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At least 469 records · Page 26

Grain refinement in titanium prevents low temperature oxygen embrittlement

Interstitial oxygen embrittles titanium, particularly at cryogenic temperatures, which necessitates a stringent control of oxygen content in fabricating titanium and its alloys. Here, we propose a structural strategy, via grain refinement, to alleviate this problem. Compared to a coarse-grained counterpart that is extremely brittle at 77 K, the uniform elongation of an ultrafine-grained (UFG) microstructure (grain size ~ 2.0 µm) in Ti-0.3wt.%O is successfully increased by an order of magnitude, maintaining an ultrahigh yield strength inherent to the UFG microstructure. This unique strength-ductility synergy in UFG Ti-0.3wt.%O is achieved via the combined effects of diluted grain boundary segregation of oxygen that helps to improve the grain boundary cohesive energy and enhanced dislocation activities that contribute to the excellent strain hardening ability. The present strategy will not only boost the potential applications of high strength Ti-O alloys at low temperatures, but can also be applied to other alloy systems, where interstitial solution hardening results into an undesirable loss of ductility.

36 MATERIALS SCIENCE↗

Grain boundary zirconia-modified garnet solid-state electrolyte

Here, we report a method for promoting electrochemical stability in garnet Li 6.4 La 3 Zr 1.4 Ta 0.6 O 12 solid-state electrolyte based on a composite two-phase oxide–oxide microstructure. Grain boundary precipitation of the controlled distribution of amorphous zirconium oxide microparticles is achieved through the addition of reactive tantalum carbide. During ambient-atmosphere sintering, the carbide decomposes through an in situ reaction, the ‘extra’ Ta substituting for Zr within the Li 6.4 La 3 Zr 1.4 Ta 0.6 O 12 lattice. Density functional theory (DFT) calculations identify a thermodynamically favourable reaction path and show how substituting Ta 5+ at Zr 4+ sites affects the crystal structure as well as bulk ionic and electronic conductivities. Quantitative stereology highlights that zirconia also acts as a sintering aid, reducing compact porosity. Cryogenic focused-ion-beam scanning electron microscopy and fractography analysis of cycled solid-state electrolytes illustrates that near-universally observed intergranular Li-metal dendrite propagation is suppressed by the two-phase microstructure, favouring transgranular dendrites instead. Importantly, DFT demonstrates that compared with the Li 6.4 La 3 Zr 1.4 Ta 0.6 O 12 surface, the zirconium oxide surface per se is less electronically conductive and does not trap excess electrons to reduce Li ions. This is a key reason for the substantial improvement in the electrochemical properties over the single-phase baseline.

36 MATERIALS SCIENCE↗

Ferroelectric HfO 2 and the importance of strain

Ferroelectric oxides based on HfO 2 show tremendous promise for the next generation of memory and logic devices. The ferroelectric polymorph is one of several that can be derived from the high symmetry cubic fluorite structure of HfO 2 . A single grain of HfO 2 may consist of a coherent mixture of multiple orientational and translational variants of different polymorphs. Here, we use symmetry-adapted strain-order parameters to elucidate the relationship between the different HfO 2 polymorphs and their symmetrically equivalent variants. We use first-principles electronic structure methods to identify minimum energy pathways and map them in subspaces of the symmetry-adapted strain order parameters. We next investigate the atomic structure of domain boundaries that separate coexisting variants of ferroelectric HfO 2 . Further, we rely on Gibbsian excess quantities and a precise specification of mechanical boundary conditions to describe the thermodynamic properties of domain boundaries. Our first-principles calculations show that the O and Hf shuffle arrangement within a domain boundary is closely related to the intermediate shuffle patterns of the homogeneous pathways between ferroelectric variants. Furthermore, the preferred structure within a boundary is very sensitive to local strain constraints imposed by the adjacent ferroelectric variants, leading to highly anisotropic domain boundary energies.

36 MATERIALS SCIENCE↗

Defect-Enabled Phase Programming of Transition Metal Dichalcogenide Monolayers

The ability to tune the local electronic transport properties of group VI transition metal dichalcogenide (TMD) monolayers by strain-induced structural phase transformations (“phase programming”) has stimulated much interest in the potential applications of such layers as ultrathin programmable and dynamically switchable nanoelectronics components. In this manuscript, we propose a new approach toward controlling TMD monolayer phases by employing macroscopic in-plane strains to amplify heterogeneous strains arising from tailored, spatially extended defects within the monolayer. Furthermore, the efficacy of our proposed approach is demonstrated via numerical simulations of emerging domains localized around arrays of holes, grain boundaries, and compositional heterointerfaces. Quantitative relations between the macroscopic strains required, spatial resolution of domain patterns, and defect configurations are developed. In particular, the introduction of arrays of holes is identified as the most feasible phase programming route.

2D materials↗

Evaluation of BISON's Transient Fission Gas Release Model on High-Burnup UO 2 MiniFuel

BISON's fission gas release (FGR) model has been evaluated and tested over several hypothetical thermal transient cases at high burnup and validated against FGR experimental data from an annealing test at high burnup. Diffusion-controlled FGR is accounted for in the model by including several physical mechanisms such as the diffusion of fission gas to grain faces, grain boundary sweeping, grain growth, and intergranular bubble growth. Under temperature variations, FGR is increased due to the development of micro-cracks at grain faces. This existing transient capability, however, was developed based on transient fuel behavior during power ramps and the associated micro-cracking process. Nevertheless, a fraction of the FGR during temperature transients such as LOCA can ensue from different mechanisms (in particular, fuel fragmentation) and present an important dependency on local burnup and high burnup structure formation. It follows that the performance and necessary developments of the existing BISON fission gas model for the analysis of LOCA-type transients need to be investigated through a systematic assessment study. Such a study is performed in this work. The model shows an overall good qualitative agreement with experimental observations on FGR during annealing tests with different temperature conditions. It also accounts well for microstructural effects on FGR. When quantitatively compared to FGR data from previously irradiated 103 MWd/kgU UO 2 discs under thermal annealing, the model shows a less satisfactory agreement with the experimental data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Irradiation Creep in Materials

A knowledge of the dimensional stability of reactor structural components, under irradiation conditions, is of major importance in the design of thermal, fast, and fusion reactors. When subjected to simultaneous mechanical loading and irradiation, structural materials exhibit a visco-plastic deformation phenomenon, referred to as irradiation creep, which can be more rapid than the deformation occurring out of irradiation. In this article, the phenomenology of this peculiar behavior is described after a short history of its discovery. Then, the theoretical mechanisms proposed in the literature during these past 60 years are presented, with a special focus on mechanisms based on stress induced preferred absorption of point defects by dislocation loops, dislocations and grain boundaries and on mechanisms based on climb-enhanced glide of dislocations. These mechanisms are discussed in the light of experimental evidences. Finally, irradiation creep in various materials, such as zirconium alloys, austenitic stainless steels, nickel-based alloys, ferritic-martensitic steels and graphite, is described.

Onimus, Fabien↗

BSMV-mediated genome editing exhibits host-specific heritability: germline transmission in barley and somatic edits in Nicotiana benthamiana

Plant RNA virus–mediated guide RNA (gRNA) delivery represents a transformative advance in genome editing technologies. Unlike conventional transformation methods that rely on labor-intensive tissue culture and regeneration for each individual gRNA delivery, viral vectors can rapidly and systemically transmit gRNAs into pre-established Cas-expressing plants, providing an accelerated route for functional genomics and trait discovery directly in planta . However, key design parameters, including subgenomic promoter choice, transcript architecture, and their effects on viral fitness and editing outcomes, remain to be elucidated for most viral platforms. We developed five Barley stripe mosaic virus (BSMV) vectors, each with distinct subgenomic promoter elements to drive single gRNA expression. These were initially evaluated in Cas9-expressing transgenic Nicotiana benthamiana plants targeting the Phytoene desaturase ( PDS ) gene to compare their editing efficiencies. Single gRNAs expressed under the duplicated γb subgenomic promoter or when fused directly to the γb genome achieved the highest mutation frequencies (up to 90% at 60 days post-inoculation), whereas β1- and β2-driven sgRNAs produced delayed and reduced editing. Thus, promoter selection critically determines gRNA accumulation and the efficacy of BSMV-mediated genome editing. The top-performing design was then applied to Cas9-expressing barley ( Hordeum vulgare ) targeting HvCMF7 (conferring green-white variegation) and HvGW2.1 (impacts grain width and weight). BSMV spread systemically throughout barley, inducing somatic and heritable mutations at frequencies up to 100%, with virus-free edited progeny. In contrast, despite robust somatic editing in N. benthamiana, no heritable mutations were detected indicating species-dependent limitations in germline transmission. Our systematic comparison of subgenomic promoter architectures establishes clear design principles for optimizing viral vector–mediated delivery. Promoter choice and transcript structure critically shape editing efficiency and viral stability. The host-specific boundary for germline editing, defined by efficient heritable editing in barley but not N. benthamiana , highlights where BSMV offers advantages and where alternative vectors or hybrid strategies are required, guiding rational platform selection for diverse crop species and applications. Collectively, these findings establish BSMV as a promising next-generation vector for rapid, tissue culture–free, and transformation-independent genome editing in cereals and other recalcitrant monocots.

barley↗

The complex structural and chemical nature of monolithic U-10Mo fuel and Zr barrier layer

Nanoscale microstructural characterization by advanced transmission electron microscopy techniques on a U-10Mo/Zr barrier layer monolithic fuel plate was performed to evaluate the microstructural evaluation after high burn-up. Gas bubble superlattice evolution, grain restructuring, and evolution of the Zr interaction layer is investigated through detailed electron microscopy characterization. The use of automated crystallographic orientation mapping to irradiated U-10Mo fuel highlights that the restructured ultra-fine grains are separated by high angle grain boundaries at a burn up of 4.42 × 10 21 fissions/cm 3 . Additionally, advanced chemical analysis and multi-variable statistical analysis shows spatial clustering of solid fission product precipitates. Finally, characterization of a newly observed porous nanocrystalline Zr region in the barrier layer is studied. Finally, this work provides insights into the grain subdivision and restructuring process while using advanced microscopy techniques to analyze fission products in neutron-irradiated U-10Mo fuel.

36 MATERIALS SCIENCE↗

Effects of dose rate on the microstructure and deuterium retention in γ-LiAlO 2 pellets

This report presents experimental findings obtained from November 2024 to September 2025. Defect accumulation and microstructural evolution during ion irradiation at elevated temperatures are governed by two competing processes: defect production, driven by dose rate, and defect recovery, controlled by defect diffusion, interaction, and annihilation. At a given dose, the resulting microstructural evolution depends on both the dose rate and irradiation temperature. As a continuation of our FY24 tritium science project, which investigated temperature effects at a fixed dose rate, this study focuses on dose-rate effects at a fixed temperature to provide deeper insights into the irradiated microstructure and compositional changes in γ-LiAlO 2 pellets. The study aims to elucidate the impact of dose rate on microstructure, precipitate morphology, deuterium retention, and lithium volatility in γ-LiAlO 2 pellets under sequential 120 keV He + and 80 keV D 2 + ion irradiation. Three dose rates of 7.3×10 4 , 2.9×10 4 and 6.8×10 5 dpa/s were applied to achieve the same total ion fluence of 2×10 17 (He + +D + )/cm 2 at 500 °C, corresponding to a maximum combined dose of 7.55 dpa at ~255 nm. The irradiated pellets were subsequently characterized using scanning transmission electron microscopy (STEM) and time-of-flight secondary ion mass spectrometry (ToF-SIMS). The microstructural response of γ-LiAlO 2 to ion irradiation was found to be strongly dose-rate dependent. At medium and high dose rates, irradiation produced a surface amorphized layer and an underlying crystalline layer containing LiAl 5 O 8 precipitates, with implanted gases accumulating and forming blisters at the crystalline-amorphous interface. It remains to be investigated whether the amorphized layer was produced by He + ion irradiation prior to D 2 + ion irradiation. In contrast, at low dose rates, the material remained crystalline, with cavities, likely gas-filled, distributed around precipitates, within the γ-LiAlO 2 matrix, and along grain boundaries. While precipitate morphology exhibited anisotropy, their size showed little sensitivity to dose rate in the applied range of this study. This result, however, does not rule out the possibility that further reductions in dose rate could influence precipitate size. High dose-rate irradiation enhanced protonium–deuterium isotopic exchange and lithium depletion in the amorphized region. Collectively, the results show that dose rate governs amorphization, gas redistribution, isotopic exchange, and lithium depletion, providing important insights into the mechanisms underlying structural evolution in γ-LiAlO 2 pellets under reactor-relevant irradiation conditions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Confinement‐Driven Inverse Domain Scaling in Polycrystalline ErMnO 3

Abstract The research on topological phenomena in ferroelectric materials has revolutionized the way people understand polar order. Intriguing examples are polar skyrmions, vortex/anti‐vortex structures, and ferroelectric incommensurabilties, which promote emergent physical properties ranging from electric‐field‐controllable chirality to negative capacitance effects. Here, the impact of topologically protected vortices on the domain formation in improper ferroelectric ErMnO 3 polycrystals is studied, demonstrating inverted domain scaling behavior compared to classical ferroelectrics. It is observed that as the grain size increases, smaller domains are formed. Phase field simulations reveal that elastic strain fields drive the annihilation of vortex/anti‐vortex pairs within the grains and individual vortices at the grain boundaries. The inversion of the domain scaling behavior has far‐reaching implications, providing fundamentally new opportunities for topology‐based domain engineering and the tuning of the electromechanical and dielectric performance of ferroelectrics in general.

36 MATERIALS SCIENCE↗

Development of Predictive Model for Accurate Rupture Time from Multi-Axial Creep in Alloy 709 with Physics-Based Simulations

A physics-based model is developed to predict multiaxial creep behavior in Alloy 709 (A709), an advanced austenitic stainless steel intended for high-temperature applications such as Sodium Fast Reactors (SFRs). Compared to conventional stainless steels like 316H, A709 offers superior high-temperature performance; however, comprehensive data on its multiaxial creep response remain limited. To address this gap, a crystal plasticity finite element (CPFE) framework is used to simulate the deformation and failure mechanisms of A709 under multiaxial loading conditions. The model incorporates an extended Hu-Cocks dislocation creep formulation that accounts for precipitation effects, along with the Sham–Needleman model to capture grain boundary cavitation-driven failure. These advanced constitutive models enable a detailed understanding of the interplay between microstructural evolution and macroscopic creep response. Furthermore, the study evaluates the predictive accuracy of various effective stress measures in estimating creep rupture life, leveraging simulated multiaxial creep data. The findings provide critical insights into the applicability of different stress measures for engineering design and life prediction of A709 components operating under complex loading conditions. This work contributes to improving the reliability of high-temperature structural components by advancing predictive modeling capabilities for advanced austenitic steels.

Alloy 709↗

Achieving High Strength and Creep Resistance in Inconel 740H Superalloy through Wire-Arc Additive Manufacturing and Thermodynamic-Guided Heat Treatment

Inconel 740H superalloy is commonly used in advanced ultra-supercritical power plants since it possesses excellent strength and creep resistance. This study investigates the microstructure and mechanical properties of Inconel 740H superalloy fabricated using wire-arc additive manufacturing. The as-printed microstructure consisted of columnar γ grains with the Laves phase and (Nb, Ti)C carbides as secondary phases. The anisotropy in grain structure increased from the bottom to the top regions, while the hardness was highest in the middle portion of the build. To guide the post-heat treatment design, thermodynamic and kinetic simulations were employed to predict the temperature and time. Complete recrystallization with the Laves phase dissolution occurred throughout the build after homogenization at 1200 °C for 2 h. The peak hardness was achieved after aging at 760 °C for 12 h with the M 23 C 6 carbides decorating the grain boundaries and γ’ precipitates in the grain interior. The yield strength (655 MPa) and ductility (29.5%) in the post-heat treated condition exceeded the design targets (620 MPa, 20%). Stress rupture tests at 750 °C showed that the high-temperature performance was at par with the wrought counterparts. The fracture mode after rupture was identified to be intergranular with the presence of grain boundary cavities along with grain boundary sliding.

36 MATERIALS SCIENCE↗

Anisotropic Hot Spot Formation at a Grain Boundary in Shock-Compressed TATB High Explosive Crystal

Secondary high explosives (HEs) exhibit rich microstructure that promotes the formation of hot spots responsible for detonation initiation, but the role of microstructural interfaces remains poorly quantified. To this end, we develop extensions for the generalized crystal-cutting method (GCCM) to prepare molecular dynamics (MD) simulation cells containing grain boundaries (GBs) and other crystal–crystal interfaces with prescribed tilt and twist orientations. Using the GCCM, we perform MD simulations of shock interactions with a GB between the (001) and (100) crystal facets in the secondary HE TATB (1,3,5-triamino-2,4,6-trinitrobenzene). Our MD simulations reveal a strong directional dependence to the formation of a hot spot at the GB interface. In particular, transmission of the shock from the (001) grain to the (100) grain yields a hot spot in the (100) grain at the GB interface, whereas no hot spot is produced when an equivalent shock transits the GB in the opposite direction. We trace the origin of this GB anisotropy to three dominant factors: (1) the intrinsic differences in shock-deformation mechanisms and wave structures for the bulk (100) and (001) grains, which leads to distinct geometries and mechanical impedances upon shock arrival to the GB depending on which grains are donor or acceptor for the transmitted shock; (2) the different time intervals separating the initial shock rise and the formation of steady wave structures in the respective donor–acceptor configurations; and (3) the differences in time scales required to re-establish local thermal equilibrium. Interfacial hot spots form when these factors combine to impede development of a steady two-wave structure and instead induce a localized, pseudosingly shocked region that undergoes a higher rate of work production (resulting in a higher temperature) compared to when the steady two-wave structure develops further from the interface. The extensions to the GCCM approach presented here are anticipated to facilitate a wide range of MD studies that focus on understanding the role of crystal–crystal interfaces in molecular materials.

organic↗

Relationship among the Crystal Structure, Texture, and Macroscopic Properties of Tetragonal (Pb,La)(Zr,Ti)O 3 Ferroelectrics Investigated by In Situ High-Energy Synchrotron Diffraction

In situ diffraction investigations have played an important role in experimentally revealing the mechanism of piezoelectric and ferroelectric properties. In this study, a pure tetragonal ferroelectric ceramic of La-doped PbZr 0.5 Ti 0.5 O 3 (LaPZT50) was investigated to eliminate the complex influence of phase coexistence. The electric field evolutions of the crystal structure, domain switching, and lattice deformation of the tetragonal phase have been revealed by in situ high-energy synchrotron X-ray diffraction. Furthermore, we found that the crystal structure of LaPZT50 is quite stable, showing a negligible change in the Pb–O bond length, unit cell volume, and spontaneous polarization upon application of an in situ external electric field. Importantly, the maximum macroscopic polarization of tetragonal LaPZT50 is defined by the 111-oriented grains. As determined by the intensity difference, the switching of non-180° domains plays a more significant role in contributing to the macroscopic strain than lattice deformation. These results further imply that the phase coexistence around the morphotropic phase boundary facilitates domain wall motion in the tetragonal phase and improves the ferroelectric and piezoelectric properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Role of scan strategies and heat treatment on grain structure evolution in Fe-Si soft magnetic alloys made by laser-powder bed fusion

A major goal in printing soft magnetic Fe-Si steels using additive manufacturing is to take advantage of the potential for complex geometric designs and site-specific grain control. One major step in the processing of these alloys is understanding how processing parameters might impact how the as-built microstructure responds to annealing (i.e. the annealing response). The impact of scan strategy on the annealing response for thin wall geometries is specifically explored. Two scan strategies were explored for a thin wall geometry that produced a strongly columnar grain structure and equiaxed grain structure. Additionally, samples from both scan strategies annealed at 1200 °C showed a marked difference in annealing response with the more equiaxed sample seeing full recrystallization and grain growth, while the more columnar grain structure saw little change in microstructure. After analysis through characterization techniques and thermal-mechanical simulations Differences in internal energy within the grains were ruled out because calculated GND density values were similar for both samples. The formation of secondary particles was ruled out as a contributing factor due to the type of oxide formations and their size. It was concluded that the contributing factor to the difference in the annealing response were a difference in the resulting grain size and the density of high angle grain boundaries. These two differences were largely attributed to differences in the thermal gradient conditions due to grains preferentially growing in the direction of the steepest thermal gradient.

36 MATERIALS SCIENCE↗

The subsurface structure of abraded Al–Zn–Mg–Cu alloy

Surface abrasion has been shown to introduce heavy shear stress and produce a few hundred nanometers thick altered surface layer (ASL) on Al alloys. Such ASLs exhibit microstructural changes at room temperature and different corrosion resistance than the underlying substrate. Here, we report how sample dimensions and temperature affect the deformed subsurface microstructure evolution on an abraded Al–Zn–Mg–Cu alloy using transmission electron microscopy (TEM) and atom probe tomography. The ASL microstructure evolves differently in the bulk sample than in the thin TEM specimen. In the freshly abraded ASL, the original η'/η precipitates and grain boundaries were deformed toward the abrasion direction. After 7-day natural aging of the freshly abraded bulk sample, well-defined subgrains formed locally in the ASL, and unusual Al 2 Cu (θ) and Mg x Zn y phases precipitated at the subgrain boundaries. However, during natural aging of this TEM specimen taken from the abraded and aged bulk samples, much faster changes occurred, including the continued formation of subgrains and θ particles in the entire ASL, and the diffusion of Zn atoms out of Mg x Zn y particles to form a Zn particle. On the other hand, no obvious microstructural changes occurred in the ASL during 3-month natural aging of the TEM specimen immediately taken from the freshly abraded sample. Finally, this work advances the understanding of how Al alloy microstructures respond during and following any shear deformation, and complex and unexpected effects of sample dimensions on the behavior.

36 MATERIALS SCIENCE↗

Whence the Interstellar Magnetic Field Shaping the Heliosphere?

Measurements of starlight polarized by aligned interstellar dust grains are used to probe the relation between the orientation of the ambient interstellar magnetic field (ISMF) and the ISMF traced by the ribbons of energetic neutral atoms discovered by the Interstellar Boundary Explorer spacecraft. We utilize polarization data, many acquired specifically for this study, to trace the configuration of the ISMF within 40 pc. A statistical analysis yields a best-fit ISMF orientation, B magpol , aligned with Galactic coordinates ℓ = 42°, b = 49°. Further analysis shows the ISMF is more orderly for "downfield" stars located over 90° from Bmagpol. The data subset of downfield stars yields an orientation for the nearby ISMF at ecliptic coordinates λ, β ≈ 219° ± 15°, 43° ± 9° (Galactic coordinates l, b ≈ 40°, 56°, ±17°). This best-fit ISMF orientation from polarization data is close to the field direction obtained from ribbon models. This agreement suggests that the ISMF shaping the heliosphere belongs to an extended ordered magnetic field. Extended filamentary structures are found throughout the sky. A previously discovered filament traversing the heliosphere nose region, "Filament A," extends over 300° of the sky, and crosses the upwind direction of interstellar dust flowing into the heliosphere. Filament A overlaps the locations of the Voyager kilohertz emissions, three quasar intraday variables, cosmic microwave background (CMB) components, and the inflow direction of interstellar grains sampled by Ulysses and Galileo. These features are likely located in the upstream outer heliosheath where ISMF drapes over the heliosphere, suggesting Filament A coincides with a dusty magnetized plasma. A filament 55° long is aligned with a possible shock interface between local interstellar clouds. A dark spot in the CMB is seen within 5° of the filament and within 10° of the downfield ISMF direction. Two large magnetic arcs are centered on the directions of the heliotail. The overlap between CMB components and the aligned dust grains forming Filament A indicates the configuration of dust entrained in the ISMF interacting with the heliosphere provides a measurable foreground to the CMB.

79 ASTRONOMY AND ASTROPHYSICS↗

Atomistic modeling of metal–nonmetal interphase boundary diffusion

Atomistic computer simulations are applied to investigate the atomic structure, thermal stability, and diffusion processes in Al–Si interphase boundaries as a prototype of metal–ceramic interfaces in composite materials. Some of the most stable orientation relationships between the phases found in this work were previously observed in epitaxy experiments. Here, a non-equilibrium interface can transform to a more stable state by a mechanism that we call interface-induced recrystallization. Diffusion of both Al and Si atoms in stable Al–Si interfaces is surprisingly slow compared with diffusion of both elements in Al grain boundaries but can be accelerated in the presence of interface disconnections. A qualitative explanation of the sluggish interphase boundary diffusion is proposed. Atomic mechanisms of interphase boundary diffusion are similar to those in metallic grain boundaries and are dominated by correlated atomic rearrangements in the form of strings and rings of collectively moving atoms.

36 MATERIALS SCIENCE↗