EAM potential (LAMMPS cubic hermite tabulation) for the Al-Cu system developed by Liu et al. (1999) v000

Chunli Liu; Leonard Borucki; XY Liu

doi:10.25950/2dd77629

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EAM_Dynamo_LiuLiuBorucki_1999_AlCu__MO_020851069572_000

Interatomic potential for Aluminum (Al), Copper (Cu).
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Title A single sentence description.	EAM potential (LAMMPS cubic hermite tabulation) for the Al-Cu system developed by Liu et al. (1999) 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.	EAM potential for the Al-Cu system developed by Liu et al. (1999). The potential was used to study electromigration in Al-Cu interconnects.
Species The supported atomic species.	Al, Cu
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/Al.html#Al-Cu)
Content Other Locations	http://enpub.fulton.asu.edu/cms/potentials/main/main.htm

Contributor	Ellad B. Tadmor
Maintainer	Ellad B. Tadmor
Developer	Chunli Liu Leonard Borucki XY Liu
Published on KIM	2018
How to Cite	This Model originally published in [1] is archived in OpenKIM [2-5]. [1] Liu X-Y, Liu C-L, Borucki LJ. A new investigation of copper’s role in enhancing Al–Cu interconnect electromigration resistance from an atomistic view. Acta Materialia. 1999;47(11):3227–31. doi:10.1016/S1359-6454(99)00186-X — (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] Liu C, Borucki L, Liu XY. EAM potential (LAMMPS cubic hermite tabulation) for the Al-Cu system developed by Liu et al. (1999) v000. OpenKIM; 2018. doi:10.25950/2dd77629 [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. 44 Citations (24 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 . “Local decomposition induced by dislocation motions inside tetragonal Al2Cu compound: slip system-dependent dynamics,” Scientific Reports. 2013. link Times cited: 0 D. Andre et al., “Dislocation-mediated plasticity in the Al2Cu θ-phase.” 2021. link Times cited: 7 H. Lin, T. Li, and H. Li, “Molecular dynamics study on the heterogeneous nucleation of liquid Al-Cu alloys on different kinds of copper substrates.,” Physical chemistry chemical physics : PCCP. 2018. link Times cited: 5 Abstract: Al-Cu alloys are widely used in aeronautics and aerospace en… read more Abstract: Al-Cu alloys are widely used in aeronautics and aerospace engineering because they exhibit outstanding performance. However, their casting characteristics are poor. Heterogeneous nucleation plays a significant role in controlling crystal growth. MD simulations are performed to explore the heterogeneous nucleation of liquid Al-Cu on a copper substrate including the heat-up process, preservation process, and freezing process. The simulation results show that the Al-Cu melt becomes layered at the liquid-solid interface and tends to be ordered in the structure because of the induced effect from the substrate. The crystal structure information is found to be gradually delivered from the substrate to the liquid, and this transmission capacity of information decays with increasing distance from the substrate. The liquid Al-Cu alloy with high copper content frozen on the single substrate tends to form a perfect crystal structure more easily, but the Al-Cu melt with low copper content between two copper substrates tends to form an arch-shaped structure, which can disappear when the copper content reaches a specific proportion. Moreover, different angles of the grooved substrates also affect the heterogeneous nucleation of the Al-Cu melt and its solidified structure. Our findings provide new insights into the defect and structural changes during heterogeneous nucleation, and our findings also promote leading-edge studies, which can provide new ideas to mechanical research. read less Q. Wei, X.-Y. Liu, and A. Misra, “Observation of continuous and reversible bcc–fcc phase transformation in Ag/V multilayers,” Applied Physics Letters. 2011. link Times cited: 19 Abstract: A continuous and reversible bcc–fcc phase transformation via… read more Abstract: A continuous and reversible bcc–fcc phase transformation via a rotation of bcc{110} or fcc{111} planes is observed in the Bain orientation relationship in a sputter deposited V/Ag multilayers using high resolution transmission electron microscopy and analyzed using molecular dynamics simulations. As a result of the continuous phase transformation, an intermediate bct phase connecting the bcc and fcc phases coexists, giving rise to the Bain path. The periodic displacement of atoms occurs in every two adjacent Ag and V layers. The alternating shear stress created by misfit strain is responsible for generating such transformation. read less G. Campbell, J. Plitzko, W. King, S. Foiles, C. Kisielowski, and G. Duscher, “Copper Segregation to the Σ5 (310)/[001] Symmetric Tilt Grain Boundary in Aluminum,” Interface Science. 2004. link Times cited: 18 H. Yoshida, T. Yamamoto, Y. Ikuhara, and T. Sakuma, “A change in the chemical bonding strength and high-temperature creep resistance in Al2O3 with lanthanoid oxide doping,” Philosophical Magazine A. 2002. link Times cited: 14 Abstract: High-temperature creep resistance in polycrystalline Al2O3 i… read more Abstract: High-temperature creep resistance in polycrystalline Al2O3 is highly improved by doping with 0.05 mol∼ lanthanoid (Ln) oxide (Ln = Sm, Eu, Tm or Lu) at 1250°C. The improvement in creep resistance probably occurs as a result of retardation of the grain-boundary diffusion in Al2O3 due to grain-boundary segregation of dopant cations. The change in chemical bonding state in grain boundaries with the segregation of Ln cations is examined by a first-principles molecular orbital calculation using the discrete variational-Xα method based on [Al5O21]27− model cluster. The result of the calculation indicates that the ionic bonding between Al and O ions, and the covalent bonding between Al and the surrounding cation, are strengthened by the presence of Ln ions. A correlation is found between the creep resistance and product of net charges of the constituent ions. The improved creep resistance must be explained in terms of a change in chemical bonding strength around the Al ion. read less P. Wang et al., “Atomistic simulation for deforming complex alloys with application toward TWIP steel and associated physical insights,” Journal of The Mechanics and Physics of Solids. 2017. link Times cited: 42 X. Zhang, L. Zhang, Z.-H. Zhang, and X. Huang, “Effect of solute atoms segregation on Al grain boundary energy and mechanical properties by first-principles study,” Mechanics of Materials. 2023. link Times cited: 1 R. Thiruchelvam, J. E. Suryana, and R. Nambatyathu, “Method to Reduce Micromasking defects caused by Cu precipitation using Ar/N2 plasma : YE: Yield Enhancement/Learning,” 2023 34th Annual SEMI Advanced Semiconductor Manufacturing Conference (ASMC). 2023. link Times cited: 0 Abstract: This paper discusses ways to reduce micro masking due to Cop… read more Abstract: This paper discusses ways to reduce micro masking due to Copper (Cu) precipitation during reactive ion etching (RIE) to form thick top metal bond pads or inductors. Adding Argon (Ar) and Nitrogen (N2) in the over etch step during metal etch can significantly reduce micro-masking caused by Cu precipitation. The introduction of Ar and N2 can have several effects on the RIE process, such as improving the ionizing effect during Al/TiN barrier etch by altering the ion energy to effectively remove the Cu precipitation at the grain boundaries of Al and TiN interfaces read less V. Krasnikov, A. Mayer, P. Bezborodova, and M. Gazizov, “Effect of Copper Segregation at Low-Angle Grain Boundaries on the Mechanisms of Plastic Relaxation in Nanocrystalline Aluminum: An Atomistic Study,” Materials. 2023. link Times cited: 2 Abstract: The paper studies the mechanisms of plastic relaxation and m… read more Abstract: The paper studies the mechanisms of plastic relaxation and mechanical response depending on the concentration of Cu atoms at grain boundaries (GBs) in nanocrystalline aluminum with molecular dynamics simulations. A nonmonotonic dependence of the critical resolved shear stress on the Cu content at GBs is shown. This nonmonotonic dependence is related to the change in plastic relaxation mechanisms at GBs. At a low Cu content, GBs slip as dislocation walls, whereas an increase in Cu content involves a dislocation emission from GBs and grain rotation with GB sliding. read less B. Li, Z. Zhang, X. Zhou, M.-men Liu, and Y. Jie, “Mechanical behavior and microstructure evolution of Al/AlCu alloy interface,” Journal of Materials Science. 2023. link Times cited: 2 B. Waters, D. S. Karls, I. Nikiforov, R. Elliott, E. Tadmor, and B. Runnels, “Automated determination of grain boundary energy and potential-dependence using the OpenKIM framework,” Computational Materials Science. 2022. link Times cited: 5 L. Zhang, Z.-H. Zhang, X. Zhang, and X. Huang, “Computational simulation of grain boundary segregation of solute atoms in nanocrystalline metals,” Journal of Materials Research and Technology. 2022. link Times cited: 4 Y. Kashyrina, A. S. Muratov, V. Kazimirov, and O. S. Roik, “X-ray diffraction study and molecular dynamic simulation of liquid Al-Cu alloys: a new data and interatomic potentials comparison,” Journal of Molecular Modeling. 2022. link Times cited: 0 L.-F. Zhu, J. Janssen, S. Ishibashi, F. Körmann, B. Grabowski, and J. Neugebauer, “A fully automated approach to calculate the melting temperature of elemental crystals,” Computational Materials Science. 2021. link Times cited: 17 J. Wang, S. Shin, A. Y. Nobakht, and A. Shyam, “Structural deformation and transformation of θ′-Al2Cu precipitate in Al matrix via interfacial diffusion,” Computational Materials Science. 2019. link Times cited: 11 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. Dziedzic, S. Winczewski, and J. Rybicki, “Structure and properties of liquid Al–Cu alloys: empirical potentials compared,” Computational Materials Science. 2016. link Times cited: 17 L. Deng, H. Deng, J.-feng Tang, X. Zhang, S. Xiao, and W. Hu, “Monte Carlo simulations of strain-driven elemental depletion or enrichment in Cu95Al5 and Cu90Al10 alloys,” Computational Materials Science. 2015. link Times cited: 1 F. Hung, J. Liao, T. Lui, and L.-H. Chen, “Electrical current induced mechanism in microstructure and nano-indention of Al-Zn-Mg-Cu (AZMC) Al alloy thin film,” Current Applied Physics. 2011. link Times cited: 8 E. Jannot, V. Mohles, G. Gottstein, and B. Thijsse, “Atomistic Simulation of Pipe Diffusion in AlCu Alloys,” Defect and Diffusion Forum. 2006. link Times cited: 11 Abstract: Activation energies for solute diffusion along dislocations … read more Abstract: Activation energies for solute diffusion along dislocations are difficult to measure experimentally. The aim of this work is to provide insight into pipe diffusion with the help of atomistic simulations. The distribution of vacancy formation energy and the activation energy for copper migration are determined in the core of an edge dislocation in aluminum. The Dimer method is used to find activation energies for vacancy migration. The activated region around the dislocation where a very high diffusivity is observed and the activation energy for copper diffusion associated with this region are interpreted with regard to the contribution of the dislocation and the contribution of the alloying. read less P. Choi, T. Al-Kassab, and R. Kirchheim, “Investigation of sputter-deposited Al-2at.%Cu layers by means of the tomographic atom probe (TAP),” Scripta Materialia. 2005. link Times cited: 7 C. Witt, C. Volkert, and E. Arzt, “Electromigration-induced Cu motion and precipitation in bamboo Al–Cu interconnects,” Acta Materialia. 2003. link Times cited: 38 T. Cale, T. Merchant, L. Borucki, and A. Labun, “Topography simulation for the virtual wafer fab,” Thin Solid Films. 2000. link Times cited: 46 R. Thiruchelvam, S. H. Siraji, and L. Koon, “Elimination of Cu Precipitation in Al-Cu films due to the Effect of Thermal Cycles,” 2023 34th Annual SEMI Advanced Semiconductor Manufacturing Conference (ASMC). 2023. link Times cited: 0 Abstract: This paper explains how copper precipitation can be eliminat… read more Abstract: This paper explains how copper precipitation can be eliminated for metal-insulator-metal (MIM) dielectric capacitor processes for technology nodes larger than 0.13um with annealing at the 350-410°C range. This is shown as an effective method to eliminate aluminum blocked etch on the bottom plate of the MIM capacitor. This is essential to prevent shorting between the dense metal lines of the bottom plate and to prevent yield loss with no impact on the final electrical test or the electromigration performance. read less X. Wang, G.-ping Cheng, Y. Zhang, Y. Wang, W. Liao, and T. A. Venkatesh, “On the Evolution of Nano-Structures at the Al–Cu Interface and the Influence of Annealing Temperature on the Interfacial Strength,” Nanomaterials. 2022. link Times cited: 1 Abstract: Molecular dynamics (MD) simulations are invoked to simulate … read more Abstract: Molecular dynamics (MD) simulations are invoked to simulate the diffusion process and microstructural evolution at the solid–liquid, cast-rolled Al–Cu interfaces. K-Means clustering algorithm is used to identify the formation and composition of two types of nanostructural features in the Al-rich and Cu-rich regions of the interface (i.e., the intermetallic Al2Cu near the Al-rich interface and the intermetallic Al4Cu9 near the Cu-rich interface). MD simulations are also used to assess the effects of annealing temperature on the evolution of the compositionally graded microstructural features at the Al–Cu interfaces and to characterize the mechanical strength of the Al–Cu interfaces. It is found that the failure of the Al–Cu interface takes place at the Al-rich side of the interface (Al2Cu–Al) which is mechanically weaker than the Cu-rich side of the interface (Cu–Al4Cu9), which is also verified by the nanoindentation studies of the interfaces. Centrosymmetry parameter analyses and dislocation analyses are used to understand the microstructural features that influence deformation behavior leading to the failure of the Al–Cu interfaces. Increasing the annealing temperature reduces the stacking fault density at the Al–Cu interface, suppresses the generation of nanovoids which are precursors for the initiation of fracture at the Al-rich interface, and increases the strength of the interface. read less S. Ma, Z. Dong, N. Zong, T. Jing, and H. Dong, “Solute-adsorption enhanced heterogeneous nucleation: the effect of Cu adsorption on α-Al nucleation at the sapphire substrate.,” Physical chemistry chemical physics : PCCP. 2021. link Times cited: 7 Abstract: Interfacial adsorption of solute atoms is a promising means … read more Abstract: Interfacial adsorption of solute atoms is a promising means to tune heterogeneous nucleation. In this study, a new method has been established to theoretically evaluate the effect of solute addition on the nucleation potency of heterogeneous nucleation interfaces. The evaluation consists of three steps: (1) analyzing the solute adsorption behavior; (2) determining the nucleation mode; and (3) evaluating the effect of solute adsorption on nucleation potency using the solute-adsorbed interface model. A combination of the ab initio and molecular dynamics methods together with the two-phase thermodynamic model was used to evaluate a prototype Al-Cu/(0001) sapphire interface. It is found that solute Cu atoms adsorb at the interface between the melt and (0001) sapphire interface. The adsorption is driven by the strengthening of the Cu-Al bonds as revealed by the Bader charge analysis which is demonstrated to reduce interfacial energy. Furthermore, it is revealed that the interfacial adoption of Cu results in the formation of an Al-Cu adsorption layer, which enhances the interfacial chemical affinity thus enlarging the nucleation driving force. Meanwhile, the lattice mismatch between the sapphire substrate and the primary Al (α-Al) nucleus is decreased by Cu addition, which lowers the barrier for nucleation. The above two effects together increase the nucleation potency of the studied interface, which is in good agreement with previous experiments. It is proposed that the effect of solute adsorption shall be considered in the search for effective substrates for tuning the nucleation. read less L. Borucki, “Taking on the Multiscale Challenge.” 2004. link Times cited: 0 H. Jo et al., “Direct strain correlations at the single-atom level in three-dimensional core-shell interface structures,” Nature Communications. 2022. link Times cited: 8 Z. Wang et al., “Symmetry-adapted graph neural networks for constructing molecular dynamics force fields,” Science China Physics, Mechanics & Astronomy. 2021. link Times cited: 9 W. Jiang, Y. Zhang, L. Zhang, and H. Wang, “Accurate Deep Potential model for the Al–Cu–Mg alloy in the full concentration space,” arXiv: Materials Science. 2020. link Times cited: 24 Abstract: Combining first-principles accuracy and empirical-potential … read more Abstract: Combining first-principles accuracy and empirical-potential efficiency for the description of the potential energy surface (PES) is the philosopher's stone for unraveling the nature of matter via atomistic simulation. This has been particularly challenging for multi-component alloy systems due to the complex and non-linear nature of the associated PES. In this work, we develop an accurate PES model for the Al-Cu-Mg system by employing Deep Potential (DP), a neural network based representation of the PES, and DP Generator (DP-GEN), a concurrent-learning scheme that generates a compact set of ab initio data for training. The resulting DP model gives predictions consistent with first-principles calculations for various binary and ternary systems on their fundamental energetic and mechanical properties, including formation energy, equilibrium volume, equation of state, interstitial energy, vacancy and surface formation energy, as well as elastic moduli. Extensive benchmark shows that the DP model is ready and will be useful for atomistic modeling of the Al-Cu-Mg system within the full range of concentration. read less S. Mojumder, M. S. H. Thakur, M. Islam, M. Mahboob, and M. Motalab, “Numerical investigation of mechanical properties of aluminum-copper alloys at nanoscale,” Journal of Nanoparticle Research. 2020. link Times cited: 5 P. Parajuli et al., “Misorientation dependence grain boundary complexions in <111> symmetric tilt Al grain boundaries,” Acta Materialia. 2019. link Times cited: 10 Y.-C. Liu and S. Lin, “A Critical Review on the Electromigration Effect, the Electroplastic Effect, and Perspectives on the Effects of Electric Current Upon Alloy Phase Stability,” JOM. 2019. link Times cited: 9 P. Parajuli, R. Mendoza-Cruz, A. Hurtado-Macías, U. Santiago, and M. Yacamán, “A Direct Observation of Ordered Structures Induced by Cu Segregation at Grain Boundaries of Al 7075 Alloys,” physica status solidi (a). 2018. link Times cited: 7 Abstract: The experimental investigation of the atomic‐scale structure… read more Abstract: The experimental investigation of the atomic‐scale structure and chemistry of the grain boundaries by resolving the sites and chemical identities of the atoms comprising the interface is crucial to understand the implication of preferential atomic segregation at grain boundaries. Here, the authors report the ordered‐structures induced by substitutional Cu segregation at the Al alloy 7075 coincidence site lattice grain boundaries, namely, ∑13b and ∑7, using Cs‐aberration corrected scanning transmission electron microscopy. Unlike the single‐atom interstitial hollow site segregation behavior at the boundary region (predicted in the theoretical studies and considered on analysis of segregation effects), the authors demonstrate segregation of Cu atoms on two columns opposite to each other across the interface forming an ordered parallel array of segregating atoms in substitutional core sites. This is the first time that this type of parallel array segregation behavior is reported. Furthermore, based on intensity profiles and scanning transmission electron microscopy Z‐contrast principle, non‐uniformly (high and low) segregated mixed atomic columns are predicted at the grain boundaries. read less L. Hale, “Comparing Modeling Predictions of Aluminum Edge Dislocations: Semidiscrete Variational Peierls–Nabarro Versus Atomistics,” JOM. 2018. link Times cited: 7 D. Zhao, O. Løvvik, K. Marthinsen, and Y. Li, “Segregation of Mg, Cu and their effects on the strength of Al Σ5 (210)[001] symmetrical tilt grain boundary,” Acta Materialia. 2018. link Times cited: 86 K. Choudhary et al., “Charge optimized many-body potential for aluminum,” Journal of Physics: Condensed Matter. 2014. link Times cited: 19 Abstract: An interatomic potential for Al is developed within the thir… read more Abstract: An interatomic potential for Al is developed within the third generation of the charge optimized many-body (COMB3) formalism. The database used for the parameterization of the potential consists of experimental data and the results of first-principles and quantum chemical calculations. The potential exhibits reasonable agreement with cohesive energy, lattice parameters, elastic constants, bulk and shear modulus, surface energies, stacking fault energies, point defect formation energies, and the phase order of metallic Al from experiments and density functional theory. In addition, the predicted phonon dispersion is in good agreement with the experimental data and first-principles calculations. Importantly for the prediction of the mechanical behavior, the unstable stacking fault energetics along the direction on the (1 1 1) plane are similar to those obtained from first-principles calculations. The polycrsytal when strained shows responses that are physical and the overall behavior is consistent with experimental observations. read less B. Jelinek et al., “Modified embedded atom method potential for Al, Si, Mg, Cu, and Fe alloys,” Physical Review B. 2011. link Times cited: 218 Abstract: A set of modified embedded-atom method (MEAM) potentials for… read more Abstract: A set of modified embedded-atom method (MEAM) potentials for the interactions between Al, Si, Mg, Cu, and Fe was developed from a combination of each element's MEAM potential in order to study metal alloying. Previously published MEAM parameters of single elements have been improved for better agreement to the generalized stacking fault energy (GSFE) curves when compared with ab initio generated GSFE curves. The MEAM parameters for element pairs were constructed based on the structural and elastic properties of element pairs in the NaCl reference structure garnered from ab initio calculations, with adjustment to reproduce the ab initio heat of formation of the most stable binary compounds. The new MEAM potentials were validated by comparing the formation energies of defects, equilibrium volumes, elastic moduli, and heat of formation for several binary compounds with ab initio simulations and experiments. Single elements in their ground-state crystal structure were subjected to heating to test the potentials at elevated temperatures. An Al potential was modified to avoid formation of an unphysical solid structure at high temperatures. The thermal expansion coefficient of a compound with the composition of AA 6061 alloy was evaluated and compared with experimental values. MEAM potential tests performed in this work, utilizing the universal atomistic simulation environment (ASE), are distributed to facilitate reproducibility of the results. read less C. Yu, X. Jijin, Y. Yang, and H. Lu, “First principles calculation of the effects of solute atom on electromigration resistance of Al interconnects,” Journal of Physics D: Applied Physics. 2009. link Times cited: 4 Abstract: Electromigration (EM) resistance of Al could be improved thr… read more Abstract: Electromigration (EM) resistance of Al could be improved through the addition of a small amount of alloying elements, such as copper and magnesium. In this paper, an Al31X (X = Sc–Zn and Mg) supercell model was constructed to calculate the effects of a solute element on the properties of face central cubic Al, including the heat of formation, diffusion energy and electronic structure, etc, by employing the density functional theory. It is found that the diffusion energy of Al near Ti, V, Cr, Cu, Zn and Mg solutes could be enhanced. Likewise, the value of the density of states of the system at the Fermi level (N(EF)), as well as that of the Al atoms at the specific sites, could also be reduced slightly by the addition of Sc, Ni, Cu, Zn and Mg. These two results indicate that the nearest neighbour Al atoms could be stabilized by Cu, Zn and Mg. Thus they would be beneficial in prolonging the EM lifetime of Al interconnects. Our calculations are in good agreement with the previous calculations and the experimental phenomenon to some extent. read less F. Sen and M. Aydinol, “Atomistic simulation of self-diffusion in Al and Al alloys under electromigration conditions,” Journal of Applied Physics. 2008. link Times cited: 9 Abstract: The effect of alloying elements on the self-diffusion behavi… read more Abstract: The effect of alloying elements on the self-diffusion behavior of Al under electromigration conditions was investigated using nonequilibrium molecular dynamics. The corresponding defect structures were also characterized energetically by Mott–Littleton approach. Pd, Cu, Mn, and Sn were found to be the most effective alloying elements that may retard the electromigration failure by increasing the activation energy for self-diffusion of Al. This increase in the activation energy is believed to be either because of the dragging effect that may be experienced in a coupled substitutional-vacancy defect structure or the energy penalty for the separation of this couple. read less C.-ming Chen and S.-wen Chen, “Electromigration effect upon the Zn/Ni and Bi/Ni interfacial reactions,” Journal of Electronic Materials. 2000. link Times cited: 45 C. Witt, “Electromigration in bamboo aluminum interconnects.” 2000. link Times cited: 2 Abstract: Elektromigration kann zur Schadigung von miniaturisierten Le… read more Abstract: Elektromigration kann zur Schadigung von miniaturisierten Leiterbahnen durch die Bildung von Poren und Hugeln fuhren. Die Lebensdauer von Aluminiumbahnen wird erheblich durch den Zusatz von Kupfer, und durch die Abdeckung mit einer Passivierungsschicht gesteigert. Die genauen Mechanismen dieser Effekte sind jedoch noch nicht vollstandig verstanden. Um diese Effekte in Leiterbahnen mit einer Bambusstruktur zu untersuchen, wurden Elektromirationsexperimente an sub-Mikrometer schmalen Leiterbahnsegmenten verschiedener Lange aus Al und Al(0.5gew%Cu), jeweils mit und ohne Passivierung durchgefuhrt. Der Zusatz von Kupfer erhoht das kritischen Produkts von Segmentlange und Stromdichte, oberhalb dessen eine Schadigung eintritt. Im Gegensatz zu Segmenten aus reinem Al, bilden sich die Hugel entfernt vom Anodenende der Segmente, und der Materialabtrag des Al als Funktion der Zeit (Driftgeschwindigkeit) nimmt in den Al(Cu) Bahnen zu. Diese Beobachtungen sind konsistent mit der Vorstellung, das die Mobilitat des Al erheblich reduziert wird, wenn die Kupferkonzentration genugend gros ist. Die Untersuchung der elektromigrationsinduzierten Umverteilung des Kupfers in unbeschadigten Segmenten zeigt, das der Kupfertransport entlang der Grenzflachen der Leiterbahnen sehr schnell ist. Auserdem wird gezeigt, das fur die Bildung von Ausscheidungen eine Kupferubersattigung von etwa der zweifachen Loslichkeitskonzentration erforderlich ist. Die statistische Verteilung des kritischen Produkts wird als Funktion der Segmentlange untersucht. Es wird demonstriert, das die Streuung mit abnehmender Lange ansteigt. Dazu wird ein Modell vorgestellt. Der Vergleich von passiviertem und unpassiviertem Al zeigt, das die kritische Spannung zur Bildung von Poren und die Driftgeschwindigkeit in etwa gleich sind, das kritische Produkt der Passivierten jedoch deutlich groser ist, was durch die Unterdruckung der Hugelbildung erklart wird. Electromigration can damage interconnects by forming voids and hillocks. The addition of a small percentage (0.5-4.0wt%) of copper to Al interconnects, and the encapsulation with a dielectric passivation layer improve the electromigration lifetime. The mechanisms by which these improvements occur are not entirely understood. The focus of this work is to better understand the passivation and the Cu effect in Al interconnects with a bamboo microstructure. Experimental investigations are performed on 0.5 µm wide Al segments of various lengths made from pure Al and Al(0.5 wt% Cu), both passivated and unpassivated. The results show that the addition of Cu increases the threshold product of segment length and current density above which damage occurs. Whereas hillocks form directly at the anode end in pure Al segments, they form some distance from the end in Al(Cu) segments. In contrast to pure Al segments, the electromigration-induced Al displacement in Al(Cu) segments shows an increasing rate (drift velocity). These observations are consistent with the idea that the Al mobility is substantially reduced if the Cu concentration is large enough. The motion of Cu is studied in undamaged segments. The dissolution of Al2Cu precipitates is consistent with the picture that Cu is transported rapidly along the interfaces. In addition, it is shown that the formation of precipitates requires a supersaturation of roughly two times the equilibrium solubility. The statistical distribution of threshold products is investigated as a function of segment length. It is shown that the mean value is roughly constant, whereas the deviation increases with decreasing segment length. The comparison of passivated and unpassivated Al shows that the passivation increases the threshold product, but that the drift velocity and void nucleation stress are the same. This suggests that the increase in reliability by passivation of interconnects is due to the suppression of hillocks. read less M. Yousefi, “Large-Scale Multiscale Modeling of Phase Transformation in Nanocrystalline Materials: Atomistic and Phase-Field Methods,” arXiv: Materials Science*. 2019. link Times cited: 0 Abstract: In this research, atomistic molecular dynamics simulations a… read more Abstract: In this research, atomistic molecular dynamics simulations are combined with mesoscopic phase-field computational methods in order to investigate phase-transformation in polycrystalline Aluminum microstructure. In fact, microstructural computational modeling of engineering materials could help to optimize their mechanical properties for industrial applications (e.g. directional solidification for turbine blades). As a result, a multiscale modeling approach is developed to find a relation between manufacturing variables (e.g. temperature) and microstructural properties of crystalline materials (e.g. grain size), which could be used to develop an advanced manufacturing process for sensitive applications. The results show that atomistic modeling of grain growth could be used as a first-principle approach in order to study phase transformation's kinetics, which could capture morphology of polycrystalline materials more accurately. On the other hand, phase-field mesoscopic approach needs less computational efforts, but still it relies on semi-empirical data to capture accurate phase transformation regimes, which makes this approach suitable for rapid examining of new manufacturing conditions as well as its effects on microstructural properties of polycrystalline materials. read less
Funding	Not available

Short KIM ID The unique KIM identifier code.	MO_020851069572_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_LiuLiuBorucki_1999_AlCu__MO_020851069572_000
DOI	10.25950/2dd77629 https://doi.org/10.25950/2dd77629 https://commons.datacite.org/doi.org/10.25950/2dd77629
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
B The letter grade B was assigned because the normalized error in the computation was 1.25538e-08 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.	vc-forces-numerical-derivative	consistency	Forces computed by the model agree with numerical derivatives of the energy; see full description.	Results	Files
F The model is C^0 continuous. This means that the model has continuous energy, but a discontinuous first derivative.	vc-dimer-continuity-c1	informational	The energy versus separation relation of a pair of atoms is C1 continuous (i.e. the function and its first derivative are continuous); see full description.	Results	Files
P Model energy and forces are invariant with respect to rigid-body motion (translation and rotation) for all configurations the model was able to compute.	vc-objectivity	informational	Total energy is unchanged and forces transform correctly under rigid-body translation and rotation; see full description.	Results	Files
P Model energy has inversion symmetry for all configurations the model was able to compute.	vc-inversion-symmetry	informational	Total energy is unchanged and forces change sign when inverting a configuration through the origin; see full description.	Results	Files
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: Al

Species: Cu

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: Al

Species: Cu

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: Cu

Species: Al

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: Cu

Species: Al

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: Cu

Species: Al

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: Al

Species: Cu

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: Cu

Species: Al

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: Al

Species: Cu

Cubic Crystal Basic Properties Table

Species: Al

Species: Cu

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 Al v004	view	2974
Cohesive energy versus lattice constant curve for bcc Cu v004	view	3243
Cohesive energy versus lattice constant curve for diamond Al v004	view	3004
Cohesive energy versus lattice constant curve for diamond Cu v004	view	2596
Cohesive energy versus lattice constant curve for fcc Al v004	view	4361
Cohesive energy versus lattice constant curve for fcc Cu v004	view	4510
Cohesive energy versus lattice constant curve for sc Al v004	view	2705
Cohesive energy versus lattice constant curve for sc Cu v004	view	3392

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 Al at zero temperature v006	view	1408
Elastic constants for bcc Cu at zero temperature v006	view	1855
Elastic constants for fcc Al at zero temperature v006	view	3903
Elastic constants for fcc Cu at zero temperature v006	view	1919
Elastic constants for sc Al at zero temperature v006	view	1983
Elastic constants for sc Cu at zero temperature v006	view	1919

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 Al at zero temperature v004		view	1305
Elastic constants for hcp Cu at zero temperature v004		view	1846

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 Cu in AFLOW crystal prototype A_cF4_225_a v001		view	58749
Equilibrium crystal structure and energy for Cu in AFLOW crystal prototype A_cI2_229_a v001		view	54258

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 AlCu in AFLOW crystal prototype A2B_tI12_140_h_a v002	view	58749
Equilibrium crystal structure and energy for AlCu in AFLOW crystal prototype A2B_tP3_123_e_a v002	view	50136
Equilibrium crystal structure and energy for AlCu in AFLOW crystal prototype A3B2_hP5_164_ad_d v002	view	50431
Equilibrium crystal structure and energy for AlCu in AFLOW crystal prototype A4B9_cP52_215_ei_3efgi v002	view	105358
Equilibrium crystal structure and energy for Al in AFLOW crystal prototype A_cF4_225_a v002	view	72443
Equilibrium crystal structure and energy for Al in AFLOW crystal prototype A_cI2_229_a v002	view	84737
Equilibrium crystal structure and energy for AlCu in AFLOW crystal prototype AB3_cF16_225_a_bc v002	view	80932
Equilibrium crystal structure and energy for AlCu in AFLOW crystal prototype AB3_cP4_221_a_c v002	view	90111
Equilibrium crystal structure and energy for AlCu in AFLOW crystal prototype AB3_oP12_47_al_ejoz v002	view	156885
Equilibrium crystal structure and energy for AlCu in AFLOW crystal prototype AB_mC20_12_a2i_c2i v002	view	84075

GrainBoundaryCubicCrystalSymmetricTiltRelaxedEnergyVsAngle__TD_410381120771_003

Relaxed energy as a function of tilt angle for a symmetric tilt grain boundary within a cubic crystal v003

Creators:
Contributor: brunnels
Publication Year: 2022
DOI: https://doi.org/10.25950/2c59c9d6

Computes grain boundary energy for a range of tilt angles given a crystal structure, tilt axis, and material.

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)
Relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in fcc Al v003	view	4231924
Relaxed energy as a function of tilt angle for a 100 symmetric tilt grain boundary in fcc Cu v001	view	5163267
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in fcc Al v001	view	33719829
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in fcc Cu v001	view	28530188
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in fcc Al v001	view	11148614
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in fcc Cu v001	view	9669730
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in fcc Al v001	view	26490206
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in fcc Cu v001	view	32321665

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 Al v007	view	1791
Equilibrium zero-temperature lattice constant for bcc Cu v007	view	1823
Equilibrium zero-temperature lattice constant for diamond Al v007	view	2079
Equilibrium zero-temperature lattice constant for diamond Cu v007	view	2655
Equilibrium zero-temperature lattice constant for fcc Al v007	view	3839
Equilibrium zero-temperature lattice constant for fcc Cu v007	view	3327
Equilibrium zero-temperature lattice constant for sc Al v007	view	1759
Equilibrium zero-temperature lattice constant for sc Cu v007	view	2271

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 Al v005		view	15440
Equilibrium lattice constants for hcp Cu v005		view	23750

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 Cu at 293.15 K under a pressure of 0 MPa v001		view	4360133

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 fcc Al at 293.15 K under a pressure of 0 MPa v002		view	725015

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 Al v004		view	49679
Phonon dispersion relations for fcc Cu v004		view	50223

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 Al v002		view	5147382
Stacking and twinning fault energies for fcc Cu v002		view	5777981

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 Al v004		view	22168
Broken-bond fit of high-symmetry surface energies in fcc Cu v004		view	27159

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 Al		view	321648
Monovacancy formation energy and relaxation volume for fcc Cu		view	352348

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 Al		view	976429
Vacancy formation and migration energy for fcc Cu		view	2101571

Errors

ElasticConstantsCubic__TD_011862047401_006

Test	Error Categories	Link to Error page
Elastic constants for diamond Al at zero temperature v001	other	view
Elastic constants for diamond Cu at zero temperature v001	other	view

LatticeConstantCubicEnergy__TD_475411767977_006

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

No Driver

Verification Check	Error Categories	Link to Error page
DimerContinuityC1__VC_303890932454_005	other	view

Files

CMakeLists.txt
LICENSE
al-cu-set.eam.alloy
kimprovenance.edn
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EAM_Dynamo_LiuLiuBorucki_1999_AlCu__MO_020851069572_000.txz	Tar+XZ	Linux and OS X archive
EAM_Dynamo_LiuLiuBorucki_1999_AlCu__MO_020851069572_000.zip	Zip	Windows archive

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This Model requires a Model Driver. Archives for the Model Driver EAM_Dynamo__MD_120291908751_005 appear below.

EAM_Dynamo__MD_120291908751_005.txz	Tar+XZ	Linux and OS X archive
EAM_Dynamo__MD_120291908751_005.zip	Zip	Windows archive

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EAM_Dynamo_LiuLiuBorucki_1999_AlCu__MO_020851069572_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

Errors

Files

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