Analysis of oscillatory rocking curve by dynamical diffraction in protein crystals.

High-quality protein crystals meant for structural analysis by X-ray diffraction have been grown by various methods. The observation of dynamical diffraction in protein crystals is an interesting topic because dynamical diffraction generally occurs in perfect crystals such as Si crystals. However, to our knowledge, there is no report yet on protein crystals showing clear dynamical diffraction. We wonder whether the perfection of protein crystals might still be low compared with that of high-quality Si crystals. Here, we present observations of the oscillatory profile of rocking curves for protein crystals such as glucose isomerase crystals. The oscillatory profiles are in good agreement with those predicted by the dynamical theory of diffraction. We demonstrate that dynamical diffraction occurs even in protein crystals. This suggests the possibility of the use of dynamical diffraction for the determination of the structure and charge density of proteins.

Geometric determination of direction of dislocations using synchrotron X-ray transmission topography.

When performing transmission polychromatic beam topography, the extensions to the line segments of the diffraction images of a straight dislocation are shown to intersect at a single point on the X-ray film. The location of this point, together with the diffraction pattern recorded on the film by synchrotron radiation, gives the crystallographic direction [hkl] of the dislocation unambiguously. The results of two synchrotron topography experiments are presented. Very long dislocations found in the center of a large 450 mm-diameter Czochralski silicon crystal align with the growth direction [001]. In the other silicon sample, the dislocations are of mixed type and along the [011] direction.

Application of laboratory micro X-ray fluorescence devices for X-ray topography.

It is demonstrated that high-resolution energy-dispersive X-ray fluorescence mapping devices based on a micro-focused beam are not restricted to high-speed analyses of element distributions or to the detection of different grains, twins and subgrains in crystalline materials but can also be used for the detection of dislocations in high-quality single crystals. Si single crystals with low dislocation densities were selected as model materials to visualize the position of dis-locations by the spatially resolved measurement of Bragg-peak intensity fluctuations. These originate from the most distorted planes caused by the stress fields of dislocations. The results obtained by this approach are compared with laboratory-based Lang X-ray topographs. The presented methodology yields comparable results and it is of particular interest in the field of crystal growth, where fast chemical and microstructural characterization feedback loops are indispensable for short and efficient development times. The beam divergence was reduced via an aperture management system to facilitate the visualization of dislocations for virtually as-grown, non-polished and non-planar samples with a very pronounced surface profile.

André Authier (1932-2023).

Obituary for André Authier.

Dislocation arrangements in 4H-SiC and their influence on the local crystal lattice properties.

Two wafers of one 4H-silicon carbide (4H-SiC) bulk crystal, one cut from a longitudinal position close to the crystal's seed and the other close to the cap, were characterized with synchrotron white-beam X-ray topography (SWXRT) in back-reflection and transmission geometry to investigate the dislocation formation and propagation during growth. For the first time, full wafer mappings were recorded in 00012 back-reflection geometry with a CCD camera system, providing an overview of the dislocation arrangement in terms of dislocation type, density and homogeneous distribution. Furthermore, by having similar resolution to conventional SWXRT photographic film, the method enables identification of individual dislocations, even single threading screw dislocations, which appear as white spots with a diameter in the range of 10 to 30 µm. Both investigated wafers showed a similar dislocation arrangement, suggesting a constant propagation of dislocations during crystal growth. A systematic investigation of crystal lattice strain and tilt at selected wafer areas with different dislocation arrangements was achieved with high-resolution X-ray diffractometry reciprocal-space map (RSM) measurements in the symmetric 0004 reflection. It was shown that the diffracted intensity distribution of the RSM for different dislocation arrangements depends on the locally predominant dislocation type and density. Moreover, the orientation of specific dislocation types along the RSM scanning direction has a strong influence on the local crystal lattice properties.

A finite difference scheme for integrating the Takagi-Taupin equations on an arbitrary orthogonal grid.

Calculating dynamical diffraction patterns for X-ray diffraction imaging techniques requires numerical integration of the Takagi-Taupin equations. This is usually performed with a simple, second-order finite difference scheme on a sheared computational grid in which two of the axes are aligned with the wavevectors of the incident and scattered beams. This dictates, especially at low scattering angles, an oblique grid of uneven step sizes. Here a finite difference scheme is presented that carries out this integration in slab-shaped samples on an arbitrary orthogonal grid by implicitly utilizing Fourier interpolation. The scheme achieves the expected second-order convergence and a similar error to the traditional approach for similarly dense grids.

Radiation-induced defects in protein crystals observed by X-ray topography.

The characterization of crystal defects induced by irradiation, such as X-rays, charged particles and neutrons, is important for understanding radiation damage and the associated generation of defects. Radiation damage to protein crystals has been measured using various methods. Until now, these methods have focused on decreased diffraction intensity, volume expansion of unit cells and specific damage to side chains. Here, the direct observation of specific crystal defects, such as dislocations, induced by X-ray irradiation of protein crystals at room temperature is reported. Dislocations are induced even by low absorbed doses of X-ray irradiation. This study revealed that for the same total absorbed dose, the formation of defects appears to critically depend on the dose rate. The relationship between dislocation energy and dose energy was analyzed based on dislocation theory associated with elasticity theory for crystalline materials. This demonstration of the crystal defects induced by X-ray irradiation could help to understand the underlying mechanisms of X-ray-induced radiation damage.

Fundamental Studies on Crystallization and Reaching the Equilibrium Shape in Basic Ammonothermal Method: Growth on a Native Lenticular Seed.

In this paper, a detailed investigation of the basic ammonothermal growth process of GaN is presented. By analyzing the crystallization on a native seed with a lenticular shape, thus with an intentionally varying off-cut, we wanted to answer some basic questions: (i) Which crystallographic planes play the most important role during growth (which planes are formed and which disappear)? (ii) What is the relationship between the growth rates in different crystallographic directions? (iii) What is the influence of the off-cut of the seed on the growth process? Two non-polar slices, namely, 12¯10 and 1¯100, as well as a 0001 basal plane slice of an ammonothermal crystal were analyzed. The examined planes were selectively etched in order to reveal the characteristic features of the growth process. The applied characterization methods included: optical microscopy with Nomarski contrast and ultraviolet illumination, X-ray topography and high-resolution X-ray diffraction, and secondary ion mass spectrometry. The obtained results allowed for creating a growth model of an ammonothermal GaN crystal on a lenticular seed. These findings are of great importance for the general understanding of the basic ammonothermal crystal growth process of GaN.

Structural Analysis of Low Defect Ammonothermally Grown GaN Wafers by Borrmann Effect X-ray Topography.

X-ray topography defect analysis of entire 1.8-inch GaN substrates, using the Borrmann effect, is presented in this paper. The GaN wafers were grown by the ammonothermal method. Borrmann effect topography of anomalous transmission could be applied due to the low defect density of the substrates. It was possible to trace the process and growth history of the GaN crystals in detail from their defect pattern imaged. Microscopic defects such as threading dislocations, but also macroscopic defects, for example dislocation clusters due to preparation insufficiency, traces of facet formation, growth bands, dislocation walls and dislocation bundles, were detected. Influences of seed crystal preparation and process parameters of crystal growth on the formation of the defects are discussed.

The Influence of the Cooling Bores on Crystal Orientation and Lattice Parameter in Single-Crystalline Cored Turbine Blades.

The areas located near the cooling bores of single-crystalline cored turbine blades made of nickel-based CMSX-4 superalloy were studied. The blades were solidified by the vertical Bridgman technique in the industrial ALD furnace. Longitudinal sections of the blades were studied by Scanning Electron Microscopy, X-ray diffraction topography, X-ray diffraction measurements of the γ'-phase lattice parameter a, and the α angle of the primary crystal orientation. The local changes in α were analyzed in relation to the changes of the dendrite's growth direction near the cooling bores. It was found that in the area approximately 3 ÷ 4 mm wide around the cooling bores, changes of α and a, both in the blade root and in the airfoil occurred. The local temperature distribution near the cooling bores formed a curved macroscopic solidification front, which caused changes in the chemical composition and, consequently, changes in the a value in a range of 0.002 Å to 0.014 Å. The mechanism of alloying elements segregation by tips of the dendrites on the bent solidification front was proposed. The multi-scale analysis that allows determining a relation between processes proceed both on a millimeter-scale and a micrometric and nanometric scale, was applied in the studies.

Heterogeneity of the Dendrite Array Created in the Root of Cored SX Turbine Blades during Initial Stage of Crystallization.

The roots of cored single-crystalline turbine blades made of a nickel-based CMSX-4 superalloy were studied. The casts were solidified by the vertical Bridgman method in an industrial ALD furnace using the spiral selector and selector continuer situated asymmetrically in the blade root transverse section. Scanning electron microscopy, the Laue diffraction and X-ray diffraction topography were used to visualize the dendrite array and the local crystal misorientation of the roots. It has been stated that heterogeneity of the dendrite array and creation of low-angle boundaries (LABs) are mostly related to the lateral dendrite branching and rapid growth of the secondary and tertiary dendrites near the surface of the continuer-root connection. These processes have an unsteady character. Additionally, the influence of the mould walls on the dendrite array heterogeneity was studied. The processes of the lateral growth of the secondary dendrites and competitive longitudinal growth of the tertiary dendrites are discussed and a method of reducing the heterogeneity of the root dendrite array is proposed.

X-ray characterization of physical-vapor-transport-grown bulk AlN single crystals.

AlN slices from bulk crystals grown under low thermomechanical stress conditions via the physical vapor transport (PVT) method were analyzed by X-ray methods to study the influence of the growth mode on the crystal quality. Defect types and densities were analyzed along axial [0001] as well as lateral growth directions. X-ray diffraction (0110) rocking-curve mappings of representative wafer cuts reveal a low mean FWHM of 13.4 arcsec, indicating the generally high crystal quality. The total dislocation density of 2 × 103 cm-2 as determined by X-ray topography is low and dislocations are largely threading edge dislocations of b = 1/3〈1120〉 type. The absence of basal plane dislocations in homogeneous crystal regions void of macroscopic defects can be linked to the low-stress growth conditions. Under the investigated growth conditions this high crystal quality can be maintained both along the axial [0001] direction and within lateral growth directions. Exceptions to this are some locally confined, misoriented grains and defect clusters, most of which are directly inherited from the seed or are formed due to the employed seed fixation technique on the outer periphery of the crystals. Seed-shaping experiments indicate no apparent kinetic limitations for an enhanced lateral expansion rate and the resulting crystal quality, specifically with regard to the growth mode on a-face facets.

The Number of Subgrain Boundaries in the Airfoils of Heat-Treated Single-Crystalline Turbine Blades.

In the present study, the dendrites deflection mechanism from the mold walls were subjected to verification regarding its heat-treated turbine rotor blades. The number of macroscopic low-angle boundaries created on the cross-section of the blades' airfoil near the tip was experimentally determined and compared to the number of low-angle boundaries calculated from a model based on the dendrites deflection mechanism. Based on the Laue patterns and geometrical parameters of airfoils, the number of low-angle boundaries occurring at the upper part of the blades airfoil after heat treatment was calculated. This number for the analyzed group of blades ranged from 5 to 9.

Evaluation of crystal quality of thin protein crystals based on the dynamical theory of X-ray diffraction.

Knowledge of X-ray diffraction in macromolecular crystals is important for not only structural analysis of proteins but also diffraction physics. Dynamical diffraction provides evidence of perfect crystals. Until now, clear dynamical diffraction in protein crystals has only been observed in glucose isomerase crystals. We wondered whether there were other protein crystals with high quality that exhibit dynamical diffraction. Here we report the observation of dynamical diffraction in thin ferritin crystals by rocking-curve measurement and imaging techniques such as X-ray topography. It is generally known that in the case of thin crystals it is difficult to distinguish whether dynamical diffraction occurs from only rocking-curve profiles. Therefore, our results clarified that dynamical diffraction occurs in thin protein crystals because fringe contrasts similar to Pendellösung fringes were clearly observed in the X-ray topographic images. For macromolecular crystallography, it is hard to obtain large crystals because they are difficult to crystallize. For thin crystals, dynamical diffraction can be demonstrated by analysis of the equal-thickness fringes observed by X-ray topography.

Effects of surface undulations on asymmetric X-ray diffraction: a rocking-curve topography study.

The results are reported of an X-ray diffraction study of an Si crystal designed and fabricated for very asymmetric diffraction from the 333 reflection for X-ray energies of 8.100 and 8.200 keV. A crystal with an asymmetry angle of 46 ±â€…0.1° between the surface and the (111) planes was studied. The grazing angles of incidence were near 1.08 and 0.33° for these two energies, respectively. Features arising from surface undulations were not observed at 8.100 keV, but were observed at 8.200 keV. The results at 8.100 keV allow an alternative explanation based on strain near the surface to be ruled out. Topographic images were obtained as a function of rocking angle, and in the case of 8.200 keV the surface morphology is evident. The results are found to be in agreement with dynamical X-ray diffraction calculations made with the Takagi-Taupin equations specialized to a surface having convex or concave features, as reported in the accompanying paper [Macrander (2020). J. Appl. Cryst. 53, 793-799].

Dynamical X-ray diffraction imaging of voids in dislocation-free high-purity germanium single crystals.

White-beam X-ray topography has been performed to provide direct evidence of micro-voids in dislocation-free high-purity germanium single crystals. The voids are visible because of a dynamical diffraction contrast. It is shown that voids occur only in dislocation-free parts of the crystal and do not show up in regions with homogeneous and moderate dislocation density. It is further suggested that the voids originate from clustering of vacancies during the growth process. A general method is proposed to verify the presence of voids for any crystalline material of high structural perfection.

The Interface and Mechanical Properties of a CVD Single Crystal Diamond Produced by Multilayered Nitrogen Doping Epitaxial Growth.

In the present investigation, a nitrogen-doped multilayer homoepitaxial single crystal diamond is synthesized on a high-pressure high temperature (HPHT) Ib-type diamond substrate using the microwave plasma chemical vapor deposition (MPCVD) method. When 0.15 sccm of nitrogen was added in the gas phase, the growth rate of the doped layer was about 1.7 times that of the buffer layer, and large conical and pyramidal features are formed on the surface of the sample. Raman mapping and photoluminescence imaging of the polished cross sectional slice shows a broadband emission, with a characteristic zero phonon line (ZPL) at 575 nm in the doped layers, and large compressive stress was formed in the nitrogen-doped layers. X-ray topography shows that the defects at the interface can induce dislocation. The pyramid feature is formed at the defect, and more nitrogen-related defects are formed in the pyramid region. Thin nitrogen-doped multilayers were successfully prepared, and the thickness of the nitrogen-doped and buffer layers was about 650 nm each. The indentation measurements reveal that the thin nitrogen-doped multilayers are ultra-tough (at least ~22 MPa m1/2), compared to the Ib-type HPHT seed substrate (~8 MPa m1/2) and the unintentionally doped chemical vapor deposition (CVD) single crystal diamond (~14 MPa m1/2).

Variation of Crystal Orientation and Dendrite Array Generated in the Root of SX Turbine Blades.

The variation of the crystal orientation and the dendrite array generated in the root of the single-crystalline (SX) turbine blades made of CMSX-4 superalloy were studied. The blades with an axial orientation of the [001] type were solidified by the industrial Bridgman technique using a spiral selector at a withdrawal rate of 3 mm/min. The analysis of the crystal orientation and dendrite arrangement was carried out using scanning electron microscopy, X-ray diffraction topography, and Laue diffraction. It was found that the lateral growth of such secondary dendrite arms, which are defined as "leading" and grow in the root at first, is related to the rotation of their crystal lattice, which is the reason for creation of the low-angle boundary (LAB) type defects. The primary crystal orientation of the selector extension (SE) area determines the areas and directions of the lateral growth of the leading arms. Additionally, it was found that in the SE areas of the root, near the connection with the selector, the spatial distribution of the [001]γ' crystallographic direction has a complex wave-like character and may be related to the shape of the crystallization front.

Defect Creation in the Root of Single-Crystalline Turbine Blades Made of Ni-Based Superalloy.

An analysis of the defects in the vicinity of the selector⁻root connection plane occurring during the creation of single-crystalline turbine blades made of CMSX-6 Ni-based superalloy was performed. X-ray diffraction topography, scanning electron microscopy, and positron annihilation lifetime spectroscopy were used. Comparing the area of undisturbed axial growth of dendrites to the area of lateral growth concluded that the low-angle boundaries-like (LAB-like) defects were created in the root as a result of unsteady-state lateral growth of some secondary dendrite arms in layers of the root located directly at the selector⁻root connection plane. Additional macroscopic low-angle boundaries (LABs) with higher misorientation angles were created as a result of concave curvatures of liquidus isotherm in platform-like regions near selector⁻root connections. Two kinds of vacancy-type defects, mono-vacancies and vacancy clusters, were determined in relation to the LABs and LAB-like defects. Only mono-vacancies appeared in the areas of undisturbed axial growth. Reasons for the creation of macroscopic LABs and LAB-like defects, and their relationships with vacancy-type defects were discussed.

Stacking faults in ß-Ga2O3 crystals observed by X-ray topography.

Planar defects in -oriented ß-Ga2O3 wafers were studied using X-ray topography. These planar defects were rectangular with dimensions of 50-150 µm, and the X-ray topography analysis revealed that they were stacking faults (SFs) enclosed by a single partial dislocation loop on the plane. The SF formation was found to be supported by a unique structural feature of the plane as a slip plane; the plane consists of close-packed octahedral Ga and O layers, allowing slips to form SFs. Vacancy arrays along the b axis in the octahedral Ga layer reduce the self-energy of the edge component in the partial dislocation extending along the b axis. It is speculated that the SFs occur during the crystal growth process for unknown reasons and then recover owing to elastic instability after initially increasing in size as crystal growth proceeds. Based on this analysis, a structural model for the SFs is proposed.