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At least 145 records · Page 8

Phase formation in the CaO–Al 2 O 3 –ZnO system as an analogue to CaO–Al 2 O 3 –MgO in spinel containing refractories

Recently, gahnite (ZnAl 2 O 4 ) is gaining attraction as a potential refractory ceramic because of the similarity of its structure and properties with those of magnesium aluminate (MgAl 2 O 4 ) spinel refractories. Formation of MgO and hibonite solid solution (CaMg x Al 12−x O 19−0.5x ; 0 ≤ x ≤ 0.18), CAM-I (Ca 2 Mg 2−3x Al 28+2x O 46 (0 ≤ x ≤ 0.3), and CAM-II (CaMg 2−3x Al 16+2x O 27 , 0 ≤ x ≤ 0.2) phases with platelet and interlocking microstructure in the CaO–Al 2 O 3 –MgO ternary system significantly enhances the high temperature mechanical properties of refractory castables. The CaO–Al 2 O 3 –ZnO ternary system has been studied, for the first time to our knowledge, in a selected compositional range with reference to the CaO–Al 2 O 3 –MgO system from 1650°C to 1700°C. The formation of ZnO and hibonite solid solution (CaZn x Al 12−x O 19−0.5x ; 0 < x < 0.18), CAZ-I (Ca 2 Zn 2−3x Al 28+2x O 46 ; 0 ≤ x ≤ 0.3), and CAZ-II (CaZn 2−3x Al 16+2x O 27 ; 0 ≤ x ≤ 0.2) phases with platelet and interlocking morphology have been found. The crystal structures and lattice parameters of ZnO and hibonite solid solution, CAZ-I, and CAZ-II are comparable, respectively, with MgO and hibonite solid solution, CAM-I, and CAM-II. Furthermore, CAZ-I and CAZ-II phases also form due to reaction between hibonite (CaO·6Al 2 O 3 ) and ZnAl 2 O 4 .

calcium aluminate cement↗

Accurate data-driven surrogates of dynamical systems for forward propagation of uncertainty

Stochastic collocation (SC) is a well-known non-intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full-field uncertainty propagation that characterizes the distributions of the high-dimensional solution fields of a model with stochastic input parameters. However, due to the highly nonlinear nature of the parameter-to-solution map in even the simplest dynamical systems, the constructed SC surrogates are often inaccurate. Here, this work presents an alternative approach, where we apply the SC approximation over the dynamics of the model, rather than the solution. By combining the data-driven sparse identification of nonlinear dynamics framework with SC, we construct dynamics surrogates and integrate them through time to construct the surrogate solutions. We demonstrate that the SC-over-dynamics framework leads to smaller errors, both in terms of the approximated system trajectories as well as the model state distributions, when compared against full-field SC applied to the solutions directly. We present numerical evidence of this improvement using three test problems: a chaotic ordinary differential equation, and two partial differential equations from solid mechanics.

42 ENGINEERING↗

Enhanced steam oxidation resistance of uranium nitride nuclear fuel pellets

Here, the steam oxidation resistance of UN and UN-(20 vol%)ZrN fuel pellets is evaluated to enhance understanding of steam corrosion mechanisms in advanced nuclear fuel materials. In situ neutron diffraction shows the modified UN fuel pellets form a (U 0.77 ,Zr 0.23 )N solid-solution and the sole crystalline oxidation product detected in bulk is (U 0.77 ,Zr 0.23 )O 2 . U 2 N 3 is not detected in significant quantities during the steam oxidation of UN or (U 0.77 ,Zr 0.23 )N and stable lattice parameters show that hydriding does not take place. Steam oxidation rates, obtained via sequential Rietveld refinement show how (U 0.77 ,Zr 0.23 )N has a higher activation energy (79 ± 1 kJmol -1 vs. 50 ± 5 kJmol -1 ), higher onset temperature (430 °C vs. 400 °C) and slower reaction rates for steam oxidation up to 616 °C, than pure UN. Throughout, both UN and (U 0.77 ,Zr 0.23 )N exhibit linear (non-protective) oxidation kinetics, signifying that degradation of the fuel pellets is caused by the evolution of gaseous products at the interface followed by oxide scale spallation. This quantitative and mechanistic understanding of material degradation enables better defined operating regimes and points towards (U,Zr)N solid solutions as a promising strategy for the design of advanced nuclear fuel materials with enhanced steam corrosion resistance.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Unraveling the discontinuous plastic flow of a Co-Cr-Fe-Ni-Mo multiprincipal-element alloy at deep cryogenic temperatures

We report an analysis of the discontinuous plastic flow of a multiprincipal-element alloy, Co 17.5 Cr 12.5 Fe 55 Ni 10 Mo 5 (atomic percent, at. %), in the temperature range of 0.5–4.2 K showing serrated deformation curves. Using the analytical techniques, we studied the statistics of the stress drops associated with the unstable plastic flow. The analysis showed that the complexity and heterogeneity of a discontinuous plastic flow were reduced when the temperature was lowered. This behavior was associated with the effects of dynamic recovery and adiabatic heating on the dislocation-density evolution.

36 MATERIALS SCIENCE↗

Two-stage formation-energy correction (NbZr, TaZr, VZr)

This bundle contains the scripts, the raw and corrected per-structure data, and the manuscript plots for the NbZr / TaZr / VZr BCC binary formation energies and the associated RMSDs. Why a two-stage correction is necessary: The "raw" formation energy of every relaxed VASP configuration is computed in the usual way, FE_raw(c) = E_alloy(c) - sum_i x_i * E_pure_i , where E_pure_i are the per-atom total energies of the pure-element reference structures (Nb, Ta, V, Zr in the same BCC supercell, with identical INCAR / KPOINTS / PAW choices). With perfectly consistent reference runs the raw FE should vanish at the two pure-element endpoints (x = 0 and x = 1) by construction. In practice this does not hold for two reasons that are present in our dataset: 1. Reference-energy inconsistency (composition-dependent bias). Even with identical input parameters, the pure-element runs (stored in `corrected_DFT_pure_element_runs/`) differ slightly from the values that would be implied by the alloy runs at near-pure compositions (a few meV/atom). This bias is approximately linear in concentration, because the residual error in E_pure_Nb (or E_pure_Ta / E_pure_V) propagates into FE_raw(c) as (1 - x) * dE_pure_1, and the corresponding error in E_pure_Zr propagates as x * dE_pure_2. Left uncorrected, this produces a non-physical "tilt" of FE_raw(x) and shifts the entire FE-vs-x cloud away from zero at the endpoints. 2. Endpoint anchoring against the audited true endpoints. The strict endpoint values (FE_x0_meVatom, FE_x1_meVatom in `corrected_fe_strict_endpoints_20260518/strict_endpoint_check_20260518.csv`) were re-derived from an independent cross-check of the pure-element runs. After stage 1 removes the linear bias, the near-pure compositions in the alloy dataset still extrapolate to values that differ slightly from these audited endpoints — because stage 1 is fit from a few near-end alloy bins, not from the audited pure-element references themselves. The README.txt file discusses how these issues are addressed by the two-stage correction, and describes folder layout, pipeline summary, and how to re-run.

36 MATERIALS SCIENCE↗

Ab initio study of mechanical and thermal properties of GeTe-based and PbSe-based high-entropy chalcogenides

GeTe-based and PbSe-based high-entropy compounds have outstanding thermoelectric (TE) performance and crucial applications in mid and high temperatures. Recently, the optimization of TE performance of high-entropy compounds has been focused on reducing thermal conductivity by strengthening the phonon scattering process to improve TE performance. We report a first-principles investigation on nine GeTe-based high-entropy chalcogenide solid solutions constituted of eight metallic elements (Ag, Pb, Sb, Bi, Cu, Cd, Mn, and Sn) and 13 PbSe-based high-entropy chalcogenide solid solutions: Pb 0.99-y Sb 0.012 Sn y Se 1-2x Te x S x (x = 0.1, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, and y = 0) and Pb 0.99-y Sb 0.012 Sn y Se 1-2x Te x S x (y = 0.05, 0.1, 0.15, 0.2, 0.25 and x = 0.25). We have investigated the mechanical properties focusing on Debye temperature (Θ D ), thermal conductivity (κ), Grüneisen parameter (γ α ), dominant phonon wavelength (λ dom ), and melting temperature (T m ). We find that the lattice thermal conductivity is significantly reduced when GeTe is alloyed into the following compositions: Ge 0.75 Sb 0.13 Pb 0.12 Te, Ge 0.61 Ag 0.11 Sb 0.13 Pb 0.12 Bi 0.01 Te, and Ge 0.61 Ag 0.11 Sb 0.13 Pb 0.12 Mn 0.05 Bi 0.01 Te. This reduction is due to the mass increase and strain fluctuations. The results also show that Ge 0.61 Ag 0.11 Sb 0.13 Pb 0.12 Bi 0.01 Te solid solution has the lowest Young’s modulus (30.362 GPa), bulk and shear moduli (18.626 and 12.359 GPa), average sound velocity (1653.128 m/sec), Debye temperature (151.689 K), lattice thermal conductivity (0.574 W.m –1 .K –1 ), dominant phonon wavelength (0.692 Å), and melting temperature (535.91 K). Moreover, Ge 0.61 Ag 0.11 Sb 0.13 Pb 0.12 Bi 0.01 Te has the highest Grüneisen parameter with a reduced and temperature-independent lattice thermal conductivity. The positive correlation between Θ D and κ is revealed. Alloying of PbSe-based high-entropy by Sb, Sn, Te, and S atoms at the Se and Pb sites resulted in much higher shear strains resulted in the reduction of phonon velocity, a reduced Θ D , and a lower lattice thermal conductivity.

74 ATOMIC AND MOLECULAR PHYSICS↗

Inhibition mechanisms of steel slag on the early-age hydration of cement

Steel slag inhibits the early-age hydration of cement. However, its mechanism is still unclear. In this paper, the early-age hydration kinetics and the evolution of the solid phases, aqueous species and microstructures in a cement-steel slag composite binder are investigated to explore how steel slag inhibits the early-age hydration of cement. Two novel phenomena are found: (1) steel slag slows the depletion of gypsum and reduces the formation of ettringite, and (2) steel slag significantly inhibits the precipitation of CH and CSH. The results show that the addition of steel slag increases the Ca concentration in the pore solution, reduces the supersaturation of the pore solution with respect to CH and inhibits the nucleation and growth of CSH. Based on the above results, the retardation mechanisms of steel slag on the initial setting of cement paste are explained.

36 MATERIALS SCIENCE↗

Vacancy-mediated transport and segregation tendencies of solutes in fcc nickel under diffusional creep: A density functional theory study

The Nabarro-Herring (NH) diffusional creep theory postulates the vacancy-mediated transport of atoms under a stress gradient as the creep mechanism under low-stress and high-temperature conditions. In multicomponent alloys, we premise that this stress-assisted flow of vacancies to and from grain boundaries will produce elemental segregation. An observation of such segregation, validated with theoretical predictions, can provide the necessary experimental evidence for the occurrence of NH creep. Theoretical calculations of the segregation tendencies via analyzing the dominant solute diffusion mechanisms and the difference in diffusivities of the elements are therefore essential. To this end, this study applies density functional theory calculations of migration barriers and solute-vacancy binding energies as input to the self-consistent mean-field theory to assess the vacancy-mediated diffusion mechanisms, transport coefficients, and segregation tendencies of Co, Cr, Mo, Re, Ta, and W solutes in face-centered-cubic Ni. We find Co, Re, and W to be slow diffusers at high temperatures and Cr, Mo, and Ta to be fast diffusers. Further analysis shows that the slow diffusers tend to always enrich at vacancy sinks over a wide range of temperatures. In contrast, the fast diffusers show a transition from depletion to enrichment as the temperature lowers. Furthermore, our analysis of the segregation tendencies under tensile hydrostatic strains shows that slow diffusers are largely unaffected by the strain and favor enrichment. On the other hand, the fast diffusers exhibit high sensitivity to strain and their segregation tendency can transition from depletion to enrichment at a given temperature. Finally, the transport coefficients calculated in this work are expected to serve as input to mesoscale microstructure models to provide a more rigorous assessment of solute segregation under NH creep conditions.

36 MATERIALS SCIENCE↗

Microstructural evaluation of the creep behavior in L-PBF Ni-based superalloys

This presentation at ICAM 2024 Conference focuses on the commonalities and differences in the creep rupture behavior and creep mechanisms for three distinct classes of laser powder-bed fusion (L-PBF) Ni-based superalloys (γ’-precipitate strengthened Haynes® 282®, γ’/γ”/δ-precipitate strengthened Alloy 718, and solid-solution strengthened Alloy 625) as compared to conventionally processed counterparts. A comparison of Larson-Miller parameter plots establishes that these alloys perform statistically within the bounds established for the wrought product, despite having dissimilar microstructural features and other artefacts associated with PBF-LB manufacturing and post-processing heat treatment. To understand the failure and the impact of composition, minor phases, and deformation defects on creep behavior, the fractography has been performed and microstructures have been evaluated in detail with SEM-EDS, EBSD, and HAADF-STEM. The underlying diffusional and dislocation creep mechanisms associated with this microstructural evaluation is discussed. This work is supported by NETL-FWP-1022408 Advanced Turbines.

Sudbrack, Chantal↗

Novel High Temperature Carbide and Boride Ceramics for Direct Power Extraction Electrode Applications. Final report

The current project aims to develop new carbide and boride ceramic materials that incorporate different metal elements (e.g., (Hf 1-x Zr x )B 2 , also called ceramic solid solutions) and understand the fundamental composition-processing-structure-property relationships for such materials. Specifically, nano powders and related nano-composites for selected mixed metal carbide and boride materials are synthesized from nano-scale mixed precursors obtained from solution-based processing via heat treatment in inert atmosphere. The obtained fine powders were then consolidated into dense ceramics via a novel flash sintering process. The mechanical properties and thermal oxidation resistance for the obtained materials were evaluated for these materials. It was found that different synthesis routes produced powders with somewhat different characteristics in terms of composition and microstructure, which then led to different properties for the final ceramics. The synthesis and processing methods demonstrated in this study might be adopted for developing other similar high temperature ceramics, while the mixed metal or solid solution ceramic materials obtained from this study might be used as hot electrodes for direction power extraction and other energy-related applications.

20 FOSSIL-FUELED POWER PLANTS↗

Real-Time Atomic-Scale Structural Analysis Resolves the Amorphous to Crystalline CaCO 3 Mechanism Controversy

Amorphous calcium carbonate (ACC) occurs as a precursor to geological and biogenic calcium carbonate (CaCO 3 ), yet its transformation pathways and reaction mechanisms remain inconsistent and controversial. In this study, we investigated the transformation of ACC to calcite under both solution and dry conditions, in the presence and absence of impurity ions, utilizing operando time-resolved synchrotron X-ray diffraction (TRXRD) and reactive transport modeling. Results demonstrate that TRXRD techniques allow us to differentiate dissolution-reprecipitation versus solid-state transformation mechanisms for amorphous to crystalline phase transitions. Specifically, we observe that in environments with abundant water, ACC transforms to calcite through a dissolution-reprecipitation mechanism. This features an activation energy of 63 ± 2 kJ/mol and unit cell volume contraction during calcite crystal growth. Conversely, under water-limited conditions, ACC to calcite transformation proceeds via a solid-state transformation mechanism, with an activation energy of 210 ± 2 kJ/mol, three times greater than the dissolution-reprecipitation route, and a unit cell expansion during crystalline calcite growth. Further, to illustrate the magnitude of these effects, the rates of calcite growth were similar during dissolution-reprecipitation at 3 °C [0.00207(35) s –1 ] and solid-state transformation at 280 °C [0.00134(11) s –1 ]. Moreover, the incorporation of an impurity, strontium, significantly retards the rate of calcite growth while expanding its unit cell but whose incorporation is history dependent. Reactive transport modeling of the dissolution–precipitation kinetics suggests that ACC must be dissolving as compact aggregates. These various transformation mechanisms drive diverse geological and biological carbonate formations, impacting their use as paleoenvironmental markers and functional materials synthesis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Influence of microstructure on replacement and porosity generation during experimental dolomitization of limestones

Replacement reactions commonly alter the multiscale pore structures of rocks during fluid-rock interactions. Analysis of these processes in various model fluid-rock systems during controlled laboratory experiments provides insights into the origins of microstructures found in natural materials. This study focused on understanding the effects of initial starting material permeability and resultant differences in transport pathways on porosity and mineralogical changes during limestone dolomitization.A series of replacement experiments (32–317 days in duration) have been conducted in which 1.59 cm (5/8 in.) diameter cores of two different limestones were reacted with saturated MgCl2 solutions at 200 °C. The Texas Cream (Austin Chalk) is a high-porosity, high-permeability limestone, whereas both the porosity and permeability of the Carthage Marble (Burlington Limestone) are relatively low. Altered limestones were imaged using scanning electron microscopy with energy-dispersive X-ray spectroscopy (SEM-EDX), Time-of-Flight Secondary Ion Mass Spectrometry (ToF–SIMS) and electron microprobe analysis (EMPA). A representative grain boundary of the low-porosity limestone was targeted for a focused ion beam (FIB) lift-out and characterized using transmission electron microscopy (TEM). These results were coupled with analyses of radial changes in the porosity distribution of the core derived from X-ray and neutron small- and ultra-small angle scattering ((U)SANS/(U)SAXS).The high-porosity/permeability limestone showed a four times faster bulk replacement rate than the lower-porosity/permeability material, and a different mechanism of porosity development. For the low-porosity limestone, a two-stage replacement occurred, with the reacted region of the core consisting of an inner rim in which the limestone was replaced by two calcite-dolomite solid solutions, and an outer rim in which the dolomite was replaced by magnesite. Elongated pores formed along grain boundaries at the initial limestone/dolomite reaction interface, and additional nanometer-scale porosity was formed at the secondary magnesite replacement rim. Grain boundaries were identified as preferential pathways for transport leading to dolomitization and a grain boundary diffusion rate was calculated based on microstructural characterization. In contrast, replacement in the high-porosity limestone was accompanied by porosity generation through replacement of individual grains by dolomite throughout the sample and, in longer runs, magnesite in outer parts of the core. These observations emphasize that both the mechanisms of the replacement reaction and the microstructure and chemistry of the replaced product are contingent on the initial structure of the starting material.

36 MATERIALS SCIENCE↗

An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture

Meshfree discretizations of state-based peridynamic models are attractive due to their ability to naturally describe fracture of general materials. However, two factors conspire to prevent meshfree discretizations of state-based peridynamics from converging to corresponding local solutions as resolution is increased: quadrature error prevents an accurate prediction of bulk mechanics, and the lack of an explicit boundary representation presents challenges when applying traction loads. Herein, we develop a reformulation of the linear peridynamic solid (LPS) model to address these shortcomings, using improved meshfree quadrature, a reformulation of the nonlocal dilatation, and a consistent handling of the nonlocal traction condition to construct a model with rigorous accuracy guarantees. In particular, these improvements are designed to enforce discrete consistency in the presence of evolving fractures, whose a priori unknown location render consistent treatment difficult. In the absence of fracture, when a corresponding classical continuum mechanics model exists, our improvements provide asymptotically compatible convergence to corresponding local solutions, eliminating surface effects and issues with traction loading which have historically plagued peridynamic discretizations. When fracture occurs, our formulation automatically provides a sharp representation of the fracture surface by breaking bonds, avoiding the loss of mass. We provide rigorous error analysis and demonstrate convergence for a number of benchmarks, including manufactured solutions, free-surface, nonhomogeneous traction loading, and composite material problems. Finally, we validate simulations of brittle fracture against a recent experiment of dynamic crack branching in soda-lime glass, providing evidence that the scheme yields accurate predictions for practical engineering problems.

42 ENGINEERING↗

Microstructure and properties of additively manufactured Al–Ce–Mg alloys

Additive manufacturing of aluminum alloys is largely dominated by a near-eutectic Al-Si compositions, which are highly weldable, but have mechanical properties that are not competitive with conventional wrought Al alloys. In addition, there is a need for new Al alloys with improved high temperature properties and thermal stability for applications in the automotive and aerospace fields. In this work, we considered laser powder bed fusion additive manufacturing of two alloys in the Al–Ce–Mg system, designed as near-eutectic (Al–11Ce–7Mg) and hyper-eutectic (Al–15Ce–9Mg) compositions with respect to the binary L → Al + Al 11 Ce eutectic reaction. The addition of magnesium is used to promote solid solution strengthening. A custom laser scan pattern was used to reduce the formation of keyhole porosity, which was caused by excessive vaporization due to the high vapor pressure of magnesium. The microstructure and tensile mechanical properties of the alloys were characterized in the as-fabricated condition and following hot isostatic pressing. The two alloys exhibit significant variations in solidification structure morphology. These variations in non-equilibrium solidification structure were rationalized using a combination of thermodynamic and thermal modeling. Both alloys showed higher yield strength than AM Al-10Si-Mg for temperatures up to 350 °C and better strength retention at elevated temperatures than additively manufactured Scalmaloy.

36 MATERIALS SCIENCE↗

Framework-Topology-Controlled Singlet Fission in Metal–Organic Frameworks

Singlet fission (SF) has been explored as a viable route to improve photovoltaic performance by producing more excitons. Efficient SF is achieved through a high degree of interchromophoric coupling that facilitates electron super exchange to generate triplet pairs. However, strongly coupled chromophores often form excimers that can serve as an SF intermediate or a low-energy trap site. The succeeding decoherence process, however, requires an optimum electronic coupling to facilitate the isolation of triplet production from the initially prepared correlated triplet pair. Conformational flexibility and dielectric modulation can provide a means to tune the SF mechanism and efficiency by modulating the interchromophoric electronic interaction. Such a strategy cannot be easily adopted in densely stacked traditional organic solids. Here, we show that the assembly of the SF-active chromophores around well-defined pores of solution-stable metal-organic frameworks (MOFs) can be a great platform for a modular SF process. A series of three new MOFs, built out from 9,10-bis(ethynylenephenyl)anthracene-derived struts, show a topology-defined packing density and conformational flexibility of the anthracene core to dictate the SF mechanism. Various steady-state and transient spectroscopic data suggest that the initially prepared singlet population can prefer either an excimer-mediated SF or a direct SF (both through a virtual charge-transfer (CT) state). Finally, these solution-stable frameworks offer the tunability of the dielectric environment to facilitate the SF process by stabilizing the CT state. Given that MOFs are a great platform for various photophysical and photochemical developments, generating a large population of long-lived triplets can expand their utilities in various photon energy conversion schemes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Sierra/Solid Mechanics 5.16 User's Guide

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.

36 MATERIALS SCIENCE↗

Phase Transfer‐Mediated Degradation of Ether‐Based Localized High‐Concentration Electrolytes in Alkali Metal Batteries

Abstract Localized high‐concentration electrolytes (LHCEs) have attracted interest in alkali metal batteries due to the advantages of forming stable solid‐electrolyte interphases (SEIs) on anodes and good chemical/electrochemical stability. Herein, a new degradation mechanism is revealed for ether‐based LHCEs that questions their compatibility with alkali metal anodes (Li, Na, and K). Specifically, the ether solvent reacts with alkali metals to generate solvated electrons (e s − ) that attack hydrofluoroether co‐solvents to form a series of byproducts. The ether solvent essentially acts as a phase‐transfer reagent that continuously transfers electrons from solid‐phase metals into the solution phase, thus inhibiting the formation of stable SEI and leading to continuous alkali metal corrosion. Switching to an ester‐based solvating solvent or intercalation anodes such as graphite or molybdenum disulfide has been shown to avoid such a degradation mechanism due to the absence of e s − .

Chen, Xiaojuan↗