Normand Mousseau
Professor of Physics and Chair
Université de Montréal

The kinetic Activation-Relaxation Technique

Over the last 6 years, my group has been hard at work with the development of kinetic ART (k-ART), an off-lattice kinetic Monte-Carlo (KMC) method with on-the-fly catalog building.

Standard KMC, developed in the 1970’s and applied to materials science the end of the 1980’s, is limited to on-lattice configurations. This meant very limited applications
in the study of semiconductors, alloys, interfaces and, in general, complex systems where (1) it is not possible to identify diffusion mechanisms beforehand and (2) off-lattice positions and elastic effects are important. While the development of kinetic ART was challenging, we developed a proof of concept in 2008 (El Mellouhi, NM and Lewis, 2008) and we have since the end of 2012 a very solid code that can now produce exciting new science.

At the moment, k-ART, based on an original use of topological classification and ART nouveau, is the only KMC method that can be applied to disordered or complex materials such as ion-bombarded crystal, amorphous semiconductors and glasses.

As such, the method opens new fields of simulations and it is attracting considerable attention that should be growing with the publication of recent atomistic simulations of the evolution of complex systems over time scales of 1 second or longer, more than 10 million times longer than anything available until now (Béland et al, 2013, and Joly et al., 2013).

Selected work



  • 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).
    Abstract: 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.
    Tags: 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).
    Tags: 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).
    Abstract: 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.
    Tags: 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).
    Tags: 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).
    Abstract: 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.
    Tags: ARTc.


  • L. K. Béland, P. Brommer, F. El-Mellouhi, J. - F. Joly, N. Mousseau, Kinetic activation-relaxation technique, Physical Review E 84, 046704 (2011).
    Abstract: 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).
    Tags: 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).
    Abstract: 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.
    Tags: ARTc.
    Attachment Full Text PDF 168.3 kb (source)
Wednesday 2 July 2014

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