Bernard Legrand

New magic numbers in metallic clusters: an unexpected metal dependence

Using a many-body tight-binding potential within the second moment approximation in a quenched molecular dynamics simulation, we calculate the internal energy of free Cu, Ag and Au clusters of various sizes and morphologies. We find that the icosahedral structure, which is the equilibrium shape for small sizes at least for Cu and Ag, adopts a very inhomogeneous atomic relaxation. More surprisingly, introducing a vacancy at the center lowers the mean energy per atom for sufficiently large size icosahedra. This means that above a critical size, which decreases from Cu to Au, the icosahedron admits a constitutional vacancy. Taking into account the stability domain of the icosahedron relative to the fcc structure (namely the Wulff polyhedron), we find that there is a stability range of size for Cu and Ag icosahedra with a central vacancy, but not for Au icosahedra. This trend along the noble metal column is discussed in view of tight-binding potential parameters.

Surface segregation in PtRh alloys revisited in the framework of the tight-binding Ising model

Abstract The recently developed tight-binding Ising model (TBIM) is used to interpret the puzzling experimental results on surface segregation in PtRh alloys. More precisely, both the nature of the segregant element (Pt) and the anomalous increase with temperature (up to 1000 K) of the surface enrichment have required some authors to invoke a generally neglected effect: the vibrational entropy. We show here that this term is indeed negligible and that the TBIM, which is derived from electronic structure, accounts for the experimental observations (Pt surface enrichment, oscillating concentration profile). As for the apparent increase in surface segregation with temperature, it is attributed to kinetics limitations which prevent from reaching the equilibrium.

Surface segregation in CuNi and AgNi alloys formulated as an area-preserving map

Abstract The tight-binding Ising model (TBIM) coupled with a mean field approximation formulated as an area-preserving map (APM) is applied to surface segregation of CuNi and very dilute Ag(Ni) alloys. In the former case, it rules out the surface segregation crossover with bulk concentration suggested by some experiments and calculations, by concluding in a Cu-enrichment independent of the concentration and the temperature. In the latter case, it accounts for the spectacular surface sandwich observed experimentally in terms of Ag-segregation at the surface of the Ni-rich precipitated phase, slightly below the temperature of phase separation.

Electronic structure of Pd clusters in the tight-binding approximation : influence of spd-hybridization

We show that including spd-hybridization in tight-binding model allows an accurate description of the local electronic density of states of Pd clusters in a large range of size and gives reliable site energies. We put in evidence a narrowing of the band with decreasing coordination number accompanied by a significant variation of the local density of states near the Fermi level according to the type of site (vertex, edge, facets or core). From the energetical point of view, we find that a quasi-linear dependence of the attractive part of the potential as a function of the coordination number is better suited than the usual square root dependence. Moreover, we point out the influence of cluster symmetry by comparing the cuboctahedral structure (fcc type) with the icosahedral one (five-fold symmetry) which is adopted by the small fcc clusters.

Molecular dynamics simulations for the Ag/Cu (111) system: from segregated to constitutive interfacial vacancies

The occurrence of an Ag layer on top of a Cu (111) substrate can result from either deposition (Ag/Cu) or strong segregation at the surface of a dilute Cu(Ag) alloy. Molecular dynamics simulations within many-body tight-binding potentials show that two structures compete: one corresponding to a rather uniform Ag (111) layer on top of a Cu (111) substrate leading to a Moire structure and the other involving constitutive vacancies forming triangular loops of partial dislocations in the first Cu substrate layer. A useful guide to predict the most efficient relaxation mechanism is to characterize the regions which undergo the largest stress. Thus, the local pressure map in the first Cu underlayer allows to predict a complementarity between the segregation of vacancies in compressive sites and the Ag enrichment, due to the larger atomic radius of the Ag atoms, in the tensile ones. Segregation energy maps, both for vacancies and Ag atoms, confirm this prediction and lead to several perspectives for the kinetics of dissolution of an Ag deposit over a Cu (111) substrate.

Magnetism: the driving force of order in CoPt, a first-principles study

CoPt equiatomic alloy orders according to the tetragonal L1(0) structure which favors strong magnetic anisotropy. Conversely, magnetism can influence the chemical ordering. We present here ab initio calculations of the stability of the L1(0) and L1(2) structures of Co-Pt alloys in their paramagnetic and ferromagnetic states. They show that magnetism strongly reinforces the ordering tendencies in this system. A simple tight-binding analysis allows us to account for this behavior in terms of some pertinent parameters.

Link between the surface wetting in Cu(Ag) and the layer-by-layer dissolution mode of a thick Ag deposit on a Cu substrate

Using a mean field approximation to an energetic model derived from the electronic structure, the tight binding Ising model (TBIM), we study the Ag c Cu 1-c (111) system in the Ag dilute limit. We find an infinite succession of first-order phase transitions when the bulk concentration approaches the solubility limit c α (T): the planes parallel to the surface, starting from the surface layer, change from almost pure Cu to almost pure Ag. The range of bulk concentration in which these transitions occur can be explored kinetically during the dissolution of a sufficiently thick Ag deposit over the (111) surface of Cu. We model such a dissolution using a kinetic model (KTBIM) whose stationary state is consistent with the equilibrium one (TBIM). It leads to a hardly non-Fickian behaviour, i.e.: an unusual layer-by-layer dissolution mode. The link between kinetics and equilibrium has to be found in the equilibrium profile of the coherent interphase boundary between two phases of concentration 1-c α and c α respectively

On a “surfactant-like” behaviour of NiAg(100) deposit

Auger experiments performed during the annealing at 620 K of one monolayer of Ni, deposited at room temperature on a Ag(100) substrate, show a very rapid decrease of the Ni signal indicating an almost immediate disappearance of Ni atoms from the surface, whereas annealing at 770 K the reverse deposit NiAg(100) does not lead to any dissolution of Ag, even after a long time. This clearly non-Fickian behaviour can be understood in terms of local equilibrium near the surface, by means of a recently developed microscopic kinetic model (KTBIM: kinetic tight-binding Ising model) taking into account the driving forces of surface segregation. Moreover, the KTBIM simulation of the dissolution of additional Ni layers, successively deposited on Ag(100), reveals the existence of a “floating” Ag bi-layer which stays above the Ni deposit, analogous to a surfactant during semiconductor growth.

Alloy surfaces and surface alloys: from equilibrium to kinetics

Abstract We study the relation between the surface segregation at thermodynamical equilibrium in an alloy AcB1−c and the kinetics of dissolution of A B or B A . This is possible within a new kinetic model based on the electronic structure: the kinetic tight-binding Ising model. In particular, the existence of a local equilibrium between the surface and the first underlayer is stressed. Some illustrations are given in the particular case of two systems, one presenting a tendency to bulk phase separation and surface layering transitions (Cuue5f8Ag) and the other a tendency to bulk ordering and surface concentration profile transitions (Ptue5f8Ni). The notion of “surface alloy” is defined in the latter case.

Surface-induced ordering in phase separation systems: influence of concentration and orientation

Abstract With regard to the modern way of analysing surface phenomena at an atomistic scale, new questions appear. This is particularly the case with the tendency to either order or phase separate, for which experiments reveal a possible reversal from the bulk to the surface. Our aim in this paper is to show, through a microscopic theoretical model derived from the tight-binding scheme, that such a behaviour can be understood. We are thus able to predict how the tendency to form heteroatomic or homoatomic pairs evolves with the number of broken bonds (surface orientation) and the alloy concentration (at least in the dilute limits). This is illustrated in the case of the Ag–Cu system, which presents a strong phase separation in the bulk and for which many experiments reveal a large variety of surface behaviours.