Nudged Elastic Band Method Research Articles

Surface Diffusion of Fe and Cu on Fe (001) Under Electric Field Using First-Principles Calculations.

First-principles calculations were performed to determine the Fe on Fe (001) evaporation field and to characterize the surface diffusion of Fe and Cu on Fe (001) and on a step structure under an applied electric field. The evaporation field of Fe on Fe (001) was calculated by the nudged elastic band (NEB) method, using the combination of the effective screening medium and constant electrode potential methods to obtain a condition of constant electric field. The calculated evaporation field of Fe on Fe (001) was 32.4 V/nm, which agrees well with the experimental value. In the surface diffusion of Fe and Cu on Fe (001) and on a step structure, the activation barrier energies were determined by the NEB method with constant applied electric field. It was found that Cu diffuse more easily on the Fe (001) and step structure than Fe under an applied electric field. The activation barrier energy of surface diffusion in the saddle point configuration is small when the distance between Cu and Fe on the surface is larger, and the activation barrier energy becomes smaller when passing through a path far away from the surface due to the effect of the electric field.

Ab initio calculations for crystalline PEO6:LiPF6 polymer electrolytes

Dry polymer electrolytes have been studied extensively because of their enhanced mechanical properties. Experimental studies have demonstrated that crystalline PEO6:LiPF6 has higher ionic conductivity than that of the amorphous phase, which seemingly contradicts the prevailing theory that amorphous polymer electrolytes have higher conduction performance. Also, the underlying mechanism at the atomic scale has remained elusive. In this work, the atomic and electronic structures of crystalline PEO6:LiPF6 are studied using ab initio density-functional theory. The results agree with experimental measurements. Additionally, the atomic-scale mechanisms of lithium ion transport in the polymer electrolytes are investigated with the climbing nudged elastic band method. The diffusion pathway and activation energy (∼0.87 eV) of lithium ions in crystalline PEO6:LiPF6 are determined.

Effects of Mo alloying on stability and diffusion of hydrogen in the Nb16H phase: a first-principles investigation.

First-principles calculations and the method of climbing-image nudged elastic band were used to investigate the effects of Mo alloying on the structural stability, mechanical properties, and hydrogen-diffusion behavior in the Nb16H phase. The Nb12Mo4H phase (26.5 at% Mo) was found to be the most thermodynamically stable structure, with a low ΔHf value (−0.26 eV) and high elastic modulus. Calculations revealed that the tetrahedral interstitial site (TIS) was the predominant location of H in both Nb16H and Nb12Mo4H phases. The calculated H-diffusion energy barrier and the diffusion coefficient of the Nb12Mo4H phase were 0.153 eV and 5.65 × 10−6 cm2 s−1 (300 K), respectively, which suggest that the addition of Mo would lead to a lower energy barrier and high diffusion coefficients for the Nb16H phase, thus improving the hydrogen-permeation properties of Nb metal.

Electrochemical performance and Li+ insertion/extraction mechanism of carbon-coated cerium metavanadate as a novel anode for lithium-ion batteries

The novel CeVO3 anode material is synthesized successfully by simple sol-gel method. The crystal structure is determined by the X-ray diffraction, where the CeVO3 possesses a stable framework and a good lithium-ion migration pathway. The corresponding electrochemical measurement shows that pure CeVO3 presents a low reversible discharge capacity and poor rate performance due to the low electronic conductivity. In order to improve the electrochemical properties, the carbon-coated CeVO3 samples are also prepared choosing sucrose as carbon source with 9.5% carbon content. The added carbon inhibits the particle growth and increases the conductivity. By carbon-coating, the corresponding electronic conductivity of the CeVO3 is increased by one order of magnitude and the lithium diffusion coefficient is increased from 6.55 × 10−11 cm2 s−1 to 2.26 × 10−10 cm2 s−1, resulting in the improvement of discharge specific capacity and rate performance. In addition, using In-situ XRD method, we determine the Li ions insertion/extraction mechanism of the CeVO3 material which can be interpreted as a solid-solution behavior. Finally, using nudged elastic band method, we calculate the possible migration paths for lithium diffusion in CeVO3 crystal which most likely prefers to along the diagonal direction of z axis and x axis.

Electronic, magnetic and transport properties of zigzag silicene nanoribbon adsorbed with Cu atom: A first-principles calculation

Abstract This paper aims to provide a detailed analysis of the electronic, magnetic and spin-dependent transport properties of Cu-adsorbed zigzag silicene nanoribbons within the density functional theory framework. The possibility of diffusion between different stable positions is studied by Nudge Elastic Band (NEB) method. As to zigzag graphene nanoribbons, the center of nearest hexagonal to the edge is the most favorable site for adsorbing Cu atom. Total energy analysis for spin-polarized calculations indicates that the antiferromagnetic (AFM) state is the magnetic ground state of zigzag silicene nanoribbons whereas adding the Cu adatom on the near edge yields ferromagnetic (FM) state with the total magnetization about 0.98 μ B . As a consequence of charge transfer from Si atoms to Cu, the spin distribution symmetry of the edges is broken and the spin magnetic moment is considerably localized on the edge with no adsorption. Further verification of the electronic properties may be obtained through investigating the conductivity behavior of the device using the current-voltage (I-V) characteristics based on density functional theory with non-equilibrium Green’s function included. Although the spin-up current increases with the bias monotonically, a spin negative different resistance phenomenon is observed for spin-down electrons. Additionally, spin-up transmission shows higher values in comparison with that for spin-down in bias window which leads to the higher current. The results hold promising applications for future nano-electronics and spintronic devices.

Electronic structure and migration of interstitial hydrogen in the rutile phase of TiO2

The formation and migration energies of interstitial hydrogen in rutile TiO2 are obtained from first principles calculations. The computational approach was based on density functional theory with a semilocal generalised-gradient approximation functional, supplemented with an on-site Hubbard term to account for correlation among the Ti 3d electrons. Charge-transition levels are calculated and compared to previous theoretical studies. The donor character of hydrogen is examined in depth, focusing in particular on the tendency to form polaron-like configurations with the unpaired electron trapped at nearby titanium ions. Distinct minimum-energy paths of hydrogen migration and associated energy barriers were determined by the nudged elastic-band method. The present findings show clearly the strong anisotropy in the energy barriers for migration within the open c channels as opposed to migration crossing adjacent channels of the rutile lattice. For the rate-limiting step which leads to macroscopic diffusion along the c axis the corresponding rate and diffusion coefficient were also determined from transition-state theory. The results are discussed in connection to existing measurements of hydrogen diffusion and recent findings from electron paramagnetic resonance, electron–nuclear double resonance and muonium spectroscopies that probed the spatial localization of the electron spin.

Proton Migration on Perfect, Vacant, and Doped MgO(001) Surfaces: Role of Dissociation Residual Groups

Although migration processes on low-coordination surface sites of a magnesium oxide (MgO) surface are important in technological applications including catalysis in gas interfaces, they are not well understood. In particular, hydrated MgO(001) surfaces present charge transfer and ionic transport phenomena that sometimes do not work properly in technological devices. On the other hand, low-coordination surface sites are chemically attractive. Given that defects and adsorbed species can be characterized by the kinetics of surface processes, in this work, we investigated proton mobility pathways produced from the dissociative adsorption of water molecules on different MgO(001) surfaces: a perfect-terrace, with an anionic vacancy, and with an Al-doped + cationic vacancy. For that purpose, we employed density-functional theory with periodic boundary conditions combined with the climbing imaged nudged elastic band method to compute energy barriers. The dissociative adsorption of water molecules on the perfect-t...

Role of hydrostatic pressure on the phase stability, the ground state, and the transformation pathways of NiTi alloy

Equiatomic NiTi shape memory alloys exhibit multiple martensitic transformations from a parent B2 phase. However, there is an apparent discrepancy between theoretical predictions and experimental observations of the transformation pathways and final products. We studied the phase stabilities of NiTi martensites with respect to the effect of hydrostatic pressure using a generalised solid-state nudge elastic band method implemented in density functional theory to simulate the minimum energy pathways of transformations. The analysis demonstrates that base-centred orthorhombic (BCO) phase is unstable, thus will undergo the BCO→B19′ phase transformation at above 9GPa pressure, as confirmed by phonon calculations.

Exploring a potential energy surface by machine learning for characterizing atomic transport

We propose a machine-learning method for evaluating the potential barrier governing atomic transport based on the preferential selection of dominant points for the atomic transport. The proposed method generates numerous random samples of the entire potential energy surface (PES) from a probabilistic Gaussian process model of the PES, which enables defining the likelihood of the dominant points. The robustness and efficiency of the method are demonstrated on a dozen model cases for proton diffusion in oxides, in comparison with a conventional nudge elastic band method.

Oxygen reduction reaction (orr) on bimetallic AuPt and AuPd(1 0 0)–electrodes: Effects of the heteroatomic junction on the reaction paths

The seek for materials to enhance the oxygen reduction reaction (orr) rate is a highly relevant topic due to its implication in fuel cell devices. Herein, the orr on bimetallic electrocatalysts based on Au-M (M = Pt, Pd) has been studied computationally, by performing density functional theory calculations. Bimetallic (100) electrode surfaces with two different Au:M ratios were proposed, and two possible pathways, associative and dissociative, were considered for the orr. Changes in the electronic properties of these materials with respect to the pure metals were acknowledged to gain understanding in the overall reactivity trend. The effect of the bimetallic junction on the stability of the intermediates O2 and OOH was also evaluated by means of geometrical and energetic parameters; being the intermediates preferably adsorbed on Pt/Pd atoms, but presenting in some cases higher adsorption energies compared with bare metals. Finally, the kinetics of the OO bond breaking in O2∗ and OOH∗ adsorbed intermediates in the bimetallic materials and the influence of the Au-M junction were studied by means of the nudge elastic-band method. A barrierless process for the scission of O2∗ was found in Au-M for the higher M ratios. Surprisingly, for Au-M with lower M ratios, the barriers were much lower than for pure Au surfaces, suggesting a highly reactive surface towards the orr. The OO scission of the OOH∗ was found to be a barrierless process in AuPt systems and nearly barrierless in all AuPd systems, implying that the reduction ofO2 in these systems proceeds via the full reduction of O2 to H2O, avoiding H2O2 formation.

Protons in cubic yttria-stabilized zirconia: Binding sites and migration pathways

Despite the fact that unusually high power generation attributed to proton conduction has been reported recently for nanostructured yttria-stabilized zirconia (YSZ) little is known about the atomistic mechanisms of proton transport and corresponding activation energies, namely the factors that dictate proton mobility. Important issues to be examined include the energetics of proton incorporation in the YSZ host, the binding of protons to intrinsic structural defects and the role of grain boundaries in proton conduction. The present study reports calculations based on density-functional theory (DFT) of defect-formation energies and energy barriers for proton migration in cubic YSZ for an yttria doping in the 10–12mol% range. For the bulk-crystalline lattice representative migration pathways are identified and the corresponding energy barriers for proton migration are calculated using the nudged elastic-band method. The feasibility for the grain boundaries to act as fast diffusion pathways for protons is also examined. For the high-angle Σ5(310) grain boundary DFT calculations were undertaken so as to determine the segregation propensity of protons as well as the magnitude of energy barriers for selected proton migration pathways at the core of this extended defect. The present calculations outline the importance of oxygen vacancies for proton migration in the bulk crystal and the ability of localized cation clusters at the grain-boundary core to act as strong obstacles to proton motion.

The magnetic structure and palaeomagnetic recording fidelity of sub-micron greigite (Fe3S4)

We present the results of a finite-element micromagnetic model of 30nm to 300nm greigite (Fe3S4) grains with a variety of equant morphologies. This grain size range covers the magnetic single-domain (SD) to pseudo single-domain (PSD) transition, and possibly also the PSD to multi-domain (MD) transition. The SD–PSD threshold d0 is determined to be 50nm≤d0≤56nm depending on grain shape. The nudged elastic-band method was used to determine the room temperature energy barriers between stable states and thus the blocking volumes. It is found that, in the absence of interparticle magnetostatic interactions, the magnetisation of equant SD greigite is not stable on a geological scale and only PSD grains ≥70nm can be expected to carry a stable magnetisation over billion-year timescales, i.e., all non-interacting SD particles are essentially superparamagnetic. We further identify a mechanism for the PSD to multi-domain (MD) transition, which is of a continuous nature from PSD nucleation up to 300nm, when structures typical of MD behaviour like closure domains begin to form.

I, N-Codoping Modification of TiO2 for Enhanced Photoelectrochemical H2O Splitting in Visible-Light Region

The donor–acceptor codoping is an effective approach to tune the photoelectrochemical properties of TiO2. Here, we systematically investigate the effects of (I+N) codoping on the electronic structures and H2O splitting reactions of anatase TiO2 by using density functional theory. It is found that the codoping of the stable charge-compensated (I+N) donor–acceptor pair in anatase TiO2 not only can prevent the recombination of photogenerated electron–hole pairs but also can effectively reduce the band gap to 2.251 eV by forming an intermediate band within the band gap. The band edge alignment of (I+N) codoped TiO2 is desirable for H2O splitting, and the calculated optical absorption curve of (I+N) codoped TiO2 verifies that (I+N) codoping can significantly improve visible-light absorption. Moreover, we also calculate the chemical reaction pathways of H2 generation via H2O splitting on (I+N) codoped TiO2 surfaces by using the climbing nudged elastic band (cNEB) method and find that the (I+N) codoping in TiO2 ...

Shear-coupled grain-boundary migration dependence on normal strain/stress

In specific conditions, grain boundary (GB) migration occurs in polycrystalline materials as an alternative vector of plasticity compared to the usual dislocation activity. The shear-coupled GB migration, the expected most efficient GB based mechanism, couples the GB motion to an applied shear stress. Stresses on GB in polycrystalline materials have however seldom a unique pure shear component. This work investigates the influence of a normal strain on the shear coupled migration of a Σ13(320)[001] GB in a copper bicrystal using atomistic simulations. We show that the yield shear stress inducing the GB migration strongly depends on the applied normal stress. Beyond, the application of a normal stress on this GB qualitatively modifies the GB migration: while the Σ13(320)[001] GB shear-couples following the 110 migration mode without normal stress, we report the observation of the 010 mode under a sufficiently high tensile normal stress. Using the Nudge Elastic Band method, we uncover the atomistic mechanism of this 010 migration mode and energetically characterize it.

Scale transition using dislocation dynamics and the nudged elastic band method

Microstructural features such as precipitates or irradiation-induced defects impede dislocation motion and directly influence macroscopic mechanical properties such as yield point and ductility. Dislocation-defect interactions involve both atomic scale and long range elastic interactions. Thermally assisted dislocation bypass of obstacles occurs when thermal fluctuations and driving stresses contribute sufficient energy to overcome the energy barrier. The Nudged Elastic Band (NEB) method is typically used in the context of atomistic simulations to quantify the activation barriers for a given reaction. In this work, the NEB method is generalized to coarse-grain continuum representations of evolving microstructure states beyond the discrete particle descriptions of first principles and atomistics. This method enables the calculation of activation energies for a 1/2[111](11¯0) glide dislocation bypassing a [001] self-interstitial atom loop of size in the range of 4–10 nm with a spacing larger than 150 nm in α-iron for a range of applied stresses and interaction geometries. Further, the study is complemented by a comparison between atomistic and continuum based prediction of barriers.

Local equilibrium configurations and minimum energy path of carbon nanotubes with Stone-Wales defects and their related pentagon-heptagon lattice defects

The energy landscape over configurational change of defects in carbon nanotube (CNT) is clarified for a variety of distributions of Stone–Wales defects and pentagon–heptagon (5–7) defects using the Peierls–Nabarro dislocation model. Based on the theoretical model, the configurational energy is estimated by relative displacement without fatal loss of accuracy, but the calculation of energy during the configurational change of defect is simplified with reduced degrees of freedom in the displacement field. The equilibrium configurations are obtained using the conjugate-gradient method, and the saddle point on the minimum-energy path between two equilibrium configurations for evolution of defects, such as the nucleation/annihilation and movement of defects, is estimated using the nudged elastic-band method. Many equilibrium configurations stably exist because of the lattice trapping of the 5–7 defects due to the relatively large Peierls–Nabarro barrier. The total energy does not only depend on the mean value of the relative displacement, but also on the complexity of the configurations of the defects, and we draw a directed graph which shows the possible paths of the configuration change of the defects. The results provide fundamental information related to the stability of the thermal activation of defects in CNT.

Temperature effects on growth configurations for Al-Mg bimetallic nanoparticles

The growth of Al atoms on a Mg hexahedral cluster with 587 atoms within the temperature range of 50–550K is studied by using molecular dynamics and embedded atom method. The energy barriers of typical diffusion processes of Al atoms on Mg clusters are calculated using nudged elastic band method. Radial distribution function is utilized to analyze the growth process. Simulation results demonstrate the temperature dependence of the shape-controlled growth of the bimetallic cluster. The deposited Al atoms are arranged in a hexahedral structure at lower temperature, and a better Mg-core/Al-shell cluster with a nearly spherical structure is obtained at 150K. As the simulated temperature increases, more and more Al adatoms enter the Mg core, and alloying in the clusters become more apparent.

Computational study of one-step polar Diels–Alder reactions using the NEB method for the minimum energy paths search

The Nudged Elastic Band (NEB) method is an algorithm to search the minimum energy path (MEP), which has been successfully applied for studying several processes that involve solid-state models; however, it has not been widely tested in discrete molecular systems. Performing density functional theory calculations, this method was employed in NWChem to find the MEP of reactions between cyclopentadiene and cyano-substituted ethylenes. Results suggest that the reaction mechanism is concerted in all systems. Also, kinetics and thermodynamics analysis were done: With respect to experimental data, energetic parameters are computed better at the M06-2X/6-31++G** level; entropy and frequency factors were poorly predicted. This is a simple methodology, where the NEB method is evaluated to find the MEP in some prototypical Diels–Alder reactions.

Application of the nudged elastic band method to the point-to-point radio wave ray tracing in IRI modeled ionosphere

Point-to-point ray tracing is an important problem in many fields of science. While direct variational methods where some trajectory is transformed to an optimal one are routinely used in calculations of pathways of seismic waves, chemical reactions, diffusion processes, etc., this approach is not widely known in ionospheric point-to-point ray tracing. We apply the Nudged Elastic Band (NEB) method to a radio wave propagation problem. In the NEB method, a chain of points which gives a discrete representation of the radio wave ray is adjusted iteratively to an optimal configuration satisfying the Fermat’s principle, while the endpoints of the trajectory are kept fixed according to the boundary conditions. Transverse displacements define the radio ray trajectory, while springs between the points control their distribution along the ray. The method is applied to a study of point-to-point ionospheric ray tracing, where the propagation medium is obtained with the International Reference Ionosphere model taking into account traveling ionospheric disturbances. A 2-dimensional representation of the optical path functional is developed and used to gain insight into the fundamental difference between high and low rays. We conclude that high and low rays are minima and saddle points of the optical path functional, respectively.

GPU-Accelerated Exploration of Biomolecular Energy Landscapes.

We present graphics processing unit (GPU)-acceleration of various computational energy landscape methods for biomolecular systems. Basin-hopping global optimization, the doubly nudged elastic band method (DNEB), hybrid eigenvector-following (EF), and a local rigid body framework are described, including details of GPU implementations. We analyze the results for eight different system sizes, and consider the effects of history size for minimization and local rigidification on the overall efficiency. We demonstrate improvement relative to CPU performance of up to 2 orders of magnitude for the largest systems.