Tight-binding Ising Model Research Articles

How to take into account local concentration in Ising-based Monte-Carlo: illustration with zirconium hydrides

We present a detailed methodology for treating local concentration dependency of pairwise interactions in Ising-based Monte-Carlo. The procedure is described through the example of interstitial ordering processes in zirconium hydrides, studied by canonical Monte-Carlo based on a concentration-dependent Tight-Binding Ising Model. The path leads to build a phase diagram of hydrogen-vacancy ordering on interstitial tetrahedral sublattice of face-centered cubic Zr-H.

Investigations of the Co-Pt alloy phase diagram with neutron diffuse scattering, inverse cluster variation method, and Monte Carlo simulations

The short-range order in a CoPt alloy was determined at 1203 and 1423 K using neutron diffuse scattering measurements. The effective pair interactions provided by data analysis reproduce well the experimental order-disorder transition temperature in Monte Carlo simulations. They complete previous results reported for the Co-Pt system and are compared to those obtained within tight-binding and ab initio formalisms. Our results show that the important dependence of the nearest-neighbor pair interactions with composition is not related to the sample magnetic state at the measured temperatures. Interactions measured in the paramagnetic domain for the CoPt alloy behave like those in the ferromagnetic domain for the ${\mathrm{Co}}_{3}\mathrm{Pt}$ and ${\mathrm{Co}}_{0.65}{\mathrm{Pt}}_{0.35}$ alloys. The effective pair interactions related to the tight-binding Ising model provide a relatively good description of the CoPt alloy thermodynamics close to the ordering temperature (short-range order and temperature of phase transformation), even if they strongly differ from those measured in this study. The average magnetic moment of Co atoms at high temperatures was determined from the analysis of the intensity contribution that is not dependent on the scattering vector. The obtained value is very close to the moment measured at room temperature or determined from ab initio calculations. This confirms the Curie-Weiss behavior of the CoPt alloy. Finally, transmission electron microscope observations carried out on samples annealed for about 30 days confirmed that the order-disorder transition takes place in the 830--843 K temperature interval at the ${\mathrm{Co}}_{3}\mathrm{Pt}$ composition.

Tight-binding Ising modeling of the interplay between bulk ordering and surface segregation in Pt-Ag nanoalloys

We use a Tight-Binding Ising Model (TBIM) with effective pair interactions depending on concentration able to reproduce the bulk phase diagram of Pt-Ag system and in particular its strong asymmetry as a function of composition. This system presents both an L11 ordered structure around equiconcentration and a wide miscibility gap on the Pt-rich side. Using Monte Carlo simulations in canonical and semi-grand canonical ensembles, we succeed in reproducing qualitatively the bulk phase diagram and we study the equilibrium configurations of the (111) and (100) surfaces, and truncated octahedron clusters. The infinite surfaces reproduce sensibly the bulk phase diagram except that they present a strong silver surface segregation limited to the top surface layer. The clusters behave differently due to the reduction of the miscibility gap when decreasing the cluster size and present two typical ordered phases related to the L11 phase: one characterized by pure concentric atomic layers starting from silver surface layer which extends up to the center of the cluster, and the other one at higher silver concentration where the L11 phase is perfectly oriented along one (111) direction of the cluster. The later one has already been reported by recent experiments [1].

Chemical ordering and surface segregation in [formula omitted] system: A theoretical study from the alloys to the nanoalloys

Monte Carlo simulations within a Tight-Binding Ising Model (TBIM) have been performed on bulk, surfaces, and nanoclusters of Ni1-cPtc alloys in order to describe and understand the competition between surface segregation and chemical ordering phenomena in nanoalloys. The effective pair interactions obtained from the DFT calculations have been applied in Monte Carlo simulations to determine the bulk and alloy surfaces configurations. The order-disorder transition temperatures in the bulk compare well with experimental data and the bulk phase diagram from the model have been compared to that determined experimentally to validate the fit. The (111), (100) and (110) crystallographic orientations surfaces Ni1-cPtc are treated. The three driving forces for the segregation of surfaces have be studied in both diluted limits, together with the phenomenon of segregation at high temperature (in the disordered state) over the entire concentration range. Finally, we analyze the competition between superficial segregation and low temperature chemical order and conclude with a similar approach on truncated octahedra of 1289 and 405 atoms.

Effect of magnetism on surface segregation in FeNi alloys

Modelling the segregation of the various chemical species in the vicinity of crystallographic defects in FeNi alloys is essential because it affects the macroscopic properties of these materials, which are widely used in technological applications. We present here a theoretical study of surface segregation, within a mean-field approach based on the tight-binding Ising model grounded on density functional theory calculations. The most important result is that, although FeNi presents none of the driving forces (i.e. surface energy, size mismatch) which generally favour surface enrichment in the same element in the whole range of concentrations, there exists a wide temperature range in which Ni is found to segregate at the surface irrespective of the concentration. This is due to a complex interplay between magnetic and ordering/phase separation effects.

Ordering and surface segregation inCo1−cPtcnanoparticles: A theoretical study from surface alloys to nanoalloys

Monte Carlo simulations within a tight-binding Ising model (TBIM) have been performed on bulk, surfaces, and nanoclusters of ${\mathrm{Co}}_{1\text{\ensuremath{-}}c}\text{\ensuremath{-}}{\mathrm{Pt}}_{c}$ alloys in order to describe and understand the competition or synergy between surface segregation and chemical ordering phenomena in nanoalloys. Considering effective pair interactions (EPIs) up to the third neighbors, we put in evidence new ordered phases at low temperature in the Co-Pt bulk phase diagram. On the infinite (100) and (111) surfaces, the Pt surface segregation leads to select the Pt-rich plan at the surface without modification of the bulk ordering in the (100) orientation but with an extension of the ordering on a larger composition range in the (111) orientation as compared to the bulk. The truncated octahedron clusters of 405 and 1289 atoms are studied. Their chemical structure is compared in their core with the bulk phase diagram and in their facets with the (111) and (100) infinite surfaces segregation isotherms. The cluster core presents an asymmetry as compared to the bulk phase diagram. The (111) facets are similar to the (111) surface, whereas the (100) facets present geometrical frustrations for the segregation versus core ordering.

Surface Segregation in Transition Metal Alloys: From Electronic Structure to Phase Portraits

The empirical models using pairwise interactions cannot be used to treat surface segregation in transition metal alloys, but we show that an effective Ising hamiltonian can be derived from their electronic structure. In addition to this Tight Binding Ising Model (TBIM) developed for a rigid lattice, a size-mismatch energy can be defined from quenched molecular dynamics calculations performed within the same tight-binding approximation. This energetic model can be coupled with a mean field approximation formulated in terms of phase portraits. Applications to some spectacular and recently observed surface phase transitions are presented.

Surface Segregation Maps Derived from Tight-Binding Ising Model

Surface segregation in transition metals can be analysed within a generalised Ising model,derived from Tight-Binding electronic structure calculations, which identifies three driving forces:the difference in surface energy and atomic volume between the two components and their tendencyto order or phase separate in the bulk. Using this ”three effects” rule, we present here general mapswhich predict the tendency of the solute metal element to segregate (or not) at the surface of a metalmatrix, for the 702 solute/matrix systems that can be formed with transition metal elements. Ourpredictions compare fairly well to the existing ab initio calculations and experimental data availableon these systems. The few exceptions, which mainly concern given matrix elements are discussed indetails.

Structure and composition of the segregated Cu in V 2O 5/Cu system

We have investigated segregation of copper at the surface of V 2O 5 films deposited onto Cu substrate by employing surface analysis techniques. X-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) confirmed that the Cu is segregated at the surface and its chemical state is Cu 2O. According to secondary ion mass spectroscopy (SIMS) and glow discharge spectroscopy (GDS), the Cu concentration inside the deposited V 2O 5 layer is low. Ultraviolet photoelectron spectroscopy (UPS) and scanning tunneling spectroscopy (STS) revealed the segregation alters the surface local density of states. Surface analysis of deposited samples in ultra high vacuum (UHV) condition verified that the segregation occurs during the deposition. We have extended kinetic tight binding Ising model (KTBIM) to explain the surface segregation during the deposition. Simulation data approve the possibility of surface segregation during room temperature deposition. These results point out that on pure Cu substrate, oxidation occurs during the segregation and low surface energy of Cu 2O is the original cause of the segregation.

Importance of proper choice of transition rates in kinetic simulations of dynamic processes

Proper transition rates in kinetic mean-field and Monte Carlo simulations of dynamic processes are very important to obtain realistic results. We show that by proper choice of the transition rates one can unify the advantages and eliminate the disadvantages of different models used in the literature [see, e.g., Senhaji et al., Surf. Sci. 274, 297 (1992 )( kinetic tight binding Ising model), Martin, Phys. Rev. B 41, 2279 (1990) and Cserhati et al., Surf. Sci. 290, 345 (1993)]. Furthermore, we also show that this choice cannot be considered simply as an extension of the previous ones. It contains an additional parameter controlling the ratio of the transition rates in the bulk and close to the surface sGsurf / Gbulkd, which influences the kinetics of surface segregation. We show that some results obtained previously need reconsideration. We illustrate, e.g., how the composition dependence of the transition rates (diffusion coefficient) influences the ‘surfactant formation and dissolution mode’. For example, the dissolution kinetics can deviate from the parabolic law on the nanoscale in accordance with our recent results [Erdelyi et al., Phys. Rev. B 69, 113407 (2004)]. Furthermore, we also present how the sGsurf / Gbulkd ratio affects the kinetic segregation isotherm.

Linear time dependence of the surfactant effect: A local equilibrium under flux

We have investigated the dissolution kinetics of an A metal thin film deposited on a (100) B metal under thermal annealing for a system with a strong B segregation (e.g., Ni/Ag). The interdiffusion is described using both Monte Carlo and mean-field simulations with an effective exchange mechanism derived from the kinetic tight-binding Ising model. Surprisingly, the surface enrichment in substrate B element is found to increase linearly with time instead of following the usual $\sqrt{t}$ law. We demonstrate that this t law occurs when the diffusion coefficient of B atoms in the A deposit is high or when the deposit thickness decreases. Moreover it is shown that, in this surfactant regime, the usual local equilibrium rule which drives the kinetics has to be generalized under the flux of B atoms coming from the deposit/substrate interface. Consequences of this new formulation on nonequilibrium dynamical behaviors during thin film dissolutions are discussed.

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.

An unusual composition profile: a LEED–TBIM study of Pt 25Cu 75( [formula omitted

The structure and composition of a disordered Pt 25Cu 75(1 1 1) sample was studied by low energy electron diffraction. The r-factor, D 1=0.096, illustrates a very good agreement between experimental and theoretical spectra. The Pt concentration versus depth oscillates around the bulk value (C 1,C 2,C 3,C 4)=(28,8,48,8 at.% Pt) . The most striking result is the quite large and unusual Pt enrichment in layer 3 ( C 3=48%) followed by the still important Pt depletion in layer 4 as opposed to the damped oscillations observed for similar Pt–Ni(1 1 1) and Pt–Co(1 1 1) alloys. This result, which is in contradiction with a previous LEIS study, is interpreted within the Tight Binding Ising Model and is related to a termination of the L1 1 phase, which exists only in the Cu–Pt system.

Theoretical investigation of chemical and morphological ordering inPdcCu1−cclusters

We present a theoretical study of ${\mathrm{Pd}}_{c}{\mathrm{Cu}}_{1\ensuremath{-}c}$ clusters from a few hundred to a few thousand of atoms, using Monte Carlo simulations and quenched molecular dynamics. This is performed within tight-binding many-body potentials, the tight-binding Ising model and the second moment approximation, which properly account for chemical and structural changes at transition-metal surfaces. The respective stabilities of the fcc, bcc, and icosahedral cluster shape are discussed in terms of competition or synergy between surface segregation and bulk ordering. Besides a finite-size effect on surface segregation, due to the limited quantity of matter, we show that chemical ordering can induce some geometrical frustrations and enhance the stability of ``stoichiometric'' clusters, the composition of which is strongly size dependent. Finally, it is found that chemical ordering leads to morphological transitions at equiconcentration.

CO adsorption on Pt xPd [formula omitted] single crystal alloy surfaces: a core level and valence band photoemission study

We present a photoelectron spectroscopy study of three single crystal Pt x Pd 1− x (1 1 1) alloy surfaces ( x=0.1, 0.5, 0.9) using synchrotron radiation. The surface and chemical sensitivity of core level photoemission allows us to quantify an oscillatory depth concentration profile and the palladium segregation at the surface of each alloy. The experimental results are compared to theory based on regular solution and tight binding Ising model formalisms, a good agreement is found. In the second part of the paper the effect of CO adsorption on the alloy surfaces is investigated. The variety of adsorption site geometry and chemistry as a function of surface segregation and bulk alloy concentration is revealed in both valence band and core level spectra.

Layer-by-layer versus surfactant dissolution modes in heteroepitaxy

~Received 18 May 1999! Dissolution of a thick A film into aB substrate during metal heteroepitaxy ( A/B) obeys general trends which are described here in the case where the corresponding AB alloy presents a tendency to bulk phase separation and to B surface segregation ~e.g., A5Ni, B5Ag). Using the kinetic tight-binding Ising model, either in the mean-field or in the Monte Carlo framework, we findlayer-by-layer dissolution modes which, depending on the annealing temperature T, are preceded ( T.Tk) or not ( T,Tk) by the rising of capping B monolayers burying an almost intact A film ~surfactantlike effect!. Tk is found to decrease as the tendency to surface segregation of the substrate element increases, which can be understood in terms of local equilibrium at both the surface and the interface of the deposit. The model gives access to the main kinetic laws which are obeyed in the two dissolution modes, i.e., the total quantity of deposit matter decreases linearly with the square root of time. @S0163-1829~99!00243-X#

How to compare superficial and intergranular segregation? A new analysis within the mixed SMA–TBIM approach

The driving forces for intergranular segregation are much less known than the ones for superficial segregation. In order to investigate the relation between grain-boundary and surface segregation, we have calculated the segregation energy for one impurity in both dilute limits for the Cu–Ag system. This is performed for the (001) surface on one hand and for the symmetrical tilt grain boundary Σ=5 (210) [001] on the other. These numerical results, obtained using N-body interatomic potentials derived from the second moment approximation (SMA) of the tight-binding scheme, are then discussed within an analytic model, the tight-binding Ising model (TBIM). This allows us to determine the relative role of the different driving forces in superficial and intergranular segregation. In particular competition or synergy between site and size effects strongly differ between surface and grain-boundary segregation. This study illustrates the efficiency of the mixed SMA–TBIM approach to predict and to analyse interfacial segregation.

Theoretical prediction of new dissolution modes during metal heteroepitaxy

By means of the kinetic tight-binding Ising model we investigate the Ni/Ag dissolution modes resulting from the thermal interdiffusion between the two elements. For a thin deposit (1 ML) we show that the dissolution proceeds by the formation of encapsulated Ni precipitates covered by two pure Ag monolayers. For a thick deposit (10 ML) we find two distinct layer-by-layer modes depending on the annealing temperature. At high temperature the kinetics start with the apparition of capping Ag monolayers on a buried almost intact Ni film ( surfactant-layer-by-layer mode). Below a critical temperature T c, the dissolution proceeds without any Ag surface enrichment ( layer-by-layer mode). We find that T c decreases when the surface driving forces which favour the segregation of the substrate elements increase.

SURFACE ALLOY FORMATION IN THE Cu–Pd(111) SYSTEM: A KTBIM APPROACH

We study the kinetics of formation and dissolution of surface alloy obtained by depositing one monolayer of Pd on Cu(111) at room temperature. This is performed within the kinetic tight-binding Ising model. We also present the equilibrium segregation isotherm for Pd c Cu 1-c(111) and show the relation between kinetics (surface alloy) and equilibrium (alloy surface) via the local equilibrium concept.

Electronic theory of the chemisorption effect on surface segregation in transition-metal alloys

The tight-binding Ising model generalized for a system consisting of a transition-metal alloy with chemisorbed adatoms is used to calculate the effect of hydrogen chemisorption on surface segregation in a CuNi alloy. The simple model of chemisorption and of the band structure of the alloy is assumed. The charge-neutrality condition is incorporated into the model.