Inelastic neutron scattering and spectroscopy methods to characterize dynamics in colloidal and soft matter systems

Colloidal systems and soft materials are well suited to neutron scattering, and the community has readily adopted elastic scattering techniques to investigate their structure. Due to their unique properties, neutrons may also be used to characterize the dynamics of soft materials over a wide range of length and time scales in situ. Both static structures and an understanding of how molecules move about their equilibrium positions is essential if we are to deliver on the promise of rationally designing soft materials. In this review we introduce the basics of neutron spectroscopy and explore the ways in which inelastic neutron scattering can be used to study colloidal and soft materials. Illustrative examples are chosen that highlight the phenomena suitable for investigation using this suite of techniques.

The spectrum-averaged cross section investigation of 117Sn(n,n')117mSn and 67Zn(n,p)67Cu reactions

The spectrum averaged cross sections (SACS) in standard neutron field, e.g. 252Cf(s.f.), is a preferable tool for cross section evaluation and validation. A set of reaction measurements with high energy thresholds was previously performed. The presented work focuses on lower energy threshold reactions, namely on the inelastic scattering of the tin foil, more specifically the reaction 117Sn(n,n')117mSn, and the zinc foil reaction, namely 67Zn(n,p)67Cu. These reactions are of special interest due to their intermediate energy range, which is essential in classical reactor dosimetry and fast reactor dosimetry. The experiments were carried out in a standard neutron field formed by 252Cf(s.f.) source in Řež. The experimental results were compared with calculations using MCNP6.2, ENDF/B-VII.1 transport library, and ENDF/B-VIII.0 and IRDFF-II cross section data library. Additionally, the calculations using CEA code DARWIN/PEPIN2 using JEFF-3.0/A were executed. The obtained experimental SACS of previously measured reactions were in good agreement with the SACS calculated using the IRDFF-II library. Additionally, the calculational reaction rate of 67Zn(n,p)67Cu was in accordance with the experimental data in case of ENDF/B-VIII.0 nuclear data library. Moreover, the calculational results of 117Sn(n,n')117mSn obtained by DARWIN/PEPIN2 code (using JEFF-3.0/A nuclear data library) are closest to the experimental results.

A rigid bender study of the bending relaxation H2O and D2O by collisions with Ar

The bending relaxation of H2O and D2O by collisions with Ar is studied at the Close Coupling level. Two new 4D PES are developed for these two systems. They are tested by performing rigid rotor calculations as well as computing the D2O-Ar  bound states. The results are compared with available theoretical and experimental data. Propensity rules for the dynamics are discussed and compared to those of H2O colliding with  Ne or He. The bending relaxation cross sections and rates are then calculated for these two systems. The results are analysed and compared with available experimental data.

Direct measurement of the PSF for Coulomb delocalization - a reconsideration

An interpretation of Coulomb delocalization, which limits the spatial resolution of inelastic TEM or STEM images, is given. We conclude that the corresponding point spread function cannot be measured as a broadening of a STEM probe.

Angle-resolved STEM using an iris aperture: Scattering contributions and sources of error for the quantitative analysis in Si

The angle-resolved electron scattering is investigated in scanning-transmission electron microscopy (STEM) using a motorised iris aperture placed above a conventional annular detector. The electron intensity scattered into various angle ranges is compared with simulations that were carried out in the frozen-lattice approximation. As figure of merit for the agreement of experiment and simulation we evaluate the specimen thickness which is compared with the thickness obtained from position-averaged convergent beam electron diffraction (PACBED). We find deviations whose strengths depend on the angular range of the detected electrons. As possible sources of error we investigate, for example, the influences of amorphous surface layers, inelastic scattering (plasmon excitation), phonon-correlation within the frozen-lattice approach, and distortions in the diffraction plane of the microscope. The evaluation is performed for four experimental thicknesses and two angle-resolved STEM series under different camera lengths. The results clearly show that especially for scattering angles below 50 mrad, it is mandatory that the simulations take scattering effects into account which are usually neglected for simulating high-angle scattering. Most influences predominantly affect the low-angle range, but also high scattering angles can be affected (e.g. by amorphous surface covering).

Conventional vs. model-based measurement of patterned line widths from scanning electron microscopy profiles

Scanning electron microscopy (SEM) is a practical tool to determine the dimensions of nanometer-scale features. Conventional width measurements use arbitrary criteria, e.g., a 50 % threshold crossing, to assign feature boundaries in the measured SEM intensity profile. To estimate the errors associated with such a procedure, we have simulated secondary electron signals from a suite of line shapes consisting of 30 nm tall silicon lines with varying width, sidewall angle, and corner rounding. Four different inelastic scattering models were employed in Monte Carlo simulations of electron transport to compute secondary electron image intensity profiles for each of the shapes. The 4 models were combinations of dielectric function theory with either the single-pole approximation (SPA) or the full Penn algorithm (FPA), and either with or without Auger electron emission. Feature widths were determined either by the conventional threshold method or by the model-based library (MBL) method, which is a fit of the simulated profiles to the reference model (FPA + Auger). On the basis of these comparisons we estimate the error in the measured width of such features by the conventional procedure to be as much as several nanometers. A 1 nm difference in the size of, e.g., a nominally 10 nm transistor gate would substantially alter its electronic properties. Thus, the conventional measurements do not meet the contemporary requirements of the semiconductor industry. In contrast, MBL measurements employing models with varying accuracy differed one from another by less than 1 nm. Thus, a MBL measurement is preferable in the nanoscale domain.

Routine determination of ice thickness for cryo-EM grids

Recent advances in instrumentation and automation have made cryo-EM a popular method for producing near-atomic resolution structures of a variety of proteins and complexes. Sample preparation is still a limiting factor in collecting high quality data. Thickness of the vitreous ice in which the particles are embedded is one of the many variables that need to be optimized for collection of the highest quality data. Here we present two methods, using either an energy filter or scattering outside the objective aperture, to measure ice thickness for potentially every image collected. Unlike geometrical or tomographic methods, these can be implemented directly in the single particle collection workflow without interrupting or significantly slowing down data collection. We describe the methods as implemented into the Leginon/Appion data collection workflow, along with some examples from test cases. Routine monitoring of ice thickness should prove helpful for optimizing sample preparation, data collection, and data processing.

Significance of matrix diagonalization in modelling inelastic electron scattering

Electron scattering is always applied as one of the routines to investigate nanostructures. Nowadays the development of hardware offers more and more prospect for this technique. For example imaging nanostructures with inelastic scattered electrons may allow to produce component-sensitive images with atomic resolution. Modelling inelastic electron scattering is therefore essential for interpreting these images. The main obstacle to study inelastic scattering problem is its complexity. During inelastic scattering, incident electrons entangle with objects, and the description of this process involves a multidimensional array. Since the simulation usually involves fourdimensional Fourier transforms, the computation is highly inefficient. In this work we have offered one solution to handle the multidimensional problem. By transforming a high dimensional array into twodimensional array, we are able to perform matrix diagonalization and approximate the original multidimensional array with its twodimensional eigenvectors. Our procedure reduces the complicated multidimensional problem to a twodimensional problem. In addition, it minimizes the number of twodimensional problems. This method is very useful for studying multiple inelastic scattering.

Simultaneous determination of sample thickness, tilt, and electron mean free path using tomographic tilt images based on Beer-Lambert law

Cryo-electron tomography (cryo-ET) is an emerging technique that can elucidate the architecture of macromolecular complexes and cellular ultrastructure in a near-native state. Some important sample parameters, such as thickness and tilt, are needed for 3-D reconstruction. However, these parameters can currently only be determined using trial 3-D reconstructions. Accurate electron mean free path plays a significant role in modeling image formation process essential for simulation of electron microscopy images and model-based iterative 3-D reconstruction methods; however, their values are voltage and sample dependent and have only been experimentally measured for a limited number of sample conditions. Here, we report a computational method, tomoThickness, based on the Beer-Lambert law, to simultaneously determine the sample thickness, tilt and electron inelastic mean free path by solving an overdetermined nonlinear least square optimization problem utilizing the strong constraints of tilt relationships. The method has been extensively tested with both stained and cryo datasets. The fitted electron mean free paths are consistent with reported experimental measurements. The accurate thickness estimation eliminates the need for a generous assignment of Z-dimension size of the tomogram. Interestingly, we have also found that nearly all samples are a few degrees tilted relative to the electron beam. Compensation of the intrinsic sample tilt can result in horizontal structure and reduced Z-dimension of tomograms. Our fast, pre-reconstruction method can thus provide important sample parameters that can help improve performance of tomographic reconstruction of a wide range of samples.

A fast cross-validation method for alignment of electron tomography images based on Beer-Lambert law

In electron tomography, accurate alignment of tilt series is an essential step in attaining high-resolution 3D reconstructions. Nevertheless, quantitative assessment of alignment quality has remained a challenging issue, even though many alignment methods have been reported. Here, we report a fast and accurate method, tomoAlignEval, based on the Beer-Lambert law, for the evaluation of alignment quality. Our method is able to globally estimate the alignment accuracy by measuring the goodness of log-linear relationship of the beam intensity attenuations at different tilt angles. Extensive tests with experimental data demonstrated its robust performance with stained and cryo samples. Our method is not only significantly faster but also more sensitive than measurements of tomogram resolution using Fourier shell correlation method (FSCe/o). From these tests, we also conclude that while current alignment methods are sufficiently accurate for stained samples, inaccurate alignments remain a major limitation for high resolution cryo-electron tomography.

Analysis of velocity-mapped ion images from high-resolution crossed-beam scattering experiments: a tutorial review

A Stark decelerator produces beams of molecules with high quantum state purity, and small spatial, temporal and velocity spreads. These tamed molecular beams are ideally suited for high-resolution crossed beam scattering experiments. When velocity map imaging is used, the Stark decelerator allows the measurement of scattering images with unprecedented radial sharpness and angular resolution. Differential cross sections must be extracted from these high-resolution images with extreme care, however. Common image analysis techniques that are used throughout in crossed beam experiments can result in systematic errors, in particular in the determination of collision energy, and the allocation of scattering angles to observed peaks in the angular scattering distribution. Using a high-resolution data set on inelastic collisions of velocity-controlled NO radicals with Ne atoms, we describe the challenges met by the high resolution, and present methods to mitigate or overcome them. PACS Codes: 34.50.-s; 37.10.Mn.

The role of symmetry in the theory of inelastic high-energy electron scattering and its application to atomic-resolution core-loss imaging

The inelastic scattering of a high-energy electron in a solid constitutes a bipartite quantum system with an intrinsically large number of excitations, posing a considerable challenge for theorists. It is demonstrated how and why the utilization of symmetries, or approximate symmetries, can lead to significant improvements in both the description of the scattering physics and the efficiency of numerical computations. These ideas are explored thoroughly for the case of core-loss excitations, where it is shown that the coupled angular momentum basis leads to dramatic improvements over the bases employed in previous work. The resulting gains in efficiency are demonstrated explicitly for K-, L- and M-shell excitations, including such excitations in the context of atomic-resolution imaging in the scanning transmission electron microscope. The utilization of other symmetries is also discussed.

Calculation of inelastic scattering processes of relativistic electrons in oriented crystals

The inelastic scattering of electrons in oriented crystals has been used to determine the positions of atoms within a crystal, to obtain site-dependent electron energy loss spectra and, more recently, to obtain an energy loss signal corresponding to the circular dichroism in X-ray absorption spectroscopy. The theoretical approaches currently used for the description of these processes are based on the nonrelativistic Schrödinger equation. Nowadays many experiments, however, are conducted with incident energies of 200 or 300 keV. Therefore it is indispensable to use a relativistic description for such processes based on the Dirac equation. Using the Coulomb gauge it is shown, that the fully relativistic cross sections for plane wave scattering are given by the modulus square of a sum of two terms: one describing the electrostatic interactions similar to the nonrelativistic theory plus one additional term describing the interaction of the specimen with the magnetic field produced by the incident electron. In crystals both terms can interfere leading to large deviations from nonrelativistic theory.

Is magnetic chiral dichroism feasible with electron vortices?

We discuss the feasibility of detecting magnetic transitions with focused electron vortex probes, suggested by selection rules for the magnetic quantum number. We theoretically estimate the dichroic signal strength in the L₂,₃ edge of ferromagnetic d metals. It is shown that under realistic conditions, the dichroic signal is undetectable for nanoparticles larger than ∼1 nm. This is confirmed by a key experiment with nanometer-sized vortices.