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Entanglement types for two-qubit states with real amplitudes

We study the set of two-qubit pure states with real amplitudes and their geometrical representation in the three-dimensional sphere. In this representation, we show that the maximally entangled states—those locally equivalent to the Bell states—form two disjoint circles perpendicular to each other. We also show that taking the natural Riemannian metric on the sphere, the set of states connected by local gates are equidistant to this pair of circles. Moreover, the unentangled or so-called product states are π/4 units away to the maximally entangled states. This is, the unentangled states are the farthest away to the maximally entangled states. In this way, if we define two states to be equivalent if they are connected by local gates, we have that there are as many equivalent classes as points in the interval [0,π/4] with the point 0 corresponding to the maximally entangled states. The point π/4 corresponds to the unentangled states which geometrically are described by a torus. Finally, for every 0<d<π/4 the point d corresponds to a disjoint pair of torus. Finally, we also show how this geometrical interpretation allows to clearly see that any pair of two-qubit states with real amplitudes can be connected with a circuit that only has single-qubit gates and one controlled-Z gate.

97 MATHEMATICS AND COMPUTING↗

Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene

A two-dimensional electron system exposed to a strong magnetic field produces a plethora of strongly interacting fractional quantum Hall (FQH) states, the complex topological orders of which are revealed through exotic emergent particles, such as composite fermions, and fractionally charged Abelian and non-Abelian anyons. Much insight has been gained by the study of multicomponent FQH states, where spin and pseudospin indices of the electron contribute additional correlation. Traditional multicomponent FQH states develop in situations where the components share the same orbital states and the resulting interactions are pseudospin independent; this homo-orbital nature is also crucial to their theoretical understanding. Here, we study “hetero-orbital” two-component FQH states, in which the orbital index is part of the pseudospin, rendering the multicomponent interactions strongly SU(2) anisotropic in the pseudospin space. Such states, obtained in bilayer graphene at the isospin transition between 𝑁 = 0 and 𝑁 = 1 electron Landau levels, are markedly different from previous homo-orbital two-component FQH states. In particular, we observe strikingly different behaviors for the parallel-vortex and reverse-vortex attachment composite fermion states, and an anomalously strong two-component 2/5 state over a wide range of magnetic field before it abruptly disappears at a high field. Our findings, combined with detailed theoretical calculations, reveal the surprising robustness of the hetero-orbital FQH effects, significantly enriching our understanding of FQH physics in this novel regime.

Bilayer graphene↗

Reconciling the Different Apparent Decay Pathways for Iron(III) Tetraphenylporphyrin Chloride: Evidence for Excited State Branching

Detailed understanding of the photophysical properties of metalloporphyrins is key to rationally exploiting them in a variety of applications ranging from photocatalysis to opto-magnetics. Previous studies of the ferric-tetraphenylporphyrin chloride have provided contradictory descriptions of the excited state evolution. Optical transient-absorption suggested initial formation of a ππ* excited state, followed by ligand-to-metal charge-transfer (LMCT) from the porphyrin ring and then decay on the ∼2 ps time scale to a metal-centered excited state that had a lifetime of ∼15 ps. In contrast, femtosecond extreme ultraviolet transient-absorption at the Fe M 2,3 -edge, while agreeing on the initial formation of an LMCT state, found evidence that this decayed in ∼2 ps to the ground state. Here, we have used K-edge transient X-ray absorption and X-ray emission, together with time-resolved X-ray solution scattering to explore this system. Based on these data, we propose a new model, consistent with both the earlier and the current data, in which photoexcited FeTPPCl evolves through three different states on the LMCT manifold, with the ∼2 ps decay now seen to involve a branching between return to the ground state (∼70%) and formation of a long-lived LMCT state (∼30%).

Excited states↗

Lifetime measurements of states of S 35 , S 36 , S 37 , and S 38 using the AGATA γ -ray tracking spectrometer

Lifetimes or lifetime limits of a small number of excited states of the sulfur isotopes with mass numbers A = 35 , 36, 37, and 38 have been measured using the differential recoil-distance method. The isotopes of sulfur were populated in binary grazing reactions initiated by a beam of 36 S ions of energy 225 MeV incident on a thin 208 Pb target which was mounted in the Cologne plunger apparatus. The combination of the PRISMA magnetic spectrometer and an early implementation of the AGATA γ-ray tracking array was used to detect γ rays in coincidence with projectile-like nuclear species. Lifetime measurements of populated states were measured within the range from about 1 to 100 ps. The number of states for which lifetime measurements or lifetime limits were possible was limited by statistics. For 35 S, the lifetime was determined for the first 1/2 + state at 1572 keV; the result is compared with a previous published lifetime value. The lifetime of the 3 - state of 36 S at 4193 keV was determined and compared with earlier measurements. No previous lifetime information exists for the (6 + ) state at 6690 keV; a lifetime measurement with large associated error was made in the present work. For 37 S, the states for which lifetime limits were established were those at 646 keV with J π = 3/2 - and at 2776 keV with J π = 11/2 - ; there are no previously published lifetime values for excited states of 37 S. Finally, a lifetime limit was established for the J π =(6 + ) state of 38 S at 3675 keV; no lifetime information exists for this state in the literature. Measured lifetime values were compared with the results of state-of-the-art shell-model calculations based on the PSDPF, SDPF-U, and FSU effective interactions. In addition, nuclear magnetic-dipole and electric-quadrupole moments, branching ratios, mixing ratios, and electromagnetic transition rates, where available, have been compared with shell-model values. The current work suffers from poor statistics; nevertheless, lifetime values and limits have been possible, allowing a useful discussion of the ability of state-of-the-art shell-model calculations to reproduce the experimental results.

electromagnetic transitions↗

Availability of state-level climate change projection resources for use in site-level risk assessment

In recent years, incorporating climate change considerations has become an important focus of organizations’ resilience planning and risk assessment efforts, including United States federal agencies. This has led to an increasing demand for higher-resolution and higher-quality climate projection information that is easy to understand for non-expert users. In particular, there is a demand for information about how climate change may affect high-impact, low-frequency (HILF) hazards that are central to risk assessments focused on infrastructure. While national-level resources like the National Climate Assessment provide information on climate impacts for different sectors and regions in the United States, downscaled information with location-specific context is often required for site-level resilience planning. As higher-resolution and higher-quality climate resources continue to be developed at the state level, it is imperative to understand ongoing and planned efforts, as well as key drivers for developing these state-level resources. Based primarily on stakeholder input from climate experts from 31 states, we identify key state-level climate resources, as well as drivers accelerating the development of these resources. We assess the availability of climate change resources, specifically those with information about HILF events that have been developed at the state level and can support users in conducting site-level resilience planning. We identify three key drivers or predictors for the development of climate change resources at the state level: (1) existence of state laws, mandates, Executive Orders, and other state policies, (2) existence of university partnerships; and (3) the makeup of the stakeholder groups (in terms of dominant discipline/expertise) participating in the effort. The diverse state strategies and resources surveyed in this study could support the incorporation of higher-resolution climate information into site-level planning.

54 ENVIRONMENTAL SCIENCES↗

Modulating Mid-Gap Electronic States Through Site-Selective Modification in B-Pbx/B'-CuyV2O5/CdS Heterostructures for Photocatalytic Hydrogen Evolution

We interfaced ..beta..-Pbx/..beta..'-CuyV2O5 compounds, with varying stoichiometries of precisely positioned Pb-ions (x) and Cu-ions (y) in interstitial sites along a tunnel-structured ?-V2O5 framework, with cysteine-capped CdS (cysCdS) quantum dots (QDs) to yield heterostructured photocatalysts. ..beta..-Pbx/..beta..'-CuyV2O5 compounds exhibit midgap electronic states with orbital contributions from both Cu 3d and stereochemically active Pb 6s states that show distinctive light-initiated reactivity with photoexcited QDs. ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures were prepared by linker-assisted assembly (LAA). Scanning and transmission electron microscopy, energy-dispersive X-ray spectroscopy, and Raman spectroscopy revealed that cysCdS QDs were deposited onto surfaces of ..beta..-Pbx/..beta..'-CuyV2O5 via LAA. HAXPES revealed that the site-selective positioning of Pb-ions and Cu-ions promoted close energetic alignment of the midgap states of ..beta..-Pbx/..beta..'-CuyV2O5 compounds with the valence-band maximum of cysCdS QDs. Transient absorption spectroscopy revealed that photogenerated holes were transferred from CdS QDs to midgap states of ..beta..-Pbx/..beta..'-CuyV2O5 compounds on time scales <50 ps. Finally, photoelectrochemical and photochemical experiments revealed that ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures promoted the photocatalytic reduction of H+ to H2. In photoelectrochemical experiments, under oxidative conditions, for all ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures, H2 was evolved at a Pt counter electrode while a sacrificial donor was oxidized at the heterostructure-functionalized working electrode. In contrast, under reductive conditions, for ..beta..-Pb0.152V2O5/CdS and ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures, H2 was evolved at the working electrode. In photochemical experiments, dispersed ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures promoted the reduction of H+ to H2 under white-light illumination; ..beta..'-Cu0.55V2O5/CdS and ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures, for which midgap states have Cu 3d orbital character, generated 2-fold more H2 than ..beta..-Pb0.152V2O5/CdS heterostructures. Cu-ion insertion thus appends additional acceptor surface states that improve ligand-mediated hole transfer from photoexcited QDs, but such states are intrinsically limited in mediating hole transport to the substrate as a result of the low mobility of holes in narrow Cu 3d-states. Our results reveal that the density and orbital character of midgap states of ..beta..-Pbx/..beta..'-CuyV2O5 compounds, tunable through recently developed site-selective ion insertion strategies, determine efficiencies of charge-transfer and charge-transport mechanisms that underpin photocatalysis.

36 MATERIALS SCIENCE↗

How Does Metal Spin State Affect Electronic Communication in Mixed-Valence Dimers? Insights from Ultrafast Near-Infrared and Soft X-ray Transient Absorption Spectroscopy

Recent advancements in photocatalysis, photovoltaics, and quantum information science take advantage of electron spin, and determining how spin multiplicity affects electron transfer is key to understanding these phenomena. Here, in this study, we examine how metal spin state affects electronic communication in an organometallic mixed-valence dimer, ferrocenyl cobaltocenium ([Fe II Cp 2 Co III Cp 2 ] + ). This complex can be photoexcited from its low-spin singlet Fe II ground state to form intermediate-spin triplet Fe II and high-spin quintet Fe II excited states. Using femtosecond optical transient absorption (OTA) spectroscopy with visible (vis), near-infrared (NIR), and short-wave IR (SWIR) probes, supported by time-dependent density functional theory (TD-DFT) calculations, we measure Fe II Co III →Fe III Co II intervalence charge transfer (IVCT) bands in each of the Fe II spin states. Mulliken–Hush analysis of the excited-state IVCT bands was used to compute the electronic coupling between the metal centers in all three spin states, which increased as quintet < triplet < singlet. Meanwhile, the peak energy of the bands, and thus the ΔG of the IVCT transition, increased as triplet < quintet < singlet. Then, to directly probe the electronic structure at each metal center, we employed picosecond soft X-ray transient absorption (XTA) spectroscopy at the Fe and Co L 3 edges. Our results show that the low-spin and high-spin states of [Fe II Cp 2 Co III Cp 2 ] + are valence-localized, while the intermediate-spin state is partially delocalized. The differences in charge delocalization are attributed to differences in orbital occupation and geometry that affect the free energy and superexchange coupling.

Burke, John H. [Univ. of Illinois at Urbana-Champa↗

Revealing the electronic structure of the current-induced metastable state in 1T-TaS 2

Among the key features for next-generation memory devices is the need for high-contrast switching between metallic and insulating states with fast switching speed and long lifetime. However, materials exhibiting such properties are rare, and their electronic structure is often poorly understood. Here, by combining state-of-the-art devices with angle-resolved photoemission spectroscopy, we study the emergence of a metastable metallic state from the insulating ground state in the charge-density wave (CDW) material 1T-TaS 2 after applying short current pulses. Analysis of the electronic structure suggests a picture in which 1T-TaS 2 transforms from a band insulator in the commensurate CDW ground state to a correlated metal in the metastable state. Moreover, the optically induced metastable state reveals a strong similarity to the current-induced one. This work provides an extensive characterization of metastable order in 1T-TaS 2 and proves how studying electronic properties under in-operando conditions is a critical step for next-generation devices.

Huber, Maximilian [Lawrence Berkeley National Labo↗

Kinetics vs Thermodynamics: Engineering Photoredox Reactivity from an Upper Excited State of Fe II

Ultrafast deactivation of metal-to-ligand charge-transfer (MLCT) states into low-lying metal-centered states has long limited the utility of first-row transition-metal complexes in a broad range of applications, including photoredox catalysis. Here we bypass such limitations using a Fe II -pyridinium carbene complex to enable electron transfer reactivity directly from a higher-lying MLCT state. Time-resolved spectroscopic data revealed that the higher-energy MLCT manifold relaxes to lower-lying metal-centered states with a time constant of ca. 3 ps. The nature of the metal-centered (MC) excited state as a 3 MC (i.e., S = 1) was inferred from variable-temperature transient absorption studies. These experiments also revealed that the ground-state recovery process occurs at or very near the “Marcus barrierless regime”, thereby allowing for an estimate of its excited-state redox potential. The detailed picture of the energetics of this compound that emerged enabled fine-tuning of competing thermodynamic and kinetic pathways to effect electron transfer from the higher-energy MLCT excited state prior to relaxation to the ligand-field manifold. We believe these results open an unexplored landscape for the use of earth-abundant first-row transition-metal-based chromophores for applications in light-to-chemical energy conversion.

charge transfer↗

High-precision mass measurements of the isomeric and ground states of 44 V: Improving constraints on the isobaric multiplet mass equation parameters of the A=44, 0 + quintet

Background: The quadratic isobaric multiplet mass equation (IMME) has been very successful at predicting the masses of isobaric analog states in the same multiplet, while its coefficients are known to follow specific trends as functions of mass number. The Atomic Mass Evaluation 2016 [Chin. Phys. C 41, 030003 (2017)] 44 V mass value results in an anomalous negative c coefficient for the IMME quadratic term; a consequence of large uncertainty and an unresolved isomeric state. The b and c coefficients can provide useful constraints for construction of the isospin-nonconserving Hamiltonians for the pf shell. In addition, the excitation energy of the 0 + , T = 2 level in 44 V is currently unknown. This state can be used to constrain the mass of the more exotic 44 Cr. Purpose: The aim of the experimental campaign was to perform high-precision mass measurements to resolve the difference between 44 V isomeric and ground states, to test the IMME using the new ground state mass value and to provide necessary ingredients for the future identification of the 0 + , T = 2 state in 44 V. Method: High-precision Penning trap mass spectrometry was performed at LEBIT, located at the National Superconducting Cyclotron Laboratory, to measure the cyclotron frequency ratios of [ 44g,m VO] + versus [ 32 SCO] + , a well-known reference mass, to extract both the isomeric and ground state masses of 44 V. Results: The mass excess of the ground and isomeric states in 44 V were measured to be -23 804.9(80) keV/c 2 and -23 537.0(55) keV/c 2 , respectively. This yielded a new proton separation energy of S p = 1 773(10) keV. Conclusion: The new values of the ground state and isomeric state masses of 44 V have been used to deduce the IMME b and c coefficients of the lowest 2 + and 6 + triplets in A = 44. The 2 + c coefficient is now verified with the IMME trend for lowest multiplets and is in good agreement with the shell-model predictions using charge-dependent Hamiltonians. The mirror energy differences were determined between 44 V and 44 Sc, in line with isospin-symmetry for this multiplet. Finally, the new value of the proton separation energy determined, to an uncertainty of 10 keV, will be important for the determination of the 0 + , T = 2 state in 44 V and, consequently, for prediction of the mass excess of 44 Cr.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Certifying almost all quantum states with few single-qubit measurements

Certifying that an n -qubit state synthesized in the laboratory is close to a given target state is a fundamental task in quantum information science. However, existing rigorous protocols applicable to general target states have potentially prohibitive resource requirements in the form of either deep quantum circuits or exponentially many single-qubit measurements. Here we prove that almost all n -qubit target states, including those with exponential circuit complexity, can be certified from only O ( n 2 ) single-qubit measurements. Given access to the target state’s amplitudes, our protocol requires only O ( n 3 ) classical computation. This result is established by a technique that relates certification to the mixing time of a random walk. Our protocol has applications for benchmarking quantum systems, for optimizing quantum circuits to generate a desired target state and for learning and verifying neural networks, tensor networks and various other representations of quantum states using only single-qubit measurements. We show that such verified representations can be used to efficiently predict highly non-local properties of a synthesized state that would otherwise require an exponential number of measurements on the state. We demonstrate these applications in numerical experiments with up to 120 qubits and observe an advantage over existing methods such as cross-entropy benchmarking.

information theory and computation↗

Generalizing Reversible Triplet–Triplet Energy Transfer as a Strategy to Increase Excited-State Lifetime in Copper(I) Charge-Transfer Chromophores

In this work, we generalize reversible triplet–triplet energy transfer (TTET) as a strategy to achieve long (μs range) excited-state lifetimes in copper(I) photosensitizers of the general formula Cu(RNacNac)(CN-Ar) (RNacNac is a substituted β-diketiminate and CN-Ar is an aryl isocyanide). Six new complexes are presented where the isocyanide is substituted with a triplet–acceptor moiety─anthracene, naphthalene, or phenanthrene. In-depth photophysical analysis reveals that energetic matching of the charge-transfer ( 3 CT) and acceptor-localized 3 (π→π*) states is key to achieving long triplet excited-state lifetimes via reversible TTET. With 2-isocyanoanthracene as the acceptor ligand, 3 CT and 3(π→π*) are not energetically proximate, and irreversible quenching of 3 CT occurs. With a small 0.1–0.2 eV gap between the two triplet states, luminescence originates from the 3 CT state with a moderate excited-state lifetime of 250 or 283 ns observed. As key to the success of this approach, we demonstrate that altering the N-substituent on the RNacNac ligand modulates the energy of the 3 CT state, giving three complexes where the 3 CT and 3 (π→π*) energies are perfectly matched and the excited-state lifetimes are much longer, spanning 1.9–2.7 μs. As such, the key lesson of this work is that long triplet-state lifetimes in these compounds can be achieved by proper “mixing and matching” of the RNacNac ligand, which influences the 3 CT energy, and the triplet acceptor group which dictates the energy of the 3 (π→π*) state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Deciphering the excited-state landscape of Cr(iii) tris(diimines) using [Cr(phen) 3 ] 3+

Earth-abundant Cr(III) polypyridines chromophores feature long-lived doublet ligand-field excited states. The thermally equilibrated 2 T 1 / 2 E ligand-field excited state manifold produces broad, structured UV-Vis-NIR absorption bands. Although ubiquitous across pseudo-octahedral Cr(III) diimine complexes, the dynamics and individual electronic transitions underlying these spectra have remained elusive. Here, we combine time-resolved spectroscopy and multiconfigurational calculations to assign ground- and excited-state absorption spectra of Cr(III) tris(1,10-phenanthroline), [Cr(phen) 3 ] 3+ , as a prototypical example for this class of complexes. Excited-state kinetics reveal a rapid biexponential decay of the initially prepared intraligand/ligand-to-metal charge transfer [ 4 ( 1 IL)/ 4 LMCT] excited state into the lowest 2 T 1 / 2 E state within 10 picoseconds, assigned to intersystem crossing and vibrational relaxation. Calculations identify broad excited-state absorption features associated with metal-centered ligand-field states ( 2 MC) mixed with intraligand ( 2 IL) transitions within the doublet manifold. These results provide detailed spectral assignments and highlight the need to include multiconfigurational ligand-based orbitals when modeling the spectral properties of Cr(III) coordination complexes.

Barth, Alexandra T. [North Carolina State Universi↗

Probing Quantum Anomalous Hall States in Twisted Bilayer WSe 2 via Attractive Polaron Spectroscopy

Moiré superlattices in semiconductors exhibit a rich variety of interaction-induced topological states, including quantum anomalous Hall (QAH) effects. A recent study hinted that twisted WSe 2 homobilayer (tWSe 2 ) could host a QAH state but lacked direct evidence of ferromagnetism, a key hallmark of this phase. Here, we report the first direct evidence of QAH states in tWSe 2 with spontaneous ferromagnetism. Specifically, we employ polarization-resolved attractive polaron spectroscopy on a dual-gated, 2° tWSe 2 and observe direct signatures of spontaneous time-reversal symmetry breaking at hole filling 𝜈 = 1. Together with a Chern number (𝐶) measurement via Streda formula analysis, we identify this magnetized state as a topological state, characterized by 𝐶 = 1. Furthermore, we demonstrate that these topological and magnetic properties are tunable via a finite displacement field, between a QAH ferromagnetic state and an antiferromagnetic state. Our findings position tWSe 2 as a highly versatile, stable, and optically addressable platform for investigating topological order and strong correlations in two-dimensional landscapes.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

High-Performance Semiempirical Excited-State Molecular Dynamics Powered by Graphics Processing Units

Here, this Letter introduces excited-state molecular dynamics in PYSEQM, a GPU-accelerated semiempirical quantum chemistry engine implemented in PyTorch. The new module enables Born–Oppenheimer molecular dynamics (BOMD) using configuration-interaction singles and random phase approximation for excited states, allowing long trajectories and large statistical ensembles to be simulated efficiently on a single GPU. We also implement an extended Lagrangian excited-state BOMD (XL-ESMD) scheme that propagates auxiliary electronic variables, enabling relaxed ground and excited-state convergence thresholds without compromising energy conservation. The excited-state BOMD implementation scales smoothly from small chromophores to a nearly 900-atom dendrimer (taking 6.5 s per MD step). PYSEQM also supports batched execution, allowing many geometries or trajectories to be evaluated in a single GPU launch, substantially increasing throughput and making ensemble-based protocols routine. As a demonstration, we compute absorption, emission, and infrared spectra from trajectories propagated on the ground and first excited states. The XL-ESMD scheme yields identical spectra at significantly lower computational cost, establishing the role of extended Lagrangian based dynamics for efficient excited-state BOMD simulations. Beyond raw performance, PYSEQM’s PyTorch foundation provides automatic differentiation for forces, efficient GPU batching, and seamless interfacing with machine learning models. These capabilities position PYSEQM as a practical platform for machine learning-augmented excited-state dynamics and lay the foundation for future data-driven nonadiabatic excited-state dynamics modeling of ultrafast spectroscopic probes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Predicting the oxidation states of Mn ions in the oxygen-evolving complex of photosystem II using supervised and unsupervised machine learning

Abstract Serial Femtosecond Crystallography at the X-ray Free Electron Laser (XFEL) sources enabled the imaging of the catalytic intermediates of the oxygen evolution reaction of Photosystem II (PSII). However, due to the incoherent transition of the S-states, the resolved structures are a convolution from different catalytic states. Here, we train Decision Tree Classifier and K-means clustering models on Mn compounds obtained from the Cambridge Crystallographic Database to predict the S-state of the X-ray, XFEL, and CryoEM structures by predicting the Mn’s oxidation states in the oxygen-evolving complex. The model agrees mostly with the XFEL structures in the dark S 1 state. However, significant discrepancies are observed for the excited XFEL states (S 2 , S 3, and S 0 ) and the dark states of the X-ray and CryoEM structures. Furthermore, there is a mismatch between the predicted S-states within the two monomers of the same dimer, mainly in the excited states. We validated our model against other metalloenzymes, the valence bond model and the Mn spin densities calculated using density functional theory for two of the mismatched predictions of PSII. The model suggests designing a more optimized sample delivery and illumiation systems are crucial to precisely resolve the geometry of the advanced S-states to overcome the noncoherent S-state transition. In addition, significant radiation damage is observed in X-ray and CryoEM structures, particularly at the dangler Mn center (Mn4). Our model represents a valuable tool for investigating the electronic structure of the catalytic metal cluster of PSII to understand the water splitting mechanism.

Plant Sciences↗

Estimation of process steady state with autoregressive models and Bayesian inference

To improve efficiency, separations engineers will typically design process circuits containing recirculating streams, which mix one or more of the process outputs with the feed material. Doing so can improve efficiency, but will cause a delay in the system reaching steady state conditions until the recirculating load mass flows stabilize. In testing separation circuits, engineers will often test a variety of factors and complete an analysis from sample results. Knowledge of if a process is at steady state, as well as the steady state conditions of a process, is essential for a valid techno-economic analysis. However, the definition of process steady state is often poorly defined, or does not include uncertainty quantification. If the performance of a process operating under two different sets of conditions are compared, an engineer who does not test for steady state or quantify steady state conditions risks producing a faulty analysis. In this work, a Bayesian statistical method for testing if all streams are at steady state is further motivated and then derived. Then after testing for steady state, the same model is used with a prior distribution that enforces a steady state assumption to estimate steady state conditions. Further, these methods were validated in a solvent extraction pilot plant where steady state conditions for all outflows were inferred with uncertainty quantification. Analysis is completed with functions available to the reader as part of the BayesMassBal (V 1.1.0) software package written in R.

01 COAL, LIGNITE, AND PEAT↗

Garnet-Type Solid-State Electrolytes: Materials, Interfaces, and Batteries

Solid-state batteries with desirable advantages, including high-energy density, wide temperature tolerance, and fewer safety-concerns, have been considered as a promising energy storage technology to replace organic liquid electrolyte-dominated Li-ion batteries. Solid-state electrolytes (SSEs) as the most vital component in solid-state batteries largely lead the future battery development. Among different types of solid-state electrolytes, garnet-type Li 7 La 3 Zr 2 O 12 (LLZO) solid-state electrolytes have particularly high ionic conductivity (10 –3 to 10 –4 S/cm) and good chemical stability against Li metal, offering a great opportunity for solid-state Li-metal batteries. Since the discovery of garnet-type LLZO in 2007, there has been an increasing interest in the development of garnet-type solid-state electrolytes and all solid-state batteries. Garnet-type electrolyte has been considered one of the most promising and important solid-state electrolytes for batteries with potential benefits in energy density, electrochemical stability, high temperature stability, and safety. In this Review, we will survey recent development of garnet-type LLZO electrolytes with discussions of experimental studies and theoretical results in parallel, LLZO electrolyte synthesis strategies and modifications, stability of garnet solid electrolytes/electrodes, emerging nanostructure designs, degradation mechanisms and mitigations, and battery architectures and integrations. We will also provide a target-oriented research overview of garnet-type LLZO electrolyte and its application in various types of solid-state battery concepts (e.g., Li-ion, Li–S, and Li–air), and we will demonstrate opportunities and perspectives as guides for future development of solid electrolytes and solid-state batteries.

25 ENERGY STORAGE↗