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At least 379 records · Page 21

Electrochemical Li intercalation in b-As y P 1–y alloys: In-situ Raman spectroscopy study

Structural evolution of b-As y P 1-y alloys with varying As concentration, y was studied during Li-intercalation using in-situ Raman spectroscopy. A monotonic redshift of all the vibrational modes corresponding to P-P bonds (A 1 g , A 2 g , B 2g ), As-As bonds (A 1 g , A 2 g , B 2g ), and As-P bonds of all the samples was observed during the initial stages of the intercalation process due to the softening of each mode caused by the intercalation driven donor-type charge-transfer from Li to b-As y P 1-y . The emergence of a new peak identified as the E g mode of gray As, above an intercalation threshold, is indicative of the presence of an intercalation-driven structural phase segregation process. Further, the A 1g mode of gray As emerging after this intercalation threshold lies in close proximity of the A 2 g Raman mode of b-As y P 1-y . All the peaks beyond the intercalation threshold show an upshift due to the co-existence of gray As with b-As y P 1-y alloys causing strain and thus hardening of the phonon modes. In the sample with the highest As concentration phase segregation takes place during the synthesis process. Computational modeling reveals the co-existence of gray As in the b-As y P 1-y alloys with high As concentrations. It also confirms the existence of a local structural segregation taking place at a critical Li concentration during the intercalation process. Furthermore, this work shows the significance of intercalation on structural changes in the search for new phases of b-As y P 1-y alloys.

2D Materials↗

Consequences of adsorbate-adsorbate interactions for apparent kinetics of surface catalytic reactions

Lateral adsorbate interactions at catalyst surfaces are known to influence adsorption energies and reaction rates. Lattice-based kinetic Monte Carlo (kMC) simulations are able to capture these influences, but such models are typically parameterized for a specific reaction network and catalyst surface. Here we report kMC simulations to probe the influence of lateral interactions on simulated rates, rate orders, apparent activation energies, and Sabatier plots. We construct a simple, two-step reaction network involving a single adsorbate and rate- limiting diatomic dissociation, employ a generic repulsive lateral interaction model consistent with known adsorbate-adsorbate interactions on metal surfaces, and a rate model consistent with known Brønsted-Evans-Polyani relationships for diatomic dissocations. Furthermore, we juxtapose reaction kinetics over a wide range of reaction conditions and catalyst binding energies, as a function of interaction strength. We find that at a given zero-coverage binding energy and external conditions, adsorbate coverage decreases monotonically with increasing interaction strength, but absolute rates can vary linearly or nonlinearly. Interactions flatten the Sabatier volcano and shift the maximum towards stronger binding. Influences on apparent rate orders and activation energies are modest and are sensitive to interaction-induced adsorbate ordering. Model predictions are sensitive to lattice size effects at high coverages. The results, modelled for a simple reaction system, highlight the generic consequences of lateral interactions and guidance for identifying their signatures in observed kinetics.

kinetic Monte Carlo↗

Supported molybdenum oxides for the aldol condensation reaction of acetaldehyde

The (retro-)aldol condensation reaction is an important chemical transformation in the upgrading of biomass-derived compounds into fuels and valuable specialty chemicals. In this study, we found that supported molybdenum oxide (MoO x ) catalysts were active and selective for the aldol condensation of acetaldehyde to crotonaldehyde under steady-state reactor conditions. Through a combination of transmission electron microscopy (TEM), ultraviolet–visible (UV–VIS) diffuse reflectance spectroscopy, Fourier transform infrared (FTIR) spectroscopy of adsorbed pyridine, and steady-state reactor testing, we determined that highly dispersed MoO x has a strong interaction with a γ-Al 2 O 3 support resulting in optimal catalyst performance at low weight loadings. In contrast, MoO x particles supported on SiO 2 have a weaker interaction with the support, resulting in a monotonic relationship between Mo loading and aldol condensation activity. The Lewis acid site density and strength are important parameters for predicting aldol condensation activity across all samples. The concentration of weak acid sites had a poor correlation with aldol condensation activity, most likely because these sites are too weak to activate acetaldehyde for the reaction. Medium and strong acid sites both had good correlations to aldol condensation activity. Results from X-ray absorption near edge structure (XANES) and acetaldehyde temperature programmed desorption (TPD) indicated that partially reduced MoO x was more active for aldol condensation, but pretreatment in reducing or oxidizing environments had no significant effect on steady-state catalytic activity. Finally, characterization of spent catalyst samples through temperature programmed oxidation (TPO) and thermogravimetric analysis (TGA) revealed that catalysts with high densities of strong acid sites tended to form more carbonaceous deposits on the surface over the course of the reaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Linear and nonlinear viscoelasticity of concentrated thermoresponsive microgel suspensions

We present an integrated experimental and theoretical study of the dynamics and rheology of self-crosslinked, slightly charged, temperature responsive soft poly(N-isopropylacrylamide) (pNIPAM) microgels over a wide range of concentration and temperature spanning the sharp change in particle size and intermolecular interactions across the lower critical solution temperature (LCST). Dramatic, non-monotonic changes in viscoelasticity are observed as a function of temperature, with distinct concentration dependence in the dense fluid, glassy, and soft-jammed regimes. Motivated by our experimental observations, we formulate a minimalistic model for the size dependence of a single microgel particle and the change of the interparticle interaction from purely repulsive to attractive upon heating. Using microscopic equilibrium and time-dependent statistical mechanical theories, theoretical predictions are quantitatively compared with experimental measurements of the shear modulus. Good agreement is found for the nonmonotonic temperature behavior that originates as a consequence of the competition between reduced microgel packing fraction and increasing interparticle attractions. Furthermore, testable predictions are made for nonlinear rheological properties such as the yield stress and strain. To our knowledge, this is the first attempt to quantitatively understand in a unified manner the viscoelasticity of dense, temperature-responsive microgel suspensions spanning a wide range of temperatures and concentrations.

42 ENGINEERING↗

Distance-dependent dielectric constant at the calcite/electrolyte interface: Implication for surface complexation modeling

Hypothesis: The electrical double layer formed at the mineral/electrolyte interface is often modeled using mean-field approaches based on a continuum description of the solvent whose dielectric constant is assumed to decrease monotonically with decreasing distance to the surface. In contrast, molecular simulations show that the solvent polarizability oscillates near the surface similar to the water density profile - as shown previously, for example, by Bonthuis et al. (D.J. Bonthuis, S. Gekle, R.R. Netz, Dielectric Profile of Interfacial Water and its Effect on Double-Layer Capacitance, Phys Rev Lett 107(16) (2011) 166102). Here, we showed that molecular and mesoscale pictures agree by spatially averaging the dielectric constant obtained from molecular dynamics simulations over the distances relevant to the mean-field representation. In addition, the values of capacitances used to describe the electrical double layer in Surface Complexation Models (SCMs) of the mineral/electrolyte interface can be estimated using molecularly informed spatially averaged dielectric constants and positions of hydration layers. Experiments: First, we used molecular dynamics simulations to model the calcite 101¯4/electrolyte interface. Next, by using atomistic trajectories, we calculated the distance-dependent static dielectric constant and water density in the direction normal to the. Finally, we applied spatial compartmentalization consistent with the model of parallel-plate capacitors connected in series to estimate SCM capacitances. Findings: Computationally expensive simulations are required to determine the dielectric constant profile of interfacial water near the mineral surface. On the other hand, water density profiles are readily assessable from much shorter simulation trajectories. Our simulations confirmed that dielectric and water density oscillations at the interface are correlated. Here, we parametrized linear regression models to estimate the dielectric constant directly from the local water density. This is a significant computational shortcut compared to slowly converging calculations relying on total dipole moment fluctuations. The amplitude of the interfacial dielectric constant oscillation can exceed the dielectric constant of the bulk water, suggesting an ice-like frozen state, but only if there are no electrolyte ions. The interfacial accumulation of electrolyte ions causes a decrease in the dielectric constant due to the reduction of water density and re-orientation of water dipoles in ion hydration shells. Finally, we show how to use the computed dielectric properties to estimate SCM's capacitances.

58 GEOSCIENCES↗

On the design of stable, consistent, and conservative high-order methods for multi-material hydrodynamics

Obtaining stable and high-order numerical solutions for multi-material hydrodynamics is an open challenge. Although slope limiters are widely used to maintain monotonicity near discontinuities, typical limiting procedures violate closure laws at the discrete level when applied to multi-material hydrodynamics equations. Due to this, the high-order expansions of quantities related by the closure laws are no longer consistent. The commonly observed symptom of this consistency-violation is that the numerical method fails to maintain constant pressure and velocity across material interfaces. This leads to sub-optimal convergence rates for smooth multi-material problems as well. Specialized limiting procedures that satisfy consistency while maintaining conservation need to be developed for such equations. A novel procedure that re-instates consistency into slope-limited high-order discretizations applied to the multi-material hydrodynamics equations is presented here. Using simple examples, it is demonstrated that the presented method satisfies closure laws at the discrete level, while maintaining conservative properties of the high-order method. Furthermore, this procedure involves a projection step which relies on the compact basis of the underlying spatial discretization, i.e. for discontinuous schemes (viz. DG and FV) the projection is local, and does not involve global matrix solves. Comparisons with conventional approaches emphasizes the necessity of the consistent closure-law preserving limiting approach, in order to maintain design order of accuracy for smooth multi-material problems.

36 MATERIALS SCIENCE↗

Structure preservation using discrete gradients in the Vlasov-Poisson-Landau system

We present a novel structure-preserving framework for solving the Vlasov-Poisson-Landau system of equations using a particle in cell (PIC) discretization combined with discrete gradient time integrators. The Vlasov-Poisson-Landau system is an accurate model for studying hot plasma dynamics at a kinetic scale where small-angle Coulomb collisions dominate. Our scheme guarantees conservation of mass, momentum and energy as well as preservation of the monotonicity of entropy production in both the time-continuous and discrete systems. We employ the conservative integrator for both the Hamiltonian Vlasov-Poisson equations and the dissipative Landau equation using the PETSc library (www.mcs.anl.gov/petsc) to showcase structure-preserving properties.

Discrete gradients↗

Computational modeling and neutron imaging to understand interface shape and solute segregation during the vertical gradient freeze growth of BaBrCl:Eu

In this work we apply continuum models to analyze phase change, heat transfer, fluid flow, solute transport, and segregation in order to understand prior neutron imaging observations of the vertical gradient freeze growth of Eu-doped BaBrCl. The models provide a rigorous framework in which to understand the mechanisms that are responsible for the complicated evolution of interface shape and dopant distribution in the growth experiment. We explain how a transition in the solid/liquid interface shape from concave to convex is driven by changes in radial heat transfer caused by furnace design. We also provide a mechanistic explanation of how dynamic growth conditions and changes of the flow structure in the melt result in complicated segregation patterns in this system. A growth pause caused by controller lock-up is shown to result in a band of solute depletion in accordance with classical theory. However, changing flow patterns during growth result in a non-monotonic axial distribution of solute that cannot be explained by simple application of classical segregation models. We assert that the approach presented here, namely the use of rigorous models in conjunction advanced diagnostics, such as neutron imaging, provides an exciting path forward for process optimization and control, accelerating the incremental advances that have, in the past, typically relied on empiricism, experience, and intuition.

36 MATERIALS SCIENCE↗

Onion-Like nanoparticles of the metal–organic framework UiO-66 synthesized by sequential spike crystal growth

Reproducible size and morphology of metal–organic framework (MOF) particles are essential for tuning these materials for applications like heterogeneous catalysis. Particle size measurements from electron micrographs provide information about the impact of changing synthetic parameters on MOF growth, but reported data are usually limited to averages and statistical distributions. Further elucidating synthetic control parameters could facilitate studies of facet-dependent and non-classical growth mechanisms. Here, in this work, phase-pure nanoparticles of the MOF UiO-66 were synthesized using alternating spikes of zirconium and hafnium-based nodes, forming an onion-like structure with alternating layers of Zr-UiO-66 and Hf-UiO-66. In conventional, bright-field transmission electron micrographs, Hf-UiO-66 and Zr-UiO-66 layers appeared darker and lighter, respectively. Alternating layers of Hf-UiO-66 and Zr-UiO-66 were also apparent in elemental maps obtained using scanning transmission electron microscopy with energy-dispersive X-ray spectroscopy. Average particle sizes increased monotonically with each spike, and no Zr-only or Hf-only particles were observed after the first spike, indicating that new material was consistently incorporated onto existing seeds. Surface area of the onion-like particles and their uptake of Ni 2+ from solution were both between the values measured for Zr-UiO-66 and Hf-UiO-66. Results demonstrate the use of sequential spikes of nodes in monitoring crystal growth in MOFs.

36 MATERIALS SCIENCE↗

In situ observation of the deformation and fracture of an alumina-alumina ceramic-matrix composite at elevated temperature using x-ray computed tomography

The deformation and fracture of a 0/90° Nextel 720 mullite fibre / alumina matrix ceramic-matrix composite material has been observed by in situ synchrotron x-ray computed micro-tomography at ambient temperature and at 1100 °C. A three-point loading configuration was used and samples were loaded monotonically until final fracture. Here, the flexural strength was found to be unaffected by temperature. 3D visualisation of the microstructure showed fracture occurred by propagation of internal cracks at stresses close to the flexural strength. Shear fractures propagated across fibre bundles that were oriented perpendicular to the flexural stress at both room temperature and 1100 °C. At the higher temperature, an additional failure mode of delamination was observed, that may arise from relaxation of thermal residual stresses and creep.

36 MATERIALS SCIENCE↗

Ordering in liquid and its heredity impact on phase transformation of Mg-Al-Ca alloys

It is a long-sought goal to achieve desired mechanical properties through tailoring phase formation in alloys, especially for complicated multi-phase alloys. In fact, unveiling nucleation of competitive crystalline phases during solidification hinges on the nature of liquid. Here we employ ab initio molecular dynamics simulations (AIMD) to reveal liquid configuration of the Mg-Al-Ca alloys and explore its effect on the transformation of Ca-containing Laves phase from Al 2 Ca to Mg 2 Ca with increasing Ca/Al ratio (r Ca/Al ). There is structural similarity between liquid and crystalline phase in terms of the local arrangement environment, and the connection schemes of polyhedras. The forming signature of Mg 2 Ca, as hinted by the topological and chemical short-range order originating from liquid, ascends monotonically with increasing r Ca/Al . However, Al 2 Ca crystal-like order increase at first and then decrease at the crossover of r Ca/Al = 0.74, corresponding to experimental composition of phase transition from Al 2 Ca to Mg 2 Ca. The origin of phase transformation across different compositions lies in the dense packing of atomic configurations and preferential bonding of chemical species in both liquid and solid. The present finding provides a feasible scenario for manipulating phase formation to achieve high performance alloys by tailoring the crystal-like order in liquid.

36 MATERIALS SCIENCE↗

Meshfree simulation and prediction of recrystallized grain size in friction stir processed 316L stainless steel

Friction stir processing (FSP) is a promising solid-phase microstructural modification technique that can repair and enhance damaged stainless steel surfaces exposed to harsh environments. The quality of the repaired material is closely correlated to the recrystallized grain size in the stir zone (SZ), which is influenced by the thermomechanical conditions dictated by FSP process parameters. Thus, establishing a reliable relationship between these parameters and recrystallized grain size in the SZ is crucial for optimizing repair quality. However, existing experimental approaches often rely on indirect temperatures measured far from the SZ, along with rough strain rate estimations, which are imprecise and time-consuming. Meanwhile, existing mesh-based modeling methods usually face numerical challenges when dealing with the large material deformations inherent in FSP. Here, to address these issues, this study introduces a meshfree process model for FSP based on the smoothed particle hydrodynamics (SPH) method, aimed at predicting process conditions under different parameters. The model is validated using experimental data from 11 combinations of tool traverse and rotation speeds on 316 L stainless steel. Correlations between process parameters, material flow, temperature, strain, strain rate, and recrystallized grain size are revealed through SPH simulations and electron backscatter diffraction (EBSD) imaging. The results show that in situ SZ temperatures range from 1071 to 1322°C, which exceed the tool temperature by over 300°C. Furthermore, SZ temperature, strain rate, and grain size increase monotonically with higher tool temperature and faster traverse speed. A relationship is then established between the model-predicted Zener-Hollomon parameter and the recrystallized grain size based on EBSD data, expressed as ln(d) = -0.364 ln(Z) + 14.673. Finally, this relationship exhibits satisfactory accuracy with errors of less than 26.9% in predicting grain sizes at various SZ locations, which offers valuable insights for optimizing FSP repair processes for 316 L stainless steel.

316L stainless steel↗

Disorder-induced time effect in the antiferromagnetic domain state of Fe 1+ y Te

Herein we report on temperature-dependent soft X-ray absorption spectroscopy (XAS) measurements utilizing linearly polarized synchrotron radiation to probe magnetic phase transitions in iron-rich Fe 1+y Te (y ≈ 0.12). X-ray magnetic linear dichroism (XMLD) signals, which sense magnetic ordering processes at surfaces, start to increase monotonically below the Néel temperature T N = 57 K. This increase is due to a progressive bicollinear antiferromagnetic (AFM) alignment of Fe spins of the monoclinic Fe 1+y Te parent phase. This AFM alignment was achieved by a [1 0 0]-oriented biasing field favoring a single-domain state during cooling across T N . Our specific heat and magnetization measurements confirm the bulk character of this AFM phase transition. On longer time scales, however, we observe that the field-biased AFM state is highly unstable even at the lowest temperature of T = 3 K. After switching off the biasing field, the XMLD signal decays exponentially with a time constant τ = 1506 s. The initial XMLD signal is restored only upon repeating a cycle consisting of heating and field-cooling through T N . We explain the time effect by a gradual formation of a multi-domain state with 90° rotated AFM domains, promoted by structural disorder, facilitating the motion of twin-domains. Significant disorder in our Fe 1+y Te sample is evident from our X-ray diffraction and specific heat data. The stability of magnetic phases in Fe-chalcogenides is an important material property, since the Fe(Te 1-x Se x ) phase diagram shows magnetism intimately connected with superconductivity.

36 MATERIALS SCIENCE↗

Valence instability and collapse of ferromagnetism in EuB 6 at high pressures

Despite the simplicity of their cubic crystal lattice, rare-earth hexaborides display complex physical properties including a (long debated) onset of metallization via magnetic polaron formation at T c1 approximate to 15 K preceding ferromagnetic ordering at T c2 approximate to 12 K. Here, in this work, we used applied pressure to tune the interplay between electronic structure and magnetism in EuB6. We probed the magnetism, valence, and structure of EuB 6 under quasi-hydrostatic pressures up to 30 GPa using X-ray techniques. Our findings show evidence for collapse of ferromagnetism above 20 GPa following a monotonic increase of mean Eu valence. While X-ray diffraction measurements in the paramagnetic state at room temperature show that the lattice retains cubic symmetry, a measurable quadrupole interaction seen by time-domain synchrotron Mössbauer spectroscopy suggests a lowering of symmetry associated with magnetic ordering, becoming more prominent across the magnetic transition. The interplay between conduction band electron count and magnetism observed under applied pressure in EuB 6 opens possibilities for fine-tuning metallization and magnetic properties of similar Eu-based semi-metal systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Study of the interplay between lower-order and higher-order energetic strain-gradient effects in polycrystal plasticity

in this report strain-gradient (SG) plasticity refers to a class of non-local theories in which gradients of plastic slip determine the storage of geometrically necessary dislocations, introducing a length-scale dependence in the mechanical behavior of crystalline materials, which is otherwise lacking in local theories. In this work, we incorporate lower-order (LO) and higher-order energetic (HOE) strain-gradient effects into a crystal plasticity fast Fourier transform (FFT)-based formulation to investigate the interplay of the length scale that each strain-gradient term introduces at the microscale, and the mechanical properties that result at the macroscale. For an applicable range of length scales, we consider two systems: a 1-D two-phase face centered cubic (FCC) laminate and a 3-D FCC polycrystal, and two uniaxial deformation modes: monotonic tension and cyclic tension–compression. We show that increases in the individual LO and HOE length scales increase the hardening rate and strength of the material, respectively. When combined, the strong LO hardening is less pronounced than the effect alone due to the lowering of the gradients due to the HOE microstress. We demonstrate that the LO and HOE hardening manifest as “isotropic” (yield surface expansion) and “kinematic” (yield surface shift) effects, respectively, consistent with their theoretical origins. We show that in cyclic loading, the Bauschinger effect emerges in both local and non-local calculations and link its origins and severity to the behavior in the strain field, slip-system rates, and the HOE microforce.

36 MATERIALS SCIENCE↗

A finite viscoelastic constitutive model for low to high strain rate response of elastomers with application of strain rate-induced glass transition

Amorphous elastomers exhibit significant rate-stiffening and unique viscous flow characteristics across a wide range of strain rates, often undergoing glass transition above a strain rate threshold. We have developed a thermodynamically-consistent and micromechanically-inspired constitutive model for soft elastomeric materials to capture the rate-dependent stress-strain behavior and hysteresis when subjected to low to high strain rates. Here, our proposed constitutive model encapsulates the viscous flow of materials through molecular motion at low strain rates and local rearrangement and alignment of the molecules trying to overcome the intermolecular resistance at high strain rates, essentially covering the glass transition. We applied our constitutive model to uniaxial compression experiments performed at low and high strain rates for polyborosiloxane (PBS) to identify the material parameters, and subsequently, performed numerical simulations of single and multi-cycle compression, stress relaxation, and small amplitude oscillatory tension-compression. Our analyses indicate that the model predicts higher total energy dissipation with increasing strain rate; however, dissipation associated with molecular relaxation decreases (forming a cusp) because, beyond a crossover strain rate, intermolecular rearrangement and alignment become dominant, which is consistent with the onset of the glass transition. For cyclic loading-unloading, we observed that dissipation over a cycle remains constant at low strain rates but decreases non-monotonically at high strain rates before becoming constant, with the peak stress over the cycle becoming higher, which can be interpreted as more loading being carried elastically by the polymer network as the intermolecular rearrangement process occurs. Additionally, our model was able to predict the qualitative nature of the storage modulus and loss modulus in the limit of small strain over a wide range of frequency sweeps.

36 MATERIALS SCIENCE↗

Effects of HFIR neutron irradiation on fracture toughness properties of standard and Ni-doped F82H

F82H is the Japanese reference reduced-activation ferritic-martensitic (RAFM) steel for fusion blanket applications. The harsh environment of a fusion reactor, such as neutron irradiation and He/H damage, can result in significant degradation of F82H fracture toughness. Therefore, understanding the fracture toughness behavior of F82H in the fusion environment is critical to ensure the long-term safe operation of the fusion reactor. Here, we summarize seven irradiation campaigns of the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory (ORNL) covering five variants of F82H steels, including F82H IEA, F82H Mod3, F82H doped with 1.4% natural Ni, F82H doped with 1.4% 58 Ni, and F82H doped with 1.4% 60 Ni. The irradiation temperatures covered the range from 220 °C to 530 °C and the neutron irradiation dose spanned 4 dpa to 70 dpa. The effects of neutron irradiation temperature, dose, materials composition, Ni doping, and He production on F82H fracture toughness are discussed. Our results showed that irradiation embrittlement monotonically decreased with increasing irradiation temperature until 400 °C for F82H IEA and F82H Mod3. F82H Mod3 showed better fracture toughness than F82H IEA both before and after neutron irradiation. We determined that 1.4% Ni alloying can be applied to F82H for simulating He effect in a fission reactor without jeopardizing the fracture toughness of the material. However, more studies are needed to understand the effect of high dose (>20 dpa) and He production on F82H fracture toughness.

36 MATERIALS SCIENCE↗

Understanding effects of chemical complexity on helium bubble formation in Ni-based concentrated solid solution alloys based on elemental segregation measurements

Here, helium bubble formation and swelling were systematically studied in Ni-based concentrated solid solution alloys containing different numbers and types of elements. Our microscopy analysis showed that although increasing the alloy chemical complexity helps suppress bubble formation in general, there is no monotonic relationship between the bubble growth rate and the number of alloying elements. Certain elements (e.g., Fe and Pd) are more effective in suppressing bubble growth than others (e.g., Cr and Mn). Atom probe tomography was applied to accurately measure elemental segregation around bubbles, revealing unique effects of certain alloying elements on vacancy migration towards bubbles. More specifically, the high vacancy mobility via Cr sites leads to a large vacancy flux and an increased bubble size, while the high degree of atomic size mismatch introduced by Pd helps deflect vacancy flow away from bubbles and decrease the amount of swelling. The effects identified in this study provide new strategies to design concentrated solid solutions with superior resistance to swelling.

36 MATERIALS SCIENCE↗