Embedded Atom Method Calculations Research Articles

Diffusion and adsorption of Au and Pt adatoms on ideal and missing row reconstructed surfaces of Au(110): DFT and EAM calculations

Density-functional theory (DFT) and embedded atom method (EAM) are used to study the adsorption and diffusion on unreconstructed (1 × 1) and reconstructed (1 × 2), (1 × 3) and (1 × 4) surfaces for homogenous Au/Au(110) and heterogeneous Pt/Au(110) systems. Adsorption energies show a strong binding for Pt than Au on all considered geometries. Additionally, adsorption on the (111) microfacet of the (1 × 2), (1 × 3) and (1 × 4) geometries is investigated. Surprisingly the adsorption of Pt on the top hcp sites of the (111) microfacet of the (1 × 2), (1 × 3) and (1 × 4) geometries leads to the exchange phenomenon. The diffusion via hopping and metastable walk is investigated for both the homo and heterogeneous systems. The hopping diffusion barrier show a slight dependence on the reconstruction order and the diffusion is found to be more costly on the missing row reconstructed surface than the unreconstructed surfaces. The potential energy profile for the diffusion via metastable walk mechanism on the (1 × 2) missing row reconstructed geometry indicates that the metastable walk diffusion is more favorable to homogeneous system than to heterogeneous system.The results of this paper are important to understand the properties of metallic reconstructed surfaces.

Chemical ordering beyond the superstructure in long-range ordered systems

To describe chemical ordering in solid solutions systems Warren–Cowley short-range parameters are ordinarily used. However, they are not directly suited for application to long-range ordered systems, as they do not converge to zero for large separations. In this paper, the theory is generalized to long-range ordered systems and chemical short-range order beyond the superstructure arrangements is discussed quantitatively on the example of a non-stoichiometric B2-ordered intermetallic alloy. Parameters of interatomic potentials are taken from an embedded atom method calculations and the degree of order is simulated by the Monte Carlo method. Both on-lattice and off-lattice methods, where the latter allows individual atoms to deviate from their regular lattice sites, were used, and the resulting effects are discussed.

Ab initiostudy of edge smoothing, atom attraction, and downward funneling in Ag/Ag(100)

The results of density-functional theory (DFT) calculations of the energy barriers for three low-barrier relaxation processes in Ag/Ag(100) growth---edge-zipping, atom attraction, and downward funneling---are presented and compared with embedded atom method (EAM) calculations. In general, we find good agreement between the DFT values for these processes and the values assumed in recent simulations of low-temperature Ag/Ag(100) growth [Shim and Amar, Phys. Rev. B 81, 045416 (2010)]. We also find reasonable agreement between our DFT results and the results of EAM calculations, although in a few specific cases there is a noticeable disagreement. In order to investigate the effects of long-range interactions, we have also carried out additional calculations for more complex configurations. While our EAM results indicate that long-range interactions such as ``pinning'' can significantly enhance the energy barriers for edge-zipping and atom attraction, these effects can be significantly weaker in our DFT calculations due to the redistribution of the electron density.

Hydrogen and self-interstitial interactions with edge dislocations in Ni: atomistic and elasticity comparisons

The interactions of hydrogen interstitial and self-interstitial with dissociated Shockley partial dislocations in fcc Ni were studied with embedded atom method calculations and the results were compared with those obtained from elasticity solutions. Such cross-correlations are important for efficient and accurate inclusion of the point defects into the dislocation dynamics simulations that are usually based on elasticity theories. The simulations were carried out using a dipole dislocation cell having periodic boundaries. The size effect, tetragonal distortions and the modulus effect were considered in the elasticity analysis. The results indicate that the elasticity solutions compare well with the atomistic results for the regions outside the Shockley partial cores, even though the interaction energies differed by approximately one order of magnitude for these two types of point defects. The range where the elasticity description of the interstitial–dislocation interaction breaks down was identified. In the self-interstitial case, the core reaction with the interstitial was observed, resulting in a larger core interaction range.

HRTEM of dislocation cores and thin‐foil effects in metals and intermetallic compounds

Examples of the observation and analysis of dislocation cores and dislocation fine structure in metals and intermetallics using high resolution transmission electron microscopy are discussed. Specific examples include the 60 degrees dislocations in aluminum, a011 edge dislocations in NiAl, and screw dislocations in Ni3Al. The effect of the thin TEM foils on the structure and imaging of these dislocations is discussed in light of embedded atom method calculations for several configurations and coupled with image simulations. Some generalizations based on these calculations are discussed. These analyses enables determination of the spreading or decomposition of the edge component of the cores, both in and out of the glide plane, which can have significant implications for the modeling of macroscopic behavior.

Calculations of diffusion and diffusion-limited processes in Ni 3Al using accelerated molecular dynamics

We present a systematic microscopic approach to diffusion and diffusion-limited processes in Ni 3Al. These processes have been identified as controlling the deformation of the material under specific circumstances. The embedded atom method calculations are done using kinetic Monte Carlo combined with the Dimer method of finding saddlepoints. We compute the tracer diffusivities as functions of composition and temperature. The comparison with available experiments is good. We find that at temperatures below about 1000 K, the diffusivity is a sharp function of composition, showing a pronounced dip on the Ni-rich side at 76 at.% Ni. This agrees well with experiment, except that the experiments show this structure setting in a temperatures below about 1300 K. We show that the structure arises from the composition dependence of both the vacancy formation energy and pre-exponential of the diffusivity. We also compute the mobility of an anti-phase boundary perpendicular to its plane, and conclude that vacancy-assistance is very plausible. We conclude that the kMC + Dimer method works well for these problems above 700 K but less effectively below, owing to the presence of short-range, low-energy hops that tend to localize the vacancy and lower the efficiency of the calculation.

Growth mechanism and structure of nickel deposited on Ag(0 0 1)

The initial growth stages of nickel deposited on Ag(0 0 1) have been investigated by LEIS, XPS, STM and XPD. Embedded atom method (EAM) calculations were performed to obtain information about the dynamics of Ni adatoms on the Ag(0 0 1) surface. Amounts of Ni ranging from submonolayers up to 4 monolayers were deposited on the Ag(0 0 1) surface under UHV conditions at room temperature. The LEIS spectra indicate that the Ni islands are almost completely covered by silver. In agreement with previous studies, STM images show that Ni grows on Ag(0 0 1) forming three dimensional islands. A significant fraction of islands with a thickness of 2–3 atomic layers is present even at coverages as low as 0.1 ML. The observation of islands protruding from the surface with heights below that expected for one atomic layer of Ni covered by one atomic layer of Ag suggests that Ni atoms are incorporated in the outermost layer of the substrate. From the EAM calculations the energy barrier for incorporation of a nickel atom into the outermost layer was found to be 0.19 eV, substantially lower than that for bridge site hopping over the substrate (0.61 eV). On the basis of the EAM calculations, a diffusion mechanism for Ni atoms incorporated within the first layer of the surface is proposed to explain the growth of Ni islands. As far as the geometric structure of the Ni film is concerned, the XPD curves indicate that at a coverage of ≈0.3 ML, the structure of the film is distorted with respect to the fcc lattice. The displacement of the forward scattering peaks towards higher polar angles is consistent with the formation of pseudomorphic Ni islands (i.e. with the same in-plane lattice parameter of the substrate). The XPD results lead to the conclusion that pseudomorphic Ni clusters coexist with undistorted fcc Ni islands. Even at the highest coverage studied here, a fraction of the islands maintains a strained fcc structure.

First-principles calculations of steering forces in epitaxial growth

Although atoms deposited during epitaxial growth strongly prefer to bind to step bottoms of existing islands, the geometrical proximity of step tops can lead to atoms landing there instead, significantly altering film morphology and contributing to growth instabilities. To shed light on such steering effects, we have mapped out the three-dimensional static potential-energy surface (PES) for Cu atoms approaching a stepped Cu(100) surface using density-functional theory (DFT). Depending on the kinetic energy of incident atoms, surface relaxations may be too sluggish, and we have therefore computed the PES both with and without allowing substrate relaxations. While a comparison with the corresponding embedded-atom-method (EAM) results indicates relatively good agreement, the DFT calculations suggest that the steering effect is slightly weaker than predicted by EAM calculations. These results also support a previous comparison with experiment, which indicated that the overall funneling probability for deposition at a [110] step edge on the Cu(100) surface is close to but slightly lower than that predicted via EAM simulations.

Observations of glide and decomposition of a⟨101⟩ dislocations at high temperatures in Ni-Al single crystals deformed along the hard orientation

Ni-44 at.% Al and Ni-50 at.% Al single crystals were tested in compression in the hard d001 ¢orientation. The dislocation processes and deformation behaviour were studied as a function of temperature, strain and strain rate. A slip transition in NiAl occurs from a⟨111⟩ slip to non-a⟨111⟩ slip at intermediate temperatures. In Ni-50 at.% Al single crystals, only a⟨010⟩ dislocations are observed above the slip transition temperature. In contrast, a a⟨101⟩{101} glide has been observed to control deformation beyond the slip transition temperature in Ni-44 at.% Al. a⟨101⟩ dislocations are observed primarily along both ⟨111⟩ directions in the glide plane. High-resolution transmission electron microscopy observations show that the core of the a⟨101⟩ dislocations along these directions is decomposed into two a⟨010⟩ dislocations, separated by a distance of approximately 2 nm. The temperature window of stability for these a⟨101⟩ dislocations depends upon the strain rate. At a strain rate of 1.4 210−4 s−1, a⟨101⟩ dislocations are observed between 800 and 1000 K. Complete decomposition of a⟨101⟩ dislocations into a⟨010⟩ dislocations occurs beyond 1000 K, leading to a⟨010⟩ climb as the deformation mode at higher temperatures. At lower strain rates, decomposition of a⟨101⟩ dislocations has been observed to occur along the edge orientation at temperatures below 1000 K. Embedded-atom method calculations and experimental results indicate that a⟨101⟩ dislocations have a large Peierls stress at low temperatures. Based on the present microstructural observations and a survey of the literature with respect to vacancy content and diffusion in NiAl, a model is proposed for a⟨101⟩{101} glide in Ni-44 at.% Al, and for the observed yield strength versus temperature behaviour of Ni-Al alloys at intermediate and high temperatures.

A misfit structure in the Co/Pt( [formula omitted]) system studied by scanning tunnelling microscopy and embedded atom method calculations

We have performed scanning tunnelling microscopy (STM) measurements of thin films of Co and CoPt alloys on Pt(1 1 1). In contrast to the interpretation of an earlier low energy electron diffraction investigation by Tsay and Shern [Surf. Sci. 396 (1998) 313] we find that the structure observed upon annealing a Pt(1 1 1) sample with a 2 ML (monolayer, ML) thick film of Co does not consist of a rotated Co film but rather of a CoPt alloy film with hexagonal areas of fcc stacking, single and double stacking faults, delimited by misfit dislocations (Shockley partial dislocations). Comparison of STM images with embedded atom method calculations confirms our model. The structure at the Pt–PtCo interface in our model is similar to that proposed by Henzler [Surf. Sci. 419 (1999) 321].

Models for adatom diffusion on fcc (001) metal surfaces

We present a class of models that describe self diffusion on several fcc(001) metal substrates within a common framework. The models are found to apply well for Cu(001), Ag(001), Au(001), Ni(001) and Pd(001).For each of these metals the models can be used to estimate the activation energy of any diffusion process using a few basic parameters which may be obtained from experiments, ab-initio or semi-empirical calculations. To demonstrate the approach, the parameters of the models are optimized to describe self-diffusion on the (001) surface, by comparing the energy barriers to a full set of barriers obtained from semi-empirical potentials via the embedded atom method (EAM). It is found that these models with at most four parameters,provide a good description of the full landscape of hopping energy barriers on FCC(001) surfaces. The main features of the diffusion processes revealed by EAM calculations are quantitatively reproducible by the models.

Observations and modelling ofa〈011〉 dislocations in NiAl at intermediate temperatures

Abstract Recent experimental evidence indicates that dislocations of the type a〈011〉 are prominent in microstructures following deformation in hard-oriented NiAl at intermediate temperatures (above the brittle-to-ductile transition temperature). The structure of a〈011〉 dislocations has been examined using diffraction-contrast transmission electron microscopy. Evidence has been found for the decomposition of a〈011〉 dislocations into two a〈001〉 dislocations. Analysis using both anisotropic elasticity and the embedded-atom method calculations has revealed that this decomposition process is energetically favourable, even though the net core energy increases upon decomposition. Based on microstructural evidence, additional decomposition occurs by a combination of climb and glide. A continuum-based dislocation model is introduced which incorporates these relevant microstructural features. The predictions of this model are compared with characteristics of deformation of NiAl in the hard orientation.

Embedded atom method calculations of vibrational thermodynamic properties of ordered and disordered Ni3Al

Recent work had suggested that vibrational effects can play a significant role in determining alloy phase equilibria. In order to better understand these effects, we investigate the vibrational properties of disordered and ordered Ni3Al using the embedded atom method and calculate vibrational thermodynamic quantities within the quasi-harmonic approximation. The vibrational entropy is found to be strongly dependent on volume. For fully relaxed structures the dependence on lattice decoration of the vibrational entropy is compared to that suggested by recent experimental results.

Reinvestigation of the surface reconstruction of Cu(001)-(2 × 2)p4g-Pd

Three recent articles [T.D. Pope, M. Vos, H.T. Tang, K. Griffiths, I.V. Mitchell, P.R. Norton, W. Liu, Y.S. Li, I. Stensgaard, E. L˦gsgaard, F. Besenbacher, Surf. Sci. 337 (1995) 79; J. Yao, Y. G. Shen, D.J. O'Connor, B.V. King, Surf. Sci. 359 (1996) 65; P.W. Murray, I. Stensgaard, E. L˦gsgaard, F. Besenbacher, Surf. Sci. 365 (1996) 591] have attempted to determine the surface composition and structure of the (2 × 2)p4g phase induced by one monolayer (ML) Pd deposition at room temperature on a Cu(001) surface. In order to remove inconsistencies arising from previous studies, the 1 ML Pd/Cu(001) surface has been reinvestigated using low-energy ion scattering (LEIS), low-energy electron diffraction (LEED), three-dimensional (3D) classical scattering simulations and embedded-atom method (EAM) calculations. Using Li + and He + ion scattering with calibration measurements on reference samples of Cu(001) and Pd(001), the surface Pd composition of the 1 ML phase was independently determined to be 53 ± 4% and 51 ± 3%, respectively. The results obtained using K + ion scattering, LEED and computer simulations are consistent with a surface structure which consists of 30% of a clock-rotated (001) Pd phase and 70% of an unreconstructed p(2 × 2) Cu Pd phase. The stability of the (2 × 2)p4g phase has been confirmed by EAM calculations.

A structural study of [formula omitted] surface alloys

The structures formed by one-half and one monolayer (ML) of Pd evaporated onto Cu(100) at 300 K were studied by low energy electron diffraction (LEED), medium energy ion scattering (MEIS), thermal desorption spectroscopy (TDS), and embedded atom method (EAM) calculations. In the half monolayer case, the LEED I( E) curves are consistent with the established c(2 × 2) surface alloy model. The MEIS data, however, suggest that a fraction of the Pd ( ∼ 1 4 ) is in “second layer” sites, in agreement with previous LEIS, TDS and XPS forward scattering measurements. The EAM simulations support the formation of alloy islands, providing a mechanism for the covering of some Pd atoms. As the deposition proceeds, however, this island formation is indicated to occur preferentially over clean copper. In the one monolayer case, a p(2 × 2)-p4g LEED pattern is observed. Analysis of the I( E) curves suggests that this arises from (100) Pd packed above the c(2 × 2) alloy. EAM calculations confirm the stability of this model. Evidence from MEIS and TDS, however, shows that the one monolayer surface as prepared in this work is inhomogeneous. c(2 × 2) and Cu rich surface domains exist in addition to those having the p4g Pd c(2 × 2) PdCu structure.

Energetics of small Pt clusters on Pt(111): Embedded-atom-method calculations and phenomenology.

We have employed the embedded-atom method (EAM) to predict the structures and energetics of clusters containing up to seven Pt atoms adsorbed on the Pt(111) surface. The calculated cluster binding energies depend primarily on the number of (nearest-neighbor) bonds between the adatoms. Clusters with the same number of adatoms divide, according to their binding energies, into subgroups (bond families) of clusters with a common number of bonds. The typical spread of binding energies in these bond families is less than 0.2 eV, while the separation between neighboring families corresponds to a mean bond strength of about 0.7 eV. Thus the most stable clusters assume geometries which maximize the number of bonds. In addition, we propose a scheme for modeling the energetics of metal adatom clusters on close-packed metal surfaces whose physical basis is the coordination dependence of metallic bonds. With a simple three-parameter model, we predict binding energies of over 20 Pt clusters in excellent agreement with the EAM calculations. The scheme provides a convenient way of including many-atom interactions in the energetics of two-dimensional (2D) metallic clusters, and should, therefore, be useful for studying the equilibrium properties of 2D metallic surfaces.

Au overlayer structures on a Ni(110) surface.

The atomic arrangement of Au atoms segregated to the (110) surface of a Ni--0.8 at. % Au alloy was studied with low-energy ion scattering (LEIS) in combination with low-energy electron diffraction (LEED). The LEED results have been published elsewhere [E. G. McRae and R. A. Malic, Surf. Sci. 177, 53 (1986)]. From this LEED work and a preliminary analysis of the present data a model for the atomic structures of Au atoms on the Ni(110) surface has been presented. In the present paper, the LEIS data were analyzed quantitatively by comparison with computer simulations. Most features of the models proposed earlier were confirmed by this analysis. We also used the (static) embedded-atom method (EAM) to calculate the positions of Au atoms on Ni(110) for various coverages. After introducing these positions in the computer simulations of the LEIS data, an even better agreement between experiment and calculation was found. At low coverages of less than 0.5 ML, the Au atoms were found to be located in substitutional Ni sites in the first Ni layer. At a Au coverage of 1.28 ML, the Au atoms are at various heights above the Ni surface, and are hexagonally packed within a 7\ifmmode\times\else\texttimes\fi{}7 unit cell with c(2\ifmmode\times\else\texttimes\fi{}4) subunits. For coverages slightly lower than 1.28 ML several other structures are predicted by our EAM calculations. These structures have indeed been found in scanning tunneling microscopy work. In addition, we discuss the observation of one-dimensional melting of the Au overlayer at a temperature of approximately 700 \ifmmode^\circ\else\textdegree\fi{}C, as observed with LEED and LEIS.

Diffusion barrier for a Ag adatom on Pt(111)

First-principles local density functional (FP-LDF) calculations for a single Ag atom adsorbed on Pt(111) are compared to scanning tunneling microscope (STM) observations of Brune et al. and to embedded atom method (EAM) results of Blandin and Massobrio. The EAM calculations predict a small static diffusion barrier, 0.05 eV which corresponds poorly to the result of the FP-LDF calculation, 0.20 eV. The STM measurements yield a diffusion barrier of 0.16 ± 0.01 eV.

Energetics of Pt adsorption on Pt(111).

First-principles local-density-functional (FP-LDF) and embedded-atom-method (EAM) total energies, for a single Pt atom adsorbed on Pt(111), are compared to each other and to field-ion-microscope (FIM) observations. Our EAM calculations predict a small barrier to diffusion and only a slight energy difference between adsorption in the fcc and hcp threefold hollows (both smaller than 1 meV). They correspond poorly to the results of the FP-LDF calculations, which imply a diffusion barrier of 0.38 eV for passage over a bridge, and a preference of 0.18 eV for the fcc against the hcp site. FIM measurements yield a diffusion barrier of (0.25\ifmmode\pm\else\textpm\fi{}0.02) eV, and imply that binding in the fcc site is preferred.

A Dislocation Model for Flow at Intermediate Temperatures in Hard-Oriented NiAl

AbstractRecent studies of single crystals and bicrystals indicate that dislocations of the type a<011> are important, and may actually control, deformation at intermediate temperatures (above the brittle-to-ductile transition temperature) in hard-oriented NiAl. In the present work, the fine structure of a<011> dislocations has been examined using both high resolution and diffraction-contrast transmission electron microscopy. Evidence has been found for the decomposition of a<011> dislocations into two a<001> dislocations. The initial driving force for the decomposition is due to core effects, as revealed by molecular statics and dynamics Embedded Atom Method calculations. Additional decomposition occurs by a combination of climb and glide. A continuum-based dislocation model is introduced which incorporates these relevant microstructural features.