Brenner potential

Many body potentials e.g. Sutton-Chen, Tersoff, " Brenner can be used to describe metals and other continuous solids such as silicon and carbon. The Brenner potential has been particularly successful with fullerenes, carbon nanotubes and diamond. Erhart and Albe have derived an analytical potential based on Brenner s work for carbon, silicon and silicon carbide. The Brenner and Tersolf potentials are examples of bond order potentials. These express the local binding energy between any pair of atoms/ions as the sum of a repulsive term and an attractive term that depends on the bond order between the two atoms. Because the bond order depends on the other neighbours of the two atoms, this apparently two-body potential is in fact many-body. An introduction and history of such potentials has recently been given by Finnis in an issue of Progress in Materials Science dedicated to David Pettifor. For a study of solid and liquid MgO Tangney and Scandolo derived a many body potential for ionic systems. 

MD simulations using Tersoff- Brenner potential to simulate covalent bonds while using Lennard-Jones to model interlayer interactions 1.4 for armchair 1.2 for zigzag Evaluating the influence of surface effect resulting in relaxed unstrained deformation and in-layer nonbonded interactions using atomistic continuum modeling approach... 

Wang et al. [30] 2005 Tersoff-Brenner potential (n,nXn,0) 7-19 0.5-1.7 Obtaining critical stresses and comparing between the buckling behavior in nano and macroscopic scale... 

We tested our ideas for several structures. Here we present our results obtained for nanotube junctions nano tori and helical nanotubes. We calculated the interatomic interactions with the help of the Brenner potential (Brenner 1990) and harmonic potentials as well. In the Breimer potential there are first neighbour and second neighbour interactions. 

Fig. 5. The activation energy for bond rotation for the (5.5) tube computed by the ab initio multigrid method. The corresponding values obtained by molecular statics using the classical Tersoff-Brenner potential are also shown. Note that while the qualitative trends are similar between the two approaches, there are substantial quantitative differences.

In Fig. 6.4 we show the performance of GAP, compared to the state-of-the-art interatomic potential, the Brenner potential [6]. The set of configurations used for testing was obtained from a long ab initio molecular dynamics run of a 64-atom supercell at 1,000 K. The absolute values of the components of the difference between the predicted and the DFT forces are shown as a function of the... 

Fig. 6.4 Force errors eompared to DFT forces for GAP and the Brenner potential in diamond. The left shows the force errors at different DFT forces. On the right, the distribution of the force errors is shown...

Fig. 6.8 Phonon dispersion of diamond calculated by GAP solid lines), the Brenner potential...

The same analytic function was used by Skinner to obtain the thermal expansion coefficient from the experimental lattice constants [12]. CXir results are shown in Fig. 6.14, together with the experimental values [12] and values calculated by LDA and GAP using the quasiharmonic approach. The results obtained by using the Brenner potential is shown in the right panel of Fig. 6.14. It can be seen that... 

Fig. 6.16 The energetics of the linear transition path from rhombohedral graphite to diamond calculated by DFT, GAP and the Brenner potential...

The reaction coordinate x corresponds to graphite at x = 0 and to diamond at X = 1. It can be seen that the Brenner potential cannot describe the change in the bonding of the carbon atoms, whereas the GAP potential reproduces the quantum mechanical barrier accurately. 

The Brenner potential can be seen as a potential where first- and second-neighbour interactions are taken into account in the potential function E r) = E r 2, r y,...). Later, we replaced this potential by the much simpler one the harmonic potential [12-14],... 

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