Stillinger- Weber model

The characteristic time of this diffusion was estimated by carrying out the molecular dynamic relaxation of the film surface within the limits of the above model at 500°C. In MD calculations, the pair interaction energy between atoms is approximated by the Buckingham pair potential (Zr O, O-O) (see Table 9.4). To describe covalent bonds more correctly, a three-body O-Zr-O term in the Stillinger-Weber form was introduced in addition to the Coulomb term. 

The model surfaces chosen for this study are shown in Figs. 15 and 16. A bare silicon surface, a silicon surface with a single monolayer of Cl chemisorbed (Fig. 15), and a silicon surface with about 2.3 monolayers of Cl mixed into the top 20 A were chosen (Fig. 16). The potentials were Feil-Stillinger-Weber, and the simulations are described by Helmer and Graves (1998). For the results shown here, Ar+ and C1+ are used as the incident ions. 

Some Properties of Silicon Obtained by the Tight-Binding (TB) Model of Ref. 20 Compared with the Results Obtained by First-Principles (LDA), the Stillinger-Weber (S-W)... 

There is another family of models that also favors local tetrahedral arrangements in the liquid phase and shows LLPTs. This family of models is based on the Stillinger Weber potential [86], originally proposed as a model for Si. It has also been reparameterized in order to model germanium [15] and water [87]. In this model, atoms interact via a basic two-body interaction term, Vzir), plus a three-body interaction term, W3 (r, 6), that favors the local tetrahedral arrangement v = V2 (r) + Xv3 (r, 9), where X controls the tetrahedrality of the model. For small values of X, the LLPT is not observed and for very large values, crystallization occurs only for intermediate values of X, the LLPT is observed in simulations [40,88]. 

The Stillinger-Weber potential is one of the best model potentials for studying the liquid and supercooled liquid phases of silicon, since the parameters of the model potential are chosen explicitly to predict the structural properties of real liquid silicon. However, whether the model faithfully captures temperature variations of thermophysical, structural, and dynamic properties are unclear, and we should expect that the results obtained from the simulation will be sensitive to the model parameters. The finding of a liquid liquid transition in supercooled silicon using the SW potential has been interrogated by Beaucage and Mousseau... 

Lastly, any underlying atomistic model can be used, whether quantum mechanically or classically based. In practice, semi empirical interatomic potentials such as EAM ° and Stillinger-Weber (three-body interaction) potentials have usually been used to model the atomistic regime. 

The CLS methodology uses an FE description to model the continuum, classical MD to simulate the evolution of the mesoscopic regime, and a TB molecular dynamics approach to include quantum effects in the overall treatment. The FE description is at the linear elastic level because its use is limited to regions where the atoms are only slightly perturbed from equilibrium. The classical molecular dynamics makes use of semiempirical potentials such as the Stillinger-Weber (SW) potential for Si. Lastly, the tight-binding method was chosen instead of other, more accurate, quantum descriptions because of its computational speed. 

The Stillinger-Weber potential has generally been used for modeling crystalline silicon however, more recently it has also been used for organic molecules as well. Another example of a three-body interatomic potential is the Tersoff potential (Tersoff 1988,1989), which also was created initially in an attempt to accurately model silicon solids. 

A simple model, which has been quite successful in solids with the diamond or zinc-blende stmcrnre, was introduced by Stillinger and Weber (Stillinger and Weber, 1985). The first term in the potential is the product of a Lennard-Jones-like pair-wise interaction and a cut-off function smoothly terminating the potential at some distance r. The second term is a multi-variable three-body potential written as a separable product of two radial functions and an angular function ... 

Computer simulations for several models (Weber and Stillinger, 1985 Ohmine, 1995) have determined that the elementary transitions between neighboring basins entail shifts of only small local groups of particles. To be precise, the difference between the inherent structures of the two basins involved in a large V-particle system is concentrated on a neighboring set of (9(1) particles the remainder particles experience at most a minor elastic response to the localized repacking (Lacks, 1998). In view of the fact that the number of such localized repacking possibilities is proportional to system size, the number of transition states (saddle points) in the boundary of any basin will be O(V), i.e., an extensive property. So too, then, will be the net kinetic exit rate from any basin at positive temperature. 

Clarke has examined the thermodynamic equation of state and the specific heat for a Lennard-Jones liquid cooled through 7 at zero pressure. He found that drops with decreasing temperature near where the selfdiffusion becomes very small. Wendt and Abraham have found that the ratio of the values of the radial distribution function at the first peak and first valley shows behavior on cooling much like that observed for the volume of real glasses (Fig. 6), with a clearly defined 7. Stillinger and Weber have studied a Gaussian core model and find a self-diffusion constant that drops essentially to zero at a finite temperature. They also find that the ratio of the first peak to the first valley in the radial distribution function showed behavior similar to that found by Wendt and Abraham" for Lennard-Jones liquids. However, the first such evidence for a nonequilibrium (i.e. kinetic) nature of the transition in a numerical simulation was obtained by Gordon et al., who observed breakaways in the equation of state and the entropy of a hard-sphere fluid similar to those in real materials. 

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