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The bulk structure of stainless steels (SS) consists of mostly convex grains whose thin (one nm) planar interfaces are called grain boundaries (GB). There are industrial contexts where SS exposed to aggressive oxidative media undergo a fast degradation due to inter-granular corrosion (IGC), a preferential attack that occurs at the grain boundaries, propagating along them and leading to grains detachment. To address the IGC issue, we developed a 3D synchronous cellular automata (CA) model. Our first goal was to obtain a GB corrosion rate that could be as isotropic as possible. We performed full angular studies, with respect to the spatial orientation of a single grain boundary, in three different cases of grid (array of cells) geometry (cubic, hexagonal close-packed (HCP), face-centered cubic (FCC)). The HCP grid appears to be the best choice, as far as isotropy of the GB corrosion rate is concerned.

The lattice fluid model of the system with short range and long range Coulomb interactions is suggested. In the framework of the collective variables method, the screening of the Coulomb interactions in the bulk is considered. It is shown that the Debye length includes additional concentration dependence inversely proportional to the square root of the mean concentration of vacant sites like what is known at the plane boundary. The Coulomb interaction contribution to the free energy of the system is calculated in the approach close to the mean spherical approximation and is given in an analytical form. The influence of the variation of the crystal field near the system boundary on the structure and characteristics of the electric double layer is investigated. As compared to the system with equal crystal potentials at the lattice sites throughout the system the pronounced difference for the electric capacitance appears at low absolute values of the surface potential and it is more pronounced for negative electric potentials. The capacitance diverges as the potential values at which the electric field tends to zero and attains negative values in regions of the surface potentials depending on their polarity and values of the surface crystal potential. Negative values of the capacitance may indicate the thermodynamic instability of the system that can result from neglecting the short range interaction contribution., Comment: 20 pages, 5 figures

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International audience; In this paper, a 3D cellular automata approach of intergranular corrosion in presented. A model is proposed, along with experimental results both qualitatively (groove morphology, groove angle distribution) and quantitatively (mass loss, corrosion rate, corrosion front evolution). Simulations have been performed using a new asynchronous algorithm: the choice of the most adequate grid is also discussed. The model investigates the statistical variation of the corrosion front and provides useful information to make predictions on material ageing.

A simple lattice model of a solid electrolyte presented as a xy-slab geometry system of mobile cations on a background of energetic landscape of the host system and a compensating field of uniformly distributed anions is studied. The system is confined in the z-direction between two oppositely charged walls, which are in parallel to xy-plane. Besides the long-range Coulomb interactions appearing in the system, the short-range attractive potential between cations is considered in our study. We propose the mean field description of this model and extend it by taking into account correlation effects at short distances. Using the free energy minimization at each of z-coordinates, the corresponding set of non-linear equations for the chemical potential is derived. The set of equations was solved numerically with respect to the charge density distribution in order to calculate the cations distribution profile and the electrostatic potential in the system along z-direction under different conditions. An asymmetry of charge distribution profile with respect to the midplane of the system is observed. The effects of the short-range interactions and pair correlations on the charge and electric field distributions are demonstrated.

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A solid state electrolyte is considered as a system consisting of cations moving through the volume of a solid body and anions whose mobility can be neglected due to their large size compared to the size of the cations. Accordingly, in the homogeneous case local charge compensation takes place. Under the action of an external electric field, cations create in the near electrode area inhomogeneous redistribution of mobile charges and electric field. The model is used for the statistical­mechanical description of high­temperature ionic conductors and current sources. To obtain the free energy functional of the mobile charge subsystem depending on the distribution of their density, the cluster expansion scheme for the renormalized Mayer functions is used. The Hamiltonian of a system consisting of electric charges moving in the field of single­particle cell potentials of average forces is used as the basis one. The binary function of the host system is expressed in terms of the screened potentials and the potentials of the average forces based on the results of the method of collective variables. The internal energy of the system is calculated taking into account the short­ and long­range effects. The Gibbs – Duhem relation was used for calculating the free energy functional of the system. The distribution of the number density of moving particles and the electric potential in the near electrode region were found from the condition of extremality of the free energy. The potentials of average forces are obtained as a result of solving a system of integral equations in the lattice approximation, with accounting of the short­ and long­range effects. The transition from the correlative function to the correlation function allowed us to identify the correlated and uncorrelated parts of the electric potential. The linear contributions of the deviation of the charge concentrations from a uniform distribution to the chemical potential are considered. The calculations take into account the contribution of the correlation between the particles in the first three coordination spheres that leads to attraction of the first, repulsion of the second and third neighbors. The description is carried out using a linear differential equation of the fourth­order with complex values of the roots of the characteristic equation. The paper analyzes the results of the analytical solution.

Intergranular corrosion can affect stainless steels even if they are in a non-sensitized state. This is the case when the corrosive medium is particularly oxidizing such as in hot and concentrated nitric acid [1]. Intergranular corrosion is characterized by the formation of triangular grooves at the level of the grain boundaries. Their progression leads to the detachment of grains with a certain periodicity. This corrosion type is quite well described and modeled by different techniques when the medium remains the same [2-3]. Nevertheless, the medium may vary in some industrial chemical processes. Therefore, this work has investigated the impact of non-stationary conditions on the evolution of the intergranular corrosion. The intergranular corrosion kinetics of a 310L stainless steel was first studied in nitric acid with different levels of VO2 + concentrations in stationary conditions. Then non-stationary experiments were performed by varying the concentration of VO2 + as a function of time by periods. The corrosion kinetics was characterized by the evolution of the mass loss of the samples and of the geometry of the grooves (angle and depth) optically measured on cross sections. Numerical simulations were also performed by cellular automata [3]. A hexagonal close-packed (HCP) grid was chosen for the simulations. A realistic 3D granular structure of the stainless steel was modeled with a Voronoi algorithm. Two corrosion probabilities (for the grains and the grain boundaries) were adequately chosen for driving the time evolution in each conditions. These probabilities were kept constant in stationary conditions and varied with time by periods in non-stationary conditions. The simulated mass loss and the surface morphology reflects the same pattern of the experiments. In stationary conditions, the corrosion reaches a steady state after a transient period corresponding to the detachment of the first layer of grains: the corrosion rate and the specific surface in contact with the solution (increased by the formation of grooves) becomes constant. The characteristics of the steady state are directly dependent on the concentration of VO2 +. In non-stationary conditions, it appears that the characteristics of the intergranular corrosion (mass loss and geometry of the grooves) at a given period are influenced by the characteristics reached after the previous period (in other chemical conditions). This influence is only transient during a time corresponding approximately to the duration necessary to the consumption of a layer of grains. [1] Fauvet, P., Corrosion issues in nuclear fuel reprocessing plants. Nuclear corrosion science and engineering. D. Feron, Woodhead Publishing. 22 (2012) 679-728. [2] B.Gwinner et al., Towards a reliable determination of the intergranular corrosion rate of austenitic stainless steel in oxidizing media. Corrosion Science 107 (2016) 60-75. [3] D.Di Caprio et al., 3D cellular automata simulations of intra and intergranular corrosion. Corrosion Science 112 (2016) 438-450.

International audience; The porosity of the anodic films grown on aluminium substrates depends on various operating conditions related to the anodization electrolyte and to the applied electrical parameters, as well as to the substrate itself. In the present study, three different aluminium substrates were studied and anodized: AA 1050 (rolled; thickness = 1 mm), AA 2024 T3 (rolled; 1 mm), and AA 2024 T3 (machined; 3 mm). For each type of anodic film, the porosity, as well as its changes during anodization, was accurately characterized using both field‐emission gun scanning electron microscopy (FEG‐SEM) and a reanodization technique. Moreover, for the first time, the corresponding tortuosity was quantified for all studied substrates. Results for rolled AA 2024 T3 and for machined AA 2024 T3 especially showed significant differences in tortuosity values, contributing towards clarifying, in part, their different wettability characteristics or anticorrosion behaviour, so far not clearly explained.

Numerical modelling is an effective tool for predicting corrosion. We make use of a stochastic Cellular Automata (CA)-based modelling for corrosion studies at a mesoscopic scale. Physico-chemical phenomena that cannot be satisfactorily described by standard deterministic and macroscopic methods are here taken into account. In this CA modelling, materials and their environments are described by a 3D lattice, where each cell has a state. The physico-chemical phenomena are represented as simple rules that define the temporal evolution of the states of the cells. These rules can be combined to model complex systems. Our model is stochastic in the sense that the transition rules are given probabilities and diffusion in the electrolyte is modelled as a random walk. Simultaneous anodic and cathodic reactions describe the corrosion mechanisms. Special emphasis is given to the electric connection between the anodic and cathodic cells. The anodic and cathodic reactions occur simultaneously, maintaining the ...

We study a model for thin film electrodeposition in which instability development by preferential adsorption and reduction of cations at surface peaks competes with surface relaxation by diffusion of the adsorbates. The model considers cations moving in a supported electrolyte, adsorption and reduction when they reach the film surface, and consequent production of mobile particles that execute activated surface diffusion, which is represented by a sequence of random hops to neighboring lattice sites with a maximum of G hop attempts (G>>1), a detachment probability epsilon, Two-column format with 12 pages, 7 figures included

International audience; We present a stochastic three dimensional (3D) model for corrosion at a mesoscopic scale. The competition between uniform and localized corrosion is studied, with special emphasis given to the connection between the anodic and cathodic reactions. Even if the reactions happen at different places, they are linked and occur simultaneously, maintaining an electric balance. We focused on the particular case of an occluded corrosion on a metal covered by a non reactive layer, where two growth regimes are evidenced and controlled by the diffusion of species in the electrolyte.

In this paper, we discuss the phenomenon of a spontaneous polarisation of a neutral hard planar interface for valence asymmetric coulombic systems. Within a field theoretical description, we account for the existence of non trivial charge density and electric potential profiles. The analysis of the phenomenon shows that the effect is related to combinatorics in relation with the existence of the two independent species cations and anions. This simple and basic feature is related to the quantum mechanical properties of the system. The theoretical results are compared with numerical simulations data and are shown to be in very good agreement, which a fortiori justifies our physical interpretation., Comment: 12 pages, 11 figures

A simple model for the effect of intergranular corrosion on overall corrosion processes is investigated using a cellular automata approach. The corroding polycrystalline material consists of domains and their boundaries. The domains represent the monocrystalline cores while their boundaries represent the inter granular defects. Either, a periodic pattern or randomly generated domains of Voronoi tessellation are used to represent the polycrystalline structure. The parameters of the model, taking into account the polycrystalline aspect of corrosion, are the domain density and the corrosion probabilities of metal grain core and grain boundary sites. The corrosion probability for grain boundary is set to a value higher than it is for the grain core. A complex surface structure appears with a high geometrical roughness when defects are not too dense. A strong correlation is established between the roughness evolution, the metal crystalline properties and the corrosion mechanism of metal dissolution. This work concerns simulations in 3D and extends the previous work limited to 2D simulations. (C) 2016 Elsevier Ltd. All rights reserved.

We apply a field-theoretical approach to study the structure and thermodynamics of a two-Yukawa fluid confined by a hard wall. We derive mean field equations allowing for numerical evaluation of the density profile which is compared to analytical estimations. Beyond the mean field approximation, analytical expressions for the free energy, the pressure, and the correlation function are derived. Subsequently, contributions to the density profile and the adsorption coefficient due to Gaussian fluctuations are found. Both the mean field and the fluctuation terms of the density profile are shown to satisfy the contact theorem. We further use the contact theorem to improve the Gaussian approximation for the density profile based on a better approximation for the bulk pressure. The results obtained are compared to computer simulation data., 32 pages, 6 figures

We study a thin film growth model with temperature activated diffusion of adsorbed particles, allowing for the formation of overhangs and pores, but without detachment of adatoms or clusters from the deposit. Simulations in one-dimensional substrates are performed for several values of the diffusion-to-deposition ratio R of adatoms with a single bond and of the detachment probability epsilon per additional nearest neighbor (NN), respectively with activation energies are Es and Eb. If R and epsilon independently vary, regimes of low and high porosity are separated at 0.075 < epsilon_c < 0.09, with vanishingly small porosity below that point and finite porosity for larger epsilon. Alternatively, for fixed values of Es and Eb and varying temperature, the porosity has a minimum at Tc, and a nontrivial regime in which it increases with temperature is observe above that point. This is related to the large mobility of adatoms, resembling features of equilibrium surface roughening. In this high-temperature region, the deposit has the structure of a critical percolation cluster due to the non-desorption condition. The pores are regions enclosed by blobs of the corresponding percolating backbone, thus the distribution of pore size s is expected to scale as s^{-tau} with tau ~ 1.45, in reasonable agreement with numerical estimates. Roughening of the outer interface of the deposits suggests Villain-Lai-Das Sarma scaling below the transition. Above the transition, the roughness exponent alpha ~ 0.35 is consistent with the percolation backbone structure via the relation alpha = 2-d_B, where d_B is the backbone fractal dimension., 15 pages, 10 figures

Random walks (RW) of particles adsorbed in the internal walls of porous deposits produced by ballistic-type growth models are studied. The particles start at the external surface of the deposits and enter their pores, in order to simulate an external flux of a species towards a porous solid. For short times, the walker concentration decays as a stretched exponential of the depth z, but a crossover to long time normal diffusion is observed in most samples. The anomalous concentration profile remains at long times in very porous solids if the walker steps are restricted to nearest neighbors and is accompanied with subdiffusion features. These findings are correlated with a decay of the explored area with z. The study of RW of tracer particles left at the internal part of the solid rules out an interpretation by diffusion equations with position-dependent coefficients. A model of RW in a tube of decreasing cross section explains those results by showing long crossovers from an effective subdiffusion regime to an asymptotic normal diffusion. The crossover position and density are analytically calculated for a tube with area decreasing exponentially with z and show good agreement with numerical data. The anomalous decay of the concentration profile is interpreted as a templating effect of the tube shape on the total number of diffusing particles at each depth, while the volumetric concentration in the actually explored porous region may not have significant decay. These results may explain the anomalous diffusion of metal atoms in porous deposits observed in recent works. They also confirm the difficulty in interpreting experimental or computational data on anomalous transport reported in recent works, particularly if only the concentration profiles are measured., 11 pages, 10 figures included

Our research on employing the cellular automata methodology to corrosion and passivation phenomena is reviewed. Examples of a peculiar pit development are found and presented. The diffusion rate in the corroding medium is argued and shown in the simulation results to affect mainly the characteristic length scale for the corrosion process. New data for the pitting corrosion development on a planar interface are presented and discussed.

A simple model describes uniform and localised corrosion. We use a mesoscopic cellular automata (CA) type approach, which has proved a powerful tool in the study of rough metal–electrolyte interfaces. The model accounts for two corrosion kinetics and their relative spatial localisation. The competition between the two forms of kinetics of corrosion is shown to reproduce several types of morphology of corrosion ranging from narrow pits or larger cavities to rough surfaces. Simulation and experimental results are compared providing insight on the relation between kinetics and morphologies of the corrosion front. We emphasize the importance of stochastic simulations in relation to CA.

In this paper, we briefly discuss a field theory approach of classical statistical mechanics. We show how an essentially entropic functional accounts for fundamental symmetries related to quantum mechanical properties which hold out in the classical limit of the quantum description. Within this framework, energetic and entropic properties are treated at equal level. Based on a series of examples on electrolytes, we illustrate how this framework gives simple interpretations where entropic fluctuations of anions and cations compete with the energetic properties related to the interaction potential.

In a series of papers we have introduced a field theoretical approach to describe the liquid state. The formalism introduces a simple Hamiltonian which includes the ideal gas free energy and the standard interaction potential between particles coupling the fields. In this paper, we discuss the role and the importance of the ideal term in this formalism. We compare our approach to the standard liquid state theory and another approach based on a field description, the density functional theory where an identical functional appears. The comparison shows that field theory sheds new light on the role of the ideal entropy an aspect which is traditionally discarded in favor of a viewpoint focusing on the interaction potential.

The aim of this work is the study of micelle formation in a solvent other than water, the ethyl-ammonium nitrate (EAN) (an ionic liquid at room temperature). The study of micelle formation will provide us with a better understanding of the interactions between the solvent and carbon chains. The critical micelle concentrations (cmc) for four different alkyl-ammonium nitrates have been experimentally determined. The method used for the determination of the cmc is based on surface tension measurements. In addition, the effect of micelle formation on molar partial volumes was checked. No volume augmentation was found in ethyl-ammonium nitrate. A theoretical model for the chemical potential of surfactants in ethyl-ammonium nitrate has also been proposed. This model served to explain the experimental results which were obtained.

In this paper, starting from the Born-Green-Yvon (BGY) equation, we derive a general expression for the contact value of the singlet distribution function near a hard wall for anisotropic fluids. This relation includes two separate contributions. One is connected to the partial bulk pressure relative to a given orientation of the molecules. The second one is connected to the anchoring phenomena and is characterized by the direct interaction between the molecules and the wall. From this relation, we then formulate the contact theorem for the density and the order parameter profiles. The results are illustrated on the case of a nematic fluid near a hard wall., Submit version

The effects of specific interactions in a two dimensional coulombic system are investigated. In the framework of a field theoretical approach, we have shown that the electric properties of the system are strongly modified when two ionic species have a tendency to demix. By means of a Langevin dynamics, we investigate here a model system where, in the absence of electrostatic interaction, the specific interactions are such that the system demixes. This phase separation cannot take place in the presence of the coulombic potential, as a result of the electroneutrality condition in the system. The snapshots of the system obtained in the simulation, show large local concentration inhomogeneities, which are also charge inhomogeneities reminiscent of the tendency of the two species to separate. This is an unusual feature in a charged system, as it corresponds to the gathering of ions of the same sign. These inhomogeneities are constituted by a continuous network of lines of ions of the same species, the adjacent line being of the opposite sign. This structure is similar to a bicontinuous phase. One property of these lines: the average distance between the lines, has been studied by means of a simple field theoretical model. The Hamiltonian includes entropy, electrostatic and specific interactions. In the mean field approximation, we obtain a distance between the lines in agreement with what is found in the simulation.

Condensed ionic systems are described in the framework of a combined approach that takes into account both long-range and short-range interactions. Short-range interaction is expressed in terms of mean potentials and long-range interaction is considered in terms of screening potentials. A system of integral equations for these potentials is constructed based on the condition of the best agreement of the system of study with the reference system. In contrast to the description of media with short-range interactions, in this text the reference distribution includes not only the field of mean potentials but also Coulomb interaction between particles. A one-component system made of ions in a neutralizing background of fixed counterions is considered. The model can be used to describe solid ionic conductors. In order to study the movement of cations on the sites of their sub-lattice, the lattice approximation of the theory is employed based on the calculation of the pair distribution function. Using the collective variables approach, a technique improving the starting expression for this function is proposed. Notably, the neglected terms in the expansion of this function are approximated by single-particle terms ensuring that the normalization condition is satisfied. As a result, the applicability of the theory is extended to a wide region of thermodynamic parameters. The chemical potential and the diffusion coefficient are calculated showing the possibility of phase transitions characteristic of the system., Comment: 14 pages, 3 figures

In this thesis, we will study in particular the localized corrosion characterized by the anodic and cathodic reactions taking place in separate places. This separation of the two electrochemical half-reactions coupled with the charge transfer (IR drop) or matter (ionic diffusion) will contribute in the explanation of the corrosion's kinetic. the morphologies of corrosion pitting, crevice ... that result. The aim of the thesis is to develop a realistic model that realize significant couplings determining the kinetics of corrosion and validate it on the basis of observations to allow predictions in the longer term. From a practical standpoint, the simulations will be developed on GPU (Graphical processing unit) by optimizing the efficiency of this parallelism type of architecture., Dans cette thèse, on va étudier plus particulièrement la corrosion localisée qui se caractérise par des réactions anodiques et cathodiques ayant lieu en des endroits distincts. Cette séparation des deux demi-réactions électrochimiques couplée avec le transfert de charge (chute ohmique) ou de matière (diffusion des ions) déterminent en grande partie la cinétique de ce type de corrosion ainsi que les morphologies de la corrosion piqûres, crevasses ... qui en résultent. L'objectif de la thèse sera de développer un modèle réaliste susceptible de rendre compte des couplages importants déterminant la cinétique de la corrosion et de le valider sur la base d'observations en vue de permettre des prédictions à plus long terme. D'un point de vue pratique, les simulations seront développées sur GPU (graphical processing unit) en optimisant l'efficacité du parallélisme sur ce type d'architecture.

Numerical modelling is complementary tool for corrosion prediction. The objective of this work is to develop a corrosion model by means of a probabilistic cellular automata approach at a mesoscopic scale. In this work, we study the morphological evolution and kinetics of corrosion. This model couples electrochemical oxydation and reduction reactions. Regarding kinetics, cellular automata models are able to describe current as a function of the applied potential for a redox reaction on an inert electrode. The inclusion of probabilities allows the description of the stochastic nature of anodic and cathodic reactions. Corrosion morphology has been studied in different context: generalised corrosion, pitting corrosion and corrosion in an occluded environment. A general tendency of two regimes is found. A first regime of uniform corrosion where the anodic and cathodic reactions occur homogeneously over the surface. A second regime of localized corrosion when there is a spatial separation of anodic and cathodic zones, with an increase of anodic reaction rate., Les modèles numériques sont un outil complémentaire pour la prédiction de la corrosion. L'objectif de cette thèse est de développer un modèle de corrosion reposant sur la méthode des automates cellulaires pour l'étude de l'évolution morphologique des surfaces, ainsi que de la cinétique de corrosion. Le modèle développé couple les demi-réactions électrochimiques d'oxydation et de réduction. Au niveau cinétique, la simulation par automates cellulaires peut alors reproduire les courbes intensité-potentiel d'une réaction redox sur électrode inerte. L'échelle spatio-temporelle choisie décrit des phénomènes de corrosion à l'échelle mésoscopique, niveau intermédiaire par rapport aux approches habituelles. Dans notre modèle, les probabilités rendent compte de la nature stochastique des réactions anodiques et cathodiques. Cette étude nous a permis de décrire l'évolution de la morphologie de la corrosion dans différents contextes: corrosion généralisée, corrosion par piqûre et corrosion en milieu confiné. Deux régimes de corrosion ont été observés: un régime de corrosion uniforme dans lequel les demi-réactions sont distribuées de manière homogène suivi par un régime de corrosion localisée, caractérisé par une séparation spatiale des zones cathodiques et anodiques.