Current potential: ThreeBodyCluster_SRS_StephensonRadnySmith_1996_Si__MO_604248666067_000
Deep Citation determination:
Does the citing paper use the current potential to generate results displayed in the paper?
Provide us with identifying information so that we know you are not a bot (you will not be added to a mailing list):
Title
A single sentence description.
Three-body cluster potential for Si by Stephenson, Radny and Smith (1996) v000
Description
A short description of the Model describing its key features including for example: type of model (pair potential, 3-body potential, EAM, etc.), modeled species (Ac, Ag, ..., Zr), intended purpose, origin, and so on.
The widely used Stillinger-Weber potential for silicon interactions has been modified to provide an accurate description of the Si(111)-(7 x 7) surface including the highly-reactive adatom and rest-atom sites. This modified potential also provides a good representation of bulk silicon, and the Si(001)-(1 x 1), Si(001)-(2 x 1), Si(111)-(1 x 1) and Si(111)-(2 x 1) surfaces. Above the melting temperature of 1683 K, however, the original Stillinger-Weber potential is probably superior.
Species
The supported atomic species.
Si
Disclaimer
A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.
This Model originally published in [1] is archived in OpenKIM [2-5].
[1] Stephenson PCL, Radny MW, Smith PV. A modified Stillinger-Weber potential for modelling silicon surfaces. Surface Science. 1996;366(1):177–84. doi:10.1016/0039-6028(96)00801-1 — (Primary Source) A primary source is a reference directly related to the item documenting its development, as opposed to other sources that are provided as background information.
[2] Stephenson PCL, Radny MW, Smith PV. Three-body cluster potential for Si by Stephenson, Radny and Smith (1996) v000. OpenKIM; 2019. doi:10.25950/244c5ddc
[3] Druecke B, Karls DS, Stephenson PCL, Radny MW, Smith PV. Three-body cluster potential by Stephenson, Radny and Smith (1996) v000. OpenKIM; 2019. doi:10.25950/f9b3bf83
[4] Tadmor EB, Elliott RS, Sethna JP, Miller RE, Becker CA. The potential of atomistic simulations and the Knowledgebase of Interatomic Models. JOM. 2011;63(7):17. doi:10.1007/s11837-011-0102-6
This panel presents information regarding the papers that have cited the interatomic potential (IP) whose page you are on.
The OpenKIM machine learning based Deep Citation framework is used to determine whether the citing article actually used the IP in computations (denoted by "USED") or only provides it as a background citation (denoted by "NOT USED"). For more details on Deep Citation and how to work with this panel, click the documentation link at the top of the panel.
The word cloud to the right is generated from the abstracts of IP principle source(s) (given below in "How to Cite") and the citing articles that were determined to have used the IP in order to provide users with a quick sense of the types of physical phenomena to which this IP is applied.
The bar chart shows the number of articles that cited the IP per year. Each bar is divided into green (articles that USED the IP) and blue (articles that did NOT USE the IP).
Users are encouraged to correct Deep Citation errors in determination by clicking the speech icon next to a citing article and providing updated information. This will be integrated into the next Deep Citation learning cycle, which occurs on a regular basis.
This panel provides information on past usage of this interatomic potential (IP) powered by the OpenKIM Deep Citation framework. The word cloud indicates typical applications of the potential. The bar chart shows citations per year of this IP (bars are divided into articles that used the IP (green) and those that did not (blue)). The complete list of articles that cited this IP is provided below along with the Deep Citation determination on usage. See the Deep Citation documentation for more information.
16 Citations (8 used)
Help us to determine which of the papers that cite this potential actually used it to perform calculations. If you know, click the .
USED (low confidence) M. Bauer, M. Probert, and C. Panosetti, “Systematic Comparison of Genetic Algorithm and Basin Hopping Approaches to the Global Optimization of Si(111) Surface Reconstructions,” The Journal of Physical Chemistry. a. 2022. link Times cited: 3
Abstract: We present a systematic study of two widely used material st… read more
Abstract: We present a systematic study of two widely used material structure prediction methods, the Genetic Algorithm and Basin Hopping approaches to global optimization, in a search for the 3 × 3, 5 × 5, and 7 × 7 reconstructions of the Si(111) surface. The Si(111) 7 × 7 reconstruction is the largest and most complex surface reconstruction known, and finding it is a very exacting test for global optimization methods. In this paper, we introduce a modification to previous Genetic Algorithm work on structure search for periodic systems, to allow the efficient search for surface reconstructions, and present a rigorous study of the effect of the different parameters of the algorithm. We also perform a detailed comparison with the recently improved Basin Hopping algorithm using Delocalized Internal Coordinates. Both algorithms succeeded in either resolving the 3 × 3, 5 × 5, and 7 × 7 DAS surface reconstructions or getting “sufficiently close”, i.e., identifying structures that only differ for the positions of a few atoms as well as thermally accessible structures within kBT/unit area of the global minimum, with T = 300 K. Overall, the Genetic Algorithm is more robust with respect to parameter choice and in success rate, while the Basin Hopping method occasionally exhibits some advantages in speed of convergence. In line with previous studies, the results confirm that robustness, success, and speed of convergence of either approach are strongly influenced by how much the trial moves tend to preserve favorable bonding patterns once these appear. read less
USED (low confidence) Y. Chen, F. Fang, X. Zhang, and X. Hu, “Molecular dynamics of nanometric processing of ion implanted monocrystalline silicon surfaces,” Transactions of Tianjin University. 2014. link Times cited: 2
USED (low confidence) Y. Chen, F. Fang, X. Zhang, and X. Hu, “Molecular dynamics of nanometric processing of ion implanted monocrystalline silicon surfaces,” Transactions of Tianjin University. 2014. link Times cited: 0
USED (low confidence) S. Zhang et al., “The study of melting stage of bulk silicon using molecular dynamics simulation,” Physica B-condensed Matter. 2011. link Times cited: 13
USED (low confidence) S. Kitamura, “Analysis of Strained Island Energetics in Ge/Si(001) Growth(Condensed matter : structure and mechanical and thermal properties),” Journal of the Physical Society of Japan. 2008. link Times cited: 0
Abstract: The numerical calculation for Ge/Si(001) heteroepitaxial gro… read more
Abstract: The numerical calculation for Ge/Si(001) heteroepitaxial growth is performed. We adopt the most widely used Stillinger–Weber potential, and the island energies of the three types, two-dimensional island, pyramid and dome, are explored as a function of the lateral size. These island energies are compared with each other to find the island morphology which has the lowest energy. Then, a growth history of the most stable growth mode is searched. Although the result reproduces qualitatively the Stranski–Krastanov growth as observed in the experiments, quantitative differences between our result and experiments in the critical wet layer thickness and the island morphology are found. read less
USED (low confidence) S. Wang et al., “THE CALCULATION OF THE SURFACE ENERGY OF HIGH-INDEX SURFACES OF SILICON AT ZERO TEMPERATURE,” Surface Review and Letters. 2006. link Times cited: 1
Abstract: We used the molecular dynamics simulation based on the Still… read more
Abstract: We used the molecular dynamics simulation based on the Stillinger–Weber (SW) interatomic potential to calculate the high-index surface energies of surfaces containing any of the stereographic surfaces of silicon at zero temperature. An empirical formula based on the structural unit model was generalized for high-index surfaces. Our simulated results show that the generalized formula can give a good estimation of the surface energy and structural feature of the high-index surfaces not only on the edge of stereographic but also within it. Our simulation and empirical formula results reveal that the closest surface has the lowest energy, so the closest (101) surface has the lowest surface energy and the (101), (111) and (001) surfaces are the extremum on the curve of surface energy versus orientation angle. Both the theoretical simulation results and the empirical formula calculation results are consistent with the available first-principles theoretical data. read less
USED (low confidence) F. Fang and Y. Chen, “Nanometric cutting of crystal surfaces modified by ion implantation.” 2015. link Times cited: 1
USED (low confidence) J. Que, M. Radny, P. V. Smith, and A. Dyson, “Application of the extended Brenner potential to the Si(111)7 × 7:H system I : cluster calculations,” Surface Science. 2000. link Times cited: 13
NOT USED (low confidence) A. Hirano, H. Sakakima, A. Hatano, and S. Izumi, “Long-range Tersoff potential for silicon to reproduce 30° partial dislocation migration,” Computational Materials Science. 2024. link Times cited: 0
NOT USED (low confidence) X. Du et al., “Machine-learning-accelerated simulations to enable automatic surface reconstruction,” Nature Computational Science. 2023. link Times cited: 2
NOT USED (low confidence) K. Farah, F. Müller-Plathe, and M. Böhm, “Classical reactive molecular dynamics implementations: state of the art.,” Chemphyschem : a European journal of chemical physics and physical chemistry. 2012. link Times cited: 71
Abstract: Reactive molecular dynamics (RMD) implementations equipped w… read more
Abstract: Reactive molecular dynamics (RMD) implementations equipped with force field approaches to simulate both the time evolution as well as chemical reactions of a broad class of materials are reviewed herein. We subdivide the RMD approaches developed during the last decade as well as older ones already reviewed in 1995 by Srivastava and Garrison and in 2000 by Brenner into two classes. The methods in the first RMD class rely on the use of a reaction cutoff distance and employ a sudden transition from the educts to the products. Due to their simplicity these methods are well suited to generate equilibrated atomistic or material-specific coarse-grained polymer structures. In connection with generic models they offer useful qualitative insight into polymerization reactions. The methods in the second RMD class are based on empirical reactive force fields and implement a smooth and continuous transition from the educts to the products. In this RMD class, the reactive potentials are based on many-body or bond-order force fields as well as on empirical standard force fields, such as CHARMM, AMBER or MM3 that are modified to become reactive. The aim with the more sophisticated implementations of the second RMD class is the investigation of the reaction kinetics and mechanisms as well as the evaluation of transition state geometries. Pure or hybrid ab initio, density functional, semi-empirical, molecular mechanics, and Monte Carlo methods for which no time evolution of the chemical systems is achieved are excluded from the present review. So are molecular dynamics techniques coupled with quantum chemical methods for the treatment of the reactive regions, such as Car-Parinello molecular dynamics. read less
NOT USED (low confidence) A. Barnard and S. Russo, “Development of an improved Stillinger-Weber potential for tetrahedral carbon using ab initio (Hartree-Fock and MP2) methods,” Molecular Physics. 2002. link Times cited: 28
Abstract: An improved interatomic potential for tetrahedral carbon is … read more
Abstract: An improved interatomic potential for tetrahedral carbon is presented. This potential is of the Stillinger-Weber (SW) type and has been determined from calculations performed on a select group of small hydrocarbon molecules, chosen for their similarities to the tetrahedral lattice of bulk diamond. Counterpoise corrected Hartree-Fock (HF) and second-order Møller-Plesset perturbation theory (MP2) calculations were performed on ethane, 2,2-dimethylpropane (neo-pentane, (C5H12), 2-dimethyl-3-dimethylbutane (neobutane, C8H18) and cyclohexane (C6H12) in order to determine the two-body (stretching) and three-body (bond bending) energies. The suitability of these molecules to model the properties of diamond was determined by comparison of CC bond length, well depth, CCC bond angle, simultaneous stretch and bend energy and force constants to those of bulk diamond. It was found that neopentane provided the best overall description of tetrahedral bonded carbon. The ab initio derived stretch and bend energies were fitted to the SW potential energy terms and the SW parameters calculated. The newly parametrized SW potential was then evaluated by calculating the stretch force constants, elastic constants and the X-point phonon modes of bulk diamond. read less
NOT USED (low confidence) M. Schaible, “Empirical Molecular Dynamics Modeling of Silicon and Silicon Dioxide: A Review,” Critical Reviews in Solid State and Materials Sciences. 1999. link Times cited: 28
Abstract: A number of computational methods have been developed over t… read more
Abstract: A number of computational methods have been developed over the last 40 years to simulate the behavior of solid materials with small dimensions. On the macro-scale, Finite Element analysis calculates mechanical stress on micron-sized cantilevers and motors. On the atomic level, newer ab initio methods compute nuclear and electronic behavior of hundred atom models with unprecedented rigor. By implementing the laws of classic mechanics, empirical Molecular Dynamics (MD) programs help bridge these two computational extremes. MD identifies nonelectronic, particle motion for large 100,000 atom cells with good success. MD derives both equilibrium and nonequilibrium properties for many complex condensed regimes; quantitatively (and qualitatively) reaffirms empirical data; aids discovery of new materials processing techniques, and helps predict unknown physical phenomena often only observable under extreme environmental settings. One material of great technical importance to the semiconductor industry is silicon (... read less
NOT USED (high confidence) K. Sasikumar and P. Keblinski, “Effect of chain conformation in the phonon transport across a Si-polyethylene single-molecule covalent junction,” Journal of Applied Physics. 2011. link Times cited: 35
Abstract: We use nonequilibrium molecular dynamics simulations to stud… read more
Abstract: We use nonequilibrium molecular dynamics simulations to study heat transfer across molecular junctions formed by alkane chains covalently bonded to crystalline silicon leads. We focus our studies on the role of chain conformation on phonon transport across junctions and along the chain. We find that in the case of straight chains, all trans conformations, the silicon-polyethylene junction conductance is 180 pW/K, and heat flows ballistically, i.e. with no resistance, along the chain. The introduction of gauche conformations (kinks) leads to a nonzero thermal resistance of the chain and also reduces the junction conductance to 100 pW/K. The chain thermal resistance is proportional to the number of gauche conformations indicating that they act as strong and independent phonon scattering centers. We attribute the 80% enhancement in junction conductance during extension from coiled to straight chain conformation to ballistic (coherent) phonon transport along a straight chain. read less
NOT USED (high confidence) A. Dongare, L. Zhigilei, A. Rajendran, and B. Lamattina, “Interatomic potentials for atomic scale modeling of metal–matrix ceramic particle reinforced nanocomposites,” Composites Part B-engineering. 2009. link Times cited: 15
NOT USED (high confidence) A. S. Barnard, S. Russo, and G. Leach, “Nearest neighbour considerations in Stillinger-Weber type potentials for diamond,” Molecular Simulation. 2002. link Times cited: 5
Abstract: Results of a preliminary investigation into the effect of va… read more
Abstract: Results of a preliminary investigation into the effect of varying the interaction cutoff on the bulk properties of diamond using a Stillinger-Weber (SW) type potential for C (Diamond) are presented. The interaction cutoff is varied over a range that includes and excludes the second-nearest neighbours. Whilst the original SW potential for silicon only included first-nearest neighbours inside the interaction cut-off, subsequent parameterizations for carbon (diamond) have also included second-nearest neighbours. Elastic and vibration properties of diamond were calculated over a range of cutoff distances used and the results show that certain lattice properties exhibit an approximately linear dependence on the interaction cut-off. read less
The long form of the KIM ID including a human readable prefix (100 characters max), two underscores, and the Short KIM ID. Extended KIM IDs can only contain alpha-numeric characters (letters and digits) and underscores and must begin with a letter.
Specifies whether this is a Portable Model (software implementation of an interatomic model); Portable Model with parameter file (parameter file to be read in by a Model Driver); Model Driver (software implementation of an interatomic model that reads in parameters).
The letter grade A was assigned because the normalized error in the computation was 1.70071e-09 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.
vc-forces-numerical-derivative
consistency
Forces computed by the model agree with numerical derivatives of the energy; see full description.
The model is C^2 continuous. This means that the model has continuous energy and continuous derivatives up to order 2.
vc-dimer-continuity-c1
informational
The energy versus separation relation of a pair of atoms is C1 continuous (i.e. the function and its first derivative are continuous); see full description.
Model energy and forces are invariant with respect to rigid-body motion (translation and rotation) for all configurations the model was able to compute.
vc-objectivity
informational
Total energy is unchanged and forces transform correctly under rigid-body translation and rotation; see full description.
All threads give identical results for tested case. Model appears to be thread-safe.
vc-thread-safe
mandatory
The model returns the same energy and forces when computed in serial and when using parallel threads for a set of configurations. Note that this is not a guarantee of thread safety; see full description.
This bar chart plot shows the mono-atomic body-centered cubic (bcc) lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
This graph shows the cohesive energy versus volume-per-atom for the current mode for four mono-atomic cubic phases (body-centered cubic (bcc), face-centered cubic (fcc), simple cubic (sc), and diamond). The curve with the lowest minimum is the ground state of the crystal if stable. (The crystal structure is enforced in these calculations, so the phase may not be stable.) Graphs are generated for each species supported by the model.
This bar chart plot shows the mono-atomic face-centered diamond lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
This graph shows the dislocation core energy of a cubic crystal at zero temperature and pressure for a specific set of dislocation core cutoff radii. After obtaining the total energy of the system from conjugate gradient minimizations, non-singular, isotropic and anisotropic elasticity are applied to obtain the dislocation core energy for each of these supercells with different dipole distances. Graphs are generated for each species supported by the model.
This bar chart plot shows the mono-atomic face-centered cubic (fcc) elastic constants predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
This bar chart plot shows the mono-atomic face-centered cubic (fcc) lattice constant predicted by the current model (shown in red) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
This bar chart plot shows the intrinsic and extrinsic stacking fault energies as well as the unstable stacking and unstable twinning energies for face-centered cubic (fcc) predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
This bar chart plot shows the mono-atomic face-centered cubic (fcc) relaxed surface energies predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
This bar chart plot shows the mono-atomic simple cubic (sc) lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.
Given an xyz file corresponding to a finite cluster of atoms, this Test Driver computes the total potential energy and atomic forces on the configuration. The positions are then relaxed using conjugate gradient minimization and the final positions and forces are recorded. These results are primarily of interest for training machine-learning algorithms.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
This Test Driver uses LAMMPS to compute the cohesive energy of a given monoatomic cubic lattice (fcc, bcc, sc, or diamond) at a variety of lattice spacings. The lattice spacings range from a_min (=a_min_frac*a_0) to a_max (=a_max_frac*a_0) where a_0, a_min_frac, and a_max_frac are read from stdin (a_0 is typically approximately equal to the equilibrium lattice constant). The precise scaling and number of lattice spacings sampled between a_min and a_0 (a_0 and a_max) is specified by two additional parameters passed from stdin: N_lower and samplespacing_lower (N_upper and samplespacing_upper). Please see README.txt for further details.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Computes the elastic constants for an arbitrary crystal. A robust computational protocol is used, attempting multiple methods and step sizes to achieve an acceptably low error in numerical differentiation and deviation from material symmetry. The crystal structure is specified using the AFLOW prototype designation as part of the Crystal Genome testing framework. In addition, the distance from the obtained elasticity tensor to the nearest isotropic tensor is computed.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Computes the cubic elastic constants for some common crystal types (fcc, bcc, sc, diamond) by calculating the hessian of the energy density with respect to strain. An estimate of the error associated with the numerical differentiation performed is reported.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Computes the elastic constants for hcp crystals by calculating the hessian of the energy density with respect to strain. An estimate of the error associated with the numerical differentiation performed is reported.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Computes the equilibrium crystal structure and energy for an arbitrary crystal at zero temperature and applied stress by performing symmetry-constrained relaxation. The crystal structure is specified using the AFLOW prototype designation. Multiple sets of free parameters corresponding to the crystal prototype may be specified as initial guesses for structure optimization. No guarantee is made regarding the stability of computed equilibria, nor that any are the ground state.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Equilibrium lattice constant and cohesive energy of a cubic lattice at zero temperature and pressure.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Calculates lattice constant of hexagonal bulk structures at zero temperature and pressure by using simplex minimization to minimize the potential energy.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
This Test Driver uses LAMMPS to compute the linear thermal expansion coefficient at a finite temperature under a given pressure for a cubic lattice (fcc, bcc, sc, diamond) of a single given species.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Given an extended xyz file corresponding to a non-orthogonal periodic box of atoms, use LAMMPS to compute the total potential energy and atomic forces.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Computes the monovacancy formation energy and relaxation volume for cubic and hcp monoatomic crystals.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
Computes the monovacancy formation and migration energies for cubic and hcp monoatomic crystals.
Test
Test Results
Link to Test Results page
Benchmark time
Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run.
Measured in Millions of Whetstone Instructions (MWI)
The Stephenson-Radny-Smith potential (SRS1996) is a three-body interatomic potential used to model free surface behavior of silicon. It is a generalized form of the classic Stillinger-Weber potential with four additional parameters to better match experimental observations and ab initio calculations of bond lengths and bond energies on the unit cell of the (111)Si free surface.
The model has eleven dimensionless parameters (, , , , , , , , , and ) and two characteristic dimensional scales ( and ). The authors chose the dimensional scales to be identical to those used in Stillinger-Weber. (Stillinger-Weber chose based on the enthalpy of atomization of silicon at and based on the equilibrium lattice spacing of silicon at . Note that there has been some variation in the precise value of from Stillinger-Weber due to a limited number of significant figures in the original parameter value and discrepancies in precise unit conversions. Here we use , which differs slightly from used elsewhere in the OpenKIM model of Stillinger-Weber and used in the LAMMPS potential.)
The authors do not precisely state how the eleven dimensionless parameters were chosen, but instead state that they were chosen to fit a combination of bulk lattice dynamic properties, equilibrium geometries of free surfaces, and bond energies on free surfaces with the constraint that the diamond structure is the most stable phase. Upon stating the values of the coefficients, which are tabulated in Table 1 (along with reference values for Stillinger-Weber), the authors then compared computed results for bond lengths and bond energies based on SRS1996 with results from Stillinger-Weber, ab initio calculations (Brommer, et al. 1992, Stich, et al. 1992 and van den Hoek, et al. 1988) and experiments (Tong, et al. 1987). These ab initio calculations and experiments presumably were used in the fitting of the parameters for SRS1996, but the method for doing so was not explained.
Table 1: Parameter values for Stephenson-Radny-Smith and Stillinger-Weber
Parameter
SRS1996
Stillinger-Weber
6.8932
7.049 556 277
0.3535
0.602 224 558 4
4
4
0
0
1.80
1.80
21.0
21.0
0.5778
1.20
0.7872
1
0.0980
1
0.0500
1/3
-0.0324
0
2.0951
2.0951
2.1672
2.1672
Two-Body Term
The pairwise potential given by the functional form in conjunction with the parameters in Table 1 is plotted below. Curves for Stillinger-Weber and the Lennard-Jones potential are also plotted for reference. We note that both SRS1996 and Stillinger-Weber have a cutoff radius at , but the Lennard-Jones potential has no inherent cutoff radius.
Three-Body Term
A contour plot of the three-body potential, with parameter values in Table 1, for the case when is shown below. A contour plot for the Stillinger-Weber potential is also shown as a basis for comparison.
Finally, the figure below shows the effect of changing and independently in while the angle is fixed at the tetrahedral angle, . The results for both SRS1996 and Stillinger-Weber as a reference are shown. (Although the three-body potential energy of Stillinger-Weber is identically zero for the tetrahedral angle, , its contour plot is shown to emphasize the contrast with SRS1996.)
Summary
Perhaps the most significant departure of SRS1996 from Stillinger-Weber is the much shallower energy well in the three-body potential term as a function of the bond angle . This makes sense in light of the fact that SRS1996 attempts to predict surface behavior, which is inherently anisotropic. Although the strong energy well at the tetrahedral angle, , makes sense for modeling of bulk phenomena using Stillinger-Weber, near the free surface bond angle energies depend on the orientation of the three atoms relative to the surface, and more flexibility in the changing of the bond angle becomes necessary. This increased flexibility in the rotational component of the three-body potential also explains why SRS1996 is not as good as Stillinger-Weber at predicting bulk phenomena. In short, Stillinger-Weber was fit to bulk crystal data and SRS1996 was fit to surface data (as well as some bulk data), and their respective accuracies for bulk versus surface phenomena reflect this.
ThreeBodyCluster_SRS_StephensonRadnySmith_1996_Si__MO_604248666067_000
