Vibrational properties of vacancy in Au using modified embedded atom method potentials

Much improved result for lattice dynamics of Au is obtained with the use of modified embedded atom method (MEAM) potentials compared to the earlier embedded atom method (EAM) potentials. The MEAM potentials along with experimental phonons are utilised to calculate local spectra of neighbours of vacancy using Green's function method. The local spectrum of first neighbour of vacancy shows general loss of modes at lower frequencies with a resonance like sharp peak near the top end of the spectrum. The spectrum of second neighbour shows small changes from the host spectra except a pronounced dip in the middle. In accordance with the obtained features of local spectra of neighbours the calculated mean-square displacements are lower for both first and second neighbours as compared to that of host atoms. The calculated formation entropy is in reasonable agreement with other calculations and available experimental values.     

Calculation of the surface energy of bcc transition metals by using the second nearest-neighbor modified embedded atom method

The surface energies for 24 surfaces of all bcc transition metals Fe, Cr, Mo, W, V, Nb and Ta have been calculated by using the second nearest-neighbor modified embedded atom method. The results show that, for all bcc transition metals, the order among three low-index surface energies E_(1 1 0) < E_(1 0 0) < E_(1 1 1) is in agreement with experimental results and E_(1 1 0) is also the lowest surface energy for various surfaces. So that from surface energy minimization, the (1 1 0) texture should be favorable in the bcc films. This is also consistent with experimental results. The surface energy for the other surfaces increases linearly with increasing angle between the surfaces (h k l) and (1 1 0). Therefore, a deviation of a surface orientation from (1 1 0) can be used to estimate the relative values of the surface energy.     

Point-defect properties in HCP rare earth metals with analytic modified embedded atom potentials

The analytic embedded atom method (EAM) type many-body potentials of hcp rare earth metals (Dy, Er, Gd, Ho, Nd, Pr, and Tb) have been constructed. The hcp lattice is shown to be energetically most stable when compared with the fcc and bcc structure, and the hcp lattice with ideal c/a. The mechanical stability of the corresponding hcp lattice with respect to large change of density and c/a ratio is examined. The phonon spectra, stacking fault and surface energy are calculated. The activation energy for vacancy diffusion in these metals has been calculated and the most possible diffusion paths are predicted. Finally, the self-interstitial atom (SIA) formation energy and volume have been evaluated for eight possible sites. This calculation suggests that the crowdion and basal split are the most stable configurations. The SIA formation energy increases linearly with the increase of the melting temperature.Received: 26 March 2003, Published online: 9 September 2003PACS: 34.20.Cf Interatomic potentials and forces - 66.30.Fq Self-diffusion in metals, semimetals, and alloys - 61.72.Ji Point defects (vacancies, interstitials, color centers, etc.) and defect clusters - 61.72.Bb Theories and models of crystal defects     

Improvement of modified analytic embedded atom method potentials for noble metals and Cu

The modified analytic embedded atom model (EAM) potentials considering farther neighbor atoms are improved for the noble metals (Ag, Au, Pt, Pd, Rh) and Cu. We not only adopt an end processing function and an enhanced smooth continuous condition for the pair potential, but also adjust the model parameters of multi-body potential by fitting a cohesive energy, a mono-vacancy formation energy, the Rose equation curve for the cohesive energy as a function of lattice parameter, a structure energy difference, elastic parameters and an equilibrium condition of crystal. The calculation results of structure energy differences misfit the experiment data for the noble metals and Cu in the unimproved EAM, because anyone of these differences have not been considered in the calculation of its model parameters. After the modification, the model showed better simulation results for the noble metals and Cu.     

Vibrational properties of straight dislocations in bcc and fcc metals within the harmonic approximation

We calculate the vibrational spectra of straight screw and edge dislocations in several body-centered cubic (bcc) (Mo and Fe) and face-centered cubic (fcc) (Cu and Al) metals within the harmonic approximation. We take advantage of the translational symmetry of straight dislocations to efficiently calculate their phonon eigenstates in the harmonic limit. This allows us to calculate the low-temperature contribution of straight screw and edge dislocations to the heat capacity of each respective metal, and show that the dominant temperature dependence below 5 K is linear. Comparison with heat capacity measurements of heavily cold-worked Cu reveals very good agreement with our calculations. At higher temperatures, the contribution from the non-linear terms becomes significant. As a result, maxima in the straight dislocation heat capacities are observed in the temperature range from 9% to 16% of the Debye temperature. We investigate the appearance of localized and resonance peaks in the vibrational spectra induced by dislocations, and study in detail their spatial spread around the dislocation cores by projecting vibrational eigenstates onto individual atoms. We study the deviation of these atomic-level vibrational free energies from that of the perfect crystal as a function of distance to the dislocation cores, and establish that, similar to the dislocation energy, the vibrational free energy of an isolated dislocation behaves logarithmically in the long-range limit. Finally, we obtain vibrational spectra for propagating waves along the dislocation line and find that the dispersion for these waves is consistent with the notion of kink formation and motion for screw dislocations.     

Indium-defect interactions in FCC and BCC metals studied using the modified embedded atom method

With the aim of developing a transferable potential set capable of predicting defect formation, defect association, and diffusion properties in a wide range of intermetallic compounds, the present study was undertaken to test parameterization strategies for determining empirical pair-wise interaction parameters in the modified embedded atom method (MEAM) developed by Baskes and coworkers. This report focuses on indium-solute and indium-vacancy interactions in FCC and BCC metals, for which a large set of experimental data obtained from perturbed angular correlation measurements is available for comparison. Simulation results were found to be in good agreement with experimental values after model parameters had been adjusted to reproduce as best as possible the following two sets of quantities: (1) lattice parameters, formation enthalpies, and bulk moduli of hypothetical equiatomic compounds with the NaCl crystal structure determined using density functional theory and (2) dilute solution enthalpies in metals as predicted by Miedema’s semi-empirical model.     

Calculation of the surface energy of hcp metals by using the modified embedded atom method

With MEAM, the surface energies of three kinds of representative surfaces, (h 0 l), (h h l) and (h k 0) belong to [0 1 0], [] and [0 0 1] crystal band, respectively, have been calculated for 13 closed-packed hexagonal (hcp) metals Co, Dy, Er, Gd, Ho, Mg, Nd, Pr, Re, Sc, Tb, Tl and Zr. For all 13 hcp metals, the basal plane (0 0 1) has the minimum surface energy. So from surface energy minimization, the (0 0 1) texture should be favored in the hcp films, this is consistent with the experimental results. The fact that the short termination corresponds to much lower surface energy than long one implies the former is more stable for those surfaces having two possible terminations. Such as the prism plane (1 0 0), only the short termination was observed in experiment.     

Interatomic potentials in transition metals

The different roles played by the valence s and d electrons in determining the bulk properties of pure transition metals is described. In the light of this the expected behaviour of the inert gas-metal and metal-metal interatomic potentials is discussed.     

Peierls potential for crowdions in the bcc transition metals

We present the first derivation of the analytic expression for the Peierls-Nabarro potential for crowdion migration using the double sine-Gordon model. The analysis is guided by the group-specific trend in the shapes of the periodic lattice potentials calculated for the body-centered-cubic transition metals in groups 5B and 6B of the periodic table. We combine density-functional calculations of the crowdion's profile and environment with an extended version of the analytical Frenkel-Kontorova model, and determine the effective potential experienced by the defect's center of mass. This reveals important underlying differences between the metals in these groups, which are inaccessible to either the numerical or analytical approaches alone, and accounts for the previously unexplained significantly higher crowdion migration temperatures observed in the metals of group 6B relative to those of group 5B.     

The non-Arrhenius migration of interstitial defects in bcc transition metals

Thermally activated migration of defects drives microstructural evolution of materials under irradiation. In the case of vacancies, the activation energy for migration is many times the absolute temperature, and the dependence of the diffusion coefficient on temperature is well approximated by the Arrhenius law. On the other hand the activation energy for the migration of self-interstitial defects, and particularly self-interstitial atom clusters, is very low. In this case a trajectory of a defect performing Brownian motion at or above room temperature does not follow the Arrhenius-like pattern of migration involving infrequent hops separated by the relatively long intervals of time during which a defect resides at a certain point in the crystal lattice. This article reviews recent atomistic simulations of migration of individual interstitial defects, as well as clusters of interstitial defects, and rationalizes the results of simulations on the basis of solutions of the multistring Frenkel–Kontorova model. The treatment developed in the paper shows that the origin of the non-Arrhenius migration of interstitial defects and interstitial defect clusters is associated with the interaction between a defect and the classical field of thermal phonons. To cite this article: S.L. Dudarev, C. R. Physique 9 (2008).     

Treatment of bcc transition metals on a modified CGW model

The vibrational spectrum and specific heat of three bcc transition metals -iron, chromium and tungsten are computed on the basis of modified Clark-Gazis-Wallis angular force model which considers volume forces of Krebs' nature. The calculations are made using the Blackman's root sampling technique for a discrete subdivision in wave-vector space. The calculated lattice specific heats and the effective Debye temperatures are compared with the available experimental data. The results show a reasonably satisfactory agreement with the experimental observations.The authors are highly thankful to Dr.Jyoti Prakash, Dr. S.Chandra for helpful discussions. One of them (H. L. K.) is thankful to C. S. I. R. India for the award of J. R. F. The computational facilities received from the I. I. T. Kanpur are also acknowledged.     

On the interaction between a vacancy and self-interstitial atom clusters in metals

Atomic-scale computer simulation is used to study the interaction between a vacancy and a cluster of self-interstitial atoms in metals with hcp, fcc and bcc crystal structure: α-zirconium, copper and α-iron. Effects of cluster size, atomic structure, dislocation nature of the cluster side and temperature are investigated. A vacancy can recombine with any interstitial in small clusters and this does not affect cluster mobility. With increasing sizes clusters develop dislocation character and their interaction with vacancies depends on whether the cluster sides dissociate into partial dislocations. A vacancy recombines only on undissociated sides and corners created with undissociated segments. Vacancies inside the cluster perimeter do not recombine but restrict cluster mobility. Temperature enhances recombination by either increasing the number of recombination sites or assisting vacancy diffusion towards such sites. The results are discussed with relevance to differences in irradiation microstructure evolution of bcc, fcc and hcp metals and higher level theoretical modelling techniques.     

Pressure-volume calculation in bcc metals using Born stability criteria

A simple analytical two-body potential φ(r) = −Ar ⁻ⁿ + B exp(−pr ^m) is considered for P-V calculations in bcc metals using Born stability criteria. It is shown that the stability of bcc metals can be expressed uniquely as a function of a parameter q (discussed in the text). The P-V calculations are done in ten bcc metals. The calculations are compared with the experimental data of shock-wave measurements and also with other potential available. It is found out that the present potential is better than the other two-body potentials in case of bcc metals. Further, the calculations done for TOEC and the first pressure derivative of SOEC are found in good agreement with the reported results.     

Liquid/vapor surface tension of metals: embedded atom method with charge gradient corrections

Molecular dynamics simulations for three embedded atom method (EAM) function sets are used to determine the liquid/vapor surface tension gamma for Al, Ni, Cu, Ag, and Au. The three EAM models differ in both the functional forms employed and the fitting procedure used. All the EAM potentials underestimate gamma but one of the models performs consistently better than the others. We show that including a correction to the local charge density associated with gradients in the density together with exploiting the invariance of the EAM potentials to appropriate transformations in the charge density can lead to improved values for gamma, as well as for solid free surface energies, within existing EAM function sets.     

Multilayer relaxation of fcc metals (001) surface: A modified embedded atom method study

The (001) surface multilayer relaxation results calculated by the modified embedded atom method (MEAM) show that Ni, Al, Rh and Ir (001) surface are ‘anomalous’ outward relaxation, while Cu, Ag, Au, Pd, Pt and Pb (001) surface are inward relaxation. For the inward relaxation metals, the relaxation between the first two layers increase for the 3d, 4d and 5d metals at the same column in the periodic table, successively. The expansion (contraction) between the first two layers at fcc (001) surfaces is accompanied by the decrease (increase) in the electronic density at the lattice of the first two layers. The surface energies results show that the surface energies decrease for all fcc (001) surfaces due to relaxation, whereas the changes not more than 5%.