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At least 631 records · Page 35

Ni and Co Incorporation in Forsterite: A Density Functional Theory Study with Hubbard Correction

Ni and Co are critical elements for the world economy and modern technologies. Mafic and ultramafic deposits represent low-grade yet abundant alternatives to traditional Ni and Co ores. Here, in this work, density functional theory (DFT) with the Hubbard U correction (DFT+U) was used to simulate the incorporation of Ni and Co in forsterite (Mg 2 SiO 4 ), the Mg endmember of olivine, a common mineral in mafic and ultramafic rocks. Hubbard U terms for Ni and Co were parametrized using a series of oxide, hydroxide, carbonate, silicate, and sulfide minerals relevant to extraction and recovery of Ni and Co from mafic and ultramafic deposits. Electronic, energetic, magnetic, and structural properties were considered in the parametrization. For each of Ni and Co, an effective Hubbard correction (U eff ) value that optimized agreement with either experimental data or a hybrid exchange-correlation functional for all of the minerals considered is reported. DFT+U ab initio molecular dynamics (AIMD) simulations of Ni and Co incorporated into the M1 and M2 octahedral sites of forsterite were then performed. Ni and Co substitution in the M1 site was more energetically favorable than substitution in the M2 site, in agreement with published partition coefficients. AIMD trajectories were used to compute extended X-ray absorption fine structure (EXAFS) spectra of Ni in the M1 and M2 sites for direct fitting to a published experimental spectrum of Ni in a natural San Carlos olivine sample. The results of the fit indicated that ordering of Ni in the M1 site was not as strong at the low Ni concentrations relevant to mafic and ultramafic silicate minerals as that at the higher concentrations of the Ni-Mg olivine solid solutions studied to date.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A numerical study of particle jetting in a dense particle bed driven by an air-blast

In this work, the particle jetting behavior in a blast-driven dense particle bed is studied at early times. Four-way coupled Euler–Lagrange simulations are performed using a high-order discontinuous Galerkin spectral element solver coupled with a high-order Lagrangian particle solver, wherein the inter-particle collisions are resolved using a discrete element method collision model. Following the experiments of Rodriguez et al. [“Formation of particle jetting in a cylindrical shock tube,” Shock Waves 23(6), 619–634 (2013)] and the simulations of Osnes et al. [“Numerical simulation of particle jet formation induced by shock wave acceleration in a Hele-Shaw cell,” Shock Waves 28(3), 451–461 (2018)], the simulations are performed in a quasi-two-dimensional cylindrical geometry (Hele-Shaw cell). Parametric studies are carried out to assess the impact of the coefficient of restitution and the strength of the incident shock on the particle jetting behavior. The deposition of vorticity through a multiphase (gas–particle) analog of Richtmyer–Meshkov instability is observed to play a crucial role in channeling the particles into well-defined jets at the outer edge of the particle bed. This is confirmed by the presence of vortex pairs around the outer jets. Furthermore, the effect of the relaxation of the relative velocity between the two phases on the vorticity generation is explored by analyzing the correlation between the radial velocity of particles and the radial velocity of the gas at the particle location.

42 ENGINEERING↗

Novel 2D velocity estimation method for large transient events in plasmas

Dynamics of fast transient events are challenging to be analyzed with high time resolution. Such events can occur in fusion plasmas such as the filaments during edge-localized modes (ELMs). Here, we present a robust method—the spatial displacement estimation—for estimating the displacements of structures with fast dynamics from high spatial and time resolution imaging diagnostics [e.g., gas-puff imaging (GPI)] with sampling time temporal resolution. First, a background suppression method is shown, which suppresses the slowly time-evolving and spatially non-uniform background in the signal. In the second step, a two-dimensional polynomial trend subtraction method is presented to tackle the remaining polynomial order trend in the signal. After performing these pre-processing steps, the spatial displacement of the propagating structure is estimated from the two-dimensional spatial cross-correlation coefficient function calculated between consecutive frames. The method is tested for its robustness and accuracy by simulated Gaussian events and spatially displaced random noise. An example application of the method is presented on propagating ELM filaments measured by the GPI system on the National Spherical Torus Experiment spherical tokamak.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Phase Switching as the Origin of Large Piezoelectric Response in Organic-Inorganic Perovskites: A First-Principles Study

Piezoelectrics are critical functional components of many practical applications such as sensors, ultrasonic transducers, actuators, medical imaging, telecommunications. So far, the best performing piezoelectrics are ferroelectric ceramics, many of which are toxic, heavy, hard, and cost-ineffective. Recently, a groundbreaking discovery of extraordinarily large piezoelectric coefficients in the family of organic-inorganic perovskites gave a hope for a cheaper, environmentally friendly, inexpensive, light-weight and flexible alternative. However, the origin of such response in organic-inorganic ferroelectrics whose spontaneous polarization is an order of magnitude smaller than for inorganic counterparts remains unclear. In this study we employ first-principles simulations to predict that the mechanism associated with large piezoelectric constants is of extrinsic origin and associated with switching between the stable phase and previously overlooked energetically competitive metastable phase that can be stabilized by the external stress. Here, the phase switching changes the polarization direction and, therefore, gives origin to large piezoelectric response, similar to PbZr$_{1-x}$Ti$_x$O$_3$ near morphotropic phase boundary. Existence of such metastable phases is likely to manifest as the dynamical molecular disorder above the Curie temperature and, therefore, could be intrinsic to the entire family of organic-inorganic ferroelectrics with such disorder.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Methods—Analyzing Electrochemical Kinetic Parameters in Deep Eutectic Solvents Using an Extended Butler-Volmer Equation

Deep eutectic solvents (DESs) are promising electrolytes for electrochemical redox reactions, which can be used in redox flow batteries (RFBs). However, in some systems like the Fe 2+/3+ redox reaction in ethaline, traditional Tafel-based kinetic analysis generates unreasonable kinetic parameters (i.e., large anodic/cathodic charge transfer coefficients ( α a , α c ) along with low exchange current densities ( i 0 )). This hinders a comprehensive kinetic and kinetic mechanism study. Here, we perform a detailed investigation of the Tafel analysis using a series of synthetic rotating disk electrode (RDE) data. We find the Tafel analysis only works well when i 0 < 0.57 i lim (limiting current density) in our scenario and leads to abnormal kinetic values once i 0 exceeds this limiting value. Thus, we propose an extended Butler-Volmer (ex-BV) analysis based on modern non-linear fitting techniques to obtain the actual kinetic parameters for such systems. The results show that this method fits the RDE data closely and generates reliable α a , α c and i 0 values, demonstrating that it is a good replacement for traditional Tafel analysis for kinetic studies in high-viscosity electrolytes such as DES systems.

Electrochemistry↗

LLEPE

LLEPE (liquid-liquid equilibrium parameter estimator) is a tool for estimating thermodynamic parameters like standard enthalpies, standard molar volumes and Pitzer coefficients, by combining Gibbs minimization with regression to multiphase equilibrium isotherm data. It also includes visualization tools to access data quality and prediction model performance.

ILOEJE, CHUKWUNWIKE↗

Sorption of Metals and Radionuclides in Cementitious Leachate Impacted Sediments from the Savannah River Site

Performance assessments (PAs) are calculations used to establish the risk posed by radioactive waste disposal facilities in the Savannah River Site (SRS). The distribution coefficient (Kd; solid/liquid concentration ratio; Csolid/liquid) is one of the key geochemical parameters used in the PA to provide a measure of how strongly the dissolved contaminants bind to solid phases; the greater the Kd value, the greater the tendency to bind to the solids. The overall purpose of this study was to measure this key parameter for several constituents of concern in the cementitious leachate impacted SRS sediment environments. Particular attention was directed at quantifying the influence of cementitious leachate from various stages of cement aging on the sorption of radioactive waste and heavy metals on SRS sediments.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Multiphysics and Multiscale Modeling of Coupled Transport of Chloride Ions in Concrete

Chloride ions (Cl−)-induced corrosion is one of the main degradation mechanisms in reinforced concrete (RC) structures. In most situations, the degradation initiates with the transport of Cl− from the surface of the concrete towards the reinforcing steel. The accumulation of Cl− at the steel-concrete interface could initiate reinforcement corrosion once a threshold Cl− concentration is achieved. An accurate numerical model of the Cl− transport in concrete is required to predict the corrosion initiation in RC structures. However, existing numerical models lack a representation of the heterogenous concrete microstructure resulting from the varying environmental conditions and the indirect effect of time dependent temperature and relative humidity (RH) on the water adsorption and Cl− binding isotherms. In this study, a numerical model is developed to study the coupled transport of Cl− with heat, RH and oxygen (O2) into the concrete. The modeling of the concrete microstructure is performed using the Virtual Cement and Concrete Testing Laboratory (VCCTL) code developed by the U.S. National Institute of Standards and Technology (NIST). The concept of equivalent maturation time is utilized to eliminate the limitation of simulating concrete microstructure using VCCTL in specific environmental conditions such as adiabatic. Thus, a time-dependent concrete microstructure, which depends on the hydration reactions coupled with the temperature and RH of the environment, is achieved to study the Cl− transport. Additionally, Cl− binding isotherms, which are a function of the pH of the concrete pore solution, Cl− concentration, and weight fraction of mono-sulfate aluminate (AFm) and calcium-silicate-hydrate (C-S-H), obtained from an experimental study by the same authors are utilized to account for the Cl− binding of cement hydration products. The temperature dependent RH diffusion was considered to account for the transport of Cl− with moisture transport. The temperature and RH diffusion in the concrete domain, composite theory, and Cl− binding and water adsorption isotherms are used in combination, to estimate the ensuing Cl− diffusion field within the concrete. The coupled transport process of heat, RH, Cl−, and O2 is implemented in the Multiphysics Object-Oriented Simulation Environment (MOOSE) developed by the U.S. Idaho National Laboratory (INL). The model was verified and validated using data from multiple experimental studies with different concrete mixture proportions, curing durations, and environmental conditions. Additionally, a sensitivity analysis was performed to identify that the water-to-cement (w/c) ratio, the exposure duration, the boundary conditions: temperature, RH, surface Cl− concentration, Cl− diffusion coefficient in the capillary water, and the critical RH are the important parameters that govern the Cl− transport in RC structures. In a case study, the capabilities of the developed numerical model are demonstrated by studying the complex 2D diffusion of Cl− in a RC beam located in two different climatic regions: warm and humid weather in Galveston, Texas, and cold and dry weather in North Minnesota, Minnesota, subjected to time varying temperature, RH, and surface Cl− concentrations.

composite theory↗

Simulating Long–Term Dynamics of Radiation Belt Electrons Using DREAM3D Model

Here, we compared the performance of DREAM3D simulations in reproducing the long-term radiation belt dynamics observed by Van Allen Probes over the entire year of 2017 with various boundary conditions (BCs) and model inputs. Specifically, we investigated the effects of three different outer boundary conditions, two different low-energy boundary conditions for seed electrons, four different radial diffusion (RD) coefficients (DLL), four hiss wave models, and two chorus wave models from the literature. Using the outer boundary condition driven by GOES data, our benchmark simulation generally well reproduces the observed radiation belt dynamics inside L* = 6, with a better model performance at lower μ than higher μ, where μ is the first adiabatic invariant. By varying the boundary conditions and inputs, we find that: (a) The data-driven outer boundary condition is critical to the model performance, while adding in the data-driven seed population doesn't further improve the performance. (b) The model shows comparable performance with DLL from Brautigam and Albert (2000, https://doi.org/10.1029/1999ja900344), Ozeke et al. (2014, https://doi.org/10.1002/2013ja019204), and Liu et al. (2016, https://doi.org/10.1002/2015gl067398), while with DLL from Ali et al. (2016, https://doi.org/10.1002/2016ja023002) the model shows less RD compared to data. (c) The model performance is similar with data-based hiss models, but the results show faster loss is still needed inside the plasmasphere. (d) The model performs similarly with the two different chorus models, but better capturing the electron enhancement at higher μ using the Wang et al. (2019, https://doi.org/10.1029/2018ja026183) model due to its stronger wave power, since local heating for higher energy electrons is under-reproduced in the current model.

79 ASTRONOMY AND ASTROPHYSICS↗

Correction to “Ruthenium Dye Excitations and Relaxations in Natural Sunlight”

An error in computing the optical rate coefficients for dye RuP was discovered in Table S4 of the Supporting Information Section S8 Model S? for this article, published in J. Phys. Chem. A, 2021, 125, 4365-4372, 10.1021/acs.jpca.1c02386. The optical rate coefficients include absorption, stimulated emission, and ground-state bleach associated with the ground state and the singlet and triplet excited states as well as for the excited-state absorption between the excited states and implicit higher-energy excited states. The optical rate coefficients for continuous solar irradiance were computed using eq 3 of the main text in which the product of the individual signal components and the solar spectrum are integrated and multiplied by the fundamental optical rate coefficient. We determined the incorrect signal components were used for RuP in the published Supporting Information Table S4. The corrected Table S4 column for RuP is presented with the reported values from the original paper in the corrected Supporting Information. New simulations have been performed using the corrected values, and the results were used to update Figures 5 and 6 and also Figure S9 in the corrected Supporting Information. The published conclusions are unchanged. The populations of RuP excited states, Figure 5, are only marginally smaller, which should be expected with minor changes to the optical rate coefficients. There is not a significant change in the results for the number of radiative and nonradiative interactions per dye per second (the optical transitions and nonradiative transitions increased, respectively, by approximately 2% and 10%, Figure 6A). The occurrence of excited-state absorption (ESA) and excited-state emission (ESE) events, Figure 6C, both decreased from the original simulation results by 20% and 33%. The most notable difference is exhibited in Figure 6B; the fraction of population moving from the lowest-energy singlet state (i.e., intersystem crossing or ultrafast nonradiative relaxation) and nonradiative relaxation from the triplet state have decreased from ~0.45 to ~0.4 and increased from ~0.35 to ~0.4, respectively..

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Measurement of prompt ${\mathrm{D^0}}$ and ${\mathrm{\overline{D}}{}^0}$ meson azimuthal anisotropy and search for strong electric fields in PbPb collisions at $\sqrt{s_\mathrm{NN}} =$ 5.02 TeV

The strong Coulomb field created in ultrarelativistic heavy ion collisions is expected to produce a rapidity-dependent difference ( Δv 2 ) in the second Fourier coefficient of the azimuthal distribution (elliptic flow, v 2 ) between D 0 ( $\bar{u}c$ ) and ${\mathrm{\overline{D}}{}^0}$ ( $u\bar{c}$ ) mesons. Motivated by the search for evidence of this field, the CMS detector at the LHC is used to perform the first measurement of Δv 2 . The rapidity-averaged value is found to be &lang;Δv2&rang;=0.001±0.001(stat)±0.003(syst) in PbPb collisions at $\sqrt{s_{NN}}$=5.02 TeV . In addition, the influence of the collision geometry is explored by measuring the D 0 and ${\mathrm{\overline{D}}{}^0}$ mesons v 2 and triangular flow coefficient ( v 3 ) as functions of rapidity, transverse momentum ( p T ), and event centrality (a measure of the overlap of the two Pb nuclei). A clear centrality dependence of prompt D 0 meson v 2 values is observed, while the v 3 is largely independent of centrality. These trends are consistent with expectations of flow driven by the initial-state geometry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Improving air leakage prediction of buildings using the fan pressurization method with the Weighted Line of Organic Correlation

In many countries, the fan pressurization method is the most frequently chosen approach for measuring the air leakage of houses. The measurements are usually performed at pressures that far exceed pressures to which buildings are exposed to under normal conditions. A fit of these tests to the power-law formulation allows an extrapolation to data points outside the measured pressure range. With the Ordinary Least Square (OLS) fitting method, the pressure exponent and flow coefficient can be determined. However, the measurement results are highly sensitive to uncertainties induced by external factors like changing wind conditions during the tests, which is neglected by OLS. This may lead to errors in the prediction of flows at lower pressures. The Weighted Line of Organic Correlation (WLOC) is an alternative approach and takes measurement uncertainty into account. In this paper, a statistical analysis of an extensive data set of pressurization measurements has been performed. Both regression techniques have been compared for almost 7500 fan pressurization measurements of six houses in 109 different house leak configurations. The variability in predicting pressure exponent and flow coefficient for both WLOC and OLS regression was analyzed using probability density functions. It was found that the Weighted Line of Organic Correlation significantly decreases the uncertainty in predicting pressure exponent, flow coefficient, and other low-pressure air leakage metrics compared to the Ordinary Least Square fitting. Here, the authors highly recommend the implementation of WLOC in current measurement standards and test equipment.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Numerical characterization of support recovery in sparse regression with correlated design

Sparse regression is employed in diverse scientific settings as a feature selection method. A pervasive aspect of scientific data is the presence of correlations between predictive features. These correlations hamper both feature selection and estimation and jeopardize conclusions drawn from estimated models. On the other hand, theoretical results on sparsity-inducing regularized regression have largely addressed conditions for selection consistency via asymptotics, and disregard the problem of model selection, whereby regularization parameters are chosen. In this numerical study, we address these issues through exhaustive characterization of the performance of several regression estimators, coupled with a range of model selection strategies. These estimators and selection criteria were examined across correlated regression problems with varying degrees of signal to noise, distributions of non-zero model coefficients, and model sparsity. Our results reveal a fundamental tradeoff between false positive and false negative control in all regression estimators and model selection criteria examined. Additionally, we numerically explore a transition point modulated by the signal-to-noise ratio and spectral properties of the design covariance matrix at which the selection accuracy of all considered algorithms degrades. Overall, we find that SCAD coupled with BIC or empirical Bayes model selection performs the best feature selection across the regression problems considered.

97 MATHEMATICS AND COMPUTING↗

Stabilization of high-performance rock-salt LiMnSbTe3 thermoelectrics with embedded van der Waals-like gaps

Rock-salt-structured compounds like lead chalcogenides are promising thermoelectrics, as their high symmetry, strong anharmonicity, and favorable phase behavior collectively lead to high performance by enabling large power factors and ultralow thermal conductivity. Here, we report LiMnSbTe 3 , a new rock-salt semiconductor stabilized through targeted chemical design by combining hexagonal MnTe with cubic LiSbTe 2 . Embedded in the highsymmetry matrix, van der Waals-like gaps form due to Sb 2 Te 3 nanoscale segregation, which acts as effective phonon-scattering centers, leading to a low lattice thermal conductivity of 0.37Wm- 1 K -1 at 873 K with alloy scattering from disordered cations. The ordered local structure of Sb2Te 3 -type vdW-like gaps and the cross-gap interaction facilitate the carrier transport. Aided by energyconverged valence bands and a paramagnon drag effect, high Seebeck coefficients and enhanced power factor can be achieved, leading to a high ZT of 1.2 at 873 K. Furthermore, introducing Mn deficiency increases ZT to 1.5, highlighting the potential for higher performance through optimized doping or alloying. A segmented single-leg thermoelectric module achieves an output power density of 0.52 Wcm -2 and an efficiency of 8.7% under ΔT of 478 K, further demonstrating its promising thermoelectric applications.

42 ENGINEERING↗

Boosting electrochemical reaction and suppressing phase transition with a high-entropy O3-type layered oxide for sodium-ion batteries

Complex phase transitions induced by interlayer slides in layered cathode materials lead to poor cycling stability and rate capability for sodium-ion batteries. Herein, we design and prepare a new six-component high-entropy oxide (HEO) layered cathode O3–Na(Fe 0.2 Co 0.2 Ni 0.2 Ti 0.2 Sn 0.1 Li 0.1 )O 2 to enable highly reversible electrochemical reaction and phase-transition behavior. The HEO cathode exhibits good cycling performance (capacity retention of ~81% after 100 cycles at 0.5C) and outstanding rate capability (capacity of ~81 mA h g –1 at 2.0C) due to the higher sodium diffusion coefficient (above 5.75 × 10 –11 cm 2 s –1 ) than most reported O3-type cathodes. Moreover, the high-entropy cathode has superior compatibility with the hard carbon anode and delivers a specific capacity of 90.4 mA h g –1 (energy density of ~267.5 W h kg –1 ). Ex situ X-ray diffraction proves that the high-entropy designing effectively suppresses the intermediate phase change to achieve reversible O3–P3 phase evolution, and in turn stabilizes the layered structure. X-ray absorption spectroscopy and Mössbauer spectrum of 57 Fe suggest that Ni 2+ /Ni 3.5+ , Co 3+ /Co 3.5+ , and part of Fe 3+ /Fe 3.5+ redox reaction contribute the charge compensation. Finally, the enhanced performance can be attributed to the disordered distribution of multi-component transition metals in HEO suppressing the ordering of electric charges and sodium vacancies, thereby inhibiting the interlayer slide and phase transition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Impact of Increased Latent Generations on Sensitivity Calculations with SCALE [Slides]

Depending on the system, energy, and/or nuclide, altering the number of latent generations can significantly impact generated sensitivity coefficients. In general, as the number of latent generations increases, the accuracy of the generated sensitivity value compared with the DP value increases and there is a significant increase in the uncertainty with generated sensitivity values. IFP generated sensitivities appear to be more stable than those with CLUTCH. Complex systems, even with IFP and increased latent generations can still produce poor results (i.e., MPC- 32). This reiterates the importance of performing DPs to confirm sensitivities. IFP-Shift and CLUTCH can take advantage of parallel computing abilities. Work continues in this area as additional parameters and calculational methods are examined to provide analysts insights to successfully generating sensitivity coefficients for confirmatory analyses and validation efforts.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Simulation of the Fast Reactor Fuel Assembly Duct-Bowing Reactivity Effect Using Monte Carlo Neutron Transport and Finite Element Analysis

This paper discusses a new method of simulating the fuel assembly duct-bowing reactivity coefficient for EBR-II run 138B. Quantification of the fuel assembly duct-bowing reactivity effect in liquid metal–cooled fast reactors has been a persistent problem since they were first designed and operated. Simulation of the duct-bowing reactivity effect is difficult because the level of detail required to simulate the effect has exceeded most modeling capabilities. The new method outlined in this paper utilizes the finite element analysis code ANSYS to analyze the thermal and structural components. Here, the displacement of the fuel assembly duct due to thermal expansion and mechanical interaction was calculated by ANSYS using recorded EBR-II run 138B temperature and power boundary value data. The displacement values were incorporated into to a Monte Carlo model of EBR-II run 138B and keff was calculated. Multiple Monte Carlo calculations were performed with duct displacement values corresponding to different reactor temperatures. Using the calculated keff values associated with the different duct displacement results allowed calculation of the duct-bowing reactivity coefficient. The duct-bowing reactivity coefficient was calculated to be –14.5 × 10 –4 $/°C/ ± 4.4%.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Thermodynamic Water Activity Explains the Unusual Electrochemical Stability of Aqueous Deep Eutectic Solvents

The presence of water in nonaqueous deep eutectic solvent (DES) electrolytes has been debated in recent years, with efforts ranging from its complete removal to willful addition. It was shown that controlled amounts of water can be beneficial, as it not only enhances the physicochemical properties of these electrolytes but also has no significant detrimental effects on their electrochemical stability. Despite these advantages, there is still limited understanding of how water interacts with DES systems at the molecular level. This study examines the water activity in ethylene glycol and glycerol, as well as their binary mixtures with choline chloride to form the DESs ethaline and glyceline, respectively. In this work, we show that the high electrochemical stability of glyceline is related to its lower water activity compared to ethaline and can be attributed to the robust H-bonding network formed by the three hydroxyl groups of glycerol. Its 3D H-bond network effectively integrates water molecules within its solvent structure, reducing degradation and maintaining stability at higher water contents. The deviations from the ideal Raoult's law behavior are reflected in the water activity and activity coefficients, which highlight the intricate H-bond interactions within DES-water mixtures. Water acts like a lubricant within the more viscous DES mixtures without being detrimental to their electrochemical performance. The presented results emphasize the necessity of customizing DES-water compositions to enhance their performance as electrolytes, especially in flow battery applications where electrochemical stability, ionic conductivity, and fluidity are of utmost importance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗