Laue Reflections Research Articles

Driekopite, Ideally PtBi, a New Mineral Species from the Driekop Platinum Pipe, Republic of South Africa

Abstract The new mineral driekopite, ideally PtBi, was found in a concentrate from the Driekop mine, one of three zoned Pt pipes (mined from 1925 to 1930) that crosscut the layered mafic and ultramafic sequences of the eastern Bushveld Complex, Republic of South Africa. The holotype grain of driekopite (∼ 22 × 13 μm) occurs in a complex, rounded aggregate ∼120 μm in diameter, in association with isoferroplatinum (Pt3Fe), hollingworthite (RhAsS), geversite (PtSb2), insizwaite (PtBi2), andrieslombaardite (RhSbS), stibiopalladinite (Pd5Sb2), sobolevskite (PdBi), possible tatyanaite (Pt9Cu3Sn4), osmium-bearing tulameenite (Pt2FeCu), and Pt-Fe alloy (∼Pt2Fe). Driekopite appears slightly orange under reflected light compared to Pt-Fe alloys. It shows moderate to strong bireflectance, varying from light yellow to brownish yellow, no pleochroism or internal reflections, and moderate to strong anisotropism. The empirical formula, calculated from the average of six wavelength-dispersive spectrometry analyses made on five grains, on the basis of two atoms, is (Pt0.68Pd0.31Fe0.01)Σ1.00(Bi0.53Sb0.43As0.02Sn0.02S0.01)Σ1.01. The mineral is hexagonal, space group P63/mmc (#194) with the refined unit-cell dimensions a = 4.1993(5), c = 5.6194(6) Å, V = 85.82 Å3, Z = 2, and Dcalc = 12.91 g/cm3. Driekopite is isostructural with NiAs, with mixed compositions of Pt and Pd at the 2a site (0.55:0.45, respectively) and Bi and Sb at the 2c site (0.63:0.37, respectively). Its crystal structure was refined to wR = 6.3% using 13 unique Laue reflections obtained using synchrotron radiation. The six strongest lines for the powder X-ray diffraction pattern calculated from the crystal structure refined from synchrotron data is [d in Å (I) (hkl)]: 3.0531 (92) (101), 2.2234 (100) (102), 2.0997 (77) , 1.5266 (28) (202), 1.2347 (24) , 1.1676 (18) . The holotype grain of driekopite is observed to be paragenetically later than isoferroplatinum and hollingworthite and is considered to be synformational with Bi-bearing geversite, insizwaite, andrieslombaardite, and sobolevskite. The entire aggregate containing these platinum-group minerals is overgrown by a rim of tulameenite and Pt-Fe alloy (∼Pt2Fe), indicating they are paragenetically the last minerals to form. Experiments designed to synthesize PtBi over the range of 200 to 500 °C were all successful. Synthetic PtBi melts congruently at 765 °C, suggesting that driekopite likely crystallized at sub-magmatic temperatures.

White Laue and powder diffraction studies to reveal mechanisms of HCP-to-BCC phase transformation in single crystals of Mg under high pressure

Mechanisms of hexagonal close-packed (HCP) to body-centered cubic (BCC) phase transformation in Mg single crystals are observed using a combination of polychromatic beam Laue diffraction and monochromatic beam powder diffraction techniques under quasi-hydrostatic pressures of up to 58 ± 2 GPa at ambient temperature. Although experiments were performed with both He and Ne pressure media, crystals inevitably undergo plastic deformation upon loading to 40–44 GPa. The plasticity is accommodated by dislocation glide causing local misorientations of up to 1°–2°. The selected crystals are tracked by mapping Laue diffraction spots up to the onset of the HCP to BCC transformation, which is determined to be at a pressure of 56.6 ± 2 GPa. Intensity of the Laue reflections from HCP crystals rapidly decrease but no reflections from crystalline BCC phase are observed with a further increase of pressure. Nevertheless, the powder diffraction shows the formation of 110 BCC peak at 56.6 GPa. The peak intensity increases at 59.7 GPa. Upon the full transformation, a powder-like BCC aggregate is formed revealing the destructive nature of the HCP to BCC transformation in single crystals of Mg.

Selection of CVD Diamond Crystals for X-ray Monochromator Applications Using X-ray Diffraction Imaging

A set of 20 single crystal diamond plates synthesized using chemical vapor deposition (CVD) was studied using X-ray diffraction imaging to determine their applicability as side-bounce (single-reflection) Laue monochromators for synchrotron radiation. The crystal plates were of optical grade (as provided by the supplier) with (001) nominal surface orientation. High dislocation density was found for all samples. Distortions in the crystal lattice were quantified for low-index Laue reflections of interests using rocking curve topography. Maps of effective radius of curvature in the scattering plane were calculated using spline interpolation of the rocking curve peak position across the studied plates. For several selected plates, nearly flat regions with large effective radius of curvature were found ( R 0 ≳ 30 − 70 m, some regions as large as 1 × 4 mm 2 ). The average width of the rocking curve for these regions was found to be about 150 μ rad (r.m.s.). These observations suggest that the selected CVD diamond plates could be used as intermediate-bandwidth monochromators refocusing the radiation source to a specific location downstream with close to 1:1 distance ratio.

Deformation behaviour of [001] oriented MgO using combined in-situ nano-indentation and micro-Laue diffraction

We report a coupled in-situ micro-Laue diffraction and nano-indentation experiment, with spatial and time resolution, to investigate the deformation mechanisms in [001]-oriented single crystal MgO. Crystal plasticity finite element modelling was applied to aid interpretation of the experimental observations of plasticity. The Laue spots showed both rotation and streaking upon indentation that is typically indicative of both elastic lattice rotation and plastic strain gradients respectively in the material. Multiple facets of streaking of the Laue peaks suggested plastic slip occurring on almost all the {101}-type slip planes oriented 45° to the sample surface with no indication of slip on the 90° {110} planes. Crystal plasticity modelling also supported these experimental observations. Owing to asymmetric slip beneath the indenter, as predicted by modelling results and observed through Laue analysis, sub-grains were found to nucleate with distinct misorientation. With cyclic loading, the mechanical hysteresis behaviour in MgO is revealed through the changing profiles of the Laue reflections, driven by reversal of plastic strain by the stored elastic energy. Crystal plasticity simulations have also shown explicitly that in subsequent loading cycles after first, the secondary slip system unloads completely elastically while some plastic strain of the primary slip reverses. Tracking the Laue peak movement, a higher degree of lattice rotation was seen to occur in the material under the indent, which gradually decreased moving laterally away. With the progress of deformation, the full field elastic strain and rotation gradients were also constructed which showed opposite lattice rotations on either sides of the indent.

On the role of secondary extinction in the measurement of the integrated intensity of X-ray diffraction peaks and in the determination of the thickness of damaged epitaxial layers

The integrated intensity of X-ray diffraction reflections has been measured for a series of epitaxial layers of AIII nitrides (GaN, AlN, AlGaN) grown on different substrates (sapphire, SiC) and characterized by different degrees of structural perfection. It has been shown that, despite a high density of dislocations and a significant broadening of the diffraction peaks, the obtained values are not described by the kinematic theory of X-ray diffraction and suggest the existence of extinction. The results have been analyzed on the basis of the Darwin and Zachariasen extinction models. The secondary extinction coefficients and the thicknesses of epitaxial layers have been determined using two orders of reflection both in the Bragg geometry (0002 and 0004) and in the Laue geometry (\(10\bar 10\)) and \(10\bar 20\)). It has been demonstrated that the secondary extinction coefficient is the greater, the smaller is the broadening of the diffraction peaks and, consequently, the dislocation density. It has been found that, for epitaxial layers with a regular system of threading dislocations, the secondary extinction coefficient for the Laue reflections is substantially greater than that for the Bragg reflections.

The structural state of epitaxial ZnO layers assessed by measuring the integral intensity of three- and two-beam X-ray diffraction

Three-beam X-ray diffraction (XRD) has been measured using the Renninger scheme in epitaxial ZnO layers with various thicknesses and degrees of crystal perfection. The integral intensity of three-beam XRD reflections has been analyzed and compared to that of two-beam reflections in the Bragg and Laue geometry. It is established that, for thin ZnO layers grown in the presence of excess oxygen, the integral intensity of three-beam diffraction peaks and Laue reflections is much smaller than that for layers of the same thickness grown in the presence of excess zinc. This fact is explained by the formation of a textured sublayer in the former case.

Diffraction post-processing of 3D dislocation dynamics simulations for direct comparison with micro-beam Laue experiments

We present a method of computing lattice rotations and elastic strains due to 3D dislocation structures discretised into straight segments. Combined with ray-tracing, it enables virtual scattering experiments where X-ray diffraction patterns that would arise from such dislocation structures are simulated. We demonstrate the diffraction post-processing of a Frank–Read source simulated using the ParaDiS discrete dislocation dynamics code. This simulation is compared to experimental synchrotron X-ray micro-beam Laue diffraction measurements of a single grain within a deformed nickel polycrystal. The simulated pattern captures the experimentally observed anisotropic broadening of Laue reflections and illustrates that heterogeneous and anisotropic lattice (re)orientation effects dominate the peak shape.

Anisotropy of elastic strains and specific features of the defect structure of a-plane GaN epitaxial films grown on r-plane sapphire

The structural state of GaN epitaxial layers grown on r-plane sapphire through metal-organic vapor phase epitaxy has been investigated using X-ray diffraction. The interplanar spacings in two directions in the (11\( \bar 2 \)0) plane of the interface and in the direction perpendicular to it, as well as the diffraction peaks in the ϑ and ϑ-2ϑ scan modes in the Bragg and Laue geometries, are measured on double- and triple-crystal diffractometers. The intensity distribution maps for asymmetric Bragg reflections are constructed for two azimuthal positions of the sample. An analysis of the data obtained has demonstrated that the elastic strain is anisotropic and that the X-ray diffraction pattern parallel to the interface plane is broadened. The layers are contracted in the [1\( \bar 1 \)00] direction and unstrained in the [0001] direction. The broadening of the Bragg reflections in the [1\( \bar 1 \)00] direction is considerably larger than that in the [0001] direction. It is shown using the Williamson-Hall plots for the Bragg and Laue reflections that these broadenings are not related to different degrees of mosaicity but are determined by the local dilatations and misorientations around defects. The data obtained are analyzed, and the conclusions regarding the dislocation structure of the samples are drawn.

Defect structure in micropillars using x-ray microdiffraction

White beam x-ray microdiffraction is used to investigate the microstructure of micron-sized Si, Au, and Al pillars fabricated by focused ion beam (FIB) machining. Comparison with a Laue pattern obtained from a Si pillar made by reactive ion etching reveals that the FIB damages the Si structure. The Laue reflections obtained from the metallic pillars fabricated by FIB show continuous and discontinuous streakings, demonstrating the presence of strain gradients.

Electromigration-Induced Plastic Deformation in Cu Damascene Interconnect Lines as Revealed by Synchrotron X-Ray Microdiffraction

AbstractThe Scanning X-Ray Submicron Diffraction (μ-SXRD) technique using focused synchrotron radiation white beam developed in the Beamline 7.3.3 at the ALS Berkeley Lab has been used to study the microstructural evolution at granular level of Cu polycrystalline lines during electromigration. Plastic deformation was observed in damascene Cu interconnect test structures during this in situ electromigration experiment and before the onset of visible microstructural damage (voiding, hillock formation). We show here that the extent of this electromigration-induced plasticity is dependent on the line width. In wide lines, plastic deformation manifests itself as grain bending and the formation of subgrain structures, while only grain rotation is observed in the narrower lines. The analysis of the Laue reflections allow for the determination of the geometrically necessary dislocation density in individual grains as well as for the misorientation angles between small angle boundaries generated by polygonization. The deformation geometry leads us to conclude that dislocations introduced by plastic flow lie predominantly in the direction of electron flow and may provide additional easy paths for the transport of point defects. Furthermore, we observe that the rotation axis of this plastic deformation coincides with one of the <112> line directions of the known slip systems for FCC crystal, and that it is always very close (within a few degrees) to the direction of the electron flow. This finding suggests a correlation of the proximity of certain <112> line directions to the direction of electron flow with the occurrence of plastic behavior. One important practical implication of this particular finding is that the grain texture of the line might thus play an important role in giving higher resistance towards early plastic response of the Cu line upon the electromigration loading.

Gradients of geometrically necessary dislocations from white beam microdiffraction

Variations in the local crystallographic orientation due to the presence of geometrically necessary dislocations and dislocation boundaries smear the distribution of intensity near Laue reflections. Here, some simple model distributions of geometrically necessary dislocations, GNDs, are used to estimate the dislocation tensor field from the intensity distribution of Laue peaks. Streaking of the Laue spots is found to be quantitatively and qualitatively distinct depending on the ratio between the absorption coefficient and the GND density gradient. In addition, different slip systems cause distinctly different Laue-pattern streaking. Experimental Laue patterns are therefore sensitive to stored dislocations and GNDs. As an example, white beam microdiffraction was applied to characterize the dislocation arrangement in a deformed polycrystalline Ni grain during in situ uniaxial tension.

White X‐ray microbeam analysis of strain and crystallographic tilt in GaN layers grown by maskless pendeoepitaxy

AbstractWe describe X‐ray and finite element analysis of dislocations, strain and crystallographic tilt in uncoalesced GaN layers grown by maskless pendeoepitaxy. The experimental results reveal that the GaN wings are tilted upward at room temperature. The distribution of strain and tilt depends on the width‐to‐height ratio of the GaN column. As the width‐to‐height ratio increases the wing tilt increases and changes more abruptly at the column/wing interface. Broadening of the GaN Laue reflections is more pronounced in the column region then in the wing region; this is in line with the inhomogeneity of both the strain and the defect density. A split in the Laue reflections from GaN films at the column/wing interface indicates the development of a low‐angle tilt boundary for samples with a large width‐to‐height ratio of the column. Spacing between the dislocations in the tilt boundary at the column/wing interface for GaN grown with maskless pendeoepitaxy is an order of magnitude larger than the dislocation spacing observed for masked lateral epitaxial growth. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Deformation of AlGaN/GaN superlattice layers according to x-ray diffraction data

Three-crystal x-ray diffractometry is used for structural studies of nitride AlGaN/GaN superlattices (SLs) grown by metal-organic chemical vapor deposition on sapphire with GaN and AlGaN buffer layers with widely varied SL period (from 50 to 3500 A), Al content in Alx Ga1−x N layers (0.1≤x≤0.5), and buffer layer composition. Satellite peaks characteristic of SLs are well pronounced up to the third order in θ-2θ scans of symmetric Bragg reflections and θ scans of the symmetric Laue geometry. The corresponding curves are well modeled by kinematic formulas. The average SL parameters, as well as the thickness, composition, and strain of individual layers, are determined using a combination of symmetric Bragg and Laue reflections. It is shown that all the samples under study are partially relaxed structures in which the elastic stresses between the entire SL and the buffer layer, as well as between individual layers, are relaxed. The AlGaN layers are stretched and the GaN layers are compressed. The GaN layer compression is larger in magnitude than the AlGaN layer tension because of thermoelastic stresses.

Quantitative analysis of dislocation arrangements induced by electromigration in a passivated Al (0.5 wt % Cu) interconnect

Electromigration during accelerated testing can induce plastic deformation in apparently undamaged Al interconnect lines as recently revealed by white beam scanning x-ray microdiffraction. In the present article, we provide a first quantitative analysis of the dislocation structure generated in individual micron-sized Al grains during an in situ electromigration experiment. Laue reflections from individual interconnect grains show pronounced streaking during the early stages of electromigration. We demonstrate that the evolution of the dislocation structure during electromigration is highly inhomogeneous and results in the formation of unpaired randomly distributed dislocations as well as geometrically necessary dislocation boundaries. Approximately half of all unpaired dislocations are grouped within the walls. The misorientation created by each boundary and density of unpaired individual dislocations is determined. The origin of the observed plastic deformation is considered in view of the constraints for dislocation arrangements under the applied electric field during electromigration.

Spatially Resolved Characterization of Electromigration-Induced Plastic Deformation in al (0.5WT% CU) Interconnect

ABSTRACTElectromigration during accelerated testing can induce early stage plastic deformation in Al interconnect lines as recently revealed by the white beam scanning X-ray microdiffraction. In the present paper, we provide a first quantitative analysis of the dislocation structure generated in individual micron-sized Al grains during anin-situelectromigration experiment. Laue reflections from individual interconnect grains show pronounced streaking after electric current flow. We demonstrate that the evolution of the dislocation structure during electromigration is highly inhomogeneous and results in the formation of unpaired randomly distributed dislocations as well as geometrically necessary dislocation boundaries. Approximately half of all unpaired dislocations are grouped within the walls. The misorientation created by each boundary and density of unpaired individual dislocations is determined.

White microbeam diffraction from distorted crystals

We present a general description of white-beam (Laue) scattering from grains with dislocations. This approach is applied to examples with equal numbers of positive and negative Burger’s vectors (paired) and with unpaired dislocations of one sign (geometrically necessary). We find that streaking of the Laue reflections is sensitive to both long-range geometrical rotations introduced by unpaired edge dislocations and to local rotation fluctuations introduced by the total number of dislocations (paired and unpaired). We demonstrate the technique by analyzing the dislocation distribution in a nanoindented Cu single crystal.

X-ray double phase retarders to compensate for off-axis aberration.

An X-ray double phase retarder system composed of two transmission-type phase retarders is proposed and developed in order to compensate for off-axis aberration (phase-shift inhomogeneity due to angular divergence of incident X-rays). The scattering planes of the two phase retarders are set to be inclined by 45 degrees with respect to the plane of incident polarization, but the two phase retarders give Bragg reflections in opposite directions. By using this X-ray optical system, vertically polarized X-rays with a 0.99 degree of linear polarization were obtained from horizontally polarized synchrotron radiation with a horizontal beam divergence of 20 arcsec (0.1 mrad). This value is favorably compared with the value of 0.87 which was obtained using a conventional single phase retarder of identical total thickness, 627 microns. The comparison was made at the nickel K-absorption edge (8333 eV) with the condition that 47% of incident X-rays were transmitted through the two phase retarder crystals. The crystals were (100)-oriented diamond plates giving asymmetric 111 Laue reflections.

High-resolution synchrotron radiation Renninger scan to examine hybrid reflections in InGaP/GaAs(001)

High-resolution synchrotron radiation Renninger scans (RS) have been used in the analysis of hybrid reflections in the InGaP/GaAs structure. Four-beam cases involving two Bragg (primary and secondary) and one Laue (secondary) reflections of the 002 Renninger scans for the GaAs substrate and the InGaP layer were analysed in detail. Different structures of asymmetry regarding the in-plane directions [110] and [1{\bar 1}0] were observed from the measurements of the same three families of four-beam cases, {1{\bar 1}}{\bar 1}/{1{\bar 1}}3, {20}0/{20}2 and {3{\bar 1}}{\bar 1}/{3{\bar 1}}3, at several φ positions. The comparison between the experimental and MULTX simulated scan clearly shows a marked asymmetry observed on the {20}0/{20}2 contributions. An asymmetric peak instead of the simulated dip appears due to the layer Laue secondary beam {20}0 crossing the layer/substrate interface to generate a hybrid peak. The break in the lattice coherence for this heterostructure is shown by the occurrence of an unexpected dip in the layer RS, which does not obey the mirror symmetry.

X-Ray Microbeam Measurement of Local Texture and Strain in Metals

AbstractSynchrotron x-ray sources provide high-brilliance beams that can be focused to submicron sizes with Fresnel zone-plate and x-ray mirror optics. With these intense, tunable or broadbandpass x-ray microbeams, it is now possible to study texture and strain distributions in surfaces, and in buried or encapsulated thin films. The full strain tensor and local texture can be determined by measuring the unit cell parameters of strained material. With monochromatic or tunable radiation, at least three independent reflections are needed to determine the orientation and unit cell parameters of an unknown crystal. With broadbandpass or white radiation, at least four reflections and one measured energy are required to determine the orientation and the unit cell parameters of an unknown crystal. Routine measurement of local texture and strain is made possible by automatic indexing of the Laue reflections combined with precision calibration of the monochromator-focusing mirrors-CCD detector system. Methods used in implementing these techniques on the MHATT-CAT beam line at the Advanced Photon Source will be discussed.

Automated Indexing of Laue Images from Polycrystalline Materials

ABSTRACTThird generation hard x-ray synchrotron sources and new x-ray optics have revolutionized x-ray microbeams. Now intense sub-micron x-ray beams are routinely available for x-ray diffraction measurement. An important application of sub-micron xray beams is analyzing polycrystalline material by measuring the diffraction of individual grains. For these measurements, conventional analysis methods will not work. The most suitable method for microdiffraction on polycrystalline samples is taking broad-bandpass or white-beam Laue images. With this method, the crystal orientation and non-isostatic strain can be measured rapidly without rotation of sample or detector. The essential step is indexing the reflections from more than one grain. An algorithm has recently been developed to index broad bandpass Laue images from multi-grain samples. For a single grain, a unique set of indices is found by comparing measured angles between Laue reflections and angles between possible indices derived from the x-ray energy bandpass and the scattering angle 2 theta. This method has been extended to multigrain diffraction by successively indexing points not recognized in preceding indexing iterations. This automated indexing method can be used in a wide range of applications.