EAM potential (LAMMPS cubic hermite tabulation) for Al optimized for melting temperature developed by Sturgeon and Laird (2000) v005

Jess B. Sturgeon; Brian B. Laird

doi:10.25950/d62edb43

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EAM_Dynamo_SturgeonLaird_2000_Al__MO_120808805541_005

There is a newer version of this item. See EAM_Dynamo_SturgeonLaird_2000_Al__MO_120808805541_006

Interatomic potential for Aluminum (Al).
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Title A single sentence description.	EAM potential (LAMMPS cubic hermite tabulation) for Al optimized for melting temperature developed by Sturgeon and Laird (2000) v005
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.	This EAM model for Al is based on the model developed by Mei-Davenport, which we have optimized to give the correct experimental melting temperature.
Species The supported atomic species.	Al
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	This model was developed as a prototype case for the Gibbs-Duhem protocol for optimizing melting points. As such, the melting point was the primary metric for its development. We have shown that the modifications to the original Mei-Davenport potential that we used to optimize T_m did not change the quality of the potential with respect to elastic constants, density, etc., but no systematic study of other properties was performed.
Content Origin	http://www.ctcms.nist.gov/potentials/Al.html

Contributor	Ryan S. Elliott
Maintainer	Ryan S. Elliott
Developer	Jess B. Sturgeon Brian B. Laird
Published on KIM	2018
How to Cite	Click here to download this citation in BibTeX format.
Citations This panel presents information regarding the papers that have cited the interatomic potential (IP) whose page you are on. The OpenKIM machine learning based Deep Citation framework is used to determine whether the citing article actually used the IP in computations (denoted by "USED") or only provides it as a background citation (denoted by "NOT USED"). For more details on Deep Citation and how to work with this panel, click the documentation link at the top of the panel. The word cloud to the right is generated from the abstracts of IP principle source(s) (given below in "How to Cite") and the citing articles that were determined to have used the IP in order to provide users with a quick sense of the types of physical phenomena to which this IP is applied. The bar chart shows the number of articles that cited the IP per year. Each bar is divided into green (articles that USED the IP) and blue (articles that did NOT USE the IP). 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See the Deep Citation documentation for more information. 71 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 . Y. Wu, K. Zhang, J. Xiao, Y. Jiang, and L. Lv, “Conjugated bilayer structure of the homogeneous solid-liquid interface of metals.,” Physical chemistry chemical physics : PCCP. 2020. link Times cited: 1 Abstract: The concept of "interfacial region" has long preva… read more Abstract: The concept of "interfacial region" has long prevailed for over half century for describing the homogeneous solid-liquid (SL) interface of metals, but its intrinsic structure is still unclear due to the homogeneity. In this study, we reveal, for the first time, the intrinsic structure of these homogeneous SL interfaces consisting of two conjugated monoatomic layers of interfacial solid (IS) and interfacial liquid (IL) with a certain degree of corrugation via molecular dynamics simulations. We named it as the conjugated bilayer structure (CBS). In the framework of CBS, only the IS + IL bilayer plays stepwise transition roles from the solid to the liquid, which defines the four-terrace nature of the interface and act simultaneously as the boundaries of the bilateral bulk phases. The inherent diffuse nature of the "interfacial region" is proven originating from the corrugation of the IS + IL bilayer and its four-terrace nature. More importantly, the CBS also explains that the interfacial free energy originates mainly from the increase in the potential energy of the IS layer relative to its counterpart bulk solid instead of the previously argued entropy loss of the liquid phase. After all these verifications and interpretations, the CBS was verified as the intrinsic structure of the homogeneous SL interface of metals. Accordingly, we argue that the concept of CBS also resolves the volume-bearing flaw of the "interfacial region" concept and can definitively locate the intrinsic surface according to the capillary wave theory. read less S. Subedi, L. Morrissey, S. M. Handrigan, and S. Nakhla, “The effect of many-body potential type and parameterisation on the accuracy of predicting mechanical properties of aluminium using molecular dynamics,” Molecular Simulation. 2020. link Times cited: 8 Abstract: ABSTRACT As opposed to traditional laboratory testing, Molec… read more Abstract: ABSTRACT As opposed to traditional laboratory testing, Molecular Dynamics (MD) offers an atomistic scale method to estimate the mechanical properties of metals. However, there is limited literature that shows the effect of interatomic potentials when determining mechanical properties. Hence, the present research was conducted to investigate the accuracy of various interatomic potentials in estimating mechanical properties of aluminium. Several types of potentials, including Embedded Atom Method (EAM), Modified EAM (MEAM) and Reactive Force Field (ReaxFF) were compared with available experimental data for pure aluminium to determine the most accurate interatomic potential. A uniaxial tensile test was performed at room temperature using MD simulations for nanoscale aluminium. Results demonstrated that those potentials parameterised with elastic constants at physically realisable temperatures were consistently more accurate. Overall, the Mishin et al. EAM potential was the most accurate when compared to single-crystal experimental values. Regardless of the potential type, the error was significantly higher for those potentials that did not consider elastic constants during development. In brief, the application of the interatomic potentials to estimate mechanical properties of a nanoscale aluminium was investigated. read less N. Nenuwe, E. Agbalagba, and E. Enaibe, “Comparative study of thermophysical properties of Nickel in liquid phase,” Ruhuna Journal of Science. 2018. link Times cited: 1 Abstract: The results of molecular dynamics simulations of the self-di… read more Abstract: The results of molecular dynamics simulations of the self-diffusion coefficient (SDC) and viscosity coefficient (VC) of liquid nickel (Ni) in a temperature range of 1720 – 2500K are presented. The temperature dependence of the SDC is determined numerically by molecular simulations with the Embedded Atom Method Finnis-Sinclair (EAMFS) potential as implemented in the Virtual Nano Lab 2017.2. The temperature dependence agrees with the Arrhenius law. Results obtained for SDC are found to overestimate available experimental results, while results for VC underestimated experimental values. Also, the validity of Stokes-Einstein relation was tested in liquid Ni and was found to be valid at all temperatures. read less O. Nenuwe and O. Osafile, “Temperature dependence of Self-diffusion coefficient (SDC) of liquid aluminum using Embedded Atom Method-Finnis-Sinclair (EAMFS) potential,” Journal of Applied Sciences and Environmental Management. 2018. link Times cited: 1 Abstract: Atomistix tool kit force field calculations have been done, … read more Abstract: Atomistix tool kit force field calculations have been done, using the embedded atom method-Finnis-Sinclair potential as implemented in Virtual Nano Lab-Atomistix Tool Kit (VNL-ATK) to study the temperature dependence of self-diffusion coefficient of liquid aluminum. Also, we calculated the shear viscosity from the Sutherland-Einstein relation, and reports that, the calculated SDC and viscosity are sensitive to temperature. Results obtained at 980, 1020 and 1060K for SDC underestimated available experimental results, while the calculated results for viscosity at 1000 and 1200K overestimated experimental data available in the literature. The underestimation might be due to the shortrange order in liquid Al. Keywords: self-diffusion, viscosity, aluminum, temperature read less V. Warshavsky and X. Song, “Perturbation theory for solid–liquid interfacial free energies,” Journal of Physics: Condensed Matter. 2010. link Times cited: 8 Abstract: A perturbation theory is developed to calculate solid–liquid… read more Abstract: A perturbation theory is developed to calculate solid–liquid interfacial free energies, including anisotropy. The method is applied to systems with inverse-power and Lennard-Jones pair potentials as well as to metal systems with embedded-atom model potentials. The results are in reasonable agreement with the corresponding ones obtained from molecular dynamics simulations. read less S. Namilae, B. Radhakrishnan, and J. R. Morris, “Atomistic simulation of the effect of Ga on crack tip opening in Al bicrystals,” Modelling and Simulation in Materials Science and Engineering. 2008. link Times cited: 6 Abstract: Liquid metal embrittlement (LME) in the Al–Ga system is stud… read more Abstract: Liquid metal embrittlement (LME) in the Al–Ga system is studied using molecular dynamics simulations. Crack tip opening loads are exerted on symmetric tilt Al bicrystals in the presence of liquid Ga. In general, the speed of crack propagation increases in the presence of Ga. However, there is significant variation in the dynamic behavior of the different boundaries studied here. We observe the formation of a sub-grain by grain boundary dissociation (grain boundary phase transformation) in [1 1 0] Σ9 and [1 1 0] Σ11 grain boundaries; this results in crack blunting even in the presence of Ga. In the Σ3 twin, the absence of alternating compressive and tensile stresses present in other boundaries results in fast Ga penetration after the crack path is formed. The structure of grain boundaries apart from thermodynamic considerations significantly affects LME. read less P. Piaggi, “Entropy as a tool for crystal discovery.” 2019. link Times cited: 1 Abstract: The computational prediction of crystal structures has emerg… read more Abstract: The computational prediction of crystal structures has emerged as an useful alternative to expensive and often cumbersome experiments. We propose an approach to the prediction of crystal structures and polymorphism based on reproducing the crystallization process on the computer. The main hurdle faced by such an approach is that crystallization usually takes place in timescales much longer than those that can be afforded with standard molecular simulations. In order to circumvent this difficulty we construct a bias potential which is a function of one or more collective variables and whose role is to promote crystallization. This approach can only have true predictive power if the collective variable is crystal structure agnostic, that is to say, it does not include information about the geometry of any particular crystal structure. In order to achieve this goal, we take inspiration from thermodynamics and propose to use an entropy surrogate as collective variable. We use an approximation for the entropy based on the radial distribution function g(r). Using this collective variable we are able to explore polymorphism in simple metals and molecular crystals. We study the case of urea and find a new polymorph stabilized by entropic effects. We also propose a projection of the collective variable onto each atom that is useful to characterize atomic environments. Lastly, we introduce a generalized Kullback-Leibler divergence that measures the distance between two radial distribution functions. We apply this divergence to the automatic classification of the polymorphs that crystallize during the simulations. read less 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 S. Ahmad, T. Brink, C. Liebscher, and G. Dehm, “Microstates and defects of incoherent Σ3 [111] twin boundaries in aluminum,” Acta Materialia. 2022. link Times cited: 4 T. Zhou, Y. Wu, and J. You, “The embedded-seed-method molecular dynamics simulation of the crystallization of Al and the influence of the artificial initial stress,” Journal of Crystal Growth. 2022. link Times cited: 0 J. Gabriel et al., “Bayesian Automated Weighting of Aggregated DFT, MD, and Experimental Data for Candidate Thermodynamic Models of Aluminum with Uncertainty Quantification,” Materialia. 2021. link Times cited: 2 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 R. Yan et al., “Structural and mechanical properties of homogeneous solid-liquid interface of Al modelled with COMB3 potential,” Computational Materials Science. 2018. link Times cited: 9 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. Shao, A. He, and P. Wang, “Atomistic simulations on the dynamic properties of shock and release melting in single crystal Al,” Computational Materials Science. 2018. link Times cited: 12 M. Mendelev et al., “Molecular dynamics simulation of the solid-liquid interface migration in terbium.,” The Journal of chemical physics. 2018. link Times cited: 16 Abstract: We developed a Tb embedded atom method potential which prope… read more Abstract: We developed a Tb embedded atom method potential which properly reproduces the liquid structure obtained from the ab initio molecular dynamics simulation, the hexagonal close packed (hcp)-body-centered cubic (bcc) phase transformation, and melting temperatures. At least three crystal phases [hcp, face-centered cubic (fcc), and bcc] described by this potential can coexist with the liquid phase. Thus, the developed potential provides an excellent test bed for studies of the completive phase nucleation and growth in a single component system. The molecular dynamics simulation showed that all crystal phases can grow from the liquid phase close to their melting temperatures. However, in the cases of the hcp and fcc growth from the liquid phase at very large supercoolings, the bcc phase forms at the solid-liquid interface in the close packed orientations in spite of the fact that both hcp and fcc phases are more stable than the bcc phase at these temperatures. This bcc phase closes the hcp and fcc phase from the liquid such that the remaining liquid solidifies into the bcc phase. The initial hcp phase then slowly continues growing in expense of the bcc phase. read less Y. Jiang, L. Lv, and Y. Wu, “Solid-Liquid Phase Transitions of FCC-Al and HCP-Mg Nanoparticles.” 2016. link Times cited: 1 E. S. Wise, M. Liu, and T. Miller, “Sputtering of cubic metal crystals by low-energy xenon-ions,” Computational Materials Science. 2015. link Times cited: 5 S. Kalidindi, J. A. Gomberg, Z. Trautt, and C. Becker, “Application of data science tools to quantify and distinguish between structures and models in molecular dynamics datasets,” Nanotechnology. 2015. link Times cited: 39 Abstract: Structure quantification is key to successful mining and ext… read more Abstract: Structure quantification is key to successful mining and extraction of core materials knowledge from both multiscale simulations as well as multiscale experiments. The main challenge stems from the need to transform the inherently high dimensional representations demanded by the rich hierarchical material structure into useful, high value, low dimensional representations. In this paper, we develop and demonstrate the merits of a data-driven approach for addressing this challenge at the atomic scale. The approach presented here is built on prior successes demonstrated for mesoscale representations of material internal structure, and involves three main steps: (i) digital representation of the material structure, (ii) extraction of a comprehensive set of structure measures using the framework of n-point spatial correlations, and (iii) identification of data-driven low dimensional measures using principal component analyses. These novel protocols, applied on an ensemble of structure datasets output from molecular dynamics (MD) simulations, have successfully classified the datasets based on several model input parameters such as the interatomic potential and the temperature used in the MD simulations. read less Y. Wu, R.-B. Li, J. Xiao, and Y. Jiang, “Crystallization in Supercooled BCC-Vanadium, HCP-Zinc and FCC-Aluminum.” 2015. link Times cited: 0 Y. Sun, W. Sun, Y. Fu, F. Wang, Y. Gao, and J.-wei Zhao, “The deformation behaviors of silver nanowires including 3D defects under tension,” Computational Materials Science. 2013. link Times cited: 7 W. Luo, W. Hu, K. Su, and F. Liu, “The calculation of surface free energy based on embedded atom method for solid nickel,” Applied Surface Science. 2013. link Times cited: 27 W. Luo, W. Hu, S. Xiao, H. Deng, and F. Gao, “Phase transition in nanocrystalline iron: Atomistic-level simulations,” International Journal of Materials Research. 2010. link Times cited: 5 Abstract: Molecular dynamics simulations, along with the modified anal… read more Abstract: Molecular dynamics simulations, along with the modified analytic embedded atom method, have been employed to study the bcc → fcc phase transition of nanocrystalline iron. The Gibbs free energies of bulk fcc and bcc iron phases are calculated as a function of temperature, and used to determine the bulk phase-transition temperature. Furthermore, the transformation temperature in the nanocrystalline iron, with a mean grain size of 3 nm, is determined to be 975 ± 25 K using the bond-order parameter method. The radial-distribution function and common neighbor analysis are used to understand the phase structure of the nanocrystalline iron and the evolution of local atomic structure. The snapshots of a two atomic layer thick slice provide a visible scenario of structural evolution during phase transition. read less J. R. Morris, M. Mendelev, and D. Srolovitz, “A comparison of crystal-melt interfacial free energies using different Al potentials,” Journal of Non-crystalline Solids. 2007. link Times cited: 23 H. Nam and D. Srolovitz, “Molecular dynamics simulation of Ga penetration along Σ5 symmetric tilt grain boundaries in an Al bicrystal,” Physical Review B. 2007. link Times cited: 31 Abstract: Liquid metal embrittlement (LME) is a common feature of syst… read more Abstract: Liquid metal embrittlement (LME) is a common feature of systems in which a low melting point liquid metal is in contact with another, higher melting point, polycrystalline metal. While different systems exhibit different LME fracture characteristics, the penetration of nanometer-thick liquid metal films along the grain boundary is one of the hallmarks of the process. We employ EAM potentials optimized for Al-Ga binary alloys in a series of molecular dynamics simulations of an Al bicrystal (with a $\ensuremath{\Sigma}5$ 36.9\ifmmode^\circ\else\textdegree\fi{}(301)/[010] symmetric tilt boundary) in contact with liquid Ga with and without an applied stress. Our simulations clarify the mechanism of LME and how it is affected by applied stresses. The interplay of stress and penetrating Ga atoms leads to the nucleation of a train of dislocations on the grain boundary below the liquid groove root which climbs down the grain boundary at a nearly constant rate. The dislocation climb mechanism and the Ga penetration are coupled. While the dislocations do relax part of the applied stress, the residual stresses keep the grain boundary open, thereby allowing more, fast Ga transport to the penetration front (i.e., Ga layer thickening process). The coupled Ga transport and ``dislocation climb'' is the key to the anomalously fast, time-independent penetration of Ga along grain boundaries in Al. The simulations explain a wide range of experimental observations of LME in the Al-Ga literature. read less M. Amini and B. Laird, “Kinetic coefficient for hard-sphere crystal growth from the melt.,” Physical review letters. 2006. link Times cited: 62 Abstract: Using molecular-dynamics simulation, we determine the magnit… read more Abstract: Using molecular-dynamics simulation, we determine the magnitude and anisotropy of the kinetic coefficient (mu) for the crystal growth from the melt for the hard-sphere system through an analysis of equilibrium capillary fluctuations in interfacial height. We find mu100 = 1.44(7), mu110 = 1.10(5), and mu111 = 0.64(3) in units of square root (kB/(mTm)), where kB is Boltzmann's constant, m is the particle mass, and Tm is the melting temperature. These values are shown to be consistent, with some exceptions, with those obtained in recent simulation results a variety of fcc metals, when expressed in hard-sphere units. This suggests that the kinetic coefficient for fcc metals can be roughly estimated from C square root (R/(MTm)), where R is the gas constant, M is the molar mass, and C is a constant that varies with interfacial orientation. read less K. Moriguchi and M. Igarashi, “Correlation between lattice-strain energetics and melting properties: Molecular dynamics and lattice dynamics using EAM models of Al,” Physical Review B. 2006. link Times cited: 14 B. F. Nicholson, P. Clancy, and S. Rick, “The interface response function and melting point of the prism interface of ice Ih using a fluctuating charge model (TIP4P-FQ),” Journal of Crystal Growth. 2006. link Times cited: 22 D. Sun et al., “Crystal-melt interfacial free energies in hcp metals: A molecular dynamics study of Mg,” Physical Review B. 2006. link Times cited: 327 Abstract: Crystal-melt interfacial free energies $(\ensuremath{\gamma}… read more Abstract: Crystal-melt interfacial free energies $(\ensuremath{\gamma})$ are computed for hcp Mg by employing equilibrium molecular-dynamics (MD) simulations and the capillary-fluctuation method (CFM). This work makes use of a newly developed embedded-atom-method (EAM) interatomic potential for Mg fit to crystal, liquid, and melting properties. We describe how the CFM, which has previously been applied to cubic systems only, can be generalized for studies of hcp metals by employing a parametrization for the orientation dependence of $\ensuremath{\gamma}$ in terms of hexagonal harmonics. The method is applied in the calculation of the Turnbull coefficient $(\ensuremath{\alpha})$ and crystalline anisotropies of $\ensuremath{\gamma}$. We obtain a value of $\ensuremath{\alpha}=0.48$, with interfacial free energies for different high-symmetry orientations differing by approximately 1%. These results are compared to those obtained in previous MD-CFM studies for cubic EAM metals as well as experimental studies of solid-liquid interfaces in hcp alloys. In addition, the implications of our results for the prediction of dendrite growth directions in hcp metals are discussed. read less X. Song and J. R. Morris, “Accurate method to calculate liquid and solid free energies for embedded atom potentials,” Physical Review B. 2003. link Times cited: 26 Abstract: Using a perturbation theory with a hard-sphere reference sys… read more Abstract: Using a perturbation theory with a hard-sphere reference system we have directly calculated free energies of fluid and solid phases of aluminum with an embedded atom model potential. Unlike other approaches such as thermodynamic integration, we do not require any simulations. Moreover, the free energies of the two different phases are calculated in a single approach, unlike approximations like the quasi-harmonic solid approach. The calculated free energies are with an average relative error 0.55% of the simulation values and the resulting melting temperature is within 5% of the simulation value. Calculations of the melting line of materials are of fundamental interest, representing a fundamental understanding of the equilibrium properties of both the solid and liquid phases, and the competition between them. Traditionally, the liquid free energy is calculated from perturbation theory or variational theory with an appropriate reference system. The crystalline free energy may be calculated with quasi read less E. Ogando, M. Caro, and A. Caro, “Reference systems for computational free energy calculations of binary solutions: role of the constrained center of mass motion,” Computational Materials Science. 2002. link Times cited: 7 R. Aga and J. R. Morris, “Modeling: The Role Of Atomistic Simulations.” 2008. link Times cited: 1 P. Piaggi and M. Parrinello, “Entropy based fingerprint for local crystalline order.,” The Journal of chemical physics. 2017. link Times cited: 87 Abstract: We introduce a new fingerprint that allows distinguishing be… read more Abstract: We introduce a new fingerprint that allows distinguishing between liquid-like and solid-like atomic environments. This fingerprint is based on an approximate expression for the entropy projected on individual atoms. When combined with local enthalpy, this fingerprint acquires an even finer resolution and it is capable of discriminating between different crystal structures. read less Z. Trautt, F. Tavazza, and C. Becker, “Facilitating the selection and creation of accurate interatomic potentials with robust tools and characterization,” Modelling and Simulation in Materials Science and Engineering. 2015. link Times cited: 14 Abstract: The Materials Genome Initiative seeks to significantly decre… read more Abstract: The Materials Genome Initiative seeks to significantly decrease the cost and time of development and integration of new materials. Within the domain of atomistic simulations, several roadblocks stand in the way of reaching this goal. While the NIST Interatomic Potentials Repository hosts numerous interatomic potentials (force fields), researchers cannot immediately determine the best choice(s) for their use case. Researchers developing new potentials, specifically those in restricted environments, lack a comprehensive portfolio of efficient tools capable of calculating and archiving the properties of their potentials. This paper elucidates one solution to these problems, which uses Python-based scripts that are suitable for rapid property evaluation and human knowledge transfer. Calculation results are visible on the repository website, which reduces the time required to select an interatomic potential for a specific use case. Furthermore, property evaluation scripts are being integrated with modern platforms to improve discoverability and access of materials property data. To demonstrate these scripts and features, we will discuss the automation of stacking fault energy calculations and their application to additional elements. While the calculation methodology was developed previously, we are using it here as a case study in simulation automation and property calculations. We demonstrate how the use of Python scripts allows for rapid calculation in a more easily managed way where the calculations can be modified, and the results presented in user-friendly and concise ways. Additionally, the methods can be incorporated into other efforts, such as openKIM. read less Y. Liu and J.-wei Zhao, “The size dependence of the mechanical properties and breaking behavior of metallic nanowires: A statistical description,” Computational Materials Science. 2011. link Times cited: 20 Y. Liu, F. Wang, J.-wei Zhao, L. Jiang, M. Kiguchi, and K. Murakoshi, “Theoretical investigation on the influence of temperature and crystallographic orientation on the breaking behavior of copper nanowire.,” Physical chemistry chemical physics : PCCP. 2009. link Times cited: 36 Abstract: In this paper, molecular dynamics simulations have been cond… read more Abstract: In this paper, molecular dynamics simulations have been conducted to study the mechanical stretching of copper nanowires which will finally lead to the formation of suspended liner atomic chains. A total of 2700 samples have been investigated to achieve a comprehensive understanding of the influence of temperature and orientation on the formation of linear atomic chains. Our results prove that linear atomic chains do exist for [100], [111] and [110] crystallographic directions. Stretching along the [111] direction exhibits a higher probability in forming the two-atom contact than that along the [110] and [100] directions. However, for longer linear atomic chains, there emerges a reversed trend. In addition, increasing temperature may decrease the formation probability for stretching along [111] and [110] directions, but this influence is less obvious for that along the [100] direction. read less J. R. Morris, U. Dahlborg, and M. Calvo-Dahlborg, “Recent developments and outstanding challenges in theory and modeling of liquid metals,” Journal of Non-crystalline Solids. 2007. link Times cited: 23 C. Vega, M. Martín-Conde, and A. Patrykiejew, “Absence of superheating for ice Ih with a free surface: a new method of determining the melting point of different water models,” Molecular Physics. 2006. link Times cited: 58 Abstract: Molecular dynamic simulations were performed for ice Ih with… read more Abstract: Molecular dynamic simulations were performed for ice Ih with a free surface. The simulations were carried out at several temperatures and each run lasted more than 7 ns. At high temperatures the ice melts. It is demonstrated that the melting process starts at the surface and propagates to the bulk of the ice block. Already at the temperatures below the melting point, we observe a thin liquid layer at the ice surface, but the block of ice remains stable along the run. As soon as the temperature reaches the melting point the entire ice block melts. Our results demonstrate that, unlike in the case of conventional simulations in the NpT ensemble, overheating of the ice Ih with a free surface does not occur. This allows one to estimate the melting point of ice at zero pressure. We applied the method to the following models of water: SPC/E, TIP4P, TIP4P/Ew, TIP4P/Ice and TIP4P/2005, and found good agreement between the melting temperatures obtained by this procedure and the values obtained either from free energy calculations or from direct simulations of the ice–water interface. read less J. L. Abascal, R. Fernández, C. Vega, and M. Carignano, “The melting temperature of the six site potential model of water.,” The Journal of chemical physics. 2006. link Times cited: 64 Abstract: The melting temperature of the six site potential of water i… read more Abstract: The melting temperature of the six site potential of water is calculated using two different methods. The first one combines free energy calculations with Hamiltonian Gibbs-Duhem integration. The second method is based on the evolution (melting or freezing) of an explicit liquid-ice interface. Both methods yield very similar results, so we propose 289K as the melting temperature of the model. The melting temperature of the six site potential of water is calculated using two different methods. The first one combines free energy calculations with Hamiltonian Gibbs-Duhem integration. The second method is based on the evolution (melting or freezing) of an explicit liquid-ice interface. Both methods yield very similar results, so we propose 289K as the melting temperature of the model. read less E. Arregui, M. Caro, and A. Caro, “Numerical evaluation of the exact phase diagram of an empirical Hamiltonian: Embedded atom model for the Au-Ni system,” Physical Review B. 2002. link Times cited: 34 Abstract: Molecular-dynamics simulations were used to calculate the Gi… read more Abstract: Molecular-dynamics simulations were used to calculate the Gibbs free energy on the entire compositional range of gold-nickel alloys described with a set of embedded atom potentials available in the literature. Thermodynamic integration and switching Hamiltonian techniques were used to obtain the exact phase diagram (with no approximations), and that corresponding to the regular approximation. Remarkable agreement for some properties, such as the solvus critical point, the congruential melting, the melting points of the pure elements, and the formation entropy of the alloy, contrasts with the poor prediction of the location of the solidus-liquidus lines, reflecting errors in the heat of solution in the liquid phase. The results are compared with recent experimental reassessment of the Au-Ni phase diagram and with ab initio calculations. read less A. Ovrutsky, A. Prokhoda, and M. Rasshchupkyna, “Simulation Techniques for Atomic Systems.” 2014. link Times cited: 3 D. R. Pratt, L. Morrissey, and S. Nakhla, “Molecular dynamics simulations of nanoindentation – the importance of force field choice on the predicted elastic modulus of FCC aluminum,” Molecular Simulation. 2020. link Times cited: 5 Abstract: ABSTRACT Molecular Dynamics (MD) was used to determine the a… read more Abstract: ABSTRACT Molecular Dynamics (MD) was used to determine the accuracy of different force fields on predicting the elastic modulus of single crystal aluminum through nanoindentation tests. In this work, nanoindentation was performed using three different types of force fields (EAM, MEAM and ReaxFF) and the resulting elastic modulus was compared to the value obtained using elastic constants from standard small strain tensile simulations. When the predicted modulus of each force field was compared to the modulus via elastic constants, the ReaxFF resultant moduli were similar to that of nanoindentation, but for EAM and MEAM the two methods produced significantly different values. Therefore, even if a force field is parameterised for elastic modulus, it does not guarantee the force field will accurately predict the modulus from other procedures. As well, two different methods for calculating modulus from indentation curves were compared: The Hertz approximation and the Oliver and Pharr (O&P) method. For EAM and MEAM force fields, the Hertz method significantly under predicted modulus while the O&P method was in better agreement with the experimental modulus. read less S. Kavousi, B. R. Novak, M. Baskes, M. A. Zaeem, and D. Moldovan, “Modified embedded-atom method potential for high-temperature crystal-melt properties of Ti–Ni alloys and its application to phase field simulation of solidification,” Modelling and Simulation in Materials Science and Engineering. 2019. link Times cited: 21 Abstract: We developed new interatomic potentials, based on the second… read more Abstract: We developed new interatomic potentials, based on the second nearest-neighbor modified embedded-atom method (2NN-MEAM) formalism, for Ti, Ni, and the binary Ti–Ni system. These potentials were fit to melting points, latent heats, the binary phase diagrams for the Ti rich and Ni rich regions, and the liquid phase enthalpy of mixing for binary alloys, therefore they are particularly suited for calculations of crystal-melt (CM) interface thermodynamic and transport properties. The accuracy of the potentials for pure Ti and pure Ni were tested against both 0 K and high temperature properties by comparing various properties obtained from experiments or density functional theory calculations including structural properties, elastic constants, point-defect properties, surface energies, temperatures and enthalpies of phase transformations, and diffusivity and viscosity in the liquid phase. The fitted binary potential for Ti–Ni was also tested against various non-fitted properties at 0 K and high temperatures including lattice parameters, formation energies of different intermetallic compounds, and the temperature dependence of liquid density at various concentrations. The CM interfacial free energies obtained from simulations, based on the newly developed Ti–Ni potential, show that the bcc alloys tend to have smaller anisotropy compared with fcc alloys which is consistent with the finding from the previous studies comparing single component bcc and fcc materials. Moreover, the interfacial free energy and its anisotropy for Ti-2 atom% Ni were also used to parameterize a 2D phase field (PF) model utilized in solidification simulations. The PF simulation predictions of microstructure development during solidification are in good agreement with a geometric model for dendrite primary arm spacing. read less L. Wu et al., “Calculation of solid–liquid interfacial free energy and its anisotropy in undercooled system,” Rare Metals. 2018. link Times cited: 6 L. Hale, “Comparing Modeling Predictions of Aluminum Edge Dislocations: Semidiscrete Variational Peierls–Nabarro Versus Atomistics,” JOM. 2018. link Times cited: 7 Y. Jiang, J. Luo, and Y. Wu, “The validation and preference among different EAM potentials to describe the solid–liquid transition of aluminum,” Modelling and Simulation in Materials Science and Engineering. 2017. link Times cited: 6 Abstract: Empirical potential is vital to the classic atomic simulatio… read more Abstract: Empirical potential is vital to the classic atomic simulation, especially for the study of phase transitions, as well as the solid-interface. In this paper, we attempt to set up a uniform procedure for the validation among different potentials before the formal simulation study of phase transitions of metals. Two main steps are involved: (1) the prediction of the structures of both solid and liquid phases and their mutual transitions, i.e. melting and crystallization; (2) the prediction of vital thermodynamic (the equilibrium melting point at ambient pressure) and dynamic properties (the degrees of superheating and undercooling). We applied this procedure to the testing of seven published embedded-atom potentials (MKBA (Mendelev et al 2008 Philos. Mag. 88 1723), MFMP (Mishin et al 1999 Phys. Rev. B 59 3393), MDSL (Sturgeon and Laird 2000 Phys. Rev. B 62 14720), ZM (Zope and Mishin 2003 Phys. Rev. B 68 024102), LEA (Liu et al 2004 Model. Simul. Mater. Sci. Eng. 12 665), WKG (Winey et al 2009 Model. Simul. Mater. Sci. Eng. 17 055004) and ZJW (Zhou et al 2004 Phys. Rev. B 69 144113)) for the description of the solid–liquid transition of Al. All the predictions of structure, melting point and superheating/undercooling degrees were compared with the experiments or theoretical calculations. Then, two of them, MKBA and MDSL, were proven suitable for the study of the solid–liquid transition of Al while the residuals were unqualified. However, potential MKBA is more accurate to predict the structures of solid and liquid, while MDSL works a little better in the thermodynamic and dynamic predictions of solid–liquid transitions. read less M. Mendelev, T. L. Underwood, and G. Ackland, “Development of an interatomic potential for the simulation of defects, plasticity, and phase transformations in titanium.,” The Journal of chemical physics. 2016. link Times cited: 122 Abstract: New interatomic potentials describing defects, plasticity, a… read more Abstract: New interatomic potentials describing defects, plasticity, and high temperature phase transitions for Ti are presented. Fitting the martensitic hcp-bcc phase transformation temperature requires an efficient and accurate method to determine it. We apply a molecular dynamics method based on determination of the melting temperature of competing solid phases, and Gibbs-Helmholtz integration, and a lattice-switch Monte Carlo method: these agree on the hcp-bcc transformation temperatures to within 2 K. We were able to develop embedded atom potentials which give a good fit to either low or high temperature data, but not both. The first developed potential (Ti1) reproduces the hcp-bcc transformation and melting temperatures and is suitable for the simulation of phase transitions and bcc Ti. Two other potentials (Ti2 and Ti3) correctly describe defect properties and can be used to simulate plasticity or radiation damage in hcp Ti. The fact that a single embedded atom method potential cannot describe both low and high temperature phases may be attributed to neglect of electronic degrees of freedom, notably bcc has a much higher electronic entropy. A temperature-dependent potential obtained from the combination of potentials Ti1 and Ti2 may be used to simulate Ti properties at any temperature. read less N. Admal, J. Marian, and G. Po, “The atomistic representation of first strain-gradient elastic tensors,” Journal of The Mechanics and Physics of Solids. 2016. link Times cited: 36 S. Wilson and M. Mendelev, “A unified relation for the solid-liquid interface free energy of pure FCC, BCC, and HCP metals.,” The Journal of chemical physics. 2016. link Times cited: 37 Abstract: We study correlations between the solid-liquid interface (SL… read more Abstract: We study correlations between the solid-liquid interface (SLI) free energy and bulk material properties (melting temperature, latent heat, and liquid structure) through the determination of SLI free energies for bcc and hcp metals from molecular dynamics (MD) simulation. Values obtained for the bcc metals in this study were compared to values predicted by the Turnbull, Laird, and Ewing relations on the basis of previously published MD simulation data. We found that of these three empirical relations, the Ewing relation better describes the MD simulation data. Moreover, whereas the original Ewing relation contains two constants for a particular crystal structure, we found that the first coefficient in the Ewing relation does not depend on crystal structure, taking a common value for all three phases, at least for the class of the systems described by embedded-atom method potentials (which are considered to provide a reasonable approximation for metals). read less L. Wu, B. Xu, Q. Li, W. Liu, and M. Li, “Anisotropic crystal–melt interfacial energy and stiffness of aluminum,” Journal of Materials Research. 2015. link Times cited: 21 Abstract: The crystal–melt interfacial free energy is an important qua… read more Abstract: The crystal–melt interfacial free energy is an important quantity governing many kinetic phenomena including solidification and crystal growth. Although general calculation methods are available, it is still difficult to obtain the interfacial energies that differ only slightly due to anisotropy. Here, we report such a calculation of Al crystal–melt interfacial energy based on the general framework of the capillary fluctuation method (CFM). The subtle dependence of both the melting temperature and interfacial free energy at melting temperature on the crystal interface orientation was examined. For Al, the average melting temperature is obtained at 934.79 ± 5 K and the orientationally averaged mean interfacial free energy is 98.35 mJ/m^2. In addition, the anisotropy of the interfacial free energy is found weak, nevertheless with the values ranked as γ_100 > γ_110 > γ_111. read less S. Wilson and M. Mendelev, “Anisotropy of the solid–liquid interface properties of the Ni–Zr B33 phase from molecular dynamics simulation,” Philosophical Magazine. 2015. link Times cited: 58 Abstract: Solid–liquid interface (SLI) properties of the Ni–Zr B33 pha… read more Abstract: Solid–liquid interface (SLI) properties of the Ni–Zr B33 phase were determined from molecular dynamics simulations. In order to perform these measurements, a new semi-empirical potential for Ni–Zr alloy was developed that well reproduces the material properties required to model SLIs in the Ni50.0Zr50.0 alloy. In particular, the developed potential is shown to provide that the solid phase emerging from the liquid Ni50.0Zr50.0 alloy is B33 (apart from a small fraction of point defects), in agreement with the experimental phase diagram. The SLI properties obtained using the developed potential exhibit an extraordinary degree of anisotropy. It is observed that anisotropies in both the interfacial free energy and mobility are an order of magnitude larger than those measured to date in any other metallic compound. Moreover, the [0 1 0] interface is shown to play a significant role in the observed anisotropy. Our data suggest that the [0 1 0] interface simultaneously corresponds to the lowest mobility, the lowest free energy and the highest stiffness of all inclinations in B33 Ni–Zr. This finding can be understood by taking into account a rather complicated crystal structure in this crystallographic direction. read less V. Thapar and F. Escobedo, “Extensions of the interfacial pinning method and application to hard core systems.,” The Journal of chemical physics. 2014. link Times cited: 13 Abstract: The precise estimation of the location of phase transitions … read more Abstract: The precise estimation of the location of phase transitions is an essential task in the study of many condensed matter systems. A recently developed technique denoted interface pinning (IP) [U. R. Pedersen, F. Hummel, G. Kresse, G. Kahl, and C. Dellago, Phys. Rev. B. 88, 094101 (2013); U. R. Pedersen, J. Chem. Phys. 139, 104102 (2013)] can accurately estimate the location of fluid-solid transition using the NP(z)T ensemble for single-component systems by computing the free energy difference between a solid and a fluid. The IP method is extended here to be applicable to different ensembles for both single-component systems and binary mixtures. A more general scheme is also proposed for the extrapolation of properties targeting coexistence conditions. This framework is used to estimate the coexistence pressure for the isotropic-rotator phase transition for three single-component polyhedral systems and to estimate isotropic-crystal coexistence compositions for a binary mixture of hard cubes and spheres. In addition, by exploring various choices for the order parameter used to distinguish between the isotropic and ordered phases, it is found that volume provides a reasonable alternative to translational order parameters which can be either more expensive to calculate or unable to pin a two-phase interfacial state. read less S. Wilson and M. Mendelev, “Dependence of solid–liquid interface free energy on liquid structure,” Modelling and Simulation in Materials Science and Engineering. 2014. link Times cited: 17 Abstract: The Turnbull relation is widely believed to enable predictio… read more Abstract: The Turnbull relation is widely believed to enable prediction of solid–liquid interface (SLI) free energies from measurements of the latent heat and the solid density. Ewing proposed an additional contribution to the SLI free energy to account for variations in liquid structure near the interface. In the present study, molecular dynamics (MD) simulations were performed to investigate whether SLI free energy depends on liquid structure. Analysis of the MD simulation data for 11 fcc metals demonstrated that the Turnbull relation is only a rough approximation for highly ordered liquids, whereas much better agreement is observed with Ewing's theory. A modification to Ewing's relation is proposed in this study that was found to provide excellent agreement with MD simulation data. read less J. R. Espinosa, E. Sanz, C. Valeriani, and C. Vega, “On fluid-solid direct coexistence simulations: the pseudo-hard sphere model.,” The Journal of chemical physics. 2013. link Times cited: 78 Abstract: We investigate methodological issues concerning the direct c… read more Abstract: We investigate methodological issues concerning the direct coexistence method, an increasingly popular approach to evaluate the solid-fluid coexistence by means of computer simulations. The first issue is the impact of the simulation ensemble on the results. We compare the NpT ensemble (easy to use but approximate) with the NpzT ensemble (rigorous but more difficult to handle). Our work shows that both ensembles yield similar results for large systems (>5000 particles). Another issue, which is usually disregarded, is the stochastic character of a direct coexistence simulation. Here, we assess the impact of stochasticity in the determination of the coexistence point. We demonstrate that the error generated by stochasticity is much larger than that caused by the use of the NpT ensemble, and can be minimized by simply increasing the system size. To perform this study we use the pseudo hard-sphere model recently proposed by Jover et al. [J. Chem. Phys. 137, 144505 (2012)], and obtain a coexistence pressure of p∗ = 11.65(1), quite similar to that of hard spheres (only about 0.6% higher). Therefore, we conclude that this model can be reliably used to investigate the physics of hard spheres in phenomena like crystal nucleation. read less L. Wang and A. van de Walle, “Ab initio calculations of the melting temperatures of refractory bcc metals.,” Physical chemistry chemical physics : PCCP. 2012. link Times cited: 13 Abstract: We present ab initio calculations of the melting temperature… read more Abstract: We present ab initio calculations of the melting temperatures for bcc metals Nb, Ta and W. The calculations combine phase coexistence molecular dynamics (MD) simulations using classical embedded-atom method potentials and ab initio density functional theory free energy corrections. The calculated melting temperatures for Nb, Ta and W are, respectively, within 3%, 4%, and 7% of the experimental values. We compare the melting temperatures to those obtained from direct ab initio molecular dynamics simulations and see if they are in excellent agreement with each other. The small remaining discrepancies with experiment are thus likely due to inherent limitations associated with exchange-correlation energy approximations within density-functional theory. read less C. Becker and M. J. Kramer, “Atomistic comparison of volume-dependent melt properties from four models of aluminum,” Modelling and Simulation in Materials Science and Engineering. 2010. link Times cited: 30 Abstract: With the increasing use of simulations in materials research… read more Abstract: With the increasing use of simulations in materials research and design, it is important to quantify the differences between, and accuracy of, models used in these simulations. Here we present the results of such a comparison for four embedded-atom models of aluminum that were optimized to have good liquid properties, particularly the melting temperatures. The effects of temperature and volume are systematically examined in the melts for bulk thermodynamic quantities, pair correlation functions and structure factors and diffusion coefficients for each interatomic potential. Where possible, these are then compared with experimental values. We find quantitative differences in the properties determined from the various interatomic potentials despite the fact that they were fit with similar sets of data. read less H. Akbarzadeh, H. Abroshan, and G. Parsafar, “Surface free energy of platinum nanoparticles at zero pressure: A molecular dynamic study,” Solid State Communications. 2010. link Times cited: 13 M. Mendelev, M. Asta, M. J. Rahman, and J. Hoyt, “Development of interatomic potentials appropriate for simulation of solid–liquid interface properties in Al–Mg alloys,” Philosophical Magazine. 2009. link Times cited: 126 Abstract: Different approaches are analyzed for construction of semi-e… read more Abstract: Different approaches are analyzed for construction of semi-empirical potentials for binary alloys, focusing specifically on the capability of these potentials to describe solid–liquid phase equilibria, as a pre-requisite to studies of solidification phenomena. Fitting ab initio compound data does not ensure correct reproduction of the dilute solid-solution formation energy, and explicit inclusion of this quantity in the potential development procedure does not guarantee that the potential will predict the correct solid–liquid phase diagram. Therefore, we conclude that fitting only to solid phase properties, as is done in most potential development procedures, generally is not sufficient to develop a semi-empirical potential suitable for the simulation of solidification. A method is proposed for the incorporation of data for liquid solution energies in the potential development procedure, and a new semi-empirical potential developed suitable for simulations of dilute alloys of Mg in Al. The potential correctly reproduces both zero-temperature solid properties and solidus and liquid lines on the Al-rich part of the Al–Mg phase diagram. read less M. Mendelev, M. Kramer, R. Ott, D. Sordelet, D. Yagodin, and P. Popel,’ “Development of suitable interatomic potentials for simulation of liquid and amorphous Cu–Zr alloys,” Philosophical Magazine. 2009. link Times cited: 334 Abstract: We present a new semi-empirical potential suitable for molec… read more Abstract: We present a new semi-empirical potential suitable for molecular dynamics simulations of liquid and amorphous Cu–Zr alloys. To provide input data for developing the potential, new experimental measurements of the structure factors for amorphous Cu64.5Zr35.5 alloy were performed. In this work, we propose a new method to include diffraction data in the potential development procedure, which also includes fitting to first-principles and liquid density and enthalpy of mixing data. To refine the new potential, we used first-principles and liquid enthalpy of mixing data published earlier combined with the densities of liquid Cu64.5Zr35.5 measured over a range of temperatures. We show that the potential predicts a liquid-to-glass transition temperature that agrees reasonably well with experimental data. Finally, we compare the new potential with two previously developed semi-empirical potentials for Cu–Zr alloys and examine their comparative and contrasting descriptions of structure and properties for Cu64.5Zr35.5 liquids and glasses. read less M. Mendelev, M. Kramer, C. Becker, and M. Asta, “Analysis of semi-empirical interatomic potentials appropriate for simulation of crystalline and liquid Al and Cu,” Philosophical Magazine. 2008. link Times cited: 365 Abstract: We investigate the application of embedded atom method (EAM)… read more Abstract: We investigate the application of embedded atom method (EAM) interatomic potentials in the study of crystallization kinetics from deeply undercooled melts, focusing on the fcc metals Al and Cu. For this application, it is important that the EAM potential accurately reproduces melting properties and liquid structure, in addition to the crystalline properties most commonly fit in its development. To test the accuracy of previously published EAM potentials and to guide the development of new potential in this work, first-principles calculations have been performed and new experimental measurements of the Al and Cu liquid structure factors have been undertaken by X-ray diffraction. We demonstrate that the previously published EAM potentials predict a liquid structure that is too strongly ordered relative to measured diffraction data. We develop new EAM potentials for Al and Cu to improve the agreement with the first-principles and measured liquid diffraction data. Furthermore, we calculate liquid-phase diffusivities and find that this quantity correlates well with the liquid structure. Finally, we perform molecular dynamics simulations of crystal nucleation from the melt during quenching at constant cooling rate. We find that EAM potentials, which predict the same zero-temperature crystal properties but different liquid structures, can lead to quite different crystallization kinetics. More interestingly, we find that two potentials predicting very similar equilibrium solid and liquid properties can still produce very different crystallization kinetics under far-from-equilibrium conditions characteristic of the rapid quenching simulations employed here. read less C. Vega, E. Sanz, J. L. Abascal, and E. Noya, “Determination of phase diagrams via computer simulation: methodology and applications to water, electrolytes and proteins,” Journal of Physics: Condensed Matter. 2008. link Times cited: 229 Abstract: In this review we focus on the determination of phase diagra… read more Abstract: In this review we focus on the determination of phase diagrams by computer simulation, with particular attention to the fluid–solid and solid–solid equilibria. The methodology to compute the free energy of solid phases will be discussed. In particular, the Einstein crystal and Einstein molecule methodologies are described in a comprehensive way. It is shown that both methodologies yield the same free energies and that free energies of solid phases present noticeable finite size effects. In fact, this is the case for hard spheres in the solid phase. Finite size corrections can be introduced, although in an approximate way, to correct for the dependence of the free energy on the size of the system. The computation of free energies of solid phases can be extended to molecular fluids. The procedure to compute free energies of solid phases of water (ices) will be described in detail. The free energies of ices Ih, II, III, IV, V, VI, VII, VIII, IX, XI and XII will be presented for the SPC/E and TIP4P models of water. Initial coexistence points leading to the determination of the phase diagram of water for these two models will be provided. Other methods to estimate the melting point of a solid, such as the direct fluid–solid coexistence or simulations of the free surface of the solid, will be discussed. It will be shown that the melting points of ice Ih for several water models, obtained from free energy calculations, direct coexistence simulations and free surface simulations agree within their statistical uncertainty. Phase diagram calculations can indeed help to improve potential models of molecular fluids. For instance, for water, the potential model TIP4P/2005 can be regarded as an improved version of TIP4P. Here we will review some recent work on the phase diagram of the simplest ionic model, the restricted primitive model. Although originally devised to describe ionic liquids, the model is becoming quite popular to describe the behavior of charged colloids. Moreover, the possibility of obtaining fluid–solid equilibria for simple protein models will be discussed. In these primitive models, the protein is described by a spherical potential with certain anisotropic bonding sites (patchy sites). read less W. Luo, W. Hu, and S. Xiao, “Melting temperature of Pb nanostructural materials from free energy calculation.,” The Journal of chemical physics. 2008. link Times cited: 22 Abstract: The thermodynamic properties of lead, including the entropy,… read more Abstract: The thermodynamic properties of lead, including the entropy, heat capacity, Gibbs free energy, and surface free energy have been studied. Based on bulk thermodynamic properties of lead, Gibbs free energy for nanostructural materials is obtained and used to calculate the size-dependent melting point depression for lead nanostructural materials. The studies indicate that the surface free energy difference between solid phase and liquid phase is a decisive factor for the size-dependent melting of nanostructural materials. The calculated results are in agreement with recent experimental values and the available molecular dynamics simulation data. read less W. Luo, W. Hu, and S. Xiao, “Size Effect on the Thermodynamic Properties of Silver Nanoparticles,” Journal of Physical Chemistry C. 2008. link Times cited: 186 Abstract: The Gibbs free energy of silver nanoparticles has been obtai… read more Abstract: The Gibbs free energy of silver nanoparticles has been obtained from the calculations of bulk free energy and surface free energy for both the solid and liquid phase. On the basis of the obtained Gibbs free energy of nanoparticles, thermodynamic properties of silver nanoparticles, such as melting temperature, molar heat of fusion, molar entropy of fusion, and temperature dependences of entropy and specific heat capacity have been investigated. Calculation results indicate that these thermodynamic properties can be divided into two parts: bulk quantity and surface quantity, and surface atoms are dominant for the size effect on the thermodynamic properties of nanoparticles. The method that the intersection of the free-energy curves for solid and liquid nanoparticles decide the melting point of nanoparticles demonstrates that the surface free-energy difference between the solid and liquid phase is a decisive factor for the size-dependent melting of nanostructural materials. read less M. Mendelev and G. Ackland, “Development of an interatomic potential for the simulation of phase transformations in zirconium,” Philosophical Magazine Letters. 2007. link Times cited: 266 Abstract: In recent years, some 30 studies have been published on the … read more Abstract: In recent years, some 30 studies have been published on the molecular dynamics (MD) of zirconium, primarily of its twinning deformation and response to radiation damage. Its low thermal neutron absorption makes it uniquely suited for the latter application. Surprisingly, currently used interatomic potentials do not encapsulate the unique properties of Zr, namely its high stacking-fault energy, anomolous self-diffusion, melting and phase transformation under temperature and pressure (or alloying). Ab initio calculations have shown deficiencies in the description of point defects, both vacancies and interstitials, using existing interatomic potentials, deficiencies that can now be rectified by refitting. Here, we show the calculation of phase transitions self-consistently and present a potential for Zr that correctly reproduces the energetics of our extended database of ab initio configurations and high-temperature phase transitions. The potential has an analytic many-body form, making it suitable for existing large-scale MD codes. We also present a best-fit potential for the hcp structure and its defects. read less C. Vega, J. L. Abascal, and I. Nezbeda, “Vapor-liquid equilibria from the triple point up to the critical point for the new generation of TIP4P-like models: TIP4P/Ew, TIP4P/2005, and TIP4P/ice.,” The Journal of chemical physics. 2006. link Times cited: 201 Abstract: The vapor-liquid equilibria of three recently proposed water… read more Abstract: The vapor-liquid equilibria of three recently proposed water models have been computed using Gibbs-Duhem simulations. These models are TIP4P/Ew, TIP4P/2005, and TIP4P/ice and can be considered as modified versions of the TIP4P model. By design TIP4P reproduces the vaporization enthalpy of water at room temperature, whereas TIP4P/Ew and TIP4P/2005 match the temperature of maximum density and TIP4P/ice the melting temperature of water. Recently, the melting point for each of these models has been computed, making it possible for the first time to compute the complete vapor-liquid equilibria curve from the triple point to the critical point. From the coexistence results at high temperature, it is possible to estimate the critical properties of these models. None of them is capable of reproducing accurately the critical pressure or the vapor pressures and densities. Additionally, in the cases of TIP4P and TIP4P/ice the critical temperatures are too low and too high, respectively, compared to the experimental value. However, models accounting for the density maximum of water, such as TIP4P/Ew and TIP4P/2005 provide a better estimate of the critical temperature. In particular, TIP4P/2005 provides a critical temperature just 7 K below the experimental result as well as an extraordinarily good description of the liquid densities from the triple point to the critical point. All TIP4P-like models present a ratio of the triple point temperature to the critical point temperature of about 0.39, compared with the experimental value of 0.42. As is the case for any effective potential neglecting many body forces, TIP4P/2005 fails in describing simultaneously the vapor and the liquid phases of water. However, it can be considered as one of the best effective potentials of water for describing condensed phases, both liquid and solid. In fact, it provides a completely coherent view of the phase diagram of water including fluid-solid, solid-solid, and vapor-liquid equilibria. read less X.-bing Feng and B. B. L. , “A 6-site force field for succinonitrile,” Molecular Physics. 2005. link Times cited: 4 Abstract: A 6-site succinonitrile force field has been developed. The … read more Abstract: A 6-site succinonitrile force field has been developed. The model has produced proper proportions of the three succinonitrile conformers, which is necessary to avoid the thermal contraction of the plastic crystal phase around the melting point. The solid and liquid densities are about 1% lower or higher than the experimental values. The melting point of the model has been adjusted using the Gibbs–Duhem integration method. The theoretical melting point is in good agreement with experiment. read less M. Mendelev, S. Han, D. Srolovitz, G. Ackland, D. Sun, and M. Asta, “Development of new interatomic potentials appropriate for crystalline and liquid iron,” Philosophical Magazine. 2003. link Times cited: 1093 Abstract: Two procedures were developed to fit interatomic potentials … read more Abstract: Two procedures were developed to fit interatomic potentials of the embedded-atom method (EAM) form and applied to determine a potential which describes crystalline and liquid iron. While both procedures use perfect crystal and crystal defect data, the first procedure also employs the first-principles forces in a model liquid and the second procedure uses experimental liquid structure factor data. These additional types of information were incorporated to ensure more reasonable descriptions of atomic interactions at small separations than is provided using standard approaches, such as fitting to the universal binding energy relation. The new potentials (provided herein) are, on average, in better agreement with the experimental or first-principles lattice parameter, elastic constants, point-defect energies, bcc–fcc transformation energy, liquid density, liquid structure factor, melting temperature and other properties than other existing EAM iron potentials. read less J. Hoyt, M. Asta, and A. Karma, “Atomistic and continuum modeling of dendritic solidification,” Materials Science & Engineering R-reports. 2003. link Times cited: 332 M. Koning, A. Antonelli, and S. Yip, “Single-simulation determination of phase boundaries: A dynamic Clausius–Clapeyron integration method,” Journal of Chemical Physics. 2001. link Times cited: 44 Abstract: We present a dynamic implementation of the Clausius–Clapeyro… read more Abstract: We present a dynamic implementation of the Clausius–Clapeyron integration (CCI) method for mapping out phase-coexistence boundaries through a single atomistic simulation run. In contrast to previous implementations, where the reversible path of coexistence conditions is generated from a series of independent equilibrium simulations, dynamic Clausius–Clapeyron integration (d-CCI) explores an entire coexistence boundary in a single nonequilibrium simulation. The method gives accurately the melting curve for a system of particles interacting through the Lennard-Jones potential. Furthermore, we apply d-CCI to compute the melting curve of an ab initio pair potential for argon and verify earlier studies on the effects of many-body interactions and quantum effects in the melting of argon. The d-CCI method shows to be effective in both applications, giving converged coexistence curves spanning a wide range of thermodynamic states from relatively short nonequilibrium simulations. read less D. Alfé, M. Gillan, and G. D. Price, “Complementary approaches to the ab initio calculation of melting properties,” Journal of Chemical Physics. 2001. link Times cited: 79 Abstract: Several research groups have recently reported ab initio cal… read more Abstract: Several research groups have recently reported ab initio calculations of the melting properties of metals based on density functional theory, but there have been unexpectedly large disagreements between results obtained by different approaches. We analyze the relations between the two main approaches, based on calculation of the free energies of solid and liquid and on direct simulation of the two coexisting phases. Although both approaches rely on the use of classical reference systems consisting of parametrized empirical interaction models, we point out that in the free energy approach the final results are independent of the reference system, whereas in the current form of the coexistence approach they depend on it. We present a scheme for correcting the predictions of the coexistence approach for differences between the reference and ab initio systems. To illustrate the practical operation of the scheme, we present calculations of the high-pressure melting properties of iron using the corrected coexis... read less M. Jia, Y. Lai, Z. Tian, and Y.-xiang Liu, “Calculation of the surface free energy of fcc copper nanoparticles,” Modelling and Simulation in Materials Science and Engineering*. 2008. link Times cited: 31 Abstract: Using molecular dynamics simulations with the modified analy… read more Abstract: Using molecular dynamics simulations with the modified analytic embedded-atom method we calculate the Gibbs free energy and surface free energy for fcc Cu bulk, and further obtain the Gibbs free energy of nanoparticles. Based on the Gibbs free energy of nanoparticles, we have investigated the heat capacity of copper nanoparticles. Calculation results indicate that the Gibbs free energy and the heat capacity of nanoparticles can be divided into two parts: bulk quantity and surface quantity. The molar heat capacity of the bulk sample is lower compared with the molar heat capacity of nanoparticles, and this difference increases with the decrease in the particle size. It is also observed that the size effect on the thermodynamic properties of Cu nanoparticles is not really significant until the particle is less than about 20 nm. It is the surface atoms that decide the size effect on the thermodynamic properties of nanoparticles. read less
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Short KIM ID The unique KIM identifier code.	MO_120808805541_005
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_SturgeonLaird_2000_Al__MO_120808805541_005
DOI	10.25950/d62edb43 https://doi.org/10.25950/d62edb43 https://commons.datacite.org/doi.org/10.25950/d62edb43
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
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KIM API Version	2.0
Potential Type	eam
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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 2.31415e-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^-1 continuous. This means that the model has discontinuous energy.	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

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

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: 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: 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: 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

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: 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

Cubic Crystal Basic Properties Table

Species: Al

Tests

Disclaimer From Model Developer

This model was developed as a prototype case for the Gibbs-Duhem protocol for optimizing melting points. As such, the melting point was the primary metric for its development. We have shown that the modifications to the original Mei-Davenport potential that we used to optimize T_m did not change the quality of the potential with respect to elastic constants, density, etc., but no systematic study of other properties was performed.

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	7450
Cohesive energy versus lattice constant curve for diamond Al v004	view	7648
Cohesive energy versus lattice constant curve for fcc Al v004	view	7718
Cohesive energy versus lattice constant curve for sc Al v004	view	11480

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	2079
Elastic constants for diamond Al at zero temperature v001	view	3903
Elastic constants for fcc Al at zero temperature v006	view	2239
Elastic constants for sc Al at zero temperature v006	view	1440

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	1242

EquilibriumCrystalStructure__TD_457028483760_003

Equilibrium structure and energy for a crystal structure at zero temperature and pressure v003

Creators:
Contributor: ilia
Publication Year: 2025
DOI: https://doi.org/10.25950/866c7cfa

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 Al in AFLOW crystal prototype A_cF4_225_a v003		view	176715
Equilibrium crystal structure and energy for Al in AFLOW crystal prototype A_cI2_229_a v003		view	218912

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	4345020
Relaxed energy as a function of tilt angle for a 110 symmetric tilt grain boundary in fcc Al v001	view	22046463
Relaxed energy as a function of tilt angle for a 111 symmetric tilt grain boundary in fcc Al v001	view	7584720
Relaxed energy as a function of tilt angle for a 112 symmetric tilt grain boundary in fcc Al v001	view	44072351

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	1408
Equilibrium zero-temperature lattice constant for diamond Al v007	view	2207
Equilibrium zero-temperature lattice constant for fcc Al v007	view	4095
Equilibrium zero-temperature lattice constant for sc Al v007	view	1983

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	16268

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	450292

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	52110

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	4646850

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	21049

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	285500

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	1280187

Errors

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Files

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LICENSE.CDDL
MDSL.eam.fs
kimprovenance.edn
kimspec.edn

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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_SturgeonLaird_2000_Al__MO_120808805541_005

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

Disclaimer From Model Developer

Errors

Files

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