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At least 757 records · Page 42
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DOE OSTI2025

Infrared spectral signatures of interfacial water at TiO 2 –electrolyte interfaces from deep potential molecular dynamics

Vibrational spectroscopy is a powerful tool for probing water at oxide–electrolyte interfaces, but its molecular interpretation can be challenging. Here, we employ deep potential long-range molecular dynamics simulations with layer-resolved spectral analysis to investigate the microscopic origins of the infrared (IR) response of water at the interface with anatase TiO 2 (101), a prototypical oxide surface. The calculated interfacial spectra exhibit characteristic modifications compared to bulk water IR spectra, including enhanced intensities, a red shifted and broadened stretching band, and a higher-frequency shoulder, in qualitative agreement with experiments. Spectral decomposition shows that these signatures originate mainly from the first interfacial water layer, dominated by surface-bound H 2 O at Ti 5C sites, with secondary contributions from the second layer. A moderate salt concentration (0.4 M NaCl) leaves both the interfacial structure and the spectra essentially unchanged, while tuning the pH strongly modulates the spectral intensity. We establish a scaling relation linking the spectral intensity to the surface water dissociation fraction and the dipole moment, both governed by interfacial electric fields. These findings provide a microscopic framework for interpreting IR spectra of oxide–electrolyte interfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

X-ray diffraction measurements and pressure determination in nanosecond compression of solids up to 600 GPa

X-ray diffraction measurements under laser-driven dynamic compression now allow us to investigate the atomic structure of matter at TPa pressures and thousands of degree temperatures with broad implications for condensed matter physics, planetary science and astronomy. Furthermore, pressure determination in these experiments often relies on velocimetry measurements coupled with modeling that requires accurate knowledge of the optical and thermo-mechanical properties of a window material, resulting in significant systematic uncertainty. Here we demonstrate different approach applicable to X-ray diffraction experiments under quasi-isentropic ramp-compression based on the use of in-situ pressure calibrants, similar to the methods often adopted in static-compression experiments with diamond anvil cells. Focusing on experiments using a diamond window, we discuss challenges and mitigation strategies for the novel approach. Our study, in addition to providing new structural information of 5 metals up to hundreds of GPa, provides validation to the currently used methods based on time-resolved measurement of the diamond free-surface velocity, and reveals that the use of in-situ calibrants enables a factor of four reduction in the pressure uncertainty in these experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Direct Measurement of the Nickel Spectrum in Cosmic Rays in the Energy Range from 8.8 GeV/$\mathcal{n}$ to 240 GeV/$\mathcal{n}$ with CALET on the International Space Station

The relative abundance of cosmic ray nickel nuclei with respect to iron is by far larger than for all other transiron elements; therefore it provides a favorable opportunity for a low background measurement of its spectrum. Since nickel, as well as iron, is one of the most stable nuclei, the nickel energy spectrum and its relative abundance with respect to iron provide important information to estimate the abundances at the cosmic ray source and to model the Galactic propagation of heavy nuclei. However, only a few direct measurements of cosmic-ray nickel at energy larger than ~ 3 GeV/n are available at present in the literature, and they are affected by strong limitations in both energy reach and statistics. In this Letter, we present a measurement of the differential energy spectrum of nickel in the energy range from 8.8 to 240 GeV/n , carried out with unprecedented precision by the Calorimetric Electron Telescope (CALET) in operation on the International Space Station since 2015. The CALET instrument can identify individual nuclear species via a measurement of their electric charge with a dynamic range extending far beyond iron (up to atomic number Z = 40 ). The particle’s energy is measured by a homogeneous calorimeter (1.2 proton interaction lengths, 27 radiation lengths) preceded by a thin imaging section (3 radiation lengths) providing tracking and energy sampling. This Letter follows our previous measurement of the iron spectrum [O. Adriani et al. (CALET Collaboration), Phys. Rev. Lett. 126, 241101 (2021).], and it extends our investigation on the energy dependence of the spectral index of heavy elements. It reports the analysis of nickel data collected from November 2015 to May 2021 and a detailed assessment of the systematic uncertainties. In the region from 20 to 240 GeV/n our present data are compatible within the errors with a single power law with spectral index -2.51 ± 0.07 .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Broadband hard X-ray attosecond pulses from extremely chirped electron beams

Attosecond pulses from free-electron lasers have opened the doors to atomic site-specific studies of bound electronic dynamics on their natural, sub-femtosecond timescales. Key to their success has been electron beam shaping techniques enabling the generation of sub-femtosecond current spikes with peak currents on the order of 10 kA. We demonstrate in an RF linac the generation of current spikes with extreme chirps on the order of 350 MeV/micron, directly competitive with the chirps expected from beam-driven plasma wakefield accelerators. Leveraging chirp-taper compensation, we use these highly chirped beams to generate hard X-ray attosecond pulses with bandwidths exceeding 30 eV, a factor of two beyond previous demonstrations. We simultaneously present the first explicit experimental evidence of chirp-taper compensation in an attosecond XFEL, finding that optimal tapering improves the bandwidth and pulse energy by factors of two and five, respectively, for our conditions. In addition to the immediate utility of such broadband hard X-ray pulses, electron beams with such extreme chirps can be utilized for unique new experimental modalities by performing further compression after the undulators. Such post-lasing compression can enable subsequent superradiant light emission at longer wavelengths, or direct excitation of quantum systems with the beam's intense space-charge field for unique attosecond pump-probe possibilities.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

A New Inelastic Neutron Spectrometer HODACA

In this study, a new multiplex-type inelastic neutron scattering spectrometer, HOrizontally Defocusing Analyzer Concurrent data Acquisition spectrometer (HODACA), was recently developed and built at the C1-1 cold neutron beam port in the neutron source reactor JRR-3 at Japan Atomic Energy Agency. The spectrometer is suitable for dynamics measurements in the energy range of -1 meV ≲ ℏω ≲ 7 meV, catering to a broad array of research fields in physics and material science. HODACA combines 24 detectors and 132 pieces of analyzer crystals and has an estimated measurement efficiency that is 70 times greater than the existing conventional triple-axis spectrometer at the C1-1 beam port. The concept, design, specification, and results of commissioning experiments are described.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

PDB-IHM: A System for Deposition, Curation, Validation, and Dissemination of Integrative Structures

Structures of many large biomolecular assemblies are now being determined using integrative approaches. In these approaches, information derived from multiple experimental and computational methods is combined to compute three-dimensional structures of multi-protein complexes and other macromolecular machines. A standalone prototype data resource for integrative structures called PDB-Dev was built, based on recommendations of the Integrative and Hybrid Methods (IHM) Task Force of the Worldwide Protein Data Bank (wwPDB). This effort included developing data standards and software tools for collecting, curating, validating, visualizing, archiving, and disseminating integrative structures that span diverse spatiotemporal scales and conformational states. Mechanisms have been created to validate integrative structures based on the experimental data underpinning them. Building upon this foundational framework, PDB-Dev has been further expanded to handle large dynamic macromolecular systems and integrative structures that combine, for example, experimental restraints with atomic coordinates computed by machine learning algorithms. Data standards and supporting tools have also been extended to capture information about biomolecular dynamics, such as conformational transitions and related kinetic data derived from biophysical methods. Recently, PDB-Dev was unified with the PDB archive and rebranded as PDB-IHM (pdb-ihm.org), further promoting FAIR (Findable, Accessible, Interoperable, and Reusable) principles of data stewardship for integrative structural biology.

IHMCIF↗
DOE OSTI2020

Accelerating Ab Initio Simulation via Nested Monte Carlo and Machine Learned Reference Potentials

As a corollary of the rapid advances in computing, ab initio simulation is playing an increasingly important role in modeling materials at the atomic scale. Two strategies are possible, ab initio Monte Carlo (AIMC) and molecular dynamics (AIMD) simulation. The former benefits from exact sampling from the correct thermodynamic distribution, while the latter is typically more efficient with its collective all-atom coordinate updates. In this study, using a relatively simple test model comprised of helium and argon, we show that AIMC can be brought up to, and even above, the performance levels of AIMD via a hybrid nested sampling/machine learning (ML) strategy. Here, ML provides an accurate classical reference potential (up to three-body explicit interactions) that can pilot long collective Monte Carlo moves that are accepted or rejected in toto à la nested Monte Carlo (NMC); this is in contrast to the single move nature of a naive implementation. Our proposed method only requires a small up front expense from evaluating the ab initio energies and forces of (100) random configurations for training. Importantly, our method does not totally rely on the trained, assuredly imperfect, interaction. We show that high performance and exact sampling at the desired level of theory can be realized even when the trained interaction has appreciable differences from the ab initio potential. Remarkably, at the highest levels of performance realized via our approach, a pair of statistically uncorrelated atomic configurations can be generated with (1) ab initio calculations.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Mechanistic study of direct coupling of CO 2 and C 2 H 4 over atomically dispersed metal at graphene edges

Direct coupling of CO 2 and ethylene (hereinafter DCCE) to acrylic acid is valuable for valorizing CO 2 to manufacture acrylate-derived products. However, previous studies in DCCE have been limited on molecular catalysts with challenges in improving catalytic performance. In this work, we employed density functional theory calculations and ab initio molecular dynamics simulations to investigate the heterogeneous catalysis of DCCE over atomically dispersed metal centers at nitrogen-doped zigzag edge of graphene. Based on competitive adsorption and structural stability, Mo, Cr, V, Ru, and Ni active sites are chosen to explore the reaction kinetics. Here, we find that the activation barriers are determined by the charge redistribution at transition states, which explains the trend of activity for the C-C coupling and the hydrogen transfer, two key steps in DCCE. Furthermore, we show that the intramolecular hydrogen transfer (rate-limiting step) is hindered due to the lack of local coordinate at the active sites. We thus propose to use co-adsorbed water as a “proton-exchanger” following a water-assisted route, and show that the activation barriers are reduced over all metal centers. Particularly, water promotes the hydrogen transfer over metals with strong CO 2 -ethylene co-activation and facile C-C coupling kinetics, which could be considered promising for DCCE. In both mechanisms, the stability of metallactone intermediate can be used to predict the catalytic activity. It is anticipated that the insights from this work can provide guidelines for mimicking well-defined multifunctional active sites in molecular catalysts to design heterogeneous catalysts for such C-C coupling, which advances catalytic utilization of CO 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Superfluid effective field theory for dark matter direct detection

We develop an effective field theory (EFT) framework for superfluid 4 He to model the interactions among quasiparticles, helium atoms and probe particles. Our effective field theory approach brings together symmetry arguments and power-counting and matches to classical fluid dynamics. We then present the decay and scattering rates for the relevant processes involving quasiparticles and helium atoms. The presented EFT framework and results can be used to understand the dynamics of thermalization in the superfluid, and can be further applied to sub-GeV dark matter direct detection with superfluid 4 He.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Evolution of Charge-Lattice Dynamics across the Kuramoto Synchronization Phase Diagram of Quantum Tunneling Polarons in Cuprate Superconductors

Because of its sensitivity to the instantaneous structure factor, S(Q,t = 0), Extended X-ray Absorption Fine Structure (EXAFS) is a powerful tool for probing the dynamic structure of condensed matter systems in which the charge and lattice dynamics are coupled. When applied to hole-doped cuprate superconductors, EXAFS has revealed the presence of internal quantum tunneling polarons (IQTPs). An IQTP arises in EXAFS as a two-site distribution for certain Cu–O pairs, which is also duplicated in inelastic scattering but not observed in standard diffraction measurements. The Cu–Sr pair distribution has been found to be highly anharmonic and strongly correlated to both the IQTPs and to superconductivity, as, for example, in YSr 2 Cu 2.75 Mo 0.25 O 7.54 (T c =84 K). In order to describe such nontrivial, anharmonic charge-lattice dynamics, we have proposed a model Hamiltonian for a prototype six-atom cluster, in which two Cu-apical-O IQTPs are charge-transfer bridged through Cu atoms by an O atom in the CuO 2 plane and are anharmonically coupled via a Sr atom. By applying an exact diagonalization procedure to this cluster, we have verified that our model indeed produces an intricate interplay between charge and lattice dynamics. Then, by using the Kuramoto model for the synchronization of coupled quantum oscillators, we have found a first-order phase transition for the IQTPs into a synchronized, phase-locked phase. Most importantly, we have shown that this transition results specifically from the anharmonicity. Finally, we have provided a phase diagram showing the onset of the phase-locking of IQTPs as a function of the charge-lattice and anharmonic couplings in our model. We have found that the charge, initially confined to the apical oxygens, is partially pumped into the CuO 2 plane in the synchronized phase, which suggests a possible connection between the synchronized dynamic structure and high-temperature superconductivity (HTSC) in doped cuprates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Thermal conductance enhanced via inelastic phonon transport by atomic vacancies at Cu/Si interfaces

Understanding and controlling heat transfer across interfaces has become an important issue for the performance of micro- and nanoscale electronics, as well as achieving a high figure of merit for thermoelectrics. Intrinsic and extrinsic defects can have a significant impact on thermal transport in bulk materials and across interfaces, but the mechanism is not well understood. Here, nonequilibrium molecular dynamics simulations are used to determine the impact of interfacial atomic vacancies on thermal transport across a Cu/Si junction. In contrast to the reduction in thermal transport typically seen with bulk defects, we find that by introducing atomic vacancies at a concentration of 6.3% near the interface in either or both materials, the interfacial thermal conductance can be increased by up to 76%. By controlling the initial positions of the vacancies and keeping track of their movements and population, we find that interfacial thermal transport is dependent on temperature, vacancy concentration, and distribution, and a positive correlation between the conductance and point defect activities (extent of vacancy migration, rate of Frenkel defect creation and annihilation) is observed. Further calculations based on the phonon density of states and normal mode decomposition reveal that the increase in interfacial thermal conductance originates primarily from high-frequency phonons, supported by enhanced inelastic phonon transport which contributes to more than 60% of the increase. Our findings suggest a practical way to manipulate inelastic phonon conversion through the presence of defects, which provides an alternative perspective on improving thermal transport between materials with a large lattice mismatch.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Development and transferability of neural-network models for plasma-surface interactions

Plasma-surface interactions are increasingly critical to modern technologies; yet, accurate molecular dynamics simulations remain limited by the capabilities of interatomic potentials. Deep Potentials (DPs) promise to revolutionize the field by providing a systematic method for producing accurate interatomic potentials. The primary challenge of DP development is selecting a dataset, which efficiently spans the set of atomic environments one expects to encounter in the subsequent molecular dynamics simulations. The computational cost of density functional theory calculations, which are the typical basis for DP development, makes it impossible to directly verify the quality of a given DP. To address this challenge, we explore the development of a deep-learned interatomic potential, “DeepREBO,” trained to reproduce the behavior of the REBO2 empirical potential, enabling direct validation of training methodology and transferability. Using an active learning framework, we begin with a minimal dataset and iteratively expand it to train a Deep Potential-Smooth Edition model that faithfully reproduces REBO2 results for 25 eV hydrogen bombardment of diamond (001), a particularly challenging case. We show that small, carefully curated datasets can outperform large, unguided ones, with effective models requiring fewer than 15 000 snapshots. Subsequent transferability tests demonstrate that while DeepREBO generalizes well to diamond (111) surfaces, performance degrades for amorphous carbon or higher-energy impacts, highlighting the need for use-case-specific training data. We also evaluate methods to improve short-range repulsion. This study outlines best practices for training robust deep potentials and underscores the importance of dataset design for predictive plasma simulations.

Ab-initio molecular dynamics↗
DOE OSTI2022

Variable-Temperature Scattering and Spectroscopy Characterizations for Temperature-Dependent Solution Assembly of PffBT4T-Based Conjugated Polymers

The solution structure of conjugated polymers (CPs) from which the films are cast is critical for tailoring the thin-film morphology thus device performance. Here, we used multimodal variable-temperature scattering and spectroscopy tools to fully quantify the solution assembly of poly[(5,6-difluoro-2,1,3-benzothiadiazol-4,7-diyl)-alt-(3,3'''-dialkyl-2,2';5',2'';5'',2'''-quaterthiophen-5,5'''-diyl)] (PffBT4T) polymers with varying side-chain lengths at different assembly temperatures. The conformational and aggregation behaviors for PffBT4T-based CPs were found to be very sensitive to both temperature and side chain length using ultraviolet–visible (UV–vis) spectroscopy, nuclear magnetic resonance (NMR) spectroscopy, dynamic light scattering (DLS), and small-angle neutron scattering (SANS). We found that with slightly increasing side chain length from 2-octyldodecyl (C8C12) to 2-nonyltridecyl (C9C13), PffBT4T-based CPs show a significant decrease in aggregation-to-dissolved chain transition temperature (10 °C), degree of aggregation, enthalpy change of aggregation, and size of the aggregates in solution. At room temperature, PffBT4T polymer strongly aggregated to form fabric structure with the film thickness of a few nanometers in thickness and hundreds of nanometers in length, as probed by atomic force microscopy (AFM), transmission electronic microscopy (TEM), and dynamic light scattering (DLS). At the elevated temperature above the aggregation-to-dissolved chain transition temperature, PffBT4T is fully dissolved and adopts a semiflexible coil conformation with the persistence length of 3.1 nm for PffBT4T-C8C12 and a slightly increased persistence length of 3.4 nm for PffBT4T-C9C13, according to temperature-dependent SANS measurements. Longer side chains of PffBT4T-C9C13 also lead to less aggregation enthalpy gain compared with PffBT4T-C8C12. This work provides a solution structure manipulating strategy of CPs and thus will inspire the molecular design and processing protocols of CPs toward higher performance electronic devices.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Unveiling defect-mediated carrier dynamics in monolayer semiconductors by spatiotemporal microwave imaging

The optoelectronic properties of atomically thin transition-metal dichalcogenides are strongly correlated with the presence of defects in the materials, which are not necessarily detrimental for certain applications. For instance, defects can lead to an enhanced photoconduction, a complicated process involving charge generation and recombination in the time domain and carrier transport in the spatial domain. Here, we report the simultaneous spatial and temporal photoconductivity imaging in two types of WS 2 monolayers by laser-illuminated microwave impedance microscopy. The diffusion length and carrier lifetime were directly extracted from the spatial profile and temporal relaxation of microwave signals, respectively. Time-resolved experiments indicate that the critical process for photoexcited carriers is the escape of holes from trap states, which prolongs the apparent lifetime of mobile electrons in the conduction band. As a result, counterintuitively, the long-lived photoconductivity signal is higher in chemical-vapor deposited (CVD) samples than exfoliated monolayers due to the presence of traps that inhibits recombination. Overall, our work reveals the intrinsic time and length scales of electrical response to photoexcitation in van der Waals materials, which is essential for their applications in optoelectronic devices.

42 ENGINEERING↗
DOE OSTI2024

All-Atom Biomolecular Simulation in the Exascale Era

Exascale supercomputers have opened the door to dynamic simulations, facilitated by AI/ML techniques, that model biomolecular motions over unprecedented length and time scales. This new capability holds the potential to revolutionize our understanding of fundamental biological processes. Herein we report on some of the major advances that were discussed at a recent CECAM workshop in Pisa, Italy, on the topic with a primary focus on atomic-level simulations. First, we highlight examples of current large-scale biomolecular simulations and the future possibilities enabled by crossing the exascale threshold. Next, we discuss challenges to be overcome in optimizing the usage of these powerful resources. Finally, we close by listing several grand challenge problems that could be investigated with this new computer architecture.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Size-dependent second-order-like phase transitions in Fe nanocluster melting from low-temperature structural isomerization

Here, in this work, the melting phase transitions of Fe n nanoclusters with 10 ≤ n ≤ 100 atoms are investigated using classical many-body molecular dynamics simulations. For many cluster sizes, surface melting occurs at much lower temperatures than core melting. Surface and core melting points and energetic melting points (temperatures of maximum heat capacity, C v ) are calculated for all cluster sizes. Melting properties are found to be strong functions of cluster structure. Cluster sizes with closed-shell structures always have first-order-like phase transitions. Almost one-third of cluster sizes in the analyzed range exhibit second-order-like phase transitions due to the presence of multiple structural configurations close in energy. 1-shell clusters with one to a few more atoms than a neighboring closed-shell structure have very low surface melting points and very high energetic melting points compared to their closed-shell counterparts. In clusters above 50 atoms with certain core structures, melting of the surface before the core was observed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Dynamic structural views in solar energy materials by femtosecond electron diffraction

Solar materials convert light into other forms of energy through excited state processes occurring on ultrafast time and atomic length scales. Understanding and controlling such nonequilibrium processes is essential for applications ranging from photovoltaics to photocatalysis. These processes are commonly studied by transient optical techniques, which resolve charge carrier dynamics. However, optical spectroscopy does not directly probe the atomic-scale motions that play a central role in the ultimate functionality of these materials. Filling this missing gap, ultrafast electron and x-ray scattering techniques enable monitoring of structural dynamics in materials with femtosecond time resolution. In this work, we focus on the use of ultrafast electron diffraction (UED) techniques to probe photoinduced energy conversion dynamics in solar energy materials. First, we discuss the use of UED as an ultrafast lattice thermometer allowing a direct probe of nonradiative relaxations such as hot carrier cooling and Auger recombination. Second, we present a time-resolved atomic pair distribution function analysis enabled by UED, which uncovers lattice deformations arising from excitation localization in materials. Finally, we provide an outlook looking toward new approaches for resolving in situ energy conversion dynamics and uncovering structure–property relationships in solar energy materials.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Growth of Hexagonal Boron Nitride from Molten Nickel Solutions: A Reactive Molecular Dynamics Study

Metal flux methods are excellent for synthesizing high-quality hexagonal boron nitride (hBN) crystals, but the atomic mechanisms of hBN nucleation and growth in these systems are poorly understood and difficult to probe experimentally. Here, we harness classical reactive molecular dynamics (ReaxFF) to unravel the mechanisms of hBN synthesis from liquid nickel solvent over time scales up to 30 ns. These simulations mimic experimental conditions by including relatively large liquid nickel slabs containing dissolved boron and a molecular nitrogen gas phase. Overall, the reaction takes place almost exclusively on the surface of the liquid nickel, owing to the low solubility of nitrogen in bulk nickel and the intermediate species’ preference for the metal–gas interface. The formation of hBN invariably begins by reaction of dinitrogen with nickel-solvated boron atoms at the surface, forming intermediate N–N–B species, which typically evolve into B–N–B units through a short-lived intermediate where a single nitrogen atom is coordinated by one nitrogen and two boron atoms. The resulting B–N–B units, in turn, coalesce with growing hBN nuclei and carry nitrogen between hBN nanocrystals in an Ostwald ripening process. The amount of hBN produced on the tens of nanosecond time scale depends critically on the boron concentration, while having a much weaker dependence on the N 2 pressure for the regime considered (N 2 pressures of 2.5–10 MPa, Ni–B solutions with 6–12% boron by atom fraction). The highest rate of hBN formation occurs at the lowest temperature considered (1750 K, just above the melting point of nickel), while no hBN sheets are formed at 2000 K or above. An analysis of the transition pathways for nitrogen atoms shows that the final step, incorporation of small B–N motifs into larger hBN sheets, is the rate-limiting step in the regimes considered. While raising the temperature from 1750 to 2000 K has little effect on the formation of intermediates (N–N–B, B–N–B, etc.), the lack of large hBN sheets at temperatures >1900 K is explained by decreased probability of the final step and increased probability of breakup of hBN into B–N motifs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗