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Citation: G.P. Purja Pun, and Y. Mishin (2017), "Optimized interatomic potential for silicon and its application to thermal stability of silicene", Physical Review B, 95(22), . DOI: 10.1103/physrevb.95.224103.
Abstract: An optimized interatomic potential has been constructed for silicon using a modified Tersoff model. The potential reproduces a wide range of properties of Si and improves over existing potentials with respect to point defect structures and energies, surface energies and reconstructions, thermal expansion, melting temperature, and other properties. The proposed potential is compared with three other potentials from the literature. The potentials demonstrate reasonable agreement with first-principles binding energies of small Si clusters as well as single-layer and bilayer silicenes. The four potentials are used to evaluate the thermal stability of free-standing silicenes in the form of nanoribbons, nanoflakes, and nanotubes. While single-layer silicene is found to be mechanically stable at zero Kelvin, it is predicted to become unstable and collapse at room temperature. By contrast, the bilayer silicene demonstrates a larger bending rigidity and remains stable at and even above room temperature. The results suggest that bilayer silicene might exist in a free-standing form at ambient conditions.

LAMMPS pair_style tersoff/mod/c (2017--Purja-Pun-G-P--Si--LAMMPS--ipr1)
Notes: This file was provided by Yuri Mishin (George Mason University) on 2 Nov. 2018. It is identical to the similarly named file in the August 22, 2018 LAMMPS distribution.
File(s):
Citation: Y.A. Du, T.J. Lenosky, R.G. Hennig, S. Goedecker, and J.W. Wilkins (2011), "Energy landscape of silicon tetra-interstitials using an optimized classical potential", physica status solidi (b), 248(9), 2050-2055. DOI: 10.1002/pssb.201147137.
Abstract: Mobile single interstitials can grow into extended interstitial defect structures during thermal anneals following ion implantation. The silicon tetra‐interstitials present an important intermediate structure that can either provide a chain‐like nucleation site for extended structures or form a highly stable compact interstitial cluster preventing further growth. In this paper, dimer searches using the tight‐binding (TB) model by Lenosky et al. and density functional calculations show that the compact ground‐state Ia4 and the I4‐chain are surrounded by high‐lying neighboring local minima.\nTo furthermore explore the phase space of tetra‐interstitial structures an empirical potential is optimized to a database of silicon defect structures. The minima hopping method combined with this potential extensively searches the energy landscape of tetra‐interstitials and discovers several new low‐energy I4 structures. The second lowest‐energy I4 structure turns out to be a distorted ground‐state tri‐interstitial bound with a single interstitial, which confirms that the ground‐state tri‐interstitial may serve as a nucleation center for the extended defects in silicon.

LAMMPS pair_style meam/spline (2011--Du-Y-A--Si--LAMMPS--ipr1)
Notes: This file was taken from the August 22, 2018 LAMMPS distribution. It is listed as being contributed by Alexander Stukowski (Technische Universität Darmstadt)
File(s):
Citation: T. Kumagai, S. Izumi, S. Hara, and S. Sakai (2007), "Development of bond-order potentials that can reproduce the elastic constants and melting point of silicon for classical molecular dynamics simulation", Computational Materials Science, 39(2), 457-464. DOI: 10.1016/j.commatsci.2006.07.013.
Abstract: The Tersoff potential is one of the most widely used interatomic potentials for silicon. However, its poor description of the elastic constants and melting point of diamond silicon is well known. In this research, three bond-order type interatomic potentials have been developed: the first one is fitted to the elastic constants by employing the Tersoff potential function form, the second one is fitted to both the elastic constants and melting point by employing the Tersoff potential function form and the third one is fitted to both the elastic constants and melting point by employing the modified Tersoff potential function form in which the angular-dependent term is improved. All of developed potentials well reproduce the elastic constants of diamond silicon as well as the cohesive energies and equilibrium bond lengths of silicon polytypes. The third potential can reproduce the melting point, while the second one cannot reproduce that. The elastic constants and melting point calculated using the third potential turned out to be C11 = 166.4 GPa, C12 = 65.3 GPa, C44 = 77.1 GPa and Tm = 1681 K. It was also found that only elastic constants can be reproduced using the original Tersoff potential function, and that our proposed angular-dependent term is a key to reproducing the melting point.

LAMMPS pair_style tersoff/mod (2007--Kumagai-T--Si--LAMMPS--ipr1)
Notes: This file was taken from the August 22, 2018 LAMMPS distribution.
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Citation: T.J. Lenosky, B. Sadigh, E. Alonso, V.V. Bulatov, T.D. Rubia, J. Kim, A.F. Voter, and J.D. Kress (2000), "Highly optimized empirical potential model of silicon", Modelling and Simulation in Materials Science and Engineering, 8(6), 825-841. DOI: 10.1088/0965-0393/8/6/305.
Abstract: We fit an empirical potential for silicon using the modified embedded atom (MEAM) functional form, which contains a nonlinear function of a sum of pairwise and three-body terms. The three-body term is similar to the Stillinger-Weber form. We parametrized our model using five cubic splines, each with 10 fitting parameters, and fitted the parameters to a large database using the force-matching method. Our model provides a reasonable description of energetics for all atomic coordinations, Z, from the dimer (Z = 1) to fcc and hcp (Z = 12). It accurately reproduces phonons and elastic constants, as well as point defect energetics. It also provides a good description of reconstruction energetics for both the 30° and 90° partial dislocations. Unlike previous models, our model accurately predicts formation energies and geometries of interstitial complexes - small clusters, interstitial-chain and planar {311} defects.

LAMMPS pair_style meam/spline (2000--Lenosky-T-J--Si--LAMMPS--ipr1)
Notes: This file was taken from the August 22, 2018 LAMMPS distribution. It is listed as being contributed by Alexander Stukowski (Technische Universität Darmstadt)
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Citation: J.F. Justo, M.Z. Bazant, E. Kaxiras, V.V. Bulatov, and S. Yip (1998), "Interatomic potential for silicon defects and disordered phases", Physical Review B, 58(5), 2539-2550. DOI: 10.1103/physrevb.58.2539.
Abstract: We develop an empirical potential for silicon which represents a considerable improvement over existing models in describing local bonding for bulk defects and disordered phases. The model consists of two- and three-body interactions with theoretically motivated functional forms that capture chemical and physical trends as explained in a companion paper. The numerical parameters in the functional form are obtained by fitting to a set of ab initio results from quantum-mechanical calculations based on density-functional theory in the local-density approximation, which include various bulk phases and defect structures. We test the potential by applying it to the relaxation of point defects, core properties of partial dislocations and the structure of disordered phases, none of which are included in the fitting procedure. For dislocations, our model makes predictions in excellent agreement with ab initio and tight-binding calculations. It is the only potential known to describe both the 30°- and 90°-partial dislocations in the glide set {111}. The structural and thermodynamic properties of the liquid and amorphous phases are also in good agreement with experimental and ab initio results. Our potential is capable of simulating a quench directly from the liquid to the amorphous phase, and the resulting amorphous structure is more realistic than with existing empirical preparation methods. These advances in transferability come with no extra computational cost, since force evaluation with our model is faster than with the popular potential of Stillinger-Weber, thus allowing reliable atomistic simulations of very large atomic systems.

LAMMPS pair_style edip (1998--Justo-J-F--Si--LAMMPS--ipr1)
Notes: This file was taken from the August 22, 2018 LAMMPS distribution.
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Citation: M.I. Baskes (1992), "Modified embedded-atom potentials for cubic materials and impurities", Physical Review B, 46(5), 2727-2742. DOI: 10.1103/physrevb.46.2727.
Abstract: In a comprehensive study, the modified embedded-atom method is extended to a variety of cubic materials and impurities. In this extension, all functions are analytic and computationally simple. The basic equations of the method are developed and applied to 26 elements: ten fcc, ten bcc, three diamond cubic, and three gaseous materials. The materials modeled include metals, semiconductors, and diatomic gases, all of which exhibit different types of bonding. Properties of these materials, including equation of state, elastic moduli, structural energies and lattice constants, simple defects, and surfaces, are calculated. The formalism for applying the method to combinations of these elements is developed and applied to the calculation of dilute heats of solution. In all cases, comparison is made to experiment or higher-level calculations when possible.

MEAM parameters
Notes: This file was sent by Mike Baskes (Los Alamos National Laboratory) and posted on 29 Jan. 2010. It includes the MEAM parameters, papers with additional information, and various property evaluations.
File(s):
Citation: J. Tersoff (1988), "New empirical approach for the structure and energy of covalent systems", Physical Review B, 37(12), 6991-7000. DOI: 10.1103/physrevb.37.6991.
Abstract: Empirical interatomic potentials permit the calculation of structural properties and energetics of complex systems. A new approach for constructing such potentials, by explicitly incorporating the dependence of bond order on local environment, permits an improved description of covalent materials. In particular, a new potential for silicon is presented, along with results of extensive tests which suggest that this potential provides a rather realistic description of silicon. The limitations of the potential are discussed in detail.

Notes: This is Tersoff's Si(B) potential, which is the original parameterization of silicon using what is commonly referred to as the "Tersoff"-potential form.

LAMMPS pair_style tersoff (1988--Tersoff-J--Si-b--LAMMPS--ipr1)
Notes: This file was created and verified by Lucas Hale. It has identical parameter values as the Si.tersoff file in the August 22, 2018 LAMMPS distribution and the parameter file used by openKIM model MO_245095684871_001.
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Citation: J. Tersoff (1988), "Empirical interatomic potential for silicon with improved elastic properties", Physical Review B, 38(14), 9902-9905. DOI: 10.1103/physrevb.38.9902.
Abstract: An alternative parametrization is given for a previous empirical interatomic potential for silicon. The new potential is designed to more accurately reproduce the elastic properties of silicon, which were poorly described in the earlier potential. The properties of liquid Si are also improved, but energies of surfaces are less accurate. Detailed tests of the new potential are described.

Notes: This is Tersoff's Si(C) potential, which was an alternative parameterization for improved elastic constants.

LAMMPS pair_style tersoff (1988--Tersoff-J--Si-c--LAMMPS--ipr1)
Notes: This file was created and verified by Lucas Hale. It has identical parameter values as the Si(C) model in the SiCGe.tersoff file in the August 22, 2018 LAMMPS distribution and the parameter file used by openKIM model MO_186459956893_001.
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Citation: J. Tersoff (1986), "New empirical model for the structural properties of silicon", Physical Review Letters, 56(6), 632-635. DOI: 10.1103/physrevlett.56.632.
Abstract: An empirical interatomic potential for covalent systems is proposed, incorporating bond order in an intuitive way. The potential has the form of a Morse pair potential, but with the bond-strength parameter depending upon local environment. A model for Si accurately describes bonding and geometry for may structures, including highly rebonded surfaces.

Notes: This is Tersoff's Si(A) potential, which used a slightly different functional form than the commonly known "Tersoff" potential form. It failed to predict diamond cubic as the ground state structure.

Citation: F.H. Stillinger, and T.A. Weber (1985), "Computer simulation of local order in condensed phases of silicon", Physical Review B, 31(8), 5262-5271. DOI: 10.1103/physrevb.31.5262.
Abstract: A model potential-energy function comprising both two- and three-atom contributions is proposed to describe interactions in solid and liquid forms of Si. Implications of this potential are then explored by molecular-dynamics computer simulation, using 216 atoms with periodic boundary conditions. Starting with the diamond-structure crystal at low temperature, heating causes spontaneous nucleation and melting. The resulting liquid structurally resembles the real Si melt. By carrying out steepest-descent mappings of system configurations onto potential-energy minima, two main conclusions emerge: (1) a temperature-independent inherent structure underlies the liquid phase, just as for "simple" liquids with only pair interactions; (2) the Lindemann melting criterion for the crystal apparently can be supplemented by a freezing criterion for the liquid, where both involve critical values of appropriately defined mean displacements from potential minima.
Citation: F.H. Stillinger, and T.A. Weber (1986), "Erratum: Computer simulation of local order in condensed phases of silicon [Phys. Rev. B 31, 5262 (1985)]", Physical Review B, 33(2), 1451-1451. DOI: 10.1103/physrevb.33.1451.

LAMMPS pair_style sw (1985--Stillinger-F-H--Si--LAMMPS--ipr1)
Notes: This file was taken from the August 22, 2018 LAMMPS distribution.
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Citation: B. Jelinek, S. Groh, M.F. Horstemeyer, J. Houze, S.G. Kim, G.J. Wagner, A. Moitra, and M.I. Baskes (2012), "Modified embedded atom method potential for Al, Si, Mg, Cu, and Fe alloys", Physical Review B, 85(24), 245102. DOI: 10.1103/physrevb.85.245102.
Abstract: A set of modified embedded-atom method (MEAM) potentials for the interactions between Al, Si, Mg, Cu, and Fe was developed from a combination of each element's MEAM potential in order to study metal alloying. Previously published MEAM parameters of single elements have been improved for better agreement to the generalized stacking fault energy (GSFE) curves when compared with ab initio generated GSFE curves. The MEAM parameters for element pairs were constructed based on the structural and elastic properties of element pairs in the NaCl reference structure garnered from ab initio calculations, with adjustment to reproduce the ab initio heat of formation of the most stable binary compounds. The new MEAM potentials were validated by comparing the formation energies of defects, equilibrium volumes, elastic moduli, and heat of formation for several binary compounds with ab initio simulations and experiments. Single elements in their ground-state crystal structure were subjected to heating to test the potentials at elevated temperatures. An Al potential was modified to avoid formation of an unphysical solid structure at high temperatures. The thermal expansion coefficient of a compound with the composition of AA 6061 alloy was evaluated and compared with experimental values. MEAM potential tests performed in this work, utilizing the universal atomistic simulation environment (ASE), are distributed to facilitate reproducibility of the results.

LAMMPS pair_style meam (2012--Jelinek-B--Al-Si-Mg-Cu-Fe--LAMMPS--ipr2)
Notes: This file was sent by Bohumir Jelinek (Mississippi State University) and posted on 3 July 2012. He noted, "This is a MEAM potential for Al, Si, Mg, Cu, Fe alloys. It works with LAMMPS, version 19 Jul 2011 or later, when compiled with MEAM support. Most of the MEAM potential results presented in the accompanying paper can be reproduced with Atomistic Simulation Environment (ASE) and testing routines are provided in ase-atomistic-potential-tests-rev60.tar.gz"
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Citation: S.V. Starikov, N.Y. Lopanitsyna, D.E. Smirnova, and S.V. Makarov (2018), "Atomistic simulation of Si-Au melt crystallization with novel interatomic potential", Computational Materials Science, 142, 303-311. DOI: 10.1016/j.commatsci.2017.09.054.
Abstract: In this work we studied crystallization of the liquid Si-Au system at rapid cooling. For this purpose we performed atomistic simulation with novel interatomic potential. Results of the simulations showed that crystallization proceeds in different ways for pure silicon and Si-Au melt. For the studied binary system, the main factor limiting crystallization is diffusion of Au atoms in the liquid state. Threshold cooling rate for crystallization significantly depends on the Au content.

LAMMPS pair_style adp (2018--Starikov-S-V--Si-Au--LAMMPS--ipr1)
Notes: These files were sent by Dr. Sergey Starikov (Joint Institute for High Temperatures, Russia) on 6 November 2017 and posted with his permission.
File(s): superseded


LAMMPS pair_style adp (2018--Starikov-S-V--Si-Au--LAMMPS--ipr2)
Notes: A new implementation was sent by Dr. Sergey Starikov on 1 October 2018 and posted with his permission with the following comments: "The old version of the potential (above) could not correctly describe several dense structures of silicon (like fcc and hcp) as the explored values of density (rho) exceeded those tabulated. As such, many structures incorrectly had energy lower than diamond lattice. This version fixes the bug by increasing the maximum tabulated rho from 1.0 to 2.0, and gives the right hierarchy of the crystal structures."
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Citation: C. Jiang, D. Morgan, and I. Szlufarska (2012), "Carbon tri-interstitial defect: A model for the DII center", Physical Review B, 86(14), . DOI: 10.1103/physrevb.86.144118.
Abstract: Using a combination of random configuration sampling, molecular dynamics simulated annealing with empirical potential, and ensuing structural refinement by first-principles density functional calculations, we perform an extensive ground-state search for the most stable configurations of small carbon interstitial clusters in SiC. Our search reveals a "magic" cluster number of three atoms, where the formation energy per interstitial shows a distinct minimum. A carbon tri-interstitial cluster with trigonal C3v symmetry is discovered, in which all carbon atoms are fourfold coordinated. In addition to its special thermodynamic stability, its localized vibrational modes are also in a very good agreement with the experimental photoluminescence spectra of the DII center in both 3C- and 4H-SiC. The DII center is one of the most persistent defects in SiC, and we propose that the discovered carbon tri-interstitial is responsible for this center.

LAMMPS pair_style edip/multi (2012--Jiang-C--Si-C--LAMMPS--ipr1)
Notes: This file was taken from the August 22, 2018 LAMMPS distribution. It is listed as being contributed by Chao Jiang (University of Wisconsin)
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Citation: P. Vashishta, R.K. Kalia, A. Nakano, and J.P. Rino (2007), "Interaction potential for silicon carbide: A molecular dynamics study of elastic constants and vibrational density of states for crystalline and amorphous silicon carbide", Journal of Applied Physics, 101(10), 103515. DOI: 10.1063/1.2724570.
Abstract: An effective interatomic interaction potential for SiC is proposed. The potential consists of two-body and three-body covalent interactions. The two-body potential includes steric repulsions due to atomic sizes, Coulomb interactions resulting from charge transfer between atoms, charge-induced dipole-interactions due to the electronic polarizability of ions, and induced dipole-dipole (van der Waals) interactions. The covalent characters of the Si–C–Si and C–Si–C bonds are described by the three-body potential. The proposed three-body interaction potential is a modification of the Stillinger-Weber form proposed to describe Si. Using the molecular dynamics method, the interaction potential is used to study structural, elastic, and dynamical properties of crystalline (3C), amorphous, and liquid states of SiC for several densities and temperatures. The structural energy for cubic (3C) structure has the lowest energy, followed by the wurtzite (2H) and rock-salt (RS) structures. The pressure for the structural transformation from 3C-to-RS from the common tangent is found to be 90 GPa. For 3C-SiC, our computed elastic constants (C11, C12, and C44), melting temperature, vibrational density-of-states, and specific heat agree well with the experiments. Predictions are made for the elastic constant as a function of density for the crystalline and amorphous phase. Structural correlations, such as pair distribution function and neutron and x-ray static structure factors are calculated for the amorphous and liquid state.

LAMMPS pair_style vashishta (2007--Vashishta-P--Si-C--LAMMPS--ipr1)
Notes: This file was taken from the August 22, 2018 LAMMPS distribution.
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Citation: P. Erhart, and K. Albe (2005), "Analytical potential for atomistic simulations of silicon, carbon, and silicon carbide", Physical Review B, 71(3), . DOI: 10.1103/physrevb.71.035211.
Abstract: We present an analytical bond-order potential for silicon, carbon, and silicon carbide that has been optimized by a systematic fitting scheme. The functional form is adopted from a preceding work [Phys. Rev. B 65, 195124 (2002)] and is built on three independently fitted potentials for Si-Si, C-C, and Si-C interaction. For elemental silicon and carbon, the potential perfectly reproduces elastic properties and agrees very well with first-principles results for high-pressure phases. The formation enthalpies of point defects are reasonably reproduced. In the case of silicon stuctural features of the melt agree nicely with data taken from literature. For silicon carbide the dimer as well as the solid phases B1, B2, and B3 were considered. Again, elastic properties are very well reproduced including internal relaxations under shear. Comparison with first-principles data on point defect formation enthalpies shows fair agreement. The successful validation of the potentials for configurations ranging from the molecular to the bulk regime indicates the transferability of the potential model and makes it a good choice for atomistic simulations that sample a large configuration space.

Notes: This entry uses the paper's Si-I interaction, which was recommended for SiC simulations.

LAMMPS pair_style tersoff (2005--Erhart-P--Si-C-I--LAMMPS--ipr1)
Notes: This file was created and verified by Lucas Hale. The parameter values are comparable to those in the SiC_Erhart-Albe.tersoff file in the August 22, 2018 LAMMPS distribution with this file using higher precision for the derived parameters.
File(s):
Citation: P. Erhart, and K. Albe (2005), "Analytical potential for atomistic simulations of silicon, carbon, and silicon carbide", Physical Review B, 71(3), . DOI: 10.1103/physrevb.71.035211.
Abstract: We present an analytical bond-order potential for silicon, carbon, and silicon carbide that has been optimized by a systematic fitting scheme. The functional form is adopted from a preceding work [Phys. Rev. B 65, 195124 (2002)] and is built on three independently fitted potentials for Si-Si, C-C, and Si-C interaction. For elemental silicon and carbon, the potential perfectly reproduces elastic properties and agrees very well with first-principles results for high-pressure phases. The formation enthalpies of point defects are reasonably reproduced. In the case of silicon stuctural features of the melt agree nicely with data taken from literature. For silicon carbide the dimer as well as the solid phases B1, B2, and B3 were considered. Again, elastic properties are very well reproduced including internal relaxations under shear. Comparison with first-principles data on point defect formation enthalpies shows fair agreement. The successful validation of the potentials for configurations ranging from the molecular to the bulk regime indicates the transferability of the potential model and makes it a good choice for atomistic simulations that sample a large configuration space.

Notes: This entry uses the paper's Si-II interaction, which gives better elastic and thermal properties for elemental silicon.

LAMMPS pair_style tersoff (2005--Erhart-P--Si-C-II--LAMMPS--ipr1)
Notes: This file was created and verified by Lucas Hale. The parameter values are identical to the ones in the parameter file used by openKIM model MO_408791041969_001.
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Citation: R. Devanathan, T. Diaz de la Rubia, and W.J. Weber (1998), "Displacement threshold energies in β-SiC", Journal of Nuclear Materials, 253(1-3), 47-52. DOI: 10.1016/s0022-3115(97)00304-8.
Abstract: We have calculated the displacement threshold energies (Ed) for C and Si primary knock-on atoms (PKA) in β-SiC using molecular dynamic simulations. The interactions between atoms were modeled using a modified form of the Tersoff potential in combination with a realistic repulsive potential obtained from density-functional theory calculations. The simulation cell was cubic, contained 8000 atoms and had periodic boundaries. The temperature of the simulation was about 150 K. Our results indicate strong anisotropy in the Ed values for both Si and C PKA. The displacement threshold for Si varies from about 36 eV along [001] to 113 eV along [111], while Ed for C varies from 28 eV along [111] to 71 eV along [111]. These results are in good agreement with experimental observations.

LAMMPS pair_style tersoff/zbl (1998--Devanathan-R--Si-C--LAMMPS--ipr1)
Notes: This file was taken from the August 22, 2018 LAMMPS distribution.
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Citation: J. Tersoff (1994), "Chemical order in amorphous silicon carbide", Physical Review B, 49(23), 16349-16352. DOI: 10.1103/physrevb.49.16349.
Abstract: While ordering in alloy crystals is well understood, short-range ordering in amorphous alloys remains controversial. Here, by studying computer-generated models of amorphous SiC, we show that there are two principal factors controlling the degree of chemical order in amorphous covalent alloys. One, the chemical preference for mixed bonds, is much the same in crystalline and amorphous materials. However, the other factor, the atomic size difference, is far less effective at driving ordering in amorphous material than in the crystal. As a result, the amorphous phase may show either strong ordering (as in GaAs), or weaker ordering (as in SiC), depending upon the relative importance of these two factors.

Notes: This parameterization uses the interactions of 1990--Tersoff-J--Si-C and the cutoff of 1989--Tersoff-J--Si-C, with a slight correction for heat of mixing.

LAMMPS pair_style tersoff (1994--Tersoff-J--Si-C--LAMMPS--ipr1)
Notes: This file was created and verified by Lucas Hale. The parameter values are comparable to the SiC_1994.tersoff file in the August 22, 2018 LAMMPS distribution, with this file having higher numerical precision for the derived mixing parameters.
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Citation: J. Tersoff (1990), "Carbon defects and defect reactions in silicon", Physical Review Letters, 64(15), 1757-1760. DOI: 10.1103/physrevlett.64.1757.
Abstract: The energies of carbon defects in silicon are calculated, using an empirical classical potential, and used to infer defect properties and reactions. Substitutional carbon is found to react with silicon interstitials, with the carbon "kicked out" to form a (100) split interstitial. This interstitial can in turn bind to a second substitutional carbon, relieving stress, in three configurations with similar energies. The results here accord well with a variety of experimental data, including defect structures, activation energies for defect motion, and coupling to strain. A discrepancy with the accepted values for carbon solubility in silicon suggests a reinterpretation of the experimental data.

Notes: This parameterization focused on studying C interstitials in bulk Si. It has a sharp cutoff not suited for unconstrained simulations.

LAMMPS pair_style tersoff (1990--Tersoff-J--Si-C--LAMMPS--ipr1)
Notes: This file was created and verified by Lucas Hale. The parameter values are comparable to the SiC_1990.tersoff file in the August 22, 2018 LAMMPS distribution, with this file having higher numerical precision for the derived mixing parameters.
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Citation: J. Tersoff (1989), "Modeling solid-state chemistry: Interatomic potentials for multicomponent systems", Physical Review B, 39(8), 5566-5568. DOI: 10.1103/physrevb.39.5566.
Abstract: A general form is proposed for an empirical interatomic potential for multicomponent systems. This form interpolates between potentials for the respective elements to treat heteronuclear bonds. The approach is applied to C-Si and Si-Ge systems. In particular, the properties of SiC and its defects are well described.
Citation: J. Tersoff (1990), "Erratum: Modeling solid-state chemistry: Interatomic potentials for multicomponent systems", Physical Review B, 41(5), 3248-3248. DOI: 10.1103/physrevb.41.3248.2.

Notes: This is Tersoff's original multicomponent potential for Si-C interactions.

LAMMPS pair_style tersoff (1989--Tersoff-J--Si-C--LAMMPS--ipr1)
Notes: This file was created and verified by Lucas Hale. The parameter values are comparable to the Si(D)-C interactions in SiCGe.tersoff file in the August 22, 2018 LAMMPS distribution, with this file having higher numerical precision for the derived mixing parameters. The parameters are identical to those in the parameter file used by openKIM model MO_171585019474_001.
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Citation: J. Tersoff (1989), "Modeling solid-state chemistry: Interatomic potentials for multicomponent systems", Physical Review B, 39(8), 5566-5568. DOI: 10.1103/physrevb.39.5566.
Abstract: A general form is proposed for an empirical interatomic potential for multicomponent systems. This form interpolates between potentials for the respective elements to treat heteronuclear bonds. The approach is applied to C-Si and Si-Ge systems. In particular, the properties of SiC and its defects are well described.
Citation: J. Tersoff (1990), "Erratum: Modeling solid-state chemistry: Interatomic potentials for multicomponent systems", Physical Review B, 41(5), 3248-3248. DOI: 10.1103/physrevb.41.3248.2.

Notes: This is Tersoff's original multicomponent potential for Si-Ge interactions.

LAMMPS pair_style tersoff (1989--Tersoff-J--Si-Ge--LAMMPS--ipr1)
Notes: This file was created and verified by Lucas Hale. The parameter values are comparable to the Si(D)-Ge interactions in SiCGe.tersoff file in the August 22, 2018 LAMMPS distribution, with this file having higher numerical precision for the derived mixing parameters. The parameters are identical to those in the parameter file used by openKIM model MO_350526375143_001.
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Citation: S. Munetoh, T. Motooka, K. Moriguchi, and A. Shintani (2007), "Interatomic potential for Si-O systems using Tersoff parameterization", Computational Materials Science, 39(2), 334-339. DOI: 10.1016/j.commatsci.2006.06.010.
Abstract: A parameter set for Tersoff potential has been developed to investigate the structural properties of Si-O systems. The potential parameters have been determined based on ab initio calculations of small molecules and the experimental data of α-quartz. The structural properties of various silica polymorphs calculated by using the new potential were in good agreement with their experimental data and ab initio calculation results. Furthermore, we have prepared SiO2 glass using molecular dynamics (MD) simulations by rapid quenching of melted SiO2. The radial distribution function and phonon density of states of SiO2 glass generated by MD simulation were in excellent agreement with those of SiO2 glass obtained experimentally.

LAMMPS pair_style tersoff (2007--Munetoh-S--Si-O--LAMMPS--ipr1)
Notes: This file was created and verified by Lucas Hale. The parameter values are comparable to the SiO.tersoff file in the August 22, 2018 LAMMPS distribution, with this file having higher numerical precision for the derived mixing parameters.
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Citation: J.Q. Broughton, C.A. Meli, P. Vashishta, and R.K. Kalia (1997), "Direct atomistic simulation of quartz crystal oscillators: Bulk properties and nanoscale devices", Physical Review B, 56(2), 611-618. DOI: 10.1103/physrevb.56.611.
Abstract: Current experimental research aims to reduce the size of quartz crystal oscillators into the submicrometer range. Devices then comprise multimillion atoms and operating frequencies will be in the gigahertz regime. Such characteristics make direct atomic scale simulation feasible using large scale parallel computing. Here, we describe molecular-dynamics simulations on bulk and nanoscale device systems focusing on elastic constants and flexural frequencies. Here we find (a) in order to achieve elastic constants within 1% of those of the bulk requires approximately one million atoms; precisely the experimental regime of interest; (b) differences from continuum mechanical frequency predictions are observable for 17 nm devices; (c) devices with 1% defects exhibit dramatic anharmonicity. A subsequent paper describes the direct atomistic simulation of operating characteristics of a micrometer scale device. A PAPS cosubmission gives algorithmic details.

LAMMPS pair_style vashishta (1997--Broughton-J-Q--Si-O--LAMMPS--ipr1)
Notes: This file was taken from the August 22, 2018 LAMMPS distribution.
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Citation: A. Nakano, R.K. Kalia, and P. Vashishta (1994), "First sharp diffraction peak and intermediate-range order in amorphous silica: finite-size effects in molecular dynamics simulations", Journal of Non-Crystalline Solids, 171(2), 157-163. DOI: 10.1016/0022-3093(94)90351-4.
Abstract: Large-scale molecular dynamics simulations of amorphous silica are carried out on systems containing up to 41472 particles using an effective interatomic potential consisting of two-body and three-body covalent interactions. The intermediate-range order represented by the first sharp diffraction peak (FSDP) in the neutron static structure factor shows a significant dependence on the system size. Correlations in the range 0.4–1.1 nm are found to play a vital role in determining the shape of the FSDP correctly. The calculated structure factor for the largest system is in excellent agreement with neutron diffraction experiments, including the height of the FSDP.

LAMMPS pair_style vashishta (1994--Nakano-A--Si-O--LAMMPS--ipr1)
Notes: This file was taken from the August 22, 2018 LAMMPS distribution.
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Citation: P. Vashishta, R.K. Kalia, J.P. Rino, and I. Ebbsjö (1990), "Interaction potential for SiO2: A molecular-dynamics study of structural correlations", Physical Review B, 41(17), 12197-12209. DOI: 10.1103/physrevb.41.12197.
Abstract: An interaction potential consisting of two-body and three-body covalent interactions is proposed for SiO2. The interaction potential is used in molecular-dynamics studies of structural and dynamical correlations of crystalline, molten, and vitreous states under various conditions of densities and temperatures. The two-body contribution to the interaction potential consists of steric repulsion due to atomic sizes, Coulomb interactions resulting from charge transfer, and charge-dipole interaction to include the effects of large electronic polarizability of anions. The three-body covalent contributions include O-Si-O and Si-O-Si interactions which are angle dependent and functions of Si-O distance. In lattice-structure calculations with the total potential function, α-cristobalite and α-quartz are found to have the lowest and almost degenerate energies, in agreement with experiments. The energies for β-cristobalite, β-quartz, and keatite are found to be higher than those for α-cristobalite and α-quartz. Molecular-dynamics calculations with this potential function correctly describe the short- and intermediate-range order in molten and vitreous states.\n In the latter, partial pair-distribution functions give Si-O, O-O, and Si-Si bond lengths of 1.62, 2.65, and 3.05 Å, respectively. The vitreous state consists of nearly ideal Si(O1/2)4 tetrahedra in corner-sharing configurations. The Si-O-Si bond-angle distribution has a peak at 142° and a full width at half maximum (FWHM) of 25° in good agreement with nuclear magnetic resonance experiments. The calculated static structure factor is also in agreement with neutron-diffraction experiments. Partial static structure factors reveal that intermediate-range Si-Si, O-O, and Si-O correlations between 4 and 8 Å give rise to the first sharp diffraction peak (FSDP). The FSDP is absent in charge-charge structure factor, which indicates that charge neutrality prevails over length scales between 4 and 8 Å. Dynamical correlations in vitreous and molten states, phonon densities of states of crystalline and vitreous SiO2, infrared spectra of crystalline, vitreous and molten states, isotope effect, distribution of rings and their structure in molten and vitreous states, and structural transformations at high pressures will be discussed in subsequent papers.

LAMMPS pair_style vashishta (1990--Vashishta-P--Si-O--LAMMPS--ipr1)
Notes: This file was taken from the August 22, 2018 LAMMPS distribution.
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Citation: B. Beeler, M. Baskes, D. Andersson, M.W.D. Cooper, and Y. Zhang (2017), "A modified Embedded-Atom Method interatomic potential for uranium-silicide", Journal of Nuclear Materials, 495, 267-276. DOI: 10.1016/j.jnucmat.2017.08.025.
Abstract: Uranium-silicide (U-Si) fuels are being pursued as a possible accident tolerant fuel (ATF). This uranium alloy fuel benefits from higher thermal conductivity and higher fissile density compared to uranium dioxide (UO2). In order to perform engineering scale nuclear fuel performance simulations, the material properties of the fuel must be known. Currently, the experimental data available for U-Si fuels is rather limited. Thus, multiscale modeling efforts are underway to address this gap in knowledge. In this study, a semi-empirical modified Embedded-Atom Method (MEAM) potential is presented for the description of the U-Si system. The potential is fitted to the formation energy, defect energies and structural properties of U3Si2. The primary phase of interest (U3Si2) is accurately described over a wide temperature range and displays good behavior under irradiation and with free surfaces. The potential can also describe a variety of U-Si phases across the composition spectrum.

LAMMPS pair_style meam (modified)
Notes: These files were sent by B. Beeler (Idaho National Laboratory) on 21 Mar. 2018 and posted with his permission. Dr. Beeler noted that the provided MEAM parameter files also require the use of a MEAM modification file to be compiled with LAMMPS.
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Date Created: October 5, 2010 | Last updated: November 09, 2018