was achieved. The gas flow in a Grimm-type source for glow discharge mass spectrometry (GDMS) was simulated and a correlation between calculated pressure and crater shape was found. Cleanness of the sample and source turned out to be essential for a fast stabilization time and reduction of the influence of light elements and molecules. Thereby, a 10 nm layer at the top surface of a sample could be quantified. Apart from the influence of density, the reflectivity of the sample surface is discussed. It is shown that a high sample reflectivity can cause up to 100% more light to be measured by the spectrometer.

Present possibilities of thin‐layer analysis by GDOES

Formation of intermetallic compounds in Ti‐Cu thin film bilayer samples has been studied between 300–475 °C by Rutherford backscattering and glancing‐angle x‐ray diffraction techniques. The first intermetallic compound to be formed was TiCu and was followed by TiCu3, the latter showed detectable deviations from the stoichiometry. The thickening of both compounds obeyed a parabolic relationship with time. The interdiffusion coefficient derived from compound formation can be described by the following expressions: TiCu:D=4.85×10−4 exp(—1.48eV/kT) cm2/sec, TiCu3:D=7.73×10−2 exp(—1.82eV/kT) cm2/sec.

Intermetallic compound formations in titanium-copper thin-film couples

Lattice constant determination from Kossel patterns observed by CCD camera

Kossel and pseudo Kossel CCD pattern in comparison with electron backscattering diffraction diagrams

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.

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

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

Im Ergebnis von Diffusionsuntersuchungen am System Cu–Ti bei Temperaturen zwischen 750°C und 850°C konnten die intermetallischen Phasen Ti2Cu, TiCu, Ti3Cu4, Ti2Cu3 und Ti2Cu7 mit Hilfe der quantitativen Elektronenstrahl-Mikroanalyse identifiziert werden. Im Zustandsschaubild dieses Systems nach Zwicker war bisher die Phase Ti3Cu4 als instabil ausgewiesen und fur Ti2Cu7 als mogliche Phase noch TiCu3 angegeben worden. Aus dem Gesetz fur das Wachstum der gesamten Diffusionszone sowie fur die einzelnen Phasen (d ∼ √t) folgt, das in diesem System bei Verwendung von Kompaktmaterial Volumendiffusion und nicht die Phasengrenzreaktion geschwindigkeitsbestimmend ist und somit die Diffusionskoeffizienten nach dem Matano-Verfahren bestimmt werden konnen. – Es wurden die chemischen Diffusionskoeffizienten fur die einzelnen Phasen bei 750°C, 800°C und 850°C sowie die partiellen Diffusionskoeffizienten DCu und DTi bei 850°C in der Ti2Cu7-Phase ermittelt. Die chemischen Diffusionskoeffizienten gehorchen Arrhenius-Gleichungen, aus denen die Diffusionsparameter Q (Aktivierungsenergie) und D0 (Frequenzkonstante) fur die identifizierten Phasen berechnet werden konnten.



As a result of diffusion studies in the binary system of Cu–Ti within a temperature range of 750°C and 850°C the intermetallic phases Ti2Cu, TiCu, Ti3Cu4, Ti2Cu3 and Ti2Cu7 have been detected by means of electron microprobe analysis. Up to now according to the equilibrium diagram of Zwicker the intermetallic phase Ti3Cu4 was reported to be instable only. By the present investigation a time dependence of the width of the total diffusion zone as well as of each of the phases, d∼ √t, has been verified, i.e. volume diffusion is dominating. The chemical diffusion coefficients of all phases have been measured for 750°C, 800°C and 850°C. The partial diffusion coefficients for Cu and Ti in Ti2Cu7 for 850°C have also been determined. The chemical diffusion coefficients follow the Arrhenius law, the activation energy Q and the frequence constant D0 could be calculated.

S. Däbritz

Papers

Lattice constant determination from Kossel patterns observed by CCD camera

Kossel and pseudo Kossel CCD pattern in comparison with electron backscattering diffraction diagrams

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

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

Diffusionsuntersuchungen am System Cu–Ti†