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At least 181 records · Page 10

Relaxation near Supermassive Black Holes Driven by Nuclear Spiral Arms: Anisotropic Hypervelocity Stars, S-stars, and Tidal Disruption Events

Nuclear spiral arms are small-scale transient spiral structures found in the centers of galaxies. Similarly to their galactic-scale counterparts, nuclear spiral arms can perturb the orbits of stars. In the case of the Galactic center (GC), these perturbations can affect the orbits of stars and binaries in a region extending to several hundred parsecs around the supermassive black hole (SMBH), causing diffusion in orbital energy and angular momentum. This diffusion process can drive stars and binaries to close approaches with the SMBH, disrupting single stars in tidal disruption events (TDEs), or disrupting binaries, leaving a star tightly bound to the SMBH and an unbound star escaping the galaxy, i.e., a hypervelocity star (HVS). Here, we consider diffusion by nuclear spiral arms in galactic nuclei, specifically the Milky Way GC. We determine nuclear-spiral-arm-driven diffusion rates using test-particle integrations and compute disruption rates. Our TDE rates are up to 20% higher compared to relaxation by single stars. For binaries, the enhancement is up to a factor of ∼100, and our rates are comparable to the observed numbers of HVSs and S-stars. Our scenario is complementary to relaxation driven by massive perturbers. In addition, our rates depend on the inclination of the binary with respect to the Galactic plane. Therefore, our scenario provides a novel potential source for the observed anisotropic distribution of HVSs. Nuclear spiral arms may also be important for accelerating the coalescence of binary SMBHs and for supplying nuclear star clusters with stars and gas.

79 ASTRONOMY AND ASTROPHYSICS↗

Sorbmatech{sup R}Cs, an Innovative Highly Selective Cs Sorbent for Wastewater Decontamination - 20065

The treatment of radioactive wastewater from the operating nuclear industry (energy production, reprocessing of spent fuel, decommissioning of shut-down facilities, etc.) or in case of incidental or accidental situation (such as Fukushima Daichii NPP accident) is an important issue requiring constant improvement of the technologies and techniques used to prevent radioactive releases into the environment and/or to reduce the production of secondary waste. CEA, Orano and CTI are collaborating since 2014, with the support of the French government's program 'investments for the future', to develop Sorbmatech{sup R}Cs, an innovative and patented selective sorbent (Grandjean and Barre 2014) to deal with the removal of radioactive {sup 137}Cs, one of the most hazardous isotope to be managed in nuclear waste, highly efficient either in agitated reactor or in column process. Sorbmatech{sup R}Cs sorbent consists of mesoporous silica particles loaded with potassium-copper hexacyanoferrate nanoparticles (KCu-HCF). This peculiar structure enables much faster sorption kinetics compared to denser crystalline structures, such as Silicotitanate or Zeolite sorbents, whose drawback consists in hindering the diffusion process through the material, and whose larger sorbent particles slow down the ion exchange process. The equilibrium of Sorbmatech{sup R}Cs is reached in few minutes, even at high flow rates in a fixed-bed column process (up to 10 m.h{sup -1} Darcy velocity) with low drop pressure. Moreover, Sorbmatech{sup R}Cs can be used over a wide pH range from 2 to 10 and has a very high selectivity towards {sup 137}Cs even in brine solution (saline, mineral or sea water). This new sorbent also has a K{sub d} higher than 10{sup 5} mL.g{sup -1} depending on the salinity of the wastewater, enabling a highly efficient removal of Cs trace in radioactive wastewater compared to Cs selective sorbent such as Zeolites and Silicotitanates. Its radiological resistance enables the treatment of high, medium and low activity wastewater. The CEA-Orano-CTI/ALSYS partnership leads to the development of a simple and low-cost synthetic route, which demonstrated large-scale manufacturing of the product on a batch of 100 kg. Two products have been developed and are ready for short run market introduction so far with grain size well adapted either for column processes or agitated reactors.. Finally, the industrial implementation has been studied and largely benefits from the properties of the sorbent. Indeed, its high sorption kinetics enable high flow rates resulting in a decrease of operation times, unit sizes, and volumes of secondary waste produced. Moreover, Sorbmatech{sup R}Cs is designed to be combined into a full and integrated solution, ranging from preliminary optimization of operating conditions through numerical dimensioning model, industrial implementation and treatment of the wastewater (through cartridge or preconditioned columns systems developed thanks to Orano's extensive expertise), to long-term stabilization of generated waste (under progress). (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Social network structure and the spread of complex contagions from a population genetics perspective

Ideas, behaviors, and opinions spread through social networks. If the probability of spreading to a new individual is a non-linear function of the fraction of the individuals’ affected neighbors, such a spreading process becomes a “complex contagion”. This non-linearity does not typically appear with physically spreading infections, but instead can emerge when the concept that is spreading is subject to game theoretical considerations (e.g. for choices of strategy or behavior) or psychological effects such as social reinforcement and other forms of peer influence (e.g. for ideas, preferences, or opinions). Here we study how the stochastic dynamics of such complex contagions are affected by the underlying network structure. Motivated by simulations of complex contagions on real social networks, we present a framework for analyzing the statistics of contagions with arbitrary non-linear adoption probabilities based on the mathematical tools of population genetics. The central idea is to use an effective lower-dimensional diffusion process to approximate the statistics of the contagion. This leads to a tradeoff between the effects of ”selection” (microscopic tendencies for an idea to spread or die out), random drift, and network structure. Our framework illustrates intuitively several key properties of complex contagions: stronger community structure and network sparsity can significantly enhance the spread, while broad degree distributions dampen the effect of selection compared to random drift. Finally, we show that some structural features can exhibit critical values that demarcate regimes where global contagions become possible for networks of arbitrary size. Our results draw parallels between the competition of genes in a population and memes in a world of minds and ideas. Our tools provide insight into the spread of information, behaviors, and ideas via social influence, and highlight the role of macroscopic network structure in determining their fate.

59 BASIC BIOLOGICAL SCIENCES↗

Mobility of tungsten clusters on tungsten surfaces

It is reported on an accelerated molecular dynamics investigation of surface transport mechanisms on W surfaces. These mechanisms likely influence the formation of nano-fuzz in fusion plasma-facing conditions. The simulations use an embedded-atom potential to investigate the diffusion mechanisms of W clusters (W n , n = 2–9) on W(1 1 0) and W(1 0 0) surfaces at 1000 K, reaching timescales beyond 10 microseconds. A number of fast moving adatom species, W n (n = 2–6), were observed. In contrast, slightly larger clusters W n (n = 7–9), especially W 8 , exhibit significantly lower diffusivities. The diffusion mechanisms of W n clusters on the W(1 1 0) surface are complex, with the most common elementary steps involving hops of monomers and dimers. Moreover, we observe tetramer hopping in the diffusion processes of W n (n = 4–7), trimer hopping in W n (n = 5, 6, 8), and pentamer hopping in W 5 on the W(1 1 0) surface. W n (n ≤ 3) and metastable W n (n > 3) clusters on the W(1 0 0) surface diffuse predominantly through monomer exchange with surface atoms. However, W clusters containing square tetramers are essentially immobile on the W(1 0 0) surface at 1000 K.

Instruments & Instrumentation↗

Interaction of magnesia-carbon refractory with metallic iron under flash ironmaking conditions

The interaction of a magnesia-carbon refractory with iron under flash ironmaking conditions has been investigated in this work. Oxidation of carbon from the magnesia-carbon refractory took place and the formation of magnesiowustite (Mg x Fe 1-x O) solid solution occurred as a result of the interaction between magnesia (MgO) in the refractory with iron (Fe). A kinetics model for the growth of magnesiowustite (Mg x Fe 1-x O) was developed based on the counterdiffusion of Fe 2+ and Mg 2+ cations through it. Experiments were conducted with iron powder and magnesia-carbon refractory in the temperature range 1200–1400 °C under gas atmospheres relevant to flash ironmaking and analyses of reacted samples using SEM-EDX and EPMA techniques confirmed the formation of magnesiowustite (Mg x Fe 1-x O). Using the kinetics model and the composition profiles determined with EPMA, the values of interdiffusion coefficient ( D ¯ F e - M g ), averaged over the composition range, were calculated. The activation energy ( E a ) for the solid-state diffusion process was determined to be 377 kJ/mol.

36 MATERIALS SCIENCE↗

Fast Na diffusion and anharmonic phonon dynamics in superionic Na 3 PS 4

The design of new solid electrolytes (SEs) hinges on identifying and tuning relevant descriptors. Phonons describe the atomic dynamics in crystalline materials and provide a basis to encode possible minimum energy pathways for ion migration, but anharmonic effects can be large in SEs. Identifying and controlling the pertinent phonon modes coupled most strongly with ionic conductivity, and assessing the role of anharmonicity, could therefore pave the way for discovering and designing new SEs via phonon engineering. In this work, we investigate phonons in Na 3 PS 4 and their coupling to fast Na diffusion, using a combination of neutron scattering, ab initio molecular dynamics (AIMD), and extended molecular dynamics based on machine-learned potentials. We identify that anharmonic soft-modes at the Brillouin zone boundary of the anharmonically stabilized cubic phase constitute key phonon modes that control the Na diffusion process in Na 3 PS 4 . We demonstrate how these strongly anharmonic phonon modes enable Na-ions to hop along the minimum energy pathways. Further, the quasi-elastic neutron scattering (QENS) measurements, supplemented with ab initio and machine-learned molecular dynamics simulations, probe the Na diffusivity and diffusion mechanism. These results offer detailed microscopic insights into the dynamic mechanism of fast Na diffusion and provide an avenue to search for further Na solid electrolytes.

42 ENGINEERING↗

IoT-based retrofit information diffusion in future smart communities

Community-scale building retrofits are not merely scaled-up versions of single-building retrofits. They involve complex challenges, such as reconciling individual interests with collective goals and managing the dynamic interplay between buildings through mechanisms like power grids and social connections. Internet of Things (IoT) connectivity holds the potential to leverage these interplays to balance individual and collective interests effectively in smart communities. One critical aspect of this interplay is information diffusion, which shapes how retrofit decisions spread among neighbors, influencing individual choices and ultimately impacting community-level retrofit outcomes. In other words, IoT-based smart devices automatically push tailored retrofit notifications to homeowners, which completely changes the format of information diffusion in the future. To investigate this influence by such information diffusion, the study used CityBES to simulate energy performance for different retrofits and applied an information diffusion model to analyze how decisions spread in a networked community of 192 buildings. The diffusion process was modeled on a weighted, directed network, capturing the dynamics of information flow and decision-making across 16 scenarios. Individual retrofit benefits were evaluated through payback years, while community-level retrofit outcomes were assessed using greenhouse gas (GHG) emission reductions. The results demonstrate that easier information diffusion among neighbors encourages households to prioritize retrofit measures that align with the majority’s optimal choices, even at the expense of individual financial benefits. In this case, such collective prioritization enhanced community-level retrofit performance, increasing GHG emission reductions by up to 29.4 %. However, this improvement came with trade-offs, as the average payback period for households extended by approximately 1.74 years. These findings highlight the potential of IoT-based information diffusion in future smart communities to coordinate individual interests with collective goals, ultimately accelerating community-level building retrofits.

Shu, Lei↗

Stochastic control with rough paths

We study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We make the link to old work of Davis and Burstein (Stoch Stoch Rep 40:203–256, 1992) and then prove a continuous-time generalization of Roger’s duality formula [SIAM J Control Optim 46:1116–1132, 2007]. The generic case of controlled volatility is seen to give trivial duality bounds, and explains the focus in Burstein–Davis’ (and this) work on controlled drift. Our study of controlled rough differential equations also relates to work of Mazliak and Nourdin (Stoch Dyn 08:23, 2008).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantifying Anionic Diffusion in 2D Halide Perovskite Lateral Heterostructures

Anionic diffusion strongly impacts the stability of halide perovskite materials, but it is still not well understood. Here, a quantitative investigation of in-plane thermally driven anionic inter-diffusion in a series of novel 2D and quasi-2D halide perovskites lateral heterostructures is reported. The calculated diffusion coefficients (D) reveal the inhibition of Br–I inter-diffusion with bulky π-conjugated organic cations compared with short-chain aliphatic organic cations. Furthermore, halide diffusion is found to be faster in quasi-2D (n > 1) than 2D perovskites (n = 1). The increment becomes less apparent as the “n” number increases, akin to the quantum confinement effect observed for band gaps. These trends are rationalized by molecular dynamics simulations of free energy barriers for halide diffusion that reveal mechanisms for suppressing diffusion. We report this work provides important fundamental insights on the anionic migration and diffusion process in halide perovskite materials.

2D materials↗

Understanding the Reliability of Solder Joints Used in Advanced Structural and Electronics Applications: Part 2 - Reliability Performance.

Whether structural or electronic, all solder joints must provide the necessary level of reliability for the application. The Part 1 report examined the effects of filler metal properties and the soldering process on joint reliability. Filler metal solderability and mechanical properties, as well as the extents of base material dissolution and interface reaction that occur during the soldering process, were shown to affect reliability performance. The continuation of this discussion is presented in this Part 2 report, which highlights those factors that directly affect solder joint reliability. There is the growth of an intermetallic compound (IMC) reaction layer at the solder/base material interface by means of solid-state diffusion processes. In terms of mechanical response by the solder joint, fatigue remains as the foremost concern for long-term performance. Thermal mechanical fatigue (TMF), a form of low-cycle fatigue (LCF), occurs when temperature cycling is combined with mismatched values of the coefficient of thermal expansion (CTE) between materials comprising the solder joint “system.” Vibration environments give rise to high-cycle fatigue (HCF) degradation. Although accelerated aging studies provide valuable empirical data, too many variants of filler metals, base materials, joint geometries, and service environments are forcing design engineers to embrace computational modeling to predict the long-term reliability of solder joints.

42 ENGINEERING↗

Combining molecular dynamics with mesoscopic Green’s function reaction dynamics simulations

In many reaction-diffusion processes, ranging from biochemical networks, catalysis, to complex self-assembly, the spatial distribution of the reactants and the stochastic character of their interactions are crucial for the macroscopic behavior. The recently developed mesoscopic Green’s Function Reaction Dynamics (GFRD) method enables efficient simulation at the particle level provided the microscopic dynamics can be integrated out. Yet, many processes exhibit non-trivial microscopic dynamics that can qualitatively change the macroscopic behavior, calling for an atomistic, microscopic description. We propose a novel approach that combines GFRD for simulating the system at the mesoscopic scale where particles are far apart, with a microscopic technique such as Langevin dynamics or Molecular Dynamics (MD), for simulating the system at the microscopic scale where reactants are in close proximity. This scheme defines the regions where the particles are close together and simulated with high microscopic resolution and those where they are far apart and simulated with lower mesoscopic resolution, adaptively on the fly. The new multi-scale scheme, called MD-GFRD, is generic and can be used to efficiently simulate reaction-diffusion systems at the particle level.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Computational diagnostics and characterization of combustion recession in diesel sprays

While low-temperature combustion (LTC) strategies have been found to mitigate nitrogen oxides and particulate matter emissions in diesel engines, studies have also associated LTC with an increase in unburnt hydrocarbons. With more recent studies on diesel after end-of-injection (AEOI), combustion recession is identified as a phenomenon where at near nozzle region, high-temperature ignition (HTI) combustion can propagate back to the nozzle tip consuming the unburnt hydrocarbons AEOI. Current literature has suggested that combustion recession is controlled by auto-ignition. However, high-fidelity simulations and detailed analysis of such a mechanism are missing. In this study, comprehensive Large Eddy Simulations of a reacting spray at “Spray A” conditions are performed, where detailed analysis of combustion recession concerning flame morphology and propagation modes are included. In particular, this study demonstrated for the first time that while combustion recession is mainly auto-ignition dominated (consistent with the literature), a cool flame was found to deflagrate towards the richer regions of the mixture, promoting mixing and increasing the mixture temperature. This leads to HTI kernels, which then grow and develop as deflagrative waves, therefore sustaining the combustion recession process. The study also detailed the extinction mechanism of combustion: the entrainment wave will overlean the near-nozzle mixtures, rendering it unable to support HTI, which leads to the extinction of the upstream flame AEOI in lower reactivity mixtures. Combustion recession is also observed to be contingent on the chemical and diffusion processes, even at low scalar dissipation rates. Finally, a new criterion for combustion recession based on chemical explosive mode is proposed and validated with previous combustion recession index to quantify the extent of HTI in near-nozzle mixtures AEOI. The newly developed metric combined with a previous experimentally-based metric can provide simple but valuable measurements of the degree and propensity of the upstream flame AEOI.

CEMA↗

NOCI-F Electronic Couplings in Assemblies of Indolonaphthyridine Molecules: From Dimers to the Full Stack

Key electronic processes related to molecular excitonic states of finite stacks of indolonaphthyridine molecules are analyzed via the non-orthogonal configuration interaction with fragments (NOCI-F) method. Indolonaphthyridine is an organic chromophore that can undergo several electronic photoexcitation-related intermolecular processes, such as exciton and electron transfer. The structures studied here are noncrystalline arrangements built as either ordered stacks of indolonaphthyridine or stacks extracted from molecular dynamics simulations including thermal disorder. Taking dimers or trimers from either model, we performed CASSCF and NOCI-F calculations to quantify the intermolecular electronic couplings governing singlet fission, excited singlet and triplet diffusion, and hole and electron diffusion processes. Also, comparing the results for the different models, we studied the effect of structural disorder and distortion on these couplings. Finally, we present a newly developed, advanced postanalysis tool. It takes the NOCI-F data as input to carry out a multifragment full Hamiltonian procedure that involves the complete stack, providing physical information not available from the dimer/trimer models, hence giving access to additional insight into the material’s properties.

coupling reactions↗

Giant interfacial spin Hall angle from Rashba-Edelstein effect revealed by the spin Hall Hanle process

The Rashba-Edelstein effect (REE), which generates interfacial spin polarization and subsequent spin current, is a compelling spin-charge conversion mechanism for spintronic applications, since it’s not limited by the elemental spin-orbit couplings. In this work we demonstrate REE at Pt/ferroelectric interfaces by showing a positive correlation between polarization and effective spin Hall angle in the recently elucidated spin Hall Hanle effects (SHHE), in which a Larmor precession of spin polarization in a diffusion process from the interface manifest as magnetoresistance and Hall effect. We show that REE leads to a large enhancement of the effective spin Hall angle of ferroelectric interface Pt/h-LuFeO 3 compared with that of Pt/Al 2 O 3 , without obvious differences in the spin relaxation time. Modeling using SHHEs involving REE as an additional source of interfacial polarization suggests that REE can lead to an interfacial spin Hall angle (0.4 ± 0.1) in Pt/h-LuFeO 3 that is one order of magnitude larger than the bulk value of Pt. Our results demonstrate that a ferroelectric interface can produce large spin-charge conversion and that SHHEs are a sensitive tool for characterizing interfacial spin-transport properties.

36 MATERIALS SCIENCE↗

Characterization and Modeling of Grain Boundary Chemistry Evolution in Ferritic Steels under Irradiation

Ferritic/martensitic (FM) steels such as HT-9, T-91 and NF12 with chromium concentrations in the range of 9-12 at.% Cr and high Cr ferritic steels (oxide dispersion strengthened steels with 12-18% Cr) are receiving increasing attention for advanced nuclear applications, e.g. cladding and duct materials for sodium fast reactors, pressure vessels in Generation IV reactors and first wall structures in fusion reactors, thanks to their advantages over austenitic alloys. Predicting the behavior of these alloys under radiation is an essential step towards the use of these alloys. Several radiation-induced phenomena need to be taken into account, including phase separation, solute clustering, and radiation-induced segregation or depletion (RIS) to point defect sinks. RIS at grain boundaries has raised significant interest because of its role in irradiation assisted stress corrosion cracking (IASCC) and corrosion of structural materials. Numerous observations of RIS have been reported on austenitic stainless steels where it is generally found that Cr depletes at grain boundaries, consistently with Cr atoms being oversized in the fcc Fe matrix. While FM and ferritic steels are also subject to RIS at grain boundaries, unlike austenitic steels, the behavior of Cr is less clear with significant scatter and no clear dependency on irradiation condition or alloy type. In addition to the lack of conclusive experimental evidence regarding RIS in F-M alloys, there have been relatively few efforts at modeling RIS behavior in these alloys. The need for predictability of materials behavior and mitigation routes for IASCC requires elucidating the origin of the variable Cr behavior. A systematic detailed high-resolution structural and chemical characterization approach was applied to ion-implanted and neutron-irradiated model Fe-Cr alloys containing from 3 to 18 at.% Cr. Atom probe tomography analyses of the microstructures revealed slight Cr clustering and segregation to dislocations and grain boundaries in the ion-irradiated alloys. More significant segregation was observed in the neutron irradiated alloys. For the more concentrated alloys, irradiation did not affect existing Cr segregation to grain boundaries and segregation to dislocation loops was not observed perhaps due to a change in the dislocation loop structure with increasing Cr concentration. Precipitation of α’ was observed in the neutron irradiated alloys containing over 9 at.% Cr. However ion irradiation appears to suppress the precipitation process. Initial low dose ion irradiation experiments strongly suggest a cascade recoil effect. The systematic analysis of grain boundary orientation on Cr segregation was significantly challenged by carbon contamination during ion irradiation or by existing carbon and therefore carbide formation at grain boundaries (sensitization). The combination of the proposed systematic experimental approach with atomistic modeling of diffusion processes directly addresses the programmatic need for developing and benchmarking predictive models for material degradation taking into account atomistic kinetics parameters

36 MATERIALS SCIENCE↗

Cosmic Rays in Intermittent Magnetic Fields

The propagation of cosmic rays in turbulent magnetic fields is a diffusive process driven by the scattering of the charged particles by random magnetic fluctuations. Such fields are usually highly intermittent, consisting of intense magnetic filaments and ribbons surrounded by weaker, unstructured fluctuations. Studies of cosmic-ray propagation have largely overlooked intermittency, instead adopting Gaussian random magnetic fields. Using test particle simulations, we calculate cosmic-ray diffusivity in intermittent, dynamo-generated magnetic fields. The results are compared with those obtained from non-intermittent magnetic fields having identical power spectra. The presence of magnetic intermittency significantly enhances cosmic-ray diffusion over a wide range of particle energies. We demonstrate that the results can be interpreted in terms of a correlated random walk.

79 ASTRONOMY AND ASTROPHYSICS↗

Thermodynamic-state and kinetic-process dependent dual ferromagnetic states in high-Si content FeMn(PSi) alloys

We have found that thermodynamic state and kinetic process co-determine the dual ferromagnetic (FM) orders in high-Si content FeMnP{sub 1−x}Si{sub x} (0.25 < x < 0.5). Alloys undergoing high temperature annealing and quenching process prefer a high magnetic moment FM state in a chemically partial disordered structure with low c/a ratio. This mechanism is suggested to be responsible for the often discussed virgin effect as well. A chemically ordered structure obtained by a slow cooling process from a relatively low annealing temperature and the increase in Si content stabilize a metastable lattice with high c/a ratio and FM order with low magnetic moment. The non-simultaneity of the magnetic and structural transitions can be responsible for the occurrence of FM state in the high c/a range. Thus, a c/a ratio that changes from high to low is physically plausible to stabilize the metastable FM order at low temperature. Our theoretical observations indicate that suitable thermodynamic state and kinetic diffusion process is crucial for optimizing magnetocaloric properties and exploring feasible magnetocaloric materials.

36 MATERIALS SCIENCE↗

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↗