Three-body cluster potential for Si by Khor and Das Sarma (1988) v000

Kok-Eam Khor; Sankar Das Sarma

doi:10.25950/8e5d84c2

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ThreeBodyBondOrder_KDS_KhorDasSarma_1988_Si__MO_722489435928_000

Interatomic potential for Silicon (Si).
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Title A single sentence description.	Three-body cluster potential for Si by Khor and Das Sarma (1988) 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.	Based on the idea that bonding energies of many substances can be modeled by pairwise interactions moderated by the local environment, we propose a new universal interatomic potential for tetrahedrally bonded materials. We obtain two basic relationships linking equilibrium interatomic distances and cohesive energies to the coordination number for a large range of phases of silicon. The relationships are also valid for germanium and carbon, covering, in the latter case, double and triple carbon-carbon bonds, where pi-bonding is important. Based on these ideas we discuss the construction of the universal interatomic potential for these three substances. This potential, which uses very few parameters, should be useful, particularly for surface studies.
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.	None

Contributor	Anshul Chawla
Maintainer	Anshul Chawla
Developer	Kok-Eam Khor Sankar Das Sarma
Published on KIM	2019
How to Cite	This Model originally published in [1] is archived in OpenKIM [2-5]. [1] Khor KE, Das Sarma S. Proposed universal interatomic potential for elemental tetrahedrally bonded semiconductors. Phys Rev B. 1988;38(5):3318–22. doi:10.1103/PhysRevB.38.3318 — (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] Khor K-E, Sarma SD. Three-body cluster potential for Si by Khor and Das Sarma (1988) v000. OpenKIM; 2019. doi:10.25950/8e5d84c2 [3] Chawla A, Karls DS, Khor K-E, Sarma SD. Three-body bond-order potential by Khor and Das Sarma (1988) v000. OpenKIM; 2019. doi:10.25950/b2df2fd7 [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 [5] Elliott RS, Tadmor EB. Knowledgebase of Interatomic Models (KIM) Application Programming Interface (API). OpenKIM; 2011. doi:10.25950/ff8f563a Click here to download the above citation in BibTeX format.
Citations 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. OpenKIM acknowledges the support of the Allen Institute for AI through the Semantic Scholar project for providing citation information and full text of articles when available, which are used to train the Deep Citation ML algorithm.	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. 78 Citations (6 used) Show Model Used Show All Help us to determine which of the papers that cite this potential actually used it to perform calculations. If you know, click the . Y. Hasegawa, T. Akiyama, A. Pradipto, K. Nakamura, and T. Ito, “Effect of Film Thickness on Structural Stability for BAlN and BGaN Alloys: Bond‐Order Interatomic Potential Calculations,” physica status solidi (b). 2020. link Times cited: 1 Abstract: The effects of film thickness on the relative stability amon… read more Abstract: The effects of film thickness on the relative stability among fivefold coordinated hexagonal and fourfold coordinated wurtzite and zinc blende structures in BAlN and BGaN alloys are theoretically investigated based on empirical bond‐order potential calculations. It is revealed that the trend of stable structure in BAlN alloys is different from that of BGaN alloys. The film thickness for the stabilization of the hexagonal structure increases with boron composition x for BxGa1–xN alloys, whereas the thickness decreases for BxAl1–xN alloys. The difference in the stabilization of the hexagonal structure between BxAl1–xN and BxGa1–xN alloys is due to the inhibition of in‐plane lattice relaxation in BxAl1–xN alloys. These results suggest that our approach using the bond‐order potential is feasible to investigate the stability of alloy systems with not only tetrahedrally coordinated forms such as the wurtzite and zinc blende structures but also specific forms containing the fivefold coordinated hexagonal structure. read less T. Ito, T. Ito, D. Ammi, T. Akiyama, and K. Nakamura, “Theoretical investigations of polytypism in AlN thin films,” physica status solidi (a). 2010. link Times cited: 1 Abstract: The polytypism in AlN is theoretically investigated using ab… read more Abstract: The polytypism in AlN is theoretically investigated using ab initio pseudopotential, empirical interatomic potential, and Monte Carlo simulation. In bulk form, 2H‐AlN is stable without polytypes because of its large energy profit to 3C, 6H, and 4H structures. On the Si(001) substrate, the AlN thin films varies their structures from 3C at the film thickness h ≤ 4 monolayers (MLs) to (0001)‐oriented 2H tilted 5° at the h ≥ 2345 MLs via (0001)‐oriented 2H with two misfit dislocations. This reveals that the large lattice mismatch system destabilizes the metastable 3C‐AlN(001) to make the stable 2H‐AlN appear with different orientation. The 4H‐AlN can be stably formed on the 4H‐SiC(11‐20) under Al‐rich condition, whereas the 2H‐AlN may appear under N‐rich condition. This results from the distinctive behavior of Al (N) after N (Al) pre‐depositions. These results are consistent with experimental findings for the polytypism in AlN thin films grown on various substrates. read less W. Chen, H. C. Cheng, and Y. Hsu, “Mechanical Properties of Carbon Nanotubes Using Molecular Dynamics Simulations with the Inlayer van der Waals Interactions,” Cmes-computer Modeling in Engineering & Sciences. 2007. link Times cited: 34 Abstract: The evaluation of the fundamental mechanical properties of s… read more Abstract: The evaluation of the fundamental mechanical properties of single/multi-walled carbon nanotubes(S/MWCNTs) is of great importance for their industrial applications. The present work is thus devoted to the determination of various mechanical properties of S/MWCNTs using molecular dynamics (MD) simulations. The study first focuses on the exploration of the effect of the weak inlayer van der Waals (vdW) atomistic interactions on the mechanical properties of S/MWCNTs. Secondly, in addition to the zig-zag and armchair types of CNTs, the hybrid type of MWCNTs that comprise a zig-zag outer tube and an inner armchair tube is also analyzed. Thirdly, the investigation is extended to deal with the influence of the axial orientation mismatch between the inner and outer layers of MWCNTs on the associated mechanical properties. Lastly, the behaviors of the interlayer shear force/strength of MWCNTs are discussed in detail. In the MD simulations, the force field between two carbon atoms is modeled with the Tersoff-Brenner (TB) potential while the inlayer/interlayer vdW atomistic interactions are simulated with the Lennard-Jones (L-J) potential. The effectiveness of the MD simulations is demonstrated by comparing the computed results with the theoretical/experimental data available in literature. Some interesting and essential results are pre1 Tsing Hua Chair Professor, Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, Taiwan 30013, R.O.C., whchen@pme.nthu.edu.tw 2 Professor, Department of Aerospace and Systems Engineering, Feng Chia University, Taichung, Taiwan 40724, R.O.C., hccheng@fcu.edu.tw 3 Graduate Student, Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, Taiwan 30013, R.O.C. sented. With different dimensions and geometries of CNTs, the inlayer vdW atomistic interactions can have up to about 9% increase of the elastic moduli, 27% decrease of the Poisson’s ratios, 12% growth of the shear moduli, and 13% enhancement of the interlayer shear strength. The mechanical properties of the hybrid MWCNTs are found to be midway between the zig-zag and armchair MWCNTs. It is also detected that the axial orientation mismatch between the inner and outer layers of a double-walled CNT has a trivial impact on the mechanical properties of CNTs. To separate the inner layer of a double-walled CNT from its outer layer, it requires a minimum external force of 0.889nN for the zig-zag type, 0.550 nN for hybrid type and 0.493nN for the armchair type. In summary, the effect of the inlayer vdW atomistic interactions can not be neglected and should receive attention in the MD simulations of the mechanical properties of CNTs. Keyword: Molecular Dynamics Simulation, Carbon Nanotubes, Inlayer van der Waals Force, Mechanical Properties. read less K. Sano, T. Akiyama, K. Nakamura, and T. Ito, “A Monte-Carlo simulation study of twinning formation in InP nanowires,” Journal of Crystal Growth. 2007. link Times cited: 20 S. Ethier and L. J. Lewis, “Epitaxial growth of Si_1−xGe_x on Si(100)2 × 1: A molecular-dynamics study,” Journal of Materials Research. 1992. link Times cited: 21 Abstract: We use molecular-dynamics simulations to study the growth of… read more Abstract: We use molecular-dynamics simulations to study the growth of pure Si, Si_0.5Ge_0.5, and pure Ge on the 2 × 1 reconstructed surface of Si(100) in a way appropriate to the fabrication of thin films by the method of molecular-beam epitaxy (MBE), namely sequential deposition of energetic atoms. The atoms interact with one another via effective potentials of the Stillinger–Weber form, with parameters adjusted such as to describe all possible types of triplet interactions. Motivated by numerous experimental studies of MBE-grown films, we investigate in particular the structure of the deposits as a function of substrate temperature. We find in all three cases that at low substrate temperatures, poorly ordered structures form, while at high substrate temperatures, epitaxial growth takes place. The presence of Ge limits the number of crystalline overlayers that form, even though it appears to favor a more-ordered structure in the initial stages of growth. For pure Ge epitaxy, in particular, only the first three layers are crystalline, after which growth appears to proceed by the formation of islands, reminiscent of the Stranski–Krastanow growth scheme, and in qualitative agreement with recent experimental and theoretical work. In all samples, annealing improves the quality of the films—at least when grown at sufficiently high substrate temperatures. The interdiffusion of the species at the substrate-deposit interface is also examined. read less S. Ethier and L. J. Lewis, “Molecular-Dynamics Study of the Growth of Si1- xGe x on Si(100)2×1,” MRS Proceedings. 1990. link Times cited: 0 Y. Xie, K. Shibata, and T. Mizoguchi, “A defect formation mechanism induced by structural reconstruction of a well-known silicon grain boundary.,” Acta Materialia. 2023. link Times cited: 1 J. Harrison, S. Stuart, and D. Brenner, “Atomic-Scale Simulation of Tribological and Related Phenomena,” Handbook of Micro/Nano Tribology. 2020. link Times cited: 3 Y. Hasegawa, T. Akiyama, A. Pradipto, K. Nakamura, and T. Ito, “Empirical interatomic potential approach to the stability of graphitic structure in BAlN and BGaN alloys,” Journal of Crystal Growth. 2018. link Times cited: 6 A. Kubo, S. Nagao, and Y. Umeno, “Molecular dynamics study of deformation and fracture in SiC with angular dependent potential model,” Computational Materials Science. 2017. link Times cited: 7 R. Kaida, T. Akiyama, K. Nakamura, and T. Ito, “Theoretical study for misfit dislocation formation at InAs/GaAs(001) interface,” Journal of Crystal Growth. 2016. link Times cited: 8 A. Akimov and O. Prezhdo, “Large-Scale Computations in Chemistry: A Bird’s Eye View of a Vibrant Field.,” Chemical reviews. 2015. link Times cited: 171 A. Erdemir and J. Luo, “Guest editorial: Special issue on superlubricity,” Friction. 2014. link Times cited: 4 S. Sinnott and D. Brenner, “Three decades of many-body potentials in materials research,” MRS Bulletin. 2012. link Times cited: 45 Abstract: A brief history of atomic simulation as it was used in chemi… read more Abstract: A brief history of atomic simulation as it was used in chemistry, physics, and materials science is presented starting with seminal work by Eyring in the 1930s through to current work and future challenges. This article provides the background and perspective needed to understand the ways in which reactive many-body potentials developed over the last three decades and have impacted materials research. It also explains the way in which this substantial impact on the field has been facilitated by increases in computational resources and traces the development of reactive potentials, which have steadily increased in complexity and sophistication over time. Together with the other contributions in this issue of MRS Bulletin , this article will help guide and inspire the next generation of computational materials scientists and engineers as they build on current capabilities to expand atomic simulation into new and exciting areas of materials research. read less M. Hirano, H. Murase, T. Nitta, and T. Ito, “Evaluation of friction transition for metal-semiconductor interfaces using model potential comprising three-body contributions,” Journal of Physics: Conference Series. 2010. link Times cited: 3 Abstract: Whether or not the friction transition [1, 2] occurs in the … read more Abstract: Whether or not the friction transition [1, 2] occurs in the frictional systems of W(011) and Si(001) atomically clean surfaces has been examined in relation to a previous ultrahigh vacuum scanning tunneling microscopy experiment investigating friction transition. This examination takes into account of empirical inter-atomic potentials with three-body interactions. To obtain equilibrium atomic arrangements of the frictional system for evaluating friction transition, the parameters of the interatomic potential applicable for tetrahedrally bonded materials were examined. From studying the criterion of the friction transition for the frictional systems of W(011) and Si(001), it has been concluded that friction transition does not occur for the real systems, which supports the experimental results of a previous ultrahigh vacuum scanning tunneling microscopy experiment. read less T. Yamashita, T. Akiyama, K. Nakamura, and T. Ito, “Theoretical investigation on the structural stability of GaAs nanowires with two different types of facets,” Physica E-low-dimensional Systems & Nanostructures. 2010. link Times cited: 15 T. Yamashita, T. Akiyama, K. Nakamura, and T. Ito, “Theoretical investigation on the structural stability of GaP nanowires with 111 facets,” Applied Surface Science. 2009. link Times cited: 1 T. Ito, N. Takasu, T. Akiyama, and K. Nakamura, “Systematic theoretical investigations for contribution of lattice constraint to novel atomic arrangements in alloy semiconductor thin films,” Applied Surface Science. 2009. link Times cited: 3 T. Yamashita, K. Sano, T. Akiyama, K. Nakamura, and T. Ito, “Theoretical investigations on the formation of wurtzite segments in group III–V semiconductor nanowires,” Applied Surface Science. 2008. link Times cited: 15 T. Ito, T. Akiyama, K. Nakamura, and T. Ito, “Theoretical investigation on structural stability of InN thin films on 3C–SiC(0 0 1),” Applied Surface Science. 2008. link Times cited: 1 Y.-long Chen and D. P. Yang, “The Basics of Lattice Dynamics.” 2007. link Times cited: 0 H. Joe, T. Akiyama, K. Nakamura, K. Kanisawa, and T. Ito, “An empirical potential approach to the structural stability of InAs stacking-fault tetrahedron in InAs/GaAs(1 1 1),” Journal of Crystal Growth. 2007. link Times cited: 7 C. Wang and K. Ho, “Tight‐Binding Molecular Dynamics Studies of Covalent Systems.” 2007. link Times cited: 3 F. S. A. Muriefah, F. Luca, and A. Togbé, “Computational Methods.” 2006. link Times cited: 171 T. Ito, K. Sano, T. Akiyama, and K. Nakamura, “A simple approach to polytypes of SiC and its application to nanowires,” Thin Solid Films. 2006. link Times cited: 34 Y. Kangawa, K. Kakimoto, T. Ito, and A. Koukitu, “Thermodynamic stability of in1-x-yGaxAlyN on GaN and InN,” Physica Status Solidi (c). 2006. link Times cited: 3 Abstract: We studied the thermodynamic stability of InGaAlN alloy base… read more Abstract: We studied the thermodynamic stability of InGaAlN alloy based on calculations of enthalpy of mixing using empirical interatomic potentials. We also investigated the influence of lattice constraint from the bottom layer, i.e., (0001)GaN or (0001)InN, on thermodynamic stability of InGaAlN thin films. The results suggest that the maximum point of enthalpy of mixing shifted toward the In-rich side in the case of InGaAlN/GaN and toward the In-poor side in the case of InGaAlN/InN compared with that of bulk In1–x–yGaxAlyN at x = 0, y = 0.5. This implies that lattice constraint from the bottom layer has a significant influence on thermodynamic stability of thin films. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) read less A. Tekin and B. Hartke, “GLOBAL GEOMETRY OPTIMIZATION OF SILICON CLUSTERS EMPLOYING EMPIRICAL POTENTIALS, DENSITY FUNCTIONALS, AND AB INITIO CALCULATIONS,” Journal of Theoretical and Computational Chemistry. 2005. link Times cited: 13 Abstract: Sin clusters in the size range n = 4–30 have been investigat… read more Abstract: Sin clusters in the size range n = 4–30 have been investigated using a combination of global structure optimization methods with DFT and ab initio calculations. One of the central aims is to provide explanations for the structural transition from prolate to spherical outer shapes at about n = 25, as observed in ion mobility measurements. Firstly, several existing empirical potentials for silicon and a newly generated variant of one of them were better adapted to small silicon clusters, by global optimization of their parameters. The best resulting empirical potentials were then employed in global cluster structure optimizations. The most promising structures from this stage were relaxed further at the DFT level with the hybrid B3LYP functional. For the resulting structures, single point energies have been calculated at the LMP2 level with a reasonable medium-sized basis set, cc-pVTZ. These DFT and LMP2 calculations were also carried out for the best structures proposed in the literature, including the most recent ones, to obtain the currently best and most complete overall picture of the structural preferences of silicon clusters. In agreement with recent findings, results obtained at the DFT level do support the shape transition from prolate to spherical structures, beginning with Si26 (albeit not completely without problems). In stark contrast, at the LMP2 level, the dominance of spherical structures after the transition region could not be confirmed. Instead, just as below the transition region, prolate isomers are obtained as the lowest-energy structures for n ≤ 29. We conclude that higher (probably multireference) levels of theoretical treatments are needed before the puzzle of the silicon cluster shape transition at n = 25 can safely be considered as explained. read less P. Gunes, Şi̇mşek S., and S. Erkoç, “a Comparative Study of Empirical Potential Energy Functions,” International Journal of Modern Physics C. 2004. link Times cited: 2 Abstract: A comparative study has been performed for silicon microclus… read more Abstract: A comparative study has been performed for silicon microclusters, Si3 and Si4, considering fifteen different empirical potential energy functions. It has been found that only two of the empirical potential energy functions give linear structure more stable for Si3, the remaining potential functions give triangular structure as more stable. In the case of Si4 microclusters eight potential functions give open tetrahedral structure as more stable, two functions give perfect tetrahedral as more stable, three functions give square structure as more stable, and two functions give linear structure as more stable. read less T. Ito, K. Nakamura, Y. Kangawa, K. Shiraishi, A. Taguchi, and H. Kageshima, “Systematic theoretical investigations of miscibility in Si1−x−yGexCy thin films,” Applied Surface Science. 2003. link Times cited: 1 F. El-Mellouhi, W. Sekkal, and A. Zaoui, “A modified Tersoff potential for the study of finite temperature properties of BP,” Physica A-statistical Mechanics and Its Applications. 2002. link Times cited: 16 T. Ito and Y. Kangawa, “Theoretical investigations of thermodynamic stability for Si1−x−yGexCy,” Journal of Crystal Growth. 2002. link Times cited: 3 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 K. Shiraishi, Y. Y. Suzuki, H. Kageshima, and T. Ito, “Theoretical investigation of inter-surface diffusion on non-planar GaAs surfaces,” Applied Surface Science. 1998. link Times cited: 7 A. Mazzone, “A molecular dynamics study of film deposition on vicinal surfaces : Ag/Si,” Philosophical Magazine Part B. 1998. link Times cited: 1 Abstract: The purpose of this study is to analyse step effects on the … read more Abstract: The purpose of this study is to analyse step effects on the deposition of Ag onto Si by using a molecular dynamics simulation method with classical interatomic potentials. The step element is contained in the vicinal shape of the Si surface and the study is divided into two parts. In the first part a study is made of the reconstruction of vicinal surfaces in Si at room temperature. The structure used in these calculations represents in a simplified form the experimental structure as it has only steps along a given miscut angle and no terraces. The second part is an analysis of the deposition of Ag onto the reconstructed Si surface either of the vicinal or of the singular type. For both reconstruction and deposition a broad investigation has been made on the effects of geometrical parameters and of physical quantities, such as interatomic potentials and heat exchange mechanisms. It has been found that the vicinal Si breaks into a more complicated structure containing many facets. This structure is... read less Z. Zhang, F. Wu, and M. Lagally, “AN ATOMISTIC VIEW OF Si(001) HOMOEPITAXY1,” Annual Review of Materials Science. 1997. link Times cited: 25 Abstract: ▪ Abstract Growth of thin films from atoms deposited from th… read more Abstract: ▪ Abstract Growth of thin films from atoms deposited from the gas phase is intrinsically a non-equilibrium phenomenon dictated by a competition between kinetics and thermodynamics. Precise control of the growth becomes possible only after achieving an understanding of this competition. In this review, we present an atomistic view of the various kinetic aspects in a model system, the epitaxy of Si on Si(001), as revealed by scanning tunneling microscopy and total-energy calculations. Fundamentally important issues investigated include adsorption dynamics and energetics, adatom diffusion, nucleation, sticking, and detachment. We also briefly discuss the inverse process of growth, removal by sputtering or etching. We aim our discussions to an understanding at a quantitative level whenever possible. read less E. Kaxiras, “Review of atomistic simulations of surface diffusion and growth on semiconductors,” Computational Materials Science. 1996. link Times cited: 17 E. P. Andribet, J. Domínguez-Vázquez, Pérez-Martı́n A., E. Alonso, and Jiménez-Rodrı́guez J. J., “Empirical approach for the interatomic potential of carbon,” Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms. 1996. link Times cited: 4 X. Liu, “New model of potential energy functions for atomic solids. Part 2. New potentials of silicon and germanium crystals,” Journal of Molecular Structure-theochem. 1995. link Times cited: 1 A. A. Valuev, A. S. Kaklyugin, and H. E. Norman, “Molecular modelling of the chemical interaction of atoms and molecules with a surface,” Russian Chemical Reviews. 1995. link Times cited: 3 Abstract: The modelling of a surface as an assembly of moving atoms in… read more Abstract: The modelling of a surface as an assembly of moving atoms interacting with one another and with an incident particle is examined. Both dynamic methods for the modelling of a surface (for short times) and probability methods (for long times) are analysed. The Massey adiabaticity criterion has been used to determine the regions of applicability of the methods of molecular dynamics. Within the framework of probability methods, the chemical bond is described with the aid of Harrison's generalised periodic system of the elements. Together with the general modeling problems, the reconstruction of the surface, physical and chemical sorption, as well as the modification of the surface and of its morphology as a result of the multiple repetition of elementary processes (precipitation, etching, corrosion) are discussed. The bibliography includes 169 references. read less V. Kirsanov and I. Yanov, “Fullerene molecule structure with an interstitial,” Physics Letters A. 1994. link Times cited: 4 M. D. Souza and G. Amaratunga, “A study of the configurations of boron in silicon using an empirical approach,” Computational Materials Science. 1994. link Times cited: 1 C. S. Carmer, B. Weiner, and M. Frenklach, “Molecular dynamics with combined quantum and empirical potentials: C2H2 adsorption on Si(100),” Journal of Chemical Physics. 1993. link Times cited: 71 Abstract: Classical trajectory calculations were employed to study the… read more Abstract: Classical trajectory calculations were employed to study the reaction of acetylene with dimer sites on the Si(100) surface at 105 K. Two types of potential energy functions were combined to describe interactions for different regions of the model surface. A quantum mechanical potential based on the semiempirical AM1 Hamiltonian was used to describe interactions between C2H2 and a portion of the silicon surface, while an empirically parametrized potential was developed to extend the size of the surface and simulate the dynamics of the surrounding silicon atoms. Reactions of acetylene approaching different sites were investigated, directly above a surface dimer, and between atoms from separate dimers. In all cases, the outcome of C2H2 surface collisions was controlled by the amount of translational energy possessed by the incoming molecule. Acetylene molecules with high translational energy reacted with silicon dimers to form surface species with either one or two Si–C bonds. Those molecules with low transl... read less X. Yin and C. E. Gounaris, “Search methods for inorganic materials crystal structure prediction,” Current Opinion in Chemical Engineering. 2022. link Times cited: 11 T. Ito, S. Inahama, T. Akiyama, and K. Nakamura, “Systematic theoretical investigations of compositional inhomogeneity in InxGa1- xN thin films on GaN(0001),” Journal of Crystal Growth. 2007. link Times cited: 4 S. Heo, S. Sinnott, D. Brenner, and J. Harrison, “Computational Modeling of Nanometer-Scale Tribology.” 2005. link Times cited: 19 R. Wagner and E. Gulari, “Simulation of Mechanisms in Strained Silicon Germanium Epitaxy,” MRS Proceedings. 2001. link Times cited: 0 Abstract: Growth of strained semiconductors can lead to self-assembly … read more Abstract: Growth of strained semiconductors can lead to self-assembly of interesting structures such as quantum dots. Simulation of this growth requires an accurate and efficient model for the interactions of lattice mismatched materials. We present a potential for calculating the bond energies in a diamond-like crystal of silicon and germanium. With this potential we predict the strain profiles in an embedded quantum dot and discuss the mechanisms of island formation. read less T. Ito, “Atomistic simulation of epitaxial growth processes.” 2001. link Times cited: 0 X. Liu, “NEW MODEL OF POTENTIAL-ENERGY FUNCTIONS FOR ATOMIC SOLIDS,” Journal of the Chemical Society, Faraday Transactions. 1995. link Times cited: 2 Abstract: A new theoretical model of potential-energy functions for at… read more Abstract: A new theoretical model of potential-energy functions for atomic solids has been developed. An angular factor has been included in this model and its effect has been discussed. Using this new model a new preliminary potential for silicon crystal has been derived. The calculated phonon dispersion curve along the [q00] direction, using this new potential, has been given. A good agreement has been found with experiment. read less T. Ito, “Structural metastability in thin films on (001) zinc blende substrate.” 1993. link Times cited: 0 S. Sarma and K. E. Khor, “Empirical potential approach to the stability and energetics of thin films and surfaces,” Applied Surface Science. 1992. link Times cited: 1 A. Carlsson, “Beyond Pair Potentials in Elemental Transition Metals and Semiconductors,” Journal of Physics C: Solid State Physics. 1990. link Times cited: 169 G. Ackland, “A Pair Potential Model of Covalent Bonding in Silicon.” 1990. link Times cited: 0 A. Carlsson, “Angular Forces in Transition Metals and Diamond Structure Semiconductors.” 1989. link Times cited: 1 D. J. Oh and R. Johnson, “A Semi-Empirical Potential for Graphite,” MRS Proceedings. 1988. link Times cited: 4 Z. Fthenakis, I. Petsalakis, V. Tozzini, and N. Lathiotakis, “Evaluating the performance of ReaxFF potentials for sp2 carbon systems (graphene, carbon nanotubes, fullerenes) and a new ReaxFF potential,” Frontiers in Chemistry. 2022. link Times cited: 7 Abstract: We study the performance of eleven reactive force fields (Re… read more Abstract: We study the performance of eleven reactive force fields (ReaxFF), which can be used to study sp2 carbon systems. Among them a new hybrid ReaxFF is proposed combining two others and introducing two different types of C atoms. The advantages of that potential are discussed. We analyze the behavior of ReaxFFs with respect to 1) the structural and mechanical properties of graphene, its response to strain and phonon dispersion relation; 2) the energetics of (n, 0) and (n, n) carbon nanotubes (CNTs), their mechanical properties and response to strain up to fracture; 3) the energetics of the icosahedral C60 fullerene and the 40 C40 fullerene isomers. Seven of them provide not very realistic predictions for graphene, which made us focusing on the remaining, which provide reasonable results for 1) the structure, energy and phonon band structure of graphene, 2) the energetics of CNTs versus their diameter and 3) the energy of C60 and the trend of the energy of the C40 fullerene isomers versus their pentagon adjacencies, in accordance with density functional theory (DFT) calculations and/or experimental data. Moreover, the predicted fracture strain, ultimate tensile strength and strain values of CNTs are inside the range of experimental values, although overestimated with respect to DFT. However, they underestimate the Young’s modulus, overestimate the Poisson’s ratio of both graphene and CNTs and they display anomalous behavior of the stress - strain and Poisson’s ratio - strain curves, whose origin needs further investigation. read less Y. Kurniawan et al., “Bayesian, frequentist, and information geometric approaches to parametric uncertainty quantification of classical empirical interatomic potentials.,” The Journal of chemical physics. 2021. link Times cited: 6 Abstract: In this paper, we consider the problem of quantifying parame… read more Abstract: In this paper, we consider the problem of quantifying parametric uncertainty in classical empirical interatomic potentials (IPs) using both Bayesian (Markov Chain Monte Carlo) and frequentist (profile likelihood) methods. We interface these tools with the Open Knowledgebase of Interatomic Models and study three models based on the Lennard-Jones, Morse, and Stillinger-Weber potentials. We confirm that IPs are typically sloppy, i.e., insensitive to coordinated changes in some parameter combinations. Because the inverse problem in such models is ill-conditioned, parameters are unidentifiable. This presents challenges for traditional statistical methods, as we demonstrate and interpret within both Bayesian and frequentist frameworks. We use information geometry to illuminate the underlying cause of this phenomenon and show that IPs have global properties similar to those of sloppy models from fields, such as systems biology, power systems, and critical phenomena. IPs correspond to bounded manifolds with a hierarchy of widths, leading to low effective dimensionality in the model. We show how information geometry can motivate new, natural parameterizations that improve the stability and interpretation of uncertainty quantification analysis and further suggest simplified, less-sloppy models. read less Y. Hasegawa, T. Akiyama, A. Pradipto, K. Nakamura, and T. Ito, “Theoretical investigations on the structural stability and miscibility in BAlN and BGaN alloys: bond-order interatomic potential calculations,” Japanese Journal of Applied Physics. 2019. link Times cited: 5 Abstract: Structural stability and miscibility of BxAl1−xN and BxGa1−x… read more Abstract: Structural stability and miscibility of BxAl1−xN and BxGa1−xN alloys including 3-fold coordinated hexagonal (Hex), 4-fold coordinated wurtzite (WZ) and zinc blende (ZB) structures are systematically investigated based on empirical bond-order potential (BOP), which incorporates electrostatic energies due to bond and ionic charges. We find that the Hex structure is stabilized for free-standing BxAl1−xN and BxGa1−xN alloys with boron composition x > 0.9 while the ZB (WZ) structure is stabilized for 0.25 ≤ x ≤ 0.9 ( x < 0.25 ) both in BxAl1−xN and BxGa1−xN alloys due to the electrostatic energy. Furthermore, the miscibility of BxAl1−xN and BxGa1−xN alloys with 4-fold coordinated structures are found to be higher than that with Hex structure owing to the chemical energy contribution to the excess energy. These results suggest that our empirical interatomic potentials approach is feasible to clarify structural stability not only for the 3-fold coordinated Hex structure but also 4-fold coordinated WZ and ZB structures in BxAl1−xN and BxGa1−xN alloys. read less S. Tsumuki, T. Akiyama, A. Pradipto, K. Nakamura, and T. Ito, “Theoretical investigations on the growth mode of GaN thin films on an AlN(0001) substrate,” Japanese Journal of Applied Physics. 2019. link Times cited: 2 Abstract: The growth modes of GaN thin films on an AlN(0001) substrate… read more Abstract: The growth modes of GaN thin films on an AlN(0001) substrate are systematically investigated using our macroscopic theory with the aid of empirical interatomic potential and ab initio calculations. Using empirical interatomic potential calculations, we demonstrate that a GaN/AlN(0001) system with misfit dislocation (MD) is stabilized compared with a coherently grown system when the GaN film thickness exceeds six monolayers. According to the calculated results including the surface energy of GaN, the macroscopic free energy calculations for the growth mode imply that the growth of GaN on AlN(0001) proceeds along the lower-energy path from two-dimensional coherent (2D-coherent) to 2D-MD under Ga-rich conditions but from 2D-coherent to three-dimensional coherent with truncated hexagonal pyramid islands consisting of { 10 1 ¯ 3 } facets under N-rich conditions owing to surface energy anisotropy, which depends strongly on the growth conditions. These results suggest that surface energy anisotropy is crucial for the growth of GaN on an AlN(0001) substrate. read less K. Yonemoto, T. Akiyama, A. Pradipto, K. Nakamura, and T. Ito, “Effect of surface reconstructions on misfit dislocation formation in InAs/GaAs(001),” Japanese Journal of Applied Physics. 2018. link Times cited: 0 Abstract: The effect of surface reconstructions on misfit dislocation … read more Abstract: The effect of surface reconstructions on misfit dislocation (MD) formation in InAs/GaAs(001) is theoretically investigated using empirical interatomic potentials. According to the calculated cohesive energy using empirical interatomic potentials, in the case of InAs/GaAs(001) system applied surface reconstruction, the system with MD of a 5/7-atom ring core structure is stable compared with a coherently grown system at 3.0 monolayer, which is larger than that of the ideal surface. This result reveals that the energy gain due to MD formation on the reconstructed surface is smaller than that of the ideal surface. The analysis of atomic configurations of the reconstructed surface with MD confirms that the strains caused by MD formation destabilize the reconstructed surface. Furthermore, we estimate the growth behavior of InAs/GaAs(001) using macroscopic theory and find that MD formation is suppressed by surface reconstruction. These results suggest that surface reconstruction is crucial for MD formation and the resultant growth behavior. read less T. Ito, T. Akiyama, and K. Nakamura, “Theoretical Investigations for Strain Relaxation and Growth Mode of InAs Thin Layers on GaAs(110),” physica status solidi (b). 2018. link Times cited: 2 Abstract: The growth mode of InAs/GaAs(110) is systematically investig… read more Abstract: The growth mode of InAs/GaAs(110) is systematically investigated using our macroscopic theory with the aid of ab initio calculations that determine the parameter values used in the macroscopic theory. Formations of misfit dislocation and island are employed as strain relaxation mechanisms. The calculated results reveal that the misfit dislocation formation generally leads to two‐dimensional growth of InAs on GaAs(110) because of its small formation energy compared with that on GaAs(001). On the other hand, three‐dimensional growth mode appears with insertion of an In0.25Ga0.75As strain‐reducing layer between InAs and GaAs, since the strain relaxation induced by the insertion layer reduces the surface energy from 51 to 49 meV Å−2 that prefers the three‐dimensional island formation. These findings are consistent with experimental results. read less T. Ito, T. Akiyama, and K. Nakamura, “Theoretical Investigations for Strain Relaxation and Growth Mode of InAs Thin layers on GaAs(111)A.” 2016. link Times cited: 6 Abstract: The growth mode of InAs/GaAs(111)A is systematically investi… read more Abstract: The growth mode of InAs/GaAs(111)A is systematically investigated using our macroscopic theory with the aid of empirical potential calculations that determine parameter values used in the macroscopic theory. Here, stacking-fault tetrahedron (SFT) found in InAs/GaAs(111)A and misfit dislocation (MD) formations are employed as strain relaxation mechanisms. The calculated results reveal that the MD formation occurs at the layer thickness h about 7 monolayers (MLs). Moreover, we found that the SFT forming at h about 4 MLs makes surface atoms move upward to reduce the strain energy to promote the two dimensional (2D) growth. Therefore, the SFT in addition to the MD plays an important role in strain relaxation in InAs thin layers on GaAs(111)A. The macroscopic free energy calculations for the growth mode imply that the InAs growth on the GaAs(111)A proceeds along the lower energy path from the 2D-coherent (h ≤ 4 MLs) to the 2D-MD (h ≥ 7 MLs) via the 2D-SFT (4 MLs ≤ h ≤ 7 MLs). Consequently, the 2D growth on the InAs/GaAs(111)A results from strain relaxation due to the formation of the SFT near the surface and the subsequent MD formation at the interface. read less R. Sakaguchi, T. Akiyama, K. Nakamura, and T. Ito, “Theoretical investigations of compositional inhomogeneity around threading dislocations in III–nitride semiconductor alloys,” Japanese Journal of Applied Physics. 2016. link Times cited: 8 Abstract: The compositional inhomogeneity of group III elements around… read more Abstract: The compositional inhomogeneity of group III elements around threading dislocations in III–nitride semiconductors are theoretically investigated using empirical interatomic potentials and Monte Carlo simulations. We find that the calculated atomic arrangements around threading dislocations in Al0.3Ga0.7N and In0.2Ga0.8N depend on the lattice strain around dislocation cores. Consequently, compositional inhomogeneity arises around edge dislocation cores to release the strain induced by dislocation cores. In contrast, the compositional inhomogeneity in screw dislocation is negligible owing to relatively small strain induced by dislocation cores compared with edge dislocation. These results indicate that the strain relief around dislocation cores is decisive in determining the atomic arrangements and resultant compositional inhomogeneity around threading dislocations in III–nitride semiconductor alloys. read less T. Ito, T. Akiyama, and K. Nakamura, “Systematic approach to developing empirical interatomic potentials for III–N semiconductors,” Japanese Journal of Applied Physics. 2016. link Times cited: 5 Abstract: A systematic approach to the derivation of empirical interat… read more Abstract: A systematic approach to the derivation of empirical interatomic potentials is developed for III–N semiconductors with the aid of ab initio calculations. The parameter values of empirical potential based on bond order potential are determined by reproducing the cohesive energy differences among 3-fold coordinated hexagonal, 4-fold coordinated zinc blende, wurtzite, and 6-fold coordinated rocksalt structures in BN, AlN, GaN, and InN. The bond order p is successfully introduced as a function of the coordination number Z in the form of p = a exp(−bZn) if Z ≤ 4 and p = (4/Z)α if Z ≥ 4 in empirical interatomic potential. Moreover, the energy difference between wurtzite and zinc blende structures can be successfully evaluated by considering interaction beyond the second-nearest neighbors as a function of ionicity. This approach is feasible for developing empirical interatomic potentials applicable to a system consisting of poorly coordinated atoms at surfaces and interfaces including nanostructures. read less T. Ito, T. Akiyama, and K. Nakamura, “Empirical interatomic potential approach to the stability of graphitic structure in ANB8−N compounds,” Japanese Journal of Applied Physics. 2014. link Times cited: 2 Abstract: Empirical bond order potential (BOP) with the aid of ab init… read more Abstract: Empirical bond order potential (BOP) with the aid of ab initio calculations is applied to investigate the structural stability of 3-fold coordinated graphitic structure for binary octet ANB8−N compounds including C, BN, BeO, Si, and AlP. The graphitic structure is favored in C and BN with small ratio of equilibrium bond length and large bond order p(3) where superscript corresponds to the coordination number. Employing simple electrostatic interaction, the structural phase diagram is successfully obtained as functions of and p(3) using critical bond order for stabilizing the graphitic structure. read less M. Hirano, “Atomistics of superlubricity,” Friction. 2014. link Times cited: 21 M. Hirano, “Atomistics of superlubricity,” Friction. 2014. link Times cited: 0 C. Henager, F. Gao, S. Hu, G. Lin, E. Bylaska, and N. Zabaras, “Simulating Interface Growth and Defect Generation in CZT – Simulation State of the Art and Known Gaps.” 2012. link Times cited: 1 Abstract: This one-year, study topic project will survey and investiga… read more Abstract: This one-year, study topic project will survey and investigate the known state-of-the-art of modeling and simulation methods suitable for performing fine-scale, fully 3-D modeling, of the growth of CZT crystals at the melt-solid interface, and correlating physical growth and post-growth conditions with generation and incorporation of defects into the solid CZT crystal. In the course of this study, this project will also identify the critical gaps in our knowledge of modeling and simulation techniques in terms of what would be needed to be developed in order to perform accurate physical simulations of defect generation in melt-grown CZT. The transformational nature of this study will be, for the first time, an investigation of modeling and simulation methods for describing microstructural evolution during crystal growth and the identification of the critical gaps in our knowledge of such methods, which is recognized as having tremendous scientific impacts for future model developments in a wide variety of materials science areas. read less K. Fichthorn, Y. Tiwary, T. Hammerschmidt, P. Kratzer, and M. Scheffler, “Analytic many-body potential for GaAs(001) homoepitaxy: Bulk and surface properties,” Physical Review B. 2011. link Times cited: 14 Abstract: We employ atomic-scale simulation methods to investigate bul… read more Abstract: We employ atomic-scale simulation methods to investigate bulk and surface properties of an analytic TersoffAbell type potential for describing interatomic interactions in GaAs. The potential is a modified form of that proposed by Albe and colleagues [Phys. Rev. B 66, 035205 (2002)] in which the cut-off parameters for the As-As interaction have been shortened. With this modification, many bulk properties predicted by the potential for solid GaAs are the same as those in the original potential, but properties of the GaAs(001) surface better match results from first-principles calculations with density-functional theory (DFT). We tested the ability of the potential to reproduce the phonon dispersion and heat capacity of bulk solid GaAs by comparing it to experiment and the overall agreement is good. In the modified potential, the GaAs(001) β2(2 × 4) reconstruction is favored under As-rich growth conditions in agreement with DFT calculations. Additionally, the binding energies and diffusion barriers for a Ga adatom on the β2(2 × 4) reconstruction generally match results from DFT calculations. These studies indicate that the potential is suitable for investigating aspects of GaAs(001) homoepitaxy. read less T. Yamashita, T. Akiyama, K. Nakamura, and T. Ito, “Effects of Facet Orientation on Relative Stability between Zinc Blende and Wurtzite Structures in Group III–V Nanowires,” Japanese Journal of Applied Physics. 2010. link Times cited: 23 Abstract: The relative stability between the wurtzite and zinc blende … read more Abstract: The relative stability between the wurtzite and zinc blende structures in InP, GaP, and GaAs nanowires with {111}/{1100} facets and those with {110}/{1120} facets is systematically investigated using our empirical interatomic potential calculations in conjunction with first-principles calculations. Moreover, we discuss chemical trends in the structural stability of InP, GaP, and GaAs nanowires. Our calculations clarify that the wurtzite structure is stabilized over the entire diameter range for nanowires with {111}/{1100} facets. In contrast, for nanowires consisting of {110}/{1120} facets, the crystal structure of nanowires depends on the nanowire diameter and the ionicity of semiconductors. This is because the surface energy difference between the {111} and {1100} surfaces is large compared with that between the {110} and {1120} surfaces. The calculated results imply that the stability of nanowire side facets is an important factor determining the crystal structure. read less H.-C. Cheng, W.-H. Chen, C.-S. Lin, Y. Hsu, and R. Uang, “On the Thermal–Mechanical Behaviors of a Novel Nanowire-Based Anisotropic Conductive Film Technology,” IEEE Transactions on Advanced Packaging. 2009. link Times cited: 10 Abstract: Extensive understanding and management of the thermal-mechan… read more Abstract: Extensive understanding and management of the thermal-mechanical characteristics of novel packaging designs during the bonding process are indispensable to the realization of the technologies. Thus, this paper attempts to explore the bonding process-induced thermal-mechanical behaviors of an advanced flip chip (FC) electronic packaging. FC packaging employs a novel anisotropic conductive film, which is a thin composite film composed of polymer matrix and thousands of millions of highly oriented, 1-D silver (Ag) nanowires on the scale of 200 nanometers in diameter. For carrying out the process simulation, a process-dependent finite element (FE) simulation methodology that integrates both thermal and nonlinear contact FE analyses and a special meshing scheme is applied. The material properties of the nanoscale Ag wires are first explored using molecular dynamics (MD) simulations. By the characterized material properties of the Ag nanowires, the effective material properties of the composite film are derived through two theoretical approaches: 1) the rule-of-mixture (ROM) technique and 2) the proposed FE method-based approach. The predicted results by these two approaches are extensively compared with each other to examine the feasibility of using the widely used ROM technique for such cases. In addition, the validity of the proposed process-dependent FE simulation methodology is also confirmed through three experiments: 1) micro-thermocouple measurement of temperature; 2) Twyman-Green Moire interferometry measurement of out-of-plane deformations; and 3) portable engineering Moire interferometry measurement of in-plane deformations. Throughout the investigation, the effectiveness of the novel interconnect technology is demonstrated. Good agreement with the experiments is also obtained. It is found that the technology may ensure good electrical performance and structural integrity, not only at room temperature but even at elevated temperature, based on its substantial contact stresses but minor peeling stresses on the bonding line, together with a moderate, process-induced warpage on the substrate. read less T. Ito, H. Joe, T. Akiyama, K. Nakamura, and K. Kanisawa, “An empirical potential approach to the formation of InAs stacking-fault tetrahedron in InAs/GaAs(111),” 2008 Conference on Optoelectronic and Microelectronic Materials and Devices. 2008. link Times cited: 0 Abstract: The structural stability of InAs stacking-fault tetrahedron … read more Abstract: The structural stability of InAs stacking-fault tetrahedron (InAs-SFT) on GaAs(111) is systematically investigated in terms of strain relaxation by using an empirical potential incorporating electrostatic energy contribution. The InAs-SFT is more stable than coherently grown InAs on GaAs(111) beyond 21 monolayers (MLs), which are comparable with critical film thickness of misfit dislocation generation. Furthermore, SFT formation in InAs is more favorable than threading dislocation formation below the film thickness of ~60 MLs. These calculated results are qualitatively consistent with experimental results. read less K. Albe, K. Nordlund, J. Nord, and A. Kuronen, “Modeling of compound semiconductors: Analytical bond-order potential for Ga, As, and GaAs,” Physical Review B. 2002. link Times cited: 151 Abstract: An analytical bond-order potential for GaAs is presented, th… read more Abstract: An analytical bond-order potential for GaAs is presented, that allows one to model a wide range of properties of GaAs compound structures, as well as the pure phases of gallium and arsenide, including nonequilibrium configurations. The functional form is based on the bond-order scheme as devised by Abell-Tersoff and Brenner, while a systematic fitting scheme starting from the Pauling relation is used for determining all adjustable parameters. Reference data were taken from experiments if available, or computed by self-consistent total-energy calculations within the local density-functional theory otherwise. For fitting the parameters, only structural data of the metallic phases of gallium and arsenide as well as those of different GaAs phases were used. A number of tests on point defect properties, surface properties, and melting behavior have been performed afterward in order to validate the accuracy and transferability of the potential model, but were not part of the fitting procedure. While point defect properties and surfaces with low As content are found to be in good agreement with literature data, the description of As-rich surface reconstructions is not satisfactory. In the case of molten GaAs we find support for a structural model based on experiment that indicates a polymerized arsenic phase in the melt. read less D. Brenner, O. Shenderova, J. Harrison, S. Stuart, B. Ni, and S. Sinnott, “A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons,” Journal of Physics: Condensed Matter. 2002. link Times cited: 3204 Abstract: A second-generation potential energy function for solid carb… read more Abstract: A second-generation potential energy function for solid carbon and hydrocarbon molecules that is based on an empirical bond order formalism is presented. This potential allows for covalent bond breaking and forming with associated changes in atomic hybridization within a classical potential, producing a powerful method for modelling complex chemistry in large many-atom systems. This revised potential contains improved analytic functions and an extended database relative to an earlier version (Brenner D W 1990 Phys. Rev. B 42 9458). These lead to a significantly better description of bond energies, lengths, and force constants for hydrocarbon molecules, as well as elastic properties, interstitial defect energies, and surface energies for diamond. read less C. Wang, B. Pan, and K. Ho, “An environment-dependent tight-binding potential for Si,” Journal of Physics: Condensed Matter. 1999. link Times cited: 116 Abstract: We present a new generation of tight-binding model for silic… read more Abstract: We present a new generation of tight-binding model for silicon which goes beyond the traditional two-centre approximation and allows the tight-binding parameters to scale according to the bonding environment. We show that the new model improves remarkably the accuracy and transferability of the potential for describing the structures and energies of silicon surfaces, in addition to the properties of silicon in the bulk diamond structure. read less M. Någård, P. U. Andersson, N. Marković, and J. Pettersson, “SCATTERING AND TRAPPING DYNAMICS OF GAS-SURFACE INTERACTIONS : THEORY AND EXPERIMENTS FOR THE XE-GRAPHITE SYSTEM,” Journal of Chemical Physics. 1998. link Times cited: 31 Abstract: We report on molecular beam experiments and molecular dynami… read more Abstract: We report on molecular beam experiments and molecular dynamics simulations of xenon scattering with incident energies E=0.06−5.65 eV from graphite. The corrugation felt by an atom interacting with the surface is found to be influenced by both surface temperature, Ts, and E. Angular distributions are significantly broadened when Ts is increased, clearly indicating corrugation induced by thermal motion of the surface also at the highest E employed. Direct scattering dominates for high E, while trapping becomes important for kinetic energies below 1 eV. The coupling between atom translation and surface modes in the normal direction is very effective, while trapped atoms only slowly accommodate their momentum parallel to the surface plane. The very different coupling normal and parallel to the surface plane makes transient (incomplete) trapping-desorption unusually pronounced for the Xe/graphite system, and atoms may travel up to 50 nm on the surface before desorption takes place. The nonlocal and soft charac... read less T. Araki, T. Akiyama, K. Nakamura, and T. Ito, “Theoretical investigation of the structural stability of zinc blende GaN thin films,” E-journal of Surface Science and Nanotechnology. 2005. link Times cited: 5 Abstract: The structural stability of zinc blende (ZB) structured GaN … read more Abstract: The structural stability of zinc blende (ZB) structured GaN thin films on ZB-GaN(001) and ZB-SiC(001) substrates is systematically investigated based on an empirical potential, which incorporates electrostatic energy due to covalent bond charges and ionic charges. The calculated energy difference between pure ZB-GaN and mixed structure of wurtzite (W) and ZB-GaN (ZB-W-GaN) on ZB-GaN(001) implies that ZB-GaN is stabilized up to the film thickness of 554 ML. Furthermore, similar calculations incorporating misfit dislocations (MDs) on ZB-SiC(001) show that ZB-GaN pseudomorphically grown on ZB-SiC(001) initially changes its structure to ZB-GaN with MD at 28 ML in good accordance with critical thickness of misfit dislocation generation of 32 ML estimated by People-Bean formula. The ZB-GaN with MD is successively transformed into ZB-GaN with MDs at 294 ML and finally ZB-W-GaN at 865 ML. These results suggest that MD generation crucially affects the stability of ZB-GaN. [DOI: 10.1380/ejssnt.2005.507] read less L. Porter, S. Yip, M. Yamaguchi, H. Kaburaki, and M. Tang, “EMPIRICAL BOND-ORDER POTENTIAL DESCRIPTION OF THERMODYNAMIC PROPERTIES OF CRYSTALLINE SILICON,” Journal of Applied Physics. 1997. link Times cited: 67 Abstract: Thermodynamic properties of silicon (diamond cubic phase) ar… read more Abstract: Thermodynamic properties of silicon (diamond cubic phase) are calculated using an empirical many-body potential developed by Tersoff [Phys. Rev. Lett. 56, 632 (1986)] based on the concept of bond order. It is shown that this model gives predictions in good agreement with experiment for those properties governed by energetics (free energy, entropy, and heat capacity). The thermal expansion coefficient is less well described, which is traced to the fact that the model potential, in its present version, is overly stiff and therefore unable to account properly for the volume dependence of the transverse acoustic modes. Furthermore, sensitivity of the potential to whether each atom remains bonded to only four neighbors indicates that the short-range nature of the potential may necessitate model improvement before it is suitable for studies of thermomechanical properties at elevated temperatures or large deformations. read less T. Ito and T. Akiyama, “Recent Progress in Computational Materials Science for Semiconductor Epitaxial Growth.” 2017. link Times cited: 5 Abstract: Recent progress in computational materials science in the ar… read more Abstract: Recent progress in computational materials science in the area of semiconductor epitaxial growth is reviewed. Reliable prediction can now be made for a wide range of problems, such as surface reconstructions, adsorption-desorption behavior, and growth processes at realistic growth conditions, using our ab initio-based chemical potential approach incorporating temperature and beam equivalent pressure. Applications are examined by investigating the novel behavior during the hetero-epitaxial growth of InAs on GaAs including strain relaxation and resultant growth mode depending growth orientations such as (111)A and (001). Moreover, nanowire formation is also exemplified for adsorption-desorption behaviors of InP nanowire facets during selective-area growth. An overview of these issues is provided and the latest achievement are presented to illustrate the capability of the theoretical-computational approach by comparing experimental results. These successful applications lead to future prospects for the computational materials design in the fabrication of epitaxially grown semiconductor materials. read less
Funding	Not available

Short KIM ID The unique KIM identifier code.	MO_722489435928_000
Extended KIM ID 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.	ThreeBodyBondOrder_KDS_KhorDasSarma_1988_Si__MO_722489435928_000
DOI	10.25950/8e5d84c2 https://doi.org/10.25950/8e5d84c2 https://commons.datacite.org/doi.org/10.25950/8e5d84c2
KIM Item Type 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).	Portable Model using Model Driver ThreeBodyBondOrder_KDS__MD_697985444380_000
Driver	ThreeBodyBondOrder_KDS__MD_697985444380_000
KIM API Version	2.0
Potential Type	kds

Verification Check Dashboard

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Grade	Name	Category	Brief Description	Full Results	Aux File(s)
P All elements claimed by model are supported in at least one of the tested configurations.	vc-species-supported-as-stated	mandatory	The model supports all species it claims to support; see full description.	Results	Files
N/A Unable to perform verification check due to an error.	vc-periodicity-support	mandatory	Periodic boundary conditions are handled correctly; see full description.	Results	Files
P Model energy has permutation symmetry for all configurations the model was able to compute.	vc-permutation-symmetry	mandatory	Total energy and forces are unchanged when swapping atoms of the same species; see full description.	Results	Files
A The letter grade A was assigned because the normalized error in the computation was 8.50726e-11 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.	Results	Files
F The model is C^0 continuous. This means that the model has continuous energy, but a discontinuous first derivative.	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.	Results	Files
P 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.	Results	Files
P Model energy has inversion symmetry for all configurations the model was able to compute.	vc-inversion-symmetry	informational	Total energy is unchanged and forces change sign when inverting a configuration through the origin; see full description.	Results	Files
N/A Unable to perform verification check due to an error.	vc-memory-leak	informational	The model code does not have memory leaks (i.e. it releases all allocated memory at the end); see full description.	Results	Files
N/A Unable to perform verification check due to an error.	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.	Results	Files
N/A Unable to perform verification check due to an error.	vc-unit-conversion	mandatory	The model is able to correctly convert its energy and/or forces to different unit sets; see full description.	Results	Files

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.

(No matching species)

Cohesive Energy Graph

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.

Species: Si

Diamond Lattice Constant

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.

Species: Si

Dislocation Core Energies

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.

(No matching species)

FCC Elastic Constants

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.

(No matching species)

FCC Lattice Constant

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.

(No matching species)

FCC Stacking Fault Energies

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.

(No matching species)

FCC Surface Energies

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.

(No matching species)

SC Lattice Constant

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.

Species: Si

Cubic Crystal Basic Properties Table

Species: Si

Tests

ClusterEnergyAndForces__TD_000043093022_003

Conjugate gradient relaxation of atomic cluster v003

Creators: Daniel S. Karls
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/b47dd4c4

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	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)
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1216
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1695
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1887
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1695
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1887
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1727
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1727
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1727
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1120
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1216
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1727
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1663
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1152
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1727
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1823
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1216
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1663
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1823
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1216
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1663
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1663
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1695
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1791
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1759
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1695
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1823
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1120
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1727
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1695
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1695
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1855
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1216
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1759
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1695
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1663
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1184
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1695
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1695
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1216
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1759
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1727
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1663
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1759
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1216
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1663
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1887
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1663
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1727
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1216
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1887
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1663
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1663
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1184
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1759
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1791
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1184
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1791
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1695
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1216
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1216
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1184
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1887
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1727
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1823
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1695
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1791
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1184
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1663
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1855
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1727
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1791
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1791
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1727
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1759
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1216
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1216
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1727
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1216
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1184
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1695
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1791
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1855
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1663
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1791
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1791
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1184
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1216
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1791
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1823
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1695
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1216
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1184
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1695
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2079
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1663
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1663
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1184
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1983
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1727
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1759
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1695
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1120
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1663
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1567
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1727
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1823
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1663
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1823
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1759
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1727
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1471
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1216
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1759
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1983
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1695
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1663
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1855
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1759
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1887
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1631
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1727
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1184
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1184
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1216
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1535
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1599
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1312
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1440
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1408
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1280
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1248
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1344
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1503
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1376

CohesiveEnergyVsLatticeConstant__TD_554653289799_003

Cohesive energy versus lattice constant curve for monoatomic cubic lattices v003

Creators:
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/64cb38c5

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)
Cohesive energy versus lattice constant curve for diamond Si v004		view	2135
Cohesive energy versus lattice constant curve for sc Si v004		view	2009

EquilibriumCrystalStructure__TD_457028483760_002

Equilibrium structure and energy for a crystal structure at zero temperature and pressure v002

Creators:
Contributor: ilia
Publication Year: 2024
DOI: https://doi.org/10.25950/2f2c4ad3

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	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 crystal structure and energy for Si in AFLOW crystal prototype A_cF136_227_aeg v002	view	13170702
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_cF8_227_a v002	view	101773
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_cI82_217_acgh v002	view	5562578
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_cP46_223_cik v002	view	204700
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_hP1_191_a v002	view	39676
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_hP40_191_hjmno v002	view	103414
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_hP4_194_f v002	view	44659
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_hP58_164_2d3i3j v002	view	178088
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_hP68_194_ef2h2kl v002	view	159388
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_mC164_15_e20f v002	view	11610568
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_mC16_12_4i v002	view	104325
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_oC92_63_ce2f2g3h v002	view	12848397
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_tI8_139_h v002	view	1060356
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_tP106_137_a5g4h v002	view	98347859

LatticeConstantCubicEnergy__TD_475411767977_007

Equilibrium lattice constant and cohesive energy of a cubic lattice at zero temperature and pressure v007

Creators: Daniel S. Karls and Junhao Li
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/2765e3bf

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)
Equilibrium zero-temperature lattice constant for diamond Si v007		view	2079
Equilibrium zero-temperature lattice constant for sc Si v007		view	1919

LinearThermalExpansionCoeffCubic__TD_522633393614_002

Linear thermal expansion coefficient of cubic crystal structures v002

Creators:
Contributor: mjwen
Publication Year: 2024
DOI: https://doi.org/10.25950/9d9822ec

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)
Linear thermal expansion coefficient of diamond Si at 293.15 K under a pressure of 0 MPa v002		view	1638515

TriclinicPBCEnergyAndForces__TD_892847239811_003

Potential energy and atomic forces of periodic, non-orthogonal cell of atoms v003

Creators: Daniel S. Karls
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/c3dca28e

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	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)
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1567
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1344
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1280
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1280
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1408
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1312
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1535
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1216
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1312
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1280
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1248
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1312
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1408
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1503
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1471
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1280
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1599
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1599
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1503
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1408
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1408
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1280
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1280
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1727
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1408
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1599
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1503
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1791
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1503
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1280
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1280
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1408
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1312
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1152
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1727
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1599
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1248
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1599
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1471
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1599
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1312
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1408
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1344
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1599
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1344
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1408
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1663
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1567
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1599
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1855
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1312
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1535
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1280
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1312
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1855
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1344
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1344
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1312
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1408
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1567
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1344
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1471
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1471
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1471
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1344
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1567
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1599
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1408
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1535
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1631
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1727
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1983
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1408
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1248
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1184
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1503
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1408
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1408
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1631
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1503
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1535
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1344
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1344
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1503
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1408
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1535
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1535
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1567
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1695
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1152
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1471
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1408
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1567
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1344
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1408
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1376
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1248
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1312
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1503
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1280
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1631
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1695
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1471
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1312
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	1695
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1408
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1599
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1471
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1184
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1503
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1184
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1344
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1791
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1440
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1312
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1471
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1983
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1312
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1471
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1599
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1631
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1503
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1344
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	1695

VacancyFormationEnergyRelaxationVolume__TD_647413317626_001

Monovacancy formation energy and relaxation volume for cubic and hcp monoatomic crystals v001

Creators:
Contributor: efuem
Publication Year: 2023
DOI: https://doi.org/10.25950/fca89cea

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)
Monovacancy formation energy and relaxation volume for diamond Si		view	254580

VacancyFormationMigration__TD_554849987965_001

Vacancy formation and migration energies for cubic and hcp monoatomic crystals v001

Creators:
Contributor: efuem
Publication Year: 2023
DOI: https://doi.org/10.25950/c27ba3cd

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)
Vacancy formation and migration energy for diamond Si		view	3285241

Errors

EquilibriumCrystalStructure__TD_457028483760_000

Test	Error Categories	Link to Error page
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_hP40_191_hjmno v000	other	view
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_mC164_15_e20f v000	other	view
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_tI8_139_h v000	other	view
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_tP106_137_a5g4h v000	other	view

EquilibriumCrystalStructure__TD_457028483760_002

Test	Error Categories	Link to Error page
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_cF4_225_a v002	other	view
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_cI12_229_d v002	other	view
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_cI16_206_c v002	other	view
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_hP2_194_c v002	other	view
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_hR8_148_cf v002	other	view
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_oF16_69_gh v002	other	view
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_tI4_141_a v002	other	view

LatticeConstantCubicEnergy__TD_475411767977_007

Test	Error Categories	Link to Error page
Equilibrium zero-temperature lattice constant for bcc Si v007	other	view
Equilibrium zero-temperature lattice constant for fcc Si v007	other	view

LatticeConstantHexagonalEnergy__TD_942334626465_005

Test	Error Categories	Link to Error page
Equilibrium lattice constants for hcp Si v005	other	view

TriclinicPBCEnergyAndForces__TD_892847239811_003

Test	Error Categories	Link to Error page
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	other	view

No Driver

Verification Check	Error Categories	Link to Error page
MemoryLeak__VC_561022993723_004	other	view
PeriodicitySupport__VC_895061507745_004	other	view

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Following are the plots for the diamond structure of Silicon assuming R = 2.3 $$A^{\circ}$$:
![](/wimage/MO_722489435928_000/Anshul/ONEYH.png){:height="500px"}
![](/wimage/MO_722489435928_000/Anshul/TWOYH.png){:height="500px"}

The graph below is plotted assuming a tetrahedral geometry and that the atom under consideration is equidistant from its neighboring 4 atoms at all times:
![](/wimage/MO_722489435928_000/Anshul/THREEYH.png){:height="500px"}

The following graph is plotted as $$b_{ij}$$(KDS) vs $$\theta_{jik}$$ for a system of 3 atoms located at the corners of a triangle. The selected atom remains at an equilibrium distance of 2.3 $$A^{\circ}$$ from the other atoms, and the bond angle at the selected atom is varied.
![](/wimage/MO_722489435928_000/Anshul/FOURYH.png){:height="500px"}

The graph below is plotted considering a system of 4 atoms located at the corners of the rhombus. One atom is selected and is moved about the direction of the diagonal passing through it, hence varying the bond angle it forms with its neighboring atoms and as well as varying the distance it is located from its neighboring atoms. In this configuration, the selected atom always stays at an equal distance from its neighboring atoms, as it is moved along the diagonal passing through it. The rest of the 3 atoms are assumed to be fixed in the system with an equilibrium angle and at equilibrium distance from each other. It is assumed that the equilibrium angle is $$109.47^\circ$$ and the equilibrium distance between the atoms is 2.3 $$A^{\circ}$$.

![](/wimage/MO_722489435928_000/Anshul/SEVENYH.png){:height="500px"}
![](/wimage/MO_722489435928_000/Anshul/EIGHTYH.png){:height="500px"}

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2019-05-08T22:29:20.027789	Anshul
2019-05-08T22:08:41.935940	Anshul

ThreeBodyBondOrder_KDS_KhorDasSarma_1988_Si__MO_722489435928_000

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BCC Lattice Constant

Cohesive Energy Graph

Diamond Lattice Constant

Dislocation Core Energies

FCC Elastic Constants

FCC Lattice Constant

FCC Stacking Fault Energies

FCC Surface Energies

SC Lattice Constant

Cubic Crystal Basic Properties Table

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