EAM potential (LAMMPS cubic hermite tabulation) for Au developed by Olsson (2010) v000

Pär A. T. Olsson

doi:10.25950/fe43ad59

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EAM_Dynamo_Olsson_2010_Au__MO_228280943430_000

Interatomic potential for Gold (Au).
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Title A single sentence description.	EAM potential (LAMMPS cubic hermite tabulation) for Au developed by Olsson (2010) v000
Description A short description of the Model describing its key features including for example: type of model (pair potential, 3-body potential, EAM, etc.), modeled species (Ac, Ag, ..., Zr), intended purpose, origin, and so on.	LAMMPS compatible EAM/alloy potential for Au. Used in a series of nanowire modeling projects.
Species The supported atomic species.	Au
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/Au.html

Contributor	Ronald E. Miller
Maintainer	Ronald E. Miller
Developer	Pär A. T. Olsson
Published on KIM	2018
How to Cite	This Model originally published in [1] is archived in OpenKIM [2-5]. [1] Olsson PAT. Transverse resonant properties of strained gold nanowires. J Appl Phys. 2010Aug;108(3). doi:10.1063/1.3460127 — (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] Olsson PAT. EAM potential (LAMMPS cubic hermite tabulation) for Au developed by Olsson (2010) v000. OpenKIM; 2018. doi:10.25950/fe43ad59 [3] Foiles SM, Baskes MI, Daw MS, Plimpton SJ. EAM Model Driver for tabulated potentials with cubic Hermite spline interpolation as used in LAMMPS v005. OpenKIM; 2018. doi:10.25950/68defa36 [4] Tadmor EB, Elliott RS, Sethna JP, Miller RE, Becker CA. The potential of atomistic simulations and the Knowledgebase of Interatomic Models. JOM. 2011;63(7):17. doi:10.1007/s11837-011-0102-6 [5] Elliott RS, Tadmor EB. Knowledgebase of Interatomic Models (KIM) Application Programming Interface (API). OpenKIM; 2011. doi:10.25950/ff8f563a Click here to download the above citation in BibTeX format.
Citations This panel presents information regarding the papers that have cited the interatomic potential (IP) whose page you are on. The OpenKIM machine learning based Deep Citation framework is used to determine whether the citing article actually used the IP in computations (denoted by "USED") or only provides it as a background citation (denoted by "NOT USED"). For more details on Deep Citation and how to work with this panel, click the documentation link at the top of the panel. The word cloud to the right is generated from the abstracts of IP principle source(s) (given below in "How to Cite") and the citing articles that were determined to have used the IP in order to provide users with a quick sense of the types of physical phenomena to which this IP is applied. The bar chart shows the number of articles that cited the IP per year. Each bar is divided into green (articles that USED the IP) and blue (articles that did NOT USE the IP). Users are encouraged to correct Deep Citation errors in determination by clicking the speech icon next to a citing article and providing updated information. This will be integrated into the next Deep Citation learning cycle, which occurs on a regular basis. OpenKIM acknowledges the support of the Allen Institute for AI through the Semantic Scholar project for providing citation information and full text of articles when available, which are used to train the Deep Citation ML algorithm.	This panel provides information on past usage of this interatomic potential (IP) powered by the OpenKIM Deep Citation framework. The word cloud indicates typical applications of the potential. The bar chart shows citations per year of this IP (bars are divided into articles that used the IP (green) and those that did not (blue)). The complete list of articles that cited this IP is provided below along with the Deep Citation determination on usage. See the Deep Citation documentation for more information. 41 Citations (32 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 . S. M. Rassoulinejad-Mousavi and Y. Zhang, “Interatomic Potentials Transferability for Molecular Simulations: A Comparative Study for Platinum, Gold and Silver,” Scientific Reports. 2018. link Times cited: 33 E. Yildirim et al., “Simple Synthesis of Monodisperse Ultrasmall Au Icosahedral Nanoparticles,” The Journal of Physical Chemistry C. 2023. link Times cited: 2 E. Pervolarakis, G. Tritsaris, P. Rosakis, and I. Remediakis, “Machine Learning for the edge energies of high symmetry Au nanoparticles,” Surface Science. 2022. link Times cited: 1 Y. Geng et al., “Dissociation of Tilt Dislocation Walls in Au,” Acta Metallurgica Sinica (English Letters). 2022. link Times cited: 0 F. Saleem et al., “Size-Dependent Phase Transformation of Noble Metal Nanomaterials.,” Small. 2019. link Times cited: 15 Abstract: As an important aspect of crystal phase engineering, control… read more Abstract: As an important aspect of crystal phase engineering, controlled crystal phase transformation of noble metal nanomaterials has emerged as an effective strategy to explore novel crystal phases of nanomaterials. In particular, it is of significant importance to observe the transformation pathway and reveal the transformation mechanism in situ. Here, the phase transformation behavior of face-centered cubic (fcc) Au nanoparticles (fcc-AuNPs), adhering to the surface of 4H nanodomains in 4H/fcc Au nanorods, referred to as 4H-AuNDs, during in situ transmission electron microscopy imaging is systematically studied. It is found that the phase transformation is dependent on the ratio of the size of the monocrystalline nanoparticle (NP) to the diameter of 4H-AuND. Furthermore, molecular dynamics simulation and theoretical modeling are used to explain the experimental results, giving a size-dependent phase transformation diagram which provides a general guidance to predict the phase transformation pathway between fcc and 4H Au nanomaterials. Impressively, this method is general, which is used to study the phase transformation of other metal NPs, such as Pd, Ag, and PtPdAg, adhering to 4H-AuNDs. The work opens an avenue for selective phase engineering of nanomaterials which may possess unique physicochemical properties and promising applications. read less H. Xie, J. Yu, T. Yu, and F. Yin, “Face-centred cubic to body-centred cubic phase transformation under [1 0 0] tensile loading,” Philosophical Magazine. 2018. link Times cited: 2 Abstract: ABSTRACT Molecular dynamics simulation was used to verify a … read more Abstract: ABSTRACT Molecular dynamics simulation was used to verify a speculation of the existence of a certain face-centred cubic (FCC) to body-centred cubic (BCC) phase transformation pathway. Four FCC metals, Ni, Cu, Au and Ag, were stretched along the [1 0 0] direction at various strain rates and temperatures. Under high strain rate and low temperature, and beyond the elastic limit, the bifurcation of the FCC phase occurred with sudden contraction along one lateral direction and expansion along the other lateral direction. When the lattice constant along the expansion direction converged with that of the stretched direction, the FCC phase transformed into an unstressed BCC phase. By reducing the strain rate or increasing the temperature, dislocation or ‘momentum-induced melting’ mechanisms began to control the plastic deformation of the FCC metals, respectively. read less P. Olsson, H. S. Park, and P. Lidström, “The Influence of shearing and rotary inertia on the resonant properties of gold nanowires,” Journal of Applied Physics. 2010. link Times cited: 25 Abstract: In a previous publication [ P. A. T. Olsson, J. Appl. Phys. … read more Abstract: In a previous publication [ P. A. T. Olsson, J. Appl. Phys. 108, 034318 (2010) ], molecular dynamics (MD) simulations have been performed to study the resonant properties of gold nanowires. It has been documented in the aforementioned publication that the eigenfrequencies of the fundamental mode follows the continuum mechanically predicted behavior when Bernoulli–Euler beam theory is used, whereas the higher order modes tend to be low in comparison to Bernoulli–Euler beam theory predictions. In this work, we have studied the resonant properties of unstressed and prestressed nanowires to explain why the eigenfrequencies of the fundamental mode follows the behavior predicted by Bernoulli–Euler beam theory while those of higher order modes are low in comparison. This is done by employing Timoshenko beam theory and studying the nanowire deformations for different modes. We find good agreement between the MD results and Timoshenko predictions due to the increasing importance of shearing and rotary inertia for higher order resonant modes. Furthermore, we argue that this type of behavior is merely a geometric effect stemming from low aspect ratio for the considered structures as a converging type of behavior is found when the aspect ratios fall between 15 and 20. Finally, we have found that classical Timoshenko beam theory that neglects nanoscale surface effects is able to, simply through utilization of the size dependent Young’s modulus, capture the dynamic properties of the gold nanowires as calculated through MD. (Less) read less L. Morrissey, “Hydrogen embrittlement of iron nanowires: investigating size and orientation dependence on loading behaviour,” Molecular Simulation. 2023. link Times cited: 0 P. Olsson et al., “Grain Size-Dependent Thermal Expansion of Nanocrystalline Metals,” Materials. 2023. link Times cited: 0 Abstract: In the present work, we have used classical molecular dynami… read more Abstract: In the present work, we have used classical molecular dynamics and quantum mechanical density functional theory modeling to investigate the grain size-dependent thermal expansion coefficient (CTE) of nanocrystalline Cu. We find that the CTE increases by up to 20% with a gradually decreasing grain size. This behavior emerges as a result of the increased population of occupied anti-bonding states and bond order variation in the grain boundary regions, which contribute to the reduced resistance against thermally-induced bond stretching and dictate the thermal expansion behavior in the small grain size limit. As a part of the present work, we have established a procedure to produce ab initio thermal expansion maps that can be used for the prediction of the grain size-dependent CTE. This can serve as a modeling tool, e.g., to explore the impact of grain boundary impurity segregation on the CTE. read less S. Xu, X. Fan, C. Gu, W. Zheng, and D. J. Singh, “Molecular Dynamics Study of the Tensile Properties of Gold Nanocrystalline Films Irradiated by Gallium Ions,” Journal of Nuclear Materials. 2023. link Times cited: 0 X. Gao, N. Li, Z. Song, K. Wu, Y. Cheng, and B.-yang Xiao, “Atomic structure evolution and linear regression fitting models for pre-breakdown electric field strength of FCC, BCC and HCP metal nano-emitters under high electric field from PIC-ED–MD simulations,” Journal of Physics D: Applied Physics. 2023. link Times cited: 1 Abstract: Multi-scale and multi-physics simulations are carried out fo… read more Abstract: Multi-scale and multi-physics simulations are carried out for nano-emitters consisting of FCC (Al, Cu and Au), BCC (V, Mo and W) and HCP (Ti, Zn and Zr) metals, using hybrid electrodynamics coupled with molecular dynamics-particle in cell simulations (PIC-ED–MD). We show that the tilting of the nano-emitter at low temperature and small electric field (E-field) is mainly caused either by the movement of partial dislocations at the apex of the nanotip or by the elastic local distortions of atomic registries away from their ideal lattice sites (FCC/BCC/HCP). At high E-field, the intense resistive heating due to the strong electron emission leads to the direct melting of the apex of nano-emitters. For nano-emitters consisting of low melting point metals such as Al, Zn and Au, the thermal runaway is driven by the elongation, thinning and necking of the molten region. Meanwhile, the elongation, thinning and sharpening produce the nano-protrusion at the apex of metal nano-emitters, and the detachment of atoms or atomic clusters from the nano-protrusion mainly contributes to the thermal runaway event for refractor metals such as Ti, Zr, Mo and W. The critical E-field strength of metal nano-emitters is found to be strongly correlated with structural parameters (atomic coordination number of liquid and equilibrium lattice constant), thermodynamic quantities (cohesive energy and enthalpy of evaporation) and phase transition temperatures (melting point and boiling point). These correlations enable us to establish either single-variable linear fitting models or multi-variable linear regression models to predict the critical E-field value for metal nano-emitters with good credibility. read less V. Kushch, “Atomistic and continuum modeling of nanoparticles: Elastic fields, surface constants, and effective stiffness,” International Journal of Engineering Science. 2023. link Times cited: 0 F. Valencia et al., “Probing the Mechanical Properties of Porous Nanoshells by Nanoindentation,” Nanomaterials. 2022. link Times cited: 2 Abstract: In this contribution, we present a study of the mechanical p… read more Abstract: In this contribution, we present a study of the mechanical properties of porous nanoshells measured with a nanoindentation technique. Porous nanoshells with hollow designs can present attractive mechanical properties, as observed in hollow nanoshells, but coupled with the unique mechanical behavior of porous materials. Porous nanoshells display mechanical properties that are dependent on shell porosity. Our results show that, under smaller porosity values, deformation is closely related to the one observed for polycrystalline and single-crystalline nanoshells involving dislocation activity. When porosity in the nanoparticle is increased, plastic deformation was mediated by grain boundary sliding instead of dislocation activity. Additionally, porosity suppresses dislocation activity and decreases nanoparticle strength, but allows for significant strain hardening under strains as high as 0.4. On the other hand, Young’s modulus decreases with the increase in nanoshell porosity, in agreement with the established theories of porous materials. However, we found no quantitative agreement between conventional models applied to obtain the Young’s modulus of porous materials. read less A. Mahata and M. Kivy, “Computational study of nanoscale mechanical properties of Fe–Cr–Ni alloy,” Molecular Simulation. 2022. link Times cited: 1 Abstract: ABSTRACT Mechanical properties of Fe–Cr–Ni alloy nanowires h… read more Abstract: ABSTRACT Mechanical properties of Fe–Cr–Ni alloy nanowires have been investigated using molecular dynamics simulation with embedded atom method and first principles approach. Various cases of uniaxial tension, compression and shear deformations have been performed and studied in this work. From the first principles calculations, the higher magnitudes of uniaxial and shear deformations resulted in higher probability of martensitic transformations. Before the first yielding, nanowires preserved the elastic stage and then the mechanical deformation proceeded in alternating quasi-elastic and yielding stages. The plastic behaviour was not observed in compression while both tensile and shear deformations showed apparent plastic behaviour. In shear deformation, due to the martensitic phase transformation, the plastic behaviour persisted for total strain of 0.6 which was much larger than that during tensile and compression. This validated the previous experimental observations. In the studied Fe–Cr–Ni nanowires, deformations were controlled by dislocations. Dislocation-mediated twinnings were captured by common neighbour analysis. Twin quantification showed that the twin activity increased with increasing strain rate. Twinnings originated from stacking faults led by 1/6 <112> Shockley partial dislocations. At elevated temperature (beyond 500 K), the materials softening happened, and 316L nanowire became more plastic under a lower stress. read less T. Zolotoukhina, M. Yamada, and S. Iwakura, “Vibrational Spectra of Nucleotides in the Presence of the Au Cluster Enhancer in MD Simulation of a SERS Sensor †,” Biosensors. 2021. link Times cited: 3 Abstract: Surface-enhanced Raman scattering (SERS) nanoprobes have sho… read more Abstract: Surface-enhanced Raman scattering (SERS) nanoprobes have shown tremendous potential in in vivo imaging. The development of single oligomer resolution in the SERS promotes experiments on DNA and protein identification using SERS as a nanobiosensor. As Raman scanners rely on a multiple spectrum acquisition, faster imaging in real-time is required. SERS weak signal requires averaging of the acquired spectra that erases information on conformation and interaction. To build spectral libraries, the simulation of measurement conditions and conformational variations for the nucleotides relative to enhancer nanostructures would be desirable. In the molecular dynamic (MD) model of a sensing system, we simulate vibrational spectra of the cytosine nucleotide in FF2/FF3 potential in the dynamic interaction with the Au20 nanoparticles (NP) (EAM potential). Fourier transfer of the density of states (DOS) was performed to obtain the spectra of bonds in reaction coordinates for nucleotides at a resolution of 20 to 40 cm−1. The Au20 was optimized by ab initio density functional theory with generalized gradient approximation (DFT GGA) and relaxed by MD. The optimal localization of nucleotide vs. NP was defined and the spectral modes of both components vs. interaction studied. Bond-dependent spectral maps of nucleotide and NP have shown response to interaction. The marker frequencies of the Au20—nucleotide interaction have been evaluated. read less T. Zolotoukhina, M. Yamada, and S. Iwakura, “Influence of the Au cluster enhancer on vibrational spectra of nucleotides in MD simulation of a SERS sensor,” Proceedings of The 1st International Electronic Conference on Biosensors. 2020. link Times cited: 2 Abstract: Surface-enhanced Raman scattering (SERS) nanoprobes have sho… read more Abstract: Surface-enhanced Raman scattering (SERS) nanoprobes have shown tremendous potential in in vivo imaging. The development of single oligomer resolution in the SERS promotes experiments on DNA and protein identification using SERS as a nanobiosensor. As Raman scanners rely on a multiple spectrum acquisition, the faster imaging in real-time is required. SERS weak signal requires averaging of the acquired spectra that erases information on conformation and interaction. To build spectral libraries, the simulation of measurement conditions and conformational variations for the nucleotides relative to enhancer nanostructures would be desirable. In the molecular dynamic (MD) model of a sensing system, we simulate vibrational spectra of the cytosine nucleotide in FF2/FF3 potential in the dynamic interaction with the Au20 nanoparticles (NP) (EAM potential). Fourier transfer of the density of states (DOS) was performed to obtain the spectra of bonds in reaction coordinates for nucleotides at a resolution 20 to 40 cm−1. The Au20 was optimized by ab initio DFT GGA and relaxed by MD. The optimal localization of nucleotide vs. NP was defined and spectral modes of both components vs. interaction studied. Bond-dependent spectral maps of nucleotide and NP have shown response to interaction. The marker frequencies of the Au20—nucleotide interaction have been evaluated. read less S. Starikov, I. Gordeev, Y. Lysogorskiy, L. Kolotova, and S. Makarov, “Optimized interatomic potential for study of structure and phase transitions in Si-Au and Si-Al systems,” Computational Materials Science. 2020. link Times cited: 19 H. L. Mai, X. Cui, and S. Ringer, “Mechanical properties of ultrathin gold nanowires from first principles: Interdependencies between size, morphology, and twin boundaries,” Physical Review Materials. 2020. link Times cited: 3 Abstract: The mechanical behavior of $\ensuremath{\langle}111\ensurema… read more Abstract: The mechanical behavior of $\ensuremath{\langle}111\ensuremath{\rangle}$ ultrathin gold nanowires (NWs) and their dependence on the correlated parameters of size (i.e., diameter $\ensuremath{\sim}1--1.6$ nm), morphology (rectangular and hexagonal prism), and ultrahigh density twin boundaries was investigated using density functional theory calculations. The parameters of size, morphology, and the presence of twins all significantly influence the mechanical behavior of Au NWs, and their effects are interdependent. Importantly, an ultrahigh density of twins in NWs enhances their strength in both morphologies, and across all sizes studied. Our calculations reveal a remarkable range of Young's modulus (60--158 GPa) and ultimate tensile strengths (3.7--14.0 GPa), suggesting that the scatter observed in experimental research involving ultrathin gold nanowires is a feature of intrinsic complexity. In particular, a ``wrinkling'' of the atomic planes along the wire axis due to a combination of anisotropic surface stresses and wire core response, is demonstrated to be largely suppressed by the presence of high-density twins. The high tensile strengths of the studied nanowires with twins is attributed to a combination of the suppression of this anisotropic phenomena and slip plane disruption. This work demonstrates that precise control of these parameters is required during synthesis to achieve target mechanical behaviour in industrial device applications. Moreover, the work demonstrates that this system has the potential to be tuned for access to a vast range of materials design space. read less M. Porterfield and D. Borca-Tasciuc, “Molecular Dynamics Simulation of Ultra-Fast Phase Transition in Water Nanofilms,” Journal of Heat Transfer. 2020. link Times cited: 1 Abstract: Molecular dynamics simulations are used to explore explosi… read more Abstract: Molecular dynamics simulations are used to explore explosive boiling of thin water films on a gold substrate. In particular, water films of 0.7, 1.6, and 2.5 nanometer thickness were examined. Three different surface wettabilities with contact angles of 11 deg, 47 deg, and 110 deg were simulated along with substrate temperatures of 400 K, 600 K, 800 K, and 1000 K. The 11 and 47 deg contact angles were obtained using a Morse interaction potential between the water film and gold substrate while the 47 and 110 deg contact angles were obtained via a Lennard-Jones potential. Evaporation was the first mode of phase change observed in all cases and explosive boiling did not occur until the substrate reached a temperature of 800 K. When explosive boiling was present for all three contact angles, it was consistently shown to occur first for the surface with a 47 deg contact angle and Lennard-Jones potential. These results suggest that explosive boiling onset is strongly dependent on the particularities of the interaction potential. For instance, the Morse potential is smoother when compared to the Lennard-Jones potential, but has more interaction sites per molecule—two hydrogen atoms and one oxygen atom versus one oxygen atom. Thus, even when the water film reaches a higher temperature with the Morse potential, explosive boiling onset is delayed as more interaction sites have to be disrupted. These results suggest that contact angle alone is insufficient and both the interaction strength and the number of atoms interacting at the interface must be considered when investigating trends of explosive boiling with surface wettability. read less S. Surulere, M. Shatalov, A. C. Mkolesia, and A. Adeniji, “A Comparative Investigation of Complex Conjugate Eigenvalues of Generalized Morse and Classical Lennard-Jones Potential for Metal Atoms.” 2020. link Times cited: 0 Abstract: The knowledge of parameter estimation for interatomic pote… read more Abstract: The knowledge of parameter estimation for interatomic potentials is useful in the computation of the vibrational structure of van der Waals molecules. On the estimation of the Generalized Morse and Classical Lennard-Jones potential energy functions, complex conjugates eigenvalues may be obtained. Different approaches can be used to solve this resulting problem. A method that uses the objective least squares function method to estimate parameters of the interatomic potentials is employed. Numerical simulation of the systems using metal atoms yields complex conjugates eigenvalues at some initial point. Other approaches of solving the complex conjugates eigenvalues problem are discussed comprehensively. read less U. Kurelchuk, P. V. Borisyuk, and O. Vasilyev, “Electron properties of 13-atom nanoparticle superlattices,” Materials Letters. 2020. link Times cited: 0 B. Bertin, J. Durinck, and J. Colin, “Dislocation emission and crack propagation during thin film buckling on substrate,” International Journal of Solids and Structures. 2020. link Times cited: 3 A. Thorn, J. Rojas-Nunez, S. Hajinazar, S. Baltazar, and A. Kolmogorov, “Toward ab Initio Ground States of Gold Clusters via Neural Network Modeling,” The Journal of Physical Chemistry C. 2019. link Times cited: 17 Abstract: Prescreening candidate structures with reliable classical po… read more Abstract: Prescreening candidate structures with reliable classical potentials is an effective way to accelerate ab-initio ground state searches. Given the growing popularity of machine learning force fields, surprisingly little work has been dedicated to quantifying their advantages over traditional potentials in global structure optimizations. In this study, we have developed a neural network (NN) model and systematically benchmarked it against a commonly used Gupta potential and an embedded atom model in the search for stable AuN clusters (30≤N≤80). An efficient simultaneous optimization of clusters in the full size range was achieved with our recently introduced multitribe evolutionary algorithm. Density functional theory (DFT) evaluations of candidate configurations identified with the three classical models revealed that the NN structures were lower in energy by at least 10 meV/atom for 30 of the 51 sizes. We also demonstrated that DFT evaluation of all NN-relaxed structures during evolutionary searches resul... read less S. Yin, G. Cheng, G. Richter, H. Gao, and Y. Zhu, “Transition of Deformation Mechanisms in Single Crystalline Metallic Nanowires.,” ACS nano. 2019. link Times cited: 31 Abstract: Twinning and dislocation slip are two competitive deformatio… read more Abstract: Twinning and dislocation slip are two competitive deformation mechanisms in face-centered cubic (FCC) metals. For FCC metallic nanowires (NWs), the competition between these mechanisms was found to depend on loading direction and material properties. Here, using in situ transmission electron microscopy tensile tests and molecular dynamics simulations, we report an additional factor, cross-sectional shape, that can affect the competition between the deformation mechanisms in single crystalline FCC metallic NWs. For a truncated rhombic cross-section, the extent of truncation determines the competition. Specifically, a transition from twinning to localized dislocation slip occurs with increasing extent of truncation. Theoretical and simulation results indicate that the energy barriers for twinning and dislocation slip depend on the cross-sectional shape of the NW. The energy barrier for twinning is proportional to the change of surface energy associated with the twinning. Thus, the transition of deformation modes can be attributed to the change of surface energy as a function of the cross-sectional shape. read less H. N. Pishkenari, F. S. Yousefi, and A. Taghibakhshi, “Determination of surface properties and elastic constants of FCC metals: a comparison among different EAM potentials in thin film and bulk scale,” Materials Research Express. 2018. link Times cited: 22 Abstract: Three independent elastic constants C11, C12, and C44 were c… read more Abstract: Three independent elastic constants C11, C12, and C44 were calculated and compared using available potentials of eight different metals with FCC crystal structure; Gold, Silver, Copper, Nickel, Platinum, Palladium, Aluminum and Lead. In order to calculate the elastic constants, the second derivative of the energy density of each system was calculated with respect to different directions of strains. Each set of the elastic constants of the metals in bulk scale was compared with experimental results, and the average relative error was for each was calculated and compared with other available potentials. Then, using the Voigt-Reuss-Hill method, approximated values for Young and shear moduli and Poisson’s ratio of the FCC metals in the bulk scale were found for each potential. Furthermore, to observe the surface effects on the metals in nanoscale, surface elastic constants of the thin films of the metals have been calculated. In the study of the thin films of materials in nanoscale, the number of surface atoms is considerable compared to all atoms of the object. This leads to an increase in the surface effects, which influence the elastic properties. By considering this fact and employing related definitions and equations, the properties of the thin films of the metals were calculated, and the surface effects for different crystallographic directions were compared. Subsequently, in some cases, comparisons among characteristics of the metals in the thin film and bulk material were made. read less J. Wu, X. F. Li, A.-Y. Tang, and K. Lee, “Free and forced transverse vibration of nanowires with surface effects,” Journal of Vibration and Control. 2017. link Times cited: 33 Abstract: This paper presents a theoretical analysis of free vibration… read more Abstract: This paper presents a theoretical analysis of free vibration and forced vibration of nanowires with surface effects. Using the Timoshenko beam theory incorporated with the surface effects, exact frequency equations are derived for various end supports. Natural frequencies and mode shapes are determined for simply supported, clamped-clamped, and clamped-free ends. Forced vibration of nanowires is also treated by superposing vibration modes of free vibration. An inverse problem is further investigated to determine the size-dependent effective Young's modulus of nanowires. Obtained results for a nanowire with residual stress and surface elasticity are confirmed by comparing them with the results using the finite element method. Theoretical natural frequencies and finite element method simulation have good agreement with the results from experimental data and molecular dynamics simulation. The effect of surface stress on forced vibration is analyzed. Residual surface tension has a more significant influence on the frequencies and a somewhat effect on the mode shapes. read less B. Xing, S. Yan, W. Jiang, and Q. Qin, “Atomistic Study for the Vibrational Properties on Σ5 Symmetric Tilt Bicrystal Copper Nanowires,” Applied Mechanics and Materials. 2016. link Times cited: 2 Abstract: In this study, an atomistic simulation was performed to inve… read more Abstract: In this study, an atomistic simulation was performed to investigate intrinsic resonance propensity of clamped-clamped copper nanowires with Σ5 (310)/[001] symmetric tilt grain boundary. Grain boundary energy γGB for bicrystal structure was calculated based on an iterative approach. The stable atomic configuration was then doubly clamped and excited via flexural oscillation under varied temperatures. From the result, the appearance of grain boundary significantly alters the resonance properties of Cu nanowires. Greater attenuation in kinetic energy can be observed with increased temperature. Quality factors attains Q ~ 1/T0.7144 and 1/T0.7249 with temperatures from kinetic energy and centroid root mean square spectrum, respectively, where the former seems more reliable to employ at elevated temperatures. read less H. N. Pishkenari, B. Afsharmanesh, and F. Tajaddodianfar, “Continuum models calibrated with atomistic simulations for the transverse vibrations of silicon nanowires,” International Journal of Engineering Science. 2016. link Times cited: 27 K. Kunal and N. Aluru, “Intrinsic dissipation in a nano-mechanical resonator,” Journal of Applied Physics. 2014. link Times cited: 16 Abstract: We investigate the effect of size on intrinsic dissipation i… read more Abstract: We investigate the effect of size on intrinsic dissipation in nano-structures. We use molecular dynamics simulation and study dissipation under two different modes of deformation: stretching and bending mode. In the case of stretching deformation (with uniform strain field), dissipation takes place due to Akhiezer mechanism. For bending deformation, in addition to the Akhiezer mechanism, the spatial temperature gradient also plays a role in the process of entropy generation. Interestingly, we find that the bending modes have a higher Q factor in comparison with the stretching deformation (under the same frequency of operation). Furthermore, with the decrease in size, the difference in Q factor between the bending and stretching deformation becomes more pronounced. The lower dissipation for the case of bending deformation is explained to be due to the surface scattering of phonons. A simple model, for phonon dynamics under an oscillating strain field, is considered to explain the observed variation in diss... read less Y. Zheng, Y. Zhao, H. F. Ye, and H. W. Zhang, “Size-dependent elastic moduli and vibrational properties of fivefold twinned copper nanowires,” Nanotechnology. 2014. link Times cited: 20 Abstract: Based on atomistic simulations, the elastic moduli and vibra… read more Abstract: Based on atomistic simulations, the elastic moduli and vibration behaviors of fivefold twinned copper nanowires are investigated in this paper. Simulation results show that the elastic (i.e., Young’s and shear) moduli exhibit size dependence due to the surface effect. The effective Young’s modulus is found to decrease slightly whereas the effective shear modulus increases slightly with the increase in the wire radius. Both moduli tend to approach certain values at a larger radius and can be suitably described by core-shell composite structure models. Furthermore, we show by comparing simulation results and continuum predictions that, provided the effective Young’s and shear moduli are used, classic elastic theory can be applied to describe the small-amplitude vibration of fivefold twinned copper nanowires. Moreover, for the transverse vibration, the Timoshenko beam model is more suitable because shear deformation becomes apparent. read less L. Morrissey, S. M. Handrigan, and S. Nakhla, “Discrepancies in the mechanical properties of gold nanowires: The importance of potential type and equilibration method,” Computational Materials Science. 2020. link Times cited: 6 J. Zhang and S. Meguid, “Piezoelectric Response at Nanoscale.” 2016. link Times cited: 1 S. Surulere, M. Shatalov, A. C. Mkolesia, and I. Fedotov, “A Modern Approach for the Identification of the Classical and Modified Generalized Morse Potential.” 2020. link Times cited: 5 Abstract: This paper proposes an approach for parameter estimation o… read more Abstract: This paper proposes an approach for parameter estimation of the Classical and Generalized Morse Potential functions. A new potential which is a modification of the Generalized Morse Potential was proposed as parameter estimates yielded complex conjugate roots using gold atom for simulation. Existing methods of parameter estimation requires the provision of initial guess values of which convergence to the optimal solution is not always guaranteed. This makes provision of initial guess values that guarantees convergence to the optimum solution more of an art than a science. The proposed objective least squares function method does not require the provision of initial guess values and it involves the minimization of two formulated objective functions using the differential numerical approach and least squares method. The built-in “Minimize” function of Mathematica® is also used to minimize the formulated objective function. Potential energy curves were constructed by fitting estimated parameter values to experimental data sets of the gold atom using values of the proposed approach and Mathematica® for performance evaluation. Errors of each constructed potential energy curves were simulated. It was observed that the errors were very small for both the Classical and Modified Generalized Morse Potential. Hence the approximations of the proposed approach are very good. read less S. Surulere, M. Shatalov, and E. Olayiwola, “Optimal interatomic potentials using modified method of least squares: Optimal form of interatomic potentials,” Open Physics. 2023. link Times cited: 0 Abstract: The problem of optimization of interatomic potentials is for… read more Abstract: The problem of optimization of interatomic potentials is formulated and solved by means of generalization of the Morse, Kaxiras–Pandey, and Rydberg potentials. The interatomic potentials are treated as solutions of some second-order ordinary differential equations which will be classified and analyzed. The most appropriate analytic form of the understudied potentials will be proposed based on a one-dimensional search for the parameter, γ \gamma , which is the power of the interatomic distance, r r . The optimal analytic form will also be proposed for metals such as gold, copper, aluminium, titanium, and the silver–copper alloy. The method of least squares will be used to estimate the potential parameters. Phenomenological potentials such as the classical Rydberg, classical Morse, generalized Morse, Kaxiras–Pandey, and classical Lennard–Jones will be studied, and new potentials based on the combination of some of the aforementioned potentials will also be proposed. Metrics such as the goal function values, will be used to identify which optimal value of the parameter, γ \gamma , is most appropriate to introduce into the preferred interatomic potential for interaction between atoms. read less S. Surulere, M. Shatalov, A. C. Mkolesia, and J. Ehigie, “A Novel Identification of the Extended-Rydberg Potential Energy Function,” Computational Mathematics and Mathematical Physics. 2019. link Times cited: 2 Z. Zheng, E. Li, N. Ding, and X. Xu, “A Molecular Dynamic Study on Nonlinear Vibration Behaviors of Fe Nanowires,” International Journal of Computational Methods. 2017. link Times cited: 1 Abstract: In this paper, vibration behaviors of Fe nanowires are inves… read more Abstract: In this paper, vibration behaviors of Fe nanowires are investigated by using the large-scale molecular dynamics (MD) simulations. It is observed that the vibration frequency of nanowires rises slightly and nonlinearly with the increase of initial actuation amplitude. Based on the atomic arrangement, a discrete spring-mass model is developed. Its nonlinear elastic relation is used to explain this phenomenon. In addition, Fe nanowires with different lengths and heights show different vibration properties in this work. The ratio between the length ([Formula: see text]) and the height ([Formula: see text]) of nanowires has a significant influence on vibration behaviors. The vibration properties of nanowires can be explained by the Euler–Bernoulli model when the ratio is relatively large, while they can be illustrated by the Timoshenko model when the ratio is relatively small. read less X.-jian Xu, Z. Deng, and B. Wang, “Closed solutions for the electromechanical bending and vibration of thick piezoelectric nanobeams with surface effects,” Journal of Physics D: Applied Physics. 2013. link Times cited: 15 Abstract: In this paper, a more accurate model is established to study… read more Abstract: In this paper, a more accurate model is established to study the influences of surface effects (SEs) including the surface elasticity, residual surface stress and surface piezoelectricity, on the electromechanical bending and vibration of the piezoelectric nanobeam (PNB) in the presence of shear deformation and rotary inertia. Analytical solutions are obtained for the electromechanical bending deflection, resonant frequency and mode shape of the PNB for three typical boundary conditions, demonstrating the significance of incorporation of shear deformation, rotary inertia and the surface parameters at different aspect ratios. The analytical solutions are found to be in good agreement with both molecular dynamics results and experimental data. The numerical results reveal that the surface elasticity plays a less significant role on the electromechanical bending and vibration than that of surface piezoelectricity and residual surface stress, and can be neglected for PNB with small aspect ratio and stiffer boundary conditions. In addition, the shear deformation and rotary inertia are found to play a larger impact effect than SEs for a stubby beam at higher vibration mode (i.e., aspect ratio less than 14 for doubly clamped beam). Moreover, the SEs are found to be increasing notably as aspect ratio increases. The continuum model established in this study will be useful for characterizing the mechanical properties of size-dependent piezoelectric structures and the design, calibration and application of PNB-based devices. read less P. Olsson and H. S. Park, “On the importance of surface elastic contributions to the flexural rigidity of nanowires,” Journal of The Mechanics and Physics of Solids. 2012. link Times cited: 57 Q. He and C. Lilley, “Resonant frequency analysis of Timoshenko nanowires with surface stress for different boundary conditions,” Journal of Applied Physics. 2012. link Times cited: 26 Abstract: The influence of both surface and shear effects on the reson… read more Abstract: The influence of both surface and shear effects on the resonant frequency of nanowires (NWs) was studied by incorporating the Young-Laplace equation with the Timoshenko beam theory. Face-centered-cubic metal NWs were studied. A dimensional analysis of the resonant frequencies for fixed-fixed gold (100) NWs were compared to molecular dynamic simulations. Silver NWs with diameters from 10 nm–500 nm were modeled as a cantilever, simply supported and fixed-fixed system for aspect ratios from 2.5–20 to identify the shear, surface, and size effects on the resonant frequencies. The shear effect was found to have a larger significance than surface effects when the aspect ratios were small (i.e., <5) regardless of size for the diameters modeled. Finally, as the aspect ratio grows, the surface effect becomes significant for the smaller diameter NWs. read less H. Zhan and Y. T. Gu, “A fundamental numerical and theoretical study for the vibrational properties of nanowires,” Journal of Applied Physics. 2012. link Times cited: 36 Abstract: Based on the molecular dynamics (MD) simulation and the clas… read more Abstract: Based on the molecular dynamics (MD) simulation and the classical Euler-Bernoulli beam theory, a fundamental study of the vibrational performance of the Ag nanowire (NW) is carried out. A comprehensive analysis of the quality (Q)-factor, natural frequency, beat vibration, as well as high vibration mode is presented. Two excitation approaches, i.e., velocity excitation and displacement excitation, have been successfully implemented to achieve the vibration of NWs. Upon these two kinds of excitations, consistent results are obtained, i.e., the increase of the initial excitation amplitude will lead to a decrease to the Q-factor, and moderate plastic deformation could increase the first natural frequency. Meanwhile, the beat vibration driven by a single relatively large excitation or two uniform excitations in both two lateral directions is observed. It is concluded that the nonlinear changing trend of external energy magnitude does not necessarily mean a non-constant Q-factor. In particular, the first order ... read less P. Olsson and H. S. Park, “Atomistic study of the buckling of gold nanowires,” Acta Materialia. 2011. link Times cited: 30
Funding	Not available

Short KIM ID The unique KIM identifier code.	MO_228280943430_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.	EAM_Dynamo_Olsson_2010_Au__MO_228280943430_000
DOI	10.25950/fe43ad59 https://doi.org/10.25950/fe43ad59 https://commons.datacite.org/doi.org/10.25950/fe43ad59
KIM Item Type Specifies whether this is a Portable Model (software implementation of an interatomic model); Portable Model with parameter file (parameter file to be read in by a Model Driver); Model Driver (software implementation of an interatomic model that reads in parameters).	Portable Model using Model Driver EAM_Dynamo__MD_120291908751_005
Driver	EAM_Dynamo__MD_120291908751_005
KIM API Version	2.0
Potential Type	eam

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 1.53175e-09 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.	vc-forces-numerical-derivative	consistency	Forces computed by the model agree with numerical derivatives of the energy; see full description.	Results	Files
P The model is C^2 continuous. This means that the model has continuous energy and continuous derivatives up to order 2.	vc-dimer-continuity-c1	informational	The energy versus separation relation of a pair of atoms is C1 continuous (i.e. the function and its first derivative are continuous); see full description.	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
P No 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
P All threads give identical results for tested case. Model appears to be thread-safe.	vc-thread-safe	mandatory	The model returns the same energy and forces when computed in serial and when using parallel threads for a set of configurations. Note that this is not a guarantee of thread safety; see full description.	Results	Files
P Unit conversion successful	vc-unit-conversion	mandatory	The model is able to correctly convert its energy and/or forces to different unit sets; see full description.	Results	Files

This bar chart plot shows the mono-atomic body-centered cubic (bcc) lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: Au

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: Au

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: Au

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: Au

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: Au

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.

Species: Au

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.

Species: Au

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: Au

Cubic Crystal Basic Properties Table

Species: Au

Tests

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 Au v004	view	7589
Cohesive energy versus lattice constant curve for diamond Au v004	view	7917
Cohesive energy versus lattice constant curve for fcc Au v004	view	7231
Cohesive energy versus lattice constant curve for sc Au v004	view	8687

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 Au at zero temperature v006	view	2335
Elastic constants for diamond Au at zero temperature v001	view	3487
Elastic constants for fcc Au at zero temperature v006	view	1663
Elastic constants for sc Au at zero temperature v006	view	1791

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 Au at zero temperature v004		view	1815

EquilibriumCrystalStructure__TD_457028483760_001

Equilibrium structure and energy for a crystal structure at zero temperature and pressure v001

Creators:
Contributor: ilia
Publication Year: 2023
DOI: https://doi.org/10.25950/e8a7ed84

Computes the equilibrium crystal structure and energy for an arbitrary crystal at zero temperature and applied stress by performing symmetry-constrained relaxation. The crystal structure is specified using the AFLOW prototype designation. Multiple sets of free parameters corresponding to the crystal prototype may be specified as initial guesses for structure optimization. No guarantee is made regarding the stability of computed equilibria, nor that any are the ground state.

Test	Test Results	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Equilibrium crystal structure and energy for Au in AFLOW crystal prototype A_cF4_225_a v001		view	73032

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 Au v007	view	1919
Equilibrium zero-temperature lattice constant for diamond Au v007	view	2687
Equilibrium zero-temperature lattice constant for fcc Au v007	view	3487
Equilibrium zero-temperature lattice constant for sc Au v007	view	2207

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 Au v005		view	17573

LinearThermalExpansionCoeffCubic__TD_522633393614_001

Linear thermal expansion coefficient of cubic crystal structures v001

Creators: Mingjian Wen
Contributor: mjwen
Publication Year: 2019
DOI: https://doi.org/10.25950/fc69d82d

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 fcc Au at 293.15 K under a pressure of 0 MPa v001		view	8706030

PhononDispersionCurve__TD_530195868545_004

Phonon dispersion relations for an fcc lattice v004

Creators: Matt Bierbaum
Contributor: mattbierbaum
Publication Year: 2019
DOI: https://doi.org/10.25950/64f4999b

Calculates the phonon dispersion relations for fcc lattices and records the results as curves.

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)
Phonon dispersion relations for fcc Au v004		view	51694

StackingFaultFccCrystal__TD_228501831190_002

Stacking and twinning fault energies of an fcc lattice at zero temperature and pressure v002

Creators:
Contributor: SubrahmanyamPattamatta
Publication Year: 2019
DOI: https://doi.org/10.25950/b4cfaf9a

Intrinsic and extrinsic stacking fault energies, unstable stacking fault energy, unstable twinning energy, stacking fault energy as a function of fractional displacement, and gamma surface for a monoatomic FCC lattice at zero temperature and pressure.

Test	Test Results	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Stacking and twinning fault energies for fcc Au v002		view	6088754

SurfaceEnergyCubicCrystalBrokenBondFit__TD_955413365818_004

High-symmetry surface energies in cubic lattices and broken bond model v004

Creators: Matt Bierbaum
Contributor: mattbierbaum
Publication Year: 2019
DOI: https://doi.org/10.25950/6c43a4e6

Calculates the surface energy of several high symmetry surfaces and produces a broken-bond model fit. In latex form, the fit equations are given by:

E_{FCC} (\vec{n}) = p_1 (4 \left( |x+y| + |x-y| + |x+z| + |x-z| + |z+y| +|z-y|\right)) + p_2 (8 \left( |x| + |y| + |z|\right)) + p_3 (2 ( |x+ 2y + z| + |x+2y-z| + |x-2y + z| + |x-2y-z| + |2x+y+z| + |2x+y-z| +|2x-y+z| +|2x-y-z| +|x+y+2z| +|x+y-2z| +|x-y+2z| +|x-y-2z| ) + c

E_{BCC} (\vec{n}) = p_1 (6 \left( | x+y+z| + |x+y-z| + |-x+y-z| + |x-y+z| \right)) + p_2 (8 \left( |x| + |y| + |z|\right)) + p_3 (4 \left( |x+y| + |x-y| + |x+z| + |x-z| + |z+y| +|z-y|\right)) +c.

In Python, these two fits take the following form:

def BrokenBondFCC(params, index):

import numpy
x, y, z = index
x = x / numpy.sqrt(x**2.+y**2.+z**2.)
y = y / numpy.sqrt(x**2.+y**2.+z**2.)
z = z / numpy.sqrt(x**2.+y**2.+z**2.)

return params[0]*4* (abs(x+y) + abs(x-y) + abs(x+z) + abs(x-z) + abs(z+y) + abs(z-y)) + params[1]*8*(abs(x) + abs(y) + abs(z)) + params[2]*(abs(x+2*y+z) + abs(x+2*y-z) +abs(x-2*y+z) +abs(x-2*y-z) + abs(2*x+y+z) +abs(2*x+y-z) +abs(2*x-y+z) +abs(2*x-y-z) + abs(x+y+2*z) +abs(x+y-2*z) +abs(x-y+2*z) +abs(x-y-2*z))+params[3]

def BrokenBondBCC(params, x, y, z):

import numpy
x, y, z = index
x = x / numpy.sqrt(x**2.+y**2.+z**2.)
y = y / numpy.sqrt(x**2.+y**2.+z**2.)
z = z / numpy.sqrt(x**2.+y**2.+z**2.)

return params[0]*6*(abs(x+y+z) + abs(x-y-z) + abs(x-y+z) + abs(x+y-z)) + params[1]*8*(abs(x) + abs(y) + abs(z)) + params[2]*4* (abs(x+y) + abs(x-y) + abs(x+z) + abs(x-z) + abs(z+y) + abs(z-y)) + params[3]

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)
Broken-bond fit of high-symmetry surface energies in fcc Au v004		view	27191

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 fcc Au		view	342924

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 fcc Au		view	1754597

Errors

GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle__TD_410381120771_003

Test	Error Categories	Link to Error page
Relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in fcc Au v000	other	view
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in fcc Au v000	other	view
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in fcc Au v000	other	view
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in fcc Au v000	other	view

LatticeConstantCubicEnergy__TD_475411767977_006

Test	Error Categories	Link to Error page
Equilibrium zero-temperature lattice constant for diamond Au	other	view

LatticeConstantHexagonalEnergy__TD_942334626465_004

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

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EAM_Dynamo_Olsson_2010_Au__MO_228280943430_000

Verification Check Dashboard

Visualizers (in-page)

BCC Lattice Constant

Cohesive Energy Graph

Diamond Lattice Constant

Dislocation Core Energies

FCC Elastic Constants

FCC Lattice Constant

FCC Stacking Fault Energies

FCC Surface Energies

SC Lattice Constant

Cubic Crystal Basic Properties Table

Tests

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