Multistep Transitions Research Articles

Ising-Like Model Hasn't Yet Said Its Last Word: Exact and Mean-Field Investigations of 2, 3 and 4-Body Interactions in 1D Ising Chain of Binuclear Spin-Crossover Solids.

We investigate the static properties of a new class of 1D Ising-like Hamiltonian for binuclear spin-crossover materials accounting for two-, three-, and four-body short-range interactions between binuclear units of spins and . The following 2-, 3-, and 4-body , , and terms are considered, in addition to intra-binuclear interactions, such as effective ligand-field energy and exchange-like coupling. An exact treatment is carried out within the frame of the transfer matrix method, leading to a 4×4 matrix from which, we obtained the thermal evolution of the thermodynamic quantities. Several situations of model parameter values were tested, among which that of competing intra- and inter-molecular interactions, leading to the occurrence of (i) one-step spin transition, (ii) two-, three-, and four-step transitions, obtained with a reasonable number of parameters. To reproduce first-order phase transitions, we accounted for inter-chains interactions, treated in the mean-field approach. Hysteretic multi-step transitions, recalling experimental observations, are then achieved. Overall, the present model not only suggests new landscapes of interaction configurations between SCO molecules but also opens new avenues to tackle the complex behaviors often observed in the properties of SCO materials.

Origins of Severe Structural Changes during Alloying-Dealloying Reactions in Black Phosphorus.

Li-alloying reactions facilitate the incorporation of a large number of Li atoms into the crystalline structures of electrodes, such as black phosphorus (BP). However, the reactions inevitably induce multistep phase transitions characterized by drastic atomic rearrangements and lattice collapse. Despite many theoretical and experimental studies on alloying mechanisms, long-term debates persist regarding the structures of the intermediate phases, the accurate pathways of phase transitions, the formation of specific configurations, and alloying/dealloying reversibility. Here, through a combination of operando electron diffraction measurements and ab initio simulations at the atomic and electronic scales, we identify key factors that govern the severe structural changes during alloying-dealloying reactions in BP. P-P bonds of three-bond P atoms are continuously broken during lithiation, generating two-bond P atoms with a high ability to accept inserted electrons and Li ions. Consequently, the pristine layered structure in BP is transformed to P7 cages in Li3P7, which then evolve to chain configurations in LiP and finally to isolated P atoms in Li3P. Specifically, the preferential formation of the P7 cage results from its lowest binding energy with three Li ions compared to other cage isomers. Furthermore, only LiP can be reversibly transformed to the crystalline structure of Li3P7 during charge, but it is thermodynamically favorable for Li3P7 and Li3P intermediates to be delithiated to amorphous structures. Our findings offer unique insights into the alloying mechanisms and deepen the fundamental understanding of alloying anode systems.

A Na-Free Surface Enables "Three-In-One" Enhancement of Structural, Interfacial and Air Stability for Sodium-Ion Battery Cathodes.

O3-type layered oxides are regarded as one of the most promising cathode materials for sodium-ion batteries. However, the multistep phase transitions, severe electrode/electrolyte parasitic reactions, and moisture sensitivity are challenging for their practical application because of the highly active Na+. Here, a Na-free layer is built on the surface of NaNi1/3Mn1/3Fe1/3O2 (NMF111) via a leaching treatment and the subsequent surface reconstruction. Accordingly, both the structural degradation from bulk to surface and the overgrowth of the solid electrolyte interface (SEI) are greatly ameliorated, which results in the improved capacity retention of modified NMF111 from 58.3% to 89.6% after 400 cycles at 1 C. Besides, the Na-free surface with rock-salt structure prevents the H+/Na+ exchange and then enables good reversibility and low polarization of the optimal NMF111 when exposed to wet air (50% RH) for 4 days. This work opens a new avenue for the comprehensive cyclability improvement of layered oxides via surface reconstruction.

Effect of Solvent Properties on the Critical Solution Temperature of Thermoresponsive Polymers.

The ability of thermoresponsive polymers to respond to temperature with a reversible conformational change makes them promising 'smart' materials for solutions in medical and biotechnological applications. In this work, two such polymers and structural isomers were studied: poly(N-isopropyl acrylamide) (PNiPAm) and poly(2-isopropyl-2-oxazoline) (PiPOx). We compare the critical solution temperatures (CST) of these polymers in D2O and H2O in the presence of Hofmeister series salts, as results obtained under these different solvent conditions are often compared. D2O has a higher dipole moment and electronegativity than H2O, which could significantly alter the CST transition. We used two complementary methods to measure the CST, dynamic light scattering (DLS) and differential scanning calorimetry (DSC) and found that the CST decreased significantly in D2O compared to H2O. In the presence of highly concentrated kosmotropes, the CST of both polymers decreased in both solvents. The influence of the kosmotropic anions was smaller than the water isotope effect at low ionic strengths but considerably higher at physiological ionic strengths. However, the Hofmeister anion effect was quantitatively different in H2O than in D2O, with the largest relative differences observed for Cl-, where the CSTs in D2O decreased more than in H2O measured by DLS but less by DSC. PiPOx was more sensitive than PNiPAm to the presence of chaotropes. It exhibited much higher transition enthalpies and multistep transitions, especially in aqueous solutions. Our results highlight that measurements of thermoresponsive polymer properties in D2O cannot be compared directly or quantitatively to application conditions or even measurements performed in H2O.

Charge-breaking domain walls separating neutral vacua in multi-Higgs models

The scalar potential of a multi-Higgs model can possess a rich structure of minima and saddle points, which evolves in an intricate way as the parameters change. In the hot early Universe, it could trigger multistep phase transitions, with exotic intermediate phases and peculiar domain wall configurations. Here, we provide a glimpse into this richness with the example of the three-Higgs-doublet model with the symmetry group Σ(36), either exact or softly broken. We present its phase diagram tracking not only the global minimum but all of its extrema. In particular, we reveal parameter space regions in which the deepest saddle point is charge breaking. This naturally leads to phase transitions between neutral vacua which involve expanding and colliding charge-breaking bubble walls. We also comment on opportunities of multistep phase transitions, on charge-breaking intermediate phases, and on phase transitions between different charge-breaking vacua. We illustrate the general discussion with two benchmark models, one of which possesses competing saddle points and allows for emergence of bubbles of the same true vacuum but with bubble walls of different nature. The intriguing cosmological implications of all these possibilities deserve dedicated study. Published by the American Physical Society 2024

Disparity-driven heterogeneous nucleation in finite-size adaptive networks.

Phase transitions are crucial in shaping the collective dynamics of a broad spectrum of natural systems across disciplines. Here, we report two distinct heterogeneous nucleation facilitating single step and multistep phase transitions to global synchronization in a finite-size adaptive network due to the trade off between time scale adaptation and coupling strength disparities. Specifically, small intracluster nucleations coalesce either at the population interface or within the populations resulting in the two distinct phase transitions depending on the degree of the disparities. We find that the coupling strength disparity largely controls the nature of phase transition in the phase diagram irrespective of the adaptation disparity. We provide a mesoscopic description for the cluster dynamics using the collective coordinates approach that brilliantly captures the multicluster dynamics among the populations leading to distinct phase transitions. Further, we also deduce the upper bound for the coupling strength for the existence of two intraclusters explicitly in terms of adaptation and coupling strength disparities. These insights may have implications across domains ranging from neurological disorders to segregation dynamics in social networks.

CFD simulation of solid/liquid phase change in commercial PCMs using the slPCMlib library

Modelling the solidification and melting behavior of phase change materials (PCMs) can present several challenges, including non-isothermal phase change, multi-step transitions, complex enthalpy-temperature relations and convective heat transfer. To tackle these challenges, this study proposes a novel numerical method based on real experimental data for modelling complex phase change behavior of commercial PCMs in Ansys Fluent CFD software. The phase transition of PCMs is simulated with the apparent heat capacity (AHC) method, which is implemented as a User-Defined Function (UDF). Heat convection is simulated with the Boussinesq approximation. The method is validated by comparing to the Ansys Fluent built-in Solidification and Melting (S&M) model for the case of piecewise constant heat capacity. The results show that AHC method provides excellent agreement with S&M model for a piecewise constant heat capacity model. In addition, the AHC method solves convergence problems even for narrow phase change temperature ranges when a smooth heat capacity function is assumed. Finally, the AHC model is also tested on a set of commercial PCMs exhibiting complex phase change behavior. Temperature dependent specific heat capacities are determined from heat capacity data provided by PCM manufacturing companies and are imported as cubic Hermite spline functions from the solid-liquid phase change material library slPCMlib available at https://slpcmlib.ait.ac.at/. From the presented case study and tested PCMs it can be concluded that the AHC method is numerically robust when used with sufficiently smooth heat capacity functions, and it can be recommended for the analysis of heat transfer with PCMs showing a complex phase change behavior.

Three-Step Ferroelastic Transitions from Hexagonal to Triclinic Phases in a Hybrid Perovskite: (1-Fluoromethyl-1-methylpyrrolidine)[CdCl3

Hybrid ferroelastic crystals have emerged as a hot research topic in recent years owing to their prospective applications in piezoelectric sensors, mechanical switches, and optoelectronic devices. Nevertheless, most of the documented materials exhibit one-step or two-step ferroelastic phase transition(s), and those with multistep ferroelastic transitions are extremely scarce. We present a new hexagonal molecular perovskite based on a fluoro-substituted flexible cyclic ammonium cation, (1-fluoromethyl-1-methylpyrrolidine)[CdCl3] (1), undergoing unusual three-step ferroelastic phase transitions from hexagonal paraelastic phase to orthorhombic, monoclinic, and triclinic ferroelastic phases at 388, 376, and 311 K, respectively, with Aizu notation of 6/mmmFmmm, mmmF2/m, and 2/mF-1, featuring spontaneous strain of 0.002, 0.023, and 0.110, respectively. Furthermore, variable-temperature single-crystal diffraction reveals that the phase-transition mechanism in 1 principally originates from intriguing dynamic change of organic cations and synchronous displacement of inorganic chains. This scarce instance of multistep hybrid ferroelastic provides important clues for finding advanced ferroelastic materials.

Strength-ductility materials by engineering a coherent interface at incoherent precipitates.

In the quest for excellent light-structural materials that can withstand mechanical extremes for advanced applications, design and control of microstructures beyond current material design strategies have become paramount. Herein, we design a coherent shell at incoherent precipitates in the 2195 aluminum alloy with multi-step metastable phase transitions. A high local strain rate via a neoteric deformation-driven metallurgy method facilitated the diffusion of Li. The original T1 (Al2CuLi) phases were transformed into coherent-shell (Li-rich) irregular-coated incoherent-core (Al2Cu) precipitates. The ultimate tensile strength and elongation reached 620 ± 18 MPa and 22.3 ± 2.2%, exhibiting excellent strength-ductility synergy. Grain boundaries, dislocation, solid solution atoms, and precipitates all contributed to the yield strength of the materials, among which precipitates occupied a dominant position, contributing approximately 56.07%. A new "incoherent-coherent interact" strain-hardening mechanism was also clarified, which was believed to be promoted in other heat-treatable alloy systems, especially with multi-step metastable phase transitions.

Multistep transitions in spin crossover materials without long-range spin state order from dimensional reduction

The interplay of distinct metal centres with elastic interactions causes multistep spin crossover with disordered spin states in the intermediate phases; via a reduction in the effective dimensionality of the material due to partial spin state order.

Hydrophobicity as a tool for programming sequential mesophase transitions of enzyme-responsive polymeric amphiphiles.

The ability of polymeric assemblies to undergo programmable cascades of mesophase transitions is prevalent in many systems in nature, where structural and functional features are tightly bound to maximize activity. In this study, we have examined the ability to program the mesophase transition rates of co-assembled enzyme-responsive polymeric micelles, through fine adjustments of the hydrophobicity of their amphiphilic components. We have utilized the different reactivities of di- and tri-block amphiphiles toward enzymatic degradation as a tool for programming formulations to undergo sequential enzymatically induced transitions from micelles to hydrogels and finally to dissolved polymers. By varying the aliphatic end-groups of PEG-dendron di-block and tri-block amphiphiles, we could demonstrate the remarkable impact of minor modifications to the di-block amphiphiles' structure and hydrophobicity on the transition rates between the different mesophases, ranging from a few hours to a week. Additionally, the study reveals how altering the relative hydrophobicity of its amphiphilic components influences the formulation ratio and enzymatic selectivity, as well as the stability and degradation rate of the resulting hydrogels. The findings underscore the importance of molecular architecture and hydrophobicity as key parameters in the design of programmable enzyme-responsive polymeric assemblies, offering insights into the ability to precisely control multi-step mesophase transitions for tailored functionality.

Complex relaxation of trapped spin-states in spin crossover materials.

A diverse range of relaxation dynamics of trapped spin-states are observed in spin crossover (SCO) materials, including exponential, sigmoidal, stretched exponential, multi-step, and mixed kinetics. We reproduce and explain this full range of relaxation behaviours using a semi-empirical, semi-classical model that combines crystal field theory with elastic inter-molecular interactions. We show that frustrated intermolecular interactions, which are responsible for multistep thermal transitions, also lead to multiple energetically competitive ordered phases, even in systems that contain only one crystallographically distinct SCO site. This rugged free energy landscape leads to dynamic disorder and thence the complex dynamics widely observed in SCO materials. Similar mechanisms are vital for understanding dynamics of more complex materials from proteins to quantum materials.

Interfacial Synergy in Mo2C/MoC Heterostructure Promoting Sequential Polysulfide Conversion in High-Performance Lithium-Sulfur Battery.

A rational design of sulfur host is the key to conquering the"polysulfide shuttle effects" by accelerating the polysulfide conversion. Since the process involves solid-liquid-solid multistep phase transitions, purposely-engineered heterostructure catalysts with various active regions for catalyzing conversion steps correspondingly are beneficial to promote the overall conversion process. However, the functionalities of the materials surface and interface in heterostructure catalysts remain unclear. In this work, an Mo2C/MoC catalyst with abundant Mo2C surface-interface-MoC surface tri-active-region is developed by in situ converting the MoZn-metal organic framework. The experimental and simulation studies demonstrate the interface can catch long-chain polysulfides and promote their conversion. Instead, the Mo2C and MoC tend to accommodate the short-chain polysulfide and accelerate their conversion and the Li2S dissociation. Benefitting from the high catalytic ability, the Li-S battery assembled with the Mo2C/MoC-S cathode shows more discrete redox reactions and delivers a high initial capacity of 1603.6 mAh g-1 at 1 C charging-discharging rate, which is over twofolds of the one assembled using individual hosts, and 80.4% capacity can be maintained after 1000 cycles at 3 C rate. This work has demonstrated a novel synergy between the interface and material surface, which will help the future design of high-performance Li-S batteries.

Electroweak phase transition in a right-handed neutrino superfield extended NMSSM

Supersymmetric models with singlet extensions can accommodate single- or multi-step first-order phase transitions (FOPT) along the various constituent field directions. Such a framework can also produce Gravitational Waves, detectable at the upcoming space-based interferometers, e.g., U-DECIGO. We explore the dynamics of electroweak phase transition and the production of Gravitational Waves in an extended set-up of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) with a Standard Model singlet right-handed neutrino superfield. We examine the role of the new parameters compared to NMSSM on the phase transition dynamics and observe that the occurrence of a FOPT, an essential requirement for Electroweak Baryogenesis, typically favours a right-handed sneutrino state below 125 GeV. Our investigation shows how the analysis can offer complementary probes for physics beyond the Standard Model besides the collider searches.

Electro-Elastic Modeling of Multi-Step Transitions in Two Elastically Coupled and Sterically Frustrated 1D Spin Crossover Chains

One-dimensional spin crossover (SCO) solids that convert between the low spin (LS) and the high spin (HS) states are widely studied in the literature due to their diverse thermal and optical characteristics which allow obtaining many original behaviors, such as large thermal hysteresis, incomplete spin transitions, as multi-step spin transitions with self-organized states. In the present work, we investigate the thermal behaviors of a system of two elastically coupled 1D mononuclear chains, using the electro-elastic model, by including an elastic frustration in the nearest neighbors (nn) bond length distances of each chain. The chains are made of SCO sites that are coupled elastically through springs with their nn and next-nearest neighbors. The elastic interchain coupling includes diagonal springs, while the nn inter-chain distance is fixed to that of the high spin state. The model is solved using MC simulations, performed on the spin states and the lattice distortions. When we only frustrate the first chain, we found a strong effect on the thermal dependence of the HS fraction of the second chain, which displays an incomplete spin transition with a significantly lowered transition temperature. In the second step, we frustrate both chains by imposing different frustration rates. Here, we demonstrate that for high frustration values, the thermal dependence of the total HS fraction exhibits multi-step spin transitions. The careful examination of the spin state structures in the plateau regions showed the coexistence of special dimerized ferro–antiferro patterns of type LL-HH-LL-HH along the first chain and HH-LL-HH-LL (H=HS and L=LS) along the second one, revealing that the two chains are antiferro-elastically coupled. This type of spatial modulation of the spin state and bond length distances is very attractive because it anticipates the possible existence of periodic structures in 2D lattices, made of alternate 1D SCO strings with HLHLHL structures, coupled in the ferro-like fashion along the interchain direction.

Suppression of multistep phase transitions of O3-type cathode for sodium-ion batteries

O3-type layered oxide cathodes have been widely investigated due to their high reversible capacities and sufficient Na+ reservoirs. However, such materials usually suffer from complex multistep phase transitions along with drastic volume changes, leading to the unsatisfied cycle performance. Herein, we report a Mg/Ti co-doped O3-type NaNi0.5Mn0.5O2, which can effectively suppress the complex multistep phase transition and realize a solid-solution reaction within a wide voltage range. It is confirmed that, the Mg/Ti co-doping is beneficial to enhance the structural stability and integrity by absorbing micro-strain and distortions. Thus, the as obtained sample delivers an outstanding cyclic performance (82.3% after 200 cycles at 1 C) in the voltage range of 2.0–4.0 V, and a high discharge capacity of 86.6 mAh/g after 100 cycles within the wide voltage range (2.0–4.5 V), which outperform the existing literatures. This co-doping strategy offers new insights into high performance O3-type cathode for sodium ion batteries.

Multi-step phase transitions and gravitational waves in the inert doublet model

The inert doublet model is a well-motivated extension of the Standard Model that contains a dark matter candidate and modifies the dynamics of the electroweak symmetry breaking. In order to detail its phenomenology, we perform a comprehensive study of cosmic phase transitions and gravitational wave signals implied by the framework, accounting for the latest results of collider experiments. We require the neutral inert scalar to constitute, at least, a subdominant part of the observed dark matter abundance. While most of the phase transitions proceed through a single step, we identify regions of the parameter space where the electroweak vacuum is reached after multiple phase transitions. The resulting gravitational wave spectrum is generally dominated by single-step transitions and, in part of the parameter space, falls within the reach of future gravitational wave detectors such as LISA, BBO or DECIGO. We find that direct detection experiments efficiently probe the part of parameter space associated with multi-step phase transitions, which remain unconstrained only in the Higgs resonance region testable with future monojet searches. The implications of the new determination of the W boson mass are also discussed.

Partially Oxidized Purely Organic Zwitterionic Neutral Radical Conductor: Multi-step Phase Transitions and Crossover Caused by Intra- and Intermolecular Electronic Interactions.

Formation of a partially charge-transfer or partially oxidized/reduced state has been one of the most important requirements for the development of highly conducting molecular materials, such as organic metals and superconductors. This requirement has been fulfilled by combining appropriate electron-donor and acceptor molecules to construct multi-component molecular complexes/salts, such as (TTF+0.59)(TCNQ-0.59) and (BEDT-TTF+0.5)2X-, where TTF = tetrathiafulvalene, TCNQ = tetracyanoquinodimethane, BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene, and X = monovalent inorganic anion. Here, we propose a methodology to fulfill this requirement by a single neutral molecule; namely, we have connected two TTF+0.5-type partially oxidized π-skeletons through a boron anion to design a purely organic zwitterionic neutral radical {[(PDT-TTF-Cat)2]+B-}•. This molecule was successfully obtained as air-stable crystals containing solvent tetrahydrofuran (THF) molecules. Measurements of electrical resistivity, magnetic susceptibility, and X-ray diffraction reveal that the partially oxidized state is certainly formed, which enables realization of a 3/4-filled electron band. Furthermore, this system has intramolecular charge degrees of freedom, attributable to the two TTF+0.5 π-skeletons introduced into the molecule. The resulting interplay of intra- and intermolecular charge degrees of freedom (or simply, intra- and intermolecular electronic interactions) has led to multi-step phase transitions and crossover, providing unique strongly correlated electron properties, such as the formation of a three-dimensional charge-ordered dimer-Mott insulating state and its melting triggered by disorder-order transformation of the co-crystallized solvent THF molecules at low temperatures.

Effect of Secondary Phases on Multi-Step Phase Transitions and Magnetocaloric Properties in MnFe-Based Alloys

This study investigated the effect of the secondary phases on multi-step phase transitions and the magnetocaloric properties depending on the Ge content in the MnFeCoPSiGe alloys. Two-step phase transitions were observed by the variations of the Fe2P-type hexagonal structure (first-order) and secondary phases (second-order). The Curie temperature alters with non-linear behavior consistent with change of the lattice parameters. In addition, the magnetic entropy change decreased with the increase of the Ge content and, subsequently, fractions of the secondary phases. However, the morphological variation of microstructure, distributed as a circular-type shape of the Fe2P-type hexagonal structure in the Ge-rich matrix, increased the magnetic entropy change. Therefore, the addition of Ge enables the control of the Curie temperature to be applicable for high temperature operating devices. The control of the secondary phases and morphology of the microstructure are crucial to improve the phase transition and magnetic entropy change.

A cocklebur-like sulfur host with the TiO2-VOx heterostructure efficiently implementing one-step adsorption-diffusion-conversion towards long-life Li–S batteries

Lithium-sulfur (Li–S) batteries are considered to be promising next-generation rechargeable system. However, the shuttle effect for lithium polysulfides (LiPSs) and slow sulfur reaction kinetics due to multistep phase transitions severely limit the practical application of Li–S batteries. Herein, via dual-strategy of heterogeneous interface and defect engineering, a cocklebur-like sulfur host with the TiO2-VOx heterostructure (CTVHs) for long-life Li–S batteries is fabricated, and atomic-level clarification of the chemical interaction between the substrate and LiPSs from a theoretical viewpoint is achieved. Benefiting from the heterostructure, the high adsorption energy heterojunction interface works as capturing centers to trap LiPSs which ensures rapid diffusion to VOx. In addition, the defect-rich spiny VOx is endowed with high catalytic activity towards LiPSs and fast lithium-ion migration so as to effectively implement one-step adsorption diffusion transformation. DFT calculations show that the introduction of a heterostructure can change the electronic structure, thereby improving the adsorption capacity of CTVHs. Electrochemical measurements reveal favorable kinetics for Li2S deposition, better cyclability, and an outstanding discharge capacity. The CTVHs/S cathode delivers a slow capacity decay rate of 0.029% per cycle and achieves nearly 100% coulombic efficiency (CE) at 0.5 C over 1400 cycles. This proposed strategy provides broad prospects to promote the adsorption-conversion of LiPSs for long-life Li–S batteries.