A method of solid–solid phase equilibrium calculation by molecular dynamics
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Abstract:
A method for evaluation of solid-solid phase equilibrium curves in molecular dynamics simulation for a given model of interatomic interaction is proposed. The method allows to calculate entropies of crystal phases and provides an accuracy comparable with that of the thermodynamic integration method by Frenkel and Ladd while it is much simpler in realization and less intense computationally. The accuracy of the proposed method was demonstrated in MD calculations of entropies for EAM potential for iron and for MEAM potential for beryllium. The bcc-hcp equilibrium curves for iron calculated for the EAM potential by the thermodynamic integration method and by the proposed one agree quite well.Keywords:
Thermodynamic integration
Embedded atom model
Realization (probability)
Potential method
A method for evaluation of solid-solid phase equilibrium curves in molecular dynamics simulation for a given model of interatomic interaction is proposed. The method allows to calculate entropies of crystal phases and provides an accuracy comparable with that of the thermodynamic integration method by Frenkel and Ladd while it is much simpler in realization and less intense computationally. The accuracy of the proposed method was demonstrated in MD calculations of entropies for EAM potential for iron and for MEAM potential for beryllium. The bcc-hcp equilibrium curves for iron calculated for the EAM potential by the thermodynamic integration method and by the proposed one agree quite well.
Thermodynamic integration
Embedded atom model
Realization (probability)
Potential method
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Interatomic potential plays an important role in molecular dynamics simulation, which determines both the efficiency and accuracy of the simulations. Lattice inversion is a method which can be used to develop interatomic potential from first principle results directly. In present work, a robust potential model based on lattice inversion is proposed. Then the potential model is applied to develop interatomic potentials for eight common FCC metals. The cohesive energy curves calculated using first principle calculations can be well reproduced, which verifies the reliability of the developed potential. Additional physical properties, including equilibrium lattice constant and cohesive energy, elastic constants, are predicted and found reasonable agreement with corresponding first principle results.
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In Molecular Dynamics (MD) simulations, interatomic potentials have significant effects on the results and calculation time, i.e. analysis sizes. In this paper, first, the crack growth behaviors in α-Fe calculated by three representative interatomic potentials, the Embedded Atom Method (EAM) potential fitted by Simonelli, G. et al., Finnis-Sinclair (FS) potential and Second Nearest-neighbor Modified EAM (MEAM) potential, are compared, and the reliability of the results obtained by the MEAM potential is confirmed based on the reproducibility of the important physical properties. Although the MEAM potential is reliable, we show that the computational time required by the MEAM potential is more than 50 times of the FS potential. Here, we propose “Hybrid Potential Method” which selectively uses different interatomic potentials according to the local atomic structure, and connects those potentials by the use of handshake method. We use FS potential, which is efficient in calculation, for bcc structure and the MEAM potential, which is accurate but time consuming, for non-bcc structures. The availability of the Hybrid Potential Method is demonstrated, and then the method is applied to crack growth simulations using large calculation models. We report the phase transformations and grain nucleation near the crack tip during crack growth.
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Angular-dependent embedded atom method potential for atomistic simulations of metal-covalent systems
A computationally efficient interatomic potential is developed for the description of interatomic interactions in multicomponent systems composed of metals, Si and Ge. The potential is based on reformulation of the embedded atom method (EAM) potential for metals and Stillinger-Weber (SW) potential commonly used for Si and Ge in a compatible functional form. The potential incorporates a description of the angular dependence of interatomic interactions into the framework of the EAM potential and, therefore, is dubbed angular-dependent EAM (A-EAM) potential. The A-EAM potential retains the properties of the pure components predicted by the original EAM and SW potentials, thus limiting the scope of potential parameterization to only the cross interactions among the components. The ability of the potential to provide an adequate description of binary systems with mixed type of bonding is illustrated for Au-Si/Ge system, with the parameters for Au-Si and Au-Ge interactions determined based on the results of density-functional theory calculations performed for several representative bulk structures and small clusters. To test the performance of the A-EAM potential at finite temperatures, the values of the enthalpy of mixing of liquid Au-Si and Au-Ge alloys, as well as the equilibrium lines on the Au-Si phase diagram are evaluated and compared with experimental data. The calculation of the phase diagram is based on the values of the excess chemical potential difference between Au and Si, evaluated in a series of semi-grand canonical ensemble Monte Carlo simulations performed for different temperatures and alloy compositions. The potential is shown to provide an adequate semiquantitative description of the thermodynamic properties of the alloy at different temperatures and in the whole range of compositions, thus showing a considerable promise for large-scale atomistic simulations of metal-Si/Ge systems.
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Summary A new formulation of EAM potential is developed for the description of interatomic interactions in metal-silicon systems. The potential is based on reformulation of the Embedded Atom Method (EAM) potential for metals and Stillinger – Weber (SW) potential for silicon in a compatible functional form. The potential is parameterized for Au-Si system and tested by comparing the predicted energies and structural properties of representative Si-Au structures to the results of LDA calculations. First molecular dynamics simulations performed with the new potential for a Au monolayer island on the 2×1 reconstructed Si (001) surface showed formation of a silicide region at room temperature as observed experimentally and in earlier Modified EAM (MEAM) simulations. The preliminary results obtained with the new computationally-efficient EAM potential show considerable promise for investigation of metal – semiconductor interfacial phenomenon.
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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.
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In recent years, nano-crystalline materials have attracted many researchers’ attention, but the fracture mechanism has not been fully clarified. In a molecular dynamics (MD) simulation, grain size and crystal orientation can be chosen, and their effects on the mechanical properties of nano-crystalline materials can be evaluated clearly. This research first compares the results of crack growth behavior in single crystalline Fe for three typical interatomic potentials (Embedded Atom Method (EAM), Finnis Sinclair (FS), and Second Nearest Neighbor Modified EAM (2NNMEAM) potentials) and a Hybrid potential method, which uses FS potential for bcc structure atoms and 2NNMEAM potential for non-bcc structure atoms. The 2NNMEAM potential is accurate, but the computation time is dozens of times that of FS potential, which is the simplest of the three interatomic potentials. Therefore, the 2NNMEAM potential requires too much calculation for the purpose of this research that analyzes the crack growth behavior in nano-crystalline metals. However, Hybrid potential is able to give results similar to those of the 2NNMEAM potential, and the calculation time is close to that of the FS potential. From these results, the crack extension behavior in relatively large nano-crystalline models is analyzed using the Hybrid potential, and we demonstrate the grain-size dependency of the fracture behavior.
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The paper describes three common types of interatomic interaction potentials used for constructing theoretical models of the matter. The pair potentials are the Morse potential and the multiparticle potentials are the embedded atom method (EAM), the modified embedded atom method (MEAM). The rules of potential constructing and the fields of their application have been considered. Three types of potentials was used for calculation the elastic properties of palladium. The aim of the work is to determine which of the potentials – Morse potential, EAM or MEAM are better suited for calculating properties of palladium. It was found that all three potential approximately equally determine the properties of palladium. However, the Morse potential has the advantage because its structure is much simpler.
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Embedded atom model
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Carbon atom
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Amorphous carbon
Carbon fibers
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