Implications of size dispersion on X-ray scattering of crystalline nanoparticles: CeO2 as a case study.

Controlling the shape and size dispersivity and crystallinity of nanoparticles (NPs) has been a challenge in identifying these parameters' role in the physical and chemical properties of NPs. The need for reliable quantitative tools for analyzing the dispersivity and crystallinity of NPs is a considerable problem in optimizing scalable synthesis routes capable of controlling NP properties. The most common tools are electron microscopy (EM) and X-ray scattering techniques. However, each technique has different susceptibility to these parameters, implying that more than one technique is necessary to characterize NP systems with maximum reliability. Wide-angle X-ray scattering (WAXS) is mandatory to access information on crystallinity. In contrast, EM or small-angle X-ray scattering (SAXS) is required to access information on whole NP sizes. EM provides average values on relatively small ensembles in contrast to the bulk values accessed by X-ray techniques. Besides the fact that the SAXS and WAXS techniques have different susceptibilities to size distributions, SAXS is easily affected by NP-NP interaction distances. Because of all the variables involved, there have yet to be proposed methodologies for cross-analyzing data from two techniques that can provide reliable quantitative results of dispersivity and crystallinity. In this work, a SAXS/WAXS-based methodology is proposed for simultaneously quantifying size distribution and degree of crystallinity of NPs. The most reliable easy-to-access size result for each technique is demonstrated by computer simulation. Strategies on how to compare these results and how to identify NP-NP interaction effects underneath the SAXS intensity curve are presented. Experimental results are shown for cubic-like CeO2 NPs. WAXS size results from two analytical procedures are compared, line-profile fitting of individual diffraction peaks in opposition to whole pattern fitting. The impact of shape dispersivity is also evaluated. Extension of the proposed methodology for cross-analyzing EM and WAXS data is possible.

Introduction to Python Dynamic Diffraction Toolkit (PyDDT): structural refinement of single crystals via X-ray phase measurements.

PyDDT is a free Python package of computer codes for exploiting X-ray dynamic multiple diffraction in single crystals. A wide range of tools are available for evaluating the usefulness of the method, planning feasible experiments, extracting phase information from experimental data and further improving model structures of known materials. Graphical tools are also useful in analytical methodologies related to the three-dimensional aspect of multiple diffraction. For general X-ray users, the PyDDT tutorials provide the insight needed to understand the principles of phase measurements and other related methodologies. Key points behind structure refinement using the current approach are presented, and the main features of PyDDT are illustrated for amino acid and filled skutterudite single crystals.

A simple formula for determining nanoparticle size distribution by combining small-angle X-ray scattering and diffraction results.

X-ray scattering and diffraction phenomena are widely used as analytical tools in nanoscience. Size discrepancies between the two phenomena are commonly observed in crystalline nanoparticle systems. The root of the problem is that each phenomenon is affected by size distribution differently, causing contrasting shifts between the two methods. Once understood, the previously discrepant results lead to a simple formula for obtaining the nanoparticle size distribution.

In-place bonded semiconductor membranes as compliant substrates for III-V compound devices.

Overcoming the critical thickness limit in pseudomorphic growth of lattice mismatched heterostructures is a fundamental challenge in heteroepitaxy. On-demand transfer of light-emitting structures to arbitrary host substrates is an important technological method for optoelectronic and photonic device implementation. The use of freestanding membranes as compliant substrates is a promising approach to address both issues. In this work, the feasibility of using released GaAs/InGaAs/GaAs membranes as virtual substrates to thin films of InGaAs alloys is investigated as a function of the indium content in the films. Growth of flat epitaxial films is demonstrated with critical thickness beyond typical values observed for growth on bulk substrates. Optically active structures are also grown on these membranes with a strong photoluminescence signal and a clear red shift for an InAlGaAs/InGaAs/InAlGaAs quantum well. The red shift is ascribed to strain reduction in the quantum well due to the use of a completely relaxed membrane as the substrate. Our results demonstrate that such membranes constitute a virtual substrate that allows further heterostructure strain engineering, which is not possible when using other post-growth methods.

X-ray dynamical diffraction in amino acid crystals: a step towards improving structural resolution of biological molecules via physical phase measurements.

In this work, experimental and data analysis procedures were developed and applied for studying amino acid crystals by means of X-ray phase measurements. The results clearly demonstrated the sensitivity of invariant triplet phases to electronic charge distribution in d-alanine crystals, providing useful information for molecular dynamics studies of intermolecular forces. The feasibility of using phase measurements to investigate radiation damage mechanisms is also discussed on experimental and theoretical grounds.

Absolute refinement of crystal structures by X-ray phase measurements.

A pair of enantiomer crystals is used to demonstrate how X-ray phase measurements provide reliable information for absolute identification and improvement of atomic model structures. Reliable phase measurements are possible thanks to the existence of intervals of phase values that are clearly distinguishable beyond instrumental effects. Because of the high susceptibility of phase values to structural details, accurate model structures were necessary for succeeding with this demonstration. It shows a route for exploiting physical phase measurements in the crystallography of more complex crystals.

Synchrotron X-ray imaging via ultra-small-angle scattering: principles of quantitative analysis and application in studying bone integration to synthetic grafting materials.

Optimized experimental conditions for extracting accurate information at subpixel length scales from analyzer-based X-ray imaging were obtained and applied to investigate bone regeneration by means of synthetic beta-TCP grafting materials in a rat calvaria model. The results showed a 30% growth in the particulate size due to bone ongrowth/ingrowth within the critical size defect over a 1-month healing period.

X-ray imaging in advanced studies of ophthalmic diseases.

Microscopic characterization of pathological tissues has one major intrinsic limitation, the small sampling areas with respect to the extension of the tissues. Mapping possible changes on vast tissues and correlating them with large ensembles of clinical cases is not a feasible procedure for studying most diseases, as for instance vision loss related diseases and, in particular, the cataract. Although intraocular lens implants are successful treatments, cataract still is a leading public-health issue that grows in importance as the population increases and life expectancy is extended worldwide. In this work we have exploited the radiation-tissue interaction properties of hard x-rays--very low absorption and scattering--to map distinct lesions on entire eye lenses. At the used synchrotron x-ray photon energy of 20 keV (wavelength lambda=0.062 nm), scattering and refraction are angular resolved effects. It allows the employed x-ray image technique to efficiently characterize two types of lesions in eye lenses under cataractogenesis: distributions of tiny scattering centers and extended areas of fiber cell compaction. The data collection procedure is relatively fast; allowing dozens of samples to be totally imaged (scattering, refraction, and mass absorption images) in a single day of synchrotron beam time. More than 60 cases of canine cataract, not correlated to specific causes, were investigated in this first application of x-rays to image entire lenses. Cortical opacity cases, or partial opacity, could be related to the presence of calcificated tissues at the cortical areas, clearly visible in the images, whose elemental contents were verified by micro x-ray fluorescence as very rich in calcium. Calcificated tissues were also observed at nuclear areas in some cases of hypermature cataract. Total opacity cases without distinguishable amount of scattering centers consist in 70% of the analyzed cases, where remarkable fissure marks owing to extended areas of fiber cell compaction are diagnosed.

Accurate triplet phase determination in non-perfect crystals--a general phasing procedure.

A completely different approach to the problem of physically measuring the invariant triplet phases by three-beam X-ray diffraction is proposed. Instead of simulating the three-beam diffraction process to reproduce the experimental intensity profiles, the proposed approach makes use of a general parametric equation for fitting the profiles and extracting the triplet phase values. The inherent flexibility of the parametric equation allows its applicability to be extended to non-perfect crystals. Exploitation of the natural linear polarization of synchrotron radiation is essential for eliminating systematic errors and to provide accurate triplet phase values. Phasing procedures are suggested and demonstrative examples from simulated data are given.

An X-ray diffractometer for accurate structural invariant phase determination.

Instrumental advances and experimental procedures for determining invariant triplet phases by three-beam X-ray diffraction are presented. A simple X-ray diffractometer is described. It allows the exploitation of the natural linear polarization of synchrotron radiation for eliminating systematic errors in triplet-phase determination. Examples of data-collection procedures with the diffractometer for composing a polarization-dependent set of azimuthal scans are given as well as the suggestion of an analytical procedure for extracting accurate triplet phases.

Enhanced x-ray phase determination by three-beam diffraction.

For decades, solving the phase problem of x-ray scattering has been a goal that, in principle, could be achieved by means of n-beam diffraction (n-BD). However, the phases extracted by the actual n-BD phasing techniques are not very precise, mainly due to systematic errors that are difficult to estimate. We present an innovative theoretical approach and experimental procedure that, combined, eliminate two major sources of error. It is a high precision phasing technique that provides the triplet-phase angle with an error of about 2 degrees.