Modified Stillinger Weber Potential Research Articles

A-C/GeTe superlattices: Effect of interfacial impedance adaptation modeling on the thermal properties

Recently, nanostructuration has been proposed to improve the performance of phase change memories. This is the case of superlattices composed of amorphous carbon and crystalline germanium telluride, which we have investigated by molecular dynamics. For this, a modified Stillinger–Weber potential is adapted to reproduce their stiffness contrast/impedance ratio. In order to study the effect of the interface interaction, two sets of parameters are used to model the interfaces with different interactions between the two materials using the properties of the softer material or the average properties between the two creating an adaptation of impedance across the layers. The effects of interface roughness and carbon diffusion at grain boundaries are studied. Using equilibrium molecular dynamics as well as the propagation of wave-packets, we show first that without impedance adaptation, the anisotropy is high, and the roughness has a marked impact on the properties. However, the introduction of impedance adaptation destroys those effects on the thermal conductivity. Finally, we show that the periodic texturing of the interface increases the transmission of in-plane transverse phonons.

Coarse-Grained Simulation of the Adsorption of Water on Au(111) Surfaces Using a Modified Stillinger-Weber Potential.

For reproducing the behavior of water molecules adsorbed on gold surfaces in terms of density of both bulk and interfacial water and in terms of structuring of water on top of gold atoms, the implementation of a multibody potential is necessary, thus the Stillinger–Weber potential was tested. The goal is using a single nonbonded potential for coarse-grained models, without the usage of explicit charges. In order to modify the angular part of the Stillinger–Weber potential from a single cosine to a piecewise function accounting for multiple equilibrium angles, employed for Au–Au–Au and Au–Au–water triplets, it is necessary to create a version of the simulation package LAMMPS that supports the assignment of multiple favored angles. This novel approach is able to reproduce the data obtained using quantum mechanical calculations and density profiles of both bulk and adsorbed water molecules obtained using classical polarizable force fields.

Investigation of strain effects on phase diagrams in the ternary nitride alloys (InAlN, AlGaN, InGaN)

In this work, we used a modified Stillinger–Weber potential and a methodology of free energy calculation based on numerical computation of the configuration partition function of an alloy, to make a comprehensive study of the properties of group-III nitride ternary compounds (InxGa1−xN; InxAl1−xN; AlxGa1−xN). The wurtzite structure was used; and the critical temperatures for the random ternary alloys are determined as 2717 K for InxAl1−xN, 1718 K for InxGa1−xN, and 177 K for AlxGa1−xN, respectively. Therefore, AlxGa1−xN has no unstable mixing region at typical growth temperatures around 1100 °C. In contrast, InxAl1−xN and InxGa1−xN exhibit a wide unstable region, which means that being thick layers, their stability as homogeneous alloys is probably limited. In agreement with other reports, it is also pointed out that the critical temperature Tc may be decreased when the layers are grown under strain. Although the compression and extension have the same effect below 1.5% strain, it is shown, for the first time, that when the compressive strain goes beyond, Tc abruptly increases in contrast to the case of tensile strain where it continues to decrease.

Modeling wave propagation induced fracture in rock with correlated lattice bond cell

The correlated lattice bond cell model (CLBC) is used to account for the characteristics of the mesostructure of rock. Each mineral grain is modeled as a discrete unit bond cell. A linear modified Stillinger–Weber potential is adopted to characterize the unit bond cell. By this method, the lattice model can not only represent the variable Poisson ratio, but can also simulate more complex fracture behaviors than the two-body interaction-based lattice model. It can precisely simulate the stress wave propagation in rock with different Poisson ratios. With a simple bond rupture criterion, the spalling fracture induced by stress wave is well simulated. To represent the heterogeneity of rock, the moduli of bond cells are assumed to be random, following a Weibull distribution. The simulation results demonstrate that the distinct spalling fracture is likely to initiate in a hard rock subjected to impact load, but not in a soft rock. The heterogeneity has little effect on the spalling fracture.

Modeling nonlinear elastic solid with correlated lattice bond cell for dynamic fracture simulation

The correlated lattice bond cell is a kind of lattice model developed for modeling nonlinear elastic solid. Unlike the usual lattice model, the present one is composed of unit cells, which can adopt any geometry with any number of bonds. The unit cells are compiled together via the particles along their boundaries to form a discrete system. The energy of unit cell is characterized by the modified Stillinger–Weber (SW) potential, in which the initial value of each bond angle in the reference configuration, not the ‘ideal’ tetrahedral angle, is taken as the reference value of this bond angle in the current configuration. This makes the modified SW potential applicable to other materials than silicon. Because the modified SW potential can simultaneously account for the bond stretch and rotation effect, the present lattice model can represent variable Poisson ratios. The bond parameters are calibrated as the function of material constants (Young’s modulus, Poisson ratio), the volume and the total bond number of a unit cell based on the ideal unit cell conception. Enriched with a more elaborate fracture mechanism than the two-body potential through the modified SW potential, the present lattice model can capture most characters of dynamic fracture, providing an efficient nonlinear elasticity modeling method for dynamic fracture simulation. For the present method can directly simulate the dynamic fracture initiation, arrest, propagation and branching in the finite deformation cases without any separate criterion, its perspective should be inspiring.

An angular embedded atom method interatomic potential for the aluminum–silicon system

A modified version of the Stillinger–Weber (SW) interatomic potential for pure Si has been developed. In contrast to the original SW form, the modified version allows one to grow diamond cubic crystal structures from the melt at high temperatures. Now, the modified SW potential has been combined with an embedded atom (EAM) description of pure Al developed by Mendelev et al to formulate an Al–Si binary potential of the angular EAM type. The Al–Si potential reproduces quite well the experimental enthalpy of mixing in the liquid. It also predicts an Al–Si phase diagram with a eutectic concentration for the liquid that agrees with experimental values within 4 at% and a eutectic temperature that differs from experimental values by just 13 K.

A modified Stillinger–Weber potential-based hyperelastic constitutive model for nonlinear elasticity

The Stillinger–Weber (SW) potential, which is a combination of the two- and three-body interaction, states that the bond energy is not only related to the distance between atoms, but also related to the bond angles subtended by this given bond and other bonds. The bond energy mechanism presented by the SW potential is different from that by the classical potentials, such as the Lennard–Jones, Tersoff and Embedded Atom potentials. Different micro energy mechanism reveals different micro fracture mechanism. The original SW potential takes the ‘ideal’ tetrahedral angle as the reference value of each bond angle in the current configuration, which makes it only applicable to the silicon materials. However, the micro fracture mechanism revealed by the SW potential should not be confined to the silicon materials. To extend the SW potential to a wider range of materials, the value of the bond angle in the reference configuration, not the ‘ideal’ tetrahedral angle, is taken as the reference value of this bond angle in the current configuration. Based on this modified SW potential, a constitutive model is developed. By this way, the micro fracture mechanism invoked by the SW potential is incorporated into the constitutive relation. Through this proposed constitutive model, it is found that the Hookean matrix derived from the SW potential matches that of a linear elastic continuum, which suggests that there exists a corresponding relationship between the micro physical parameters of SW potential and the macro material constants. The corresponding micro–macro parameter relationship is derived in this paper. To examine the application of this method to other materials, it is used to simulate the mixed fracture growth in concrete under static and dynamic load. The simulation results suggest that the present method can capture the characters of fracture growth in the quasi-brittle materials. It suggests that the constitutive model based on the modified SW potential can be applied to materials other than silicon. Because the interatomic potential-incorporated constitutive model makes the fracture criterion as the intrinsic property of a constitutive relation, it presents many advantages in fracture simulation. This paper enriches the constitutive relation with the micro fracture mechanism presented in SW potential, providing a new micro constitutive model for materials. Besides this, it also provides a feasible approach to calibrating the parameters of the SW potential for a certain material.

Energetics of the 30∘ Shockley partial dislocation in wurtzite GaN

Abstract In the present work, we have investigated the relative energy of different core configurations of the 30∘ Shockley partial dislocation in wurtzite GaN. By using a modified Stillinger–Weber potential, we have carried out large scale calculations on models containing many thousands of atoms. Both glide and shuffle configurations have been considered within the two core polarities (Ga, N). Similarly to what was reported for conventional semiconductors, our calculations showed that the reconstructed glide configurations are energetically favoured over the shuffle ones.

A potential for simulating the atomic assembly of cubic AB compounds

Stillinger–Weber interatomic potentials can be used to study the crystal growth of AB compounds with the zinc-blende (B3) structure, but have been unable to be used for other cubic structured compounds. Here we extend a recently modified Stillinger–Weber potential for cubic elements so that it is suited for studying the growth of cubic compounds with the B1 and B2 structures. We also parameterize the potential for the Mg–O system. The potential is shown to accurately model the lattice constants and the cohesive energies of the fcc Mg, fcc O, and the B1 MgO structures. It also correctly ensures that the equilibrium phase of each of these materials possesses the lowest cohesive energy with respect to all their other phases. The potential correctly predicts crystalline growth during molecular dynamics simulations of the vapor deposition of fcc Mg and B1 MgO thin films. The results also reveal the formation of various defects in the films, including islands and twins in Mg, interstitials and disrupted regions on the MgO growth surface, and local un-oxidized regions at the MgO/Mg interface during the oxidation of Mg. The simulation approach enables the study of atomic assembly processes controlling the formation of these defects.

A potential for simulating the atomic assembly of cubic elements

Molecular dynamics simulations using Stillinger–Weber potentials have been widely used to study the growth of diamond-cubic materials since these potentials are easily parameterized to ensure that the diamond-cubic structure has the lowest cohesive energy. However, Stillinger–Weber potentials can only be used to model cubic crystals with the diamond-cubic structure. Here we generalize the Stillinger–Weber potential formulism and explore its application to other cubic crystal structures. Parameterization of this modified Stillinger–Weber potential is exemplified by developing potentials for four elements: Si (diamond-cubic), Ni (face-centered-cubic), Fe (body-centered-cubic), and Po (simple-cubic). The parameterized potentials predict well the cohesive energy and lattice constants of each element. Molecular dynamics simulations are used to test the ability of the potentials to simulate the crystalline assembly of these materials from their atomic vapor. Defects are found in the films grown under kinetically constrained conditions.

Boron ripening in amorphous silicon by large scale molecular dynamics simulations

We have developed an efficiently scalable molecular dynamics code based on a modified Stillinger–Weber potential for silicon and boron atoms and we have employed it to characterize amorphous silicon–boron alloys with 1% of boron concentration. We prove that B ripening mechanisms are efficient in creating a large population of B precipitates whose structural properties are fully characterized.

A modified empirical potential for energetic calculations of planar defects in GaN

The Stillinger–Weber empirical potential was modified and its parameters were determined to achieve a realistic description of the microscopic structure and the energetics of different planar defects and their interactions in wurtzite GaN. The formulation was based on the adjustment of the parameters in order to represent the Ga–Ga, N–N and Ga–N bonds. The input data comprises of the different crystalline phases of gallium, nitrogen and GaN. A satisfactory agreement on the values of the energy versus atomic volume per atom was obtained compared to those derived by ab initio calculations and experimental data for all the cases studied. By employing the modified Stillinger–Weber potential the energy of translation domain boundaries, which have been observed experimentally in GaN thin films, was calculated providing results comparable with ab initio calculations.

Crystallization study of model tetrahedral semiconductors

The microscopic mechanisms leading to crystallization are not yetfully understood. This is due, in part, to the lack of atomistic as wellas interatomic interaction models for a wide range of materials thatcan lead to crystallization on a computer-simulation timescale, i.e.< 100ns. While the nucleation in close-packed systems has been extensively studied,there are almost no numerical results for covalent tetrahedral semiconductors. Wepresent here the simulation results of crystallization from the liquid andamorphous states of a 1000-atom model of silicon, described with a modifiedStillinger–Weber potential. With this potential, it is possible to crystallize themodel in as little as a few nanoseconds, which opens a door to detailed studies ofthe nucleation processes in covalent systems. Using topological analysis, we alsopresent a first characterization of the structural fluctuations of the nucleationcentres in this system and give a rough estimate for the critical size of thesecentres.

The dislocations of low-angle grain boundaries in GaN epilayers: a HRTEM quantitative study and finite element stress state calculation

During epitaxy of GaN on sapphire grains form a mosaic structure. The distance between edge dislocations in these boundaries is from 2 to 15 nm. The strain around the dislocations is quantitatively measured by processing of HRTEM images. The dislocation core distribution maps and in plane Burgers vectors components are derived from the experimental strain tensor by applying the continuum dislocation theory. Experimental results were compared with the atomic models of edge dislocations calculated using a modified Stillinger–Weber potential for different atomic configurations of the cores. It is concluded that the strain field extracted from simulated images matches with that of observed dislocations. Starting from experimental distortion distribution data, the finite element calculations are used to estimate the stress around the boundaries.

Energetic Calculation of Coincidence Grain Boundaries with a Modified Stillinger-Weber Potential

Energetic Calculation of Coincidence Grain Boundaries with a Modified Stillinger-Weber Potential

Energetic Calculation of Coincidence Grain Boundaries with a Modified Stillinger-Weber Potential

Potential energy of two coincidence grain boundaries, Σ = 7 and 19, was calculated with a Stillinger-Weber potential previously adapted to wurtzite GaN in order to take into account the Ga–Ga and N–N wrong bonds. Their atomic structures, determined before by high resolution electron microscopy, are based on 5/7 and 8 atom ring structural units. By using periodical boundary conditions, it is shown that the high angle grain boundary Σ = 7 (Θ = 21°79/[0001]) has always a smaller energy than Σ = 19 (Θ = 13°17/[0001]).

Structures of Si and Ge clusters under modified Stillinger-Weber potential

Structural behaviors of silicon and germanium clusters under the recently proposed modified Stillinger-Weber (SW) potential have been studied by molecular dynamics method along with the conjugate-gradient optimization. Since the SW potentials have been derived from the properties of bulk materials, it gives relatively large discrepancy when the cluster number is small, e. g. n=3 and 4. When n>4, the ground-state structures under the modified SW potential are close to that from the first-principle calculation. The binding energies are also improved under the modified SW potential. These results may be attributed to the relative enhancement of the two-body term over the three-body term in the modified SW potential, which leads to structures with a preferential coordination number 4. Structural behaviors of germanium clusters are similar to those of silicon.