Crystallographic analysis of the lattice metric (CALM) from single electron backscatter diffraction or transmission Kikuchi diffraction patterns

A new software is presented for the determination of crystal lattice parameters from the positions and widths of Kikuchi bands in a diffraction pattern. Starting with a single wide-angle Kikuchi pattern of arbitrary resolution and unknown phase, the traces of all visibly diffracting lattice planes are manually derived from four initial Kikuchi band traces via an intuitive graphical user interface. A single Kikuchi bandwidth is then used as reference to scale all reciprocal lattice point distances. Kikuchi band detection, via a filtered Funk transformation, and simultaneous display of the band intensity profile helps users to select band positions and widths. Bandwidths are calculated using the first derivative of the band profiles as excess-deficiency effects have minimal influence. From the reciprocal lattice, the metrics of possible Bravais lattice types are derived for all crystal systems. The measured lattice parameters achieve a precision of <1%, even for good quality Kikuchi diffraction patterns of 400 × 300 pixels. This band-edge detection approach has been validated on several hundred experimental diffraction patterns from phases of different symmetries and random orientations. It produces a systematic lattice parameter offset of up to ±4%, which appears to scale with the mean atomic number or the backscatter coefficient.

Beyond integration: modeling every pixel to obtain better structure factors from stills

Most crystallographic data processing methods use pixel integration. In serial femtosecond crystallography (SFX), the intricate interaction between the reciprocal lattice point and the Ewald sphere is integrated out by averaging symmetrically equivalent observations recorded across a large number (104−106) of exposures. Although sufficient for generating biological insights, this approach converges slowly, and using it to accurately measure anomalous differences has proved difficult. This report presents a novel approach for increasing the accuracy of structure factors obtained from SFX data. A physical model describing all observed pixels is defined to a degree of complexity such that it can decouple the various contributions to the pixel intensities. Model dependencies include lattice orientation, unit-cell dimensions, mosaic structure, incident photon spectra and structure factor amplitudes. Maximum likelihood estimation is used to optimize all model parameters. The application of prior knowledge that structure factor amplitudes are positive quantities is included in the form of a reparameterization. The method is tested using a synthesized SFX dataset of ytterbium(III) lysozyme, where each X-ray laser pulse energy is centered at 9034 eV. This energy is 100 eV above the Yb3+ L-III absorption edge, so the anomalous difference signal is stable at 10 electrons despite the inherent energy jitter of each femtosecond X-ray laser pulse. This work demonstrates that this approach allows the determination of anomalous structure factors with very high accuracy while requiring an order-of-magnitude fewer shots than conventional integration-based methods would require to achieve similar results.

X-ray investigation of strained epitaxial layer systems by reflections in skew geometry

Four different SiGe/Si layer structures, pseudomorphically grown and (partially) relaxed, are used as examples to demonstrate that reflections in symmetric skew geometry can successfully be used to realize a complex analysis of these systems. Taking the intensity exactly along the truncation rod of a reciprocal lattice point, it is possible to simulate this diffraction curve and determine the layer parameter in the projection according to the netplane tilt relative to the surface. The main precondition for this technique and for performing reciprocal space mapping with sufficiently high resolution is a low angular divergence of the incident and detected beams perpendicular to the diffraction plane, which can also be achieved by suitable optical elements on laboratory-based diffractometers.

Improved crystal orientation and physical properties from single-shot XFEL stills

X-ray diffraction patterns from still crystals are inherently difficult to process because the crystal orientation is not uniquely determined by measuring the Bragg spot positions. Only one of the three rotational degrees of freedom is directly coupled to spot positions; the other two rotations move Bragg spots in and out of the reflecting condition but do not change the direction of the diffracted rays. This hinders the ability to recover accurate structure factors from experiments that are dependent on single-shot exposures, such as femtosecond diffract-and-destroy protocols at X-ray free-electron lasers (XFELs). Here, additional methods are introduced to optimally model the diffraction. The best orientation is obtained by requiring, for the brightest observed spots, that each reciprocal-lattice point be placed into the exact reflecting condition implied by Bragg's law with a minimal rotation. This approach reduces the experimental uncertainties in noisy XFEL data, improving the crystallographicRfactors and sharpening anomalous differences that are near the level of the noise.

Structure of Magnetically Ordered Si:Mn

The structure studies of single crystalline silicon implanted at 340 K or 610 K with Mn+ ions (Si:Mn) and subsequently processed under atmospheric and enhanced hydrostatic pressure at up to 1270 K are reported. The defect structure was determined by an analysis of X-ray diffuse scattering around the 004 reciprocal lattice point and by electron microscopy. High resolution X-ray diffraction techniques based on the conventional source of radiation were used for this purpose. The crystal structure of Si:Mn and the Si1-xMnx precipitates in the implantation – disturbed layer were studied by synchrotron radiation diffraction in the grazing incidence geometry. Processing of Si:Mn results in crystallization of amorphous Si within the buried implantation – disturbed layer and in formation of Mn4Si7 precipitates. Structural changes are dependent both on temperature of the Si substrate at implantation and on processing parameters.

Determination by high-resolution X-ray diffraction of shape, size and lateral separation of buried empty channels in silicon-on-nothing architectures

High-resolution multi-crystal X-ray diffraction was employed to characterize silicon-on-nothing samples made by a one-dimensional periodic planar array of buried empty channels. When the channels are normal to the scattering plane, under the constraint of lattice continuity from the perfect substrate to the surface, this periodic array gives rise to a well defined Fraunhofer diffraction in a scan crossing a selected reciprocal lattice point and normal to the reciprocal lattice vector (transverse or ω scan). In a longitudinal scan (ω/2θ scan crossing the reciprocal lattice point and parallel to the reciprocal lattice vector) interference fringes are observed. By analysis of the ω scan and numerical fit of the ω/2θ scan, the period of the buried empty channels and their shape, size and lateral gap were easily determined, thanks to the high-resolution optics used for the measurements.

The φ Extent of the Reflection Range in the Oscillation Method According to the Mosaicity-Cap Model

New expressions for the φ extent of the reflection range in the oscillation method are derived by the combination of analytical geometry with the reciprocal-space and Ewald-sphere formalisms. The effect of crystal mosaicity is described by the extension of a reciprocal-lattice point into a cap. The effective cylindrical coordinates of the reciprocal-lattice point, corresponding to the cap points lying in the plane in which the cap has its maximum φ extent, are introduced. The effect of beam divergence and wavelength spread are accounted for by consideration of a nest of the Ewald spheres. The expressions for intersection of the mosaicity cap with the nest of the Ewald spheres are used to check whether a reflection is fully or partially registered during the crystal oscillations. The presented formulas have been incorporated into software for processing area-detector data.

On-line diffraction pattern analysis and phase identification using a JEM 2000FX AEM with a macintosh-based program

A number of computer programs have been written to aid in the indexing of transmission electron diffraction pattcrns. These programs are useful for determining crystallographic orientation and for phase identification and often simplify the analysis of complex patterns. Over the last few years there has been a trend toward automated electron microscopy. It is natural to extend this automation to real time diffraction pattern analysis and phase identification using A/D data acquisition boards and computer software to interface the modern AEM with an electron diffraction database (EDD). This paper describes a real-time Macintosh-based system (hardware and software) for automated electron diffraction pattern analysis and phase identification developed for the JEM 2000FX AEM. Crystallographic analysis with this system is attractive because of the rapid analysis time, ease of implementation, and it is inexpensive compared to buying a digitizing board and video system.Computer-aided diffraction pattern-indexing programs typically require the user to input reciprocal lattice point spacings (r-spacings) and the interplanar angle measurements for at least three non-colinear lattice points in the pattern. It is also necessary to know the crystal structure and lattice constants of the sample.