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

Mes travaux en matériaux et en matière condensée ciblent avant tout les matériaux complexes et désordonnés tels que le silicium amorphe, les verres et les matériaux défectueux. Je m’intéresse tout particulièrement à l’étude des propriétés structurales et dynamiques de ces systèmes.

Puisque l’évolution de ceux-ci se produit sur des temps macroscopiques (de la milliseconde au million d’années), je travaille donc également à développement des algorithmes qui permettent d’atteindre ces échelles de temps tout en maintenant une description correcte au niveau atomique, des algorithmes tels que la technique d’activation et de relaxation, par exemple.

Voici quelques-uns de mes plus récents projets :

Articles de cette rubrique

Propriétés structurales, cinétiques et thermodynamiques des matériaux amorphes et désordonnés

Les semiconducteurs amorphes sont un de mes principaux thèmes de recherche 25 ans. À l’aide de méthodes diverses, telles que l’algorithme de Wooten, Winer et Weaire, ART, ART nouveau, ART cinétique et dynamique moléculaire, et en collaboration avec de nombreux collègues, j’ai travaillé depuis 10 ans à la caractérisation de la structure de ces matériaux, ainsi que des mécanismes de diffusion et de relaxation (Kerrache et al, 2011 ; Joly et al. 2013). Je me suis également intéressé à l’évolution de la surface d’énergie de matériaux amorphes et désordonnés, démontrant un excellent accord avec les mesures de diffraction par rayon X, de calorimétrie et de nanocalorimétrie (voir, par exemple, Kallel et al., PRL 2010 ; Béland et Mousseau, PRB 2013).

À plusieurs reprises, nos résultats ont permis d’avancer sur des questions débattues depuis longtemps. Par exemple, nous avons pu démontrer que, contrairement à une interprétation tirée des mesures expérimentales, les lacunes ne diffusent pas en bloc dans le silicium amorphe, mais qu’elles demeurent piégées ou se dissocient rapidement au moment de sauter (Joly et al., PRB 2013). Ces résultats nous forcent à repenser la notion de défauts dans les matériaux désordonnés. Grâce des simulations d’ART cinétique couvrant plus d’une seconde, nous avons aussi pu caractériser directement les mécanismes atomiques responsables de la relaxation de systèmes désordonnés, proposant un mécanisme en deux temps pour ces systèmes (Béland et al., PRL 2013). Sortant des approches traditionnelles, nous avons également démontré, parmi mes diverses contributions à ce domaine, qu’une phase liquide à faible densité observée dans de nombreuses simulations numériques était très sensible aux détails des champs de force utilisés, remettant en question la validité de ces observations difficilement vérifiables expérimentalement (Beaucage et Mousseau, 2005).

Quelques-uns de mes travaux sur le sujet



  • J. - F. Joly, L. K. Béland, P. Brommer, N. Mousseau, Contribution of vacancies to relaxation in amorphous materials: A kinetic activation-relaxation technique study, Physical Review B 87, 144204 (2013).
    Résumé : The nature of structural relaxation in disordered systems such as amorphous silicon (a-Si) remains a fundamental issue in our attempts at understanding these materials. While a number of experiments suggest that mechanisms similar to those observed in crystals, such as vacancies, could dominate the relaxation, theoretical arguments point rather to the possibility of more diverse pathways. Using the kinetic activation-relaxation technique, an off-lattice kinetic Monte Carlo method with on-the-fly catalog construction, we resolve this question by following 1000 independent vacancies in a well-relaxed a-Si model at 300 K over a timescale of up to one second. Less than one percent of these survive over this period of time and none diffuse more than once, showing that relaxation and diffusion mechanisms in disordered systems are fundamentally different from those in the crystal.
    Mots-clés : Amorphe.


  • A. Kerrache, N. Mousseau, L. J. Lewis, Amorphous silicon under mechanical shear deformations: Shear velocity and temperature effects, Physical Review B 83, 134122 (2011).
    Résumé : Mechanical shear deformations lead, in some cases, to effects similar to those resulting from ion irradiation. Here we characterize the effects of shear velocity and temperature on amorphous silicon (a-Si) modeled using classical molecular-dynamics simulations based on the empirical environment-dependent interatomic potential (EDIP). With increasing shear velocity at low temperature, we find a systematic increase in the internal strain leading to the rapid appearance of structural defects (fivefold-coordinated atoms). The impacts of externally applied strain can be almost fully compensated by increasing the temperature, allowing the system to respond more rapidly to the deformation. In particular, we find opposite power-law relations between the temperature and the shear velocity and the deformation energy. The spatial distribution of defects is also found to depend strongly on temperature and strain velocity. For low temperature or high shear velocity, defects are concentrated in a few atomic layers near the center of the cell, while with increasing temperature or decreasing shear velocity, they spread slowly throughout the full simulation cell. This complex behavior can be related to the structure of the energy landscape and the existence of a continuous energy-barrier distribution.
    Mots-clés : Amorphe.


  • H. Kallel, N. Mousseau, F. Schiettekatte, Evolution of the Potential-Energy Surface of Amorphous Silicon, Physical Review Letters 105, 045503 (2010).
    Résumé : The link between the energy surface of bulk systems and their dynamical properties is generally difficult to establish. Using the activation-relaxation technique, we follow the change in the barrier distribution of a model of amorphous silicon as a function of the degree of global relaxation. We find that while the barrier-height distribution, calculated from the initial minimum, is a unique function that depends only on the level of relaxation, the reverse-barrier height distribution, calculated from the final state, is independent of global relaxation, following a different function. Moreover, the resulting gained or released energy distribution is a simple convolution of these two distributions indicating that the activation and relaxation parts of the elementary relaxation mechanism are completely independent. This characterized energy landscape can be used to explain nanocalorimetry measurements.
    Mots-clés : Amorphe.
    Pièce jointe Full Text PDF 302 ko (source)


  • G. T. Barkema, N. Mousseau, High-quality continuous random networks, Physical Review B 62, 4985-4990 (2000).
    Résumé : The continuous random network (CRN) model is an idealized model for perfectly coordinated amorphous semiconductors. The quality of a CRN can be assessed in terms of topological and configurational properties, including coordination, bond-angle distributions, and deformation energy. Using a variation on the sillium approach proposed 14 years ago by Wooten, Winer, and Weaire, we present 1000-atom and 4096-atom configurations with a degree of strain significantly less than the best CRN available at the moment and comparable to experimental results. The low strain is also reflected in the electronic properties. The electronic density of state obtained from ab initio calculation shows a perfect band gap, without any defect, in agreement with experimental data.
    Mots-clés : Amorphe.

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.

  • 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.

  • 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.


  • 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)

La technique d’Activation et de Relaxation (ART)

Les premières méthodes numériques pour trouver des chemins de diffusion remontent au années 1970 et 1980 et ont été développées dans la communauté de physico-chimie. Ces méthodes permettaient de traiter des molécules de quelques atomes. La technique d’activation et de relaxation (\emphActivation-Relaxation Technique ou ART et ART nouveau), mise au point par Barkema et moi-même en 1996, fut la première méthode pour la recherche de chemins de transition \emphouverts pour des grands systèmes, i.e. plusieurs centaines ou milliers d’atomes. Cette méthode et d’autres similaires proposées par la suite par d’autres groupes sont maintenant utilisées régulièrement en physique, en chimie et en science des matériaux et ont été incorporées dans de nombreux codes distribués à travers le monde. En constant développement, ART nouveau se maintient parmi les méthodes les plus efficaces de recherche de chemins de diffusion (Machado-Charry et coll., 2011).

Au cours des 10 dernières années, ART nouveau a été au coeur de mes recherche et m’a permis de faire des contributions originales et importantes dans de nombreux domaines dont : les matériaux amorphes, la diffusion de défauts dans les semiconducteurs et les métaux, le repliement et l’agrégation des protéines, etc. Ces méthode est également la base pour de nombreux algorithmes que j’ai développés depuis 10 ans incluant : POP-ART (Chubynsky et coll., 2006), une méthode qui couple la dynamique moléculaire et ART nouveau ; ART holographique (Dupuis et NM, 2012), un algorithme multiéchelle pour le repliement de protéines ; ARTIST (Yun et coll., 2006), un algorithme activité en coordonnées internes ; et ART cinétique (El-Mellouhi, Lewis et Mousseau, 2008), discuté ci-dessous. ART nouveau est utilisé par de nombreux groupes à travers le monde, notamment en Chine, en France, aux Pays-bas et aux États-Unis.

Quelques-uns de mes travaux sur le sujet



  • P. Ganster, L. K. Béland, N. Mousseau, First stages of silicon oxidation with the activation relaxation technique, Physical Review B 86, 075408 (2012).
    Résumé : Using the art nouveau method, we study the initial stages of silicon oxide formation. After validating the method's parameters with the characterization of point defects diffusion mechanisms in pure Stillinger-Weber silicon, which allows us to recover some known results and to detail vacancy and self-interstitial diffusion paths, the method is applied onto a system composed of an oxygen layer deposited on a silicon substrate. We observe the oxygen atoms as they move rapidly into the substrate. From these art nouveau simulations, we extract the energy barriers of elementary mechanisms involving oxygen atoms and leading to the formation of an amorphouslike silicon oxide. We show that the kinetics of formation can be understood in terms of the energy barriers between various coordination environments.
    Mots-clés : ART.


  • N. Mousseau, L. K. Béland, P. Brommer, J. - F. Joly, F. El-Mellouhi, E. Machado-Charry, et al., The Activation-Relaxation Technique: ART Nouveau and Kinetic ART, Journal of Atomic, Molecular, and Optical Physics 2012, 925278 (2012).
    Résumé : 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.
    Mots-clés : ART.


  • J. - F. St-Pierre, N. Mousseau, Large loop conformation sampling using the activation relaxation technique, ART-nouveau method, Proteins: Structure, Function, and Bioinformatics 80, 1883-1894 (2012).
    Résumé : We present an adaptation of the ART-nouveau energy surface sampling method to the problem of loop structure prediction. This method, previously used to study protein folding pathways and peptide aggregation, is well suited to the problem of sampling the conformation space of large loops by targeting probable folding pathways instead of sampling exhaustively that space. The number of sampled conformations needed by ART nouveau to find the global energy minimum for a loop was found to scale linearly with the sequence length of the loop for loops between 8 and about 20 amino acids. Considering the linear scaling dependence of the computation cost on the loop sequence length for sampling new conformations, we estimate the total computational cost of sampling larger loops to scale quadratically compared to the exponential scaling of exhaustive search methods. Proteins 2012; © 2012 Wiley Periodicals, Inc.
    Mots-clés : ART, flexibilite.


  • N. Mousseau, E. Machado-Charry, L. K. Béland, D. Caliste, L. Genovese, T. Deutsch, et al., Optimized energy landscape exploration using the ab initio based activation-relaxation technique, The Journal of Chemical Physics 135, 034102 (2011).
    Résumé : Unbiased open-ended methods for finding transition states are powerful tools to understand diffusion and relaxation mechanisms associated with defect diffusion, growth processes, and catalysis. They have been little used, however, in conjunction with ab initio packages as these algorithms demanded large computational effort to generate even a single event. Here, we revisit the activation-relaxation technique (ART nouveau) and introduce a two-step convergence to the saddle point, combining the previously used Lanczós algorithm with the direct inversion in interactive subspace scheme. This combination makes it possible to generate events (from an initial minimum through a saddle point up to a final minimum) in a systematic fashion with a net 300–700 force evaluations per successful event. ART nouveau is coupled with BigDFT, a Kohn-Sham density functional theory (DFT) electronic structure code using a wavelet basis set with excellent efficiency on parallel computation, and applied to study the potential energy surface of C20 clusters, vacancydiffusion in bulk silicon, and reconstruction of the 4H-SiC surface.
    Mots-clés : ART.


  • M. - R. Yun, R. Lavery, N. Mousseau, K. Zakrzewska, P. Derreumaux, ARTIST: An activated method in internal coordinate space for sampling protein energy landscapes, Proteins: Structure, Function, and Bioinformatics 63, 967-975 (2006).
    Résumé : We present the first applications of an activated method in internal coordinate space for sampling all-atom protein conformations, the activation–relaxation technique for internal coordinate space trajectories (ARTIST). This method differs from all previous internal coordinate-based studies aimed at folding or refining protein structures in that conformational changes result from identifying and crossing well-defined saddle points connecting energy minima. Our simulations of four model proteins containing between 4 and 47 amino acids indicate that this method is efficient for exploring conformational space in both sparsely and densely packed environments, and offers new perspectives for applications ranging from computer-aided drug design to supramolecular assembly. Proteins 2006. © 2006 Wiley-Liss, Inc.
    Mots-clés : ART, flexibilite.
    Pièce jointe 90.pdf 410.3 ko
  • Malek, Rachid, Mousseau, Normand, Barkema, Gerard T., dans Advances in materials theory and modeling - bridging over multiple length and time scale, Bulatov, Vasily, Colombo, Luciano, Cleri, Fabrizio, Lewis, Laurent J., Mousseau, Normand, Éd. (Materials Research Society, Symposium proceedings, 2001), vol. 677, p. AA8.4.
    Mots-clés : ART.


  • G. T. Barkema, N. Mousseau, Event-Based Relaxation of Continuous Disordered Systems, Physical Review Letters 77, 4358-4361 (1996).
    Résumé : A computational approach is presented to obtain energy-minimized structures in glassy materials. This approach, the activation-relaxation technique (ART), achieves its efficiency by focusing on significant changes in the microscopic structure (events). The application of ART is illustrated with two examples: the structure of amorphous silicon and the structure of Ni80P20, a metallic glass.
    Mots-clés : ART.


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