The advent of high-speed x-ray photon correlation spectroscopy now allows the study of critical phenomena in fluids to much smaller length scales and over a wider range of temperatures than is possible with dynamic light scattering. We present an x-ray photon correlation spectroscopy study of critical fluctuation dynamics in a complex fluid typical of those used in liquid-liquid extraction (LLE) of ions, dodecane-DMDBTDMA with extracted aqueous $\mathrm{Ce}({\mathrm{NO}}_3{)}_3$. We observe good agreement with both static and dynamic scaling without the need for significant noncritical background corrections. Critical exponents agree with 3D Ising values, and the fluctuation dynamics are described by simple exponential relaxation. The form of the dynamic master curve deviates somewhat from the Kawasaki result, with a more abrupt transition between the critical and noncritical asymptotic behavior. The concepts of critical phenomena thus provide a quantitative framework for understanding the structure and dynamics of LLE systems and a path forward to new LLE processes.

Understanding the microscopic origin of the superior electromechanical response in relaxor ferroelectrics requires knowledge not only of the atomic-scale formation of polar nanodomains (PNDs) but also the rules governing the arrangements and stimulated response of PNDs over longer distances. Using x-ray coherent nanodiffraction, we show the staggered self-assembly of PNDs into unidirectional mesostructures that we refer to as polar laminates in the relaxor ferroelectric 0.68PbMg_1/3Nb_2/3O₃-0.32PbTiO₃(PMN-0.32PT). We reveal the highly heterogeneous electric-field–driven responses of intra- and interlaminate PNDs and establish their correlation with the local strain and the nature of the PND walls. Our observations highlight the critical role of hierarchical lattice organizations on macroscopic material properties and provide guiding principles for the understanding and design of relaxors and a wide range of quantum and functional materials.

Extractant aggregation in liquid–liquid extraction organic phases impacts extraction energetics and is related to the deleterious efficiency-limiting liquid–liquid phase transition known as third phase formation.

Dark-field X-ray microscopy is a lens-based technique that enables real-space imaging of heterogeneous micro- and meso-scale ordered materials. However, achieving accurate three-dimensional (3D) reconstruction often requires meticulous sample alignment or rastering, requiring complex rotational setups and extended acquisition times. To address these challenges, we introduce a structured illumination technique optimized for 3D imaging of ordered materials at sub-micrometer length scales. Our approach employs a coded aperture to spatially modulate the incident X-ray beam, enabling 3D structural reconstruction from images captured at various aperture positions. Unlike current 3D imaging approaches, which often rely on rotational or rastering methods, our technique uses scanning X-ray silhouettes of the coded aperture for depth resolution along the diffraction axis. This eliminates the need for sample rotation or rastering, resulting in a highly stable and efficient imaging modality. We validated the efficacy of this approach through experimental imaging of an isolated twin domain within a bulk single crystal of an iron pnictide using a dark-field X-ray microscope. This advancement aligns with the enhanced brightness upgrades of modern synchrotron radiation facilities, unlocking new possibilities for high-resolution imaging of ordered materials.

Dynamics in dense hard-sphere systems close to crystallization and vitrification is governed by their orientational order.