Eng

Rare earth elements are indispensable for a wide range of advanced technologies, which underscores their strategic importance. This study investigates the kinetics of extracting heavy rare earth elements—lutetium, thulium, yttrium, erbium, and dysprosium—from industrial phosphoric acid solutions generated during apatite processing. A comparative approach using both solvent and solid-phase extraction with di-(2-ethylhexyl)phosphoric acid (D2EHPA) was applied to elucidate the underlying mechanisms. Optimal solvent extraction parameters ($V_{aq}:V_{org}$ = 2:1, ${\phi }_{D2EHPA}$ = 0.2, 298 K, stirring at 350 rpm) achieved efficiencies exceeding 85%. Efficient solid-phase recovery was attained under mild conditions (298 K, m:V = 1:10, shaking at 100 opm). The rate-limiting steps were identified as diffusion-controlled for solvent extraction, governed primarily by agitation intensity, and as a mixed external–internal diffusion regime for solid-phase extraction. Calculated activation energies for each element corroborate these findings.

Clarifying the mechanical properties and failure patterns of layered coal–rock combinations in coal-measure strata is critical to guiding hydraulic fracturing design in petroleum and mining engineering. This paper investigates the mechanical properties, failure patterns, and stress distributions of sandstone–coal–sandstone (SCS) and mudstone–coal–mudstone (MCM) combinations under different confining pressures and thickness ratios based on the 3D combined finite–discrete element method (3D FDEM). The results show that the mechanical strength of the SCS combination is higher than that of the MCM combination under the same conditions. As the thickness ratio increases, the overall peak stress and elastic modulus of the combination decrease gradually and eventually approach those of the pure coal. As confining pressure increases, the peak stress of layered coal–rock combinations rises gradually, plastic behaviors become increasingly prominent, and the failure mode of the mudstone layer transitions from tensile-dominated to shear-dominated. Under different thickness ratios and confining pressures, the coal layer in the combinations primarily develops shear-dominated cracks, whereas the sandstone layer mainly generates tensile-dominated cracks. An increase in confining pressure elevates the critical thickness ratio for sandstone layer failure in the SCS combination. Essentially, the changes in stress state caused by rock types, thickness ratios, and confining pressures are important reasons for the variations in the failure patterns of each layer in layered coal–rock combinations. The key findings of this paper are expected to provide theoretical guidance for the field design of petroleum and coal mine engineering.

In this study, we employ impedance spectroscopy to investigate the internal mechanisms influencing the efficiency and performance of perovskite solar cells (PSCs). Using SCAPS-1D software (version 3.3.10), we simulate the FTO/ZnO/MASnI₃/NiOx/Au heterostructure to analyze the complex impedance (Z*) and electric modulus (M*). This approach allows us to differentiate between bulk material properties and interface phenomena, such as ion migration, charge transport, and recombination dynamics. Through Nyquist and Bode plots, we identify three distinct relaxation processes associated with charge migration, interface polarization, and charge injection/extraction at the electrodes. To achieve a more comprehensive understanding, we model the impedance and modulus spectra using an equivalent electrical circuit, which accurately reproduces the experimental data. Our analysis reveals that increasing the bias voltage extends the relaxation times for charge transport and interface polarization, highlighting a decline in performance under higher operational voltages. This performance drop is attributed to elevated resistive losses and enhanced recombination processes, which become more pronounced at higher fields. These findings emphasize the importance of optimizing both bulk material properties and interface engineering to mitigate losses and improve the overall performance and stability of PSCs.