Journal: Journal of applied crystallography
Monte Carlo (MC)-based refinement software to analyze the atomic arrangements of perovskite oxide ultrathin films from the crystal truncation rod intensity is developed on the basis of Bayesian inference. The advantages of the MC approach are (i) it is applicable to multi-domain structures, (ii) it provides the posterior probability of structures through Bayes' theorem, which allows one to evaluate the uncertainty of estimated structural parameters, and (iii) one can involve any information provided by other experiments and theories. The simulated annealing procedure efficiently searches for the optimum model owing to its stochastic updates, regardless of the initial values, without being trapped by local optima. The performance of the software is examined with a five-unit-cell-thick LaAlO3 film fabricated on top of SrTiO3. The software successfully found the global optima from an initial model prepared by a small grid search calculation. The standard deviations of the atomic positions derived from a dataset taken at a second-generation synchrotron are ±0.02 Å for metal sites and ±0.03 Å for oxygen sites.
A new synchrotron X-ray powder diffraction instrument has been built and commissioned for long-duration experiments on beamline I11 at Diamond Light Source. The concept is unique, with design features to house multiple experiments running in parallel, in particular with specific stages for sample environments to study slow kinetic systems or processes. The instrument benefits from a high-brightness X-ray beam and a large area detector. Diffraction data from the commissioning work have shown that the objectives and criteria are met. Supported by two case studies, the results from months of measurements have demonstrated the viability of this large-scale instrument, which is the world’s first dedicated facility for long-term studies (weeks to years) using synchrotron radiation.
Data correction is probably the least favourite activity amongst users experimenting with small-angle X-ray scattering: if it is not done sufficiently well, this may become evident only during the data analysis stage, necessitating the repetition of the data corrections from scratch. A recommended comprehensive sequence of elementary data correction steps is presented here to alleviate the difficulties associated with data correction, both in the laboratory and at the synchrotron. When applied in the proposed order to the raw signals, the resulting absolute scattering cross section will provide a high degree of accuracy for a very wide range of samples, with its values accompanied by uncertainty estimates. The method can be applied without modification to any pinhole-collimated instruments with photon-counting direct-detection area detectors.
Transmission X-ray diffraction imaging in both monochromatic and white beam section mode has been used to measure quantitatively the displacement and warpage stress in encapsulated silicon devices. The displacement dependence with position on the die was found to agree well with that predicted from a simple model of warpage stress. For uQFN microcontrollers, glued only at the corners, the measured misorientation contours are consistent with those predicted using finite element analysis. The absolute displacement, measured along a line through the die centre, was comparable to that reported independently by high-resolution X-ray diffraction and optical interferometry of similar samples. It is demonstrated that the precision is greater than the spread of values found in randomly selected batches of commercial devices, making the techniques viable for industrial inspection purposes.
The certification of a new standard reference material for small-angle scattering [NIST Standard Reference Material (SRM) 3600: Absolute Intensity Calibration Standard for Small-Angle X-ray Scattering (SAXS)], based on glassy carbon, is presented. Creation of this SRM relies on the intrinsic primary calibration capabilities of the ultra-small-angle X-ray scattering technique. This article describes how the intensity calibration has been achieved and validated in the certified Q range, Q = 0.008-0.25 Å(-1), together with the purpose, use and availability of the SRM. The intensity calibration afforded by this robust and stable SRM should be applicable universally to all SAXS instruments that employ a transmission measurement geometry, working with a wide range of X-ray energies or wavelengths. The validation of the SRM SAXS intensity calibration using small-angle neutron scattering (SANS) is discussed, together with the prospects for including SANS in a future renewal certification.
A new model is proposed for the measurement errors incurred in typical small-angle X-ray scattering (SAXS) experiments, which takes into account the setup geometry and physics of the measurement process. The model accurately captures the experimentally determined errors from a large range of synchrotron and in-house anode-based measurements. Its most general formulation gives for the variance of the buffer-subtracted SAXS intensity σ(2)(q) = [I(q) + const.]/(kq), where I(q) is the scattering intensity as a function of the momentum transfer q; k and const. are fitting parameters that are characteristic of the experimental setup. The model gives a concrete procedure for calculating realistic measurement errors for simulated SAXS profiles. In addition, the results provide guidelines for optimizing SAXS measurements, which are in line with established procedures for SAXS experiments, and enable a quantitative evaluation of measurement errors.
The humidity surrounding a sample is an important variable in scientific experiments. Biological samples in particular require not just a humid atmosphere but often a relative humidity (RH) that is in equilibrium with a stabilizing solution required to maintain the sample in the same state during measurements. The controlled dehydration of macromolecular crystals can lead to significant increases in crystal order, leading to higher diffraction quality. Devices that can accurately control the humidity surrounding crystals while monitoring diffraction have led to this technique being increasingly adopted, as the experiments become easier and more reproducible. Matching the RH to the mother liquor is the first step in allowing the stable mounting of a crystal. In previous work [Wheeler, Russi, Bowler & Bowler (2012). Acta Cryst. F68, 111-114], the equilibrium RHs were measured for a range of concentrations of the most commonly used precipitants in macromolecular crystallography and it was shown how these related to Raoult’s law for the equilibrium vapour pressure of water above a solution. However, a discrepancy between the measured values and those predicted by theory could not be explained. Here, a more precise humidity control device has been used to determine equilibrium RH points. The new results are in agreement with Raoult’s law. A simple argument in statistical mechanics is also presented, demonstrating that the equilibrium vapour pressure of a solvent is proportional to its mole fraction in an ideal solution: Raoult’s law. The same argument can be extended to the case where the solvent and solute molecules are of different sizes, as is the case with polymers. The results provide a framework for the correct maintenance of the RH surrounding a sample.
pyFAI is an open-source software package designed to perform azimuthal integration and, correspondingly, two-dimensional regrouping on area-detector frames for small- and wide-angle X-ray scattering experiments. It is written in Python (with binary submodules for improved performance), a language widely accepted and used by the scientific community today, which enables users to easily incorporate the pyFAI library into their processing pipeline. This article focuses on recent work, especially the ease of calibration, its accuracy and the execution speed for integration.
Planar defects in -oriented β-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.
The symmetry of the intermediate high-temperature phase of PbHfO3 has been determined unambiguously to be orthorhombic using a combination of high-resolution X-ray diffraction and birefringence imaging microscopy measurements of crystal plates. While lattice parameter measurements as a function of temperature in the intermediate phase are consistent with either orthorhombic or tetragonal symmetry, domain orientations observed in birefringence imaging microscopy measurements utilizing the Metripol system are only consistent with orthorhombic symmetry with the unit cell in the rhombic orientation of the pseudocubic unit cell.