Modified Analytical Embedded Atom Method Research Articles

Study on MAEAM Multi-Body Potentials with Farther Neighbor Atoms for HCP Metals

An end processing method of the pair-potential of modified analytical embedded atom method (MAEAM) was suggested for hcp metals with farther neighbor atoms. Through fitting the elastic constants, the cohesive energy and two equilibrium conditions of hcp metal crystals correctly, we changed the pair-potential parameters and the modification term parameters of the multi-body potential. The model calculations fully demonstrate the structure stability and the unrelaxed mono-vacancy properties of six hcp metals: Co, Mg, Re, Ru, Ti and Zr.

Stiffening and End Processing of MAEAM Pair Potential for FCC Metals

A stiffening function and a truncated function of the pair-potential of the modified analytical embedded atom method (MAEAM) were suggested for fcc metals. Through fitting the mono-vacancy migration energy, the elastic constants, the cohesive energy and an equilibrium condition of fcc metal crystals correctly, we determined the stiffening parameter and changed the pair-potential parameters and the modification term parameter of the multi-body potential for fcc metals: Ag, Al, Au, Cu, Ir, Ni, Pd, Pt, and Rh. The model calculations fully demonstrate the phonon dispersion curves and the unrelaxed mono-vacancy properties of the nine fcc metals.

End Processing of MAEAM Pair Potential for BCC Metals

An end processing function of the pair-potential of modified analytical embedded atom method (MAEAM) was suggested for bcc metals. Through fitting the elastic constants, cohesive energy and an equilibrium condition of bcc metal crystals correctly, we changed the pair-potential parameters and the modification term parameter of the multi-body potential. The model calculations fully demonstrate the structure stabilities and the phonon dispersion curves of seven bcc transition metals: Cr, Fe, Mo, Nb, Ta, V and W.

CALCULATION OF PHONON DISPERSION FOR TRANSITION METALS V, Nb AND Ta

Combining the modified analytic embedded atom method (MAEAM) with lattice dynamics theory, the phonon dispersion along five symmetry directions have been calculated for three transition metals V, Nb and Ta . A good agreement between calculations and experiments along three high symmetry directions [q00], [qqq] and [qq0] implies that the predicted phonon dispersion along the other two directions [1qq] and [Formula: see text] are well behaved. Along each direction, the phonon frequency decreases for V, Nb and Ta successively may be related to the ratio of the cohesive energy to atomic mass.

Study of the structural and atomic diffusive properties of the ordered Cu3Au (110) surface

AbstractThe structural properties, the formation and migration energies of a single vacancy migrating intralayer and interlayer in the CuAu‐terminated (110) surface of Cu3Au ordered alloy have been calculated and discussed by using the modified analytical embedded‐atom method (MAEAM) and molecular dynamics (MD) methods. The surface layer exhibits rippling that the Au atoms are raised above Cu atoms about 0.117 Å in the topmost layer. The displacements of the topmost two layers are comparatively larger, while the third layer relaxes slightly and there are no changes in the nether layers. From energy minimization, the vacancy is most likely to be formed in the first layer (1L), especially on the Au site. The surface vacancy shows the smallest formation energy compared to the interlayer and bulk vacancies, while the corresponding value converges after the fifth layer (5L). For Cu vacancy originally sited in the second layer (2L) and migrated intralayer and interlayer, the diffusion without causing the local disorder is the most favorable, and the vacancy tends to migrate to the topmost layer. In the topmost layer of the CuAu‐terminated (110) surface, the circularity path is preferred over the beeline path. Copyright © 2011 John Wiley & Sons, Ltd.

Anisotropy analysis of surface energy and prediction of surface segregation for fcc metals

In the atomic scale, the surface energy anisotropy analysis of 38 surface planes of 10 fcc metals Cu, Ag, Au, Ni, Pd, Pt, Rh, Al, Ir and Pb have been simulated by using the elemental variables φ* and nWS and modified analytical embedded-atom method (MAEAM). The results show that the close-packed surface (111) of fcc metals which have the lowest surface energies will grow preferentially, the surface energies for all the other surface planes increase linearly with cosθ(hkl), where cosθ(hkl) are the angles between the surface planes (hkl) and (111), which is consistent with the experimental and the linear-muffin-tin-orbital atomic-sphere approximation (LMTO－ASA) results. A graphical approach which correctly explains the relation of the surface segregation energy and surface energy is employed. We conclude that the surface segregation takes place or not is mainly determined by the rule that an impurity (solute) with lower surface energy will segregate to the surface of the host (solution) with higher surface energy.

Atomistic simulation of the point defects in TaW ordered alloy

Combining molecular dynamics (MD) simulation with modified analytic embedded-atom method (MAEAM), the formation, migration and activation energies of the point defects for six-kind migration mechanisms in B2-type TaW alloy have been investigated. The results showed that the anti-site defects TaW and WTa were easier to form than Ta and W vacancies owing to their lower formation energies. Comparing the migration and activation energies needed for six-kind migration mechanisms of a Ta (or W) vacancy, we found that one nearest-neighbour jump (1NNJ) was the most favourable because of its lowest migration and activation energies, but it would lead to a disorder in the alloy. One next-nearest-neighbour jump (1NNNJ) and one third-nearest-neighbour jump (1TNNJ) could maintain the ordered property of the alloy but required higher migration and activation energies. So the 1NNNJ and 1TNNJ should be replaced by straight [100] six nearest-neighbor cyclic jumps (S[100]6NNCJ) (especially) or bent [100] six nearest-neighbour cyclic jumps (B[100]6NNCJ) and [110] six nearest-neighbor cyclic jumps ([110]6NNCJ), respectively.

Molecular dynamics simulation of interfacial defects with modified potential based on the first-principle

The interfacial molecular structure of materials with different lattice constants is simulated by using the method of molecular dynamics (MD). Potential of modified analytical embedded atom method (MAEAM) is used for non-interfacial atoms. To simulate the state of interfacial atoms, further modifications are applied to the MAEAM potential based on the first-principle simulation results. It is concluded that a small change of potential may greatly influence the interfacial molecular structure. Void and diffusions can be observed in the simulation results. It is also found that the pre-existed dot defects before bonding can decrease the number of interfacial defects greatly, thereby, can increase the strength of the interface.

The di-vacancy diffusion in B 2-type Mo–Ta ordered alloy

The formation and diffusion mechanisms of di-vacancies in the ordered Mo–Ta alloy of the B 2-type have been investigated by combining the modified analytic embedded-atom method (MAEAM) with molecular dynamic (MD) simulation. From the minimization of the formation energy or the maximization of the binding energy we know that the stability of the di-vacancy configurations decreases in the direction 1 nn Mo–Ta, 2 nn Ta–Ta and 2 nn Mo–Mo, whereas the 4 nn Mo–Ta, 3 nn Ta–Ta and 3 nn Mo–Mo configurations are unstable and tend to congregate to the former three stable configurations (e.g. “2 nn” means “second nearest neighbor” etc.). Taking into account the minimization of the migration or activation energies we also know that, for all six types of the di-vacancy configurations, the multi-jumps involving a series of 1 nn-jumps are energetically more favorable than either one-jump or two-jump diffusion mechanisms. Furthermore, the three stable configurations of the 1 nn Mo–Ta di-vacancy are not only easy to form, but also easy to migrate especially by the four-jump mechanism.

The melting behaviors of the Nb(1 1 0) nanofilm: a molecular dynamics study

By using molecular dynamics (MD) and the modified analytic embedded atom method (MAEAM), we have studied the melting point, the melting mechanism and the correspondingly dynamical behaviors of a Nb(1 1 0) nanofilm. Firstly, in accordance to the MD time dependence of the potential energy, the melting point of this nanofilm has been roughly estimated. Then, the melting mechanism of the nanofilm have been analyzed in detail with the application of the structure factor. The results clearly indicate that the melting transition of the 8th, 9th, and 10th atomic layer of the nanofilm has been characterized by the exponential, polynomial and linear sequence respectively when the thickness of the quasiliquid film attains to about 1.3 nm. Thirdly, the dynamical behaviors of the nanofilm melting, such as the melting front propagation velocity and the kinetic coefficient, which have also been analyzed, demonstrate that the melting front propagation velocity has linearly increased with the incremental temperature and the evaluated kinetic coefficient has approximately equaled 1.43 m/( sK). Finally, by extrapolating the melting front propagation velocity to zero, we can accurately deduce the melting point of the Nb(1 1 0) nanofilm to 2568.3 K, which is much lower than the counterpart (2740 K) of the bulk niobium.

The MAEAM Model and Anharmonic Theory for the Bulk Modulus of Al Metal

The modified analytic embedded atom method (MAEAM) model and the anharmonic theory are used to study the bulk modulus of f cc Al metal. The result shows that the bulk modulus can be described by a quadratic function of temperature. The result is in good agreement with the experimental data and theoretical results calculated by the first principle calculation etc. This outcome indicates that the temperature dependence of the bulk modulus for f cc Al metal can be academically studied with the MAEAM model combining with the anharmonic theory.

Atomistic simulations for the non-equilibrium surface premelting and melting of Nb(1 1 0) plane

In the present paper molecular dynamics (MD) simulations have been preformed to investigate the surface melting process and microscopic mechanism of Nb(1 1 0) plane in the atomic scale with a modified analytic embedded atom method (MAEAM). On the basis of the MD relaxation dependence of averaged internal energy and layer structure factor at given temperatures, the melting point of the sample has been estimated to be 2510 K. Then by the above results the Nb(1 1 0) plane melting process has been approximately divided into two stages: first the layer-by-layer premelting phase in the surface region and then a simultaneous abrupt melting transition for the inner layers. According to the variation of the averaged internal energy of the inner atomic layer, the melting latent heat has been calculated and the result is in good agreement with the experimental value. The simulated snapshots of atomic configuration for Nb(1 1 0) plane have indicated that the dynamically microscopic mechanism of melting nucleation during the melting transition.

Atomistic simulation of the vacancy diffusion in (0 0 1) surface of MoTa alloy

The formation and diffusion of a single Mo or Ta vacancy in the (0 0 1) surface of the B 2-type MoTa alloy have been investigated by using modified analytical embedded-atom method (MAEAM). The results show that the effect of the surface on the vacancy is only down to the sixth layer. It is easier for the vacancy to form in the first layer. Comparing the migration energy of the vacancy migrating in the intra-layer, to the upper layer and to the nether layer via 2NN jump, we find that the vacancy in the first or second layer is preferred to migrate in intra-layer, and that in the third or fourth layer is favorable to migrate to the upper layer. Although 1NN jump will result in an anti-site so that a disorder in the order alloy, it may also occur due to the much lower migration energy especially for the vacancy in the second and third layer to migrate to the first and second layer, respectively.

Atomistic simulation of helium bubble nucleation in palladium

A palladium crystal has been constructed with 11808 atoms. 55 helium atoms occupied the octahedral position of palladium crystal are introduced and retained in a spherical region. Molecular dynamic simulations are performed in a constant temperature and constant volume ensemble (NVT) with temperature controlled by Nose–Hoover thermostat. The interactions between palladium atoms are described with modified analytic embedded atom method (MAEAM), the interactions between palladium atom and helium atom are in the form of Morse potential, and the interactions between helium atoms are in the form of L–J potential function. With the analysis of the radial distribution function (RDF) and microstructure, it reveals that some of helium atoms form a series of clusters with different size, and the nucleation core is random at low temperature, and which is the embryo of helium bubble. Increasing temperature can accelerate the process of bubble nucleation, and the clusters will aggregate and coalesce into a bigger one in which there are no palladium atoms, and it is considered as a helium bubble.

Self-interstitial configuration in molybdenum studied by modified analytical embedded atom method

The stability of various atomic configurations containing a self-interstitial atom (SIA) in a model representing Mo has been investigated using the modified analytical embedded atom method (MAEAM). The lattice relaxations are treated with the molecular dynamics (MD) simulation at absolute zero of temperature. Six relatively stable self-interstitial configurations and formation energies have been described and calculated. The results indicate that the [111] dumbbell interstitial S111 has the lowest formation energy, and in ascending order, the sequence of the configurations is predicted to be S111, C, S110, T, S001 and O. From relaxed displacement field up to the fifth-NN atoms of six configurations, we know that the relaxed displacements depend not only on separation distances of the NN atoms from the defect centre but also strongly on the direction of the connected line between the NN atoms and the defect centre. The equilibrium distances between two nearest atoms in the core of the S111, C, S110, T, S001 and O configurations are 0.72a, 0.72a, 0.71a, 0.72a, 0.70a and 0.70a, respectively.

Atomistic simulation of the point defects in B2-type MoTa alloy

The formation and migration mechanisms of three different point defects (mono-vacancy, anti-site defect and interstitial atom) in B 2 -type MoTa alloy have been investigated by combining molecular dynamics (MD) simulation with modified analytic embedded-atom method (MAEAM). From minimization of the formation energy, we find that the anti-site defects Mo Ta and Ta Mo are easier to form than Mo and Ta mono-vacancies, while Mo and Ta interstitial atoms are difficult to form in the alloy. In six migration mechanisms of Mo and Ta mono-vacancies, one nearest-neighbor jump (1NNJ) is the most favorable due to its lowest activation and migration energies, but it will cause a disorder in the alloy. One next-nearest-neighbor jump (1NNNJ) and one third-nearest-neighbor jump (1TNNJ) can maintain the ordered property of the alloy but require higher activation and migration energies, so the 1NNNJ and 1TNNJ should be replaced by straight [1 0 0] six nearest-neighbor cyclic jumps (S[1 0 0]6NNCJ) or bent [1 0 0] six nearest-neighbor cyclic jumps (B[1 0 0]6NNCJ) and [1 1 0] six nearest-neighbor cyclic jumps ([1 1 0]6NNCJ), respectively. Although the migrations of Mo and Ta interstitial atoms need much lower energy than Mo and Ta mono-vacancies, they are not main migration mechanisms due to difficult to form in the alloy.

Thermal dynamics properties of bcc Mo nanofilm from MD simulation

Using molecular dynamics simulation with the modified analytic embedded-atom method (MAEAM), we calculated Gibbs free energy and surface free energy of bcc Mo with high melting temperature Tf, and further obtained the Gibbs free energy of its nanofilms. Based on the Gibbs free energy of nanofilms, we investigated the heat capacity of molybdenum nanofilms at constant pressure or at constant volume. The analysis reveals that the molar heat capacity of bulk sample is lower than that of the nanofilms, and the difference increases with the decrease of the film thickness. It is also observed that such size effect of Mo nanofilm is not really significant until the thickness is less than about 15—20nm. It is the surface atoms that determine the size effect on the thermodynamic properties of nanofilms. The difference between CV and CP of nanofilms is firstly analysed quantitatively and the calculated result for CV/CP varies linearly with T/Tf and relates directly to film thickness.

Atomistic simulation of the self‐diffusion in Mg (001) surface

AbstractBoth the formation energies and the intra‐ and inter‐layer diffuse activation energies of a vacancy in the first six lattice planes of Mg (001) surface have been calculated by combining the modified analytical embedded‐atom method (MAEAM) with molecular dynamics (MD). The results show that the effect of the surface on the formation and migration of the vacancy is only down to the third‐layer. It is easer for a single vacancy to form and to migrate in the first layer. Furthermore, the vacancy in the second layer is favorable to migrate to the first layer. This is in agreement with the experimental results that the first layer has the highest concentration of the vacancy. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Properties of mono-vacancy in L1 2-type Ni 3Al ordered alloy

The relaxed structures and the formation and migration energies of the mono-vacancy in L1 2-type Ni 3Al ordered alloy have been investigated by combining the modified analytical embedded-atom method (MAEAM) with molecular dynamics (MD) simulation. The movements of the atoms in the vicinity of the mono-vacancy are toward the vacancy, except for the second-nearest-neighbor Al atoms and the fifth-nearest-neighbor Ni atoms around an Al vacancy and the third-nearest-neighbor Al atoms and the fourth-nearest-neighbor Ni atoms around a Ni vacancy that move outward from the vacancy. Furthermore, each of the atoms in the vicinity of either an Al or a Ni vacancy moves approximately along a line connected between the atom and the vacancy. From energy minimization, it is easy for a Ni vacancy to form and to migrate in one nearest-neighbor jump.

MAEAM investigation of the structural stability and theoretical strength of Fe crystals under uniaxial loading

AbstractThe structural stability and theoretical strength of BCC crystal Fe under uniaxial loading have been investigated with the modified analytic embedded‐atom method (MAEAM). Even if an orthorhombic path is applied, the deformation is spontaneous along the tetragonal path till Milstein modified Born criterion B22‐B23>0 is violated at λ1=0.9064 in the compressive region. The branched orthogonal path with lower compressive stress σ1 and energy E is preferred over the conventional tetragonal Bain path. A stress‐free FCC phase with the local maximum energy of ‐4.2186eV appearing either in compressive region (orthorhombic path) at λ1=0.8923 or in tensile region (tetragonal path) at λ1=1.2619 is unstable and would slip spontaneously into its near neighbor stress‐free mBCT phase with the local minimum energy of ‐4.2270eV. The initial BCC phase with the lowest energy of ‐4.280eV is the most stable in correspondence with the actual behavior of Fe. Furthermore, the stable region ranges from ‐79.7eV/nm3 to 30.6eV/nm3 in the theoretical strength or from 0.9064 to 1.1788 in the stretch λ1 correspondingly. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)