Potentiel de Lennard-Jones | EPFL Graph Search

Le potentiel de Lennard-Jones, qui est plus précisément une énergie potentielle, décrit l'interaction entre deux atomes au sein d'un gaz monoatomique de type gaz rare. Bien que ne faisant appel qu'à la seule distance entre deux centres il est également utilisé pour l'interaction de molécules. On peut alors l'interpréter comme potentiel moyen. Son expression en fonction de la distance r entre les deux atomes est : :E_\mathrm p(r)=4,E_0,\left[\left(\frac{d}{r}\right)^{12}-\left(\frac{d}{r}\right)^{6}\right] Le potentiel s'annule pour r {{=}} d et possède un minimum en r/d = 2 ≈ 1,12246.... Le terme à la puissance 6, terme attractif dominant à grande distance, porte le nom d'interaction de Van der Waals. En revanche, l'exposant 12 du terme répulsif, dominant à courte distance, est empirique : il s'agit là de rendre compte de façon ad hoc de la répulsion de Pauli entre les électrons, qui empêche l'interpénétration mutuelle des nuages électroniques

Instanton theory of ground-state tunneling splittings with general paths

Mihael Erakovic, Christophe Louis Joseph Jean-Luc Vaillant

We derive a multidimensional instanton theory for calculating ground-state tunneling splittings in Cartesian coordinates for general paths. It is an extension of the method by Mil'nikov and Nakamura [J. Chem. Phys. 115, 6881 (2001)] to include asymmetric paths that are necessary for calculating tunneling splitting patterns in multi-well systems, such as water clusters. The approach avoids multiple expensive matrix diagonalizations to converge the fluctuation prefactor in the ring-polymer instanton (RPI) method, and instead replaces them by an integration of a Riccati differential equation. When combined with the string method for locating instantons, we avoid the need to converge the calculation with respect to the imaginary time period of the semiclassical orbit, thereby reducing the number of convergence parameters of the optimized object to just one: the number of equally spaced system replicas used to represent the instanton path. The entirety of the numerical effort is thus concentrated in optimizing the shape of the path and evaluating hessians along the path, which is a dramatic improvement over RPI. In addition to the standard instanton approximations, we neglect the coupling of vibrational modes to external rotations. The method is tested on the model potential of malonaldehyde and on the water dimer and trimer, giving close agreement with RPI at a much-reduced cost. Published under license by AIP Publishing.

2020

An Atomistic Simulation Method for Oxygen Impurities in Aluminium Based on Variable Charge Molecular Dynamics

Andreas Elsener

Impurities are known to have a significant impact on materials properties. In particular, the presence of impurities can change mechanical properties and stabilize the microstructure by reducing grain growth and recrystallization processes. In the past atomistic simulations, in particular molecular dynamics, have contributed a lot to the understanding of deformation mechanisms in nanocrystalline metals. Especially, insights into details of dislocation/GB interactions have been gained. Additionally, simulations on coupled grain boundary migration in bicrystalline samples have played an important role in understanding stress assisted grain growth in nanocrystalline metals. However, all these simulations have been performed on monatomic systems. This means that the role of impurities has not yet been considered in these simulations. Some of the important difference between experiments and simulations could be removed by introducing dilute O distributions to computational Al samples. For this purpose, a simulation method is required which can deal with the oxidation of Al atoms around the O impurities and which can simulate the ionic and metallic nature of bonding simultaneously. Here, a method is suggested which fulfills the requirements by modifying the variable charge method of Streitz and Mintmire [Phys. Rev. B 50, 11996 (1994)]. A local chemical potential approach which optimizes the charge on only those atoms expected to be ionic is developed. Additionally the EAM potential for the non-electrostatic interaction given in the publication of Streitz and Mintmire is substituted by empirical potentials which treat the Al-Al interactions with a well-known Al potential. The Al-O and O-O interactions in these EAM potentials are fitted for the simulation of dilute O impurities in Al and additionally for the simulation of corundum in case of a second potential. The aforementioned developments are applied to study the effect of O impurities on the deformation of nc Al. A fully three-dimensional nc sample containing 15 grains of 12 nm grain-size is deformed with a dilute O content in the triple junction lines. The impact of O impurities on dislocation propagation is also considered in a sample which consists of a single grain extracted from a large molecular dynamics simulation. This simulation geometry contains a perfect dislocation, which is pinned at the surrounding grain boundary network. Therefore it allows the study of pinning strength and after unpinning the propagation behavior of the dislocation under various O impurity distributions. Additionally, the role of O impurities on coupled GB migration is investigated by studying two bicrystalline samples with different O distributions in both of them. In the discussion, the emphasis is on the simulation method. Especially, the significance of the samples, simulation conditions and the performance of the method in the different applications are discussed. Additionally, the different developments (local chemical potential approach and EAM potentials) are critically analyzed and improvements for future simulations of impurities are suggested.

EPFL2010

Controlling the Long-Range Corrections in Atomistic Monte Carlo Simulations of Two-Phase Systems

Dominic John Tildesley

The long-range correction to the surface tension can amount to up to 55% of the calculated value of the surface tension for cutoffs in the range of 2.1-6.4 sigma. The calculation of the long-range corrections to the surface tension and to the configurational energy in two-phase systems remains an active area of research. In this work, we compare the long-range corrections methods proposed by Guo and Lu (J. Chem. Phys. 1997, 106, 3688-3695) and Janecek (J. Phys. Chem. B 2006, 110, 6264-6269) for the calculation of the surface tension and of the coexisting densities in Monte Carlo simulations of the truncated Lennard-Jones potential and the truncated and shifted Lennard-Jones potential models. These methods require an estimate of the long-range correction at each step in the Monte Carlo simulation. We apply the full version of the Guo and Lu method, which involves the calculation of a double integral that contains a series of density differences, and we compare these results with the simplified version of the method which is routinely used in two-phase simulations. We conclude that the cutoff dependencies of the surface tension and coexisting densities are identical for the full versions of Guo and Lu and Janecek methods. We show that it is possible to avoid applying the long-range correction at every step by using the truncated Lennard-Jones potential with a cutoff r(c) >= 5.5 sigma. The long-range correction can then be applied at the end of the simulation. The limiting factor in the accurate calculation of this final correction is an accurate estimate of the coexisting densities. Link-cell simulations performed using a cutoff r(c) = 5.5 sigma require twice as much computing time as those with a more typical cutoff of r(c) = 3.0 sigma. The application of the Janecek correction increases the running time of the simulation by less than 10%, and it can be profitably applied with the shorter cutoff.