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At least 1,099 records · Page 61

Conceptual Design of a Thermal–to-14-MeV Neutron Conversion Device for Use in the Advanced Test Reactor

Here, this paper details the conceptual design of a thermal-to-14-MeV neutron converter consisting of a mixture of lithium and deuterium in a blanket material. Such a device operates a two-step reaction, first generating tritons via thermal neutron absorption in the tritium breeding material, and in the second step, high-energy neutrons are produced either via deuterium-tritium fusion reaction or with tritium reacting with lithium. A thermal-to-14-MeV neutron converter significantly hardens the neutron spectrum by virtually removing thermal neutrons and adding a high-energy 14 MeV component to the neutron spectrum. While similar concepts have been previously proposed and tested in other reactors, the unique characteristics of the Advanced Test Reactor (ATR), namely its important thermal flux (up to $10^{15}$ n.cm$^{-2}$.s$^{-1}$) makes it markedly attractive for obtaining a very large fast neutron flux, usable for irradiation studies under neutron flux conditions prototypical of fusion reactors. The paper provides a description of a new computational scheme developed for handling the coupled neutron-triton transport mechanism using the Geant4 toolkit. Resulting neutron spectra and high-energy neutron yields are summarized for different irradiation positions and potential neutron breeder materials. Maximum predicted thermal-to-14-MeV neutron yields are on the order of $2.10^{-4}$, which is consistent with previous studies found in the literature. Thus, when placed inside the ATR, such a neutron converter will be providing the largest high-energy neutron source available for activation and irradiation studies of materials foreseen for use in fusion reactors. Future steps will involve qualifying the computational scheme using the ATR critical facility using activation foil measurements.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Synthesis of Zn2NbN3 ternary nitride semiconductor with wurtzite-derived crystal structure

Binary III-N nitride semiconductors with wurtzite crystal structure such as GaN and AlN have been long used in many practical applications ranging from optoelectronics to telecommunication. The structurally related ZnGeN2 or ZnSnN2 derived from the parent binary compounds by cation mutation (elemental substitution) have recently attracted attention, but such ternary nitride materials are mostly limited to II-IV-N2 compositions. This paper demonstrates synthesis and characterization of zinc niobium nitride (Zn2NbN3) – a previously unreported II2-V-N3 ternary nitride semiconductor. The Zn2NbN3 thin films are synthesized using a one-step adsorption-controlled growth, and a two-step deposition/annealing method that suppresses the loss of Zn and N. Measurements indicate that this sputtered Zn2NbN3 crystalizes in cation-disordered wurtzite-derived structure, in contrast to chemically related rocksalt-derived Mg2NbN3 compound, also synthesized here for comparison using the two-step method. The estimated wurtzite lattice parameter ratio of Zn2NbN3 is 1.55, and the optical absorption onset is at 2.1 eV. Both of these values are lower compared to published Zn2NbN3 computational values of c/a = 1.62 and Eg = 3.5 - 3.6 eV. Additional theoretical calculations indicate that this difference is due to cation disorder in experimental samples, suggesting a way to tune the structural parameters and the resulting properties of heterovalent ternary nitride materials. Overall, this work expands the wurtzite family of nitride semiconductors to include Zn2NbN3, and suggests that related II2-V-N3 and other ternary nitrides should be possible to synthesize.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Fabrication of field-effect transistors with transfer-free nanostructured carbon as semiconducting channel material

Carbon nanostructures as active channel material in field effect transistors (FETs) are appealing in microelectronics for their improved performance such as high speed and low energy dissipation. However, these devices require the incorporation of nanostructure transfer steps in the fabrication process flow, which makes difficult its application in large scale integration circuits. Here we present a novel method for the fabrication of FETs with nanostructured carbon in the channel with p-type semiconducting properties and intermediate drain-source current (IDS) on/off ratio. The method is based on the use of Ni nanoparticles in the source-drain gap region as seed material for the formation of carbon nanostructures in the FET channel. FETs without Ni nanoparticles in the channel showed no modulation of IDS as a function of gate voltage. The device fabrication process does not require any carbon nanostructure transfer steps since it directly forms carbon nanostructures electrically connected to the device's source and drain electrodes via electron-beam evaporation of carbon and conventional lithographic processes. Since all device fabrication steps are compatible with Si technology processes, they are capable of being further optimized following process development protocols practiced by the semiconductor industry.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Implicit and coupled fluid plasma solver with adaptive Cartesian mesh and its applications to non-equilibrium gas discharges

In this work, we present a new fluid plasma solver with adaptive Cartesian mesh (ACM) based on a full-Newton (nonlinear, implicit) scheme for non-equilibrium gas discharge plasma. The electrons and ions are described using drift-diffusion approximation coupled to Poisson equation for the electric field. The electron-energy transport equation is solved to account for electron thermal conductivity, Joule heating, and energy loss of electrons in collisions with neutral species. The rate of electron-induced ionization is a function of electron temperature and could also depend on electron density (important for plasma stratification). The ion and gas temperature are kept constant. The transport equations are discretized using a non-isothermal Scharfetter-Gummel scheme to resolve possible large temperature gradients in the sheaths. We demonstrate the new solver for simulations of direct current (DC) and radiofrequency (RF) discharges. The implicit treatment of the coupled equations allows using large time steps. The full-Newton method (FNM) enables fast nonlinear convergence at each time step, offering significantly improved simulation efficiency. We discuss the selection of time steps for solving different plasma problems. The new solver enables solving several problems we could not solve before with existing software: two- and three-dimensional structures of the entire DC discharges including cathode and anode regions, electric field reversals and double-layer formation, the normal cathode spot and an anode ring, moving striations in diffuse and constricted DC discharges, and standing striations in RF discharges. The developed FNM-ACM technique offers many benefits for tackling the disparity of gas discharge plasma systems' time scales and nonlinearity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Design, construction, and testing of no-insulation small subscale solenoids for compact tokamaks

Fusion energy systems studies (FESS) for next-step devices based on the most promising magnetic configurations indicate that high magnetic fields and high current density for magnet coil systems may reduce device size and lower the cost. High current density and radiation resistant fusion magnets are particularly beneficial for low cost, low aspect ratio compact reactor designs such as Fusion Nuclear Science Facility (FNSF), Fusion Pilot Plant (FPP) of low-aspect ratio spherical tokamak (ST) or compact stellarators. Unlike typical high field magnets for nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI), or high energy physics research applications, neutron irradiation damage to organic insulations in the coil winding pack is a critical issue for next generation fusion reactors where orders of magnitude higher neutron fluence than those in present experimental reactors such as ITER are expected. Moreover, a high coil winding pack current density is needed for high field magnets in low cost, compact radial build next step fusion reactors. The slow current charging time, however, is an issue in fully non-insulated coils. In this work, we present the design, construction and testing of subscale Nb3Sn solenoids, up to half the diameter of the central solenoid (CS) for National Spherical Torus Experiment (NSTX), with and without inter-layer insulation for enhancing radiation resistance while improving the winding pack current density and coil performance. The major radius for the NSTX/NSTX-Upgrade (reference for compact ST) is 0.854/0.934 meter, and 4.8 meters for FNSF. The magnetic field for NSTX/NSTX-U at the plasma center is 0.6/1 Tesla and 9 Tesla for FNSF. The inner diameter of the central solenoid coil is 0.2/0.4 meter for NSTX/NSTX-U and 1.2 meters for FNSF. The current charging and discharging behavior of the prototype solenoids was investigated to quantify performance advantages of a simplified coil fabrication without error-prone vacuum pressure impregnation (VPI) for the removal of epoxy organic insulation. Scalability of the no insulation concept for fusion can be addressed via engineered coating for novel insulation on contact resistance or intra-layer no insulations. Radiation resistance and coil winding efficiency were significantly improved in the no insulation coils for next step compact fusion reactors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Skyrmion dynamics and topological sorting on periodic obstacle arrays

Abstract We examine skyrmions under a dc drive interacting with a square array of obstacles for varied obstacle size and damping. When the drive is applied in a fixed direction, we find that the skyrmions are initially guided in the drive direction but also move transverse to the drive due to the Magnus force. The skyrmion Hall angle, which indicates the difference between the skyrmion direction of motion and the drive direction, increases with drive in a series of quantized steps as a result of the locking of the skyrmion motion to specific symmetry directions of the obstacle array. On these steps, the skyrmions collide with an integer number of obstacles to create a periodic motion. The transitions between the different locking steps are associated with jumps or dips in the velocity–force curves. In some regimes, the skyrmion Hall angle is actually higher than the intrinsic skyrmion Hall angle that would appear in the absence of obstacles. In the limit of zero damping, the skyrmion Hall angle is 90°, and we find that it decreases as the damping increases. For multiple interacting skyrmion species in the collective regime, we find jammed behavior at low drives where the different skyrmion species are strongly coupled and move in the same direction. As the drive increases, the species decouple and each can lock to a different symmetry direction of the obstacle lattice, making it possible to perform topological sorting in analogy to the particle sorting methods used to fractionate different species of colloidal particles moving over two-dimensional obstacle arrays.

36 MATERIALS SCIENCE↗

Prediction of transport in the JET DTE2 discharges with TGLF and NEO models using the TGYRO transport code

Abstract The JET Deuterium-Tritium-Experiment Campaign 2 (DTE2) has demonstrated the highest-ever fusion energy production. To forecast the transport dynamics within these discharges, the TGLF and NEO models within the TGYRO transport code were employed. A critical development in this study is the new quasilinear transport model, TGLF-SAT2, specifically designed to resolve discrepancies identified in JET deuterium discharges. This model accurately describes the saturated three-dimensional (3D) fluctuation spectrum, aligning closely with a database of nonlinear CGYRO turbulence simulations, thereby enhancing the predictive accuracy of TGYRO simulations. In validating against the JET DTE2 discharges across two primary operating scenarios, TGYRO effectively predicted the temperature profiles within a broad radial window ( ρ ∼ 0.2–0.85), though with minor ion temperature discrepancies near the core. However, a consistent underprediction of electron density profiles by 20% across the simulation domain was noted, indicating areas for future refinement. To achieve a self-consistent steady-state solution based on the JET DTE2 discharges, an integrated modeling workflow TGYRO-STEP within the OMFIT framework was introduced. This workflow iterates among the core transport, the pedestal pressure and the MHD equilibrium, ultimately yielding a converged solution that significantly reduces dependence on experimental boundary conditions for temperature and density profiles. The integrated simulation results show negligible differences in electron density and temperature profiles compared to standalone TGYRO modeling, while the ion temperature profile is lower due to the updated boundary condition in TGYRO-STEP. The application of the TGYRO-STEP workflow to JET DTE2 discharges serves as a crucial test to validate its robustness and highlights its limitations, providing valuable insights for its potential future application in ITER and Fusion Power Plant deuterium and tritium prediction modeling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Domain-specific compilers for dynamic simulations of quantum materials on quantum computers

Abstract Simulation of the dynamics of quantum materials is emerging as a promising scientific application for noisy intermediate-scale quantum (NISQ) computers. Due to their high gate-error rates and short decoherence times, however, NISQ computers can only produce high-fidelity results for those quantum circuits smaller than some given circuit size. Dynamic simulations, therefore, pose a challenge as current algorithms produce circuits that grow in size with each subsequent time-step of the simulation. This underscores the crucial role of quantum circuit compilers to produce executable quantum circuits of minimal size, thereby maximizing the range of physical phenomena that can be studied within the NISQ fidelity budget. Here, we present two domain-specific (DS) quantum circuit compilers for the Rigetti and IBM quantum computers, specifically designed to compile circuits simulating dynamics under a special class of time-dependent Hamiltonians. The compilers outperform state-of-the-art general-purpose compilers in terms of circuit size reduction by around 25%–30% as well as wall-clock compilation time by around 40% (dependent on system size and simulation time-step). Drawing on heuristic techniques commonly used in artificial intelligence, both compilers scale well with simulation time-step and system size. Code for both compilers is open-source and packaged into a full-stack quantum simulation software with tutorials included for ease of use for future researchers wishing to perform dynamic simulations of quantum materials on quantum computers. As our DS compilers provide significant improvements in both compilation time and simulation fidelity, they provide a building block for accelerating progress toward physical quantum supremacy.

Physics↗

Indexed improvements for real-time trotter evolution of a (1 + 1) field theory using NISQ quantum computers

Today's quantum computers offer the possibility of performing real-time calculations for quantum field theory scattering processes motivated by high energy physics. In order to follow the successful roadmap which has been established for the calculation of static properties at Euclidean time, it is crucial to develop new algorithmic methods to deal with the limitations of current noisy intermediate-scale quantum (NISQ) devices and to establish quantitative measures of the progress made with different devices. In this paper, we report recent progress in these directions. We show that nonlinear aspects of the trotter errors allow us to take much larger step then suggested by low-order analysis. This is crucial to reach physically relevant time scales with today's NISQ technology. We propose to use an index averaging absolute values of the difference between the accurately calculated trotter evolution of site occupations and their actual measurements on NISQ machines (G index) as a measure to compare results that have been obtained from different hardware platforms. Using the transverse Ising model in one spatial dimension with four sites we apply this metric across several hardware platforms. We study the results including readout mitigation and Richardson extrapolations and show that the mitigated measurements are very effective based on the analysis of the trotter step size modifications. Furthermore, we discuss how this advance in the trotter step size procedures can improve quantum computing physics scattering results and how this technical advance can be applied to other machines and noise mitigation methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning

Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems and the absence of time-invariance. The nonequilibrium properties of many-body systems can be described by the dynamics of the correlator, or the Green's function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff–Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time numerical simulation. In this paper, we develop an operator-learning framework based on recurrent neural networks (RNNs) to address this challenge. We utilize RNNs to learn the nonlinear mapping between Green's functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green's functions. Besides significant savings per each time step, the new methodology reduces the temporal computational complexity from $O(N_t^3)$ to $O(N_t)$ where N t is the number of steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through various numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.

97 MATHEMATICS AND COMPUTING↗

High-throughput characterization, correlation, and mapping of leaf photosynthetic and functional traits in the soybean ( Glycine max ) nested association mapping population

We report photosynthesis is a key target to improve crop production in many species including soybean [Glycine max (L.) Merr.]. A challenge is that phenotyping photosynthetic traits by traditional approaches is slow and destructive. There is proof-of-concept for leaf hyperspectral reflectance as a rapid method to model photosynthetic traits. However, the crucial step of demonstrating that hyperspectral approaches can be used to advance understanding of the genetic architecture of photosynthetic traits is untested. To address this challenge, we used full-range (500–2,400 nm) leaf reflectance spectroscopy to build partial least squares regression models to estimate leaf traits, including the rate-limiting processes of photosynthesis, maximum Rubisco carboxylation rate, and maximum electron transport. In total, 11 models were produced from a diverse population of soybean sampled over multiple field seasons to estimate photosynthetic parameters, chlorophyll content, leaf carbon and leaf nitrogen percentage, and specific leaf area (with R 2 from 0.56 to 0.96 and root mean square error approximately <10% of the range of calibration data). We explore the utility of these models by applying them to the soybean nested association mapping population, which showed variability in photosynthetic and leaf traits. Genetic mapping provided insights into the underlying genetic architecture of photosynthetic traits and potential improvement in soybean. Notably, the maximum Rubisco carboxylation rate mapped to a region of chromosome 19 containing genes encoding multiple small subunits of Rubisco. We also mapped the maximum electron transport rate to a region of chromosome 10 containing a fructose 1,6-bisphosphatase gene, encoding an important enzyme in the regeneration of ribulose 1,5-bisphosphate and the sucrose biosynthetic pathway. The estimated rate-limiting steps of photosynthesis were low or negatively correlated with yield suggesting that these traits are not influenced by the same genetic mechanisms and are not limiting yield in the soybean NAM population. Leaf carbon percentage, leaf nitrogen percentage, and specific leaf area showed strong correlations with yield and may be of interest in breeding programs as a proxy for yield. This work is among the first to use hyperspectral reflectance to model and map the genetic architecture of the rate-limiting steps of photosynthesis.

54 ENVIRONMENTAL SCIENCES↗

Conjugate Multimode Heat Transfer Analysis of Cryogenic EXLO Manipulation

Abstract In this study, a conjugate radiation/conduction multimode heat transfer analysis of cryogenic focused ion beam (FIB) milling steps necessary for producing ex situ lift out specimens under cryogenic conditions (cryo-EXLO) is performed. Using finite volume for transient heat conduction and enclosure theory for radiation heat transfer, the analysis shows that as long as the specimen is attached or touching the FIB side wall trenches, the specimen will remain vitreous indefinitely, while actively cooled at liquid nitrogen (LN2) temperatures. To simulate the time needed to perform a transfer step to move the bulk sample containing the FIB-thinned specimen from the cryo-FIB to the cryo-EXLO cryostat, the LN2 temperature active cooling is turned off after steady-state conditions are reached and the specimen is monitored over time until the critical devitrification temperature is reached. Under these conditions, the sample will remain vitreous for >3 min, which is more than enough time needed to perform the cryo-transfer step from the FIB to the cryostat, which takes only ∼10 s. Cryo-transmission electron microscopy images of a manipulated cryo-EXLO yeast specimen prepared with cryo-FIB corroborates the heat transfer analysis.

Materials Science↗

Algebraic compression of quantum circuits for Hamiltonian evolution

Here unitary evolution under a time-dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as Trotterization, which leads to circuits the depth of which scales with the number of steps. When the circuit elements are limited to a subset of SU(4) - or equivalently, when the Hamiltonian may be mapped onto free fermionic models - several identities exist that combine and simplify the circuit. Based on this, we present an algorithm that compresses the Trotter steps into a single block of quantum gates using algebraic relations between adjacent circuit elements. This results in a fixed depth time evolution for certain classes of Hamiltonians. We explicitly show how this algorithm works for several spin models, and demonstrate its use for adiabatic state preparation of the transverse field Ising model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Driven-dissipative quantum mechanics on a lattice: Simulating a fermionic reservoir on a quantum computer

The driven-dissipative many-body problem remains one of the most challenging unsolved problems in quantum mechanics. The advent of quantum computers may provide a unique platform for efficiently simulating such driven-dissipative systems. But, there are many choices for how one can engineer the reservoir. One can simply employ ancilla qubits to act as a reservoir and then digitally simulate them via algorithmic cooling. A more attractive approach, which allows one to simulate an infinite reservoir, is to integrate out the bath degrees of freedom and describe the driven-dissipative system via a master equation, that can also be simulated on a quantum computer. In this work, we consider the particular case of noninteracting electrons on a lattice driven by an electric field and coupled to a fermionic thermostat. Then, we provide two different quantum circuits: the first one reconstructs the full dynamics of the system using Trotter steps, while the second one dissipatively prepares the final nonequilibrium steady state in a single step. We run both circuits on the IBM quantum experience. For circuit (i), we achieved up to five Trotter steps. When partial resets become available on quantum computers, we expect that the maximum simulation time can be significantly increased. Lastly, the methods developed here suggest generalizations that can be applied to simulating interacting driven-dissipative systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Crystal truncation rods from miscut surfaces with alternating terminations

Miscut surfaces of layered crystals can exhibit a stair-like sequence of terraces having periodic variation in their atomic structure. For hexagonal close-packed and related crystal structures with an αβαβ stacking sequence, there have been long-standing questions regarding how the differences in adatom attachment kinetics at the steps separating the terraces affect the fractional coverage of α vs. β termination during crystal growth. To demonstrate how surface X-ray scattering can help address these questions, we develop a general theory for the intensity distributions along crystal truncation rods (CTRs) for miscut surfaces with a combination of two terminations. We consider half-unit-cell-height steps, and variation of the coverages of the terraces above each step. Example calculations are presented for the GaN (0001) surface with various reconstructions. These show which CTR positions are most sensitive to the fractional coverage of the two terminations. We compare the CTR profiles for exactly oriented surfaces to those for vicinal surfaces having a small miscut angle, and investigate the circumstances under which the CTR profile for an exactly oriented surface is equal to the sum of the intensities of the corresponding family of CTRs for a miscut surface.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Suppression of metal-to-insulator transition and stabilization of superconductivity by pressure in Re 3 Ge 7

The effect of pressure on the low-temperature states of the Re 3 ⁡Ge 7 is investigated by both electrical and Hall resistance and magnetization measurements. At ambient pressure, the temperature-dependent resistance of Re 3 ⁡Ge 7 behaves quasilinearly from room temperature down to 60 K, then undergoes a two-step metal-to-insulator transition (MIT) at temperatures T 1 =59.4K and T 2 =58.7K, which may be related to a structural phase transition or occurrence of charge-density wave ordering. Upon applying pressure, the two-step (T 1 ,T 2 ) MIT splits into three steps (T 1 ,T 2 . and T 3 ) above 1 GPa, and all traces of MITs are fully suppressed by ~8 GPa. Subsequently, the onset of bulk superconductivity (SC) occurs between 10.8 and 12.2 GPa and persists to our highest pressure of 26.8 GPa. At 12.2 GPa the superconducting transition temperature, T c , and upper critical field, H c ⁢2 reach the maximum of T c (onset) ~5.9 K and H c ⁢2 (1.8 K) ~14 kOe. Finally, our results not only present the observation of SC under high pressure in Re 3 ⁡Ge 7 but also delineate the interplay between SC and other competing electronic states by creating a T-p phase diagram for this potentially topologically nontrivial system Re 3 ⁡Ge 7 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Primordial black holes arise when the inflaton falls

Primordial Black Holes (PBHs) have entered the forefront of theoretical cosmology, due their potential role in phenomena ranging from gravitational waves, to dark matter, to galaxy formation. While producing PBHs from inflationary fluctuations naively would seem to require a large deceleration of the inflaton from its velocity at the horizon exit of CMB scales, in this work we demonstrate that an acceleration from a relatively small downward step in the potential that is transited in much less than an e-fold amplifies fluctuations as well. Depending on the location of the step, such PBHs could explain dark matter or the black holes detected by the gravitational wave interferometers. Furthermore, the perturbation enhancement has a natural interpretation as particle production due to the non-adiabatic transition associated with the step.

79 ASTRONOMY AND ASTROPHYSICS↗

Dy adsorption on and intercalation under graphene on 6 H -SiC(0001) surface from first-principles calculations

Previous experimental observations motivate clarification of configuration stabilities and kinetic processes for intercalation of guest atoms into a layered van der Waals material such as a graphene-SiC system. From our first-principles density functional theory (DFT) calculations, we analyze Dy adsorption and intercalation for graphene on a 6H-SiC(0001) surface, where the system includes two single-atom-thick graphene layers: the top-layer graphene (TLG) and the underling buffer-layer graphene (BLG) above the terminal Si layer. Our chemical potential analysis shows that intercalation of a single Dy atom into the gallery between TLG and BLG is more favorable than adsorption on TLG but that intercalation into the gallery underneath BLG is highly unfavorable. We obtain diffusion barriers of ~0.45 and 0.54 eV for a Dy atom diffusing on and under TLG, respectively. We find that the direct penetration of a Dy atom from the graphene top into the gallery under TLG is almost inhibited below a temperature of ~1400 K due to a large global barrier of at least ~3.5 eV. Instead, we find that a single Dy atom on TLG can easily intercalate by crossing a TLG step (e.g., a zigzag step presaturated by a Dy chain or a reconstructed zigzag step zz57). Additionally, we also perform DFT calculations for different Dy coverages to demonstrate how the favorability of Dy intercalation, as well as the corresponding interlayer spacings, depend on the coverage. Consequently, we can provide general insight and guidance for extensively studied systems involving intercalation of foreign atoms into graphene on a SiC substrate.

36 MATERIALS SCIENCE↗