Costate Research Articles

Bifunctional NiCo-CuO Nanostructures: A Promising Catalyst for Energy Conversion and Storage.

This investigation explores the potential of co-incorporating nickel (Ni) and cobalt (Co)into copper oxide (CuO)nanostructures for bifunctional electrochemical charge storage and oxygen evolution reactions (OER). A facile wet chemical synthesis method is employed to co-incorporate Ni and Co into CuO, yielding diverse nanostructured morphologies, including rods, spheres, and flake. The X-ray diffraction (XRD) and Raman analyses confirmed the formation of NiCo-CuO nanostructure, with minor phases of nickel oxide (NiO)and cobalt tetraoxide (Co3O4). High-resolution Transmission Electron Microscope (HRTEM) also confirms the diverse morphologies and the minor phases of oxides. Synchrotron X-ray absorption spectroscopy revealed higher charge states of Cu, Ni, and Co in the NiCo-CuO nanostructure, enhancing its charge storage and OER. Site-selective X-ray absorption near edge structure analysis elucidated the spatial distribution of Cu, Ni, and Co in the nanostructure. Furthermore, extended X-ray absorption fine structure spectroscopy provided insights into the local atomic structures, revealing increased coordination numbers and interatomic distances in the NiCo-CuO nanostructure. In situ Raman analysis discloses the transformation of Co3O4 into cobalt hydroxide (Co(OH)2) and cobalt oxide (CoO) into cobalt oxyhydroxide (CoOOH) The NiCo-CuO nanostructures exhibited superior specific capacitance, favorable Tafel behavior, and low overpotential positioning as promising bifunctional materials for energy storage and conversion applications. This work contributes to the development of efficient CuO nanocatalysts.

Oxygen‐Vacancy Rich Co3O4/CeO2 Interface for Enhanced Oxygen Reduction and Evolution Reactions

Oxygen reduction and evolution reactions (ORR and OER, respectively) are the two most extensively studied reactions in electrochemistry. Herein, we report the synthesis of Co3O4/CeO2/GNP (GNP=graphene nanoplatelet) electrocatalyst for ORR and OER that exhibits an early onset potential (0.85 V) and half‐wave potential (E1/2) of 0.69 V for ORR. The reported catalyst is highly durable with 87.6% retention of its initial current after a 6 h chronoamperometry test compared to 72.5% by Pt/C. It exhibits a negligible shift of E1/2 after 10,000 potential cycles for ORR. Heterogeneous oxide/oxide interfaces, oxygen vacancies and semicrystalline nature are inferenced to play a dominant role in altering the collective catalytic efficiency of Co3O4/CeO2/GNP. High concentration of oxygen vacancy defects (68%) in Co3O4/CeO2/GNP is presumed to play a dominant role here. The catalyst is bifunctional for ORR and OER with a bifunctionality index of 0.98 V and operates at an overpotential of ƞ10= 440 mV for OER. Ex‐situ X‐ray absorption studies indicate an increased average oxidation state of Co by 15% in Co3O4/CeO2/GNP compared to Co3O4/GNP, aiding in preserving its inherent catalytic nature of spinel Co3O4.

Optimal control of electric vehicle by Short-term Costate Estimation method of Pontryagin’s minimum principle

Pontryagin’s minimum principle (PMP) is a foundational theory to obtain optimal control of dynamic systems by the change of their state and cost function over time. Compared to programming-based optimization methods, it offers the advantage of providing rapid computation and an algebraic comprehension of the optimal solution. However, particularly for large-scale systems, constructing their costate dynamics and ensuring numerical stability is quite a difficult task. This study introduces a novel method called as the Short-term Costate Estimation method based on PMP (SCEMP). It aims to efficiently obtain optimal control for large-scale systems by employing an iterative algorithm cored by the PMP. The objective is to minimize energy consumption while a car is running, achieved by regulating the distribution ratio of traction torque between the front and rear wheels. The key concept of SCEMP lies in obtaining a discrete optimal control through the sequential process of forward integration of the state equation and backward integration of the costate equation within a pre-defined near-future time frame. Costate dynamics is formulated with a cost function evaluated within a surrogate model, which not only offers a simplified representation of the plant dynamics but also serves as a reference model for controlling the plant model. Verification is conducted within a simulation environment. The SCEMP achieved results that approached the global optimum obtained from Dynamic Programming (DP) within a margin of up to 1%, while requiring approximately one-tenth of the computation time needed by DP.

XAS and XPS Analysis on Surface Reconstruction By Chemical Treatment of Ba0.5Sr0.5Co0.8Fe0.2O3

Alkaline water electrolysis is expected to play a vital role in hydrogen production systems using renewable electricity. However, the intermittent nature of renewable electricity can often cause electrolysis cells to shut down. Such interruptions result in reverse currents that accelerate catalyst degradation. Extensive studies of catalytic activity have elucidated that the oxygen evolution reaction (OER) is contingent on certain descriptors [1]. Recently, the focus has been placed on the surface structure of the catalysts, as the actual OER occurs on the catalyst surface [2]. Previous research has demonstrated that the surfaces of numerous oxide materials with high OER activity undergo surface reconstruction under OER, resulting in the formation of metal oxyhydroxide phases [3]. This surface reconstruction has been reported after OER experiments, although it is challenging to analyze large numbers of samples in this manner. In order to efficiently study and utilize the state of the catalyst surface for material design, a method is needed to induce the surface reconstruction through chemical treatments. Consequently, the present study examines the chemical state of the surface following chemical treatment of perovskite-type oxide Ba0.5Sr0.5Co0.8Fe0.2O3 (BSCF) by stirring in an alkaline solution, employing X-ray absorption spectroscopy (XAS) and X-ray photoelectron spectroscopy (XPS). BSCF was synthesized using the sol-gel process. The as-prepared samples were subjected to stirring under four different conditions: in 1 M or 7 M KOH solutions with either oxygen or nitrogen bubbling for a duration of 21 hours. The structural and chemical properties were characterized using X-ray diffraction (XRD), XAS, and XPS. XAS measurements were conducted at the BL-2 and BL-11 beamlines of the Ritsumeikan University SR Center. Both total electron yield and partial fluorescence yield modes were employed. XRD analysis did not reveal any significant peak shifts or the formation of a second phase, indicating that the bulk structure of the samples remained unchanged. Comparative studies of the O K-edge XAS for both as-prepared and chemically treated BSCF samples in 7 M KOH with oxygen bubbling were conducted. The peak at approximately 530 eV is attributed to the transition from O 1s to the 3d orbitals of transition metals combined with O 2p. In the as-prepared sample, this peak exhibited low intensity. However, in the chemically treated sample, sharp peaks were observed at approximately 529 eV and 532 eV. These findings indicate that the surface of the perovskite-type oxide underwent a transformation to an oxyhydroxide of Co or Fe, as evidenced by the presence of peaks characteristic of transition metal oxyhydroxides. Despite these surface changes, the results from Co and Fe L-edge XAS showed no peak shifts, indicating that the valence states of Co and Fe remained unchanged. XPS analysis revealed a decrease in the surface concentrations of Ba and Sr. This work is based on results obtained from the project commissioned by the New Energy and Industrial Technology Development Organization (NEDO) of Japan. (JPNP 20003). [1] J. Suntivich, K. May, H. Gasteiger, J. Goodenough, and Y. Shao-Horn, Science, 334, 1383-1385 (2011). [2] I. C. Man, H. Su, F. Call-Vallejo, H. A. Hansen, J. I. Martínez, N. G. Inoglu, J. Kitchin, T. F. Jaramillo, J. K. Nørskov, and J. Rossmeisl, ChemCatChem, 3, 1159-1165 (2011). [3] E. Fabbri, M. Nachtegaal, T. Binninger, X. Cheng, B. Kim, J. Durst, F. Bozza, T. Graule, R. Schaublin, L.Wiles, M. Pertisi, N. Danilovic, K. E. Ayers, and T. J. Schmidt, Nat. Mater., 16, 925-934 (2017).

Investigating the Electronic Structure of a Complex Oxide Catalyst for Alkaline Water Electrolysis By Operando X-Ray Absorption Spectroscopy

Environmental and energy shortage issues arise due to the excess consumption of fossil fuels, which requires immediate attention to realize the dream of an energy society with virtually zero carbon dioxide emissions. In this context, H2 generated by the water electrolysis technology is considered as a possible substitute for fossil fuels due to its prominent features, such as high gravimetric energy density and zero carbon emission.1 In water electrolysis, the anodic oxygen evolution reaction (OER) is a multielectron transfer reaction that makes overall water electrolysis kinetically sluggish and dominated by noble metal oxides such as IrO2 and RuO2.2 However, their high prices and poor stability under strongly acidic or basic conditions hindered their practical applicability. Therefore, to fulfill this goal, it is necessary to reduce the cost and increase the efficiency and durability of water electrolysis by developing alternative OER electrocatalysts with earth abundant elements. Among various transition metal oxides, Perovskite oxides emerged as a potential OER catalyst due to their low cost, flexibility,and tailorable properties. However, the poor stability of typical BSCF during OER remains a significant issue that hindered its widespread application. Meanwhile, recent reports show that the complex oxide hex-BSCF exhibits superior OER performance than 3C-BSCF. 3However, the detailed information about the intermediates generated during the OER process and the relationship between OER activity and electronic changes of hex-BSCF remains unclear.Therefore, in this study, we synthesized several types of composite oxide, water electrocatalysts Ba4Sr4(Co1-xFex)4O15 (x = 0 to 1.0), and clarified the relationship between the OER activity and the amount of Fe added. The electrochemical investigations showed a volcanic relationship between the OER activity and the amount of Fe added, and the catalyst with an added Fe amount of 0.2 (x=0.2) showed the highest OER activity (Figure 1a). To eliminate the effect of oxygen bubbles attached to the catalyst surface, a forced-flow cell was developed to determine the actual OER activity. The electronic structure change of the catalyst/electrolyte interface during water electrolysis, was analyzed in detail by operando soft X-ray absorption spectroscopy (XAS) by measuring oxygen K - edge. The characteristic peaks originated in the range of 531eV to 532eV, corresponding to the intermediate region between CoOOH and FeOOH.2 The intensity of this characteristic peak is strongly correlated with its OER activity. Further, the ex-situ hard X-ray absorption spectroscopy (XAFS) shown in Figure 1b revealed that the valence state of Co decreases when a small amount of Fe is added, and hex-BSCF82 has the lowest metal-oxygen coordination number and minimum octahedral sites occupation. Hence, the doped Fe pre-occupies the octahedral sites, and the Co is forced to the tetrahedral sites, consequently enhancing the OER activity. Figure 1

Unravelling the Relationship between Crystallographic Structure and Oxygen Evolution Reaction Activity of Nickel Cobalt Oxide Thin Films

The development of a sustainable energy system relies on the production of green hydrogen. One of the major challenges for water splitting is the synthesis of platinum group metal-free oxygen evolution reaction (OER) electrocatalysts. Spinel nickel cobalt oxides (NCOs) have attracted particular interest due to their stable electrocatalytic performance. The less researched rock-salt NCOs, however, are also promising due to their ability to convert to the OER-active hydroxide phase1. Further development of NCO electrocatalysts requires fundamental understanding of their crystallographic structure-OER performance relationship. This work addresses ~20 nm atomic layer deposited (ALD) NCO thin film systems with a broad composition range to unravel the above-mentioned relationship.Our previously developed ALD supercycle process2 based on Ni(MeCp)2, CoCp2 and O2 plasma is employed to generate a full range of chemical compositions, such that the phase transition from Ni-rich rock-salt films to Co-rich films at ~55 at.% Co can be observed. Extensive material characterisation reveals that the phase transition is accompanied by an increase in the +3/+2 ratio of the oxidation state of both Ni and Co. Electrochemical analysis in 1M KOH shows an optimal performance for the 30 at.% Co rock-salt film after 500 CV cycles and a synergistic effect between cobalt and nickel such that NCO films are more OER active than Co3O4 and NiO. The films show a composition-dependent activation during CV cycling, where a decrease in activation is observed for increasing Co at.%. No activation is observed for the spinel films. The activation is driven by bulk transformation to the active (oxy)hydroxide phase and is accompanied by an increase in electrochemical surface area (ECSA) up to a factor 8 for rock-salt films. The overpotential after cycling is corrected for the increase in ECSA using an original method, which reveals that Ni-rich spinel structure films are intrinsically more active3.The use of model systems in combination with extensive material characterisation and prolonged electrochemical testing allows us to distinguish two classes of NCO catalysts, the instantly active and highly stable Co-rich spinel films and the high surface area Ni-rich rock-salt phase which develops upon extensive activation . Placing these results in perspective, we conclude that application of these catalysts on high surface area 3D electrodes would benefit from the more intrinsically active spinel NCO films, whilst activated rock-salt films would be the preferred choice for thin film electrocatalysis studies. These results also show that rock-salt NCO films (<40 at.% Co) could be a more sustainable alternative to the more commonly used spinel NCO films. 1Gebreslase et al. J. Energy Chem. 2022, 67, 101-137 2van Limpt et al. JVSTA, 2023, 41, 032407 3van Limpt et al. Adv. Energy Mat. under review Figure 1

Evolution of structural, magnetic and transport properties of 3d-5d based double perovskites Nd2–xSrxCoIrO6

The evolution of the structural, magnetic and transport properties of the intermediate compounds Nd2-xSrxCoIrO6withx= 0.2, 0.4, 0.6, 1 and 1.5 have been studied to establish important roles of sizes and oxidation states of cations on various phases. The replacement of Nd3+by Sr2+primarily influences the oxidation states of Co (Co2+→Co3+) and Ir (Ir4+→Ir5+) ions to maintain the charge neutrality in the entire system. The Sr dopants give rise to an increasing Co/Ir antisite disorder (ASD) to accommodate the variation of charge state and ionic radius of Co and Ir. The nature of magnetic interaction induced by Sr changes from being a ferrimagnetic (FIM) to a more dominant antiferromagnetic. The suppression of the second magnetic transition below 30 K in samples forx>0.2 is entirely due to dilution of the Nd-Nd magnetic interaction. The combined effects of ASD and mixed oxidation state of Co and Ir ions generate various types of magnetic exchange pathways and create competitive magnetic interactions to stabilize a particular magnetic ground state. In the middle compound NdSrCoIrO6, a Griffith like phase in the temperature region 65-150 K and exchange bias field of 658 Oe at 2.3 K under a cooling field of 50 kOe has been observed. The compounds show an insulating kind of behaviour, and with hole doping the value of room temperature resistivity drastically decreases. The nature of conduction is found to follow three dimensional Mott's variable range hopping process.

Pontryagin Neural Networks for the Class of Optimal Control Problems With Integral Quadratic Cost

This work introduces Pontryagin Neural Networks (PoNNs), a specialised subset of Physics-Informed Neural Networks (PINNs) that aim to learn optimal control actions for optimal control problems (OCPs) characterised by integral quadratic cost functions. PoNNs employ the Pontryagin Minimum Principle (PMP) to establish necessary conditions for optimality, resulting in a two-point boundary value problem (TPBVP) that involves both state and costate variables within a system of ordinary differential equations (ODEs). By modelling the unknown solutions of the TPBVP with neural networks, PoNNs effectively learn the optimal control strategies. We also derive upper bounds on the generalisation error of PoNNs in solving these OCPs, taking into account the selection and quantity of training points along with the training error. To validate our theoretical analysis, we perform numerical experiments on benchmark linear and nonlinear OCPs. The results indicate that PoNNs can successfully learn open-loop control actions for the considered class of OCPs, outperforming the commercial software GPOPS-II in terms of both accuracy and computational efficiency. The reduced computational time suggests that PoNNs hold promise for real-time applications.

Regulating the Spin-State of Cobalt in Three-Dimensional Covalent Organic Frameworks for High-Performance Sodium-Iodine Rechargeable Batteries.

Although the catalytic activity is heavily reliant on the electronic structure of the catalyst, understanding the impact of electron spin regulation on electrocatalytic performance is still rarely investigated. This work presents a novel approach involving the single-atom coordination of cobalt (Co) within metalloporphyrin-based three-dimensional covalent organic frameworks (3D-COFs) to facilitate the catalytic conversion for sodium-iodine batteries. The spin state of Co is modulated by altering the oxidation state of the porphyrin-centered Co, achieving optimal catalysis for iodine reduction. Experimental results demonstrate that CoII and CoIII are incorporated into the 3D-COFs, exhibiting spin ground states of S=1/2 and S=0, respectively. The low spin state of CoIII is favorable to hybridize with the sp 3d orbitals of I3 -, thus facilitating the conversion of I3 - to I-. Density-functional theory (DFT) calculations further reveal that the presence of CoIII enhances iodide adsorption and accelerates the formation of NaI in 3D-COFs-CoIII, thereby promoting its rapid kinetic behaviors. Notably, the I2@3D-COFs-CoIII cathode achieves a high reversible capacity of 227.7 mAh g-1 after 200 cycles at 0.5 C and demonstrates exceptional cyclic stability, exceeding 2000 cycles at 10 C with a minor capacity fading rate of less than one 0.01 % per cycle.

Regulating the Spin‐State of Cobalt in Three‐Dimensional Covalent Organic Frameworks for High‐Performance Sodium‐Iodine Rechargeable Batteries

AbstractAlthough the catalytic activity is heavily reliant on the electronic structure of the catalyst, understanding the impact of electron spin regulation on electrocatalytic performance is still rarely investigated. This work presents a novel approach involving the single‐atom coordination of cobalt (Co) within metalloporphyrin‐based three‐dimensional covalent organic frameworks (3D‐COFs) to facilitate the catalytic conversion for sodium‐iodine batteries. The spin state of Co is modulated by altering the oxidation state of the porphyrin‐centered Co, achieving optimal catalysis for iodine reduction. Experimental results demonstrate that CoII and CoIII are incorporated into the 3D‐COFs, exhibiting spin ground states of S=1/2 and S=0, respectively. The low spin state of CoIII is favorable to hybridize with the sp 3d orbitals of I3−, thus facilitating the conversion of I3− to I−. Density‐functional theory (DFT) calculations further reveal that the presence of CoIII enhances iodide adsorption and accelerates the formation of NaI in 3D‐COFs‐CoIII, thereby promoting its rapid kinetic behaviors. Notably, the I2@3D‐COFs‐CoIII cathode achieves a high reversible capacity of 227.7 mAh g−1 after 200 cycles at 0.5 C and demonstrates exceptional cyclic stability, exceeding 2000 cycles at 10 C with a minor capacity fading rate of less than one 0.01 % per cycle.

Process and mechanism of Zn and Co leaching from cobalt xanthate slag enhanced by oxidative roasting

Cobalt xanthate slag is the waste slag produced by the use of xanthate cementation and decontamination before the wet refining and electrowinning of Zn, in which Zn, Co, Cd, etc., and butyl xanthate exist in the form of hydrophobic complexes, which are poorly soluble with water. In addition, most of the cobalt xanthate in the slag exists in the form of high-valent Co, which lowers the extraction rate when directly leaching the metal elements. In this study, the atmosphere of the roasting process is regulated to destroy the hydrophobic complexes and change the mineral phase structure of the cobalt xanthate slag. In the cobalt xanthate slag, the Co and Fe valence states change during the roasting and leaching steps; specifically, during the roasting process, the complexes first decompose into CS2, reducing part of the Co3+. Following the disappearance of this sulfur-rich environment, the oxygen in the flowing air oxidises Fe2+ to Fe3+, but the valence state of Co remains unchanged. During the subsequent leaching process, Co3+ and Fe2+ further react to realise the benign transformation of Co3+ to Co2+ and Fe2+ to Fe3+ without an added redox agent. The rapid redox reaction between Co3+ and Fe2+ controls Co3O4 dissolution; thus, the reaction rate is controlled by the slower process of internal diffusion. Under the optimal roasting conditions, the Co3+ content in cobalt xanthate slag decreases to 21.10 % and that of Fe2+ to 48.78 %. Consequently, the optimum Zn and Co leaching rates reach 99.92 % and 99.57 %, respectively, and only 0.86 % of Fe in the final leaching solution exists in the form of Fe2+.

Occurrence and enrichment of critical metals in ferromanganese deposits in the western Pacific

Co-rich ferromanganese nodules and crusts are economically valuable deep-sea ferromanganese deposits widely distributed in the western Pacific Ocean and are rich in critical metals such as Co, Ni, Cu and rare earth elements (REEs). However, the lack of fine delineation and systematic comparisons of the distributions of these critical metals in these ferromanganese deposits limits the understanding of the occurrence states of Co, Ni, Cu and REEs and the metallogenesis of ferromanganese deposits. Therefore, the authors selected one nodule and one crust from the western Pacific Ocean, and utilized high-resolution methods such as micro-area X-ray fluorescence spectrometry (μ-XRF), laser-ablation inductively-coupled plasma time-of-flight mass spectrometry (LA-ICP-TOF-MS), and laser-ablation inductively-coupled plasma mass spectrometry (LA-ICP-MS) to depict elemental distribution and elemental profile.The results show that the ferromanganese deposits are predominantly composed of Fe-vernadite with low Mn/Fe ratios. Co, Ni and Cu exist primarily in the manganate octahedral layer of Fe-vernadite. REEs mostly exist in feroxyhite of Fe-vernadite, and manganate octahedral layer of Fe-vernadite also have high Ce content. Co, Ni and Cu contents of ferromanganese deposits are closely correlated with Mn/Fe ratios: Co, Ni and Cu contents increase with Mn/Fe ratios until the Mn/Fe ratios rises up to 4, and remain stable when Mn/Fe ratios > 6. The enrichment of Co, Ni and Cu in ferromanganese deposits is controlled by the redox conditions of seawater during accretion, whereas REEs enrichment is related to Mn and Fe fluxes in seawater during accretion. The coupling relationships between elemental distributions help to reveal the elemental occurrence state, and the geochemistry of ferromanganese deposits are analyzed to identify element enrichment mechanism.

OPTIMIZING ROYALTY PAYMENTS FOR MAXIMUM ECONOMIC BENEFIT: A CASE STUDY UTILIZING MODIFIED SHOOTING AND DISCRETIZATION METHODS

This research delves into the application of the modified shooting method for the numerical resolution of non-standard optimal control (OC) problems. More precisely, it concentrates on scenarios where the final state value component remains unknown and unconstrained, leading to a non-zero final shadow value or costate variable. Moreover, the objective function involved a piecewise royalty function, which poses a challenge due to its lack of differentiability within a specific time interval. Consequently, the novel modified shooting method was employed to ascertain the elusive final state value. The model’s differentiability is maintained throughout by adopting a continuous hyperbolic tangent (tanh) approximation. In addition, the construction of the Sufahani-Ahmad-Newton-Golden-Royalty Algorithm (SANGRA) and Sufahani-Ahmad-Powell-Golden-Royalty Algorithm (SAPGRA) was accomplished using the C++ programming language to formulate the problem. The outcomes of these algorithms, satisfying the criteria for optimality, were juxtaposed with non-linear programming (NLP) techniques such as Euler and Runge-Kutta, aside from Trapezoidal and Hermite-Simpson approximations. This groundbreaking discovery carries extensive practical implications as it propels the field forward and ensures the application of contemporary problem-solving methodologies. Moreover, the study underscores the significance of fundamental theory in effectively tackling current economic challenges.

Enhanced energy storage efficiency of an innovative three-dimensional nickel cobalt metal organic framework nanocubes with molybdenum disulphide electrode material as a battery-like supercapacitor

Recently, metal-organic frameworks (MOFs) with transition metal sulfides have gained much attention as electrode materials for supercapacitors (SCs). In this work, 3D-NCMOF@MS NCs, incorporating two-dimensional molybdenum disulphide (2D-MS) nanosheets and three-dimensional nickel cobalt-MOF nanocubes (3D-NCMOF NCs) are synthesized by a solvothermal and precipitation process. Owing to their enhanced electrical conductivity and huge surface area, the 3D-NCMOF@MS NCs produce superior electrochemical responses in SCs compared to 2D-MS and 3D-NCMOF NCs. The results demonstrate that the synergistic 3D-NCMOF@MS NCs increased specific capacitance up to 1048 Fg−1 at 1 Ag−1, revealing outstanding cycle stability with a capacitance retention of 99.06 %. Besides, the exposed high-power density of 3D-NCMOF@MS NCs reached 400 W kg−1 as well as an outstanding maximum energy density of 188.64 Wh kg−1. Such synergistic effects of the multivalent states of Ni, Co, and Mo promote electrochemical characteristics, implying that the 3D-NCMOF@MS NCs could potentially be used in energy storage systems, boosting electrochemical performance.

Theoretical investigations of optoelectronic properties, photocatalytic performance as a water splitting photocatalyst and band gap engineering with transition metals (TM = Fe and Co) of K3VO4, Na3VO4 and Zn3V2O8: a first-principles study.

First-principles density functional investigations of the structural, electronic, optical and thermodynamic properties of K3VO4, Na3VO4 and Zn3V2O8 were performed using generalized gradient approximation (GGA) via ultrasoft pseudopotential and density functional theory (DFT). Their electronic structure was analyzed with a focus on the nature of electronic states near band edges. The electronic band structure revealed that between 6% Fe and 6% Co, 6% Co significantly tuned the band gap with the emergence of new states at the gamma point. Notable variations were highlighted in the electronic properties of Na3V(1-x)Fe x O4, Na3V(1-x)Co x O4, K3V(1-x)Fe x O4, K3V(1-x)Co x O4, Zn3(1-x)V2(1-x)Co x O8 and Zn3(1-x)V2(1-x)Fe x O8 (where x = 0.06) due to the different natures of the unoccupied 3d states of Fe and Co. Density of states analysis as well as α (spin up) and β (spin down) magnetic moments showed that cobalt can reduce the band gap by positioning the valence band higher than O 2p orbitals and the conduction band lower than V 3d orbitals. Mulliken charge distribution revealed the presence of the 6s2 lone pair on Zn, greater population and short bond length in V-O bonds. Hence, the hardness and covalent character develops owing to the V-O bond. Elastic properties, including bulk modulus, shear modulus, Pugh ratio and Poisson ratio, were computed and showed Zn3V2O8 to be mechanically more stable than Na3VO4 and K3VO4. Optimal values of optical properties, such as absorption, reflectivity, dielectric function, refractive index and loss functions, demonstrated Zn3V2O8 as an efficient photocatalytic compound. The optimum trend within finite temperature ranges utilizing quasi-harmonic technique is illustrated by calculating thermodynamic parameters. Theoretical investigations presented here will open up a new line of exploration of the photocatalytic characteristics of orthovanadates.

Heat-Equation-Based Smoothing Homotopy Method for Nonlinear Optimal Control Problems

This paper presents a new heat-equation-based smoothing homotopy method for solving nonlinear optimal control problems with the indirect method. The surrogates, derived from the heat equation solution, are first incorporated into the necessary conditions as replacement of the terminal state and costate variables. The homotopy process is then applied to the heat conduction time: a longer time results in a more uniform temperature distribution and greater stability against initial temperature variations, thereby making the corresponding homotopy problem much easier to solve; zero time implies no heat conduction and reverts to the original problem. Furthermore, capitalizing on the heat equation’s boundedness characteristic, an efficient approach for determining the hypersensitive parameters is proposed, thus obviating the necessity of manual tuning. Challenging numerical examples are provided to demonstrate the superior performance of the proposed method, indicating that its convergence and efficiency are significantly enhanced compared to the original smoothing homotopy methods.

Synergistic interface engineering of ZnCo2O4/NiMnCo-layered double hydroxides for boosted reactivity in advanced supercapacitor electrodes

NiMn layered double hydroxide (LDH) exhibits high redox activity as a cathode material for hybrid supercapacitors, but it has the disadvantages of low conductivity and poor stability. In this work, the electrochemical properties of NiMnCo-LDH with different Co contents prepared by electrodeposition were tested. The results showed that the addition of an appropriate amount Co increased the adsorption of OH− on NiMn-LDH and improved the reactivity of the material. ZnCo-MOF grown on carbon cloth was transformed into flake ZnCo2O4 by calcination, and NiMnCo-LDH was electrodeposited on it to prepare ZnCo2O4/NiMnCo-LDH composite electrode. The core-shell structure increases the reaction area between the LDH material and the electrolyte. Physical characterization and density functional theory (DFT) calculations show that the structure and electronic distribution of ZnCo2O4/NiMnCo-LDH at the heterogeneous interface are reconstructed, which increases the valence state of Co and Mn elements, and finally exhibits enhanced electrochemical performance. Due to the existence of this synergistic effect, the specific capacity of the electrode is as high as 231.5 mAh g−1, with excellent stability demonstrated after 5000 cycles compared to the NiMnCo-LDH. The assembled hybrid supercapacitor exhibits a high energy density of 39.4 Wh kg−1, and has high cycle stability (90 % after 5000 cycles).

Comparison between Co(II) and Ni(II) cycling at goethite-water interfaces: Interplay with Fe(II)-catalyzed recrystallization

Cobalt (Co) and nickel (Ni) are critical metals for modern renewable energy technologies as well as essential micronutrients for terrestrial plant health and marine primary production. Both metals are commonly surface-adsorbed onto and/or structurally-incorporated into iron (oxyhydr)oxide minerals, such as goethite (α-FeOOH), that are ubiquitously present in soils and sediments at the Earth’s surface. In sub- and anoxic environments, aqueous ferrous iron (Fe(II)) generated from dissimilatory Fe(III) reduction can induce the recrystallization of goethite and subsequently influences the speciation and mobilization of associated metals, e.g., Co(III) being reduced to Co(II). While it is generally considered that divalent Co and Ni behave similarly at goethite-water interfaces, there lacks a direct comparison of their cycling through goethite in response to Fe(II)-catalyzed recrystallization. Here, under circumneutral anoxic conditions with and without addition of aqueous Fe(II), we performed batch reaction experiments on Co(II)-substituted goethite and Co(II) and Ni(II) sorption experiments on pure goethite. The redox state and coordination environment of Co associated with goethite were determined using high energy resolution fluorescence detected X-ray absorption spectroscopy at the Co K-edge, and the distribution of solid-bound Co and Ni in goethite following sorption was revealed by sequential dissolution. Our results show that substitution of Co(II) for Fe(III) in goethite has less negative feedback on Fe(II)-catalyzed recrystallization than Ni(II), which may be related to their differing structural distortions as evidenced by EXAFS. In the absence of Fe(II), aqueous Co(II) is more favourably adsorbed onto and incorporated deeper into goethite than Ni(II), suggesting that Co(II) is more structurally compatible with goethite. The presence of Fe(II) markedly enhances the structural incorporation of both Co(II) and Ni(II) as a result of goethite recrystallization, which in turn can be inhibited by the accumulation of metals at the mineral surface. Furthermore, structurally-incorporated Co(II) is more difficult to be released back into solution (i.e. sum of aqueous and extract fractions) than Ni(II) during Fe(II)-catalyzed goethite recrystallization. Overall, our work highlights the significant differences between Co(II) and Ni(II) in their cycling at goethite-water interfaces and intricate interplay with Fe(II)-catalyzed recrystallization. This improves our understanding of their mobilization and distribution in anoxic goethite-rich systems and can provide useful insights for their enrichment and extraction from natural and artificial laterites generated from the enhanced weathering of ultramafic mine tailings.

Co(III)–Co(II)–Co(III) edge-sharing trinuclear complexes having the doubly methoxido-bridged core bridged by acetato ligand

Two trinuclear cobalt complexes with the edge-sharing linear-type framework having benzylbis(2-pyridylmethyl)amine (bbpma), [{CoIII(bbpma)(μ-O2CCH3)(μ-OCH3)2}2CoII](X)2 (X=ClO4; [1](ClO4)2, X =PF6; [1](PF6)2), and one corresponding complex having ethylbis(2-pyridylmethyl)amine (ebpma), [{CoIII(ebpma)(μ-O2CCH3)(μ-OCH3)2}2CoII](PF6)2 ([2](PF6)2), were synthesized and the crystallographic and electronic structures were investigated. X-ray crystallography and magnetic measurements suggested that [1](PF6)2 and [2](PF6)2 were in the mixed-valent state and the mixed-spin state of Co(III)–Co(II)–Co(III) (LS-HS-LS), in which the electron spins were much localized on the central Co(II).

Mainardi smoothing homotopy method for solving nonlinear optimal control problems

This paper proposes a new type of smoothing homotopy method for solving general nonlinear optimal control problems via the indirect method, leveraging the Mainardi kernel as the smoothing kernel. The Mainardi kernel is firstly derived from the fundamental solution of the time-fractional diffusion-wave equation, representing a generalized form of the Gaussian kernel. By altering the fractional derivative order, the kernel can seamlessly switch between non-Gaussian and Gaussian forms. Then, parts of the two-point boundary value problems are convolved with the smoothing kernel, and the resulting surrogates are incorporated into the necessary conditions, replacing the terminal state and costate variables. The homotopy process is used for the smoothing parameter: increasing this parameter enhances the smoothing effect, simplifying the homotopy problems, while a parameter value of zero implies no smoothing, reverting to the original problems. Additionally, explicit expressions for the Mainardi kernel at specific derivative orders are derived, avoiding the inefficiencies associated with fractional derivatives. Simulation examples demonstrate that the proposed method offers significant advantages in flexibility and convergence compared to the traditional Gaussian smoothing homotopy method.