Normand Mousseau
Professeur de physique et titulaire de la Chaire UdeM
Matériaux complexes, énergie et ressources naturelles

ART cinétique : une méthode de Monte Carlo cinétique hors-réseau

Un de mes principaux axes de recherche depuis 6 ans porte sur le développement de la méthode ART cinétique, un algorithme de Monte-Carlo cinétique (MCC) hors réseau avec construction d’un catalogue d’événements à la volée.

Le but de cet algorithme est de pouvoir suivre la dynamique de systèmes complexes au niveau atomique sur des temps expérimentaux, d’une seconde ou plus. La MCC traditionnelle, qui remonte aux années 1970, est limitée aux applications sur réseau, c’est à dire à des modèles simplifiés où les atomes sont contraints de se déplacer de case en case. Si cette méthode donne de bons résultats pour l’étude de certains systèmes très simples, elle n’est pas applicable aux matériaux complexes et désordonnés.

Après plusieurs années d’efforts, ART cinétique, dont les idées initiales ont été développées en collaboration avec F. El-Mellouhi et Laurent Lewis en 2008 (El-Mellouhi, Mousseau et Lewis, 2008), est aujourd’hui la seule méthode pouvant simuler ces systèmes sur des temps longs. Depuis deux ans, elle nous a permis de réaliser des travaux innovateurs et importants. Ainsi, grâce à des études sur la relaxation du silicium soumis à la radiation ionique dix à 100 millions de fois plus longues que ce qui avait été réalisé jusqu’à présent, nous avons pu reproduire et expliquer des résultats de nanocalorimétrie s’étendant sur 30 secondes (Béland et coll., PRL 2013) ! Déjà, notre code est utilisé par des laboratoires aux États-Unis, en France et au Royaume-Uni.

Quelques-uns de mes travaux sur le sujet



  • 0scar A. Restrepo, N. Mousseau, F. El-Mellouhi, O. Bouhali, M. Trochet, C. S. Becquart, Diffusion properties of Fe–C systems studied by using kinetic activation–relaxation technique, Computational Materials Science 112, Part A, 96-106 (2016).
    Résumé : Diffusion of carbon in iron is associated with processes such as carburization and the production of steels. In this work, the kinetic activation–relaxation technique (k-ART) – an off-lattice self-learning kinetic Monte Carlo (KMC) algorithm – is used to study this phenomenon over long time scales. Coupling the open-ended ART nouveau technique to generate on-the-fly activated events and NAUTY, a topological classification for cataloging, k-ART reaches timescales that range from microseconds to seconds while fully taking into account long-range elastic effects and complex events, characterizing in details the energy landscape in a way that cannot be done with standard molecular dynamics (MD) or KMC. The diffusion mechanisms and pathways for one to four carbon interstitials, and a single vacancy coupled with one to several carbons are studied. In bulk Fe, k-ART predicts correctly the 0.815 eV barrier for a single C-interstitial as well as the stressed induced energy-barrier distribution around this value for 2 and 4 C interstitials. For vacancy–carbon complex, simulations recover the DFT-predicted ground state. K-ART also identifies a trapping mechanism for the vacancy through the formation of a dynamical complex, involving C and neighboring Fe atoms, characterized by hops over barriers ranging from ∼0.41 to ∼0.72 eV that correspond, at room temperature, to trapping time of hours. At high temperatures, this complex can be broken by crossing a 1.5 eV barrier, leading to a state ∼0.8 eV higher than the ground state, allowing diffusion of the vacancy. A less stable complex is formed when a second C is added, characterized by a large number of bound excited states that occupy two cells. It can be broken into a V–C complex and a single free C through a 1.11 eV barrier.
    Mots-clés : ARTc.

  • N. Mousseau, P. Brommer, J. - F. Joly, L. K. Béland, F. El-Mellouhi, G. K. N'Tsouaglo, et al., Following atomistic kinetics on experimental timescales with the kinetic Activation-Relaxation Technique, Computational Materials Science 100, 111-123 (2015).
    Mots-clés : ARTc.

  • M. Trochet, L. K. Béland, P. Brommer, J. - F. Joly, N. Mousseau, Diffusion of point defects in crystalline silicon using the kinetic ART method, Phys. Rev. B 91, 224106 (2015).
    Mots-clés : ARTc.

  • G. K. N'Tsouaglo, L. K. Béland, J. - F. Joly, P. Brommer, N. Mousseau, P. Pochet, Probing potential energy surface exploration strategies for complex systems, J. Chem. Theory Comput. 11, 1970-1977 (2015).
    Résumé : The efficiency of minimum-energy configuration searching algorithms is closely linked to the energy landscape structure of complex systems. Here we characterize this structure by following the time evolution of two systems, vacancy aggregation in Fe and energy relaxation in ion-bombarded c-Si, using the kinetic Activation-Relaxation Technique (k-ART), an off-lattice kinetic Monte Carlo (KMC) method, and the well-known Bell-Evans-Polanyi (BEP) principle. We also compare the efficiency of two methods for handling non-diffusive flickering states -- an exact solution and a Tabu-like approach that blocks already visited states. Comparing these various simulations allow us to confirm that the BEP principle does not hold for complex system since forward and reverse energy barriers are completely uncorrelated. This means that following the lowest available energy barrier, even after removing the flickering states, leads to rapid trapping: relaxing complex systems requires crossing high-energy barriers in order to access new energy basins, in agreement with the recently proposed replenish-and-relax model [Béland et al., PRL 111, 105502 (2013)] This can be done by forcing the system through these barriers with Tabu-like methods. Interestingly, we find that following the fundamental kinetics of a system, though standard KMC approach, is at least as efficient as these brute-force methods while providing the correct kinetics information.
    Mots-clés : ARTc.


  • L. K. Béland, Y. Anahory, D. Smeets, M. Guihard, P. Brommer, J. - F. Joly, et al., Replenish and Relax: Explaining Logarithmic Annealing in Ion-Implanted c-Si, Physical Review Letters 111, 105502 (2013).
    Résumé : We study ion-damaged crystalline silicon by combining nanocalorimetric experiments with an off-lattice kinetic Monte Carlo simulation to identify the atomistic mechanisms responsible for the structural relaxation over long time scales. We relate the logarithmic relaxation, observed in a number of disordered systems, with heat-release measurements. The microscopic mechanism associated with this logarithmic relaxation can be described as a two-step replenish and relax process. As the system relaxes, it reaches deeper energy states with logarithmically growing barriers that need to be unlocked to replenish the heat-releasing events leading to lower-energy configurations.
    Mots-clés : ARTc.


  • L. K. Béland, P. Brommer, F. El-Mellouhi, J. - F. Joly, N. Mousseau, Kinetic activation-relaxation technique, Physical Review E 84, 046704 (2011).
    Résumé : We present a detailed description of the kinetic activation-relaxation technique (k-ART), an off-lattice, self-learning kinetic Monte Carlo (KMC) algorithm with on-the-fly event search. Combining a topological classification for local environments and event generation with ART nouveau, an efficient unbiased sampling method for finding transition states, k-ART can be applied to complex materials with atoms in off-lattice positions or with elastic deformations that cannot be handled with standard KMC approaches. In addition to presenting the various elements of the algorithm, we demonstrate the general character of k-ART by applying the algorithm to three challenging systems: self-defect annihilation in c-Si (crystalline silicon), self-interstitial diffusion in Fe, and structural relaxation in a-Si (amorphous silicon).
    Mots-clés : ARTc.


  • F. El-Mellouhi, N. Mousseau, L. J. Lewis, Kinetic activation-relaxation technique: An off-lattice self-learning kinetic Monte Carlo algorithm, Physical Review B 78, 153202 (2008).
    Résumé : Many materials science phenomena are dominated by activated diffusion processes and occur on time scales that are well beyond the reach of standard molecular-dynamics simulations. Kinetic Monte Carlo (KMC) schemes make it possible to overcome this limitation and achieve experimental time scales. However, most KMC approaches proceed by discretizing the problem in space in order to identify, from the outset, a fixed set of barriers that are used throughout the simulations, limiting the range of problems that can be addressed. Here, we propose a flexible approach—the kinetic activation-relaxation technique (k-ART)—which lifts these constraints. Our method is based on an off-lattice, self-learning, on-the-fly identification and evaluation of activation barriers using ART and a topological description of events. Using this method, we demonstrate that elastic deformations are determinant to the diffusion kinetics of vacancies in Si and are responsible for their trapping.
    Mots-clés : ARTc.
    Pièce jointe Full Text PDF 168.3 ko (source)
mercredi 2 juillet 2014

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