Activation-relaxation Technique Research Articles

On the capabilities of k-ART over MD for the study of the kinetics of small point defect clusters in α-Fe

Molecular Dynamics simulations, while contributing to the understanding of the mechanisms of diffusion and interactions of point defects and their clusters, are inherently limited in their temporal scope (few nanoseconds). This constraint becomes particularly evident when studying the dynamics of vacancies at low temperatures, where their jump frequency is exceedingly low, posing challenges for accurate reproduction. Additionally, the size of the simulation box imposes constraints, influencing the representation of the system and potentially affecting the accuracy of results. A relatively new kinetic activation-relaxation technique (k-ART) efficiently resolves the limitations of MD simulations, such as computation time and system dimensionality, without the need for a priori knowledge of the simulated system. This technique enables simulations lasting up to several seconds and encompassing systems with higher dimensions. In this paper we check the validity of k-ART to reproduce accurately the migration mechanisms and energies of point defects and small clusters, previously obtained by MD and validated experimentally. We point out the advantages and difficulties of using AKMC with k-ART.

Diffusion mechanisms for spinel ferrite NiFe2O4 by using kinetic activation-relaxation technique.

Mass transport in bulk spinel ferrites NiFe2O4 is studied computationally using the kinetic activation-relaxation technique (k-ART), an off-lattice kinetic Monte Carlo algorithm. Diffusion mechanisms-difficult to observe with molecular dynamics-are described by k-ART. Point defects are assumed to be responsible for ionic diffusion; thus, both cation and anion defects are investigated. This work focuses on vacancies and interstitials by comparing their properties with two Buckingham potential parameterizations: one with nominal charges and the other with partial charges. Both potentials are corrected at short distances, thus allowing interstitial diffusion and avoiding the catastrophic infinite energies appearing with Buckingham at short distances. The energy landscape along different pathways is described in detail. Both potentials predict the same mechanisms but different migration energies. Mechanisms by which a normal spinel is transformed to an inverse spinel via cation diffusion are unveiled, and diffusion coefficients are predicted. We find that interstitial Ni diffusion involves the movement of two Ni ions and that O interstitials trigger a collective diffusion of O ions, while an O vacancy diffuses by an O ion moving to the center of a cuboctahedron.

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.

Exploring potential energy surfaces to reach saddle points above convex regions.

Saddle points on high-dimensional potential energy surfaces (PES) play a determining role in the activated dynamics of molecules and materials. Building on approaches dating back more than 50 years, many open-ended transition-state search methods have been developed to follow the direction of negative curvature from a local minimum to an adjacent first-order saddle point. Despite the mathematical justification, these methods can display a high failure rate: using small deformation steps, up to 80% of the explorations can end up in a convex region of the PES, where all directions of negative curvature vanish, while if the deformation is aggressive, a similar fraction of attempts lead to saddle points that are not directly connected to the initial minimum. In high-dimension PES, these reproducible failures were thought to only increase the overall computational cost, without having any effect on the methods' capacity to find all saddle points surrounding a minimum. Using activation-relaxation technique nouveau (ARTn), we characterize the nature of the PES around minima, considerably expanding on previous knowledge. We show that convex regions can lie on activation pathways and that not exploring beyond them can introduce significant bias in the saddle-point search. We introduce an efficient approach for traversing the convex regions, almost eliminating exploration failures, while multiplying by almost 10 the number of identified unique and connected saddle points as compared to the standard ARTn, thus underlining the importance of correctly handling convex regions for completeness of saddle point explorations.

Critical assessment of hydrogen pipe diffusion at dislocations in metals

Hydrogen-dislocation interactions have always been a crucial problem in understanding and predicting the long-standing hydrogen embrittlement (HE) phenomenon in structural metals. Particularly with respect to hydrogen diffusion, dislocations have often been assumed with the ability to facilitate hydrogen transport via dislocation pipe diffusion (DPD). Yet the experimental and theoretical studies supporting DPD remain elusive and even controversial. In this work, hydrogen kinetics at dislocations in two representative metal systems, fcc Ni and bcc Fe, were systematically investigated combining comprehensive atomistic and kinetic activation relaxation technique simulations to reveal atomic details while enabling long-time (i.e., microsecond to second) hydrogen diffusion analysis. The dislocations were found to favor hydrogen trapping and provide regions of low migration barriers for hydrogen. However, these regions of low barriers only lead to localized fast short-circuit H diffusion, but do not translate into DPD over long time, which is attributed to fast hydrogen diffusion pathways along the dislocation line direction being periodically bound by high hydrogen migration barriers. Using the polyhedral structural units (PSUs) as an effective tool, we further quantitatively analyzed the correlation between hydrogen diffusion behaviors and local dislocation structures, illustrating the structural origin leading to local short-circuit diffusion and inhibition of DPD at dislocations. The new mechanistic insights gained not only are critical for understanding hydrogen-dislocation interaction, but also advances the general knowledge on hydrogen-microstructure interaction in structural metals.

Overview of kinetic Monte Carlo methods used to simulate microstructural evolution of materials under irradiation

Kinetic Monte Carlo (KMC) methods are commonly used to simulate the microstructure evolution of metals under irradiation due to their ability to generate the random walks underlying defect-mediated diffusion processes at the atomic scale. However, the range of applicability of KMC methods is severely limited by the kinetic trapping of the simulated trajectories within low energy basins presenting small intra-basin barriers. This results in dramatically reducing the efficiency of the classical KMC algorithm. Kinetic trapping can be alleviated by implementing non-local jumps relying on the theory of absorbing Markov chains. A factorisation of an auxiliary absorbing transition matrix then allows to generate escaping paths and first-passage times out of trapping basins. Although, the speed-up can be of several orders of magnitudes, this is sometimes not enough for very long-term prediction. We must then turn to homogenised rate-equation formulation of the problem. Usually solved deterministically, the corresponding large ordinary differential equation system often suffers from the curse of dimensionality. Dedicated Monte Carlo schemes can simulate the coarse-grained rate equations based on a chemical master equation. Finally, we show the relevance of relaxing the rigid-lattice assumption in the calculation of the free energy barriers and attempt frequencies to capture elastic effects that are important for certain systems, such as high entropy alloys. The activation-relaxation technique can be used for this purpose in kinetic Monte Carlo studies of slow diffusion processes.

Kinetics of hydrogen and vacancy diffusion in iron: A kinetic activation relaxation technique (k-ART) study

Kinetics of hydrogen and vacancy diffusion in iron: A kinetic activation relaxation technique (k-ART) study

PARTn: A plugin implementation of the Activation Relaxation Technique nouveau that takes over the FIRE minimisation algorithm

Nowadays, the interoperability and interfacing of codes and libraries have become crucial aspects of software development and engineering, and the basis for enabling and simplifying the sharing of methods and tools, both within and among communities. One of the most important bottlenecks that arises when developing and maintaining an interface of a library with an already existing software, is to keep it aligned with the development route of the latter. This might include significant changes, such as changes in the data structures used by the library, which are communicated through the interface.In this paper, an approach for inserting a new algorithm into existing software is presented, through a minimally invasive interface, that takes over an already present algorithm, and thus changes its original purpose. The approach is applied to the well-established Activation-Relaxation Technique nouveau (ARTn) algorithm, that is revisited and re-engineered to bias and take over the FIRE minimization algorithm, as presently implemented in two community codes for atomistic simulations, namely Quantum ESPRESSO (PWscf) and LAMMPS. ARTn is a well established single-ended saddle-point search algorithm that allows for the exploration of potential energy surfaces. The resulting algorithm acts as a plugin, and is distributed in the form of an external library (pARTn). Program summaryProgram Title: plugin Activation Relaxation Technique nouveau (pARTn)CPC Library link to program files:https://doi.org/10.17632/xpwr56d2yk.1Developer's repository link:https://gitlab.com/mammasmias/artn-pluginLicensing provisions: Apache-2.0/GPLv3Programming language: Modern Fortran and C++Nature of problem: Original ARTn implementation was difficult to interface, port and maintain.Solution method: Full refactoring and re-engineering into a library, which utilizes and biases a minimization algorithm already implemented in the engine, to make it behave as ARTn. The biasing is done by reverse-engineering specific external conditions that drive the displacement of atoms.

Calculation of the recombination radii between various point defects and defect clusters in nickel via kinetic Activation Relaxation Technique

The recombination radii between various point defects and defect clusters are essential input parameters for mathematical and computational models of radiation-induced damage evolution. In this work, such recombination radii is calculated by the kinetic Activation Relaxation Technique (k-ART)—an off-lattice, self-learning kinetic Monte Carlo algorithm—in conjunction with molecular dynamics simulations. We found vacancy clusters exhibit larger average recombination radii with interstitials than single vacancies, reaching as large as 2.2a0 (a0 is the lattice parameter of nickel). Such recombination enhancement can be attributed to the intensified distortion near cluster surfaces. Unlike vacancy clusters, free surfaces feature smaller recombination radii than single vacancies. Their recombination radii are correlated with the angle between surface normal and <110> directions. Finally, the recombination radii of interstitial clusters are larger than vacancy clusters and strongly depends on the cluster configurations. Overall, the recombination radii of most internal defect clusters range from ∼2a0 to ∼2.4a0. Because previous research has found that recombination radii affect the density-size distribution of point defect clusters but not the fraction of a particular defect, our analysis suggests that given an accurate initial estimate of cluster density-size distributions, choosing a uniform recombination radius for different clusters in object kinetic Monte Carlo simulations should be sufficient to predict subsequent microstructural evolution.

Evaluating approaches for on-the-fly machine learning interatomic potentials for activated mechanisms sampling with the activation-relaxation technique nouveau.

In the last few years, much effort has gone into developing general machine-learning potentials capable of describing interactions for a wide range of structures and phases. Yet, as attention turns to more complex materials, including alloys and disordered and heterogeneous systems, the challenge of providing reliable descriptions for all possible environments becomes ever more costly. In this work, we evaluate the benefits of using specific vs general potentials for the study of activated mechanisms in solid-state materials. More specifically, we test three machine-learning fitting approaches using the moment-tensor potential to reproduce a reference potential when exploring the energy landscape around a vacancy in Stillinger-Weber silicon crystal and silicon-germanium zincblende structures using the activation-relaxation technique nouveau (ARTn). We find that a targeted on-the-fly approach specific to and integrated into ARTn generates the highest precision on the energetics and geometry of activated barriers while remaining cost-effective. This approach expands the types of problems that can be addressed with high-accuracy ML potential.

Structure and Migration Mechanisms of Small Vacancy Clusters in Cu: A Combined EAM and DFT Study.

Voids in face-centered cubic (fcc) metals are commonly assumed to form via the aggregation of vacancies; however, the mechanisms of vacancy clustering and diffusion are not fully understood. In this study, we use computational modeling to provide a detailed insight into the structures and formation energies of primary vacancy clusters, mechanisms and barriers for their migration in bulk copper, and how these properties are affected at simple grain boundaries. The calculations were carried out using embedded atom method (EAM) potentials and density functional theory (DFT) and employed the site-occupation disorder code (SOD), the activation relaxation technique nouveau (ARTn) and the knowledge led master code (KLMC). We investigate stable structures and migration paths and barriers for clusters of up to six vacancies. The migration of vacancy clusters occurs via hops of individual constituent vacancies with di-vacancies having a significantly smaller migration barrier than mono-vacancies and other clusters. This barrier is further reduced when di-vacancies interact with grain boundaries. This interaction leads to the formation of self-interstitial atoms and introduces significant changes into the boundary structure. Tetra-, penta-, and hexa-vacancy clusters exhibit increasingly complex migration paths and higher barriers than smaller clusters. Finally, a direct comparison with the DFT results shows that EAM can accurately describe the vacancy-induced relaxation effects in the Cu bulk and in grain boundaries. Significant discrepancies between the two methods were found in structures with a higher number of low-coordinated atoms, such as penta-vacancies and di-vacancy absortion by grain boundary. These results will be useful for modeling the mechanisms of diffusion of complex defect structures and provide further insights into the structural evolution of metal films under thermal and mechanical stress.

Diffusion of oxygen vacancies formed at the anatase (101) surface: An activation-relaxation technique study

${\mathrm{TiO}}_{2}$ is a technologically important material. In particular, its anatase polymorph plays a major role in photocatalysis, which can also accommodate charged and neutral vacancies. There is, however, scant theoretical work on the vacancy charge and associated diffusion from surface to subsurface and bulk in the literature. Here, we aim to understand +2 charge and neutral vacancy diffusion on anatase (101) surface using 72- and 216-atom surface slabs employing a semilocal density functional and the Hubbard model. The activation-relaxation technique nouveau coupled with quantum espresso is used to investigate the activated mechanisms responsible for the diffusion of oxygen vacancies. The small-slab model overstabilizes the +2 charged topmost surface vacancy, which is attributed to the strong Coulomb repulsion between vacancy and neighboring ${\mathrm{Ti}}^{+4}$ ions. The larger slab allows atoms to relax parallel to the surface, decreasing the +2 charged topmost surface vacancy stability. The calculated surface-to-subsurface barriers for the +2 charged vacancy and diffusion of the neutral vacancy on a slab of 216 atoms are 0.82 and 0.52 eV, respectively. Furthermore, the bulk vacancy prefers to migrate toward the subsurface with relatively low activation barriers 0.19 and 0.27 eV and the reverse process has to overcome 0.38- and 0.40-eV barriers for the +2 charged and the neutral vacancies. This explains the experimentally observed high concentration of vacancies at the subsurface sites rather than in the bulk, and the dynamic diffusion of vacancies from the bulk to the subsurface and from the subsurface to the bulk is highly likely on the surface of anatase (101). Finally, we provide a plausible explanation for the origin of recently observed subsurface-to-surface diffusion of oxygen vacancy from the calculated results.

Internal mechanical dissipation mechanisms in amorphous silicon

Using activation-relaxation technique nouveau (artn), we search for two-level systems (TLSs) in models of amorphous silicon ($a$-Si). The TLSs are mechanisms related to internal mechanical dissipation and represent the main source of noise in the most sensitive frequency range of the largest gravitational wave detectors as well as one of the main sources of decoherence in many quantum computers. We show that in $a$-Si, the majority of the TLSs of interest fall into two main categories: bond-defect hopping, where neighbors exchange a topological defect, and Wooten-Winer-Weaire bond exchange. The distribution of these categories depends heavily on the preparation schedule of the $a$-Si. We use our results to compute the mechanical loss in amorphous silicon, leading to a loss angle of ${10}^{\ensuremath{-}3}$ at room temperature, decreasing to ${10}^{\ensuremath{-}4}$ at 150 K in some configurations. Our modeling results indicate that multiple classes of events can cause experimentally relevant TLSs in disordered materials and therefore multiple attenuation strategies might be needed to reduce their impact.

Unexpected role of prefactors in defects diffusion: The case of vacancies in the 55Fe-28Ni-17Cr concentrated solid-solution alloys

Variations in diffusion rates of simple point defects, such as vacancies and interstitials, are generally assumed to be dominated by energy barriers, as demonstrated for example by the large number of kinetic Monte Carlo studies that rest on constant rate prefactors. While this is mostly correct when energy barriers are well separated from each other, typically in crystals, entropic variations between the local minima and associated activated states become increasingly important as energy barriers of diffusion-mediating-mechanisms get closer, typically in disordered environments. The unexpected slower defect diffusion observed in high entropy alloys, which are characterized by the presence of a large number of different elements in roughly equal proportions, has brought us to revisit the role of prefactors. Combining the Activation-Relaxation Technique nouveau (ART nouveau) and the harmonic approximation for computing diffusion prefactors, we find that vacancy diffusion prefactors in a 55Fe-28Ni-17Cr concentrated solution alloy modeled with EAM empirical potentials can vary by up to six orders of magnitude, at almost constant energy barrier. This variation, mostly associated with changes in local pressure, suggests that prefactor could play a much more important role than previously thought in the defect kinetics of high entropy alloys and of disordered systems in general.

Activation–Relaxation Technique: An efficient way to find minima and saddle points of potential energy surfaces

The Activation–Relaxation Technique (ARTn) is an efficient technique for finding the minima and saddle points of multidimensional functions such as the potential energy surface of atomic systems in chemistry. In this work we detail and illustrate significant improvements made to the algorithm, regarding both preprocessing and the activation process itself. As showcased, these advances significantly reduce ARTn computational costs, especially when applied with ab initio description. With these modifications, ARTn establishes itself as a very efficient method for exploring the energy landscape and chemical reactions associated with complex mechanisms.

Statistical distribution of spontaneous recombination radii of Frenkel pairs in FCC and BCC metals

The recombination radius of Frenkel pairs induced by incident high-energy particles represents a critical determinant of irradiation-induced microstructure evolution. A better understanding of the atomistic processes controlling recombination can help us determine more accurately the average recombination radius, an essential input parameter of mesoscale models of radiation damage evolution. This work used the kinetic activation relaxation technique—an off-lattice, self-learning kinetic Monte Carlo algorithm in conjunction with molecular dynamics simulations—to study the statistical distribution of the recombination radii in six FCC (nickel, copper, silver, gold, palladium, and platinum) and one BCC (iron) metals. We found that recombination can occur from the 2nd nearest neighbor site to as far as the 15th neighbor site. Long-range recombination is realized via crowdion formation along <110> directions. Vacancies were found to diminish the recombination energy barrier, yet no correlation was found between energy barriers and the average recombination radius. Instead, the average recombination radius increases linearly with elastic constants. Although the atomic displacement fields near self-interstitials are identical in different metals, metals with higher elastic constants exhibit larger local stresses and broader stress distribution, facilitating long-range recombination. Similarly, hydrostatic pressure enhances the average recombination radius by rising elastic constants of the compressed structure. Thus, it is the elastic constants that determine the average recombination radius, not energy barriers.

Grain boundary plane rotation analysis for FCC bicrystal structures using MD simulation

Grain boundary (GB) plane rotation, one of the GB engineering mechanisms, was investigated using the activation–relaxation technique by molecular dynamics simulation. The simulation systems considered in this work are bicrystals with Lennard-Jones-type interatomic potential. The systems of four GB types established are symmetric (SYM), asymmetric (ASYM), symmetric zigzag (SZ), and high-angle zigzag (HZ) models. Of the first two models, [Formula: see text]5 (310) for SYM and [Formula: see text] tilted for ASYM particularly provided reference atomic potential energy distributions and structures at minimum energy state at 0 K. The characteristic of SYM is the discrete atomistic potential distributions which are distinct from ASYM. The other two models based on zigzag-like GBs were created by rotating GB planes about [001] at the center of a [Formula: see text]5 (310)[Formula: see text]GB system for the SZ case and a high-angle GB system for the HZ case. Simulation results show that the initially tilted GBs kinetically transferred to relaxed states for shorter-length GBs through a series of curved GBs. The GBs consist of different combinations of order defect segments, amorphous regions, and defect-free regions. A mechanism proposed is the GB plane rotation, the rate of which is structure-dependent. A low-[Formula: see text] coincidence site lattice boundary section can stabilize the systems at a specified metastable state.

Pressure effect on diffusion of carbon at the 85.91∘〈100〉 symmetric tilt grain boundary of α -iron

The diffusion mechanism of carbon in iron plays a vital role in carburization processes, steel fabrication, and metal dusting corrosion. In this paper, using the kinetic activation-relaxation technique (k-ART), an off-lattice kinetic Monte Carlo algorithm with on-the-fly catalog building that allows to obtain diffusion properties over large time scales taking full account of chemical and elastic effects coupled with an EAM potential, we investigate the effect of pressure on the diffusion properties of carbon in $85.{91}^{\ensuremath{\circ}}\phantom{\rule{4pt}{0ex}}\ensuremath{\langle}100\ensuremath{\rangle}$ symmetric tilt grain boundaries (GB) of $\ensuremath{\alpha}$-iron up to a pressure of 12 kbar at a single temperature of 600 K. We find that, while the effect of pressure can strongly modify the C stability and diffusivity in the GB in ways that depend closely on the local environment and the nature of the deformation, isotropic and uniaxial pressure can lead to opposite and nonmonotonous effects regarding segregation energy and activation barriers. These observations are relevant to understanding of the evolution of heterogeneous materials, where variations of local pressure can alter the carbon diffusion across the material.

Diffusion mechanism of bound Schottky defect in magnesium oxide

In simple ionic crystals, intrinsic point defects must satisfy electrical neutrality and exist as Schottky defects. In magnesium oxide (MgO), a Schottky defect is then a combination of anionic and cationic vacancies. Since vacancies are charged, the stable configuration of the Schottky defect corresponds to a bound pair of vacancies of opposite signs. In this study, we investigate the kinetics of formation and migration of such a bound pair on long timescales reaching in some cases thousands of seconds using the kinetic activation-relaxation technique, an off-lattice kinetic Monte Carlo method with an event catalog built on-the-fly during static molecular simulations. We show that the diffusion of this bound Schottky defect involves the migration of vacancies bounded to the first and third neighbor sites of the crystal structure with an apparent migration energy which cannot be inferred from the migration energies expected from isolated defects. Overall, this study gives insights and constraints on the oxygen diffusion mechanism reported experimentally in high-purity MgO samples.

Stability of native point defects in α-Al2O3 under aqueous electrochemical conditions

The formation energies of native point defects in crystalline α-Al2O3 were investigated by combining first principles-based methods and theoretical models in a grand canonical framework. For defect formation reactions in this framework, the chemical potentials of chemical species and electrons can be constrained by the conditions of aqueous electrochemical systems, where liquid water is thermodynamically stable. Activation relaxation technique (ART) simulations using an empirical interatomic potential were implemented to discover candidates for stable configurations of point defects. Density functional theory (DFT) calculations were then used to confirm the accurate energetics of the candidate defect configurations. The results show that, except Al vacancies, the most stable defect configurations are generated by simply adding/removing atoms at particular high-symmetry sites. We also investigated the stability of these point defects as a function of the chemical potentials of both electron and oxygen. The results reveal that, at the conditions of thermodynamic stability for liquid water in aqueous electrochemical systems, Al vacancies as the most stable point defects in α-Al2O3 can be generated in exothermic defect formation reactions with negative formation energies. These thermodynamic tendencies provide critical insights into the nature of passive films formed under aqueous electrochemical conditions, particularly explaining of the formation of amorphous structures of passive alumina.