Abstract: While machine learning approaches have been successfully used to represent interatomic potentials, their speed has typically lagged behind conventional formalisms. This is often due to the complexity of the structural fingerprints used to describe the local atomic environment and the large cutoff radii and neighbor lists used in the calculation of these fingerprints. Even recent machine learned methods are at least 10 times slower than traditional formalisms. An implementation of a rapid artificial neural network (RANN) style potential in the LAMMPS molecular dynamics package is presented here which utilizes angular screening to reduce computational complexity without reducing accuracy. For the smallest neural network architectures, this formalism rivals the modified embedded atom method (MEAM) for speed and accuracy, while the networks approximately one third as fast as MEAM were capable of reproducing the training database with chemical accuracy. The numerical accuracy of the LAMMPS implementation is assessed by verifying conservation of energy and agreement between calculated forces and pressures and the observed derivatives of the energy as well as by assessing the stability of the potential in dynamic simulation. The potential style is tested using a force field for magnesium and the computational efficiency for a variety of architectures is compared to a traditional potential models as well as alternative ANN formalisms. The predictive accuracy is found to rival that of slower methods. Additionally, the transferability of the formalism is demonstrated by correctly predicting the Mg phase diagram include the pressure dependence on melting temperature and the presence of a high pressure BCC phase.

Abstract: Magnesium (Mg) activates <c + a> dislocation slip on the second order pyramidal slip plane. This slip mode is very complex compared to other modes including several metastable structures. Due to the complexity and very similar energies of the different structures, reliably modelling this slip mode is challenging. The problem is exacerbated when considering alloying, in which a combination of 1st order and 2nd order pyramidal slip is usually observed. Motivated by the need for a high fidelity potential for Mg alloys, we have developed first a highly accuracy potential for pure Mg. The new potential shows better agreement with density functional theory and experimental calculations than previous interatomic potentials for Mg. With the help of this new potential, we demonstrate that the basal dissociated <c + a> core is not sessile, as previously thought, and that constant stress molecular dynamics demonstrate clear preference for the 2nd order pyramidal system over the 1st order system.

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).

Abstract: Interatomic potentials for pure Mg and the Mg-Al binary system have been developed based on the modified embedded-atom method (MEAM) potential formalism. The potentials can describe various fundamental physical properties of pure Mg (bulk, point defect, planar defect and thermal properties) and alloy behaviors (thermodynamic, structural and elastic properties) in reasonable agreement with experimental data or higher-level calculations. The applicability of the potential to atomistic investigations on the deformation behavior of pure Mg and the effect of alloying element Al on it is discussed.

Abstract: Crystal-melt interfacial free energies (γ) 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 γ in terms of hexagonal harmonics. The method is applied in the calculation of the Turnbull coefficient (α) and crystalline anisotropies of γ. We obtain a value of α=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.

Abstract: Recent molecular dynamics simulations of the growth of [Ni0.8Fe0.2/Au] multilayers have revealed the formation of misfit-strain-reducing dislocation structures very similar to those observed experimentally. Here we report similar simulations showing the formation of edge dislocations near the interfaces of vapor-deposited (111) [NiFe/CoFe/Cu] multilayers. Unlike misfit dislocations that accommodate lattice mismatch, the dislocation structures observed here increase the mismatch strain energy. Stop-action observations of the dynamically evolving atomic structures indicate that during deposition on the (111) surface of a fcc lattice, adatoms may occupy either fcc sites or hcp sites. This results in the random formation of fcc and hcp domains, with dislocations at the domain boundaries. These dislocations enable atoms to undergo a shift from fcc to hcp sites, or vice versa. These shifts lead to missing atoms, and therefore a later deposited layer can have missing planes compared to a previously deposited layer. This dislocation formation mechanism can create tensile stress in fcc films. The probability that such dislocations are formed was found to quickly diminish under energetic deposition conditions.

Abstract: Recent molecular dynamics simulations of the growth of [Ni0.8Fe0.2/Au] multilayers have revealed the formation of misfit-strain-reducing dislocation structures very similar to those observed experimentally. Here we report similar simulations showing the formation of edge dislocations near the interfaces of vapor-deposited (111) [NiFe/CoFe/Cu] multilayers. Unlike misfit dislocations that accommodate lattice mismatch, the dislocation structures observed here increase the mismatch strain energy. Stop-action observations of the dynamically evolving atomic structures indicate that during deposition on the (111) surface of a fcc lattice, adatoms may occupy either fcc sites or hcp sites. This results in the random formation of fcc and hcp domains, with dislocations at the domain boundaries. These dislocations enable atoms to undergo a shift from fcc to hcp sites, or vice versa. These shifts lead to missing atoms, and therefore a later deposited layer can have missing planes compared to a previously deposited layer. This dislocation formation mechanism can create tensile stress in fcc films. The probability that such dislocations are formed was found to quickly diminish under energetic deposition conditions.

Abstract: A set of modified embedded-atom method (MEAM) potentials for the interactions between Al, Si, Mg, Cu, and Fe was developed from a combination of each element's MEAM potential in order to study metal alloying. Previously published MEAM parameters of single elements have been improved for better agreement to the generalized stacking fault energy (GSFE) curves when compared with ab initio generated GSFE curves. The MEAM parameters for element pairs were constructed based on the structural and elastic properties of element pairs in the NaCl reference structure garnered from ab initio calculations, with adjustment to reproduce the ab initio heat of formation of the most stable binary compounds. The new MEAM potentials were validated by comparing the formation energies of defects, equilibrium volumes, elastic moduli, and heat of formation for several binary compounds with ab initio simulations and experiments. Single elements in their ground-state crystal structure were subjected to heating to test the potentials at elevated temperatures. An Al potential was modified to avoid formation of an unphysical solid structure at high temperatures. The thermal expansion coefficient of a compound with the composition of AA 6061 alloy was evaluated and compared with experimental values. MEAM potential tests performed in this work, utilizing the universal atomistic simulation environment (ASE), are distributed to facilitate reproducibility of the results.

Abstract: Interatomic potentials for pure Mg and the Mg-Al binary system have been developed based on the modified embedded-atom method (MEAM) potential formalism. The potentials can describe various fundamental physical properties of pure Mg (bulk, point defect, planar defect and thermal properties) and alloy behaviors (thermodynamic, structural and elastic properties) in reasonable agreement with experimental data or higher-level calculations. The applicability of the potential to atomistic investigations on the deformation behavior of pure Mg and the effect of alloying element Al on it is discussed.

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.

Abstract: Monte-Carlo simulations are done to determine Mg enrichment at various grain-boundaries of Al–10%Mg alloys at hot working temperatures. The interatomic potentials used in the simulations are developed using the force-matching method. The Mg segregation levels at the grain-boundaries are found to vary from 20% to 40%. The segregation enrichment differences at different grain-boundary sites are explained in terms of atomic size and local hydrostatic stress. The segregation level varies strongly with [110] tilt boundaries from low to high angle while showing minimal variation with [100] twist boundaries. Segregation levels are found to have some correlation with grain-boundary energy. The effect on grain-boundary decohesion due to Mg segregation is found to be a modest (10--35%) reduction in fracture energy compared to the fracture energy in pure Al.

Abstract: A set of embedded-atom method (EAM) potentials for Al-Mg alloys are developed using the "force matching" method. The potentials are fitted to both experimental data and a massive quantum mechanical database of atomic forces at finite temperatures. Using the potentials, Monte Carlo simulations are performed to study Mg segregation at different low-index surfaces of an Al alloy with 1–10 at% Mg. Surface enrichments of Mg of the order of 80% are found, and the segregation behavior is generally anisotropic. A set of discrete lattice-plane calculations, based on the nearest-neighbor broken-bond model corrected for strain energy, are shown to drastically reduce the anisotropy of surface segregation.

Abstract: Because of its very large c/a ratio, zinc has proven to be a difficult element to model using semi-empirical classical potentials. It has been shown, in particular, that for the modified embedded atom method (MEAM), a potential cannot simultaneously have an hcp ground state and c/a ratio greater than ideal. As an alloying element, however, useful zinc potentials can be generated by relaxing the condition that hcp be the lowest energy structure. In this paper, we present a MEAM zinc potential, which gives accurate material properties for the pure state, as well as a MEAM ternary potential for the Mg-Al-Zn system which will allow the atomistic modeling of a wide class of alloys containing zinc. The effects of zinc in simple Mg-Zn for this potential is demonstrated and these results verify the accuracy for the new potential in these systems.

Abstract: Interatomic potentials for pure Ca and Mg-X (X=Y,Sn,Ca) binary systems have been developed on the basis of the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The potentials can describe various fundamental physical properties of pure Ca (bulk, defect and thermal properties) and the alloy behavior (structural, thermodynamic and defect properties of solid solutions and compounds) of binary systems in reasonable agreement with experimental data or first-principles and other calculations. The applicability of the developed potentials to atomistic investigations of the deformation behavior of Mg and its alloys is discussed together with some challenging points that need further attention.

Abstract: Mg–Zn–Ca alloys are representative Mg alloys with high formability at room temperature. Their high formability is thought to be related to slip, twinning, and recrystallization of the alloys, but the detailed mechanisms have not yet been clarified. To enable atomistic simulations for investigating those behaviors, an interatomic potential for the Mg–Zn–Ca ternary system was developed. The development was based on the second nearest-neighbor modified embedded-atom method formalism, combining previously developed Mg–Zn and Mg–Ca potentials with the newly developed Zn–Ca binary potential. The Zn–Ca and Mg–Zn–Ca potentials reproduce structural, elastic, and thermodynamic properties of compounds and solution phases of relevant alloy systems in reasonable agreement with experimental data, first-principles and CALPHAD calculations. The applicability of the developed potentials is demonstrated through calculations of the effects of Zn and Ca solutes on the generalized stacking fault energy for various slip systems, segregation energy on twin boundaries, and volumetric misfit strain.

Abstract: We have obtained effective medium theory interatomic potential parameters suitable for studying Cu-Mg metallic glasses. We present thermodynamic and structural results from simulations of such glasses over a range of compositions. We have produced low-temperature configurations by cooling from the melt at as slow a rate as practical, using constant temperature and pressure molecular dynamics. During the cooling process we have carried out thermodynamic analyses based on the temperature dependence of the enthalpy and its derivative, the specific heat, from which the glass transition temperature may be determined. We have also carried out structural analyses using the radial distribution function (RDF) and common neighbor analysis (CNA). Our analysis suggests that the splitting of the second peak, commonly associated with metallic glasses, in fact, has little to do with the glass transition itself, but is simply a consequence of the narrowing of peaks associated with structural features present in the liquid state. In fact, the splitting temperature for the Cu-Cu RDF is well above T_g. The CNA also highlights a strong similarity between the structure of the intermetallic alloys and the amorphous alloys of similar composition. We have also investigated the diffusivity in the supercooled regime. Its temperature dependence indicates fragile-liquid behavior, typical of binary metallic glasses. On the other hand, the relatively low specific-heat jump of around 1.5k_B/atom indicates apparent strong-liquid behavior, but this can be explained by the width of the transition due to the high cooling rates.

Abstract: We develop an interatomic potential intended for the study of Mg-H system using atomistic methods. The reported potential has an angular-dependent form and can be used for simulation of pure magnesium, as well as for consideration of binary cases including Mg and H. Summary of the performed tests on elastic, thermophysical and diffusional properties proves that the potential has a wide range of applicability. For example, it can be used to model phase transitions existing in pure magnesium (liquid <-> hcp and bcc <-> hcp). We also show how the model represents energies of different point defects and stacking faults in Mg. The primary purpose of the potential is the simulation of hydrogen behavior in magnesium. Here we show examples of the hydrogen diffusion and clusterization in hcp magnesium. Also, it is shown that the proposed potential reproduces stable structures for some of the existing magnesium hydrides: α-MgH2 (P42/mnm) and γ-MgH2 (Pbcn).

Abstract: Interatomic potentials for pure Li and the Mg-Li binary system have been developed based on the second nearest-neighbor modified embedded-atom method formalism. The potentials can describe various fundamental physical properties of pure Li (bulk, point defect, planar defect and thermal properties) and alloy behaviors (thermodynamic, structural and elastic properties) in reasonable agreement with experimental data or higher-level calculations. The applicability of the potential to atomistic investigations on the deformation behavior of Mg alloys and the effect of Li is demonstrated.

Abstract: Interatomic potentials for the Mg-Nd and Mg-Pb binary systems have been developed within the framework of the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The potentials describe a wide range of fundamental materials properties (thermodynamic, structural and elastic properties of compound and solution phases) of relevant systems in reasonable agreement with experimental data or first-principles and CALPHAD calculations. The applicability of the developed potentials to atomistic simulations on deformation behavior in Mg and its alloys is demonstrated by showing that the potentials reproduce related material properties reasonably and are transferable sufficiently.

Abstract: Interatomic potentials for the Mg-Nd and Mg-Pb binary systems have been developed within the framework of the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The potentials describe a wide range of fundamental materials properties (thermodynamic, structural and elastic properties of compound and solution phases) of relevant systems in reasonable agreement with experimental data or first-principles and CALPHAD calculations. The applicability of the developed potentials to atomistic simulations on deformation behavior in Mg and its alloys is demonstrated by showing that the potentials reproduce related material properties reasonably and are transferable sufficiently.

Abstract: Interatomic potentials for pure Ca and Mg-X (X=Y,Sn,Ca) binary systems have been developed on the basis of the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The potentials can describe various fundamental physical properties of pure Ca (bulk, defect and thermal properties) and the alloy behavior (structural, thermodynamic and defect properties of solid solutions and compounds) of binary systems in reasonable agreement with experimental data or first-principles and other calculations. The applicability of the developed potentials to atomistic investigations of the deformation behavior of Mg and its alloys is discussed together with some challenging points that need further attention.

Abstract: Interatomic potentials for pure Ca and Mg-X (X=Y,Sn,Ca) binary systems have been developed on the basis of the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The potentials can describe various fundamental physical properties of pure Ca (bulk, defect and thermal properties) and the alloy behavior (structural, thermodynamic and defect properties of solid solutions and compounds) of binary systems in reasonable agreement with experimental data or first-principles and other calculations. The applicability of the developed potentials to atomistic investigations of the deformation behavior of Mg and its alloys is discussed together with some challenging points that need further attention.

Abstract: Interatomic potentials for pure Zn and Mg-Zn binary system have been developed on the basis of the second nearest-neighbor modified embedded-atom method formalism. The potentials describe fundamental material properties of pure Zn (bulk, defect, and thermal properties) reasonably and reproduce the alloy behavior (thermodynamic, structural, and elastic properties of compounds and solution phases) of Mg-Zn alloys well in good agreement with experiments, first-principles and CALPHAD. The applicability of the developed potentials to atom-scale investigations on the slip behavior of Mg-Zn alloys is also demonstrated by showing that the calculated effects of Zn on the general stacking fault energy on the basal, prismatic and pyramidal planes are consistent with first-principles calculations.

Abstract: We present here simulation results on the dynamical structure factor of the C14 Laves Phase of MgZn₂, the simplest of the Mg–(Al,Zn) Frank-Kasper alloy phases. The dynamical structure factor was determined in two ways. Firstly, the dynamical matrix was obtained in harmonic approximation from ab-initio forces. The dynamical structure factor can then be computed from the eigenvalues of the dynamical matrix. Alternatively, Molecular Dynamics simulations of a larger sample were used to measure the correlation function corresponding to the dynamical structure factor. Both results are compared to data from neutron scattering experiments. This comparison also includes the intensity distribution, which is a very sensitive test. We find that the dynamical structure factor determined with either method agrees reasonably well with the experiment. In particular, the intensity transfer from acoustic to optic phonon modes can be reproduced correctly. This shows that simulation studies can complement phonon dispersion measurements.

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).