Equilibrium ordering properties of Au–Pd alloys and nanoalloys

Equilibrium configurations of bulk and surface Au–Pd alloys as well as of nanoalloy clusters are studied using Metropolis Monte Carlo importance sampling and the embedded atom method. The clusters contain about 1000 atoms. Three ordered bulk phases are predicted at low temperature, centred on compositions around 25%, 50%, and 75% Pd. The predicted order–disorder transition temperatures partially disagree with the available experimental results, but they are in good agreement with ab initio calculations. Surface enrichment in Au is systematically predicted, accompanied by partial subsurface enrichment in Pd, best enhanced around the equiatomic overall composition. The subsurface enrichment in Pd is suggested to play a decoupling role between surface and bulk conditions and, subsequently, ordered surface structures not induced by the order in the bulk are predicted at low temperatures. Clusters display similar segregation and ordering properties as flat infinite surfaces. However, the stability of the ordering at cluster surfaces is not globally characterized. The order–disorder transitions in the clusters occur at temperatures between 50 and 100 K lower than in the bulk. The disorder appears at the surface and proceeds to the core as the temperature is increased.     

Atomistic simulation of Fe deposition and alloy formation on Pt substrates

Fe-Pt alloys are of significant importance toward future applications of high-density magnetic recording media. In this work, we apply the BFS method for alloys to study the energetic pathway for subsurface Fe-Pt alloy formation upon deposition of Fe atoms on Pt(1 0 0), Pt(1 1 1), and vicinal Pt(9 9 7) substrates. The simulation results indicate preference for Fe atoms to occupy sites in the Pt subsurface layers and form an ordered alloy phase upon deposition on a low-index Pt surface. This behavior results in Pt surface segregation leading to nucleation of 3D Pt islands. However, the energetics behind deposition of Fe on Pt(9 9 7) indicate that Fe atoms prefer decoration of Pt step edges prior to formation of the ordered Fe-Pt surface alloy, where the ordered alloy is observed to form at the edges of the monoatomic surface steps. In each case presented here, the results are in agreement with experiment, and the formation of a Fe-Pt subsurface alloy is explained by a simple analysis emerging from the competition between BFS strain and chemical energy contributions.     

Surface energies of the solid solutions between Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, and W

The surface energy for different surface orientations of the solid solutions as a function of concentration formed by Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, and W is computed and analyzed using the BFS method for alloys. Similarities and differences among the different binary alloys are examined in terms of strain and chemical effects.     

Solute-atom segregation at symmetric twist and tilt boundaries in binary metallic alloys on an atomic-scale

Monte Carlo and overlapping distributions Monte Carlo (ODMC) techniques are employed to simulate grain boundary (GB) segregation in a number of single-phase binary metallic alloys—the Au-Pt, Cu-Ni, Ni-Pd, and Ni-Pt systems. For a series of symmetric [001] twist and [001] tilt boundaries, with coincident site lattice (CSL) structures, we demonstrate that the Gibbsian interfacial excess of solute is a systematic function of the misorientation angle. We also explore in detail whether the GB solid solution behavior is ideal or nonideal by comparing the results of Monte Carlo and ODMC simulations. The range of binding free energies of specific atomic sites at GBs for solute atoms is also studied. The simulational results obtained demonstrate that the thermodynamic and statistical thermodynamic models commonly used to explain GB segregation are too simple to account for the microscopic segregation patterns observed, and that it is extremely difficult. If not impossible, to extract the observed microscopic information employing macroscopic models.     

Reversed surface segregation in palladium-silver alloys due to hydrogen adsorption

It is well known that silver segregates to the surface of pure and ideal Pd–Ag alloy surfaces. By first-principles band-structure calculations it is shown in this paper how this may be changed when hydrogen is adsorbed on a Pd–Ag(1 1 1) surface. Due to hydrogen binding more strongly to palladium than to silver, there is a clear energy gain from a reversal of the surface segregation. Hydrogen-induced segregation may provide a fundamental explanation for the hydrogen or reducing treatments that are required to activate hydrogen-selective membrane or catalyst performance.     

The chemical potential in surface segregation calculations: AgPd alloys

We put forward a technique for calculating the surface segregation profile in substitutional disordered alloys. The surface internal energy and the effective bulk and surface chemical potentials are calculated using the full charge density exact muffin-tin orbitals method, combined with the coherent potential approximation. The application of our approach is demonstrated to the close-packed surface of Ag_cPd_1−c random alloys with 0 < c < 1. The surface concentration profile, surface energy and segregation energy are investigated as functions of bulk composition. The present results are compared with former theoretical and experimental data. It is found that at low temperature, Ag segregates to the surface layer for the entire bulk composition range. At 0 K, the subsurface layer contains 100% Pd for c ? 0.4, and somewhat more than (2c − 1) Ag in alloys with c > 0.5. The temperature dependence of the segregation profile is significant for Pd rich alloys and for alloys with intermediate concentrations. At temperatures ?600 K, the subsurface layer is obtained to be almost bulk like.     

Atomistic modeling of Zn deposition on the low index faces of Cu

The formation process of Zn/Cu surface alloys is investigated using the Bozzolo-Ferrante-Smith (BFS) method for alloys. The effects of the crystallographic orientation on the deposition process, formation of surface alloys as a function of temperature and coverage, Zn surface migration, and interdiffusion in the Cu substrate, are modeled and discussed with atom-by-atom energy analyses and large scale simulations.     

A method for the study of surface segregation in multicomponent alloys

A simple algorithm for the determination of segregation profiles in multicomponent systems based on a mean field formalism and a quantum approximate method for the energetics is introduced. The method is described and applied to two ternary systems, concentrating on the changes in segregation patterns relative to the corresponding binary cases.     

Interfacial segregation in Ag-Au,Au-Pd,and Cu-Ni alloys: I. (100) surfaces

Atomistic simulations of segregation to (100) free surface in Ag–Au, Au–Pd, and Cu–Ni alloy systems have been performed for a wide range of temperatures and compositions within the solid solution region of these alloy phase diagrams. In addition to the surface segregation profiles, surface free energies, enthalpies, and entropies were determined. These simulations were performed within the framework of the free energy simulation method, in which an approximate free energy functional is minimized with respect to atomic coordinates and atomic site occupation. The effects of the relaxation with respect to either the atomic positions or the atomic concentrations are discussed. For all alloy bulk compositions (0.05 C 0.95) and temperatures (400 T(K) 1,100) examined, Ag, Au, and Cu segregates to the surface in the Ag–Au, Au–Pd, and Cu–Ni alloy systems, respectively. The present results are compared with several theories for segregation. The resultant segregation profiles in Au–Pd and Ag–Au alloys are shown to be in good agreement with an empirical segregation theory, while in Cu–Ni alloys the disagreement in Ni-rich alloys is substantial. The width of the segregation profile is limited to approximately three to four atomic planes. The surface thermodynamic properties depend sensitively on the magnitude of the surface segregation, and some of them are shown to vary linearly with the magnitude of the surface segregation.     

Nucleus size and Zeldovich factor in two-dimensional nucleation at the Kossel crystal (0 0 1) surface

A Monte Carlo simulation method to determine the growth probability of two-dimensional clusters on the Kossel (0 0 1) surface is described. From this growth probability the nucleus size and the Zeldovich factor for two-dimensional nucleation were obtained. For low supersaturations the Gibbs-Thomson equation describes the supersaturation dependency of the nucleus size very well. At higher supersaturations a deviation from the predicted nucleus sizes is observed. This is mainly due to the size dependence of the apparent specific step free energy and/or the shape factor of the nucleus. A small systematic deviation between the theoretical and actual growth probability is observed and explained.     

Atomistic simulation of the surface structure of electrolytic manganese dioxide

Atomistic simulation methods were used to investigate the surface structures and stability of pyrolusite and ramsdellite polymorphs of electrolytic manganese dioxide (EMD). The interactions between the atoms were described using the Born model of Solids. This model was used to calculate the structures and energies of the low index surfaces {0 0 1}, {0 1 0}, {0 1 1}, {1 0 0}, {1 0 1} and {1 1 0} for both pyrolusite and ramsdellite. Pyrolusite is isostructural with rutile and similar to rutile the {1 1 0} surface is found to be the most stable with the relaxed surface energy 2.07 J m⁻². In contrast, for ramsdellite the {1 0 1} surface is the most stable with a surface energy of 1.52 J m⁻². Pyrolusite {1 0 0} and ramsdellite {1 0 0}_b surfaces have equivalent energies of 2.43 J m⁻² and 2.45 J m⁻², respectively and similar surface areas and hence are the likely source for the intergrowths. Finally, comparison of the energies of reduction suggests that the more stable surfaces of pyrolusite are more easily reduced.     

Site segregation in size-mismatched nanoalloys: Application to Cu-Ag

In order to determine the energetic driving forces for surface segregation in bimetallic clusters, we use a combined approach coupling numerical simulations within an N-body interatomic potential and a lattice-gas model. This approach, which has been used successfully to study both the superficial segregation in semi-infinite alloys and the intergranular segregation, allows us to determine the relative contributions of the three elementary driving forces for the different sites of the cluster surface (vertices, edges and facets) in both dilute limits for the Cu-Ag system. We show that the segregation hierarchy based on broken-bond arguments (preferential segregation to the vertex sites, less to edge sites, and least to facet sites) is not at all universal. In particular, unusual hierarchies are predicted when the sizes of the constituents are strongly different. Furthermore, we compare the segregation driving forces for cubo-octahedral and icosahedral clusters. They are similar for the vertex sites and edge sites, whereas they differ significantly for the sites of the triangular facets. The segregation of the species with the largest atomic radius (Ag) is indeed largely enhanced in the icosahedral structure due to dilations of the orthoradial distances.     

Atomistic mechanisms for the ordered growth of Co nanodots on Au(7 8 8): a comparison between VT-STM experiments and multi-scaled calculations

Hetero-epitaxial growth on a strain-relief vicinal patterned substrate has revealed unprecedented 2D long range ordered growth of uniform cobalt nanostructures. The morphology of a sub-monolayer Co deposit on a Au(1 1 1) reconstructed vicinal surface is determined by using variable temperature scanning tunneling microscopy (VT-STM). A rectangular array of nanodots (3.8 nm × 7.2 nm) is found for a particularly large deposit temperature range lying from 65 to 300 K. This paper focuses on the early stage of growth at temperatures between 35 and 480 K. Atomistic mechanisms leading to the nanodots array are elucidated by comparing statistical analysis of VT-STM images with multi-scaled numerical calculations. Molecular dynamics allows the quantitative determination of the activation energies for the atomic motion, whereas the kinetic Monte Carlo method simulates the submonolayer Co growth over mesoscopic time scale and space scale.     

Atomistic origin of the thermodynamic activation energy for self-diffusion and order-order relaxation in intermetallic compounds II: Monte Carlo simulation of B2-ordering binaries

Abstract

The validity of previously derived formulae expressing the activation energies for self-diffusion and ‘order–order’ relaxations in intermetallics in terms of the activation energies of more elementary processes involved in the phenomena is tested by simulation of particular binary systems. The simulation results were in good agreement with the tested formulae. It was shown that the relationship between the activation energies observed in triple-defect B2-ordering binaries, where the value of the activation energy for order–order relaxations is substantially lower than that for self-diffusion, does not hold in the case of non-triple-defect binaries. Using the tested formulae, the origin of the effect was elucidated and attributed to the atomistic origin of the tendency for triple-defect disordering.     

Reduced-order modeling of time-dependent reflectance profiles from purely scattering media

Due to the widespread existence and importance of foam, inverse techniques for characterizing industrial foams are of interest. An essential element in an inverse method used to characterize a foam layer is a model of the time-dependent reflectance of a laser pulse. Monte Carlo methods may be used to accurately model reflectance, but these methods are computationally expensive. Computationally efficient methods based on the diffusion approximation have been developed, but this approach is not sufficiently accurate in many cases of interest. Therefore, a computationally efficient and robust method is desirable. This paper presents a computationally efficient method for modeling the time-dependent reflectance of a laser pulse from a non-absorbing, scattering plane layer that is based on reduced-order modeling techniques. The accuracy of the proposed method is demonstrated by comparing reflectance profiles for randomly selected foam layer properties with corresponding profiles that were generated from Monte Carlo simulations.     

Atomistic structure of stepped surfaces

Atomistic computer simulation with embedded atom method (EAM) interatomic forces was used to study the structure of surface steps on the {111} unreconstructed surface in fcc metallic materials. The energetics and local atomic relaxation behavior of ledges parallel to the 110 direction were studied using a potential describing lattice properties of Au. The vacancy formation energies in the stepped surfaces was also studied, and it was found that the energy of formation of a vacancy in a terrace is the same as that in the perfect unstepped surface. This value is 30% lower than that of the bulk. The vacancy formation energy in the ledge is reduced by a factor of two with respect to that of the terraces. The structure of the “up ledge” (A step) is different from the “down ledge” (B step). These differences do not significantly affect the energy of the ledges, although they do affect the vacancy formation energies in sites in the second surface layer near the ledge. The implications of the results for the formation of kinks and the general structure of high index surfaces are discussed.     

Energy loss spectra of low primary energy (E0 ? 1 keV) electrons backscattered by silicon dioxide

A Monte Carlo simulation is described and utilized to calculate the energy distribution spectra of the electrons backscattered by silicon dioxide. Spectra are presented for incident energies of 250 eV, 500 eV, and 1000 eV. Spectra interpretation is based on a semiquantitative valence-band structure model for SiO₂ crystals.     

Monte Carlo investigation of the correlation between magnetic and chemical ordering in NiFe alloys

The Ni_xFe_1−x alloys close to the stoichiometric Ni₃Fe composition are modeled by means of Monte Carlo simulations. To describe the atomic and magnetic configurations, the Ising and Heisenberg models with nearest-neighbor interactions have been used, respectively. The pairwise interactions have been fitted to the experimentally measured Curie and Kurnakov temperatures, the Fe-Fe magnetic exchange interaction has been considered antiferromagnetic. The mutual influence of the magnetic and chemical ordering is evidenced and a good agreement with the phase diagram is obtained. Our numerical results show that the magnetic order is able to increase the Kurnakov temperature and, reciprocally, the chemical order is responsible for a rise in the Curie temperature. Also, the influence of the applied magnetic field on the chemical order is investigated and an increase of the Kurnakov temperature with the external field is observed.     

Surface and transport properties of Au-In liquid alloys

Thermodynamic quantities on Au-In liquid alloys have been used as the input data for the interaction parameter calculations in the framework of the complex formation model (CFM). Once the interaction energies are computed the surface (surface tension and surface composition) and transport properties (chemical diffusion and viscosity) as well as the microscopic functions (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter) have been calculated. The concentration and temperature dependent surface tension values have been compared with our new set of experimental data, obtained by the large drop method in the temperature range of T = 1273-1493 K. The anomalous change of surface tension for some alloy compositions may be attributed to a retention of order in the Au-In melts which is similar to the atomic arrangement in solid Au-In.