The tetragonal intermetallic compound ${\mathrm{EuAl}}_4$ hosts an exciting variety of low-temperature phases. In addition to a charge density wave below 140 K, four ordered magnetic phases are observed below 15.4 K in zero field. Recently, a skyrmion phase was proposed based on Hall effect measurements under a $c$-axis magnetic field. We present a detailed investigation of the phase transitions in ${\mathrm{EuAl}}_4$ under $c$-axis magnetic field. Our dilatometry, heat-capacity, DC magnetometry, AC magnetic susceptibility, and resonant ultrasound spectroscopy measurements reveal three magnetic phase transitions not previously reported. The first key result is a detailed $\mathit{H}\parallel \left[001\right]$ magnetic phase diagram mapping the seven phases we observe. Second, we identify a high-field phase, phase VII, which directly corresponds to the region were skyrmions have been previously suggested. Our results provide guidance for future studies exploring the complex magnetic interactions and spin structures in ${\mathrm{EuAl}}_4$.

High-mass-loading cathodes are crucial for achieving high energy density in all-solid-state batteries from the lab scale to industry. However, as mass-loading increases, electrochemical performance is significantly compromised due to sluggish kinetics. In this work, operando neutron imaging is deployed on a high-mass-loading NMC 811 cathode of 33 mg/cm² (5.0 mAh/cm²) and directly visualizes the lithiation prioritization of the cathode active material (CAM) from the solid electrolyte membrane side to the current collector side. In addition to the tortuosity, another key limitation on ion transfer in the cathode arises from the mismatch between the uniform distribution of the solid electrolyte (catholyte) in the conventional composite cathode and the non-uniform Li⁺ flux generated by the faradaic reaction of CAMs. Therefore, we engineer a gradient in the catholyte concentration to match the Li⁺ flux distribution as a means of eliminating the ion transfer obstacle. This approach demonstrates enhanced rate performance, even with high-mass-loading cathodes. A LiCoO₂ composite cathode with 100 mg/cm² high-mass-loading exhibits an areal capacity of 10.4 mAh/cm² at a current density of 2.25 mA/cm². This work provides insight into the ion-transport limitation in thick cathodes and demonstrates an effective gradient design to overcome the kinetic barrier and achieve high battery performance.

Resonant ultrasound spectroscopy is used to nondestructively measure the elastic resonances of small solids to elucidate the material's elastic properties or other qualities like size, shape, or composition. Here, we introduce the software RUScal for the purpose of determining elastic properties by analyzing the eigenfrequencies of solid specimens with common shapes, such as rectangular parallelepipeds, cylinders (solid and hollow tube), ellipsoids, and octahedrons, as well as irregularly shaped ellipsoids that can be described analytically. All symmetry classes are supported, from isotropic to triclinic, along with the option to add or remove up to three orthogonal mirror planes as well as the ability to reorient the crystal axes with respect the sample edges via Euler angles. Additional features include tools to help find initial sets of elastic constants, including grid exploration and Monte Carlo methods, a tool to analyze frequencies as a function of sample length or crystal orientation, an error analysis tool to assess fit quality, and formatting of the input and output files for batch fitting, e.g., as a function of temperature. This software was validated with published resonant ultrasound spectroscopy data for various materials, shapes, and symmetries with noted improvements in calculation time compared to finite element methods.