
Anna FRANCHINI
Professore Associato Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede exFisica

Home 
Curriculum(pdf) 
Didattica 
Pubblicazioni
2019
 Attractive interactions between likeoriented surface steps from an
ab initio
perspective: Role of the elastic and electrostatic contributions
[Articolo su rivista]
Righi, Giulia; Franchini, Anna; Magri, Rita
abstract
In this work, we show that by using the density functional approach, in which the electronic degrees of freedom are separated by the ionic ones, it is possible to individuate and separately study the elastic and electrostatic step interactions, traditionally introduced in the literature as the only two kinds of step interaction expected at T=0. We have applied the method to the technologically important GaAs(001) surface and found some unexpected results for the relatively short step distances accessible to the ab initio approaches, contradicting those of the continuum models so far employed for the study of the elastic step interactions: (i) the sign of the step interaction depends on the step termination and is due to the electrostatic interaction; (ii) the elastic interaction does not contribute to the step interaction, contrary to the common belief of a strong elastic repulsive interaction between likeoriented steps. We show that this is due to the electron behavior. When considering only ion displacements and pointlike steps as in the continuum theories, we recover the classical results and repulsive step elastic interactions; (iii) the experimentally observed Ab step termination shows a weakly attractive step interaction whereby attractive step interactions between likeoriented steps on an unstrained surface are believed not to exist. The proposed method of separating elastic and electrostatic interactions for further analysis of their dependence on the configurational degrees of freedom can be extended to other defective situations.
2018
 Metalsupport interaction in catalysis: The influence of the morphology of a nanooxide domain on catalytic activity
[Articolo su rivista]
Najafishirtari, Sharif; Guglieri, Clara; Marras, Sergio; Scarpellini, Alice; Brescia, Rosaria; Prato, Mirko; Righi, Giulia; Franchini, Anna; Magri, Rita; Manna, Liberato; Colombo, Massimo
abstract
Using wet chemistry synthesis methods we prepared nanodumbbell structures as a model oxide supported metal catalyst. In this peculiar configuration, a single metallic domain (M) is connected to a single metal oxide (MOx) one. The size, composition and morphology of each domain can be carefully controlled, allowing us to investigate the effects resulting from a hollow morphology of the MOx domains, while all other material’s properties were kept constant. We chose the CO oxidation as a model oxidation reaction and increasing the population of nanocrystals (NCs) with hollow oxide domains resulted in a decrease in catalytic activity. Despite the manipulation of oxide morphology affected the surface charge of the Au domain, the bulk oxide reducibility and the crystallinity of the nanosized oxide support, the rate limiting step of CO oxidation was not affected. The same apparent activation energy was indeed measured independently from the population of NCs with hollow oxide domains. The difference in catalytic performance was thus ascribed to a different number of interfacial active sites when the morphology evolved from full to hollow.
2011
 Effects of the commensurability and disorder on friction for the system Xe/Cu
[Articolo su rivista]
FRANCHINI, Anna; BORTOLANI, Virginio; SANTORO, Giorgio; K., Xheka
abstract
We present molecular dynamics simulations of static friction for a monolayer of Xe deposited on a thick slab of Cu for two different geometries. The interaction potential between Xe and Cu has been derived from DFT calculations. The first geometry is the commensurate adsorption geometry (√3 ×√3)R30◦ suggested by LEED, corresponding to a coverage 1/3, where all Xe atoms are on top positions. The second one corresponds to a coverage 0.36 and is characterized by a large surface unit cell, containing 9 Xe atoms in different disordered positions. This largeunit cell mimics an incommensurate case. Our analysis points out the effect of the order/disorder in tribological properties of a realistic threedimensional system.
2010
 Sliding friction of N2 on Pb(111)
[Articolo su rivista]
FRANCHINI, Anna; BORTOLANI, Virginio; SANTORO, Giorgio; BRIGAZZI, Marco
abstract
Molecular dynamics simulations of the sliding friction between two thick solid slabs are performed. The upper body is formed of light N2 particles and the substrate of heavy Pb atoms. Among the various mechanisms that are responsible for the friction, we consider the phonon–phonon interaction between the two blocks. To provide evidence of the phonon interaction, we compare two different systems. For the first we consider the substrate as formed of atoms fixed in the equilibrium (111) positions. In the second system the Pb atoms can be displaced from the ideal positions, under their mutual interactions. A comparison with recently obtained experimental data will be discussed.
2010
 Theory of Friction with Applied Load
[Articolo su rivista]
Bortolani, Virginio; Franchini, Anna; Santoro, Giorgio; Brigazzi, Marco
abstract
We present a molecular dynamics simulation for the static friction under the effect of load. We chose a system formed by slabs of molecules of N2 deposited on a (111) surface of Pb. In contrary to many calculations, we assume that the Pb atoms are not kept fixed in the lattice positions, but can vibrate in their own phonon’s field. This has the important consequence that the upper and lower block can exchange energy and momentum. During the molecular dynamics simulation, the two systems can reach a thermodynamical equilibrium. When in our moleculardynamics simulation the equilibrium is reached the N2 plane at the interface reconstructs. The unit cell is still hexagonal but it contains 16 molecules in disordered positions. These positions of the N2 molecules are strongly modified by the presence of load. For small load there is a small increase of the disorder that produces a small reduction in the static friction. For larger loads the formation of clusters begins, and for high loads the size of theclusters increases and there is a tendency to the formation of vacancies. These effects are producing a large increase in the force friction. We can then distinguish different regions that characterize the behaviour of the static friction as a function of the load.
2010
 Un'esperienza didattica innovativa per l'insegnamento della relatività
[Relazione in Atti di Convegno]
Brigazzi, Marco; Santoro, Giorgio; Franchini, Anna; I., Cigarini
abstract
Guardando le indicazioni nazionali per l’insegnamento della fisica nelle scuole di ogni ordine e grado si può notare che la fisica moderna pur ampiamente menzionata viene confinata solonell’ultima parte dell’ultimo anno scolastico periodo critico per le attività didattiche dove impegni legati alla preparazione dell’esame finale portano ad una loro sottovalutazione.Nella pratica di classe la fisica viene quindi di fatto confinata solo ai concetti sviluppati nella prima metà dell’800 relativi alla meccanica classica ed alla elettrodinamica dei sistemi statici oin lento movimento.Nelle discipline tecniche invece vengono utilizzati concetti e teorie sviluppati nella cosiddetta epoca moderna dalla prima metà del XX secolo ad oggi; basti pensare a questo propositoall’elettronica dove vengono studiate le proprietà di conduzione nei sistemi descritti microscopicamente dalla teoria delle bande, alla tecnologia meccanica dove viene fatto cenno agli strumentidi analisi dei materiali basati sull’uso delle radiazioni ionizzanti, all’elettrotecnica dove i concetti basilari come l’effetto fotoelettrico e l’effetto Compton vengono usati per la progettazione di sistemi di produzione o utilizzazione dell’energia elettrica quali i pannelli fotovoltaicio meccanismi di apertura basati su sensori ad infrarossi usati nell’edilizia.
2009
 Theoretical investigation of the anticorrugation effects on the tribological properties of the Xe/Cu interface
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio; Santoro, Giorgio; Brigazzi, Marco
abstract
We present a molecular dynamics study of the slip time and static friction for a slab of Xe deposited on a slab of Cu. To put in evidence the role played by the phonon field of the two blocks, we compare results obtained with a substrate formed by fixed atoms with one formed by mobile atoms. In the last case the scattering between Xe and Cu mobile atoms is inelastic andthere is an exchange of momentum and energy between the two blocks which produces disorder in the interface plane. This disorder favors a decrease of the static friction and a consequentincrease of the slip time. We describe the interaction between Xe and Cu with a phenomenological multiion potential which gives rise to an anticorrugation of the charge distribution and reproduces very well the ab initio density functional calculations. Our model potential is a linear superposition of a corrugating potential and an anticorrugating one. For this reason we can study the static friction by passing from an anticorrugated to a fully corrugated system. We also investigate the slip time and we compare our results with recent experimental data measured with the quartz crystal microbalance technique.
2008
 Theory of the static friction: temperature and corrugation effects
[Articolo su rivista]
Franchini, Anna; Brigazzi, Marco; Santoro, Giorgio; Bortolani, Virginio
abstract
We present a study of the static friction, as a function of temperature, between two thick solid slabs. The upper one is formed of light particles and the substrate of heavy particles. We focus our attention on the interaction between the phonon fields of the two blocks and on the interface corrugation, among the various mechanisms responsible for the friction. To give evidence of the role played by the dynamical interaction of the substrate with the upper block, we consider both a substrate formed by fixed atoms and a substrate formed by mobile atoms. To study the effect of the corrugation, we model it by changing the range parameter σ in the LennardJones interaction potential. We found that in the case of the mobile substrate there is a largemomentum transfer from the substrate to the upper block. This momentum transfer increases on increasing the temperature and produces a large disorder in the upper block favouring a decreaseof the static friction with respect to the case for a rigid substrate. Reducing the corrugation, we found that with a rigid substrate the upper block becomes nearly commensurate, producing anenhancement of the static friction with respect to that with a mobile substrate.
2008
 Thermal effects in static friction: thermolubricity
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio; Santoro, Giorgio; Brigazzi, Marco
abstract
We present a molecular dynamics analysis of the static friction between two thick slabs. The upper block is formed by N2 molecules and the lower block by Pb atoms. We study the effects of the temperature as well as the effects produced by the structure of the surface of the lower block on the static friction. To put in evidence the temperature effects we will compare the results obtained with the lower block formed by still atoms withthose obtained when the atoms are allowed to vibrate (e.g., with phonons). To investigate the importance of the geometry of the surface of the lower block we apply the external force in different directions, with respect to a chosen crystallographic direction of the substrate. We show that the interaction between the lattice dynamics of the two blocks is responsible for the strong dependence of the static friction on the temperature. The latticedynamics interaction between the two blocks strongly reduces the static friction, with respect to the case of the rigid substrate. This is due to the large momentum transfer between atoms and the N2 molecules which disorders the molecules of the interface layer. A further disorder is introduced by the temperature. We perform calculations at T=20 K which is a temperature below the melting, which for our slab is at 50 K. We found that because of the disorder the static friction becomes independent of the direction of the external applied force. The very low value of the static friction seems to indicate that we are in a regime of thermolubricity similar to that observed in dynamical friction.
2007
 Localized spin modes in ferromagnetic cylindrical dots with inplane magnetization
[Articolo su rivista]
Roberto, Zivieri; Santoro, Giorgio; Franchini, Anna
abstract
A study of spin localized excitations in ferromagnetic tangentially magnetized dots of cylindrical shape and of nanometric size is presented. A recently formulated variational theory permits us to study the most representative localized spin modes of the spectrum. One of these, the fundamental mode, is mainly localized in the central part of the dot endfaces and is analogous to the Kittel uniform mode in ellipsoids. We also investigate the dynamical properties of spin modes localized in the lateral part of the dot endfaces along the direction of the applied magnetic field, studying the dependence of their localization on the variational parameter and the applied magnetic field. Finally, a comparisonof the calculated frequencies of some of these localized modes with available experimental data is performed.
2007
 Simulations of the temperature dependence of static friction at the N2/Pb interface
[Articolo su rivista]
Brigazzi, Marco; Santoro, Giorgio; Franchini, Anna; Bortolani, Virginio
abstract
A molecular dynamics approach for studying the static friction between two bodies, an insulator and a metal, as a function of the temperature is presented. The upper block is formed by N2 molecules and the lower block by Pb atoms. In both slabs the atoms are mobile. The interaction potential in each blockdescribes properly the lattice dynamics of the system. We show that the lattice vibrations and the structural disorder are responsible for the behaviour of the static friction as a function of the temperature. We found that a large momentumtransfer from the Pb atoms to the N2 molecules misplaces the N2 planes in the proximity of the interface. Around T = 20 K this effect produces the formation of an hcp stacking at the interface. By increasing the temperature, the hcp stacking propagates into the slab, toward the surface. Above T = 25 K, our analysis shows a sharp, rapid drop of more than three order of magnitudein the static friction force due to the misplacing of planes in the stacking of the fcc(111) layers, which are no longer in the minimum energy configuration. Above T = 35 K, we also observe a tendency for the splitting of planes and the formation of steps near the surface. By increasing the temperature we obtain thesubsequent melting of the N2 slab interface layer at T = 50 K. The temperature behaviour of the calculated static friction is in good agreement with recent measurements made with the quartz crystal microbalance (QCM) method on the same system.
2006
 Interaction of an external impurity with the surface intrinsic mode in a Heisenberg chain
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio; Wallis, Rf
abstract
In this paper we have demonstrated the existence of surface intrinsic localized modes in onedimensional classical spin systems. These modes have frequencies above the top of the magnon band and are more localized than the corresponding modes that were found in the lattice dynamics. By numerical methods we have studied the forward evolution in time. These entities are stable in time for many time steps. Also, we consider the interaction of these surface excitations with an external dipolar field. We have first considered the case in which the external dipole is parallel to the spins of the bulk. According to the distance of the impurity from the surface we find that at a particular distance a new surface mode appears, that we have called a mixed mode because it is formed by a localized state at the surface plus a plane wave. At large distances the dipole traps the surface mode, while at small distances the external impurity potential is so strong that all the spins are forced to be aligned in the z direction. For the case in which the external magnetic dipole is antiparallel to the bulk spins there are no mixed modes and the external impurity is so strong that the surface modes are trapped at large distances, and the bulk modes are trapped at very short distances.
2005
 Transition from smooth sliding to stickslip motion in a single frictional contact
[Articolo su rivista]
O. M., Braun; M., Peyrard; Bortolani, Virginio; Franchini, Anna; Vanossi, Andrea
abstract
We show that the transition from smooth sliding to stickslip motion in a single planar frictional junction always takes place at an atomicscale relative velocity of the substrates.
2004
 Coupling of intrinsic localized modes in doped polar semiconductors with plasmons
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio; R. F., Wallis
abstract
We present a detailed analysis of the interaction between intrinsic localized modes and plasmons in a doped polar semiconductor. The investigation has been performed for an anharmonic onedimensional diatomic lattice with alternating interactions coupling successive neighbours. The system simulates a row of atoms in the <111> direction of a IIIV semiconductor. Specific calculations have been performed for GaN, because it has a large gap between the acoustic and optical phonon branches. The calculations of the intrinsic localized modes have been performed by using twobody potentials to describe the interactions. We have used the rotating wave approximation and we have found the intrinsic localized modes in the phonon gap. The interaction with the plasmon has been studied by adding to the equations of motion the alternating electric field which is related to the electron density of the plasmons. We obtain an expression for the electric dynamical polarization associated with the intrinsic localized modes and with the plasmons. We derive an expression for the dielectric function of the coupled system. The zeros of the dielectric function give the frequency of the combined modes. We have found two regimes in which combined modes are possible. One is related to small anharmonicity of the potential. The combined mode has a frequency above the top of the optical branch and can be explained in terms of the theory of the harmonic dielectric response of polar lattice vibrations. The second regime is related to high anharmonicity. The combined modes exist only for a finite slab. We show that on increasing the anharmonicity, i.e. the amplitude of the intrinsic localized mode, the width of the slab increases. The frequency of the combined mode is inside the phonon gap. We have also studied the dynamical stability of these modes.
2004
 Intrinsic localized modes and their interaction with the plasmon electric field in one dimensional zincblende lattice
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio; Wallis, R. F.
abstract
In this paper we study the behavior of a diatomic nonlinear onedimensional lattice which represents the (111)direction of a zincblende threedimensional crystal. In these nonlinear lattices are present intrinsic localized modes dueto the anharmonicity. These modes lie in the vibrational gap between acoustic and optical linear spectrum. Consideringa highly doped GaN semiconductor we examine the coexistence of the localized modes with the electronic plasmaoscillations. We derive an expression for the plasmon electric field, we study the dynamics of the anharmonic lattice inpresence of this electric field and we calculate the dielectric function of the coupled system. The zeroes of the dielectricfunction give the frequencies of the coupled modes.
2004
 Modeling study of microscopic sliding on irregular substrates
[Articolo su rivista]
Vanossi, Andrea; Bishop, A. R.; Franchini, Anna; Bortolani, Virginio
abstract
In connection with microscopic solid friction phenomena, we study the underdamped dynamics of a driven Frenkel–Kontorova chain subject to a substrate potential defined by the sum of two sinusoidal function with different periodicity.We simulate microscopic sliding over quasiperiodic and multiplewell (periodic) substrates. We comment on thenature of the particle dynamics in the vicinity of the pinning–depinning transition point and consider the role played bythe coverage variable on the depinning mechanism. We also investigate on the different nonlinear excitations formingduring sliding and characterizing the dynamical states observed at different strengths of the imposed driving. Thedependence of the static friction on the ratio of the model interaction strengths is analyzed.
2004
 The interaction of intrinsic localized modes in the gap of doped semiconductors with plasmons
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio; Vanossi, Andrea; Rf, Wallis
abstract
We present a theoretical investigation of the interaction of intrinsic localized modes with plasmons. The anharmonic localized modes for a ID diatomic lattice are determined using a twobody potential which describes the interactions among particles in a zincblende structure material. The localized mode frequency is inside the gap between acoustic and optical phonons. Calculations have been performed for GaN because it has a large phonon gap, can be highly ndoped, and the plasma frequency of free carriers is in the range of phonon and intrinsic localized mode frequencies. To study the coupling we add to the equations of motion an electric field to simulate the plasmon. Solving the system we obtain the dynamical displacements pattern from which we evaluate the total polarization. From the polarization we determine the frequency of the combined mode for which the dielectric function is zero. In this investigation we have analysed both the case of small localized mode amplitudes and the case of larger amplitudes, obtaining different behaviour. In the first case the mixed mode has a frequency above the top of the optical branch, which can be explained in terms of the theory of the harmonic dielectric response of polar lattice vibrations. In the second case the coupled mode exists only for a finite slab, and its frequency is inside the phonon gap.
2002
 Anharmonic effects in a finite FrenkelKontorova type chain
[Articolo su rivista]
Vanossi, Andrea; Franchini, Anna; Bortolani, Virginio
abstract
The features of the ground state and the phonon frequency spectrum of a finite FrenkelKontorova type model are investigated in presence of quartic anharmonic nearestneighbor interactions. The different computational techniques used allow us to determine with great accuracy the critical parameter for the groundstate symmetry breaking transition, showing its dependence on the strength of the interatomic anharmonicity introduced. The phonon gap. the linearized vibrational modes and their parity are also studied in the vicinity of the transition point. (C) 2002 Elsevier Science B.V. All rights reserved.
2002
 Singlephonon scattering from clean flat metal surfaces
[Articolo su rivista]
Franchini, Anna; Santoro, Giorgio
abstract
In this paper we review the recent advances of the He atom scattering experiments and the theoretical interpretation of the timeofflight (TOF) spectra relative to clean flat metal surfaces in the onephonon regime. We discuss the atomsurface scattering mechanism, including the anomalies in the metal surface phonon spectrum and the details of the atomsurface interaction potential. In particular we focus the discussion on the anticorrugating effects in the TOF intensities.
2002
 Surface and gap intrinsic localized modes in onedimensional lattices
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio; Rf, Wallis
abstract
In this paper we discuss the intrinsic localized modes of diatomic anharmonic chains for two different geometries, which simulate a row of a zincblende threedimensional crystal or a row of an alkalihalide crystal. The modes are determined with two different potential models. using the full potential or the Taylor expansion truncated to fourth order. We obtain bulk modes and two kind of surface modes in the frequency gap between acoustical and optical phonons. (C) 2002 Elsevier Science B.V. All rights reserved.
2002
 Surface thermal expansion of Ag(110)
[Articolo su rivista]
Franchini, Anna; C., Magherini; Santoro, Giorgio
abstract
In this paper we calculate the surface thermal expansion of Ag(1 1 0). applying the perturbation theory to treat the effects of the anharmonic part of the interatomic potential. Results relative to the relaxation of the interlayer distance are presented for different temperatures. These results confirm the alternate contraction and expansion at room temperature and the enhancement of the anharmonicity in the surface region. (C) 2002 Elsevier Science B.V. All rights reserved.
2002
 Theory of intrinsic localized modes in diatomic chains: beyond the rotating wave approximation
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio; Rf, Wallis
abstract
Intrinsic localized modes in the gap of a diatomic chain with free ends are discussed in detail by going beyond the rotating wave approximation. We include in the time dependence of the displacements terms up to cos(2omegat). We consider a finite chain of particles interacting with nearestneighbour interactions. We study amplitudes of the intrinsic localized modes smaller than 0.25 Angstrom. In this range of amplitudes the full potential can be well represented by an expansion in powers of the displacements up to fourthorder terms. The use of a force constant model allows us to simplify the problem. As a test case we consider a chain of LiI atoms. We found intrinsic localized modes in the gap. The amplitudes of the first harmonic term (cos(omegat)) are of even or odd parity, whereas we prove that the amplitudes of the static part and those of the second harmonic can have only even symmetry. The main result of the paper is that the amplitudes associated with the second harmonic are two or three orders of magnitude less than those of the first harmonic. Furthermore, the frequency of the localized modes are modified by less than 1% by the inclusion of the second harmonic.
2001
 Interpretation of inelastic scattering of He from Cu surfaces in the anticorrugated potential model
[Articolo su rivista]
Santoro, Giorgio; Franchini, Anna; Bortolani, Virginio; Dl, Mills; Rf, Wallis
abstract
In this paper we demonstrate that inclusion of the anticorrugation effects in the pseudopotential describing the dynamic interaction of neutral He atoms with phonons of Cu(1 1 1) and Cu(1 0 0) surfaces can resolve the long standing discrepancy between the inelastic scattering intensities inferred from HASTOF and from the electron energy loss spectroscopy data.
2000
 Intrinsic localized modes in the onedimensional zincblende structure: twobody potential versus anharmonic force constant model
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio; R. F., Wallis
abstract
In this paper we examine the existence of anharmonic localized modes using a full twobody potential to describe all interactions between particles in a zincblendestructure material, and we make a comparison with the results obtained with a nearestneighbour force constant model that includes interactions up to quartic anharmonicity. We show that for amplitude up to a maximum displacement of the order of 0.25 Angstrom there are no appreciable differences between the two approaches, while for the largest amplitudes the force constant model gives unphysical results.
2000
 Surface and gap intrinsic localized modes in onedimensional IIIV semiconductors
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio; Rf, Wallis
abstract
A theoretical investigation has been made of intrinsic localized vibrational modes in an anharmonic onedimensional diatomic lattice with alternating force constants coupling successive neighbours. This system simulates a row of atoms in the (1 1 1) direction of a IIIV semiconductor. Specific calculations have been carried out for GaN, because it has a large gap between acoustic and optical branches. We study smallamplitude atom vibrations (up to 0.4 Angstrom), accessible to experimental detection, in order to legitimize the expansion of the full potential to include cubic and quartic terms. We consider then nearestneighbour interactions through harmonic as well as cubic and quartic anharmonic interactions to study the interplay between cubic and quartic terms in the frequencies of the localized modes. The force constants were determined empirically by fitting the longitudinal branches in the GammaL direction of GaN. We have studied both gap and surface intrinsic localized modes. Zincblendestructure chains are of particular interest, because the lack of inversion symmetry prevents the classification of the modes as even or odd parity. Nevertheless, modes were found that closely resemble the even or oddparity modes of an NaClstructure chain. Their frequencies lie inside the gap for GaN. The absence of inversion symmetry permits a variety of surface modes to exist, depending on whether the bond at the surface is strong or weak and the atom at the surface is light or heavy. All surface mode frequencies for GaN lie inside the gap as found with the use of the full potential.
1999
 Cesium under pressure: Firstprinciples calculation of the bcctofcc phase transition
[Articolo su rivista]
Carlesi, S; Franchini, Anna; Bortolani, Virginio; Martinelli, S.
abstract
In this paper we present the ab initio calculation of the structural properties of cesium under pressure. The calculation of the total energy is done in the localdensity approximation of densityfunctional theory, using a nonlocal pseudopotential including the nonlinear core corrections proposed by Louie et al. The calculation of the pressurevolume diagram for both bcc and fee structures allows us to prove that the transition from bcc to fee structure is a firstorder transition. [S01631829(99)006177].
1998
 Anticorrugation in inelastic Heatom scattering from Rh(111) surfaces
[Articolo su rivista]
Santoro, Giorgio; Franchini, Anna; Bortolani, Virginio
abstract
Recent measurements supported by nb initio calculations have shown that the interaction of He atoms with transition metal surfaces is anticorrugating, i.e., the electron density seen by He is higher in the bridge positions than in the ontop positions. By shifting the electron charge density away from the atomic positions and using the EsbjergNorskov approach to determine the interaction potential, we evaluate the inelastic reflection coefficients of He with Rh(lll). The structure factor introduced by the anticorrugation explains, in a simple way, the high intensity observed for the resonant mode.
1998
 Dynamical properties of Rh(111):H(1x1) surface
[Articolo su rivista]
Santoro, Giorgio; Franchini, Anna; Bortolani, Virginio
abstract
In the experimental He atom scattering timeofflight spectra of rhodium covered with hydrogen there is no evidence of the anomalous high intensity of the resonant mode present in the clean surface. In this paper we explain the different behaviour of clean and covered rhodium (111) surface in terms of the "corrugating" effect of the electron density of hydrogen atoms. For clean surface the surface electronic density is shifted with respect to the lattice atomic positions, i.e. there is an "anticorrugating" effect that enhances the intensity of the longitudinal resonant mode which becomes dominant for some scattering geometries. For the covered surface the hydrogen atoms remove the anticorrugation, the charge profile becomes corrugated and the intensity of the longitudinal resonant vibrational mode remains very weak with respect to the Rayleigh wave intensity.
1998
 Intrinsic localized modes in the bulk and at the surface of anharmonic chains
[Relazione in Atti di Convegno]
Bortolani, Virginio; Franchini, Anna; Wallis, R. F.
abstract
In this paper we will review recents results relative to localized modes induced by anharmonicity in onedimensional lattices. We will show that localized modes exists in monoatomic chains with and without a local inhomogeneity in the anharmonic force field. We will compare the discrete and the quasicontinuum intrinsic even and odd localized solutions. This analysis is carried out by taking into account harmonic and quartic anharmonic interactions. We will also present results for the diatomic chains showing the presence of surface modes ad gap modes related to the maximum of the acoustic band. In this analysis will be also studied the effect of the cubic anharmonicity. One of the major effetcs of the cubic anharmonicity is to produce gap modes that split off from the bottom of the optical branch.
1998
 Localized modes in an anharmonic diamondstructure chain
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio; Wallis, Rf
abstract
In this paper we study localized vibrational modes in a chain of atoms with the same mass, but with two alternating force constants between nearest neighbors. This model simulates a row of atoms in the [111] direction of a diamond or silicon crystal. Cubic and quartic anharmonicity are included in the potential. The harmonic and quartic anharmonic terms produce intrinsic localized modes with frequencies above the optical branch and in the gap. The inclusion of cubic terms with negative coefficients reduces the frequencies, leads to new localized modes in the gap, and introduces static distortions of the chain. Modes of both even and odd parity occur. Surface modes occur when the localization is near a free end.
1997
 Surface localized modes in anharmonic systems at low dimensionality
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio; Wallis, Rf
abstract
In this paper we discuss in detail the localized vibrational modes in monoatomic and diatomic onedimensional chains induced by anharmonicity. Analysis of the effects of the quartic anharmonic interactions in the Vibrational spectrum shows, in the monoatomic case, the appearance of surface modes, not allowed in the harmonic field, and of highfrequency modes. In the diatomic case we found two types of surface mode, the first reminiscent of the harmonic one and the second entirely due to the anharmonicity, and two localized gap modes arising from the top of the acoustic branch with odd parity centered on a heavy atom and even parity centered on a light atom. The introduction of cubic anharmonicity produces odd and even gap localized modes arising from the bottom of the optical branch and affects the surface modes.
1997
 Theory of kink and domainwall excitations in translationally invariant lattices with quartic anharmonicity
[Articolo su rivista]
Bortolani, Virginio; Franchini, Anna; Wallis, Rf
abstract
A theoretical investigation has been made of localized excitations having the form of kinks or domain walls in translationally invariant monatomic lattices with harmonic and quartic anharmonic interactions between nearestneighbor atoms. Antisymmetric kinks are found for negative values of the anharmonic coefficient. Symmetric kinks are found to be poorly defined for translationally invariant anharmonic potentials. In the case of domain walls, stable solutions were obtained only for negative values of the anharmonic coefficient. These results are compared with those for onsite quartic anharmonicity.
1996
 Anomalous linewidth behavior of the S3 surface resonance on Ag(110)
[Articolo su rivista]
G., Bracco; L., Bruschi; R., Tatarek; Franchini, Anna; Bortolani, Virginio; Santoro, Giorgio
abstract
We report detailed He atom scattering measurements of the phonon linewidth for the Rayleigh mode S1 and the resonant mode S3 of Ag(110) along the whole <(Gamma) over bar><(Y) over bar> side of the surface Brillouin zone as a function of the sample temperature. The novel behaviour observed for the resonance linewidth is explained by including the mixedmode nature into the anharmonic calculations performed within the framework of the Bornvon Karman model.
1996
 Effects of the cubic vs quartic anharmonicity in gap and surface localized modes of diatomic chains
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio; Wallis, R. F.
abstract
In this paper we discuss in detail the gap localized vibrational modes in a diatomic anharmonic chain. We consider a finite (even or odd9 number of particles interacting with nearest neighbours harmonic and cubic and quartic anharmonic force constants. The analysis of the effect of these anharmonic interactions shows that in the gap there are localized modes arising from the top of the acoustic branch with odd parity if they are centerewd on a heavy atom and even parity if they are centered on a light atom. These acoustic gap modes are related to the quartic anharmonicity, while there are localized modes arising from the bottom of the optical branch in presence of cubic anharmonicity. Th optical odd parity modes are centered on a light atom and the even parity modes are centered on a heavy atom. In addition to these gap modes we have found two types of surface modes. One which is remenescent of the surface mode occurring on a finite diatomic harmonic chain and the other entirely due to the anhermonicity.
1996
 Intrinsic localized modes in the bulk and at the surface of anharmonic diatomic chains
[Articolo su rivista]
FRANCHINI, Anna; BORTOLANI, Virginio; Wallis, RF
abstract
Intrinsic localized vibrational modes in a diatomic anharmonic chain are discussed in detail. We consider a finite (even or odd) number of particles interacting with nearestneighbor harmonic and cubic and quartic anharmonic potentials. For suitable values of the potential parameters we find two odd parity modes localized about light and heavy atoms, respectively, with frequencies above the top of the optical branch. In the gap there are localized modes arising from the top of the acoustic branch with odd parity if they are centered on a heavy atom and even parity if centered on a light atom. There are also two localized modes originating from the bottom of the optical branch. The odd parity mode is centered on a light atom, while the even parity mode is centered on a heavy atom. In addition, we have found two types of surface modes. One is the anharmonic version of the surface mode occurring in a finite diatomic harmonic chain with frequency in the gap, and the other is entirely due to the anharmonicity. The latter mode has its frequency above the top of the optical branch. A comparison with other work is given.
1996
 Localized modes in monoatomic and diatomic chains due to the anharmonicity
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio; Corsini, F.
abstract
Intrinsic localized modes due to the anharmonicty are discussed in detail in the case of monoatomic chains considering a finite (even or odd) number of particles interacting with nearest neighbours harmonic and quartic anharmonic force constants. We find odd parity and even parity localized modes above the maximum harmonic frequency in the monoatomic case. These modes persist modifying the anharmonic force constant at the center of the chain, but their envelope shape becomes double peaked. Preliminary resylts for diatomic chains are also presented. In tis case we find odd localized modes above the maximum harmonic frequency and in the gap between the acoustic and optic continuum.
1995
 Inhomogeneous onedimensional anharmonic chains
[Relazione in Atti di Convegno]
Franchini, Anna; Bortolani, Virginio; Corsini, F.; Wallis, R. F.
abstract
In this paper we present numerical calculations of intrinsic localized modes of a monoatomic onedimensional chain with free ends and quartic anharmonicity. We study in particular the case of even and odd parity modes in presence of an inhomogeneity in the quartic force constants located in the center of the chain to preserve the symmetry of the solutions. In the limit of low anharmonicity we study also the analytical solutions of the Non Linear Schreodinger equation that we obtain from the continuum approximation of the equations of motion.
1994
 Inelastic Heatom scattering from metal surfaces
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio
abstract
In this paper we review the recent advances in the theory of Heatom inelastic scattering used to study the lattice dynamics of metal surfaces. We discuss the importance of the Hesurface interaction potential and the various techniques employed up to now to determine the Surface phonon dispersions. The anharmonic contributions to the onephonon linewidth are also discussed.
1994
 Localized modes in inhomogeneous onedimensional anharmonic lattices
[Articolo su rivista]
Wallis, R. F.; FRANCHINI, Anna; BORTOLANI, Virginio
abstract
We present numerical calculations for the determination of localized modes in onedimensional finite chains of atoms with free ends containing harmonic and quartic anharmonic interactions. By adding step by step the quartic term we can follow the formation of even and odd localized modes arising from the highest harmonic frequency mode. We have studied the role of crystal inhomogeneity by introducing a modification of the fourthorder force constant between neighboring atoms at the center of the chain, where the localized mode has its maximum displacement. For large weakening of this force constant the localized mode develops a doublepeaked structure, as has been found in the continuum limit. In the case of asymmetrical local inhomogeneity the localized mode remains stable and moves toward the atom with the inhomogeneity. We also show the existence of anharmonic surface modes localized at the end of the chain.
1994
 Role of the Heatom surface potential on the Cu(001) phonon determination
[Articolo su rivista]
Franchini, Anna; Santoro, Giorgio; Bortolani, Virginio; Bellman, A. G.; Cvetko, D.; Floreano, F.; Morgante, A.; Peloi, M.; Tommasini, F.; Zambelli, T.
abstract
We present new measurements of He atom inelastic scattering from the (001) surface of Copper. Our results confirmed the recent data obtained in Gottingen and show that at large momentum transfer in the GM direction the intensity of the longitudinal resonance is larger than that of the Rayleigh wave. We interpret these results by evaluating the reflection coefficient in the Distorted Wave Born Approximation. By taking the He surface interaction potential as a sum of nonspherical pairwise potential we are able to explain quantitatively the behavior of the experimental spectra.
1994
 Surface phonon linewidth of Al
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio; Santoro, Giorgio; Wallis, R. F.; Maradudin, A. A.
abstract
In this paper we present a numerical calculation of the Rayleigh wave phonon linewidth based on a cubic anharmonic expansion of the interatomic potential of the crystal. The linewidth is evaluated at high symmetry points of the twodimensional Brillouin Zone (SBZ) of the Al low Miller indices surfaces for various temperatures. The results are consistent with the experimental He surface scattering measurements and show an enhanced linewidth with respect to the nulk transverse one.
1993
 COMPARISON BETWEEN PHENOMENOLOGICAL AND PSEUDOPOTENTIAL FORCECONSTANTS FOR THE LATTICEDYNAMICS OF AL
[Articolo su rivista]
Wallis, Rf; Maradudin, Aa; Bortolani, Virginio; Eguiluz, Ag; Quong, Aa; Franchini, Anna; Santoro, Giorgio
abstract
In this paper we present a critical comparison of,calculations of phonondispersion curves for aluminum, based on pseudopotential and empirical forceconstant methods. The former method is.based on both perturbative and nonperturbative evaluations of the total energy of the crystal. In the perturbative approach the total energy is evaluated to second order in the electronion interaction with a local pseudopotential. In the nonperturbative approach the electronion interaction is treated exactly using a nonlocal ab initio pseudopotential. In the empirical forceconstant method the total energy is represented by a sum of twobody and threebody terms, the latter being restricted to interactions among triplets of nearest neighbors and of nearest and nextnearest neighbors. All models include physical mechanisms for ensuring the breakdown of the Cauchy relation. We show that in each method convergence of the calculated phonon frequencies requires the inclusion of longrange interactions. The radialforce constants obtained by the empirical and perturbative pseudopotential methods are very similar for the first three shells of neighbors. On the other hand, the tangential force constants differ markedly, a reflection of the different physical mechanisms that come into play in the various models in the establishment of equilibrium.
1993
 Comparison of semiempirical and abinitio pseudopotential calculations of the latticedynamics of aluminium surfaces with Hescattering timeofflight spectra
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio; Santoro, Giorgio; Celli, V.; Eguiluz, A. G.; Gaspar, J. A.; Gester, M.; Lock, A.; Toennies, J. P.
abstract
We report a detailed comparison of two theoretical methods for the study of the surface lattice dynamics of spbonded aluminum and compare the results with Heatom timeofflight spectra for the (001), (110), and (111) surfaces of this metal. One of the theoretical methods is a semiempirical Bornvon Karman scheme in which the interatomic force constants are related to central pairwise forces and also to ''angledependent'' interactions between triplets of atoms. The other method is an ab initio scheme in which the interatomic force constants are calculated from the electrondensity response function and secondorder pseudopotential perturbation theory. Both schemes require the inclusion of longrange central forces (up to ten nearest neighbors) in order to obtain converged results. In addition, the semiempirical approach must include threebody forces up to secondnearest neighbors to allow for the breakdown of the Cauchy relation, which in the ab initio method arises as a direct consequence of the volume dependence of the effective pair potential. The semiempirical approach reproduces accurately the surface phonondispersion curves calculated with the ab initio scheme. The leading surface force constants obtained in both methods have similar values, which provides justification for the physical significance of the semiempirical force constants. Both methods reproduce, with great accuracy, the experimental dispersion relations for the Rayleigh surface phonons, except for the case of the (110) surface. Assuming that the He atom couples only to the ion cores, the reflection coefficients calculated in both methods reproduce well the intensities of the weak resonances observed in the He timeofflight spectra below the longitudinal edge. These structures can be explained in terms of Fano resonances.
1993
 Elastic and inelastic interactions of He and Ne atoms with metals surfaces
[Articolo su rivista]
Bortolani, Virginio; D., Cvetko; F., Floreano; Franchini, Anna; A., Lausi; A., Morgante; M., Peloi; Santoro, Giorgio; F., Tommasini; T., Zambelli; Af, Bellman
abstract
The experimental information accumulated in recent years on elastic and inelastic scattering of He and Ne atoms from metal surfaces is analysed by describing the atomsurface interaction as a superposition of pseudopairwise potentials. These are chosen according to the quite accurate potentials presently available for van der Waals pairs and take a phenomenological account for many body effects. The emerging picture is quite satisfactory and allows the physical interaction of a given atomsurface system to be predicted with excellent accuracy. In particular the coupling of He atoms to the surface vibrational modes is considered with attention focused on He inelastic scattering from Cu(001).
1993
 Surface Phonon Linewidth
[Relazione in Atti di Convegno]
Franchini, Anna
abstract
In this paper are presented theoretical calculations of the linewidth of the Rayleigh phonon propagating along high symmetry directions of the (111) surfrace of Aluminium both for different temperatures and for different values of the phonon momentum. The interatomic potential pf the crystal contains both a harmonic part which describes the normal vibrations of the crystal and a cubic part which is the dominant term of the lifetimes of the vibrations. The calculations show a rapid decay when either the temperature of the momentum transfer decrease, and a large anisotropy with the direction od the momentum transfer.
1992
 The phonons of the Al surfaces: comparison between semiempirical and abinitio calculations
[Articolo su rivista]
Franchini, Anna; Bortolani, Virginio; Santoro, Giorgio; Ja, Gaspar; Ag, Eguiluz
abstract
We report inelastic Heatom surface scattering data for the lowindex surfaces of aluminum. The experimental data are analyzed by using a semiempirical Bornvon Karman model in which both twobody and threebody interactions are taken into account and by using an ab initio pseudopotential approach. Our analysis shows that the semiempirical model containing longrange forces agrees with great accuracy with the pseudopotential calculations for what concerns both the range of the interactions and the dispersion of the surface vibrational modes. The calculations of the reflection coefficients allow us to study the nature of the weak resonances observed in the timeofflight spectra. These structures are related to a picking up of modes with polarization vector normal to the surface due to the modification introduced by the surface on the entire force field. Our analysis of Al proves that for simple metals an accurate semiempirical model can reproduce with great accuracy both the surface lattice dynamics, without introducing new free parameters in the surface interatomic potential, as well as an ab initio pseudopotential calculation.
1992
 Theory of the anharmonic linewidths of surface phonons in aluminum
[Articolo su rivista]
Franchini, Anna; Santoro, Giorgio; Bortolani, Virginio; Maradudin, Aa; Wallis, Rf
abstract
A theoretical investigation has been made of the linewidth of the Rayleigh mode on the Al(111) surface due to cubic anharmonic interactions between atoms. The normalmode frequencies and eigenvectors for the harmonic crystal were calculated by using a model containing central interactions extending up to tenthnearest neighbors and threebody interactions extending up to secondnearest neighbors. This model reproduces with great accuracy the experimental bulkphonon frequencies as well as the surfacephonon frequencies. The linewidths were evaluated along the SIGMABAR direction as a function of the lateral momentum transfer and at the MBAR point as a function of the temperature. The results compare favorably with recent experimental data.
1990
 AngleResolved Thermal Desorption and Timeofflight spectra:NeCu(111)
[Articolo su rivista]
Bortolani, Virginio; Brivio, G. P.; Franchini, Anna; Grimley, T. B.; Santoro, Giorgio
abstract
The angleresolved thermal desorption flux, and timeofflight spectrum have been computed for NeCu( 111) using a microscopic description of the phonons of Cu( 1 I 1 ), and a realistic gassolid potential. The angular distribution is narrower than cosine at 5 K, quasicosine at 10 K, and distinctly noncosine at 20 and 30 K with the maximum away from the surface normal. The desorption is driven by longwavelength phonons, but the precise angular dependence results from the temperaturedependent interplay of statistical and dynamical factors. He desorbing from graphite shows similar features.
1990
 Comparison of abInitio and Phenomenological Calculations of Surface Phonons
[Articolo su rivista]
Eguiluz, A. G.; Gaspar, J. A.; Bortolani, Virginio; Franchini, Anna; Santoro, Giorgio
abstract
In this paper we will address to the problem of the physical meaning of the force constants by comparing the forces acting betwen atoms both in the surface region and in the bulk, calculated in the framework of a sophisticated force constant model and the corresponding forces evaluated in the framework of an apriori pseudopotential theory, where the electronion system is treated perturbatively by considering the effect of the electronic screening and the roel od the electronelectron term on the electronphono interaction.
1990
 Explanation of the Force Constant Softening in Noble Metals: the Case of Au(111)
[Articolo su rivista]
Bortolani, Virginio; Ercolessi, F.; Tosatti, E.; Franchini, Anna; Santoro, Giorgio
abstract
A new mechanism for the well known inplane force softening on the noble metal surfaces is presented. The mechanism is discussed in terms of a manybody force scheme and is shown to amount to an effective decrease of the lateral atomic ‘size’ of the surface atom. Its strong sensitivity to surface relaxation and reconstruction is emphasized. As a nontrivial illustration we calculate the phonon density of states of Au(111) and show that the large softening leading to the observed anomalous longitudinal resonance is directly related to our proposed mechanism. We also discuss the importance of the surface stress on the statics and dynamics of these surfaces.
1990
 Far Infrared Vibrational Spectroscopy in CrSi_2
[Articolo su rivista]
A., Borghesi; A., Piaggi; Franchini, Anna; G., Guizzetti; Nava, Filippo; Santoro, Giorgio
abstract
We present and discuss reflectance and trasmittance measurements on CrSi, polycrystalline films in the (100 + 700) cm' wavenumber range. The spectra show that the compound has a nonmetallic behaviour. The strong and sharp structures observed are interpreted on the basis of the symmetry properties of the normal modes of CrSie, and their strength is attributed to a dynamical charge. Moreover, preliminary lattice dynamicscalculations allow to explain the relative intensity of the infraredactive modes.
1990
 Multiphonon Effects in Atom Surface Scattering: the Case of Pt(111)
[Articolo su rivista]
Celli, V.; Himes, D.; Bortolani, Virginio; Franchini, Anna; Santoro, Giorgio
abstract
In this paper we show that the huge structures recently observed experimentally ith the Hesurface atom scattering technique by using hot beams can be related with some confidence to multiphonon scattering events.
1990
 The Origin of Force Constant Softening on the Close Packed Noble Metal Surfaces
[Articolo su rivista]
Bortolani, Virginio; Ercolessi, F.; Tosatti, E.; Franchini, Anna; Santoro, Giorgio
abstract
A qualitatively new mechanism is proposed for the wellknown inplane force softening found on many noblemetal surfaces. The mechanism is discussed in terms of one of the recently developed manybody force schemes and is shown to amount to an effective decrease of the lateral atomic .sizes of the surface atom. Its strong sensitivity to the strength of the manybodyforce terms, as well as to surface relaxation and reconstruction, is emphasized. As a nontrivial illustration, we calculate the phonons of Au(lll), and show that the exceedingly large softening leading to the recently observed anomalous longitudinal resonance is directly related to our proposed mechanism.
1990
 Thermal Desorption of Light Rare Gases from Metals: onephonon Processes
[Articolo su rivista]
Bortolani, Virginio; Franchini, Anna; Nizzoli, F.; Santoro, Giorgio
abstract
In this paper we report calculations of the ADF and of the TOF spectra of the physisorbed system NeCu(111) at very low coverage: specifically we consider a onephonon driven desorption process, which uses an accurate description of the surface lattice dynamics and a Morse gassurface potential, whose parameters are fitted in order to obtain the experimental boun states of Ne on a copper surface.
1990
 Vibrational effects in Desorption of Light Rare Gases from Metals
[Articolo su rivista]
Brivio, G. P.; Grimley, T. B.; Bortolani, Virginio; Franchini, Anna; Santoro, Giorgio
abstract
The angleresolved thermal desorption flux for NeCu(111) has been computed at 5, 10 and 15 K in the Distorted Wave Born Approximation using an accurate microscopic description of the surface lattice dynamics, and a realistic gassolid potential. The angular distribution narrows as the temperature is lowered, being broader than the equilibrium theory cosine law at 15 and 10 K and narrower than it at 5 K. The TimeofFlight spectra of the desorbed atoms are also analysed.
1989
 DebyeWaller factor for He/Pt(111)
[Articolo su rivista]
Bortolani, Virginio; Celli, V.; Franchini, Anna; Idiodi, J.; Santoro, Giorgio; Kern, K.; Poelsema, B.; Comsa, G.
abstract
We report accurate measurements of the dependence of the specular reflectivity on surface temperature and on incident angle, for He scattering off Pt(111). The usual DebyeWaller formula with a Beeby correction fits the data, provided that the effective well depth is adjusted. We show that a full calculation of the DebyeWaller exponent also reproduces the data. The inelastic atomsurface interaction and the surface phonon spectrum used in the calculation are the ones that reproduce the timeofflight data obtained in separate experiments. No further adjustable parameters are needed.
1989
 Surface Resonant Phonons of Ag(110)
[Articolo su rivista]
Tatarek, R.; Bracco, G.; Tommasini, F.; Franchini, Anna; Bortolani, Virginio; Santoro, Giorgio; Wallis, R. F.
abstract
A study of the dynamics of the Ag(110) surface in the ḡGȲ direction is presented. The experimental TOF spectra show the existence of two low frequency modes with high scattering intensity and a dispersionless high frequency mode with a smaller intensity. The theoretical analysis based on a force constant model that contains longrange central interactions and shortrange angular forces explains accurately both the dispersions and the scattering intensities of the three modes in terms of resonant and localized vibrations related to the modifications of the surface force constants caused by the different role played by the manybody forces in the surface region.
1989
 Surface phonons on the Pt(111) surface: a comparison of Hescattering experiments with lattice dynamical calculations
[Articolo su rivista]
Bortolani, Virginio; Franchini, Anna; Santoro, Giorgio; Toennies, J. P.; Woll, C. H.; Zhang, G.
abstract
Angular distributions and surfacephonon dispersion curves have been measured by Heatom scattering for clean Pt between T=160 and 373 K and for PtH(1×1) at 160 K along the 〈110〉 and 〈112〉 azimuths. Inelasticscattering intensities over a wide range of wave vectors are also reported for the clean surface. The results are analyzed with use of the distortedwave Born approximation for a model potential describing the Heatom–Ptsurface potential. A set of 14 force constants adjusted to the bulkphonon dispersion data cannot explain the measured timeofflight spectra and the observed firstlayer relaxation. However, by modifying at the surface the nearestneighbor tangential force constants (α1’’=1.7α1b, and α1’=1.3α1b), the radial force constants (β1’’=0.39β1b), and the threebody force constant (γ1’’=0.037γ1b)— where the superscripts ∥ and ⊥ denote forces within the surface plane and between the first and second planes, respectively—a good fit to all the data is achieved. The new surface force constants are discussed in terms of electroniccharge redistribution within the first layer.
1988
 Phonons at the surface of the nearlyfreeelectron metal Al(111): realisation of an ideal surface
[Articolo su rivista]
LOCK, A.; TOENNIES, J. P.; WOLL, C. H.; BORTOLANI, Virginio; SANTORO, Giorgio; FRANCHINI, Anna
abstract
Surface phonons of the nearlyfreeelectron metal Al(111) have been measured by highresolution Heatom timeofflight experiments for four different directions. This is the first surface which shows no evidence for an anomalous resonant mode found on the noble metals and Pt and attributed to a strong (≊50%) reduction of surface lateral force constants. By fitting the timeofflight spectra via a latticedynamical simulation the surface interlayer force constant is found to agree to within ±3% with the bulk value and the lateral force constant reduction is less than 20%.
1988
 Surface Lattice Dynamics of Cu(111)
[Articolo su rivista]
Franchini, Anna; Santoro, Giorgio; Bortolani, Virginio
abstract
We presnet a lattice dynamical calculation of the Cu(111) surface, based on the slab method in the framework of a force constant parametrization scheme that includes central and angular interactions.
1988
 Theory of surface resonant phonons on the open (110) surface of Silver
[Articolo su rivista]
FRANCHINI, Anna; SANTORO, Giorgio; BORTOLANI, Virginio; WALLIS, R. F.
abstract
Recent timeofflight measurements have been interpreted in terms of a forceconstant model. We show that for phonon waves propagating along the ΓX direction, containing nearest neighbors, it is necessary to introduce a large softening of the lateral surface force constants (40%) in agreement with earlier calculations on the Ag(111) surface.
1987
 Calculation of DebyeWaller factor for atomsurface scattering:He on Ag(111)
[Articolo su rivista]
Idiodi, J.; Bortolani, Virginio; Franchini, Anna; Santoro, Giorgio; Celli, V.
abstract
By a consistent application of the distortedwave Born approximation, the DebyeWaller exponent for the scattering of He atoms from the Ag(111) surface is directly computed. When diffraction is negligible, as in this case, the decrease in specular intensity is simply obtained by summing the scattering due to all possible onephonon processes. Using onephonon computed intensities that agree with experiment along highsymmetry directions of the surface Brillouin zone, we find that the computed DebyeWaller exponent agrees with experiment and corresponds to an effective Debye temperature of 241 K. All corrections to the eikonaltype formula, 2W=4pz2〈uz2〉, are automatically included. In particular, the contribution of phonons with high parallel momentum is sharply cut off.
1987
 Inelastic Phonon Scattering of Helium atoms from the reconstructed Au(111) surface
[Articolo su rivista]
Santoro, Giorgio; Franchini, Anna; Bortolani, Virginio; Harten, U.; Toennies, J. P.; Woll, C. H.
abstract
We present inelastic atomsurface phonon scattering timeofflight spectra for the reconstructed Au(111) surface. The shapes of the spectra are compared with calculated reflection coefficients based on a simplified lattice dynamical model for the reconstructed surface. The force constants were determined from a best fit of the surface phonon dispersion curves and the lateral atomatom interactions in the surface layer were found to be 30% of the bulk value. The theoretical spectra reproduce the overall lineshape of the experimental spectra and reveal additional features which can be attributed to the reconstruction of the surface layer with respect to the substrate.
1987
 Surface phonon dispersion on Cu(110): a comparison of experiment and theory
[Articolo su rivista]
Black, E.; Franchini, Anna; Bortolani, Virginio; Santoro, Giorgio; Wallis, R. F.
abstract
The surfacephonon frequencies of the open (110) surface of Cu have been investigated by means of forceconstant models. Agreement with experiment is achieved by introducing a surface stress normal to the surface pointing toward the crystal. This force accounts for the charge redistribution which gives rise to the observed contraction of the surface interlayer spacing. In the ΓY direction, where the nearest neighbors do not lie on the surface, a weakening of the surface radial force constants is not necessary as for the (111) surface. The model used explains quite satisfactorily the three modes observed experimentally.
1987
 The phonon frequencies of the (111) surface of Platinum: existence of three localized modes
[Articolo su rivista]
Bortolani, Virginio; Franchini, Anna; Santoro, Giorgio
abstract
The He surface reflection coefficients have been evaluated for the Pt(111) surface by using a long range force constants model for the bulk phonons. The lowering of the lateral surface force constants allows one to explain in a quantitative manner the existence of all the peaks observed in the experimental spectra.
1986
 Inelastic He scattering from metal surfaces
[Articolo su rivista]
Bortolani, Virginio; Franchini, Anna; Santoro, Giorgio
abstract
We present inelastic aton surface phonon scattering time of flight spectra for the reconstructed Au(111) and for the Pt(111) unreconstructed surface.
1985
 On the detection of pseudo surface modes in Ag(111) with Hesurface scattering
[Articolo su rivista]
Bortolani, Virginio; Franchini, Anna; Nizzoli, F.; Santoro, Giorgio
abstract
We evaluate the surface phonon dispersion relations of Ag(111) within a force constants parametrization of the bulk dynamics. By changing the surface force constants we are able to explain all the salient features appearing in the experimental time of flight spectra. The parallel momentum Q has been considered along the direction [110] of the surface Brillouin zone. We show that the peaks of the time of flight spectra are related to the Rayleigh wave, to the pseudo Rayleigh wave and to a new resonance of longitudinal character. A comparison is made with the [112] direction.
1985
 Surface phonon calculations in metals and comparison with experimental techniques
[Relazione in Atti di Convegno]
Bortolani, Virginio; Franchini, Anna; Santoro, Giorgio
abstract
Surface phonon calculations in metals and comparison with experimental techniques
1985
 Theory of Reconstruction in clean and covered metallic surfaces
[Relazione in Atti di Convegno]
Santoro, Giorgio; Franchini, Anna
abstract
In this paper we discuss the microscopical origin of the reconstruction of the clean and covered metal surfaces and the crytical behaviour of the observed phase transitions. Among the models invoked to account for the formation of the reconstructed phase, we focus our attention on the electronic mechanism that seems to explain the energetics of these systems. A special attention will be done on W(100) and W(100):H, that have been extensively studied both experimentally and theoretically.
1984
 Erratum:Explanation of the Anomalous Peak Observed in HeAtom Scattering from Ag(111) (Physical Review Letters)
[Articolo su rivista]
Bortolani, V.; Franchini, A.; Nizzoli, F.; Santoro, G.
abstract
1984
 Explanation of the anomalous peak observed in the He/Ag(111) atom scattering
[Articolo su rivista]
Bortolani, Virginio; Franchini, Anna; Nizzoli, F.; Santoro, Giorgio
abstract
The inelastic He/Ag(111) cross section has been evaluated in the onephonon distortedwave Born approximation. The authors use an atomsurface potential made up by a repulsive part derived from a superposition of atomic charges and by the attractive van der Waals interaction. The surface phonon density of states is evaluated within a forceconstants parametrization of the bulk dynamics. By changing the surface force constants the authors are able to explain all the salient features appearing in the experimental timeofflight spectra.
1984
 One phonon scattering of He atoms from the Ag(111) surface
[Relazione in Atti di Convegno]
Bortolani, Virginio; Franchini, Anna; Santoro, Giorgio
abstract
One phonon scattering of He atoms from the Ag(111) surface: calculation od the cross section in the Distorted Wave Born Approximation.
1984
 The interface polycarbonateglass: a theoretical study of Brillouin spectra and photoelestic properties
[Articolo su rivista]
Nizzoli, F.; Franchini, Anna; Santoro, Giorgio
abstract
We present calculations of surface waves and Brillouin scattering intensity for polycarbonate films supported by a pyrex substrate in the thickness range 00.6 µm. Comparison between calculated and experimental spectra shows that it is possible to obtain accurate information concerning the thickness of the film and the value and sign of the photoelastic constants.
1983
 Calculation of potential cutoff for onephonon atomsurface scattering
[Articolo su rivista]
Bortolani, Virginio; Franchini, Anna; Garcia, N.; Nizzoli, F.; Santoro, Giorgio
abstract
A cluster calculation for Cu(111), Ag(111), and Au(111) shows that the lateral Fourier transform of the charge deformation due to a displacement of a single surface atom is a Gaussian exp(Q2 / 2Qc2). This is proportional to the scattering amplitude for onephonon exchange atomsurface scattering and produces a cutoff in the cross section. The values of Qc are evaluated for the abovementioned surfaces, explaining very well the experimental observations. We also find a simple formula that should be useful to experimentalists in calculating the cutoff.
1983
 Calculation of the EELS spectra of the Ni(001) surface with p(2x2) and c(2x2) overlayers of Oxygen
[Articolo su rivista]
Bortolani, Virginio; Franchini, Anna; Nizzoli, F.; Santoro, Giorgio
abstract
We present a force constant slab calculation of the nickel (001) surface phonons with p(2×2) and c(2×2) oxygen overlayers. According to very recent experimental results we assume in both configurations an equal distance of 0.9 Å between the oxygen overlayer and the nickel surface. With two adjustable parameters (the ONi force constants) we are able to reproduce with good accuracy the position and the lineshape of the four peaks present in the experimental EELS spectra. The nature of these peaks is investigated in detail and the noticeable difference between the spectra of the two overlayers is explained.
1983
 Calculation of the eels spectra of the Ni(001) surface with p(2×2) and c(2×2) overlayers of oxygen
[Relazione in Atti di Convegno]
Bortolani, V.; Franchini, A.; Nizzoli, F.; Santoro, G.
abstract
We present a force constant slab calculation of the nickel (001) surface phonons with p(2×2) and c(2×2) oxygen overlayers. According to very recent experimental results we assume in both configurations an equal distance of 0.9 Å between the oxygen overlayer and the nickel surface. With two adjustable parameters (the 0Ni force constants) we are able to reproduce with good accuracy the position and the lineshape of the four peaks present in the experimental EELS spectra. The nature of these peaks is investigated in detail and the noticeable difference between the spectra of the two overlayers is explained. © 1983 Elsevier Scientific Publishing Company.
1983
 Theory of inelastic Ne scattering from the Ni(111) surface
[Articolo su rivista]
Bortolani, Virginio; Franchini, Anna; Nizzoli, F.; Santoro, Giorgio; Benedek, G.; Celli, V.
abstract
The recent inelastic Ne scattering data for Ni(111) by Feuerbacher and Willis are theoretically analyzed in the framework of the distorted wave Born approximation. A Nesurface soft potential model is inferred from twobody NeNi interactions and the manybody effects due to the phononinduced surface electron charge redistribution are qualitatively described by threebody forces. The surfaceprojected phonon densities for the Ni(111) surface are calculated from a force constant model including threebody forces. The cutoff produced by the softness of the NeNi potential accounts for the observed crossover from Rayleighwave to bulk phonon scattering regimes. The onephonon picture correlates well with experiments for outgoing angles slightly apart from the specular condition (Rayleighwave regime) whereas for larger deviations from the specular condition (bulk phonon regime) multiphonon contributions are important.
1983
 Theory of onephonon scattering of atoms from metal surfaces: application to He:Ag(111)
[Articolo su rivista]
Bortolani, Virginio; Franchini, Anna; Nizzoli, F.; Santoro, Giorgio; Benedek, G.; Celli, V.; Garcia, N.
abstract
We present explicit expressions for onephonon scattering of atoms from metal surfaces, within the distorted wave Born approximation by including Van der Waals forces. A comparison is made with the recent highresolution time of flight spectra for He/Ag(1 1 1). We explain in quantitative terms the position and the intensity of the peaks due to scattering from the Rayleigh wave of silver. Also the bulk phonons contribute to the spectra, but the calculated intensities underestimate the data.
1982
 Calculation of the phonon spectrum of the Ni(111) surface covered with Oxygen
[Relazione in Atti di Convegno]
Bortolani, Virginio; Franchini, Anna; Nizzoli, F.; Santoro, Giorgio
abstract
Calculation of the phonon spectrum of the Ni(111) surface covered with Oxygen: comparison of the P(2x2) and Sqrt(3)xSqrt(3)R30° overlayer geometry.
1982
 Surface phonon calculation of the (111) Ni surface with adsorbed Oxygen
[Articolo su rivista]
Bortolani, Virginio; Franchini, Anna; Nizzoli, F.; Santoro, Giorgio
abstract
In the framework of a central and angular force constant model we have evaluated the phonon spectrum and the loss function of the Ni (111) surface with p(2×2) and ( )R30° adsorbed lattices of Oxigen. The calculations compare well with recent EELS experimental data. We give reason of the different origin of the weaks observed in the measured spectra in terms of either the modes of the substrate or of the modes induced by the adsorbate.
1981
 Surface lattice dynamics of Nickel
[Articolo su rivista]
Bortolani, Virginio; Franchini, Anna; Nizzoli, F.; Santoro, Giorgio
abstract
In the framework of a central and angular force constants mode1,we have evaluated the phonon spectrum and the loss function of the Ni(111) surface covered with Oxigen. We explain quantitatively the main features of the observed electron energy loss spectra.
1981
 Surface lattice dynamics of clean and covered nickel
[Articolo su rivista]
Bortolani, Virginio; F., Nizzoli; Santoro, Giorgio; Franchini, Anna
abstract
The phonon spectrum of the (111) and (001) clean surfaces ofnickel has been evaluated by using the slab method In order todescribe the bulk fcc nickel we have introduced bond stretchingand angle bending force constants up to second nelghbours Thenumerical values of the force constants have been determined by aleastsquare fit of the experimental bulk phonons The calculationshave been carried out with a 31 layer slabThe available EELS experiments on these surfaces wereperformed with covered surfaces, where some interacuon occursbetween the overlayer and the substrate In order to make acomparison between theory and experiments we have thereforeevaluated the phonon spectrum of N1 (111) covered with halfmonolayer of oxygen with the p(2 x 2) and (3 x 3)R30 ° orderedstructures The comparison between the loss spectra and oursurface local densities of phonon states turns out to be very good.