Nudged Elastic Band Method Research Articles

First principles validation of energy barriers in Ni75Al25

Precipitates in nickel-based superalloys form during heat treatment on a time scale inaccessible to direct molecular dynamics simulation, but can be studied using kinetic Monte Carlo (KMC) modelling. This requires reliable values for the barrier energies separating distinct configurations over the trajectory of the system. In this study, we validate vacancy migration barriers found with the Activation-Relaxation Technique nouveau (ARTn) method in partially ordered Ni75Al25 with a monovacancy using published potentials for the atomic interactions against first-principles methods. In a first step, we confirm that the ARTn barrier energies agree with those determined with the nudged elastic band (NEB) method. As the number of atoms used in those calculations is too great for direct ab initio calculations, we cut the cell size to 255 atoms, thus controlling finite size effects. We then use the plane-wave density functional theory code CASTEP and its inbuilt NEB method in the smaller cells. This provides us with a continuous validation chain from first principles to KMC simulations with interatomic potentials (IPs). We evaluate the barrier energies of five further IPs with NEB, demonstrating that none yields values with sufficient reliability for KMC simulations, with some of them failing completely. This is a first step towards quantifying the errors incurred in KMC simulations of precipitate formation and evolution.

Development of a machine learning interatomic potential for exploring pressure-dependent kinetics of phase transitions in germanium.

We introduce a data-driven potential aimed at the investigation of pressure-dependent phase transitions in bulk germanium, including the estimate of kinetic barriers. This is achieved by suitably building a database including several configurations along minimum energy paths, as computed using the solid-state nudged elastic band method. After training the model based on density functional theory (DFT)-computed energies, forces, and stresses, we provide validation and rigorously test the potential on unexplored paths. The resulting agreement with the DFT calculations is remarkable in a wide range of pressures. The potential is exploited in large-scale isothermal-isobaric simulations, displaying local nucleation in the R8 to β-Sn pressure-induced phase transformation, taken here as an illustrative example.

Comparative study of nudged elastic band and molecular dynamics methods for diffusion kinetics in solid-state electrolytes

Abstract Considerable efforts are being made to transition current lithium-ion and sodium-ion batteries towards the use of solid-state electrolytes. Computational methods, specifically nudged elastic band (NEB) and molecular dynamics (MD) methods, provide powerful tools for the design of solid-state electrolytes. The MD method is usually the choice for studying the materials involving complex multiple diffusion paths or having disordered structures. However, it relies on simulations at temperatures much higher than working temperature. This paper studies the reliability of the MD method using the system of Na diffusion in MgO as a benchmark. We carefully study the convergence behavior of the MD method and demonstrate that total effective simulation time of 12 ns can converge the calculated diffusion barrier to about 0.01 eV. The calculated diffusion barrier is 0.31 eV from both methods. The diffusion coefficients at room temperature are 4.3×10-9 and 2.2×10-9 cm2/s, respectively, from the NEB and MD methods. Our results justify the reliability of the MD method, even though high temperature simulations have to be employed to overcome the limitation on simulation time.

Strain-Controlled Formation Energy and Migration of Nitrogen Vacancy in Al1-xScxN: A First-Principles Study.

The impact of strain on the formation energy and migration behavior of nitrogen vacancies (VNs) in Al1-xScxN has been investigated by first-principles calculations. The formation energy of VNs is obtained by total energy calculations. The migration barrier calculation utilizes the climbing nudged elastic band method. It is found that the formation energy of VNs is highly tunable with respect to the strain. The formation energy of VNs increases with the tensile strain increasing to +4% and decreases with the increasing compressive strain to -4%. A minimum formation energy of 4.11 eV is obtained when -4% strain is applied. Furthermore, the migration behavior of VNs is studied by calculating the migration barriers. Calculation results show that the migration barrier is strongly affected by strain. When the strain is -4%, the barrier is 2.46 eV while the barrier is increased to 2.71 eV under +4% strain. Therefore, a tensile strain can prevent the formation and migration of VNs. These findings suggest that strain engineering may serve as a tool for regulating VNs behavior in Al1-xScxN, potentially alleviating the ferroelectric degradations associated with VNs.

Spin Crossover and Exchange Effects on Oxygen Evolution Reaction Catalyzed by Bimetallic Metal Organic Frameworks.

Bimetallic metal-organic frameworks (BMOFs) have shown a superior oxygen evolution reaction (OER) performance, attributed to the synergistic effects of dual metal sites. However, the significant role of these dual-metal synergies in the OER is not yet fully understood. In this study, we employed density functional theory to systematically investigate the OER performance of NiAl- and NiFe-based BMOFs by examining all possible spin states of each intermediate across diverse external potentials and pH environments. We found that the spin state featuring a shallow hole trap state and Ni ions with a higher oxidation state serve as strong oxidizing agents, promoting the OER. An external potential-induced spin crossover was observed in each intermediate, resulting in significant changes in the overall reaction and activation energies due to altered energy levels. Combining the constant potential method and the electrochemical nudged elastic band method, we mapped the minimum free energy barriers of the OER under varied external potential and pH by considering the spin crossover effect for both NiAl and NiFe BMOFs. The results showed that NiFe exhibits better OER thermodynamics and kinetics, which is in good agreement with experimentally measured OER polarization curves and Tafel plots. Moreover, we found that the improved OER kinetics of NiFe not only is attributed to lower barriers but also is a result of improved electrical conductivity arising from the synergistic effects of Ni-Fe dual-metal sites. Specifically, replacing the second metal Al with Fe leads to two significant outcomes: a reduction in both the band gap and the effective hole mass compared to NiAl, and the initiation of super- and double-exchange interactions within the Ni-F-Fe chain, thereby enhancing electron transfer and hopping and leading to the improved OER kinetics.

Physical Prior Mean Function-Driven Gaussian Processes Search for Minimum-Energy Reaction Paths with a Climbing-Image Nudged Elastic Band: A General Method for Gas-Phase, Interfacial, and Bulk-Phase Reactions.

The climbing-image nudged elastic band (CI-NEB) method serves as an indispensable tool for computational chemists, offering insight into minimum-energy reaction paths (MEPs) by delineating both transition states (TSs) and intermediate nonstationary structures along reaction coordinates. However, executing CI-NEB calculations for reactions with extensive reaction coordinate spans necessitates a large number of images to ensure a reliable convergence of the MEPs and TS structures, presenting a computationally demanding optimization challenge, even with mildly costly electronic-structure methods. In this study, we advocate for the utilization of physically inspired prior mean function-based Gaussian processes (GPs) to expedite MEP exploration and TS optimization via the CI-NEB method. By incorporating reliable prior physical approximations into potential energy surface (PES) modeling, we demonstrate enhanced efficiency in multidimensional CI-NEB optimization with surrogate-based optimizers. Our physically informed GP approach not only outperforms traditional nonsurrogate-based optimizers in optimization efficiency but also on-the-fly learns the reaction path valley during optimization, culminating in significant advancements. The surrogate PES derived from our optimization exhibits high accuracy compared to true PES references, aligning with our emphasis on leveraging reliable physical priors for robust and efficient posterior mean learning in GPs. Through a systematic benchmark study encompassing various reaction pathways, including gas-phase, bulk-phase, and interfacial/surface reactions, our physical GPs consistently demonstrate superior efficiency and reliability. For instance, they outperform the popular fast inertial relaxation engine optimizer by approximately a factor of 10, showcasing their versatility and efficacy in exploring reaction mechanisms and surface reaction PESs.

Magnetization reversal and stability of vortex state in convex shaped cylindrical nanodisks

Cylindrical nanodisks typically exhibit in-plane magnetization reversal comprising of nucleation and propagation of a vortex closure state. Present work investigates the magnetization reversal process in a cylindrical disk of radius ranging from 20 nm to 100 nm in which the flat surfaces at top and bottom are modified to convex shaped surfaces. It is found that the nucleation of vortex state no longer occurs as a result of this surface modification. Instead, a buckled magnetization state is nucleated which transforms to reverse buckled state yielding a square hysteresis loop. However, the out-of-plane hysteresis loop exhibits a vortex state at remanence. Analytical calculation of total free energy of both vortex as well as buckled state and the comparison thereof shows that the vortex state is ground state if radius of nanodisk is above 60 nm . Below this critical radius, buckled state is the ground state. But the non-appearance of vortex state at remanence in in-plane hysteresis loop of all of the nanodisks indicates a presence of energy barrier between vortex and buckled state. Height of the energy barrier is estimated using nudged elastic band method (NEBM) in all cases which proves that the energy barrier for vortex state weakens and the barrier for buckled state intensifies with the reduction of nanodisk size. At the critical radius of 60 nm , crossover of the two barrier heights occurs. Eventually, at the radius of 30 nm , the vortex state becomes totally unstable which can be toppled to buckled state with the slightest of perturbation.

An ab initio guided study on the shear-induced fcc-hcp transition: A case study of (Ti,Al)N/ZrN multilayers

The cubic-wurtzite phase transition of (Ti,Al)N-based thin films at high temperatures is the chief determing factor for their thermal stability. Nevertheless, its mechanism of atomic shear is not yet well explored theoretically. Here, we correlate the coherent interfaces with wurtzite formation within (Ti,Al)N/ZrN multilayers by a combined ab initio and experimental study. Compared to (Ti,Al)N, the multilayer exhibits a delayed formation of hexagonal close-packed (hcp) wurtzite-type AlN phase, which is encapsulated by face-centered cubic (fcc-)(Ti,Zr)N and fcc-(Zr,Ti)N layers when annealed at 1200 °C. Based on the orientation relationships of (200)fcc//(0001)hcp and (220)fcc//(01-10)hcp among hcp-AlN and neighboring fcc-(Ti,Zr)N as well as fcc-(Zr,Ti)N by the solid-state nudged elastic band (SS-NEB) method, two mechanisms for atomic shear during fcc-hcp transition are proposed. The introduction of ZrN layers effectively suppresses the fcc-hcp transition, due to higher activation energies induced by the coherent interfaces.

Atomistic simulations of dislocation activity in Si nanofibers in Al-Si eutectics

Atomistic simulations were used to elucidate the mechanisms of localized plasticity and fracture in Si nanofibers embedded in Al matrix, with uniaxial tensile straining along the fiber axis. The Si nanofibers within the Al matrix exhibited large non-linear elastic strains followed by localized plasticity with the latter accounting for approximately 5 % permanent length increase in the fibers. On the other hand, simulations with aligned Si nanofibers in vacuum (no Al matrix) exhibited elastic deformation only followed by cleavage fracture. Localized plasticity in Si nanofibers is accomplished by gliding of “zonal” partial dislocations with Burgers vector b=aSi3〈112〉, which leads to synchronous shear of two shuffle-sets. Local stress concentration in Si nanofibers due to non-screw segments of dislocation loops around fibers triggers yielding in the nanofibers through the activation of dislocation sources at or near the interfaces but only below some critical fiber diameter, highlighting the role of nanoscale refinement in activating plasticity in embedded Si nanofibers in Al matrix. In addition, the kinetic barriers associated with the glide of edge/screw zonal dislocation in the perfect crystal and twinned crystal are computed using climbing-image nudge elastic band method. A higher mobility of the zonal dislocation in the twinned crystal suggests that twin boundaries can assist in dislocation glide parallel to the boundary. On the other hand, a nano-crack is nucleated at the interaction position of a glide partial dislocation with an intersecting growth twin boundary suggesting that intersecting twins serve to block glide and provide sites for crack nucleation.

Prediction of primary knock-on damage during electron microscopy characterization of lithium-containing materials

To fulfill power and energy demands, lithium-ion battery (LIB) is being considered as a promising energy storage device. For the development of LIBs, high-resolution electron microscopy characterization of battery materials is crucial. During this characterization, the interaction of beam-electrons with Li-containing materials causes damage through several processes, especially knock-on damage. In this study, we investigated this damage by determining the probability of knock-on damage and performing Monte Carlo simulation. For this objective, the threshold displacement energies (TDEs) were computed using sudden approximation technique for three sets of materials, including pure elements, LiX (X = F, Cl, Br), and Li2MSiO4 (M = Fe, Co, Mn). By including the Climbing-Image Nudge Elastic Band (CI-NEB) method into the sudden approximation approach, it was found that the accuracy of the predicted TDEs could be improved. Results also indicated that at moderate electron energies, the knock-on damage for Li in both its elemental and compound forms maximized. In addition, it was shown that the TDE should be the principal parameter for assessing the Li sensitivity to knock-on damage across similar structures. Nonetheless, other parameters, including cross-section, density, weight fraction, atomic weight, and atomic number, were found to impact the knock-on damage.

Initial structural transformation of Mg-Sm binary alloys during early isothermal aging

ABSTRACT The initial structural transformation of Mg-Sm binary alloys on early isothermal aging is investigated by first-principles calculations. There are three typical precipitate structures in this period, namely hexagonal structure, continuous zigzag structure, and discontinuous zigzag structure (˅˄ structure), which are the main transition state structures formed. The formation of clusters is a dynamic process needing to combine vacancy formation and migrations. Among these structures, the lower vacancy formation energy and dilute mixing energy (byproducts of the solute-vacancy binding energy calculation) make hexagonal clusters more possible to form and explain experimental observation of hexagonal structure abundant existing in the matrix, although its formation energy is slightly higher. Furthermore, vacancy-assisted diffusion in doped Mg lattices is calculated using the nudge elastic band method to investigate the kinetics of the cluster formation.

Computational Studies of the Effect of Nitrogen Dopants and Oxygen Vacancies on Li+ Conduction in Lithium Lanthanum Titanate Electrolytes

Our recent experiments have shown that nitrogen doping can effectively improve the ionic conductivity of lithium lanthanum titanate (LLTO) electrolytes. Herein, computational studies are performed to study the mechanisms of ionic conductivity with density-functional theory and machine learning approaches. To elucidate the relationship between nitrogen concentration and oxygen vacancy, the energy for nitrogen doping into the lattice and the formation energy for oxygen vacancy were computed. Oxygen vacancies were found more likely to be created at higher level of nitrogen dopants. The calculations also discovered the potential formation of nitrogen bonds, generating vacancy-like pathways for Li+ conduction. In addition, the minimum-energy pathways for Li+ migration in pristine and various doped LLTO materials were analyzed using the nudged-elastic band method. To correlate energetics and structural features of the different LLTO materials, several machine learning methods were successfully constructed, where the neighboring sites with oxygen vacancies are identified as the major factor influencing the energies and hopping barriers compared with nitrogen dopants. The new insights can guide the design and synthesis of anion dopped oxide electrolytes in solid-state lithium-ion batteries.

First-Principles Study of Hydrogen Dynamics in Monoclinic TiO

The existence of intrinsic vacancies in cubic (monoclinic) TiO suggests opportunity for hydrogen absorption, which was addressed in recent experiments. In the present work, based on first-principles calculations, the preferences are studied for the hydrogen absorption sites and diffusion paths between them. The oxygen vacancies are found to be the primary hydrogen traps with absorption energy of −2.87 eV. The plausible channels for hydrogen diffusion between adjacent vacancy sites (ordered in the monoclinic TiO structure) are compared with the help of calculations using the nudge elastic band method. Several competitive channels are identified, with barrier heights varying from 2.87 to 3.71 eV, that are high enough to ensure relative stability of trapped hydrogen atoms at oxygen vacancy sites. Moreover, the possibility of adsorption of molecular hydrogen was tested and found improbable, in the sense that the H2 molecules penetrating the TiO crystal are easily dissociated (and released atoms tend to proceed toward oxygen vacancy sites). These results suggest that hydrogen may persist in oxygen vacancy sites up to high enough temperatures.

Atomistic determination of Peierls barriers of dislocation glide in nickel

The Peierls barrier measures the lattice resistance to dislocation glide in crystalline solids. We use the nudged elastic band (NEB) method to calculate the Peierls barriers for screw and edge dislocation glide in a face-centered cubic (FCC) metal of Ni. The minimum energy paths (MEPs) across single or sequential Peierls barriers are determined under shear loading. The NEB results show the decreasing Peierls barrier with increasing shear stress, giving the Peierls stress at which the Peierls barrier vanishes. The effects of boundary condition and system size on Peierls barriers are studied by comparing strain- and stress-controlled NEB results. Furthermore, the free-end NEB methods are applied to determine MEPs with improved computational efficiency. The NEB results are also used to evaluate the energetic driving force of dislocation glide, which is consistent with that determined from the Peach-Koehler force. The accuracy of the present NEB results based on an empirical interatomic potential is assessed by comparison with a machine-learning potential. This work demonstrates the robust and efficient quantification of Peierls barriers to dislocation glide in an FCC metal, and it lays a solid foundation for the atomistic determination of Peierls barriers in compositionally complex alloys with the FCC structure in future studies.

Theoretical Study on the Mechanism of CO* Electrochemical Reduction on Cu(111) under Constant Potential

In order to understand the mechanism of the electrochemical reduction of CO* on Cu(111), which competitively generates two intermediates, CHO* and COH*, we performed a first principles calculation on these two electrocatalytic reactions, including the solvent effect and imposing a constant potential. The transition states of the two reactions under constant potential conditions were located by the electrochemical nudged elastic band (eNEB) method and the charge effect in the two reactions was elucidated by charge correction in the constant potential model and Bader charge analysis. It was found that the two reactions have different potential dependencies and involve different degrees of partial charge transfer. In addition, we confirmed that the COH* reaction pathway exists only in a certain potential range when using the implicit solvent model.

Nudged elastic stiffness band method: A method to solve kinks problems of reaction paths.

The nudged elastic band (NEB) method has been widely employed for reaction path (RP) finding; however, certain NEB calculations do not converge to the minimum energy paths (MEPs) because of the occurrence of kinks, which are caused by the free bending of bands. Thus, we propose an extension of the NEB method, called the nudged elastic stiffness band (NESB) method, which adds the stress of stiffness using a beam theory. Here we present results from three examples: the NFK potential, the RPs of the Witting reaction, and finding saddle points for a set of five chemical reaction benchmarks. The results showed that the NESB method has three advantages: to decrease the number of iterations, shrink the length of the pathways from reducing unnecessary fluctuations, and find TS structures by converging to paths close to the MEPs for systems that have sharp curves on the MEPs.

Accelerated Workflow for Antiperovskite‐based Solid State Electrolytes

AbstractWe developed and implemented a multi‐target multi‐fidelity workflow to explore the chemical space of antiperovskite materials with general formula X3BA (X=Li, Na, Mg) and Pm‐3m space group, searching for stable high‐performance solid state electrolytes for all‐solid state batteries. The workflow is based on the calculation of thermodynamic and kinetic properties, including phase and electrochemical stability, semiconducting behavior, and ionic diffusivity. To accelerate calculation of the kinetic properties, we use a surrogate model to predict the transition state structure during ionic diffusion. This reduces the calculation cost by more than one order of magnitude while keeping the mean error within 73 meV of the more accurate nudged elastic band method. This method identifies 14 materials that agree with the experimentally reported results as some of the best solid state electrolytes. Moreover, this approach is general and chemistry neutral, so can be applied to other battery chemistries and crystal prototypes.

New insights into the effect of zirconium dopant on tritium release from Li2TiO3 (001) surface from first-principles calculation

The influence of zirconium (Zr) dopants on tritium release from Li2TiO3 (001) surface was researched by density functional theory (DFT) calculations. The energy barriers for T2 and T2O molecules formation on undoped and doped surfaces were calculated and compared by using climbing-image nudged elastic band (CI-NEB) method. It was found that T2O is more easily generated than T2 on the surfaces. And Zr dopants can significantly promote the production and release for T2O on the surface of Li2TiO3. Especially when Zr atoms doping ratio is to be 3.12 atom % (Zr3), the barrier of T2O formation changed from 0.97 eV on undoped surface to spontaneous formation on doped surface. The energy barrier for T2O desorption on the surface also decreases to a smaller energy barrier of about 0.42 eV. Although the catalytic effect of Zr doping on T2 formation on the surface is relatively weak. The electronic characteristics show that the doping of Zr atoms can influence the charge transfer of surface atoms, making OT group more likely to appeal to adjacent T atom, which may be the reason for promoting the formation of T2O by Zr dopants. This study can provide useful details for the effect mechanism and catalytic behavior of Zr dopants on the release of tritium from Li2TiO3 surface.

DFT Simulation of a Gold Electrode Vapor-Deposition Growth Process and the Effect of Defects on the Electrode Work Function.

While two-dimensional (2D) semiconductors are explored as field-effect transistor (FET) channel materials for decreasing the short channel effects, electrical contact with 2D semiconductors is a major issue. Many efforts have been made toward this issue. However, the discrepancy in the contact type and the Schottky barrier height from the same contact is present in experiments. This discrepancy supposedly should be associated with the vapor-deposition electrode structures, on which little attention had been focused. Here, the crystal growth of the gold vapor-deposition electrode is simulated by adding gold atoms to the gold substrate one by one in the framework of density functional theory, and for every step, the spontaneously searching adsorption site method is used to find thermodynamically stable adsorption sites and the climbing nudged elastic band method is used to find kinetically stable ones. Simulation shows that the Au(111) face grows according to the ABC sequence packing, and possible defects are interstitial, vacancy, and the partly filled nascent layer (PFNL). These defects have an unequal effect on the electrode work function. The PFNL may be a non-negligible factor responsible for the discrepancy.

Influence of External Conditions on the Black-to-Yellow Phase Transition of CsPbI3 Based on First-Principles Calculations: Pressure and Moisture

All-inorganic CsPbI3 perovskite has emerged as a promising candidate for next-generation solar cells. However, owing to the poor structural stability of black phase CsPbI3 perovskite at room temperature, it spontaneously transforms to the yellow, photoinactive, nonperovskite phase at room temperature, limiting further development of CsPbI3 perovskite solar cells. To better understand the mechanism driving such undesirable phase transformation, we examine the thermodynamics and kinetics associated with γ-to-δ phase transformation using density functional theory calculation. A solid-state nudged elastic band method was employed to find minimum energy pathways assuming a concerted solid-state phase transformation between these two phases. The gas molecules representing atmospheric (H2O, O2, and N2) and inert (Ar) ambient environments, as well as applied external pressure, were considered to examine the influence of external conditions on the black-to-yellow phase transition. Our calculation reveals that, with increasing pressure, the thermodynamic driving force for converting the γ-phase to the δ-phase increases, whereas a larger activation energy must be overcome for the phase transition to occur. We also investigate the moisture-induced phase transformation with an H2O molecule and its dissociated species (H+/OH–) and demonstrate that the reaction energy barriers can be significantly lowered in the presence of H2O or OH–. On the other hand, other nonpolar species (O2, N2, and Ar) have a negligible effect on the phase transformation kinetics, while they might reduce the thermodynamic driving force for the phase transformation and suppress the undesirable phase transformation. Our theoretical prediction could support recent observations that the γ-to-δ phase transformation occurs rapidly and catalytically in the presence of moisture, whereas in dry argon and dry oxygen atmospheres, the γ-CsPbI3 remains stable.