Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “density functional calculations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

First principles investigation of dopants and defect complexes in CdSe$_x$Te$_{1-x}$

Se alloying is a common approach to improve the performance of CdTe solar cells by tuning the bandgap, defect levels, and carrier density. A fundamental understanding of these improvements, specifically the effect of Se alloying on the behavior of defects and dopants in CdTe, remains unclear. Here, in this work, we present a density functional theory (DFT) study of point defect energetics in CdTe and CdSe x Te 1-x with x = 0.25, leading to a comparison of how native defects, dopants (As and Cu), impurities (Cl and O), and related defect complexes behave in CdTe vs CdSe x Te 1-x . Our calculations, performed by combining semi-local and nonlocal hybrid functionals, show a general lowering of the formation energies of native defects as well as substitutional defects formed by As and Cl upon Se addition. For successful p-type doping with As, destabilizing Cl-based defects in the CdSeTe lattice would be essential. We find evidence for some low-energy defect complexes of As, Cl, and O in CdSe 0.25 Te 0.75 . The computed defect formation energies further enable estimates of temperature-dependent defect concentrations and self-consistent Fermi levels. A comparison of defect energetics with the energies of impurity phases reveals that As, Cu, Cl, and O overwhelmingly prefer being segregated to unwanted As 2 O 5 , AsCl 3 , Cd 2 AsCl 2 , and CuO x phases rather than remain at defect sites, but such segregation is less likely to happen in CdSe 0.25 Te 0.75 than in CdTe. Overall, our work presents a list of likely defects and complexes in CdTe and Se-incorporated CdTe, paving the way to explain and mitigate limited dopant activation in experimental observations.

CdTe↗
DOE OSTI2025

Generalized framework for likelihood-based field-level inference of growth rate from velocity and density fields

Measuring the growth rate of large-scale structures ( f ) as a function of redshift has the potential to break degeneracies between modified gravity and dark energy models, when combined with expansion-rate probes. Direct estimates of peculiar velocities of galaxies have attracted interest as a means of estimating fσ 8 . In particular, field-level methods can be used to fit the field nuisance parameter along with cosmological parameters simultaneously. This article aims to provide the community with a unified framework for the theoretical modeling of the likelihood-based field-level inference by performing fast field covariance calculations for velocity and density fields. Our purpose is to lay the foundations for a nonlinear extension of the likelihood-based method at the field level. We have developed a generalized framework, implemented in the dedicated software flip to perform a likelihood-based inference of fσ 8 . We derived a new field covariance model, which includes wide-angle corrections. We also included the models previously described in the literature inside our framework. We compared their performance against ours, and we validated our model by comparing it with the two-point statistics of a recent N-body simulation. The tests we performed have allowed us to validate our software and determine the appropriate wavenumber range to integrate our covariance model and its validity in terms of separation. Our framework allows for a wider wavenumber coverage to be used in our calculations than in previous works, which is particularly interesting for nonlinear model extensions. Finally, our generalized framework allows us to efficiently perform a survey geometry-dependent Fisher forecast of the fσ 8 parameter. We show that the Fisher forecast method we developed gives an error bar that is 30% closer to a full likelihood-based estimation than a standard volume Fisher forecast.

Ravoux, Corentin↗
DOE OSTI2025

Production of neutron-rich isotopes for 𝑍 ≥ 98 in the 238 U + 248 Cm reaction

Multinucleon transfer (MNT) reactions in actinide systems are a promising method to synthesize transuranium neutron-rich elements. Appropriate theoretical approaches are needed to understand the mechanisms behind MNT. We employ a microscopic approach to calculate neutron-rich isotope production in the reaction 238 U + 248 Cm system. Here, the stochastic mean-field (SMF) approach is used to calculate the primary cross sections in MNT reactions based on the quasifission and inverse quasifission processes, and a statistical de-excitation model with GEMINI ++ code to calculate the secondary fragment cross sections. The calculated cross sections using SMF and GEMINI ++ explain available experimental results for the 238 U + 248 Cm system at 𝐸 c.m. = 898.7 MeV energy. This shows the effectiveness and applicability of the quantal diffusion approach, based on the SMF theory, in heavy-ion collisions. Production of transuranium neutron-rich elements with a proton number up to 𝑍=101 is obtained with sizable cross sections. Theoretical results calculated for the 𝑍=102–105 region, for which there are no experimental data, show that the cross-section values would be lower than the microbarn level. SMF theory does not contain any adjustable parameters other than the standard parameters of the energy density functional used in the TDHF theory and is an important approach for the microscopic understanding of reaction mechanisms.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Computing nuclear response functions with time-dependent coupled-cluster theory

We compute nuclear response functions by solving the time-dependent 𝐴-body Schrödinger equation, recording the time-dependent transition moment and extracting spectral information via Fourier transforms. The solution of the time-dependent many-body problem accounts for correlations on top of the mean field by taking advantage of a time-dependent formulation of coupled-cluster theory. As a validation, we focus on electric dipole transitions in 4 He and 16 O and compare moments of the response function distribution to the results of an equivalent static framework, finding negligible discrepancies. We investigate how proton and neutron densities evolve in time, and we see the traditional picture of soft and giant dipole resonances as collective oscillations of protons and neutrons emerging from our calculations in 16 O and 24 O. Furthermore, this method also allows us to investigate the behavior of the nucleus in the presence of a strong electric field. In that regime, the behavior of the system becomes chaotic. Qualitatively, the spectral information obtained in this limit is in line with previous time-dependent mean-field results.

Ab initio calculations↗
DOE OSTI2025

Developing reliable machine learning interatomic potential for Fe–Cr–Ni austenitic alloys

Gaining atomistic understanding of mechanical behavior of heat-resistant structural materials such as Fe–Cr–Ni-based alloys requires an approach with an accuracy close to density functional theory (DFT) that considers the intrinsic properties of the bulk lattice and important defects such as stacking faults, grain boundaries, and surfaces. This work aims to develop reliable machine learning interatomic potential (MLIAP) at cross-scale for Fe–Cr–Ni ternary alloys with a focus on the face-centered-cubic (fcc) solid solution structure. Leveraging the advantages of moment tensor potentials, which typically necessitate a relatively small training dataset and enable rapid calculations using the large-scale atomic/molecular massively parallel simulator package, we ensure the stability and accuracy of the trained potentials. Important defects such as stacking faults, grain boundaries, and surfaces for wide-range compositions are investigated. Structural, thermal, elastic, and defect properties are determined from molecular dynamics simulations comprising several thousand atoms, generated via canonical Monte Carlo simulations guided by the trained potential. The trained potential allows efficient atomic simulations of structural, thermal, and mechanical properties of fcc Fe–Cr–Ni solid solution alloys as a function of composition and temperature. Therefore, the MLIAP approach represents a major advancement from DFT calculations that are limited to small simulation sizes and traditional molecular dynamics simulations using relatively low accuracy potentials. Furthermore, this work outlines a practical foundation for further investigating the structural evolution and mechanical behavior of austenitic stainless steel and nickel-based alloys in a wide array of applications in extreme environments.

Crystal structure↗
DOE OSTI2026

Systematic correction of the density functional theory spectra via a quantum Monte Carlo approach

Numerical outputs and driver scripts supporting auxiliary-boson corrected diffusion Monte Carlo (ABCDMC) benchmarks on second-row neutral atoms, cations, and dications, plus a C2 molecule active-space study. Includes NIST reference energies, ABCDMC timestep extrapolation summaries, orbital generation inputs, singles-only CASCI driver scripts, an O-atom basis-set convergence study, and the PyQMC boson code snapshot used for the calculations.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Ab Initio Molecular Dynamics Insights into Stress Corrosion Cracking and Dissolution of Metal Oxides

Oxide phases such as α-Fe2O3 (hematite) and α-Al2O3 (corundum) are highly insoluble in water; however, subcritical crack growth has been observed in humidity nonetheless. Chemically induced bond breaking at the crack tip appears unlikely due to sterically hindered molecular transport. The molecular mechanics of a crack in corundum with a reactive force field reveal minimal lattice trapping, leading to bond breaking before sufficient space opens for water transport. To address this, we model a pre-built blunt crack with space for H2O molecule adsorption at the tip and show that it reduces fracture toughness by lowering the critical J-integral. Then, we explore stress-enhanced dissolution to understand the mechanism of crack tip blunting in the oxide/water system. Density functional theory combined with metadynamics was employed to describe atomic dissolution from flat hematite and corundum surfaces in pure water. Strain accelerates dissolution, stabilizing intermediate states with broken bonds before full atom detachment, while the free energy profile of unstrained surfaces is almost monotonic. The atomistic calculations provided input for a kinetic model, predicting the shape evolution of a blunt crack tip, which displays three distinct regimes: (i) dissolution primarily away from the tip, (ii) enhanced blunting near but not at the apex, and (iii) sharpening near the apex. The transition between regimes occurs at a low strain, highlighting the critical role of water in the subcritical crack growth of oxide scales, with dissolution as the fundamental microscopic mechanism behind this process.

Chemistry↗
DOE OSTI2025

Zero-Field NMR and Millitesla-SLIC Spectra for >200 Molecules from Density Functional Theory and Spin Dynamics

NMR is usually performed at magnetic fields of 1 T and above to obtain sufficient sensitivity and spectral dispersion to identify chemicals based on chemical shifts and J couplings. At lower fields, the advent of hyperpolarization technologies and sensitive detectors can address sensitivity concerns. However, it remains disputed whether spectral signatures at zero and ultra-low fields are sufficient for chemical identification. Here, we report an all–electron DFT-based batch calculation of J-coupling constants, which are used to generate J coupling NMR spectra at zero field and 6.5 mT for over 200 small molecules. In the developed computational tool chain, we first used the all-electron FHI-aims code to calculate the molecular J couplings and chemical shifts. We then fed the calculated NMR parameters into the NMR simulation package SPINACH to simulate both heteronuclear J coupling spectra at zero-field, and homonuclear J coupling spectra as spin-lock induced crossing (SLIC) spectra at ultra-low field (6.5 mT). The resulting spectra demonstrate that zero and ultra-low field NMR spectra can represent unique identifiers of chemical structure for small molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Decoding the proton’s gluonic density with lattice QCD-informed machine learning

We present a first machine learning-based decoding of the gluonic structure of the proton from lattice QCD using a variational autoencoder inverse mapper (VAIM). Harnessing the power of generative AI, we predict the parton distribution function (PDF) of the gluon given information on the reduced pseudo-Ioffe-time distributions (RpITDs) as calculated from an ensemble with lattice spacing a ≈ 0.09 fm and a pion mass of M π ≈ 310 MeV. The resulting gluon PDF is consistent with phenomenological global fits within uncertainties, particularly in the intermediate-to-high-x region where lattice data are most constraining. A subsequent correlation analysis confirms that the VAIM learns a meaningful latent representation, highlighting the potential of generative AI to bridge lattice QCD and phenomenological extractions within a unified analysis framework.

Gluon parton distribution function↗
DOE OSTI2025

Role of Electron Correlation beyond the Active Space in Achieving Quantitative Predictions of Spin-Phonon Relaxation

Single-molecule magnets (SMMs) are promising candidates for molecular-scale data storage and processing due to their strong magnetic anisotropy and long spin relaxation times. However, as temperature rises, interactions between electronic states and lattice vibrations accelerate spin relaxation, significantly limiting their practical applications. Recently, ab initio simulations have made it possible to advance our understanding of phonon-induced magnetic relaxation, but significant deviations from experiments have often been observed. The description of molecules’ electronic structure has been mostly based on complete active space self-consistent field (CASSCF) calculations, and the impact of electron correlation beyond the active space remains largely unexplored. In this study, we provide the first systematic investigation of spin-phonon relaxation in SMMs with post-CASSCF multiconfigurational methods, specifically CAS followed by second-order perturbation theory and multiconfiguration pair-density functional theory. Taking Co(II)- and Dy(III)-based SMMs as case studies, we analyze how electron correlation influences spin-phonon relaxation rates across a range of temperatures, comparing theoretical predictions with experimental observations. Our findings demonstrate that post-CASSCF treatments make it possible to achieve quantitative predictions for Co(II)-based SMMs. For Dy(III)-based systems, however, accurate predictions require consideration of additional effects, underscoring the urgent necessity of further advancing the study of the effects of electronic correlation in these complex systems.

Energy↗
DOE OSTI2025

Anomalous thermal transport in Eshelby twisted van der Waals nanowires

Dislocations in van der Waals (vdW) layered nanomaterials induce strain and structural changes that substantially impact thermal transport. Understanding these effects could enable the manipulation of dislocations for improved thermoelectric and optoelectronic applications, but experimental insights remain limited. Here, in this study, we use synthetic Eshelby twisted vdW GeS nanowires (NWs) with single screw dislocations as a model system to explore the interplay between dislocation-induced structural modifications and lattice thermal conductivity. Our measurements reveal a monoclinic structure stabilized by the dislocation, leading to a substantial drop in thermal conductivity for larger-diameter NWs (70% at room temperature), supported by first-principles calculations. Interestingly, we also find an anomalous enhancement of thermal conductivity with decreasing diameter in twisted NWs, contrary to typical trends in non-twisted GeS NWs. This is attributed to increased conductivity near the NW cores due to compressive strain around the central dislocations, and aligns with a density-functional-theory-informed core–shell model. Our results highlight the critical role of dislocations in thermal conduction, providing fundamental insights for defect and strain engineering in advanced thermal applications.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Electronic correlations and topology in Kondo insulator PuB 6

Utilizing a combination of dynamical mean field theory (DMFT) and density functional theory, it has been theoretically proposed that PuB 6 is a strongly correlated topological insulator characterized by nontrivial 𝐙 2 topological invariants and metallic surface states [X. Deng et al., Phys. Rev. Lett. 111, 176404 (2013)]. Here, we demonstrate through low-temperature magnetotransport measurements and first-principles calculations that PuB 6 exhibits characteristics of a topological Kondo insulating state. These features include a transition in electrical resistivity from high-temperature, thermally activated behavior with a narrow gap at the Fermi level (Δ⁢𝜌 ∼ 20 meV) to a distinctive low-temperature plateau, as well as a surface-to-volume dependence of electrical resistivity at low temperatures. The topological nature of PuB 6 is further supported by the theoretical calculations, which show that GGA + 𝑈 is capable of capturing electronic, topological, and lattice properties of PuB 6 with much lower computational cost than DMFT.

36 - MATERIALS SCIENCE↗
DOE OSTI2025

Mechanistic Insights into Oxygen Reduction Reaction on Metal Cathode Over BaZrO 3 -Based Electrolyte under Moist Atmosphere: Interfacial Interactions and Reaction Pathways

The oxygen reduction reaction (ORR) is a critical process that often governs the overall performance of electrochemical systems such as proton conducting solid oxide fuel cells. Despite its significance, the current understanding about the ORR, especially when it involves H 2 O is still limited. In this study, the proton involved ORR (PI-ORR) on metal cathode (e.g., Pt) over BaZrO 3 (BZO) electrolyte is investigated using density functional theory (DFT) under moist atmosphere. Two scenarios are considered: one at relatively high temperature (900 K) in the presence of oxygen vacancy in BZO substrate and one at relatively low temperature (700 K) without oxygen vacancy. We systematically explored oxygen vacancy effects on adsorption sites and proton transfer pathways, calculated energy profiles and Gibbs free energies for elementary steps along the O 2 dissociated and the O 2 concerted reaction pathways. We also evaluated H 2 O impacts on intermediate oxygen species (*O and *OH) through Ab Initio molecular dynamics. These analyses revealed pathway-dependent reaction mechanisms and hydration effects at triple-phase boundary, advancing fundamental understanding of PI-ORR in metal cathode/Ba-based electrolyte systems for energy applications.

08 - HYDROGEN↗
DOE OSTI2025

Ab initio calculations of overlap integrals for μ → e conversion in nuclei

The rate for μ → e conversion in nuclei is set to provide the most stringent test of lepton-flavor symmetry and a window into physics beyond the Standard Model. However, to disentangle new lepton-flavor-violating interactions, in combination with information from μ → ey and μ → 3e, it is critical that uncertainties at each step of the analysis be controlled and fully quantified. In this regard, nuclear response functions related to the coupling to neutrons are notoriously problematic, since they are not directly constrained by experiment. We address these shortcomings by combining ab initio calculations with a recently improved determination of charge distributions from electron scattering by exploiting strong correlations among charge, point-proton, and point-neutron radii and densities. We present overlap integrals for 27 Al, 48 Ca, and 48 Ti including full covariance matrices, allowing, for the first time, for a comprehensive consideration of nuclear structure uncertainties in the interpretation of μ → e experiments.

ab initio calculations↗
DOE OSTI2025

From Micro-environments to Macroscopic Effects: How the Alkaline Hydrogen Evolution Reaction Drives Cu Cathodic Corrosion

Cathodic corrosion of copper (Cu) has posed a significant challenge for over a century, impeding various technological progresses such as electrochemical conversion of CO 2 (eCO 2 RR) into fuels and other value-added carbon products. Here, in this study, employing a combined Density Functional Theory (DFT) and kinetic Monte Carlo (kMC) simulation approach, we delve into the atomistic level mechanism driving this phenomenon in Cu. Our hypothesis posits the pivotal role of alkaline hydrogen evolution reaction (HER) in facilitating cathodic corrosion in Cu. We rigorously develop a pH-dependent hydroxide (OH) adsorption mechanism and calculate the equilibrium OH coverage (𝜃 OH ) at varying pH levels, the thermodynamic stability of subsurface oxygen (O sub ), as well as the Cu-vacancy mediated diffusion of subsurface oxygens (O sub ). Through comprehensive analysis, we establish correlation among various microenvironments, including oxygen diffusion in subsurface layers, pH-dependent OH adsorption, and Cu dissolution into the electrolyte as (Cu-OH) complexes. Furthermore, our investigation explores the correlation between surface coordination environment of active sites and cathodic corrosion of Cu. Finally, by integrating DFT-derived thermodynamic data into a kMC model, we successfully predict the formation of experimentally observed corrosion pits on Cu-surfaces. This combined approach not only advances our fundamental understanding of Cu cathodic corrosion but also offers insights crucial for developing effective corrosion mitigation strategies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Data for "Plasmon-driven exciton formation in a non-equilibrium Fermi liquid"

This repository contains source data for key plots presented in the manuscript "Plasmon-driven exciton formation in a non-equilibrium Fermi liquid." Experimental data that was analyzed in Igor Pro 8 are presented as the .pxp files used to generate individual sub-plots. Electronic spectral function calculations are provided as .txt files, in which consecutive rows refer to the meshgrid x coordinate, y coordinate, spectral function (and, where relevant, axis-projected local angular momentum). We additionally include the Wannier model and DFT-obtained bulk band structure on which the Wannier model was based. Files are named as the number of the figure in the manuscript to which they correspond, with additional details included where necessary. Details of file names: 2a_DOS_Lxz_Ek_KGM_40layer_xnum_800kpt_tot.txt: Density of states, xz-axis projected local orbital angular momentum, for 800 points along the K-Gamma-M path, for a 40-layer model. 2c_composite_y.pxp: ARPES (angle-resolved photoemission spectroscopy) spectra along the ky axis, including both a scan near the Fermi level and a scan at high kinetic energies. 2d_LCP_RCP_diff_Sect_20K.pxp: difference between ARPES constant energy cuts at T=20 K at E0 + 0.23 eV taken with left- and right-circularly polarized photons. The polarization-integrated intensity at the constant energy cut is also included. 2e_DOS_L45_E11pt79_m0pt25to0pt25_xnum_800kpt_tot.txt: Density of states, xz-projected local orbital angular momentum, and corresponding k-points in two dimensions from ab-initio electronic structure calculations for a constant-energy cut. 3a_[x]_[y]ps: ARPES cut under excitation at a fluence of x uJ/cm2, measured y ps after photoexcitation. Measurements were performed at 9 K. 3b_[x]: Energy distribution curves under excitation at a fluence x uJ/cm2 at selected delay times after photoexcitation. 4a_ImSigma_vs_temperature.pxp: Imaginary self energy (extracted from ARPES linewidths) at different energies above E0 for selected lattice temperatures. 4b_EELS_lowE.pxp: Electron energy loss spectrum over a low energy range 5b_diff_55m15.pxp: Difference between momentum-integrated Tr-ARPES traces at 55 uJ/cm2 and 15 uJ/cm2 photoexcitation. Time-dependent intensity at each energy level has been normalized to a maximum of 1 for each individual fluence prior to subtraction. 5d_invtau_at_EX_vs_fluence.pxp: decay rate at a specified energy EX for different excitation fluences, from single exponential fits. NOTE: Analyses based on the Wannier model presented here should cite both the associated Article and this dataset. For all other files in the repository, citing the dataset alone is sufficient.

Acharya, Rishi [University of Illinois] (ORCID:000↗
DOE OSTI2026

Disorder-induced magnetoelastic behaviors of MnTexSbyBi1-x-y alloys

This dataset contains input and output files from density functional theory (DFT) simulations used to study the disorder-induced magnetoelastic behaviors of MnTexSbyBi1-x-y (0 ≤ x + y ≤ 1) alloys and their binary end members MnTe, MnSb, and MnBi. The alloys adopt the hexagonal NiAs-type (nickeline) structure and span ternary (MnTexSb1-x, MnTexBi1-x, MnBixSb1-x), and quaternary compositions across the full MnTe–MnSb–MnBi composition triangle. For each alloy composition, the dataset provides DFT calculations in three magnetic configurations: A-type antiferromagnetic (AFM), C-type AFM, and ferromagnetic (FM). Every magnetic configuration folder contains the fully relaxed crystal structure (CONTCAR), VASP input parameters (INCAR), and the main VASP output file (OUTCAR), from which total electronic energies, Mn magnetic moments, lattice parameters, and percent volume changes between magnetic states are extracted. These data are used to construct compositional phase diagrams, evaluate thermodynamic stability (formability), and map magnetoelastic responses across the alloy space. For A-type AFM and FM configurations, additional data are provided as follows: (i) FORCE_CONSTANTS and thermal_properties.yaml files at the top level of A-type_AFM/ and FM/ folders — present only for compositions marked with an asterisk (*) in Table I of the main text. These are derived from Phonopy finite-displacement calculations on full disordered 128-atom supercells and provide vibrational free energy, entropy (Svib)contribution from explicit disorder calculations. (Table I of the associated main manuscript) (ii) A VCA/ subfolder within A-type_AFM/ and FM/, containing FORCE_CONSTANTS and thermal_properties.yaml from Virtual Crystal Approximation phonon calculations (without spin-orbit coupling). VCA data are available for all compositions and are used to estimate vibrational contributions to the Gibbs free energy across the full composition space. (iii) A SOC/ subfolder containing CONTCAR, INCAR, and OUTCAR from spin-orbit coupling calculations, providing relativistic corrections to electronic energies and lattice parameters (Tables S2–S3 of the SM, and Table I of the main manuscript). (iv) A SOC/VCA/ subfolder containing FORCE_CONSTANTS and thermal_properties.yaml from VCA phonon calculations performed within the SOC framework, combining relativistic and vibrational thermodynamic corrections. The computed properties are used to map the AFM–FM magnetic crossover near MnTe0.75Sb0.25, demonstrate disorder- and spin-induced phonon broadening, identify a semiconductor-to-metal crossover, and quantify the pronounced magnetoelastic volume response near the magnetic phase boundary.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Intrinsic Layer-Dependent Surface Energy and Exfoliation Energy of van der Waals Materials

Stacking and twisting 2D van der Waals (vdW) layers have become versatile platforms to tune the electron correlation. These platforms rely on exfoliating vdW materials down to a single vdW layer and a few vdW layers. We calculate the intrinsic layer-dependent surface and exfoliation energies of typical vdW materials such as graphite, h-BN, black P, MX 2 (M = Mo or W; X = S, Se, or Te), MX (M = Ga or In; X = S, Se, or Te), Bi 2 Te 3 , and MnBi 2 Te 4 using density functional theory. For exchange-correlation functionals with explicit vdW interaction, a single vdW layer always has the smallest surface energy, giving a surface energy reduction when compared to that of thicker vdW layers. Furthermore, the magnitude of this surface energy reduction quickly decreases with an increase in the number of atomic layers inside the single vdW layer for different vdW materials. Such atomic-layer dependence in surface energy reduction helps explain the different effectiveness of exfoliation for different vdW materials down to a single vdW layer.

Anode materials↗