LAMMPS Modified Tersoff potential for Si by Kumagai et al. (2007) v000

Satoshi Izumi; Shotaro Hara; Shinsuke SAKAI; Tomohisa Kumagai

doi:10.25950/9d94dc3d

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Sim_LAMMPS_ModifiedTersoff_KumagaiIzumiHara_2007_Si__SM_773333226968_000

Interatomic potential for Silicon (Si).
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Title A single sentence description.	LAMMPS Modified Tersoff potential for Si by Kumagai et al. (2007) v000
Description	This potential corresponds to the 'MOD' potential given in T. Kumagai, S. Izumi, S. Hara, S. Sakai, Comp. Mat. Sci., 39, 457 (2007). Abstract: The Tersoff potential is one of the most widely used interatomic potentials for silicon. However, its poor description of the elastic constants and melting point of diamond silicon is well known. In this research, three bond-order type interatomic potentials have been developed: the first one is fitted to the elastic constants by employing the Tersoff potential function form, the second one is fitted to both the elastic constants and melting point by employing the Tersoff potential function form and the third one is fitted to both the elastic constants and melting point by employing the modified Tersoff potential function form in which the angular-dependent term is improved. All of developed potentials well reproduce the elastic constants of diamond silicon as well as the cohesive energies and equilibrium bond lengths of silicon polytypes. The third potential can reproduce the melting point, while the second one cannot reproduce that. The elastic constants and melting point calculated using the third potential turned out to be C11 = 166.4 GPa, C12 = 65.3 GPa, C44 = 77.1 GPa and Tm = 1681 K. It was also found that only elastic constants can be reproduced using the original Tersoff potential function, and that our proposed angular-dependent term is a key to reproducing the melting point.
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
Content Origin	NIST IPRP (https://www.ctcms.nist.gov/potentials/Si.html)

Contributor	Daniel S. Karls
Maintainer	Daniel S. Karls
Developer	Satoshi Izumi Shotaro Hara Shinsuke SAKAI Tomohisa Kumagai
Published on KIM	2019
How to Cite	This Simulator Model originally published in [1] is archived in OpenKIM [2-4]. [1] Kumagai T, Izumi S, Hara S, Sakai S. Development of bond-order potentials that can reproduce the elastic constants and melting point of silicon for classical molecular dynamics simulation. Computational Materials Science [Internet]. 2007;39(2):457–64. Available from: http://www.sciencedirect.com/science/article/pii/S0927025606002254 doi:10.1016/j.commatsci.2006.07.013 — (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] Izumi S, Hara S, SAKAI S, Kumagai T. LAMMPS Modified Tersoff potential for Si by Kumagai et al. (2007) v000. OpenKIM; 2019. doi:10.25950/9d94dc3d [3] 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 [4] 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). 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See the Deep Citation documentation for more information. 134 Citations (82 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 . X. Zhang, M. Hu, K. Giapis, and D. Poulikakos, “Schemes for and Mechanisms of Reduction in Thermal Conductivity in Nanostructured Thermoelectrics,” Journal of Heat Transfer-transactions of The Asme. 2012. link Times cited: 20 Abstract: Nonequilibrium molecular dynamics (NEMD) simulations were pe… read more Abstract: Nonequilibrium molecular dynamics (NEMD) simulations were performed to investigate schemes for enhancing the energy conversion efficiency of thermoelectric nanowires (NWs), including (1) roughening of the nanowire surface, (2) creating nanoparticle inclusions in the nanowires, and (3) coating the nanowire surface with other materials. The enhancement in energy conversion efficiency was inferred from the reduction in thermal conductivity of the nanowire, which was calculated by imposing a temperature gradient in the longitudinal direction. Compared to pristine nanowires, our simulation results show that the schemes proposed above lead to nanocomposite structures with considerably lower thermal conductivity (up to 82% reduction), implying ~5X enhancement in the ZT coefficient. This significant effect appears to have two origins: (1) increase in phonon-boundary scattering and (2) onset of interfacial interference. The results suggest new fundamental–yet realizable ways to improve markedly the energy conversion efficiency of nanostructured thermoelectrics. read less F. Chu et al., “Prediction of sub-pyramid texturing as the next step towards high efficiency silicon heterojunction solar cells,” Nature Communications. 2023. link Times cited: 1 J.-C. Griesser, G. Moras, and L. Pastewka, “Yielding under compression and the polyamorphic transition in silicon.” 2023. link Times cited: 0 Abstract: We investigate the behavior of amorphous silicon under hydro… read more Abstract: We investigate the behavior of amorphous silicon under hydrostatic compression using molecular simulations. During compression, amorphous silicon undergoes a discontinuous nonequilibrium transition from a low-density to a high-density structure at a pressure of around $13$-$16$~GPa. Ensemble-averaged density and elastic constants change discontinuously across the transition. Densification of individual glassy samples occurs through a series of discrete plastic events, each of which is accompanied by a vanishing shear modulus. This is the signature of a series of elastic instabilities, similar to shear transformation zones observed during shear yielding of glasses. We compare the structure obtained during compression with a near-equilibrium form of amorphous silicon obtained by quenching a melt at constant pressure. This gives structures identical to nonequilibrium compression at low and high pressure, but the transition between them occurs gradually rather than discontinuously. Our observations indicate that the polyamorphic transition is of a nonequilibrium nature, and it has the characteristics of a yield transition that occurs under compression instead of shear. read less S. Kohara et al., “Relationship between diffraction peak, network topology, and amorphous-forming ability in silicon and silica,” Scientific Reports. 2021. link Times cited: 7 E. T. Karim, M. He, A. Salhoumi, L. Zhigilei, and P. Galenko, “Kinetics of solid–liquid interface motion in molecular dynamics and phase-field models: crystallization of chromium and silicon,” Philosophical Transactions of the Royal Society A. 2021. link Times cited: 4 Abstract: The results of molecular dynamics (MD) simulations of the cr… read more Abstract: The results of molecular dynamics (MD) simulations of the crystallization process in one-component materials and solid solution alloys reveal a complex temperature dependence of the velocity of the crystal–liquid interface featuring an increase up to a maximum at 10–30% undercooling below the equilibrium melting temperature followed by a gradual decrease of the velocity at deeper levels of undercooling. At the qualitative level, such non-monotonous behaviour of the crystallization front velocity is consistent with the diffusion-controlled crystallization process described by the Wilson–Frenkel model, where the almost linear increase of the interface velocity in the vicinity of melting temperature is defined by the growth of the thermodynamic driving force for the phase transformation, while the decrease in atomic mobility with further increase of the undercooling drives the velocity through the maximum and into a gradual decrease at lower temperatures. At the quantitative level, however, the diffusional model fails to describe the results of MD simulations in the whole range of temperatures with a single set of parameters for some of the model materials. The limited ability of the existing theoretical models to adequately describe the MD results is illustrated in the present work for two materials, chromium and silicon. It is also demonstrated that the MD results can be well described by the solution following from the hodograph equation, previously found from the kinetic phase-field model (kinetic PFM) in the sharp interface limit. The ability of the hodograph equation to describe the predictions of MD simulation in the whole range of temperatures is related to the introduction of slow (phase field) and fast (gradient flow) variables into the original kinetic PFM from which the hodograph equation is obtained. The slow phase-field variable is responsible for the description of data at small undercoolings and the fast gradient flow variable accounts for local non-equilibrium effects at high undercoolings. The introduction of these two types of variables makes the solution of the hodograph equation sufficiently flexible for a reliable description of all nonlinearities of the kinetic curves predicted in MD simulations of Cr and Si. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’. read less T. Menold, M. Ametowobla, and J. Werner, “Signatures of self-interstitials in laser-melted and regrown silicon,” AIP Advances. 2021. link Times cited: 2 Abstract: Photoluminescence spectroscopy investigates epitaxially regr… read more Abstract: Photoluminescence spectroscopy investigates epitaxially regrown silicon single crystals after pulsed laser melting for atomic-level lattice defects. The measurements identify a transition from a regime free of defect-related spectral lines to a regime in which spectral lines appear originating from small self-interstitial clusters. This finding of self-interstitial clusters indicates supersaturated concentrations of self-interstitials within the regrown volume. Molecular dynamics simulations confirm that recrystallization velocities vre ≈ 1 m/s after laser melting lead to supersaturation of both self-interstitials and vacancies. Their concentrations ci and cv in the regrown volumes are ci ≈ cv ≈ 1017 cm−3. An analytical model based on time-dependent nucleation theory shows a very strong dependence of self-interstitial aggregation to clusters on the cooling rate after solidification. This model explains the transition identified by photoluminescence spectroscopy. read less L. N. Abdulkadir, K. Abou-El-Hossein, P. B. Odedeyi, M. Liman, and A. I. Jumare, “RSM and MD—a roughness predictive model and simulation comparison of monocrystalline optical grade silicon,” The International Journal of Advanced Manufacturing Technology. 2020. link Times cited: 1 B. Bauerhenne and M. E. Garcia, “Performance of state-of-the-art force fields for atomistic simulations of silicon at high electronic temperatures,” The European Physical Journal Special Topics. 2019. link Times cited: 5 Z. Zheng, H. Zhan, Y. Nie, A. Bo, X. Xu, and Y. T. Gu, “General existence of flexural mode doublets in nanowires targeting vectorial sensing applications.,” Physical chemistry chemical physics : PCCP. 2019. link Times cited: 1 Abstract: Nanowires (NWs) are one of the fundamental building blocks f… read more Abstract: Nanowires (NWs) are one of the fundamental building blocks for nanoscale devices, and have been frequently utilized as mechanical resonators. Earlier studies show that ultra-sensitive vectorial sensing toolkits can be fabricated by changing the flexural mode of NWs to oscillation doublets along two orthogonal directions. Based on in silico studies and the Timoshenko beam theory, this work finds that the dual orthogonal flexural mode of NWs can be effectively controlled through the proper selection of their growth direction. It is found that metallic NWs with a directional-independent shear modulus possess a single flexural mode. However, NWs with a directional-dependent shear modulus naturally exhibit flexural mode doublets, which do not disappear even with increasing slenderness ratio. Further studies show that such a feature generally exists in other NWs, such as Si NWs. Mimicking a pendulum configuration as used in NW-based scanning force microscopy, the cantilevered 110 Si NW demonstrates zeptogram mass resolution and a force sensitivity down to the order of 10-24 N Hz-1/2 (yN Hz-1/2) in both transverse directions. The findings in this work open up a new and facile avenue to fabricate 2D vectorial force sensors, which could enable ultra-sensitive and novel detection devices/systems for 2D effects, such as the anisotropy strength of atomic bonds. read less L. M. Sandonas, G. Cuba-Supanta, R. Gutierrez, A. Dianat, C. Landauro, and G. Cuniberti, “Enhancement of thermal transport properties of asymmetric Graphene/hBN nanoribbon heterojunctions by substrate engineering,” Carbon. 2017. link Times cited: 23 Z. Zhang and H. Urbassek, “Comparative Study of Interatomic Interaction Potentials for Describing Indentation into Si Using Molecular Dynamics Simulation,” Applied Mechanics and Materials. 2017. link Times cited: 5 Abstract: We compare the performance of three interatomic interaction … read more Abstract: We compare the performance of three interatomic interaction potentials for describing the evolution of plasticity and phase transformations in Si: the well established Stillinger-Weber potential, a recent modification used in the description of Al/Si composites, and a modification of the well known Tersoff potential. We show that the generation of dislocations and the evolution of plasticity are well described by the Stillinger-Weber potential and its modification, while the phase transformation to the high-pressure bct5 modification and the subsequent amorphization are better included in the modified Tersoff potential. read less Y. Hoshino, “Diffusion and aggregation process of oxygen embedded around an amorphous/crystal interface of Si(001) studied by molecular dynamics simulation,” Journal of Applied Physics. 2017. link Times cited: 0 Abstract: I performed empirical molecular dynamics (MD) simulations to… read more Abstract: I performed empirical molecular dynamics (MD) simulations to understand the peculiar migration behavior of oxygen embedded in an amorphous Si (a-Si) layer near the crystal/amorphous (c/a) Si interface and investigated the time evolution of the atomic configuration at high temperatures from 1200 to 1500 K. The previously proposed sweeping effect, which is demonstrated in terms of the oxygen migration and precipitation in silicon taking place along the moving c/a interface, was definitely confirmed in this MD simulation. [Hoshino et al., J. Phys. D: Appl. Phys. 49, 315106 (2016)] In the present study, I reproducibly found the theoretical evidence of the novel sweeping and aggregation phenomenon of oxygen occurring in the recrystallization process of a-Si. The temperature-dependence revealed that the relationship between the displacement velocity of the oxygen and the c/a interface plays an important role in interpreting the behavior. The oxide precipitations in the recrystallized Si as well as the sweeping ... read less S. Das and A. Dutta, “Elastic behavior of crystalline/amorphous core/shell silicon nanowires,” 2017 Devices for Integrated Circuit (DevIC). 2017. link Times cited: 0 Abstract: Using atomistic simulations, we study the elastic properties… read more Abstract: Using atomistic simulations, we study the elastic properties of silicon nanowires with amorphous shells. These structures were simulated by heating the perfect crystalline nanowires followed by rapid quenching. Virtual straining experiments exhibited a linear stress-strain behavior, which was further used to extract the Young's moduli of the nanowires. Simulations were carried out for nanowires of different diameters and shell thicknesses. We found that increase in the core-diameter resulted in enhanced stiffness constant. This trend could be explained by a simple composite model. Furthermore, the computations suggested that the core-shell interface did not have any pronounced effect on the Young's modulus of the nanowires. read less C. Chen, Y. She, H. Xiao, J.-wen Ding, J. Cao, and Z. X. Guo, “Enhancing the ballistic thermal transport of silicene through smooth interface coupling,” Journal of Physics: Condensed Matter. 2016. link Times cited: 5 Abstract: We have performed nonequilibrium molecular dynamics calculat… read more Abstract: We have performed nonequilibrium molecular dynamics calculations on the length (L ?>) dependence of thermal conductivity (K ?>) of silicene both supported on and sandwiched between the smooth surfaces, i.e. h-BN, at room temperature. We find that K ?> of silicene follows a power law K∝Lβ ?>, with β ?> increasing from about 0.3–0.4 under the effect of interface coupling, showing an enhancement of the ballistic thermal transport of silicene. We also find that β ?> can be further increased to about 0.6 by increasing the interface coupling strength for the silicene sandwiched between h-BN. The increase of β ?> for the supported case is found to come from the variation of the flexural acoustic (ZA) phonon mode and the first optical phonon mode induced by the substrate, whereas the unusual increase of β ?> for the sandwiched case is attributed to the increment of velocities of all three acoustic phonon modes. These findings provide an interesting route for manipulating the ballistic energy flow in nanomaterials. read less S. Zhao et al., “Amorphization and nanocrystallization of silicon under shock compression,” Acta Materialia. 2016. link Times cited: 101 J. Zhang, Y. Hong, Z. Tong, Z. Xiao, H. Bao, and Y. Yue, “Molecular dynamics study of interfacial thermal transport between silicene and substrates.,” Physical chemistry chemical physics : PCCP. 2015. link Times cited: 41 Abstract: In this work, the interfacial thermal transport across silic… read more Abstract: In this work, the interfacial thermal transport across silicene and various substrates, i.e., crystalline silicon (c-Si), amorphous silicon (a-Si), crystalline silica (c-SiO2) and amorphous silica (a-SiO2) are explored by classical molecular dynamics (MD) simulations. A transient pulsed heating technique is applied in this work to characterize the interfacial thermal resistance in all hybrid systems. It is reported that the interfacial thermal resistances between silicene and all substrates decrease nearly 40% with temperature from 100 K to 400 K, which is due to the enhanced phonon couplings from the anharmonicity effect. Analysis of phonon power spectra of all systems is performed to interpret simulation results. Contradictory to the traditional thought that amorphous structures tend to have poor thermal transport capabilities due to the disordered atomic configurations, it is calculated that amorphous silicon and silica substrates facilitate the interfacial thermal transport compared with their crystalline structures. Besides, the coupling effect from substrates can improve the interface thermal transport up to 43.5% for coupling strengths χ from 1.0 to 2.0. Our results provide fundamental knowledge and rational guidelines for the design and development of the next-generation silicene-based nanoelectronics and thermal interface materials. read less X. Hao and H. Cui, “Electronic, elastic properties and hardness of the novel tetragonal silicon,” Journal of the Korean Physical Society. 2014. link Times cited: 8 Abstract: Silicon is an important material for technical applications.… read more Abstract: Silicon is an important material for technical applications. Recently, a long-puzzling metastable phase of silicon (T12-Si) has been theoretically identified. In this work, we used first-principles calculations to study the electronic and elastic properties and the hardness of this new silicon allotrope to enrich the relevant information. These properties of cubic Si (c-Si) were also calculated for comparison. The results show that the T12-Si is mechanically anisotropic and has a lower bulk modulus and shear modulus than c-Si. Its theoretical hardness is 10.3 GPa, smaller than the value of 13.5 GPa for c-Si. Analyses of the electronic properties reveal that T12-Si is an indirect band gap crystal with a gap value of 0.69 eV, making it a promising semiconductor for future technical applications and that covalent sp3-hybridization is the main interaction in this crystal. The reason the calculated hardnesses of c-Si and T12-Si are rather small compared to that of diamond is also discussed. read less L. Shokeen and P. Schelling, “An empirical potential for silicon under conditions of strong electronic excitation,” Applied Physics Letters. 2010. link Times cited: 24 Abstract: We present an empirical potential developed for silicon unde… read more Abstract: We present an empirical potential developed for silicon under conditions of strong electronic excitation. We show the essentially athermal nature of the melting transition when the electronic temperature is extremely high. The resulting liquid is shown to be distinct from ordinary liquid silicon. For less intense excitations, we determine the thermal melting temperature and demonstrate the possible existence of a regime where ordinary thermodynamic melting can occur but at a reduced temperature Tm. We show laser-induced softening of the lattice can lead to lattice cooling for very short time scales (∼100 fs), an effect never before recognized. read less M. Li, X.-W. Lei, T. Lu, and T. Fujii, “Deformation mechanism of ripplocation in silicon–graphite composites,” Materials Today Communications. 2024. link Times cited: 0 W. Chena, Y. Zhai, Y. Bai, Z. Li, and H. Wang, “Heat transfer mechanism for abnormal enhancement of thermal conductivity in a nanofluidic system by molecular dynamics,” Powder Technology. 2023. link Times cited: 0 M. D. Mihai et al., “Athermal annealing of pre-existing defects in crystalline silicon,” Acta Materialia. 2023. link Times cited: 1 X. Huang et al., “Robust microscale structural superlubricity between graphite and nanostructured surface,” Nature Communications. 2023. link Times cited: 3 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 E. Mørtsell, D. Zhao, A. Autruffe, Y. Chen, M. Sabatino, and Y. Li, “The Nature of a Low Angle Grain-Boundary in a Si Bi-Crystal with Added Fe Impurities,” SSRN Electronic Journal. 2023. link Times cited: 0 W. Wan, Z. Sun, Z. Xiong, and C. Tang, “Misorientation and Temperature Dependence of Small Angle Twist Grain Boundaries in Silicon: Atomistic Simulation of Directional Growth,” Crystal Growth & Design. 2023. link Times cited: 1 M. Maździarz, “Transferability of interatomic potentials for silicene,” Beilstein Journal of Nanotechnology. 2023. link Times cited: 1 Abstract: The ability of various interatomic potentials to reproduce t… read more Abstract: The ability of various interatomic potentials to reproduce the properties of silicene, that is, 2D single-layer silicon, polymorphs was examined. Structural and mechanical properties of flat, low-buckled, trigonal dumbbell, honeycomb dumbbell, and large honeycomb dumbbell silicene phases, were obtained using density functional theory and molecular statics calculations with Tersoff, MEAM, Stillinger–Weber, EDIP, ReaxFF, COMB, and machine-learning-based interatomic potentials. A quantitative systematic comparison and a discussion of the results obtained are reported. read less J. Zhang, B. He, and B. Zhang, “Failure mode change and material damage with varied machining speeds: a review,” International Journal of Extreme Manufacturing. 2023. link Times cited: 2 Abstract: High-speed machining (HSM) has been studied for several deca… read more Abstract: High-speed machining (HSM) has been studied for several decades and has potential application in various industries, including the automobile and aerospace industries. However, the underlying mechanisms of HSM have not been formally reviewed thus far. This article focuses on the solid mechanics framework of adiabatic shear band (ASB) onset and material metallurgical microstructural evolutions in HSM. The ASB onset is described using partial differential systems. Several factors in HSM were considered in the systems, and the ASB onset conditions were obtained by solving these systems or applying the perturbation method to the systems. With increasing machining speed, an ASB can be depressed and further eliminated by shock pressure. The damage observed in HSM exhibits common features. Equiaxed fine grains produced by dynamic recrystallization widely cause damage to ductile materials, and amorphization is the common microstructural evolution in brittle materials. Based on previous studies, potential mechanisms for the phenomena in HSM are proposed. These include the thickness variation of the white layer of ductile materials. These proposed mechanisms would be beneficial to deeply understanding the various phenomena in HSM. read less W. Wan and C. Tang, “Structures and energies of computed silicon (001) small angle mixed grain boundaries as a function of three macroscopic characters,” Acta Materialia. 2022. link Times cited: 0 C. Tang, W. Wan, L. Huang, R. He, and L. Zhou, “On the Formation and Multiplicity of Si [001] Small Angle Symmetric Tilt Grain Boundaries: Atomistic Simulation of Directional Growth,” Crystal Growth & Design. 2022. link Times cited: 2 R. Abram, D. Chrobak, J. Byggmästar, K. Nordlund, and R. Nowak, “Comprehensive structural changes in nanoscale-deformed silicon modelled with an integrated atomic potential,” Materialia. 2022. link Times cited: 2 J. Luo, C. Zhou, Q. Li, Y. Lin, and L. Liu, “Atomic Transport Properties of Silicon Melt at High Temperature,” SSRN Electronic Journal. 2022. link Times cited: 3 W. Wan, C. Tang, and W. Zou, “Exploring Silicon [001] Small Angle Symmetric Tilt Grain Boundaries: Structures, Energies and Stress fields,” Applied Surface Science. 2022. link Times cited: 4 P. Lou, H.-Q. Pan, and Y. Wu, “Solid-liquid coexistence simulation of silicon melting point and reverse fitting correction potential function,” Other Conferences. 2022. link Times cited: 0 Abstract: In molecular dynamics simulation, the phase transition is a … read more Abstract: In molecular dynamics simulation, the phase transition is a rather complex process, and the melting point of materials simulated often deviates greatly from the experimental reported ones. Therefore, this article simulates the phase transition temperature of silicon and tries to reduce the influence of the large error from the simulation results. We use the StillingerWeber (SW) potential to simulate the solid-liquid coexistence method and the direct heating method are used respectively to compare and simulate the melting process of silicon. The influence of atomic number on the solid-liquid coexistence simulation process of melting point is discussed, and the influence of time step and potential function directly on the melting process is further discussed. Finally, we tried to modify the SW potential function to get better results. The selected computer algorithm has been further discussed in the section "Inverse fitting Analysis". read less V. Kuryliuk, S. Semchuk, K. Dubyk, and R. Chornyi, “Structural features and thermal stability of hollow-core Si nanowires: A molecular dynamics study,” Nano-Structures & Nano-Objects. 2022. link Times cited: 3 R. Fallahpour and R. Melnik, “A MOLECULAR DYNAMICS STUDY OF NANOWIRE RESONATOR BIO-OBJECT DETECTION,” Journal of Mechanics in Medicine and Biology. 2021. link Times cited: 1 Abstract: This paper presents a comprehensive analysis, carried out by… read more Abstract: This paper presents a comprehensive analysis, carried out by the molecular dynamics (MD) simulations, of the vibrations of silicon nanowire (SiNW) resonators, having diverse applications including biological and medical fields. The chosen approach allows us to obtain a better understanding of the nanowire (NW) materials’ characteristics, providing a more detailed insight into the behavior of nanostructures, especially when the topic of interest is relevant to their dynamics, interatomic interactions, and atoms trajectories’ prediction. We first simulate a SiNW to study its frequency of vibrations using MD simulations. Then, we add a molecule of human immunodeficiency virus as an example to investigate the potential of the SiNW resonator for the detection of tiny bio-objects. The developed technique and its application to the detection of tiny objects, such as viruses, are discussed in the context of several key effects pertinent to the design of SiNW. read less M. Eghbalian, R. Ansari, and S. Rouhi, “Effects of geometrical parameters and functionalization percentage on the mechanical properties of oxygenated single-walled carbon nanotubes,” Journal of Molecular Modeling. 2021. link Times cited: 8 X. H. Huang, Y.-J. Hu, and Q. An, “Locking of Screw Dislocations in Silicon due to Core Structure Transformation,” The Journal of Physical Chemistry C. 2021. link Times cited: 2 L. M. Sandonas, A. R. Méndez, R. Gutierrez, G. Cuniberti, and V. Mujica, “Nanoscale Phononic Analog of the Ranque-Hilsch Vortex Tube,” Physical review applied. 2021. link Times cited: 1 Abstract: Thermal management is a current global challenge that must b… read more Abstract: Thermal management is a current global challenge that must be addressed exhaustively. We propose the design of a nanoscale phononic analog of the Ranque-Hilsch vortex tube in which heat flowing at a given temperature is split into two different streams going to the two ends of the device, inducing a temperature asymmetry. Our nanoscale prototype consists of two carbon nanotubes (capped and open) connected by molecular chains. The results show that the structural asymmetry in the contact regions is the key factor for producing the flux asymmetry and, hence, the induced temperature-bias effect. The effect can be controlled by tuning the thermal-equilibration temperature, the number of chains, and the chain length. Deposition on a substrate adds another variable to the manipulation of the flux asymmetry but the effect vanishes at very large substrate temperatures. Our study yields insights into the thermal management in nanoscale materials, especially the crucial issue of whether the thermal asymmetry can survive phonon scattering over relatively long distances, and thus provides a starting point for the design of a nanoscale phononic analog of the Ranque-Hilsch vortex tube. read less T. Reichenbach, G. Moras, L. Pastewka, and M. Moseler, “Solid-Phase Silicon Homoepitaxy via Shear-Induced Amorphization and Recrystallization.,” Physical review letters. 2021. link Times cited: 2 Abstract: We study mechanically induced phase transitions at tribologi… read more Abstract: We study mechanically induced phase transitions at tribological interfaces between silicon crystals using reactive molecular dynamics. The simulations reveal that the interplay between shear-driven amorphization and recrystallization results in an amorphous shear interface with constant thickness. Different shear elastic responses of the two anisotropic crystals can lead to the migration of the amorphous interface normal to the sliding plane, causing the crystal with lowest elastic energy density to grow at the expense of the other one. This triboepitaxial growth can be achieved by crystal misorientation or exploiting elastic finite-size effects, enabling the direct deposition of homoepitaxial silicon nanofilms by a crystalline tip rubbing against a substrate. read less P. Wei, P. Gao, J. Yang, and W. Pu, “Atomic-scale friction along various scan paths starting at different points,” Microsystem Technologies. 2021. link Times cited: 1 L. N. Abdulkadir, A. Bello, M. Bawa, and A. M. Abioye, “Nanometric behaviour of monocrystalline silicon when single point diamond turned—a molecular dynamics and response surface methodology analysis,” Engineering Research Express. 2020. link Times cited: 3 Abstract: Hard and brittle materials such as silicon and silicon carbi… read more Abstract: Hard and brittle materials such as silicon and silicon carbide are widely used in aerospace and integrated circuit. They are often poorly machined owing to non-linearity in machining process and complexities in selecting suitable machining parameters and tool geometry. The experimental difficulty involved in observing nanoscale physical phenomena (i.e. in-process measurement problems, inaccessible contact area of tool and workpiece, and the difficulty of surface analysis) has led to the use of molecular dynamics (MD) and response surface methodology (RSM) to investigate effect of tool edge radius, rake and clearance angles on monocrystalline silicon in this research. The response of subsurface deformation depth (SSD), tool temperature, kinetic friction cutting and thrust forces to tool edge radius, rake and clearance angles showed that SSD increased as the rake angle, edge radius and clearance angle increased while kinetic friction reduced as they increased. The increase in SSD as the clearance angle increased as observed in this study can be associated to the interactive/combined influence of the effects of both edge radius and rake angle. read less S. Gelin, A. Champagne-Ruel, and N. Mousseau, “Enthalpy-entropy compensation of atomic diffusion originates from softening of low frequency phonons,” Nature Communications. 2020. link Times cited: 16 L. N. Abdulkadir, K. Abou-El-Hossein, and M. Liman, “Comparative Study of Optical Silicon Nanomachining Experimental Results and MD Simulation Outputs,” Solid State Phenomena. 2020. link Times cited: 0 Abstract: The high strength and good optical performance offered by op… read more Abstract: The high strength and good optical performance offered by optical grade silicon could be considered as the reason for its wide usage as optical materials in many industries including electronic, metrology, infrared (IR) optics and solar cells. Due to this, nanoscale manufacturing of these products requires superior quality and enhanced functional performance of the produced materials. Because recent studies have been focusing on correlating both surface and subsurface nature alterations with better functional performance, an MD study of the experiment was carried out in comparison with experiment to match the observed MD model features to the experimental result obtained. The MD study was observed to conform with the Ra result as obtained in the experiment. read less J. Hickman and Y. Mishin, “Thermal conductivity and its relation to atomic structure for symmetrical tilt grain boundaries in silicon.,” Physical review materials. 2020. link Times cited: 9 Abstract: We perform a systematic study of thermal resistance/conducta… read more Abstract: We perform a systematic study of thermal resistance/conductance of tilt grain boundaries (GBs) in Si using classical molecular dynamics. The GBs studied are naturally divided into three groups according to the structural units forming the GB core. We find that, within each group, the GB thermal conductivity strongly correlates with the excess GB energy. All three groups predict nearly the same GB conductivity extrapolated to the high-energy limit. This limiting value is close to the thermal conductivity of amorphous Si, suggesting similar heat transport mechanisms. While the lattice thermal conductivity decreases with temperature, the GB conductivity slightly increases. However, at high temperatures it turns over and starts decreasing if the GB structure undergoes a premelting transformation. Analysis of vibrational spectra of GBs resolved along different directions sheds light on the mechanisms of their thermal resistance. The existence of alternating tensile and compressive atomic environments in the GB core gives rise to localized vibrational modes, frequency gaps creating acoustic mismatch with lattice phonons, and anharmonic vibrations of loosely-bound atoms residing in open atomic environments. read less G. Plummer and G. Tucker, “Bond-order potentials for theTi3AlC2andTi3SiC2MAX phases,” Physical Review B. 2019. link Times cited: 12 S. Shinzato, M. Wakeda, and S. Ogata, “An atomistically informed kinetic Monte Carlo model for predicting solid solution strengthening of body-centered cubic alloys,” International Journal of Plasticity. 2019. link Times cited: 26 L. N. Abdulkadir and K. Abou-El-Hossein, “Diamond tool wear mode, path and tip temperature distribution considering effect of varying rake angle and duncut/Redge ratio,” Surface Topography: Metrology and Properties. 2019. link Times cited: 8 Abstract: Diamond tool wear has been proven to strongly depend on the … read more Abstract: Diamond tool wear has been proven to strongly depend on the temperature at the cutting zone. This is because the elevated temperature so attained during machining not only lowers carbon cohesion energy thereby reducing the fracture toughness of diamond tool due to C–C bond weakening but also facilitates high rate of carbon diffusion from diamond tool into silicon workpiece leading to high tool wear. This research therefore studied the response of diamond tool wear path and mode to changing rake angle and duncutRedge ratio during ultraprecision single point diamond turning of a monocrystalline silicon. It was observed from the study that the tool with larger rake angle and high duncutRedge ratio experienced stronger cutting resistance from the workpiece thereby causing the kinetic friction to be high. Additionally, silicon carbide (Tribochemistry) formation was observed to be through both solid-state single phase and multiphase reaction which are in tandem with sp 3 –sp 2 disorder (graphitization) of diamond with bulk of the observed tool wear happening in the flank face which could be due to increasing rake angle influence on the changing duncutRedge ratio. read less H. Dai, J. Chen, and G. Liu, “A numerical study on subsurface quality and material removal during ultrasonic vibration assisted cutting of monocrystalline silicon by molecular dynamics simulation,” Materials Research Express. 2019. link Times cited: 30 Abstract: Molecular dynamics (MD) simulation is used to study the subs… read more Abstract: Molecular dynamics (MD) simulation is used to study the subsurface quality and material removal of single crystal silicon with a diamond tool during ultrasonic elliptical vibration assisted cutting (UEVAC), 1D ultrasonic vibration assisted cutting (1D UVAC) and traditional cutting (TC) process. In the simulations, a long-range analytical bond order potential is used to describe the interaction inside the silicon specimen, providing a more accurate depiction of the atomic scale mechanisms of ductile plasticity, brittle fracture, and structural changes in silicon. The results show that UEVAC and 1D UVAC in cutting brittle material silicon causes a much smaller cutting force, much lower von Mises stress at the subsurface, larger material remove rate, lower compressive normal stress σ x x and σ y y , and smaller shear stress τ x y . In addition, the hydrostatic stress of subsurface for TC and 1D UVAC is much higher than that for UEVAC, which results in fewer Si-II and bct5-Si formed from the original Si-I in UEVAC. Moreover, the number of other atoms for UEVAC is overall smaller than those of using TC and 1D UVAC, which confirms that UEVAC produces a better subsurface. And atomic flow field analysis shows that the UEVAC tends to cut silicon in a more ductile mode. Besides, the temperature in front of tool edge and below the tool flank face of TC is much higher. This means that 1D UVAC and UEVAC have a positive effect on the tool life. However, the temperature in subsurface zone is overall larger, which reveals that 1D UVAC and UEVAC have a negative effect on the subsurface temperature. read less T. Xiao et al., “Rapid microwave synthesis of coaxial SiC/carbon fibre (SiC/CF) with improved oxidation resistance and wettability,” Ceramics International. 2019. link Times cited: 6 Y. Wei, Y. Li, D. Huang, C. Zhou, and J. Zhao, “Fracture properties of nanoscale single-crystal silicon plates: Molecular dynamics simulations and finite element method,” Engineering Fracture Mechanics. 2018. link Times cited: 10 G. Moras et al., “Shear melting of silicon and diamond and the disappearance of the polyamorphic transition under shear,” Physical Review Materials. 2018. link Times cited: 21 X. Yuan and Y. Wang, “Radial deformation of single-walled carbon nanotubes adhered to solid substrates and variations of energy: Atomistic simulations and continuum analysis,” International Journal of Solids and Structures. 2018. link Times cited: 8 F. González-Cataldo, F. Corvacho, and G. Gutiérrez, “Melting curve of Si by means of the Z-method,” Journal of Physics: Conference Series. 2018. link Times cited: 1 Abstract: The melting curve of silicon is investigated through classic… read more Abstract: The melting curve of silicon is investigated through classical molecular dynamics simulations. We explore pressures from 0 to 20 GPa using the EDIP, Stillinger-Weber, and Tersoff interactomic potentials. Using the Z method, we demonstrate that the predicted melting temperature Tm can be significantly overestimated, depending on the potential chosen. Our results show that none of the potentials explored is able to reproduce the experimental melting curve of silicon by means of the Z-method. However, the EDIP potential does predict the change in the Clapeyron slope, associated with the diamond to β-tin phase transition. read less Y. Zhou, Z. X. Guo, S. Chen, H. Xiang, and X. Gong, “Anisotropic in-plane thermal conductivity in multilayer silicene,” Physics Letters A. 2018. link Times cited: 5 S. Starikov, N. Lopanitsyna, D. Smirnova, and S. Makarov, “Atomistic simulation of Si-Au melt crystallization with novel interatomic potential,” Computational Materials Science. 2018. link Times cited: 20 L. Sementa, G. Barcaro, S. Monti, and V. Carravetta, “Molecular dynamics simulations of melting and sintering of Si nanoparticles: a comparison of different force fields and computational models.,” Physical chemistry chemical physics : PCCP. 2018. link Times cited: 17 Abstract: Melting and sintering of silicon nanoparticles are investiga… read more Abstract: Melting and sintering of silicon nanoparticles are investigated by means of classical molecular dynamics simulations to disclose the dependence of modelling on the system type, the simulation procedure and interaction potential. The capability of our parametrization of a reactive force field ReaxFF to describe such processes is assessed through a comparison with formally simpler Stillinger-Weber and Tersoff potentials, which are frequently used for simulating silicon-based materials. A substantial dependence of both the predicted melting point and its variation as a function of the nanoparticle size on the simulation model is also highlighted. The outcomes of the molecular dynamics simulations suggest that the trend of the nanoparticulate sintering/coalescence time vs. temperature could provide a valid tool to determine the melting points of nanoparticles theoretically/experimentally. read less S. Das and A. Dutta, “Design of fracture-resistant silicon structure with molecular dynamics simulation,” Computational Materials Science. 2017. link Times cited: 0 Q.-K. Wang, C. Chai, Q. Fan, and Y. Yang, “Physical Properties of C-Si Alloys in C2/m Structure,” Communications in Theoretical Physics. 2017. link Times cited: 14 Y. He, H. Li, F. Wei, J. Qi, Q. Meng, and Y. Sui, “Mechanical properties of multilayer hexagonal silicon under uniaxial tension,” Computational Materials Science. 2017. link Times cited: 10 S. Goel, S. Chavoshi, and A. Murphy, “Molecular dynamics simulation (MDS) to study nanoscale machining processes.” 2017. link Times cited: 2 Abstract: 1 Molecular dynamics simulation (MDS) to study nanoscale cut… read more Abstract: 1 Molecular dynamics simulation (MDS) to study nanoscale cutting processes Saurav Goel1, Saeed Zare Chavoshi2 and Adrian Murphy3 1Precision Engineering Institute, School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, Bedfordshire, MK430AL, UK 2Mechanical Engineering Department, Imperial College London, London, SW7 2AZ, UK 3School of Mechanical and Aerospace Engineering, Queen’s University, Belfast, BT9 5AH, UK Corresponding author Tel.: +44 1234754132, Email address: sgoel.diamond@gmail.com read less L. Tan, C. Chai, Q. Fan, and Y. Yang, “Mechanical and electronic properties of C–Si alloys in the P2221 structure,” Chinese Journal of Physics. 2016. link Times cited: 8 Y. Zhao et al., “Molecular dynamics simulation of nano-indentation of (111) cubic boron nitride with optimized Tersoff potential,” Applied Surface Science. 2016. link Times cited: 25 Z. Zhang, A. Stukowski, and H. Urbassek, “Interplay of dislocation-based plasticity and phase transformation during Si nanoindentation,” Computational Materials Science. 2016. link Times cited: 28 A. Peguiron, G. Moras, M. Walter, H. Uetsuka, L. Pastewka, and M. Moseler, “Activation and mechanochemical breaking of C–C bonds initiate wear of diamond (110) surfaces in contact with silica,” Carbon. 2016. link Times cited: 57 E. Hahn and M. Meyers, “Grain-size dependent mechanical behavior of nanocrystalline metals,” Materials Science and Engineering A-structural Materials Properties Microstructure and Processing. 2015. link Times cited: 162 X.-Y. Zhou, H. Ren, B. Huang, and T.-Y. Zhang, “Surface-induced size-dependent ultimate tensile strength of thin films,” Physics Letters A. 2015. link Times cited: 8 R. Matsumoto, S. Seki, S. Taketomi, and N. Miyazaki, “Hydrogen-related phenomena due to decreases in lattice defect energies—Molecular dynamics simulations using the embedded atom method potential with pseudo-hydrogen effects,” Computational Materials Science. 2014. link Times cited: 18 L. Shokeen and P. Schelling, “Role of electronic-excitation effects in the melting and ablation of laser-excited silicon,” Computational Materials Science. 2013. link Times cited: 18 M. Timonova and B. Thijsse, “Thermodynamic properties and phase transitions of silicon using a new MEAM potential,” Computational Materials Science. 2010. link Times cited: 13 P. Schelling, “Phase behavior and kinetics of a new bond-order potential for silicon,” Computational Materials Science. 2008. link Times cited: 24 L. Feng, X. Zhang, W. Li, M. Liu, and X. Yao, “Multiple structural phase transitions in single crystal silicon subjected to dynamic loading,” Scripta Materialia. 2024. link Times cited: 0 L. Marqués, M. Aboy, P. López, I. Santos, L. Pelaz, and G. Fisicaro, “Atomistic modeling of laser-related phenomena,” Laser Annealing Processes in Semiconductor Technology. 2021. link Times cited: 0 B. Bauerhenne, “Empirical MD Simulations of Laser-Excited Matter,” Materials Interaction with Femtosecond Lasers. 2021. link Times cited: 0 O. Koroleva and A. Mazhukin, “Atomistic modeling of the thermophysical characteristics of silicon in the region of the semiconductor-metal phase transition,” Keldysh Institute Preprints. 2018. link Times cited: 0 J. Zhang, Y. Hong, M. Liu, Y. Yue, Q. Xiong, and G. Lorenzini, “Molecular dynamics simulation of the interfacial thermal resistance between phosphorene and silicon substrate,” International Journal of Heat and Mass Transfer. 2017. link Times cited: 81 S. Das and A. Dutta, “Elastic behavior of amorphous-crystalline silicon nanocomposite: An atomistic view,” Physica E-low-dimensional Systems & Nanostructures. 2017. link Times cited: 3 L. Sang, “Affect of the graphene layers on the melting temperature of silicon by molecular dynamics simulations,” Computational Materials Science. 2016. link Times cited: 8 Q. Fan et al., “Prediction of novel phase of silicon and Si–Ge alloys,” Journal of Solid State Chemistry. 2016. link Times cited: 31 S. Goel, X. Luo, A. Agrawal, and R. Reuben, “Diamond machining of silicon: A review of advances in molecular dynamics simulation,” International Journal of Machine Tools & Manufacture. 2015. link Times cited: 314 R. Alsayegh, “Vision-augmented molecular dynamics simulation of nanoindentation,” Journal of Nanomaterials. 2015. link Times cited: 7 Abstract: We present a user-friendly vision-augmented technique to car… read more Abstract: We present a user-friendly vision-augmented technique to carry out atomic simulation using hand gestures. The system is novel in its concept as it enables the user to directly manipulate the atomic structures on the screen, in 3D space using hand gestures, allowing the exploration and visualisation of molecular interactions at different relative conformations. The hand gestures are used to pick and place atoms on the screen allowing thereby the ease of carrying out molecular dynamics simulation in a more efficient way. The end result is that users with limited expertise in developing molecular structures can now do so easily and intuitively by the use of body gestures to interact with the simulator to study the system in question. The proposed system was tested by simulating the crystal anisotropy of crystalline silicon during nanoindentation. A long-range (Screened bond order) Tersoff potential energy function was used during the simulation which revealed the value of hardness and elastic modulus being similar to what has been found previously from the experiments. We anticipate that our proposed system will open up new horizons to the current methods on how an MD simulation is designed and executed. read less S. Seki, R. Matsumoto, Y. Inoue, S. Taketomi, and N. Miyazaki, “Development of EAM Potential for Fe with Pseudo-Hydrogen Effects and Molecular Dynamics Simulation of Hydrogen Embrittlement,” Journal of The Society of Materials Science, Japan. 2012. link Times cited: 6 Abstract: Numerous studies have reported that solute hydrogen atoms an… read more Abstract: Numerous studies have reported that solute hydrogen atoms and lattice defects have strong interactions, and that hydrogen atoms significantly change the stability and/or mobility of lattice defects. Although molecular dynamics (MD) simulations can treat complicated interactions of various lattice defects, the time scale is insufficient to treat hydrogen diffusion so as to influence the lattice-defect generation and cooperative motion of hydrogen atoms and lattice defects. Here we developed an interatomic potential for Fe with pseudo-hydrogen effects on lattice-defect energies and performed MD simulations of tensile loading. First, we estimated the lattice-defect energies of Fe and hydrogen-trap energies of lattice defects by using first-principle calculations and evaluated the lattice-defect energies under a practical gaseous hydrogen environment. Second, we refitted the existing embedded-atom-method potential for Fe to represent the lattice-defect energies amended by hydrogen effects. Finally, we confirmed that our potential is applicable for various phenomena by estimating the reproducibility of grain-boundary energies that are not employed for potential fitting. Our tensile-loading simulations of a nano specimen show that hydrogen reduces elongation at rupture. read less M. Hu, X. Zhang, K. Giapis, and D. Poulikakos, “Atomistic Mechanisms of Enhancing Energy Conversion Efficiency of Nanostructured Thermoelectrics.” 2011. link Times cited: 0 В. И. Мажукин et al., “Модификация кинетической модели Вильсона-Френкеля и атомистическое моделирование скорости плавления/кристаллизации металлов,” Математическое моделирование. 2023. link Times cited: 0 Abstract: В рамках кинетико-атомистического подхода предложен новый по… read more Abstract: В рамках кинетико-атомистического подхода предложен новый подход к построению температурной зависимости стационарной скорости распространения межфазной границы «твeрдое тело-жидкость» в металлах (алюминий, медь и железо) с различной кристаллографической ориентацией. Рассматриваемый температурный диапазон включает область предельно допустимых значений перегрева/переохлаждения для каждого из металлов. Выполнена существенная модификация известной кинетической модели с диффузионным ограничением Вильсона-Френкеля, которая использовалась для построения функции отклика. Проведено атомистическое моделирование процессов плавления/кристаллизации алюминия, меди и железа в рассматриваемом температурном диапазоне с использованием трех потенциалов взаимодействия семейства потенциалов «погруженного атома». Из сопоставления результатов моделирования с данными модифицированной кинетической модели построена функция отклика скорости интерфейса в области предельно допустимых значений перегрева/переохлаждения в металлах с использованием критерия наименьших квадратов. Использование в расчeтах модифицированной кинетической модели Вильсона-Френкеля существенно увеличивает точность функции отклика в рассматриваемом температурном диапазоне. Полученная температурная зависимость скорости движения межфазной границы является диффузионно-ограниченной и описывается одним и тем же уравнением для каждого металла в рассматриваемом температурном диапазоне. read less H. Niu et al., “A machine-learning interatomic potential to understand primary radiation damage of silicon,” Computational Materials Science. 2023. link Times cited: 3 D. Vizoso, G. Subhash, K. Rajan, and R. Dingreville, “Connecting Vibrational Spectroscopy to Atomic Structure via Supervised Manifold Learning: Beyond Peak Analysis,” Chemistry of Materials. 2023. link Times cited: 1 Abstract: Vibrational spectroscopy is a nondestructive technique commo… read more Abstract: Vibrational spectroscopy is a nondestructive technique commonly used in chemical and physical analyses to determine atomic structures and associated properties. However, the evaluation and interpretation of spectroscopic profiles based on human-identifiable peaks can be difficult and convoluted. To address this challenge, we present a reliable protocol based on supervised manifold learning techniques meant to connect vibrational spectra to a variety of complex and diverse atomic structure configurations. As an illustration, we examined a large database of virtual vibrational spectroscopy profiles generated from atomistic simulations for silicon structures subjected to different stress, amorphization, and disordering states. We evaluated representative features in those spectra via various linear and nonlinear dimensionality reduction techniques and used the reduced representation of those features with decision trees to correlate them with structural information unavailable through classical human-identifiable peak analysis. We show that our trained model accurately (over 97% accuracy) and robustly (insensitive to noise) disentangles the contribution from the different material states, hence demonstrating a comprehensive decoding of spectroscopic profiles beyond classical (human-identifiable) peak analysis. read less J. A. Vita and D. Trinkle, “Exploring the necessary complexity of interatomic potentials,” Computational Materials Science. 2021. link Times cited: 8 A. Hamedani et al., “Primary radiation damage in silicon from the viewpoint of a machine learning interatomic potential,” Physical Review Materials. 2021. link Times cited: 6 A. A. Zhuravlev, K. Abgaryan, and D. Reviznikov, “Multiscale Discrete Element Modeling,” Symmetry. 2021. link Times cited: 1 Abstract: A multiscale approach to discrete element modeling is presen… read more Abstract: A multiscale approach to discrete element modeling is presented. A distinctive feature of the method is that each macroscopic discrete element has an associated atomic sample representing the material’s atomic structure. The dynamics of the elements on macro and micro levels are described by systems of ordinary differential equations, which are solved in a self-consistent manner. A full cycle of multiscale simulations is applied to polycrystalline silicon. Macroscale elastic properties of silicon were obtained only using data extracted from the quantum mechanical properties. The results of computational experiments correspond well to the reference data. read less S. Sukhomlinov and M. Müser, “A mixed radial, angular, three-body distribution function as a tool for local structure characterization: Application to single-component structures.,” The Journal of chemical physics. 2020. link Times cited: 6 Abstract: A mixed radial, angular three-body distribution function g3(… read more Abstract: A mixed radial, angular three-body distribution function g3(rBC, θABC) is introduced, which allows the local atomic order to be more easily characterized in a single graph than with conventional correlation functions. It can be defined to be proportional to the probability of finding an atom C at a distance rBC from atom B while making an angle θABC with atoms A and B, under the condition that atom A is the nearest neighbor of B. As such, our correlation function contains, for example, the likelihood of angles formed between the nearest and the next-nearest-neighbor bonds. To demonstrate its use and usefulness, a visual library for many one-component crystals is produced first and then employed to characterize the local order in a diverse body of elemental condensed-matter systems. Case studies include the analysis of a grain boundary, several liquids (argon, copper, and antimony), and polyamorphism in crystalline and amorphous silicon including that obtained in a tribological interface. read less Y. Zuo et al., “A Performance and Cost Assessment of Machine Learning Interatomic Potentials.,” The journal of physical chemistry. A. 2019. link Times cited: 413 Abstract: Machine learning of the quantitative relationship between lo… read more Abstract: Machine learning of the quantitative relationship between local environment descriptors and the potential energy surface of a system of atoms has emerged as a new frontier in the development of interatomic potentials (IAPs). Here, we present a comprehensive evaluation of ML-IAPs based on four local environment descriptors --- atom-centered symmetry functions (ACSF), smooth overlap of atomic positions (SOAP), the Spectral Neighbor Analysis Potential (SNAP) bispectrum components, and moment tensors --- using a diverse data set generated using high-throughput density functional theory (DFT) calculations. The data set comprising bcc (Li, Mo) and fcc (Cu, Ni) metals and diamond group IV semiconductors (Si, Ge) is chosen to span a range of crystal structures and bonding. All descriptors studied show excellent performance in predicting energies and forces far surpassing that of classical IAPs, as well as predicting properties such as elastic constants and phonon dispersion curves. We observe a general trade-off between accuracy and the degrees of freedom of each model, and consequently computational cost. We will discuss these trade-offs in the context of model selection for molecular dynamics and other applications. read less J. Harrison, J. Schall, S. Maskey, P. Mikulski, M. T. Knippenberg, and B. Morrow, “Review of force fields and intermolecular potentials used in atomistic computational materials research,” Applied Physics Reviews. 2018. link Times cited: 99 Abstract: Molecular simulation is a powerful computational tool for a … read more Abstract: Molecular simulation is a powerful computational tool for a broad range of applications including the examination of materials properties and accelerating drug discovery. At the heart of molecular simulation is the analytic potential energy function. These functions span the range of complexity from very simple functions used to model generic phenomena to complex functions designed to model chemical reactions. The complexity of the mathematical function impacts the computational speed and is typically linked to the accuracy of the results obtained from simulations that utilize the function. One approach to improving accuracy is to simply add more parameters and additional complexity to the analytic function. This approach is typically used in non-reactive force fields where the functional form is not derived from quantum mechanical principles. The form of other types of potentials, such as the bond-order potentials, is based on quantum mechanics and has led to varying levels of accuracy and transferability. When selecting a potential energy function for use in molecular simulations, the accuracy, transferability, and computational speed must all be considered. In this focused review, some of the more commonly used potential energy functions for molecular simulations are reviewed with an eye toward presenting their general forms, strengths, and weaknesses.Molecular simulation is a powerful computational tool for a broad range of applications including the examination of materials properties and accelerating drug discovery. At the heart of molecular simulation is the analytic potential energy function. These functions span the range of complexity from very simple functions used to model generic phenomena to complex functions designed to model chemical reactions. The complexity of the mathematical function impacts the computational speed and is typically linked to the accuracy of the results obtained from simulations that utilize the function. One approach to improving accuracy is to simply add more parameters and additional complexity to the analytic function. This approach is typically used in non-reactive force fields where the functional form is not derived from quantum mechanical principles. The form of other types of potentials, such as the bond-order potentials, is based on quantum mechanics and has led to varying levels of accuracy and transferabilit... read less A. Bartók, J. Kermode, N. Bernstein, and G. Csányi, “Machine Learning a General-Purpose Interatomic Potential for Silicon,” Physical Review X. 2018. link Times cited: 291 Abstract: The success of first principles electronic structure calcula… read more Abstract: The success of first principles electronic structure calculation for predictive modeling in chemistry, solid state physics, and materials science is constrained by the limitations on simulated length and time scales due to computational cost and its scaling. Techniques based on machine learning ideas for interpolating the Born-Oppenheimer potential energy surface without explicitly describing electrons have recently shown great promise, but accurately and efficiently fitting the physically relevant space of configurations has remained a challenging goal. Here we present a Gaussian Approximation Potential for silicon that achieves this milestone, accurately reproducing density functional theory reference results for a wide range of observable properties, including crystal, liquid, and amorphous bulk phases, as well as point, line, and plane defects. We demonstrate that this new potential enables calculations that would be extremely expensive with a first principles electronic structure method, such as finite temperature phase boundary lines, self-diffusivity in the liquid, formation of the amorphous by slow quench, and dynamic brittle fracture. We show that the uncertainty quantification inherent to the Gaussian process regression framework gives a qualitative estimate of the potential's accuracy for a given atomic configuration. The success of this model shows that it is indeed possible to create a useful machine-learning-based interatomic potential that comprehensively describes a material, and serves as a template for the development of such models in the future. read less L. Pastewka, A. Klemenz, P. Gumbsch, and M. Moseler, “Screened empirical bond-order potentials for Si-C,” Physical Review B. 2013. link Times cited: 110 Abstract: Typical empirical bond-order potentials are short ranged and… read more Abstract: Typical empirical bond-order potentials are short ranged and give ductile instead of brittle behavior for materials such as crystalline silicon or diamond. Screening functions can be used to increase the range of these potentials. We outline a general procedure to combine screening functions with bond-order potentials that does not require to refit any of the potential's properties. We use this approach to modify Tersoff's [Phys. Rev. B 39, 5566 (1989)], Erhart & Albe's [Phys. Rev. B 71, 35211 (2005)] and Kumagai et al.'s [Comp. Mater. Sci. 39, 457 (2007)] Si, C and Si-C potentials. The resulting potential formulations correctly reproduce brittle materials response, and give an improved description of amorphous phases. read less R. Jones, C. Weinberger, S. Coleman, and G. Tucker, “Introduction to Atomistic Simulation Methods.” 2016. link Times cited: 1 T. Kumagai and S. Izumi, “Development of a Software to Optimize Parameters of Interatomic Potentials for Solid Systems,” Transactions of the Japan Society of Mechanical Engineers. A. 2011. link Times cited: 9 Abstract: Generally, it is difficult to develop practical interatomic … read more Abstract: Generally, it is difficult to develop practical interatomic potentials which can be used in classical molecular dynamics calculations, since a method for development had not been established. In order to solve such problems, we had proposed a framework to develop interatomic potentials. However, the framework had not been widely used due to the difficulty of coding a process to optimize potential-parameters, which was involved in the framework. In this work, a practical software to optimize potential-parameters for solid systems, was developed based on real-coded genetic algorithm (GA). Fitness (=optimization-function) in GA for potential-parameter optimization could be calculated in practical time, and a concept of the corresponded module in GA-code was proposed. The developed software has an extensible structure: a user can define a new crystal-structure, or a new potential function to use in potential-parameter optimization by defining a corresponded class for that in separated header files. Convenient interfacial class to calculate equilibrium material properties of crystals and that to calculate material properties of user-inputted atomic-structures were prepared to define optimization-function. Several sample input files and header files were available for easy starting. As a result of distribution, several effective interatomic potentials were developed by using the software. As a sample of the development of interatomic potential, Tersoff-type potential for SiO2 systems were shown. read less J.-C. Griesser, L. Frérot, J. A. Oldenstaedt, M. Müser, and L. Pastewka, “Analytic elastic coefficients in molecular calculations: Finite strain, nonaffine displacements, and many-body interatomic potentials,” Physical Review Materials. 2023. link Times cited: 1 Abstract: Elastic constants are among the most fundamental and importa… read more Abstract: Elastic constants are among the most fundamental and important properties of solid materials, which is why they are routinely characterized in both experiments and simulations. While conceptually simple, the treatment of elastic constants is complicated by two factors not yet having been concurrently discussed: finite-strain and non-affine, internal displacements. Here, we revisit the theory behind zero-temperature, finite-strain elastic constants and extend it to explicitly consider non-affine displacements. We further present analytical expressions for second-order derivatives of the potential energy for two-body and generic many-body interatomic potentials, such as cluster and empirical bond-order potentials. Specifically, we revisit the elastic constants of silicon, silicon carbide and silicon dioxide under hydrostatic compression and dilatation. Based on existing and new results, we outline the effect of multiaxial stress states as opposed to volumetric deformation on the limits of stability of their crystalline lattices. read less O. Koroleva, M. Demin, A. Mazhukin, and V. Mazhukin, “Modeling of electronic and phonon thermal conductivity of silicon in a wide temperature range,” Journal of Physics: Conference Series. 2021. link Times cited: 7 Abstract: In the present article, using the methods of mathematical mo… read more Abstract: In the present article, using the methods of mathematical modeling, the thermal conductivity of silicon was obtained in a wide temperature range (0.3 ≼ T ≼ 3 kK), including the region of semiconductor-metal phase transformations. As it is known, there are two mechanisms of heat transfer in a solid: elastic lattice vibrations and free electrons, therefore, in the study of the thermal conductivity of silicon, the lattice and electronic components were taken into account. The lattice (phonon) thermal conductivity in this work was determined within the framework of the atomistic approach. The Stillinger–Weber and Kumagai–Izumi–Hara–Sakai interaction potentials were used for modeling. The results of the comparison of the phonon thermal conductivity obtained from the simulation results with the used interaction potentials are presented. The modeling of the thermal conductivity of the electronic subsystem of silicon with intrinsic conductivity in this work is based on the use of the quantum statistics of the electron gas using the Fermi–Dirac integrals. The total thermal conductivity of silicon, obtained as the sum of the electronic and phonon components, is compared with the experimental data. read less W. Nöhring, J.-C. Griesser, P. Dondl, and L. Pastewka, “Surface lattice Green’s functions for high-entropy alloys,” Modelling and Simulation in Materials Science and Engineering. 2021. link Times cited: 0 Abstract: We study the surface elastic response of pure Ni, the random… read more Abstract: We study the surface elastic response of pure Ni, the random alloy FeNiCr and an average FeNiCr alloy in terms of the surface lattice Green’s function. We propose a scheme for computing per-site Green’s function and study their per-site variations. The average FeNiCr alloys accurately reproduces the mean Green’s function of the full random alloy. Variation around this mean is largest near the edge of the surface Brillouin-zone and decays as q −2 with wavevector q towards the Γ-point. We also present expressions for the continuum surface Green’s function of anisotropic solids of finite and infinite thickness and show that the atomistic Green’s function approaches continuum near the Γ-point. Our results are a first step towards efficient contact calculations and Peierls–Nabarro type models for dislocations in high-entropy alloys. read less D. Klein, E. Eisfeld, and J. Roth, “Molecular dynamics simulations of the laser ablation of silicon with the thermal spike model,” Journal of Physics D: Applied Physics. 2020. link Times cited: 9 Abstract: The purpose of this work is to model laser ablation of silic… read more Abstract: The purpose of this work is to model laser ablation of silicon on an atomistic scale in combination with a mesoscale model for the description of the electron-phonon interaction and an electron-temperature dependent interaction potential. The well-known continuum two-temperature model (TTM) for solids with highly excited electrons is extended from metals to silicon by explicitly taking charge carrier transport effects into account (nTTM). This is accomplished by the drift-diffusion limit of the Boltzmann-transport equation leading to the so called thermal-spike model (TSM). The model is further enhanced by extending the static modified Tersoff potential to a dynamical carrier excitation dependent interaction potential. We compare the TSM and nTTM with regard to physical correctness, numerical stability and applicability in the context of large-scale massive parallel high performance computing. read less W. Xu, Y. Jiao, and J. Fish, “An atomistically-informed multiplicative hyper-elasto-plasticity-damage model for high-pressure induced densification of silica glass,” Computational Mechanics. 2020. link Times cited: 6 A. Martini, S. Eder, and N. Dörr, “Tribochemistry: A Review of Reactive Molecular Dynamics Simulations,” Lubricants. 2020. link Times cited: 40 Abstract: Tribochemistry, the study of chemical reactions in tribologi… read more Abstract: Tribochemistry, the study of chemical reactions in tribological interfaces, plays a critical role in determining friction and wear behavior. One method researchers have used to explore tribochemistry is “reactive” molecular dynamics simulation based on empirical models that capture the formation and breaking of chemical bonds. This review summarizes studies that have been performed using reactive molecular dynamics simulations of chemical reactions in sliding contacts. Topics include shear-driven reactions between and within solid surfaces, between solid surfaces and lubricating fluids, and within lubricating fluids. The review concludes with a perspective on the contributions of reactive molecular dynamics simulations to the current understanding of tribochemistry, as well as opportunities for this approach going forward. read less C. Liu et al., “Influence of micro grooves of diamond tool on silicon cutting: a molecular dynamic study,” Molecular Simulation. 2020. link Times cited: 2 Abstract: ABSTRACT During single-point diamond turning of hard and bri… read more Abstract: ABSTRACT During single-point diamond turning of hard and brittle materials, tool wear is a dominant factor that influences machinability. In the wear process, micro grooves on the flank face is an important character of tool wear, which leads to the formation of subcutting edges and the ductile to brittle transition. In this paper, classical molecular dynamic simulations of nanometric cutting of silicon by a diamond tool with V-shape grooves were carried out to explore the effect of groove geometry on the workpiece and tool integrity. The evolution of tool wear and machined surface integrity was discussed. Simulation result shows that grooves have a significant influence on the stress and temperature distributions of the tool, which has a great influence on tool deterioration. Grooves with sharp edges will lead to severe tool wear and bring deep subsurface damage of the machined surface. However, the subsurface damage of the machined surface can be restrained with blunt grooves since the pressure is reduced. With a comprehensive understanding and controlling of groove, tool wear can be suppressed and high-quality surface can be achieved. read less Z. Fan, Y. Wang, X. Gu, P. Qian, Y. Su, and T. Ala‐Nissila, “A minimal Tersoff potential for diamond silicon with improved descriptions of elastic and phonon transport properties,” Journal of Physics: Condensed Matter. 2019. link Times cited: 10 Abstract: Silicon is an important material and many empirical interato… read more Abstract: Silicon is an important material and many empirical interatomic potentials have been developed for atomistic simulations of it. Among them, the Tersoff potential and its variants are the most popular ones. However, all the existing Tersoff-like potentials fail to reproduce the experimentally measured thermal conductivity of diamond silicon. Here we propose a modified Tersoff potential and develop an efficient open source code called GPUGA (graphics processing units genetic algorithm) based on the genetic algorithm and use it to fit the potential parameters against energy, virial and force data from quantum density functional theory calculations. This potential, which is implemented in the efficient open source GPUMD (graphics processing units molecular dynamics) code, gives significantly improved descriptions of the thermal conductivity and phonon dispersion of diamond silicon as compared to previous Tersoff potentials and at the same time well reproduces the elastic constants. Furthermore, we find that quantum effects on the thermal conductivity of diamond silicon at room temperature are non-negligible but small: using classical statistics underestimates the thermal conductivity by about 10% as compared to using quantum statistics. read less S. Vishnubhotla, R. Chen, S. Khanal, X. Hu, A. Martini, and T. Jacobs, “Matching Atomistic Simulations and In Situ Experiments to Investigate the Mechanics of Nanoscale Contact,” Tribology Letters. 2019. link Times cited: 15 H. Dai, H. Du, J. Chen, and G. Chen, “Influence of elliptical vibration on the behavior of silicon during nanocutting,” The International Journal of Advanced Manufacturing Technology. 2019. link Times cited: 25 J. Luo, A. Alateeqi, L. Liu, and T. Sinno, “Carbon solubility in liquid silicon: A computational analysis across empirical potentials.,” The Journal of chemical physics. 2019. link Times cited: 4 Abstract: The nucleation and growth of SiC precipitates in liquid sili… read more Abstract: The nucleation and growth of SiC precipitates in liquid silicon is important in the crystallization of silicon used for the photovoltaic industry. These processes depend strongly on the carbon concentration as well as the equilibrium solubility relative to the precipitate phase. Here, using a suite of statistical thermodynamic techniques, we calculate the solubility of carbon atoms in liquid silicon relative to the β-SiC phase. We employ several available empirical potentials to assess whether these potentials may reasonably be used to computationally analyze SiC precipitation. We find that some of the Tersoff-type potentials provide an excellent picture for carbon solubility in liquid silicon but, because of their severe silicon melting point overestimation, are limited to high temperatures where the carbon solubility is several percent, a value that is irrelevant for typical solidification conditions. Based on chemical potential calculations for pure silicon, we suggest that this well-known issue is confined to the description of the liquid phase and demonstrate that some recent potential models for silicon might address this weakness while preserving the excellent description of the carbon-silicon interaction found in the existing models. read less Y. Lysogorskiy, T. Hammerschmidt, J. Janssen, J. Neugebauer, and R. Drautz, “Transferability of interatomic potentials for molybdenum and silicon,” Modelling and Simulation in Materials Science and Engineering. 2019. link Times cited: 14 Abstract: Interatomic potentials are widely used in computational mate… read more Abstract: Interatomic potentials are widely used in computational materials science, in particular for simulations that are too computationally expensive for density functional theory (DFT). Most interatomic potentials have a limited application range and often there is very limited information available regarding their performance for specific simulations. We carried out high-throughput calculations for molybdenum and silicon with DFT and a number of interatomic potentials. We compare the DFT reference calculations and experimental data to the predictions of the interatomic potentials. We focus on a large number of basic materials properties, including the cohesive energy, atomic volume, elastic coefficients, vibrational properties, thermodynamic properties, surface energies and vacancy formation energies, which enables a detailed discussion of the performance of the different potentials. We further analyze correlations between properties as obtained from DFT calculations and how interatomic potentials reproduce these correlations, and suggest a general measure for quantifying the accuracy and transferability of an interatomic potential. From our analysis we do not establish a clearcut ranking of the potentials as each potential has its strengths and weaknesses. It is therefore essential to assess the properties of a potential carefully before application of the potential in a specific simulation. The data presented here will be useful for selecting a potential for simulations of Mo or Si. read less L. N. Abdulkadir and K. Abou-El-Hossein, “Observed edge radius behavior during MD nanomachining of silicon at a high uncut chip thickness,” The International Journal of Advanced Manufacturing Technology. 2018. link Times cited: 12 X. Yuan and Y. Wang, “Adhesion of carbon nanotubes on elastic substrates with finite thickness,” Journal of Applied Physics. 2018. link Times cited: 5 Abstract: How carbon nanotubes (CNTs) interact with substrates is fund… read more Abstract: How carbon nanotubes (CNTs) interact with substrates is fundamental for understanding their physical properties. In existing theoretical and modeling studies, the substrates are considered to be rigid with semi-infinite thickness. In this work, the effects of finite substrate thickness and elasticity are analyzed theoretically and numerically for free boundary conditions. Based on the energy-variational approach, considering the interfacial van der Waals interactions and bending strain energies stored in CNTs and substrates, the governing equations and boundary conditions are derived analytically. The theoretical predictions are in reasonable agreement with the results of molecular dynamics simulations. When the substrate is sufficiently thick, the results of the present theoretical model are entirely consistent with previous models for the infinite-thickness substrate. However, for relatively thin substrates, the effect of substrate thickness is significant due to the geometric large deformation. Three stable adhesive states (initial non-adhesive, partially adhesive, and fully wrapping states) can be achieved, dependent on the substrate thickness, the number of CNT walls, and the interfacial adhesion work. The stability of adhesive configurations is explored by analyzing the energy variations corresponding to the adhesive deformation. We show that there exist several modes of energy variations, depending on the adhesion work and the substrate-CNT bending stiffness ratio, which exhibit linear and nonlinear influences, respectively. Our results could serve as guidelines to design CNT-on-substrate systems.How carbon nanotubes (CNTs) interact with substrates is fundamental for understanding their physical properties. In existing theoretical and modeling studies, the substrates are considered to be rigid with semi-infinite thickness. In this work, the effects of finite substrate thickness and elasticity are analyzed theoretically and numerically for free boundary conditions. Based on the energy-variational approach, considering the interfacial van der Waals interactions and bending strain energies stored in CNTs and substrates, the governing equations and boundary conditions are derived analytically. The theoretical predictions are in reasonable agreement with the results of molecular dynamics simulations. When the substrate is sufficiently thick, the results of the present theoretical model are entirely consistent with previous models for the infinite-thickness substrate. However, for relatively thin substrates, the effect of substrate thickness is significant due to the geometric large deformation. Three s... read less R. Darkins, P. Ma, S. Murphy, and D. Duffy, “Simulating electronically driven structural changes in silicon with two-temperature molecular dynamics,” Physical Review B. 2018. link Times cited: 14 Abstract: Radiation can drive the electrons in a material out of therm… read more Abstract: Radiation can drive the electrons in a material out of thermal equilibrium with the nuclei, producing hot, transient electronic states that modify the interatomic potential energy surface. We present a rigorous formulation of two-temperature molecular dynamics that can accommodate these electronic effects in the form of electronic-temperature-dependent force fields. Such a force field is presented for silicon, which has been constructed to reproduce the ab initio-derived thermodynamics of the diamond phase for electronic temperatures up to 2.5eV, as well as the structural dynamics observed experimentally under nonequilibrium conditions in the femtosecond regime. This includes nonthermal melting on a subpicosecond timescale to a liquidlike state for electronic temperatures above ∼1eV. The methods presented in this paper lay a rigorous foundation for the large-scale atomistic modeling of electronically driven structural dynamics with potential applications spanning the entire domain of radiation damage. read less L. N. Abdulkadir, K. Abou-El-Hossein, A. I. Jumare, M. Liman, T. A. Olaniyan, and P. B. Odedeyi, “Review of molecular dynamics/experimental study of diamond-silicon behavior in nanoscale machining,” The International Journal of Advanced Manufacturing Technology. 2018. link Times cited: 38 L. N. Abdulkadir, K. Abou-El-Hossein, A. I. Jumare, M. Liman, T. A. Olaniyan, and P. B. Odedeyi, “Review of molecular dynamics/experimental study of diamond-silicon behavior in nanoscale machining,” The International Journal of Advanced Manufacturing Technology. 2018. link Times cited: 0 X. Yuan and Y. Wang, “Adhesion of single- and multi-walled carbon nanotubes to silicon substrate: atomistic simulations and continuum analysis,” Journal of Physics D: Applied Physics. 2017. link Times cited: 13 Abstract: The radial deformation of carbon nanotubes (CNTs) adhering t… read more Abstract: The radial deformation of carbon nanotubes (CNTs) adhering to a substrate may prominently affect their mechanical and physical properties. In this study, both classical atomistic simulations and continuum analysis are carried out, to investigate the lateral adhesion of single-walled CNTs (SWCNTs) and multi-walled CNTs (MWCNTs) to a silicon substrate. A linear elastic model for analyzing the adhesion of 2D shells to a rigid semi-infinite substrate is constructed in the framework of continuum mechanics. Good agreement is achieved between the cross-section profiles of adhesive CNTs obtained by the continuum model and by the atomistic simulation approach. It is found that the adhesion of a CNT to the silicon substrate is significantly influenced by its initial diameter and the number of walls. CNTs with radius larger than a certain critical radius are deformed radially on the silicon substrate with flat contact regions. With increasing number of walls, the extent of radial deformation of a MWCNT on the substrate decreases dramatically, and the flat contact area reduces—and eventually vanishes—due to increasing equivalent bending stiffness. It is analytically predicted that large-diameter MWCNTs with a large number of walls are likely to ‘stand’ on the silicon substrate. The present work can be useful for understanding the radial deformation of CNTs adhering to a solid planar substrate. read less E. Dontsova and R. Ballarini, “Atomistic modeling of the fracture toughness of silicon and silicon-silicon interfaces,” International Journal of Fracture. 2017. link Times cited: 6 G. P. P. Pun and Y. Mishin, “Optimized interatomic potential for silicon and its application to thermal stability of silicene,” Physical Review B. 2017. link Times cited: 35 Abstract: An optimized interatomic potential has been constructed for … read more Abstract: An optimized interatomic potential has been constructed for silicon using a modified Tersoff model. The potential reproduces a wide range of properties of Si and improves over existing potentials with respect to point defect structures and energies, surface energies and reconstructions, thermal expansion, melting temperature, and other properties. The proposed potential is compared with three other potentials from the literature. The potentials demonstrate reasonable agreement with first-principles binding energies of small Si clusters as well as single-layer and bilayer silicenes. The four potentials are used to evaluate the thermal stability of free-standing silicenes in the form of nanoribbons, nanoflakes, and nanotubes. While single-layer silicene is found to be mechanically stable at zero Kelvin, it is predicted to become unstable and collapse at room temperature. By contrast, the bilayer silicene demonstrates a larger bending rigidity and remains stable at and even above room temperature. The results suggest that bilayer silicene might exist in a free-standing form at ambient conditions. read less T. Remington, B. Remington, E. Hahn, and M. Meyers, “Deformation and failure in extreme regimes by high-energy pulsed lasers: A review,” Materials Science and Engineering A-structural Materials Properties Microstructure and Processing. 2017. link Times cited: 51 T. D. Nguyen, “GPU-accelerated Tersoff potentials for massively parallel Molecular Dynamics simulations,” Comput. Phys. Commun. 2017. link Times cited: 44 X. Hu, N. Chan, A. Martini, and P. Egberts, “Tip convolution on HOPG surfaces measured in AM-AFM and interpreted using a combined experimental and simulation approach,” Nanotechnology. 2017. link Times cited: 8 Abstract: Amplitude modulated atomic force microscopy (AM-AFM) was use… read more Abstract: Amplitude modulated atomic force microscopy (AM-AFM) was used to examine the influence of the size of the AFM tip apex on the measured surface topography of single highly oriented pyrolytic graphite (HOPG) atomic steps. Experimental measurements were complemented by molecular dynamics simulations of AM-AFM and the results from both were evaluated by comparison of the measured or simulated width of the topography at the step to that predicted using simple rigid-body geometry. The results showed that the step width, which is a reflection of the resolution of the measurement, increased with tip size, as expected, but also that the difference between the measured/simulated step width and the geometric calculation was tip size dependent. The simulations suggested that this may be due to the deformation of the bodies and the effect of that deformation on the interaction force and oscillation amplitude. Overall, this study showed that the resolution of AM-AFM measurements of atomic steps can be correlated to tip size and that this relationship is affected by the deformation of the system. read less G. Khara, S. Murphy, S. Daraszewicz, and D. Duffy, “The influence of the electronic specific heat on swift heavy ion irradiation simulations of silicon,” Journal of Physics: Condensed Matter. 2016. link Times cited: 30 Abstract: The swift heavy ion (SHI) irradiation of materials is often … read more Abstract: The swift heavy ion (SHI) irradiation of materials is often modelled using the two-temperature model. While the model has been successful in describing SHI damage in metals, it fails to account for the presence of a bandgap in semiconductors and insulators. Here we explore the potential to overcome this limitation by explicitly incorporating the influence of the bandgap in the parameterisation of the electronic specific heat for Si. The specific heat as a function of electronic temperature is calculated using finite temperature density functional theory with three different exchange correlation functionals, each with a characteristic bandgap. These electronic temperature dependent specific heats are employed with two-temperature molecular dynamics to model ion track creation in Si. The results obtained using a specific heat derived from density functional theory showed dramatically reduced defect creation compared to models that used the free electron gas specific heat. As a consequence, the track radii are smaller and in much better agreement with experimental observations. We also observe a correlation between the width of the band gap and the track radius, arising due to the variation in the temperature dependence of the electronic specific heat. read less J. L. Braun et al., “Size effects on the thermal conductivity of amorphous silicon thin films,” Physical Review B. 2016. link Times cited: 87 Abstract: In this study, we investigate thickness-limited size effects… read more Abstract: In this study, we investigate thickness-limited size effects on the thermal conductivity of amorphous silicon thin films ranging from 3 to 1636 nm grown via sputter deposition. While exhibiting a constant value up to ~100 nm, the thermal conductivity increases with film thickness thereafter. The thickness dependence we demonstrate is ascribed to boundary scattering of long wavelength vibrations and an interplay between the energy transfer associated with propagating modes (propagons) and nonpropagating modes (diffusons). A crossover from propagon to diffuson modes is deduced to occur at a frequency of ~1.8 THz via simple analytical arguments. These results provide empirical evidence of size effects on the thermal conductivity of amorphous silicon and systematic experimental insight into the nature of vibrational thermal transport in amorphous solids. read less S. Zhao, E. Hahn, B. Kad, B. Remington, E. Bringa, and M. Meyers, “Shock compression of [001] single crystal silicon,” The European Physical Journal Special Topics. 2016. link Times cited: 4 J. Yu, Y. Zhang, and J. Hales, “Milestone report on MD potential development for uranium silicide.” 2016. link Times cited: 0 Abstract: This report summarizes the progress on the interatomic poten… read more Abstract: This report summarizes the progress on the interatomic potential development of triuranium-disilicide (U3Si2) for molecular dynamics (MD) simulations. The development is based on the Tersoff type potentials for single element U and Si. The Si potential is taken from the literature and a Tersoff type U potential is developed in this project. With the primary focus on the U3Si2 phase, some other U-Si systems such as U3Si are also included as a test of the transferability of the potentials for binary U-Si phases. Based on the potentials for unary U and Si, two sets of parameters for the binary U-Si system are developed using the Tersoff mixing rules and the cross-term fitting, respectively. The cross-term potential is found to give better results on the enthalpy of formation, lattice constants and elastic constants than those produced by the Tersoff mixing potential, with the reference data taken from either experiments or density functional theory (DFT) calculations. In particular, the results on the formation enthalpy and lattice constants for the U3Si2 phase and lattice constants for the high temperature U3Si (h-U3Si) phase generated by the cross-term potential agree well with experimental data. Reasonable agreements are also reached on the elastic constants of U3Si2,more » on the formation enthalpy for the low temperature U3Si (m-U3Si) and h-U3Si phases, and on the lattice constants of m-U3Si phase. All these phases are predicted to be mechanically stable. The unary U potential is tested for three metallic U phases (α, β, γ). The potential is found capable to predict the cohesive energies well against experimental data for all three phases. It matches reasonably with previous experiments on the lattice constants and elastic constants of αU.« less read less S. Zhao et al., “Pressure and shear-induced amorphization of silicon,” Extreme Mechanics Letters. 2015. link Times cited: 45 P. Brommer, A. Kiselev, D. Schopf, P. Beck, J. Roth, and H. Trebin, “Classical interaction potentials for diverse materials from ab initio data: a review of potfit,” Modelling and Simulation in Materials Science and Engineering. 2014. link Times cited: 76 Abstract: Force matching is an established technique to generate effec… read more Abstract: Force matching is an established technique to generate effective potentials for molecular dynamics simulations from first-principles data. This method has been implemented in the open source code potfit. Here, we present a review of the method and describe the main features of the code. Particular emphasis is placed on the features added since the initial release: interactions represented by analytical functions, differential evolution as optimization method, and a greatly extended set of interaction models. Beyond the initially present pair and embedded-atom method potentials, potfit can now also optimize angular dependent potentials, charge and dipolar interactions, and electron-temperature-dependent potentials. We demonstrate the functionality of these interaction models using three example systems: phonons in type I clathrates, fracture of α-alumina, and laser-irradiated silicon. read less V. Lipp, B. Rethfeld, M. E. Garcia, and D. Ivanov, “Atomistic-continuum modeling of short laser pulse melting of Si targets,” Physical Review B. 2014. link Times cited: 41 Abstract: We present an atomistic-continuum model to simulate ultrasho… read more Abstract: We present an atomistic-continuum model to simulate ultrashort laser-induced melting processes in semiconductor solids on the example of silicon. The kinetics of transient non-equilibrium phase transition mechanisms is addressed with a Molecular Dynamics method at atomic level, whereas the laser light absorption, strong generated electron-phonon non-equilibrium, fast diffusion and heat conduction due to photo-excited free carriers are accounted for in the continuum. We give a detailed description of the model, which is then applied to study the mechanism of short laser pulse melting of free standing Si films. The effect of laser-induced pressure and temperature of the lattice on the melting kinetics is investigated. Two competing melting mechanisms, heterogeneous and homogeneous, were identified. Apart of classical heterogeneous melting mechanism, the nucleation of the liquid phase homogeneously inside the material significantly contributes to the melting process. The simulations showed, that due to the open diamond structure of the crystal, the laser-generated internal compressive stresses reduce the crystal stability against the homogeneous melting. Consequently, the latter can take a massive character within several picoseconds upon the laser heating. Due to negative volume of melting of modeled Si material, -7.5%, the material contracts upon the phase transition, relaxes the compressive stresses and the subsequent melting proceeds heterogeneously until the excess of thermal energy is consumed. The threshold fluence value, at which homogeneous nucleation of liquid starts contributing to the classical heterogeneous propagation of the solid-liquid interface, is found from the series of simulations at different laser input fluences. On the example of Si, the laser melting kinetics of semiconductors was found to be noticeably different from that of metals with fcc crystal structure. read less S. Goel, “The current understanding on the diamond machining of silicon carbide,” Journal of Physics D: Applied Physics. 2014. link Times cited: 139 Abstract: The Glenn Research Centre of NASA, USA (www.grc.nasa.gov/WWW… read more Abstract: The Glenn Research Centre of NASA, USA (www.grc.nasa.gov/WWW/SiC/, silicon carbide electronics) is in pursuit of realizing bulk manufacturing of silicon carbide (SiC), specifically by mechanical means. Single point diamond turning (SPDT) technology which employs diamond (the hardest naturally-occurring material realized to date) as a cutting tool to cut a workpiece is a highly productive manufacturing process. However, machining SiC using SPDT is a complex process and, while several experimental and analytical studies presented to date aid in the understanding of several critical processes of machining SiC, the current knowledge on the ductile behaviour of SiC is still sparse. This is due to a number of simultaneously occurring physical phenomena that may take place on multiple length and time scales. For example, nucleation of dislocation can take place at small inclusions that are of a few atoms in size and once nucleated, the interaction of these nucleations can manifest stresses on the micrometre length scales. The understanding of how these stresses manifest during fracture in the brittle range, or dislocations/phase transformations in the ductile range, is crucial to understanding the brittle–ductile transition in SiC. Furthermore, there is a need to incorporate an appropriate simulation-based approach in the manufacturing research on SiC, owing primarily to the number of uncertainties in the current experimental research that includes wear of the cutting tool, poor controllability of the nano-regime machining scale (effective thickness of cut), and coolant effects (interfacial phenomena between the tool, workpiece/chip and coolant), etc. In this review, these two problems are combined together to posit an improved understanding on the current theoretical knowledge on the SPDT of SiC obtained from molecular dynamics simulation. read less V. Dozhdikov, A. Basharin, and P. Levashov, “Two-phase simulation of the crystalline silicon melting line at pressures from -1 to 3 GPa.,” The Journal of chemical physics. 2012. link Times cited: 32 Abstract: Results of a numerical investigation of crystalline silicon … read more Abstract: Results of a numerical investigation of crystalline silicon melting line within the range of pressures from -1 to 3 GPa are presented. A two-phase molecular dynamics method is applied to obtain temperature, pressure, and densities of solid and liquid phases on the melting line. Using a special procedure we ensure the strict control of the two-phase equilibrium in the simulation cell. To describe the interaction between the atoms four classic potentials have been chosen: the Stillinger-Weber one and three modified variants of the Tersoff potential. For the Stillinger-Weber and Tersoff potentials in the modification by Kumagai-Izumi-Hara-Sakai a good coincidence with experimental data on crystalline Si melting temperature is obtained within the range of pressure from 0 to 3 GPa. Calculations of the solid and liquid phase densities on the silicon melting line for the Stillinger-Weber potential are also in close agreement with experiments. read less S. Zhang et al., “Voronoi Structural Evolution of Bulk Silicon upon Melting,” Chinese Physics Letters. 2011. link Times cited: 2 Abstract: The Voronoi structural evolution of silicon upon melting is … read more Abstract: The Voronoi structural evolution of silicon upon melting is investigated using a molecular dynamics simulation. At temperatures below the melting point, the solid state system is identified to have a four-fold coordination structure 〈4,0,0,0〉. As the temperature increases, the five-fold coordination 〈2,3,0,0〉 and six-fold coordination structures 〈2,2,2,0〉 and 〈0,6,0,0〉 are observed. This is explained in terms of increasing atomic displacement due to thermal motion and the trapping of the moving atoms by others. At temperatures above the melting point, nearly all of the four-fold coordination structures grows into multiple-fold coordination ones. read less L. Shokeen and P. Schelling, “Thermodynamics and kinetics of silicon under conditions of strong electronic excitation,” Journal of Applied Physics. 2011. link Times cited: 28 Abstract: We present a detailed analysis of a recently-developed empir… read more Abstract: We present a detailed analysis of a recently-developed empirical potential to describe silicon under conditions of strong electronic excitation. The parameters of the potential are given as smooth functions of the electronic temperature Te, with the dependence determined by fitting to finite-temperature density-functional theory calculations. We analyze the thermodynamics of this potential as a function of the electronic temperature Te and lattice temperature Tion. The potential predicts phonon spectra in good agreement with finite-temperature density-functional theory, including the previously predicted lattice instability. We predict that the melting temperature Tm decreases strongly as a function of Te. Electronic excitation has a strong effect on the rate of crystallization from the melt. In particular, high Te results in very slow kinetics for growing crystal from the melt, due mainly to the fact that diamond becomes much less stable as Te increases. Finally, we explore annealing amorphous Si (a-Si) ... read less A. Kiselev, “Molecular dynamics simulations of laser ablation in covalent materials.” 2017. link Times cited: 1 Abstract: 15 Deutsche Zusammenfassung 18 I. Theoretical background 27… read more Abstract: 15 Deutsche Zusammenfassung 18 I. Theoretical background 27 read less S. Lai, I. Setiyawati, T. Yen, and Y. H. Tang, “Studying lowest energy structures of carbon clusters by bond-order empirical potentials,” Theoretical Chemistry Accounts. 2016. link Times cited: 10 M. Timonova and B. Thijsse, “Optimizing the MEAM potential for silicon,” Modelling and Simulation in Materials Science and Engineering. 2010. link Times cited: 25 Abstract: By applying simulated annealing techniques we fit the modifi… read more Abstract: By applying simulated annealing techniques we fit the modified embedded atom method (MEAM) potential to a database of ab initio energies for silicon and construct an improved parametrization of this potential. In addition, we introduce a new, reference-free version of the MEAM potential. This MEAM version is also fitted to the silicon data and shows an even better agreement, although the improvement is modest. Finally, we investigate whether increasing the number of different angular terms in the MEAM potential from 3 to 4 will lead to a better potential. The aim of this work is to determine a broad-ranged potential, one that is reliable in many different low- and high-energy atomic geometries in silicon crystals, molecules, near defects and under strain. To verify this, the performance of the new potentials is tested in different circumstances that were not explicitly included in the fit: relaxed defect energies, thermal expansion, melting temperature and liquid silicon. The new MEAM parametrizations found in this work, called MEAM-M and RF-MEAM, are shown to be overall more accurate than previous potentials—although a few defect energies are exceptions—and we recommend them for future work. The melting temperatures are closer to the experiment than those of other MEAM potentials, but they are still too high. read less M. Zhao et al., “Ultrarapid Multimode Microwave Synthesis of Nano/Submicron β-SiC,” Materials. 2018. link Times cited: 4 Abstract: This paper presents the design, development and realization … read more Abstract: This paper presents the design, development and realization of a fast and novel process for the synthesis of 3C silicon carbide (β-SiC) nanorods and submicron powder. Using SiO2 (or Si) and activated carbon (AC), this process allows β-SiC to be synthesized with almost 100% purity in timeframes of seconds or minutes using multimode microwave rotary tube reactors under open-air conditions. The synthesis temperature used was 1460 ± 50 °C for Si + AC and 1660 ± 50 °C for SiO2 + AC. The shortest β-SiC synthesis time achieved was about 20 s for Si + AC and 100 s for SiO2 + AC. This novel synthesis method allows for scaled-up flow processes in the rapid industrial-scale production of β-SiC, having advantages of time/energy saving and carbon dioxide emission reduction over comparable modern processes. read less “The Tersoff potential for extreme environment,” arXiv: Materials Science. 2018. link Times cited: 0 Abstract: A novel modification of the Tersoff potential for Si is pres… read more Abstract: A novel modification of the Tersoff potential for Si is presented. The modification improves the transferability of the Tersoff potential for liquid states without the change of original parameters and with no alteration of bulk properties. Also, the modification introduces a correction term for high-pressure states. The modification is meaningful considering that by high energy irradiations local liquid structures and unstable high-pressure manifolds may occur, therefore an interatomic potential must have an acceptable reliability on high thermal/pressure situations to simulate such phenomenon. Particularly, in the modification, a new screening function replaces the radial cutoff function and the bond order function is slightly changed. Also, a repulsive energy function is replaced by a correction function within a specific pair distance. read less
Funding	Not available

Short KIM ID The unique KIM identifier code.	SM_773333226968_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.	Sim_LAMMPS_ModifiedTersoff_KumagaiIzumiHara_2007_Si__SM_773333226968_000
DOI	10.25950/9d94dc3d https://doi.org/10.25950/9d94dc3d https://commons.datacite.org/doi.org/10.25950/9d94dc3d
KIM Item Type	Simulator Model
KIM API Version	2.1
Simulator Name The name of the simulator as defined in kimspec.edn.	LAMMPS
Potential Type	tersoff
Simulator Potential	tersoff/mod
Run Compatibility	portable-models

Verification Check Dashboard

(Click here to learn more about Verification Checks)

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
P Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.	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 1.87329e-10 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
P The model is C^1 continuous. This means that the model has continuous energy and continuous 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
F Memory leak detected.	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 Thread safety can only be checked for KIM Models.	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

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.

Species: Si

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.

Species: Si

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.

Species: Si

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	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1951
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2943
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2143
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2239
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2879
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2879
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2239
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2143
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	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2911
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2143
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2751
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2815
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2047
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2943
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2975
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2751
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2111
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2239
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2847
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2143
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2239
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
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	2815
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	1919
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2239
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2751
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2783
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2815
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2751
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2111
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2751
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2879
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2815
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2847
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2815
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2111
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2015
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2783
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
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	2079
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2239
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2751
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2751
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2111
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2783
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
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	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2783
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2879
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2239
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2111
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	3071
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2239
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2239
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2783
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2847
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2847
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2751
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2239
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2111
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2239
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2111
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2111
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2847
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2111
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2783
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2111
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2111
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2783
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2815
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2783
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2239
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2751
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2879
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2751
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2815
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2751
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2783
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2879
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2047
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2239
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2751
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2815
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2239
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2783
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2783
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2751
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	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2111
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2143
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2751
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2879
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2879
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2239
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2687
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2143
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2815
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2751
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2783
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2815
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2783
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2495
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2559
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2751
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2783
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2207
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2335
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2847
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2271
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2399
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2143
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2175
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2623
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2719
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2655
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2239
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2463
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2591
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2431
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2783
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2367
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2527
Conjugate gradient relaxation of random finite cluster of Si atoms v003	view	2303

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	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 bcc Si v004	view	1760
Cohesive energy versus lattice constant curve for diamond Si v004	view	1711
Cohesive energy versus lattice constant curve for fcc Si v004	view	1914
Cohesive energy versus lattice constant curve for sc Si v004	view	1914

ElasticConstantsCubic__TD_011862047401_006

Elastic constants for cubic crystals at zero temperature and pressure v006

Creators: Junhao Li and Ellad Tadmor
Contributor: tadmor
Publication Year: 2019
DOI: https://doi.org/10.25950/5853fb8f

Computes the cubic elastic constants for some common crystal types (fcc, bcc, sc, diamond) by calculating the hessian of the energy density with respect to strain. An estimate of the error associated with the numerical differentiation performed is reported.

Test	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)
Elastic constants for bcc Si at zero temperature v006	view	2175
Elastic constants for diamond Si at zero temperature v001	view	15611
Elastic constants for fcc Si at zero temperature v006	view	2175
Elastic constants for sc Si at zero temperature v006	view	2431

ElasticConstantsHexagonal__TD_612503193866_004

Elastic constants for hexagonal crystals at zero temperature v004

Creators: Junhao Li
Contributor: jl2922
Publication Year: 2019
DOI: https://doi.org/10.25950/d794c746

Computes the elastic constants for hcp crystals by calculating the hessian of the energy density with respect to strain. An estimate of the error associated with the numerical differentiation performed is reported.

Test	Test Results	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Elastic constants for hcp Si at zero temperature v004		view	2229

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	2360200
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_cF4_225_a v002	view	53469
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_cF8_227_a v002	view	119029
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_cI12_229_d v002	view	175839
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_cI16_206_c v002	view	104762
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_cI82_217_acgh v002	view	393178
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_cP46_223_cik v002	view	205794
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_hP1_191_a v002	view	57056
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_hP2_194_c v002	view	44598
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_hP40_191_hjmno v002	view	151511
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_hP4_194_f v002	view	74209
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_hP58_164_2d3i3j v002	view	147094
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_hP68_194_ef2h2kl v002	view	114047
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_mC164_15_e20f v002	view	1361979
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_mC16_12_4i v002	view	57904
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_oC92_63_ce2f2g3h v002	view	361845
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_oF16_69_gh v002	view	141204
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_tI4_141_a v002	view	48426
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_tI8_139_h v002	view	46421
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_tP106_137_a5g4h v002	view	360151

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	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 bcc Si v007	view	5822
Equilibrium zero-temperature lattice constant for diamond Si v007	view	7613
Equilibrium zero-temperature lattice constant for fcc Si v007	view	5886
Equilibrium zero-temperature lattice constant for sc Si v007	view	6206

LatticeConstantHexagonalEnergy__TD_942334626465_005

Equilibrium lattice constants for hexagonal bulk structures at zero temperature and pressure v005

Creators: Daniel S. Karls and Junhao Li
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/c339ca32

Calculates lattice constant of hexagonal bulk structures at zero temperature and pressure by using simplex minimization to minimize the potential energy.

Test	Test Results	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Equilibrium lattice constants for hcp Si v005		view	29448

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	875309

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	2367
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2623
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2431
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2591
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2399
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2239
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2143
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2623
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2687
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2559
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2591
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2111
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2623
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2303
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2367
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2559
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2367
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2495
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2719
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2623
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2879
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2399
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2239
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2399
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2655
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2847
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2367
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2719
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2495
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2495
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2559
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2655
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2431
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2175
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2271
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2879
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	1919
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2367
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2815
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2431
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2335
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2591
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2271
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2623
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2207
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	3007
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2271
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2591
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2335
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2751
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2783
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2431
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2623
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2335
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2335
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2271
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2719
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2623
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2559
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2815
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed bcc structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2431
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2783
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2271
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1887
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2367
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2303
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2751
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2719
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2495
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2655
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2335
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2751
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2559
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2719
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2239
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2367
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2559
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2847
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2591
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2655
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2079
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2495
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2207
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2559
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2431
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2239
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2655
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2687
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2431
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2591
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2143
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2239
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2367
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2431
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2303
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2559
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2495
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2495
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2207
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2623
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2623
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2687
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2399
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2719
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2655
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2559
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2111
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2399
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2399
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2399
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	3039
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2239
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2431
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2335
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2495
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2335
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2303
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2431
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2719
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2751
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2559
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2495
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2751
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2335
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2207
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2271
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	1951
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2687
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2175
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2271
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2815
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2623
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2271
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2495
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2559
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2719
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2655
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2175
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2559
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2367
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2495
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2239
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed diamond structure v003	view	2271
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2335
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2911
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2015
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2047
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2687
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2143
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2559
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2399
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2559
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2335
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2623
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2239
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2655
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2111
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed random structure v003	view	2431
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2783
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2303
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2239
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2687
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2335
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2303
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2143
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2559
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2303
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2559
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2495
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2559
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2463
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2495
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2751
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2527
Potential energy and atomic forces of periodic, non-orthogonal cell of Si atoms in a perturbed sh structure v003	view	2623

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	1089363

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	5828388

Errors

CohesiveEnergyVsLatticeConstant__TD_554653289799_002

Test	Error Categories	Link to Error page
Cohesive energy versus lattice constant curve for sc Silicon	other	view

EquilibriumCrystalStructure__TD_457028483760_000

Test	Error Categories	Link to Error page
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_hP2_194_c v000	other	view
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_mC16_12_4i v000	other	view
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_tI4_141_a v000	other	view
Equilibrium crystal structure and energy for Si in AFLOW crystal prototype A_tI8_139_h 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_hR8_148_cf v002	other	view

LinearThermalExpansionCoeffCubic__TD_522633393614_001

Test	Error Categories	Link to Error page
Linear thermal expansion coefficient of diamond Si at 293.15 K under a pressure of 0 MPa v001	other	view

No Driver

Verification Check	Error Categories	Link to Error page
PeriodicitySupport__VC_895061507745_004	other	view

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Sim_LAMMPS_ModifiedTersoff_KumagaiIzumiHara_2007_Si__SM_773333226968_000

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BCC Lattice Constant

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Diamond Lattice Constant

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FCC Lattice Constant

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FCC Surface Energies

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Cubic Crystal Basic Properties Table

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