It is observed that the factorization approximation of the scattering intensity holds even for small vesicle radii (∼30 nm). However, the simulations show that, for very small vesicles, a curvature-induced asymmetry arises in the EDP, with sizeable effects on the SAXS curve. It is also demonstrated that thermal fluctuations in shape and the size polydispersity have distinguishable signatures in the SAXS intensity. Polydispersity gives rise to low-q features, whereas thermal fluctuations predominantly affect the scattering at larger q, related to membrane bending rigidity. Finally, it is shown that simulation of fluctuating vesicle ensembles can be used for analysis of experimental SAXS curves.Improper ferroelectric mechanisms are increasingly under investigation for their potential to expand the current catalogue of functional materials whilst promoting couplings between ferroelectricity and other technologically desirable properties such as ferromagnetism. This work presents the results of an in situ synchrotron X-ray diffraction experiment performed on samples of Ca2.15Sr0.85Ti2O7 in an effort to elucidate the mechanism of hybrid improper ferroelectric switching in this compound. By simultaneously applying an electric field and recording diffraction patterns, shifts in the intensity of superstructure peaks consistent with one of the switching mechanisms proposed by Nowadnick & Fennie [Phys. Rev. B, (2016), 94, 104105] are observed. While the experiment only achieves a partial response, comparison with simulated data demonstrates a preference for a one-step switching mechanism involving an unwinding of the octahedral rotation mode in the initial stages of switching. These results represent some of the first reported experimental diffraction-based evidence for a switching mechanism in an improper ferroelectric.Small-angle X-ray scattering (SAXS) is an effective characterization technique for multi-phase nanocomposites. The structural complexity and heterogeneity of biological materials require the development of new techniques for the 3D characterization of their hierarchical structures. Emerging SAXS tomographic methods allow reconstruction of the 3D scattering pattern in each voxel but are costly in terms of synchrotron measurement time and computer time. To address selleck compound , an approach has been developed based on the reconstruction of SAXS invariants to allow for fast 3D characterization of nanostructured inhomogeneous materials. SAXS invariants are scalars replacing the 3D scattering patterns in each voxel, thus simplifying the 6D reconstruction problem to several 3D ones. Standard procedures for tomographic reconstruction can be directly adapted for this problem. The procedure is demonstrated by determining the distribution of the nanometric bone mineral particle thickness (T parameter) throughout a macroscopic 3D volume of bovine cortical bone. The T parameter maps display spatial patterns of particle thickness in fibrolamellar bone units. #link# Spatial correlation between the mineral nano-structure and microscopic features reveals that the mineral particles are particularly thin in the vicinity of vascular channels.A previously reported multi-scale model for (ultra-)small-angle X-ray (USAXS/SAXS) and (very) small-angle neutron scattering (VSANS/SANS) of live Escherichia coli was revised on the basis of compositional/metabolomic and ultrastructural constraints. The cellular body is modeled, as previously described, by an ellipsoid with multiple shells. However, scattering originating from flagella was replaced by a term accounting for the oligosaccharide cores of the lipopolysaccharide leaflet of the outer membrane including its cross-term with the cellular body. This was mainly motivated by (U)SAXS experiments showing indistinguishable scattering for bacteria in the presence and absence of flagella or fimbrae. The revised model succeeded in fitting USAXS/SAXS and differently contrasted VSANS/SANS data of E. coli ATCC 25922 over four orders of magnitude in length scale. Specifically, this approach provides detailed insight into structural features of the cellular envelope, including the distance of the inner and outer membranes, as well as the scattering length densities of all bacterial compartments. The model was also successfully applied to E. coli K12, used for the authors' original modeling, as well as for two other E. coli strains. Significant differences were detected between the different strains in terms of bacterial size, intermembrane distance and its positional fluctuations. These findings corroborate the general applicability of the approach outlined here to quantitatively study the effect of bactericidal compounds on ultrastructural features of Gram-negative bacteria without the need to resort to any invasive staining or labeling agents.Measurements, calculations and design ideas to mitigate background caused by extraneous scattering in small-angle neutron scattering (SANS) instruments are presented. Scattering includes processes such as incoherent scattering, inelastic scattering and Bragg diffraction. Three primary sources of this type of background are investigated the beam stop located in front of the detector, the inside lining of the detector vessel and the environment surrounding the sample. SANS measurements were made where materials with different albedos were placed in all three locations. Additional measurements of the angle-dependent scattering over the angular range of 0.7π-0.95π rad were completed on 16 different shielding materials at five wavelengths. The data were extrapolated to cover scattering angles from π/2 to π rad in order to estimate the materials' albedos. Modifications to existing SANS instruments and sample environments to mitigate extraneous scattering from surfaces are discussed.The refractive index of a y-cut SiO2 crystal surface is reconstructed from orientation-dependent soft X-ray reflectometry measurements in the energy range from 45 to 620 eV. Owing to the anisotropy of the crystal structure in the (100) and (001) directions, a significant deviation of the measured reflectance at the Si L 2,3 and O K absorption edges is observed. The anisotropy in the optical constants reconstructed from these data is also confirmed by ab initio Bethe-Salpeter equation calculations for the O K edge. This new experimental data set expands the existing literature data for quartz crystal optical constants significantly, particularly in the near-edge regions.