Modified Analytical Embedded Atom Method Research Articles

Computer simulation study of self-diffusion in Pd(1 1 1) surface

Both the formation energies and the intra- and inter-layer activation energies of self-diffusion of a single vacancy in the first five planes of Pd(1 1 1) surface have been investigated by means of molecular dynamics (MD) in conjunction with the semi-empirical many-body potential of the modified analytical embedded-atom method (MAEAM). The results show that the effect of the surface on the vacancy is only down to the fourth layer. It is easier 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.

Calculation of phonon spectrum for noble metals by modified analytic embedded atom method (MAEAM)

In the harmonic approximation, the atomic force constants are derived and the phonon dispersion curves along four major symmetry directions [00ζ], [0ζζ], [ζζζ] and [0ζ1] (or Δ, Σ, Λ and Z in group-theory notation) are calculated for four noble metals Cu, Ag, Au and Pt by combining the modified analytic embedded atom method (MAEAM) with the theory of lattice dynamics. A good agreement between calculations and measurements, especially for lower frequencies, shows that the MAEAM provides a reasonable description of lattice dynamics in noble metals.

Atomistic simulation of point defects in L1 2-type Au 3Cu ordered alloy

The properties of L1 2-type Au 3Cu ordered alloy and the structure of vacancies and anti-site defects are investigated by molecular dynamics (MD) simulations. The modified analytical embedded-atom method (MAEAM) is used to describe the energies and interatomic interactions. Energy minimization predicts that the anti-site defect is easier to form than a mono-vacancy. For the di-vacancy, both Au–Au and Au–Cu di-vacancies are stable configurations. For migration of mono-vacancy, one nearest-neighbor jump of an Au vacancy and six nearest-neighbors cyclic jumps of a Cu vacancy are favorable.

Self-diffusion of Ni in B2 type intermetallic compound NiAl

Combining molecular dynamic (MD) simulation with modified analytic embedded-atom method (MAEAM) potential, the formation, migration and activation energies of Ni self-diffusion in intermetallic compound NiAl have been calculated for five diffusion mechanisms, NNN jump, [1 1 0] 6JC, straight [1 0 0] 6JC, bent [1 0 0] 6JC and triple-defect diffusion. The results show that the Ni self-diffusion is dominated by the triple-defect diffusion mechanism since it requires essentially the lowest migration or activation energy ( Q = 2.769 eV) in the five diffusion mechanisms. This is consistent with the conclusion of Frank et al.

Atomistic study of self-diffusion in Cu–Ag immiscible alloy system

Combining molecular dynamic (MD) simulation with modified analytic embedded-atom method (MAEAM) potential, the formation, migration and activation energies have been calculated for four-kind migrations of Cu vacancy and three-kind migrations of Ag vacancy in Cu–Ag immiscible alloy system. The equilibrium concentration of Cu vacancies is greater than that of Ag vacancies owing to the formation energy of Cu vacancy (1.012 eV) is lower than that of Ag vacancy (1.169 eV). Comparing the migration or activation energy needed for four-kind migrations of Cu vacancy and three-kind migrations of Ag vacancy show that the favorable migration mechanism is the nearest-neighbor (NN) jump for Cu vacancy, while the straight [0 1 0] six-jump cycle (6JC) for Ag vacancy. Furthermore, the activation energy of the NN jump of Cu vacancy (2.164 eV) is lower than that of straight [0 1 0] 6JC of Ag vacancy (2.404 eV) also show that the former is more favorable. We conclude accordingly that the primary migration mechanism is the NN jump of an abundance of Cu vacancies.

Anharmonic effects on Be(0 0 0 1): A molecular dynamics study

Using molecular dynamics simulations and a modified analytic embedded atom method (MAEAM), the anharmonic effects of Be(0 0 0 1) surface have been studied in the temperature range from 0 K to 1400 K. The temperature dependence of the interlayer separation, mean square vibrational displacement, phonon frequencies and phonon line width, and layer structure factor are calculated. The obtained results for temperature dependence of interlayer separation and mean square displacement show that the anharmonic effects are small in the temperature range from 0 K to 1100 K. The calculated layer order parameters indicate that Be(0 0 0 1) surface loses its long-range translational order, but do not premelt up to 50 K below the bulk melting point. The surface disordering may result from strongly contracted c/ a ratio of Be.

The properties and structures of the mono- and the di- vacancy in Cu crystal

The structures and energies of formation and migration of the mono- and di-vacancy in Cu crystal have been described and calculated with modified analytical embedded atom method (MAEAM). The lattice relaxation is considered with molecular dynamics (MD) method at T=0 K. The results show the FN di-vacancy is the most stable and likely occurs in practice from the energy minimization. Compared with the mono-vacancy, the formation energy of the FN di-vacancy is higher than that of a mono-vacancy, but lower than that of two isolated mono-vacancy. The preferred migration mechanism of the FN di-vacancy is multi-jump of either vacancy (rotating the di-vacancy). The calculated migration energy of the FN di-vacancy is lower than that of a mono-vacancy, so the FN di-vacancy is easier to migrate. All of the calculated results are in good agreement with the experimental values.

Energy calculation of (0 1 1) twist grain boundary in noble metals

With modified analytical embedded atom method (MAEAM), the energy of (0 1 1) twist grain boundary (GB) has been calculated for three noble metals Cu, Ag and Au. The results show that the unrelaxed energy keeps almost constant with twist angle θ except several cusps at low Σ boundaries. The GB energies drop significantly after expansion perpendicular to the boundary. In-boundary translation results in a periodic energy variation and the rectangular period is 1/ Σ of their own CSL smallest unit cell. Three specific positions, the corners or centre of the periodic rectangle, or the midpoints of the sides, are preferable in GB translation.

Energy calculation for symmetrical tilt grain boundaries in iron

Abstract An atomic study of [0 0 1] symmetrical tilt grain boundary (STGB) in iron has been made with modified analytical embedded atom method (MAEAM). The energies of two rigid-body crystals joined together directly are unrealistically high due to very short distance between atoms near grain boundary (GB) plane in either crystal. For each of 27 (h k 0) GB planes, a relative slide between grains could result in a decrease in GB energy and a minimum value could be obtained at specific translation distance Lmin/L(h k 0). Three lowest minimum-energies are corresponding to (3 1 0), (5 3 0) and (5 1 0) boundary successively, from minimization of GB energy, these boundaries should be preferable in (h k 0) boundaries. In addition, the minimum energy increases with increasing ∑, but decreases with increasing interplanar spacing.

Atomic-scale calculation of energies of Cu (001) twist boundaries

Unrelaxed energies for Cu (001) twist grain boundaries (GBs) are calculated using a Modified Analytical Embedded Atom Method (MAEAM). The results show that, except zero energy at 0 degrees (perfect crystal), a small cusp exists at a twist angle of 36.87 degrees corresponding to Σ = 5, which agrees with experimental results. For other misorientations, the GB energies keep almost constant even at a twist angle as small as 1.94 degrees. Homogeneous expansion and the expansion perpendicular to the GB plane result in obvious decrease of energy, especially the latter.

Atomic-scale calculation of interface energy for Ag/Ni

The energies of (0 0 1)Ag/(1 1 1)Ni, (0 1 1)Ag/(1 1 1)Ni and (1 1 1)Ag/(1 1 1)Ni twist boundaries have been calculated with modified analytical embedded atom method (MAEAM). The results show that the interface energies corresponding to (1 1 1)Ag/(1 1 1)Ni, (0 0 1)Ag/(1 1 1)Ni and (0 1 1)Ag/(1 1 1)Ni increase successively and three lowest energies corresponding to twist angles θ = 2.10°, 15° and 28.93° for (1 1 1)Ag/(1 1 1)Ni, (0 0 1)Ag/(1 1 1)Ni and (0 1 1)Ag/(1 1 1)Ni are 272, 743.3 and 1094.3 mJ/m 2, respectively. The epitaxial growth of Ag film on (1 1 1)Ni substrate driven solely by minimization of interface energy should result in the predominance of (1 1 1) grains, especially twist angle θ = 2.10°.

Energy analysis for (1 1 1) twist grain boundary in noble metals

With modified analytical embedded atom method (MAEAM), the energies of twist grain boundaries (GBs) have been calculated for three noble metals, Cu, Ag and Au with the same FCC structure. The results are similar for all the three metals: (1) the unrelaxed energies keep almost constant with twist angles θ; (2) after expansion perpendicular to the boundary, GB energies drop significantly to less than one-third of their surface energies respectively; (3) in-boundary translation results in periodic energy variation with the period of L Σ / Σ, but the energy variation is slight.

Calculating the energies for Ag(001) twist boundaries utilizing the modified analytical embedded atom method

AbstractThe unrelaxed energies for Ag(001) twist grain boundaries (GBs) have been calculated using the modified analytical embedded atom method (MAEAM). The results show that, besides zero energy in a perfect crystal (corresponding to the twist angle 0°), the second smallest GB energy corresponds to the twist angle 36.87°. This is consistent with the experimental results. For other twist angles, the GB energies remain nearly constant even for a twist angle as small as 1.94°. Translation parallel to the boundary plane could result in a periodic change in GB energy. Copyright © 2004 John Wiley & Sons, Ltd.

Temperature dependence of atomic relaxation and vibrations for the vicinal Ni(9 7 7) surface: a molecular dynamics study

Using molecular dynamics simulations and a modified analytic embedded-atom method (MAEAM), the relaxations and vibrations of Ni(9 7 7) surface are studied in the temperature range of 100–1500 K, The calculated results for the temperature dependence of phonon frequencies, line-width and the mean square amplitude show that the anharmonic effects are small for temperatures up to 900 K. The calculated interlayer separation for the first and second surface decreases, and the distance along the x direction increases between the topmost and second surface, with increasing temperature. In addition, the calculated layer structure factor indicates that the Ni(9 7 7) surface is well ordered and does not premelt up to a temperature of 1700 K.

Self-diffusion of Al and Pb atoms in Al–Pb immiscible alloy system

Al–Pb binary alloy system exhibits a positive heat mixing that precludes intermixing by conventional techniques, it is possible to achieve solid state alloying between these two immiscible elements in nanostructures by mechanical alloying (MA). The studies of detailed atomistic diffusion process of dynamic movement for Al and Pb were carried out by computer simulation, in conjunction with modified analytic embedded atom method (MAEAM). Computational results have clarified that the nearest-neighbor diffusion path is the dominant jump vector for both Al and Pb atom diffusion. The migration energies along this path have been estimated to be 0.35083 and 0.10538 eV, respectively. The self-diffusion activation energies for Al and Pb along NN jump are 0.99557 and 0.85919 eV, respectively. The calculated results reveal that Pb atom diffuses much faster than Al atom does, which concluded that Pb atom is the diffusive species in Al–Pb immiscible alloy system. The calculated self-diffusion activation energies for nano-sized Al and Pb grains are 0.83192 and 0.70455 eV, respectively. They are lower than that for normal sized Al and Pb grains, which facilitates the atomic diffusion and alloying during MA process in Al–Pb immiscible alloy system.

Theoretical analysis of interface energy for unrelaxed Ag(001)/Ni(001) twist interface boundaries with MAEAM

AbstractInterfacial energies for unrelaxed Ag(001)/Ni(001) twist interface boundaries with near‐coincidence site lattices have been calculated using the modified analytical embedded atom method (MAEAM). The results show that the interfacial energies are strongly dependent on the azimuthal misorientation θ. The first six lowest interfacial energies correspond to θ = 10.3, 15.26, 6.34, 37.88, 26.57 and 12.34°, which correspond to the coincidence interface boundaries of Σ = 25/20, 13/10, 41/32, 13/10, 5/4 and 37/29, respectively. Considering only the interfacial energy, we can predict that these interface boundaries are successively preferable for epitaxial growth of silver film on (001)‐oriented nickel substrate. Copyright © 2004 John Wiley & Sons, Ltd.

Analytic embedded-atom method approach to studying the surface segregation of Al–Mg alloys

In the present paper, the modified analytic embedded-atom method (MAEAM) many-body potentials are provided for fcc and hcp elements. The segregation energies of Mg in Al host are calculated with the MAEAM potentials. The composition depth profiles of Al–Mg alloys are obtained with Monte Carlo simulation method based on grand canonical ensemble. It is found that Mg segregates strongly to the surface layers at 600 K and the composition near the surface is monotonic to the bulk one. The simulation results are reasonable agreement with other experimental and theoretical data.

Atomistic simulation of the segregation profiles in Mo–Re random alloys

Simple modified analytic embedded atom method (MAEAM) many-body potentials are constructed for bcc molybdenum and hcp rhenium metal in the present paper. Using the MAEAM and analytic alloy potentials, the segregation profiles for (1 0 0) surface in Mo–Re bcc-type random alloys were studied with Monte Carlo simulation technology. The simulation results show that the topmost surface is almost completely enriched with molybdenum, the subsurface is depleted of molybdenum, and the molybdenum concentration oscillates toward the bulk value. The simulation results are in good agreement with available low-energy electron diffraction and low-energy ion scattering experiment data, and the calculations from tight-binding Ising model.

Modified analytic EAM potentials for the binary immiscible alloy systems

Modified analytic embedded atom method (MAEAM) type potentials have been constructed for seven binary immiscible alloy systems: Al–Pb, Ag–Ni, Fe–Cu, Ag–Cu, Cu–Ta, Cu–W and Cu–Co. The potentials are fitted to the lattice constant, cohesive energy, unrelaxed monovacancy formation energy and elastic constants for only pure metals which consist the immiscible alloy systems. In order to test the reliability of the constructed MAEAM potentials, formation enthalpies of disordered alloys for those seven binary immiscible alloy systems have been calculated. The calculated results are in general agreement with the experimental data available and those theoretical results calculated by other authors. As only very limited experimental information is available for alloy properties in immiscible alloy systems, the MAEAM is demonstrated to be a reasonable method to construct the interatomic potentials for immiscible alloy systems because only the properties of pure elements are needed in calculation.

Surface segregation of Al–Pb immiscible alloy system with Monte Carlo simulation

Modified analytic embedded atom method (MAEAM) potentials for pure Al, Pb and Al–Pb alloy have been constructed using physical quantities only for pure Al and Pb. Application of these potentials to the simulation of segregation in the (100) surface of Al 50Pb 50 alloy shows that Pb segregates to the topmost surface layer and depletes strongly on the subsurface layer. Pb concentration has a damped oscillation in the whole composition range.