Modified Analytical Embedded Atom Method Research Articles

Calculation of formation enthalpies for Alfcc-Xbcc (X=Cr, Fe, Mo, Ta, V and W) binary alloys with MAEAM

The structural properties and formation enthalpies of the Al–Cr, Al–Fe, Al–Mo, Al–Ta, Al–V and Al–W binary systems are investigated by the modified analytic embedded atom method (MAEAM). The procedure to calculate the enthalpies of formation for fcc-bcc crystal structure alloys is given. It can be obtained from the calculations that all formation enthalpies of these binary alloys are negative, and the results of the MAEAM model are in agreement with the literature. The negative formation enthalpies of Al-based binary alloys indicate that the chemical interaction of two components can strengthen the stability of compounds. In addition, the formation enthalpies of stable alloy compounds calculated by the MAEAM are consistent with research. The reliability of the MAEAM model for predicting enthalpy of formation is proved by comparison with experimental data. The effects of the interactions between the constituent atoms were discussed based on the enthalpies of formation and alloy crystal structures.

Effects of vacancies on plasticity and phase transformation in single-crystal iron under shock loading

A characteristic region with vacancy concentration ranging from 0% to 2% was introduced into the single-crystal iron to investigate the effects of vacancies on plasticity and phase transformation of single-crystal iron under shock loading. The simulations were implemented by applying non-equilibrium molecular dynamics simulations with an excellent modified analytic embedded-atom method (MAEAM) potential. A fixed piston velocity of vp = 0.5 km/s was applied in our simulations, under which no plasticity or phase transformation occurred in the perfect single-crystal iron based on the description of the used MAEAM potential. The plasticity and phase transformation in iron were observably influenced by the vacancies as shown in this work. Significant anisotropy of shock response was distinctly exhibited. The nucleation and growth of dislocation loops emitting from the vacancy region were clearly observed in the sample that was shocked along the [110] direction, and the activated slip systems were determined as (112¯)[111] and (112)[111¯]. The vacancies and the vacancies-induced dislocation loops provided preferential nucleation positions for the subsequent phase transformation, which resulted in the phenomenon that the phase transformation product (HCP phase) always preferentially appeared in the vacancy region. The influences of different vacancy concentrations on plasticity and phase transformation were also discussed.

Determination Overlapping Interface Structure in the ξ´-Al-Ni-Rh Approximant Phase

The structure of the overlapping interface in ξ´-Al-Ni-Rh was determined by calculating the total energy of super lattices containing defect structures using the modified analytic embedded-atom method (MAEAM). The structure analyses indicated that only two equivalent types of interfaces exist, which are defined as the PF and PI types. Calculation of the PF- and PI-type super cells indicated that the interface between the close-packed P layer and the slightly puckered I layer has a lower energy and may be a static interface. Although the PI-type overlapping interface may seriously corrupt decagonal cluster columns in the approximant phase, it causes relatively less corruption of the metallic bonds than the PF mode. The total energies of the three types of super lattices caused by different displacement vectors between the two domains found in ξ´-Al-Ni-Rh were also calculated. The domain boundary translated with a vector of r =a + c is the most static state among the three type super lattices from energy perspective.

Phonon Spectrum and Resonance with Acoustic Wave of Lithium by Lattice Dynamics and the Modified Analytic Embedded-Atom Method

The phonon spectrum and resonance are studied by lattice dynamics and using the second nearest-neighbor (2NN) modified analytic embedded-atom method (MAEAM). Through deriving the expressions for atomic force constants, the phonon spectrum of lithium metal is calculated along three principal directions ([100], [110], [111]). The calculated and experimental values are in good agreement. On this basis, the phonon dispersion of acoustic wave is added to the phonon spectrum of lithium metal and the transverse wave and longitudinal wave of resonance frequencies are calculated. It is proposed that terahertz acoustic wave can be used to produce resonance with metal lithium electrodes, which would break the detrimental lithium dendrites during the charge process of Li batteries. The method can also be used to calculate the phonon spectrum and the resonance frequencies of other metal electrodes.

Phonon dispersion on Ag (100) surface: A modified analytic embedded atom method study**Project supported by the National Natural Science Foundation of China (Grant Nos. 61471301 and 61078057), the Scientific Research Program Funded by Shaanxi Provincial Education Department, China (Grant No. 14JK1301), and the Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant No. 20126102110045).

Within the harmonic approximation, the analytic expression of the dynamical matrix is derived based on the modified analytic embedded atom method (MAEAM) and the dynamics theory of surface lattice. The surface phonon dispersions along three major symmetry directions , and X̄M̄ are calculated for the clean Ag (100) surface by using our derived formulas. We then discuss the polarization and localization of surface modes at points X̄ and M̄ by plotting the squared polarization vectors as a function of the layer index. The phonon frequencies of the surface modes calculated by MAEAM are compared with the available experimental and other theoretical data. It is found that the present results are generally in agreement with the referenced experimental or theoretical results, with a maximum deviation of 10.4%. The agreement shows that the modified analytic embedded atom method is a reasonable many-body potential model to quickly describe the surface lattice vibration. It also lays a significant foundation for studying the surface lattice vibration in other metals.

Atomic simulation for influence of helium atom on movement of edge dislocation in nickel

The molecular dynamics (MD) simulation and the modified analytical embedded-atom method (MAEAM) were used to study the influence of a He atom on the movement of the edge dislocation in Ni. First, the calculated Burgers vector distribution shows that the equilibrium dissociation distance (Ded) and the stacking fault energy (Esf) between two partial edge dislocations are about 25.95 Å and 108 mJ/m2, respectively. Then, the obtained formation energies (Ef) of a He atom at some different sites demonstrate that the He atom is attracted and repelled in the tension and compression regions, respectively. And the He–dislocation interaction reveals that an interstitial He atom plays a more significant role in the dislocation movement than a substitutional He atom. Finally, it is found that the movement of an interstitial He atom is apparent as the first partial dislocation bypasses and the edge dislocation offers fast-diffusion path for the migration of a He atom.

MOLECULAR DYNAMICS SIMULATION OF THE SIZE EFFECT ON THE ELASTIC PROPERTIES OF THEB2-NiAlNANOFILM

In the paper, molecular dynamics simulation with the modified analytical embedded atom method (MAEAM) is applied to study the size effect on the elastic properties of the B 2- NiAl nanofilm. The simulation results indicate that there is a critical thickness, which is about 5.38 nm, to distinguish the size dependence of the elastic properties of the nanofilm. On the one hand, these properties, such as the averaged cohesive energy and the bulk modulus, change evidently as the size is smaller than the critical thickness and the change tendency is tightly controlled by the surface atom composition. On the other hand, as the nanofilm size exceeds the critical one, the calculated values of the elastic properties are almost independent of the film thickness. Relatively, the bulk modulus magnitude of the nanofilm is apparently larger than that of the corresponding bulk material. Finally, the inherent mechanisms of the size impacting on the elastic properties of the B 2- NiAl nanofilm have been discussed in more detail. The strengthening effect of the bulk modulus results from the smaller multilayer relaxation of the interlayer distance as compared to those of the bulk materials.

Simulation studies on the influence of nanofilm thickness on the elastic properties of B2-NiAl

In this paper the molecular dynamics (MD) technique and the modified analytic embedded atom method (MAEAM) are applied to study the influence of size and surface condition of the nanofilm on the elastic properties of B2-NiAl, The elastic properties of the bulk NiAl alloy and the size dependence of the surface energy of nanofilms are first calculated. It is found that the calculated results of the elastic properties are consistent with those from experiments and theories; and the surface energy, which is barely influenced by the thickness, is controlled by the surface atomic composition. On this basis, our investigations are mainly focused on the relationship between the elastic properties of nanofilms and their thickness. The obtained results indicate that the elastic properties of the nanofilm may change exponentially with the increasing thickness, which can also be regulated by the surface atomic composition. Furthermore, the inherent mechanism of the thicknes and surface that affects this relationship is analyzed in detail, showing that the surface atomic composition and the deviation of interplanar spacing in nanofims are two major factors for determining the thickness dependence of the elastic properties. These are in good agreement with the previous theoretical and experimental studies.

Atomistic Simulation of the Self-Diffusion in Very Thin Cu (001) Film by Using MAEAM

The self-diffusion in very thin Cu (001) film that formed by 2~11 atomic layers have been studied by using modified analytic embedded atom method (MAEAM) and a molecular dynamic (MD) simulation. The vacancy formation is the most easily in of Cu (001) thin film formed by any layers. The vacancy formation energy 0.5054eV in of the Cu (001) thin film formed by layers is the highest in all the values in the ones that formed by layers. The vacancy in and 3 is easily migrated to layer, and the vacancy in is easily migrated in intra-layer, and the vacancy in is easily migrated to when the corresponding atomic layer is existed. The vacancy formation and diffusion will not be affected by the atomic layer when the Cu (001) thin film is formed by more than ten layers ().

Description of Surface Energy Anisotropy for BCC Metals

Surface energy anisotropy (SEA) has long been a hot topic in interface science as it has an important role in the interface/surface behaviours for crystalline phases. Most studies aim to determine the numerical values of the anisotropic surface energy in some particular orientations, but few investigate the whole orientation-dependent trend, or the morphology of the polar plot. The present work propose descriptions for SEA of both body centred cubic (BCC) and face centred cubic (FCC) metals by considering the interactions between an atom and its 1st, 2nd and 3rd nearest neighbouring (NN) atoms. The expression makes use of only three coefficients K1, K2 and K3 which are correspondent to the contribution of 1st, 2nd and 3rd NN interactions respectively. This allows estimation of surface energy for all crystallographic orientations if the values for (111), (100) and (110) orientations are provided. Matching of our model with modified analytical embedded-atom method (MAEAM) results demonstrates less than 0.5% average relative error. We also construct the polar plots of BCC metals based on our model and compare them with some other models.

The alloying element dependence of the local lattice deformation and the elastic properties of Ni3Al: A molecular dynamics simulation

Molecular dynamics (MD) together with the modified analytical embedded atom method (MAEAM) is employed to study the alloying elements (Re, Ru, Co, and Ta) dependence of the elastic properties of L12-Ni3Al. The investigations indicate that the calculated elastic properties of Ni3Al are in reasonable agreement with the previous results. The substituting formation energies of the alloying elements in Ni3Al are calculated to determine the site preference. It is found out that Re, Ru, and Ta atoms prefer to occupy the Al sites, and the Co atom prefers to occupy the Ni site. Based on Re, Ru, and Ta substituting the 1st, 2nd, 3rd, and 4th nearest-neighbor atoms, we ascertain that the substituting manners of these alloying elements have a decisive effect on the bulk modulus and the local crystal lattice of Ni3Al. Moreover, for Re, the bonding interaction plays a predominant role in the improvement in the bulk modulus of Ni3Al, whereas the size effect of Ru and Ta on the improvement in the bulk modulus is more obvious. Finally, the potential reasons of which the alloying elements enhance the bulk modulus are discussed in details.

Comparison of Surface Energy of Bcc Alkali Metals and Transition Metals Using Maeam

The surface energies of the low index (100), (110) and (111) planes of some bcc alkali metals (Li,Na,K,Rb,Cs) and for the bcc transition metals (Fe,W,Mo,Cr,Ta,Nb and V) have been calculated using the Modified Analytical Embedded Atom Method (MAEAM).The surface energy of each (hkl) plane in alkali metals was found to be much more lower than those of the transition metals. The experimental values of surface energies are not tied to specific surfaces and are obtained for polycrystalline materials. They do not correlate with computed values published for any of these surfaces. This is expected since experiments give direct results. For all bcc metals the order of the surface energy is such that Es(110) < Es(100) < Es(111) which is in agreement with the results obtained except for (111) surface. Our calculated result shows that Es(111) < Es(110) < Es(100). This is not in agreement with the result of MAEAM.[1]

Atomic Simulation of Size Effect and Surface Properties of Aluminum Nanoparticles

Here, modified analytic embedded atom method (MAEAM) has been utilized to simulate size effect and surface properties of aluminum (Al) nanoparticles. According to the simulation results, we can find that lattice parameter and excess stored energy are size dependent. The simulated excess stored energy ranges from 2.12 to 57.61 kJ/mol, which is in the same order of magnitude with experiment results; surface energy of Al nanoparticles ranges from 0.78 to 1.10 J/m2, which is not invariant but size related. Furthermore, non-uniform lattice distortion has been observed in Al nanoparticles, and mainly concentrates in the first and second shell of surface layers. Theoretical research based on our simulation results provides a novel method to predict excess stored energy of metallic nanoparticles.

Atomic Diffusion in the (001) Surface of Cu<sub>3</sub>Ag Ordered Alloy

Both the formation and migration energies of a single vacancy migrating intra- and inter-layer of the CuAg-terminated (001) surface or Cu-terminated (001) surface for Cu3Ag ordered alloy have been calculated by using the modified analytical embedded-atom method (MAEAM) with the molecular dynamics (MD) method. The surface effects on the vacancy formation and migration are all down to 6L for the CuAg-terminated (001) surface, but is respectively down to 5L and 6L for the Cu-terminated (001) surface. The vacancy energetically formed in the 1L. There is a vacancy aggregation tendency in the 1L as well as in the bulk the Cu vacancy is easier to be formed than the Ag vacancy.

面心立方过渡金属自扩散的改进分析型嵌入原子法分析

采用改进分析型嵌入原子法(MAEAM)计算了面心立方过渡金属Ni、Pd、Pt、Cu、Ag、Au和Al自扩散过程中的能量。对于最近邻(NN)和次近邻(NNN)二种扩散机制，其能量曲线均为对称曲线且能量的最大值均位于各自扩散路径的中点。计算得到的单空位形成能、迁移能和自扩散激活能比用嵌入原子法(EAM)计算的结果更接近NN扩散的实验数据。计算结果表明NN扩散的激活能最低(迁移能也为最低)，因此面心立方过渡金属中的最可几扩散为单空位最近邻扩散。 The energy during the process of self-diffusion in FCC transition metals Ni, Pd, Pt, Cu, Ag, Au and Al has been calculated by using modified analytic embedded-atom method (MAEAM). For each kind of two diffusion mechanisms nearest-neighbor (NN) and next-nearest-neighbor (NNN), the energy curve is symmetric and the maximum value of the energy appears at the middle point of the diffusion path. Determined mono-vacancy formation energy , migration energy and activation energy for self-diffusion agree well with available experimental data of NN diffusion and are better than those obtained by the embedded-atom method (EAM). Compared the energies corresponding to two diffusion mechanisms, the NN diffusion needs the lowest activation energy (and thus the lowest migration energy). So that, the NN mono-vacancy diffusion is favorable in FCC transition metals.

Atomistic simulation for the γ′-phase volume fraction dependence of the interfacial behavior of Ni-base superalloy

By means of molecular dynamics (MD) and the modified analytic embedded-atom method (MAEAM), we investigate the effect of the γ′-phase volume fraction (γ′-VF) on the apparent interface energy, the critical thickness of the interface transition region (ITR) and the binding mechanism of the γ/γ′ interface. The results indicate that the apparent interface energy increases linearly with the ITR width increasing. Then, by extrapolating the ITR width Δl to zero, we can obtain the interface energy which is equal to the limiting value of the apparent interface energy. The volume fraction of the γ′-phase has no influence on the interface energy and the critical thickness of the ITR. The interface energy is in reasonable agreement with the previous results and the critical value of the ITR width is about 1.7nm which also agrees well with the experimental and theoretical ones. Finally, the γ′-VF dependence of the apparent interface energy and the interface separation of the ITR with about 1.7nm thickness are analyzed in more detail. The results reveal that the crystalline configuration of Ni-base superalloy (NBSA) with (60–70%) γ′-VF is the stablest, which is similar to the previous investigations.

Structure and Stability of BCC Crystals Fe, V, Nb and Ta under Hydrostatic Loading

The structural stability and theoretical strength of BCC crystals Fe, V, Nb and Ta under hydrostatic loading have been investigated by using the modified analytical embedded atom method (MAEAM). For all the calculated BCC crystals, the failures occur while the relation m >0 is violated in compression and k >0 is violated in tension. It found that the stable regions are 0.9269~1.1495, 0.9270~1.1545, 0.9268~1.1449 and 0.9268 ~ 1.1427 in the lattice stretch l or the corresponding -408.89 ~ 123.54, -186.96 ~ 131.43, -259.07 ~ 152.53 and -283.92 ~137.04eV/nm3 in the theoretical strength for Fe, V, Nb and Ta, respectively. The calculated maximum tensile stresses smax of Fe, V, Nb and Ta are 123.57, 131.74, 154.45 and 137.85eV/nm3 and the corresponding lattice stretch lmax ??are 1.1527, 1.1617, 1.1661 and 1.1545. The calculated maximum tensile stress smax and the corresponding lattice stretch lmax ??of Fe are consistent well with the results of Ab initio calculation.

Atomistic simulation on the shape dependence of the melting behavior of V nanowire

The modified analytical embedded atom method (MAEAM) has been used to study the cross-sectional shape dependence of the melting of vanadium nanowire (NW). The results indicate that the effect of the shape on the melting behavior is apparent. For the prefect crystal, the calculated thermodynamic properties including the melting temperature and the latent heat of melting, which are evidently higher than those of the NWs, are in good agreement with the previously corresponding value. For NWs, by monitoring the temperature dependence of the potential energy and heat capacity, the melting temperature of Tr-, Te-, and Cr-NW has been accurately determined to be 1730 K, 1790 K, and 1760 K, respectively. The melting temperature discrepancy of NWs predicates that the shape effect is prominent. On the basis of the obtained melting point of NW, we study the temperature dependence of the atomic fraction of all shells to explore the effect of cross-sectional shape on the melting behavior. Compared with the melting transition of three NWs, it is found that the melting behavior of triangular nanowire (Tr-NW) with the relatively larger shape factor is significantly different from that of other shape NW. Finally, the cross-sectional shape dependent melting mechanism of NWs is further studied by displaying the atomic snapshots at some given temperatures.

SHAPE DEPENDENCE OF THE PREMELTING OF NANOWIRE: A MOLECULAR DYNAMICS STUDY

Molecular dynamics (MD) and modified analytical embedded atom method (MAEAM) are used to study the effect of the cross-sectional shape on the nanowire (NW) premelting. The results indicate that the premelting phenomenon occurs far below the melting point. The temperature dependence of mean square displacement (MSD) shows that the shape effect on the premelting phenomenon is obvious. Based on the detailed analysis of the atomic configuration, the premelting activation energy (PAE), and the shape factor, we have further found that the cross-sectional shape has an important effect on the premelting mechanism of the NW.

Molecular dynamics simulations of point defects in plutonium grain boundaries

A modified analytic embedded atom method (MAEAM) potential is constructed for fcc δ-Pu. Molecular dynamics (MD) simulations with the potential are performed to investigate the interactions between two symmetrical tilt grain boundaries (GBs) and point defects such as He atom, vacancy and self-interstitial atom (SIA) in Pu. The calculated results show that point defect formation energies are on average lower than those in the lattice but variations from site to site along the GBs are very remarkable. Both substitutional and interstitial He atoms are trapped at GBs. Interstitial He atom is more strongly bound at the GB core than the substitutional He atom. The binding energy of SIA at GB core is higher than those of He atom and vacancy. GB core can bind many He atoms and SIAs due mainly to the fact that it contains many vacancies. Compared with He atom and SIA, the vacancy far from GB core is difficult to diffuse into the core. The GBs can act as sinks and sources of He atoms and SIAs, which may be a reason for the swelling of Pu after a period of self-irradiation because of the higher concentration of vacancy in the bulk.