A comparison of the KOSSEL and the X‐ray Rotation‐Tilt Technique

There are world‐wide efforts to analyse micron regions of compact samples by means of X‐ray diffraction (“X‐ray Microdiffraction”). Two micro diffraction procedures, the KOSSEL technique excited by electron or synchrotron radiation beams and the new X‐ray Rotation‐Tilt Method (XRT), are compared to show their possibilities and limitations. Some selected examples of new applications are presented.     

Automatic detection and high resolution fine structure analysis of conic X‐ray diffraction lines

The presented method demonstrates a first step in the development of a high resolution “Residual stress microscope” and facilitates through the implementation of largely automated procedures a fast detection of diffraction lines in the form of conic sections. It has been implemented for, but is not exclusively used for the Kossel technique and the “X‐ray Rotation‐Tilt Method” (XRT). The resulting multifaceted evaluable data base of many X‐ray diffraction radiographies can be used not only for the systematic analysis of anomalies in diffraction lines (reflection fine structure), but also for direct calculation and output of precision residual stress tensors. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

X‐ray Reflectivity from Sinusoidal Surface Relief Gratings

The sinusoidal shape of light‐induced surface relief gratings of polymers can be probed by x‐ray scattering techniques. A particular approach of kinematic x‐ray scattering theory is developed to interpret experimental scattering curves. The simulations demonstrate the particular sensitivity of x‐ray reflectivity for very small grating amplitudes. At angles of incidence close to the critical angle of total external reflection a grating amplitude h < 2 nm already provides measurable grating peaks. In general the grating amplitude h can be measured from the envelope function over the grating peak maxima. The capability of the approach is demonstrated by simulation of the reflection curve recorded from a polymer sample with non uniform grating height.     

Grazing Incidence In‐plane Diffraction Measurement of In‐plane Mosaic with Microfocus X‐ray Tubes

The in‐plane mosaic structure of Au/Fe and GaN‐based epitaxial layers has been determined directly by laboratory‐based grazing incidence in‐plane x‐ray diffraction in which Bragg reflections normal to the plane of the wafer are probed. High intensity and acceptable signal‐to‐noise can be obtained with no modifications to commercially available equipment. Excellent agreement is obtained between measurements of the same Au/Fe multilayer samples at the European Synchrotron Radiation Facility in Grenoble and with the laboratory system employing a focused x‐ray beam from a microfocus generator. The technique is particularly important for the GaN‐based systems as it uniquely provides a measure of the so‐called twist mosaic independent of the out‐of plane (tilt) mosaic.     

X‐ray Topographic Characterization of L‐Arginine Phosphate Monohydrate Crystals

L‐arginine phosphate monohydrate (LAP) organic crystals were investigated by X‐ray Lang topography. Selected topographs of nearly perfect seeded grown and self‐nucleated crystals show that typical defects inside are grown‐in and post‐growth dislocations, growth sector boundaries, and microbes, while their features are presented and discussed. No structural defects associated to the presence of step bunching on the (100) surface of the crystal have been observed by X‐ray topography.     

X‐ray powder diffraction structural characterization of Ba1‐xEuxTiO3 ternary oxides

The single‐phase Ba_1‐xEu_xTiO₃ (0.1≤x≤0.4) samples have been synthesized by solid state reaction under high pressure and ‐temperature. X‐ray powder diffraction data was determined by MS Modeling using Reflex Powder Indexing technique. The Ba_1‐xEu_xTiO₃ series exhibited an interesting orthorhombic‐tetragonal‐cubic structural transformation as Eu composition increases, the distinct change of the X‐ray diffraction peak profile in the vicinity of 45.5º is characteristic of structural transformation. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

X‐ray interferometric investigation of homogeneity of substances

The influence of inhomogeneous distribution of substance density on interference patterns of X‐rays is investigated. It is shown experimentally that during preliminary transition of superposing Roentgen waves through samples with inhomogeneous distribution of substance density, irregular phase shifts occur in these waves, leading to disappearance of interference patterns. Special two‐ and three crystal interferometers are developed for such investigations.     

Single‐crystal sapphire microstructure for high‐resolution synchrotron X‐ray monochromators

We report on the growth and characterization of sapphire single crystals for X‐ray optics applications. Structural defects were studied by means of laboratory double‐crystal X‐ray diffractometry and white‐beam synchrotron‐radiation topography. The investigations confirmed that the main defect types are dislocations. The best quality crystal was grown using the Kyropoulos technique. Therein the dislocation density was 10²–10³ cm⁻² and a small area with approximately 2*2 mm² did not show dislocation contrast in many reflections. This crystal has suitable quality for application as a backscattering monochromator. A clear correlation between growth rate and dislocation density is observed, though growth rate is not the only parameter impacting the quality.     

Spatially resolved X‐ray diffraction as a tool for strain analysis in laterally modulated epitaxial structures

Spatially resolved X‐ray diffraction (SRXRD) is applied for micro‐imaging of strain in laterally modulated epitaxial structures. In GaAs layers grown by liquid phase epitaxial lateral overgrowth (ELO) on SiO₂‐masked GaAs substrates a downward tilt of ELO wings caused by their interaction with the mask is observed. The distribution of the tilt magnitude across the wings width is determined with μm‐scale spatial resolution. This allows measuring of the shape of the lattice planes in individual ELO stripes. If a large area of the sample is studied the X‐ray imaging provides precise information on the tilt of an individual wing and its distribution. In heteroepitaxial GaSb/GaAs ELO layers local mosaicity in the wing area is found. By the SRXRD the size of microblocks and their relative misorientation were analyzed. Finally, the SRXRD technique was applied to study distribution of localized strain in AlGaN epilayers grown by MOVPE on bulk GaN substrates with AlN mask. X‐ray mapping proves that by mask patterning strain in AlGaN layer can be easily engineered, which opens a way to produce thicker, crack‐free AlGaN layers with a higher Al content needed in GaN‐based laser diodes. All these examples show that high spatial and angular resolutions offered by SRXRD makes the technique a powerful tool to study local lattice distortions in semiconductor microstructures. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

X‐ray structural phase analysis of CdTe semiconductor annealed in air

X‐ray structural phase analysis of CdTe semiconductor, thermally annealed in air at temperature range 373‐773 K and annealing time 24 hrs, is investigated applying Rietveld method. The results showed that at low temperatures < 523 K, oxygen diffuses into the (1/21/21/2) interstitial sites of the CdTe lattice and its relative occupancy increases with the annealing temperature. For higher temperatures ≥ 523 K, the thermally grown oxide CdTeO₃ phase is developed on expense of CdTe phase. The percentage phase abundance of each phase is determined at each temperature applying a standardless method. The rate of oxidation with temperature is found to be non‐linear.     

Growth imperfections in oriented grown KDP crystals by X‐ray topographic analysis

Potassium dihydrogen phosphate (KDP) crystals were restrained to grow in two dimensions only, using a specially designed platform. This enables us to grow the blanks of frequency conversion elements that satisfy type‐II phase matching direction out of a type‐II phase‐matched seed crystal. Synchrotron radiation topography was used to study the growth mechanism of these profiling grown KDP crystals. It is found that both dislocation growth mechanism and layer growth mechanism were involved in the growing process. Inclusions, growth striations and dislocations were the main defects that influenced the crystalline quality of these crystals. High‐resolution X‐ray diffraction was employed to study the lattice integrality of the crystal.     

X‐ray Propagation in Distorted Crystals: From Dynamical to Kinematical Theory

The successive studies of the propagation of x‐rays in crystals distorted by a strain gradient whose magnitude is characterized by a parameter β are presented. It is shown how the new wavefield that appears when βΓ (Γ being the classical extinction length) is much larger than 1 pumps intensity out of the normal wavefield, which explains the transition from the dynamical to the kinematical theory. The quantity βΓ can be increased either by increasing the distortion or by using smaller wavelengths or structure factors as checked experimentally on Si_1‐xGe_x crystals.     

Re‐Investigation of the Structure of 7Bi2O3 · 2WO3 by Single‐Crystal X‐ray Diffraction

The structure of the oxygen‐deficient compound 7Bi₂O₃ · 2WO₃, a fluorite‐derivative phase considered a candidate for electronic applications because of its high ionic conductivity, is investigated by singlecrystal X‐Ray diffraction employing Ag‐Kα radiation (λ = 0.5608 Å) to minimize the effect of the absorption by the heavy metals. The space‐group type is I4₁, the acentric subgroup of I4₁/a that was previously suggested from powder‐diffraction data and precession‐camera photographs. Lattice parameters are a = 12.513(2), c = 11.231(4) (Z = 2.5). The sample is twinned by syngonic merohedry, class I, with volume ratio of the individuals 0.58/0.42. The ordering of W partly confirms previous models, with one W fully occupying one of the sites on special position. However, the remaining W goes in a site on general position, which shares with Bi, resulting thus more diluted in the structure. The oxygen vacancies are partly ordered in three of the ten anion sites.     

Photoacoustic and X‐ray Studies on H+ Ion Implanted n‐GaAs

Qualitative and quantitative analysis on the defects in H⁺ ion implanted (30keV with doses 10¹⁴, 10¹⁵, 10¹⁶ and 10¹⁷ ions/cm²) n‐GaAs are carried out here by Atomic Force Microscopy (AFM), XRD and Photoacoustic measurements, for various doses. The close agreement between these measurements reveal that even the microscopic strain parameter ∈₁ (from XRD) can be viewed microscopically with photoacoustics. Various thermal parameters are computed for the 30 keV H⁺ ion implanted n‐GaAs and reported for the first time.     

X‐ray Diffraction Topography at a Synchrotron Radiation Source Applied to the Study of Bonded Silicon on Insulator Material

New possibilities of X‐ray diffraction topography offered by the modern synchrotron radiation sources for the investigation of wafer‐bonded material are demonstrated. They allowed detecting defects and long‐range strain fields at and close to the bonding interface. A quantitative estimation of the deformation of the region near to the bonding interface was possible e.g. by investigating focussing distances and dominant spatial frequencies of contrast patterns (often in the order of 200 μm). In typical wafer bonded material the maximum bonding‐induced inclination of the lattice planes was in the order of 10 arcsec and the approximate amplitude of the deformation in the order of 1.5 nm. The sensitivity of the presented methods to characterize the influence of various process parameters was demonstrated.     

Observation of the δ to ε Zr‐hydride transition by in‐situ synchrotron X‐ray diffraction

We investigate the formation and dissolution of hydrides in commercially pure zirconium powder in‐situ using high‐energy synchrotron X‐ray radiation. Experimental results showed a continuous phase transition between the δ and ε zirconium hydride phases with indication of a second order phase transformation.     

Analysis of X‐ray extinction in crystals with inhomogeniously distributed dislocations

The secondary extinction theory of Zachariasen for mosaic crystals as well as the formalism of Becker&Coppens have been used for substructure analysis (lattice disorientations, block size, density of excess dislocations, etc.) in crystals with inhomogeniously distributed dislocations in the Bragg case of diffraction geometry. In the case of large crystals D_S ≫ Λ_hkl the mean total density ρ_D of randomly distributed dislocations was also estimated taking into account additionally the primary X‐ ray extinction treatment. In this connection two cases are considered: I) pure secondary extinction related to arrangement of dislocation walls and II) mixed extinction in crystals with large subgrains related to randomly distributed dislocations and arrangement of dislocation walls. In order to check the considerations, the experimental and calculated data were compared for Be (model I) and Cu (model II) single crystals. The weakly distorted single crystals of Be and Cu were experimentally investigated in the Bragg case of diffraction geometry using Cu Kα₁ radiation by means of double crystal diffractometer. A new experimental procedure was proposed. Using alternative technique for substructure analysis (for instance EBSD) the reliability of analysis based on extinction phenomenon in weakly distorted single crystals has been checked. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quantitative Determination of Crystalline Na5P3O10 –I (Form‐I) in Commercial Tripolyphosphate using X‐ray Diffraction Patterns

An x‐ray diffraction method (XRD) for quantitative determination of the crystalline Na₅P₃O₁₀‐I (Form‐I) in a mixture of Form‐I/Form‐II was applied for commercial pentasodium tripolyphosphate analysis. The XRD pattern of the Form‐I shows the unique non‐overlapping 2θ peak at a position of ≈ 21.8 deg. and also at ≈ 29.0 deg. (Cu radiation). The area (integral of the intensity) under the peaks is proportional to the amount of the Form‐I in the mixture covering the range up to 100 wt.%. That enables one to obtain a calibration line and to determine the amount of Form‐I in the mixture of Form‐I/Form‐II and also in commercial pentasodium tripolyphosphate. Commercial samples with high Form‐I concentration, in case they are contaminated with sodium pyrophosphate (Na₄P₂O₇), should be diluted with Form‐II to bring the concentration of the Form‐I below 50 wt.% in the analysed sample.     

Synthesis and X‐ray powder diffraction studies of semiconducting alloys in the system AgCd2‐xZnxGaS4

X‐ray powder technique was used in the investigation of AgCd₂GaS_4–'AgZn₂GaS₄' section to determine the region of AgCd₂GaS₄‐based solubility. It was established that the solid solution forms up to 75 mol.% 'AgZn₂GaS₄'. The refinement of AgCd_0.5Zn_1.5GaS₄ structure was performed. This alloy crystallizes in orthorhombic structure (space group Pmn2₁ ) with unit cell parameters a =0.78772(2), b =0.67221(2), c =0.64019(2) nm, V =0.33899(3) nm³. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Divergent beam hard X‐ray diffraction used for the simultaneous imaging of radiographic and crystallographic information

A transmission method and experimental set‐up were developed for the nondestructive characterisation of the quality of bulk single crystals/ large coarsely crystalline polycrystals or components. The method works by combination of X‐ray projection microscopy (X‐ray shadow microscopy) with bremsstrahlung interferences from divergent beam hard X‐rays, in order to form simultaneously enlarged radiographic images and crystallographic information in one measurement. The method and equipment are patent registered. In the paper some of the first results are presented. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)