Fabienne Berthier

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

Abstract 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.

Paper: Identifiability and distinguishability concepts in electrochemistry

Although the notions of structural identifiability and distinguishability are now well accepted in some domains of mathematical modeling such as econometrics, biology and pharmacokinetics, much remains to be done in others. The relevance of these notions to the building of phenomenological models in electrochemistry is illustrated by considering the Volmer-Heyrovsky reaction and three mechanisms for dissolution-passivation. It is shown that some classical methods for collecting data cannot ensure suitable identifiability and distinguishability properties. In some cases, simple modifications of the experimental procedure can remove these ambiguities. In others, one may resort to more recent techniques of investigation.

Bifurcation analysis for the Volmer-Heyrovsky mechanism

A new shape of multisteady states current-potential curve is presented for the Volmer-Heyrovsky mechanism under Frumkin isotherm conditions. Linear stability of the steady states is studied for galvanostatic and potentiostatic regulation by drawing the pole and zero map of the electrode impedance. Non-linear stability is studied by calculating linear potential sweep voltammograms. The shapes of the voltammograms and those of steady state current-potential curves are the same as the shapes of the curves observed in the experimental study of the pitting of metals.

New Structures and Atomistic Analysis of the Polymorphism for the ∑ = 5 (210) [001] Tilt Boundary

Using interatomic potentials derived from the second moment approximation of the tight-binding scheme, we study the relative stabilities for the different structures of the ∑ = 5 (210) [001] tilt boundary in Cu and Ag. Relatively to the numerous previous studies, we obtain two new structures characterised by a larger periodicity along the tilt axis. Depending on the metal and on subtle features of the potentials, we show a very significant evolution of the relative stabilities. Using a local analysis on the different sites of the grain boundary, we link the stability of a given structure to peculiar features of the interatomic potential and to physical properties of the metal.

Numerical solution of coupled systems of ordinary and partial differential equations. Application to the study of electrochemical insertion reactions by linear sweep voltammetry

Abstract Modelling of some electrochemical reactions leads to systems combining ordinary differential equations (ODE) and partial differential equations (PDE). Using the Laplace transform method, the mass-transfer equations can be solved for thin-layer materials to give theoretical expressions for the related transfer functions containing terms such as tanh τs / τs or coth τs / τs or a combination of these terms, depending on the mass-transfer boundary conditions. Using transfer functions makes it possible to transform the PDEs into systems of ODEs of infinite size which can be solved numerically after truncation. This method is used here to study electrochemical insertion reactions in thin films of host materials by linear sweep voltammetry (LSV).

On the nature of the spontaneous oscillations observed for the Koper-Sluyters electrocatalytic reaction

Abstract The study of an electrocatalytic mechanism is presented. Closed form solutions are given for the steady-state behaviour, facilitating the linear stability analysis. It is shown that two types of oscillations may be exhibited for this self-oscillating electrocatalytic reaction: small amplitude harmonic oscillations and large amplitude relaxation oscillations. The existence of these oscillations and their form depend on the reaction conditions. The Hopf bifurcation is supercritical and small amplitude harmonic oscillations exist only over a very narrow range of electrode potentials. The electrocatalytic reaction behaviour is that of a so-called ‘canard’.

Choice of experimental method induced by structural properties of mechanisms

The interest of checking structural properties of reaction mechanisms prior to any attempt at estimating their kinetic parameters is illustrated by considering the identifiability of the parameters of the Volmer-Heyrovsky mechanism. The technique employed applies to any of the small-signal methods used for the study of electrochemical mechanisms, as well as to signals involving large deviations. It turns out that steady-state measurements, electrochemical impedance spectroscopy and linear sweep voltammetry do not make it possible to estimate the kinetic parameters unambiguously, even from noise-free data, contrary to electrogravimetry. This type of analysis, which seems still largely ignored among electrochemists, can be used for the choice of experimental procedures to be employed.

Multiscale Modelling of the Ageing Kinetics of a 2D Deposit

We compare three models of 2D precipitation kinetics that give access to different time-space scales. Kinetic Monte Carlo simulations (KMC), cluster dynamics (CD) and nucleation-growth-coalescence model (NGCM), based on a same atomic model, lead to an excellent agreement as long as the interfacial free energy is evaluated accurately and the interaction between diffusion fields is taken into account in the CD. The NGCM model noticeably improves the previous approaches of the same kind by using a constrained-equilibrium hypothesis to describe the solid solution. Moreover, in the coalescence regime, we show that CD leads to cluster distributions that are wider and more symmetric than the LSW distribution due to the probabilistic feature of the growth law of a cluster, that makes it differ from the purely deterministic NGCM approach.

Identifiability and Distinguishability Concepts in Electrochemistry

Abstract If the notions of structural idendfiability and disdnguishability are now well accepted in some domains of mathematical modeling such as econometrics, biology or pharmacokinetics, much remains to be done in others. The relevance of these notions to the building of phenomenological models in electrochemistry is illustrated by considering the Volmer-Heyrovsky reaction and three mechanisms for dissolution-passivation. It is shown that some classical methods for collecting data cannot ensure suitable idendfiability and distinguishability properties while more recent techniques are able to remove these ambiguities.

Equilibrium Distribution of Alloyed Nanowires

The size distribution and the total density of clusters of a one-dimensional pure deposit can be expressed analytically from the Ising model. For a codeposit, the alloying effect and the presence of broken bonds at the cluster edges lead to inhomogeneities of the chemical composition of the clusters. We investigate the influence of codeposition on the size distribution of clusters in the case of an alloy that forms an ideal solution. We obtain the exact solution for the size distribution of clusters while the complete characterization of the system results from coupled analytical formulae in the grand-canonical ensemble. The results of this analytical model are successfully compared with those obtained by Monte Carlo simulations.