Materials and Condensed Matter
My work in materials science and condensed matter is focused on complex and disordered materials such as amorphous silicon, glasses and defective materials. I am mostly interested in understanding their structural and dynamical properties. Since evolution of materials takes place over macroscopic timescale (from 1 ms to millions of years), I have also been actively involved in the development of new methodologies giving access to this time scale such as the Activation-Relaxation Technique and related algorithms.
Here are a few of my recent projets:
Articles in this section
Structural, kinetic and thermodynamical properties of amorphous and disordered materials
Amorphous semiconductors have been a major research theme for me for more than 20 years, now. In collaboration with Barkema, I have produced some of the best models of amorphous silicon (Barkema and NM, PRB 2000) that remain a reference 13 years after their publication and are still used by groups around the world for various studies (most recently on the topic of hyperuniformity - Xie et al, PNAS 2013).
Using a combination of methods such as the Wooten-Winer-Weaire algorithm, ART, ART nouveau, kinetic ART and molecular dynamics, and in collaboration with various colleagues, I have characterized in details the diffusion and relaxation mechanisms (for example,; Kerrache et al, 2011; Joly et al, PRB 2013) and the evolution of the energy landscape in amorphous and disordered silicon, in excellent agreement with X-ray, calorimetry and nanocalorimetry experiments (for example, Kallel et al, PRL 2010; Béland et al, PRL 2013). Among others, we have demonstrated clearly that, contrary to a common interpretation of experimental experimental, vacancies do not diffuse as a whole in a-Si, they either remain fixe or rapidly dissociate as they jump (Joly et al, 2013).
We have also recently, through simulation on a few systems, suggested that glasses, at low temperature at least, relax through a two-step replenish-and-relax mechanism, where high barriers are necessary to move from one energy basin to another. Similarly, we have shown that coordination defects are not necessary for relaxation, even at relatively low-temperature (Joly et al, PRB 2013). We demonstrated also that the existence of a low-density liquid phase in computer simulations was very sensitive to the choice of forcefield, suggesting that very careful simulations were needed to ensure that validity of this hypothesis (Beaucage and NM, 2005).
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).
Abstract: 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.
A. Kerrache, N. Mousseau, L. J. Lewis, Amorphous silicon under mechanical shear deformations: Shear velocity and temperature effects, Physical Review B 83, 134122 (2011).
Abstract: 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.
H. Kallel, N. Mousseau, F. Schiettekatte, Evolution of the Potential-Energy Surface of Amorphous Silicon, Physical Review Letters 105, 045503 (2010).
Abstract: 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.
G. T. Barkema, N. Mousseau, High-quality continuous random networks, Physical Review B 62, 4985-4990 (2000).
Abstract: 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.
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).
I. H. Sahputra, A. Chakrabarty, O. Restrepo, O. Bouhali, N. Mousseau, C. S. Becquart, et al., Carbon adsorption on and diffusion through the Fe(110) surface and in bulk: Developing a new strategy for the use of empirical potentials in complex material set-ups, physica status solidi (b) , n/a-n/a (2016).
Abstract: Oil and gas infrastructures are submitted to extreme conditions and off-shore rigs and petrochemical installations require expensive high-quality materials to limit damaging failures. Yet, due to a lack of microscopic understanding, most of these materials are developed and selected based on empirical evidence leading to over-qualified infrastructures. Computational efforts are necessary, therefore, to identify the link between atomistic and macroscopic scales and support the development of better targeted materials for this and other energy industry. As a first step towards understanding carburization and metal dusting, we assess the capabilities of an embedded atom method (EAM) empirical force field as well as those of a ReaxFF force field using two different parameter sets to describe carbon diffusion at the surface of Fe, comparing the adsorption and diffusion of carbon into the 110 surface and in bulk of α-iron with equivalent results produced by density functional theory (DFT). The EAM potential has been previously used successfully for bulk Fe–C systems. Our study indicates that preference for C adsorption site, the surface to subsurface diffusion of C atoms and their migration paths over the 110 surface are in good agreement with DFT. The ReaxFF potential is more suited for simulating the hydrocarbon reaction at the surface while the subsequent diffusion to subsurface and bulk is better captured with the EAM potential. This result opens the door to a new approach for using empirical potentials in the study of complex material set-ups.
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.
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.
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).
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).
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.
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).
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.
The Activation-Relaxation Technique
While the first numerical methods for finding transition states (saddle points) go back to the 1970s and 1980s, with work in the physical chemistry community, ART, developed by Barkema and I in 1996, was the first open-ended search method for transition states designed for large systems, i.e. hundreds and thousands of atoms instead of a few atoms. ART, ART nouveau (an improved algorithm proposed by Malek and I in 2000) and similar methods by other groups are now routinely used in chemistry, physics and materials science around the world and are incorporated in many standard codes.
ART has been an important tool in my research, as it allowed me to make original and fundamental contributions in a number of fields including : amorphous materials, defect diffusion in semiconductors and metals, protein folding and flexibility, protein aggregation, etc. This includes identifying diffusion and folding mechanisms, characterization of the energy landscape, sampling of configurational space and the identification of new low-energy structures. This method has also formed the basis for a number of accelerated algorithms that I have developed over the years including POP-ART, that couples MD and ART, holographic ART (Dupuis and NM, 2012), for multiscale protein folding, and kinetic ART (El-Mellouhi, NM and Lewis, 2008), described below. With these methods, I have established myself as one of the world’s leading developers of accelerated algorithms. ART nouveau is currently used by a number of groups around the world, notably in China, France, the Netherlands and the USA.
P. Ganster, L. K. Béland, N. Mousseau, First stages of silicon oxidation with the activation relaxation technique, Physical Review B 86, 075408 (2012).
Abstract: 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.
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).
Abstract: 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.
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).
Abstract: 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.
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).
Abstract: 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.
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).
Abstract: 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.
Malek, Rachid, Mousseau, Normand, Barkema, Gerard T., in Advances in materials theory and modeling - bridging over multiple length and time scale, Bulatov, Vasily, Colombo, Luciano, Cleri, Fabrizio, Lewis, Laurent J., Mousseau, Normand, Eds. (Materials Research Society, Symposium proceedings, 2001), vol. 677, p. AA8.4.
G. T. Barkema, N. Mousseau, Event-Based Relaxation of Continuous Disordered Systems, Physical Review Letters 77, 4358-4361 (1996).
Abstract: 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.