47 research outputs found
Using Bayes formula to estimate rates of rare events in transition path sampling simulations
Transition path sampling is a method for estimating the rates of rare events
in molecular systems based on the gradual transformation of a path distribution
containing a small fraction of reactive trajectories into a biased distribution
in which these rare trajectories have become frequent. Then, a multistate
reweighting scheme is implemented to postprocess data collected from the staged
simulations. Herein, we show how Bayes formula allows to directly construct a
biased sample containing an enhanced fraction of reactive trajectories and to
concomitantly estimate the transition rate from this sample. The approach can
remediate the convergence issues encountered in free energy perturbation or
umbrella sampling simulations when the transformed distribution insufficiently
overlaps with the reference distribution.Comment: 11 pages, 8 figure
Point defect modeling in materials: coupling ab initio and elasticity approaches
International audienceModeling point defects at an atomic scale requires careful treatment of the long-range atomic relaxations. This elastic field can strongly affect point defect properties calculated in atomistic simulations because of the finite size of the system under study. This is an important restriction for ab initio methods which are limited to a few hundred atoms. We propose an original approach coupling ab initio calculations and linear elasticity theory to obtain the properties of an isolated point defect for reduced supercell sizes. The reliability and benefit of our approach are demonstrated for three problematic cases: the self-interstitial in zirconium, clusters of self-interstitials in iron, and the neutral vacancy in silicon
Neighbors Map: an Efficient Atomic Descriptor for Structural Analysis
Accurate structural analysis is essential to gain physical knowledge and
understanding of atomic-scale processes in materials from atomistic
simulations. However, traditional analysis methods often reach their limits
when applied to crystalline systems with thermal fluctuations, defect-induced
distortions, partial vitrification, etc. In order to enhance the means of
structural analysis, we present a novel descriptor for encoding atomic
environments into 2D images, based on a pixelated representation of graph-like
architecture with weighted edge connections of neighboring atoms. This
descriptor is well adapted for Convolutional Neural Networks and enables
accurate structural analysis at a low computational cost. In this paper, we
showcase a series of applications, including the classification of crystalline
structures in distorted systems, tracking phase transformations up to the
melting temperature, and analyzing liquid-to-amorphous transitions in pure
metals and alloys. This work provides the foundation for robust and efficient
structural analysis in materials science, opening up new possibilities for
studying complex structural processes, which can not be described with
traditional approaches
The Activation-Relaxation Technique : ART nouveau and kinetic ART
The evolution of many systems is dominated by rare activated events that occur on timescale ranging from nanoseconds to the hour or more. For such systems, simulations must leave aside the full thermal description to focus specifically on mechanisms that generate a configurational change. We present here the activation relaxation technique (ART), an open-ended saddle point search algorithm, and a series of recent improvements to ART nouveau and kinetic ART, an ART-based on-the-fly off-lattice self-learning kinetic Monte Carlo method
Diffusion rates of Cu adatoms on Cu(111) in the presence of an adisland nucleated at FCC or HCP sites
The surface diffusion of Cu adatoms in the presence of an adisland at FCC or
HCP sites on Cu(111) is studied using the EAM potential derived by Mishin {\it
et al.} [Phys. Rev. B {\bf 63} 224106 (2001)]. The diffusion rates along
straight (with close-packed edges) steps with (100) and (111)-type microfacets
(resp. step A and step B) are first investigated using the transition state
theory in the harmonic approximation. It is found that the classical limit
beyond which the diffusion rates follow an Arrhenius law is reached above the
Debye temperature. The Vineyard attempt frequencies and the (static) energy
barriers are reported. Then a comparison is made with the results of more
realistic classical molecular dynamic simulations which also exhibit an
Arrhenius-like behavior. It is concluded that the corresponding energy barriers
are completely consistent with the static ones within the statistical errors
and that the diffusion barrier along step B is significantly larger than along
step A. In contrast the prefactors are very different from the Vineyard
frequencies. They increase with the static energy barrier in agreement with the
Meyer-Neldel compensation rule and this increase is well approximated by the
law proposed by Boisvert {\it et al.} [Phys. Rev. Lett. {\bf 75} 469 (1995)].
As a consequence, the remaining part of this work is devoted to the
determination of static energy barriers for a large number of diffusion events
that can occur in the presence of an adisland. In particular, it is found that
the corner crossing diffusion process for triangular adislands is markedly
different for the two types of borders (A or B). From this set of results the
diffusion rates of the most important atomic displacements can be predicted and
used as input in Kinetic Monte-Carlo simulations
Efficient and transferable machine learning potentials for the simulation of crystal defects in bcc Fe and W
Data-driven, or machine learning (ML), approaches have become viable alternatives to semiempirical methods to construct interatomic potentials, due to their capacity to accurately interpolate and extrapolate from first-principles simulations if the training database and descriptor representation of atomic structures are carefully chosen. Here, we present highly accurate interatomic potentials suitable for the study of dislocations, point defects, and their clusters in bcc iron and tungsten, constructed using a linear or quadratic input-output mapping from descriptor space. The proposed quadratic formulation, called quadratic noise ML, differs from previous approaches, being strongly preconditioned by the linear solution. The developed potentials are compared to a wide range of existing ML and semiempirical potentials, and are shown to have sufficient accuracy to distinguish changes in the exchange-correlation functional or pseudopotential in the underlying reference data, while retaining excellent transferability. The flexibility of the underlying approach is able to target properties almost unattainable by traditional methods, such as the negative divacancy binding energy in W or the shape and the magnitude of the Peierls barrier of the
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screw dislocation in both metals. We also show how the developed potentials can be used to target important observables that require large time-and-space scales unattainable with first-principles methods, though we emphasize the importance of thoughtful database design and degrees of nonlinearity of the descriptor space to achieve the appropriate passage of information to large-scale calculations. As a demonstration, we perform direct atomistic calculations of the relative stability of
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dislocations loops and three-dimensional C15 clusters in Fe and find the crossover between the formation energies of the two classes of interstitial defects occurs at around 40 self-interstitial atoms. We also compute the kink-pair formation energy of the
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screw dislocation in Fe and W, finding good agreement with density functional theory informed line tension models that indirectly measure those quantities. Finally, we exploit the excellent finite-temperature properties to compute vacancy formation free energies with full anharmonicity in thermal vibrations. The presented potentials thus open up many avenues for systematic investigation of free-energy landscape of defects with ab initio accuracy
Relaxation volumes of microscopic and mesoscopic irradiation-induced defects in tungsten
The low-energy structures of irradiation-induced defects in materials have been studied extensively over several decades, as these determine the available modes by which a defect can diffuse or relax, and how the microstructure of an irradiated material evolves as a function of temperature and time. Consequently, many studies concern the relative energies of possible defect structures, and empirical potentials are commonly fitted to or evaluated with respect to these. But recently [S. L. Dudarev et al., Nucl. Fusion 58, 126002 (2018)], we have shown that other parameters of defects not directly related to defect energies, namely, their elastic dipole tensors and relaxation volumes, determine the stresses, strains, and swelling of reactor components under irradiation. These elastic properties of defects have received comparatively little attention. In this study, we compute relaxation volumes of irradiation-induced defects in tungsten using empirical potentials and compare to density functional theory results. Different empirical potentials give different results, but some clear potential-independent trends can be identified. We show that the relaxation volume of a small defect cluster can be predicted to within 10% from its point-defect count. For larger defect clusters, we provide empirical fits as a function of defect cluster size. We demonstrate that the relaxation volume associated with a single primary-damage cascade can be estimated from the primary knock-on atom energy. We conclude that while annihilation of defects invariably reduces the total relaxation volume of the cascade debris, there is still no conclusive verdict about whether coalescence of defects reduces or increases the total relaxation volume. Published under license by AIP Publishing.Peer reviewe