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International audience; The buckling of a gold thin film deposited on a rigid substrate has been numerically investigated by means of static molecular dynamics simulations. Three different regimes of deformation have been identified depending on the values of the adhesion energy of the film on its substrate (Gamma(int)). For low adhesion energy, the buckling and gliding through dislocation emission into the interface have been observed. For intermediate values of Gamma(int), the dissociation of the interfacial dislocations into the film leads to the formation of a Lomer-Cottrell lock that stops the buckle extension, promoting thus the propagation of a crack accompanied by the emission of dislocations. It results in the formation of a twin. For large values of Gamma(int,) the kinking of the interfacial crack has been evidenced along with dislocation nucleation at its tip leading to twins again. Finally, the different evolutions of the film have been summarized in a "behavior" diagram displayed in the plane of applied strain and adhesion energy variables. (C) 2019 Elsevier Ltd. All rights reserved.

International audience; In the framework of the continuum elastic theory, the equilibrium positions of Shockley partial dislocations have been determined as a function of their distance from the free surface. It is found that the dissociation width decreases with the decreasing depth, except for a depth range very close to the free surface for which the dissociation width is enlarged. A similar behaviour is also predicted when Shockley dislocation pairs are regularly arranged, whatever the wavelength. These results derived from the elastic theory are compared to STM observations of the reconstructed (1 1 1) surface in gold, which is usually described by a Shockley dislocations network.

International audience; The interaction of deformation twins with interfaces in nanostructured Cu/Ag is studied using molecular dynamics simulations. The influence of the interface structure on twin nucleation, propagation and thickening is analysed, and the role of the misfit interfacial dislocations mesh is detailed. In particular, we show that the interface can induce, directly or indirectly via Lomer dislocations, the nucleation of twinning dislocations. A thorough description of the involved mechanisms is given. Through this atomic scale approach, our study offers some useful understanding of the mechanical twinning process in nanolamellar composites, where twinning appears to be a common plasticity mechanism.

We report investigations on gold single crystals carried out with the help of an original experimental set-up, combining a scanning tunneling microscope and a compression device under ultra high vacuum, that allows for in situ observations of stressed surfaces at the atomic scale. It is observed that a macroscopic compression strain may induce a reorganization of the Au(111) surface reconstruction, known as the chevron-like pattern. Molecular dynamics simulations using a modified embedded atom method potential have been carried out to highlight the elementary dislocation mechanisms at the origin of such an evolution.

We report investigations of gold single crystals carried out with the help of an original apparatus combining ultrahigh vacuum scanning tunneling microscopy and a compression device for in situ observations. It is demonstrated that the herringbone reconstruction on Au(111) is highly influenced by the appearance of slip traces that result from the emergence at the free surface of moving dislocations in the bulk. A reorganization of the herringbones in a $\mathsf{U}$-shaped pattern is directly observed but only on the lower terrace associated with the slip trace. In addition, kinks have been experimentally evidenced along the slip traces at the atomic scale. Molecular dynamics simulations using a modified embedded atom method potential have demonstrated that the kinks are related to the evolution of the Au(111) reconstruction. In particular, a linear relation between the size of the kinks and the period of the $\mathsf{U}$-shaped pattern is determined.

The effect of grain boundaries (GB) on the buckling of an Al thin film delaminated from its substrate is investigated by means of molecular dynamics simulations at finite temperature. It is evidenced that the GB localizes the plasticity and deeply modifies the profile of the buckled thin film through the formation of a vertical fold at the location of the initial GB. Several plasticity mechanisms have been also described such as the development of extrinsic faults or the formation of uncommon C’D and CD’ dislocations. In this context, the folding angle and plastic strain in the film have been analyzed through a careful counting of the emerging dislocations at the film surfaces. The buckling profile of the film has been then analytically determined in the framework of the Foppl–von Karman’s (FvK) theory of thin plates and successfully compared with the simulated ones. The modifications of the film pattern in light of the different plastic (dislocations) and elastic (buckling) phenomena are finally discussed.

Thin films submitted to internal/external stresses are known to undergo buckling over a critical stress level. In the case of a rigid substrate, depending on the stress anisotropy, three elementary buckling structures are expected: straight-sided, bubble or telephone cord buckles. In this context, the effect of the substrate elasticity on the expected buckled morphologies is explored. The post-buckling equilibrium shapes that develop on parallel delaminated stripes of films for a biaxial compressive stress state are studied. Finite elements methods calculations are carried out to simulate the various equilibrium configurations. A morphological map is extracted and plotted as a function of the stress components in the longitudinal (i.e. along the stripe direction) and transversal direction (i.e. perpendicular to the stripe direction). It is shown that the stability domains of the elementary buckles are shifted down to lower stresses as the substrate stiffness is decreased. In addition, the stability domain of the telephone cord buckles is shown to be enlarged. Finally, an intermediate domain between bubbles and both straight-sided and telephone cord buckles is evidenced on the morphological map. The buckles are in this case characterized by hook-like or bone-like structures. This latter buckling structure has been experimentally observed by atomic force microscopy on nickel/polycarbonate systems.

International audience; The effect of surface step and twin boundary on the mechanical twinning process in nanoscale face-centred cubic metallic films was studied using atomistic simulations. Aluminium was considered as a model material but comparisons were made with silver and copper. Surface steps were identified as privileged sites for twin nucleation at lower stresses, leading to the formation of only one large twin in defect-free films. In presence of a coherent twin boundary which acts as a strong barrier to the propagation of dislocations, the extension of nucleated twins is much more limited but the density of secondary twin boundaries is found higher. The key role played by Lomer dislocations, resulting from the interaction between incipient twins and the coherent twin boundary, on the nucleation of new twins was demonstrated. These findings shed light on some elementary mechanisms that can be involved in the elaboration of nanotwinned materials with interesting mechanical properties.

The stability of a strained cuboidal island deposited on a substrate has been numerically investigated by means of finite element simulations in the case where the structure is submitted to misfit strain resulting from the lattice mismatch between the island and the substrate. In the hypothesis where the surface energy is isotropic, it is found that, depending on the island volume, the formation of a truncated or inverted truncated pyramid can be favored by the misfit strain with respect to the cuboidal shape. A shape diagram is finally provided as a function of the misfit strain and island volume.

The effect of steps on the herringbone pattern appearing at the $\mathrm{Au}(111)$ surface is explored. Scanning tunneling microscopy investigations show that the number of alternating fcc and hcp regions decreases with the decreasing width of the terrace, in fair agreement with atomistic simulations. It is demonstrated that the steps locally release the tensile surface stresses, leading to a reorganization of the herringbone pattern.

The shape transition of a one-layer thick strained island deposited on a semi-infinite substrate has been theoretically investigated from an energy variation calculation. It is found that depending on the misfit strain, the initially circular island may become unstable beyond a critical size and can evolve toward an elliptical shape. As the surface of the island increases, another transition is expected to occur which consists in the ellipse splitting into two identical circular islands of smaller size. A shape diagram is finally displayed for the island as a function of the misfit strain and island surface and a scenario of nanostructure evolution is discussed.

The mechanics of thin film buckle delamination has been widely studied, with the assumption of perfect (flat) interfaces. This work is reporting a study of the evolution of an initially straight-sided buckle propagating in a thin film lying on a substrate in the presence of a step at the film/substrate interface, resulting from the plastic deformation of the substrate. Assuming the interface toughness depends on the mode mixity, it has been found using finite elements calculations that depending on the step orientation and height, the initially straight propagation of the buckle can be perturbed so that the buckle eventually propagates along the step. The critical parameters (orientation and height) of the step have been then determined, which characterizes the transition from a straight propagation perpendicular to the compression axis to a propagation along the inclined step. A “behavior” diagram has been finally presented for the buckle, where the propagation, either perpendicularly to the step or along it have been displayed versus the step height and orientation.

Atomistic simulations based on experimental observations provide the first evidence that the interface delamination of a thin film from its substrate may start from interface steps. Buckling of the film after interface gliding from both edges of its delaminated part is also observed. In the framework of the Foppl–von Karman theory of thin plates, the expression of the critical strain beyond which the film buckles has been then analytically determined as a function of the step height and gliding displacements. Both numerical and analytical results confirm that the formation of blisters is favoured in the neighbourhood of interfacial imperfections.

A theoretical model for the simultaneous thin film buckling and interface delamination from its substrate has been derived from a Griffith’s criterion which includes plastic events localized at the film–substrate interface. The predictions of the model have been validated by atomistic simulations of the delamination and buckling of a Cu thin film deposited on a W substrate. This model accounts for the stable propagation of the buckle edges without requiring any estimate of the dependence of the adhesion energy on the mode mixity.

Numerical simulations based on finite-strain elasticity and a phase-field model of dislocations reveal that dislocations are emitted at the crack-front delamination of a circular blister. It is shown that the phenomenon induces a sliding in the film-substrate interface that modifies the shape of the buckling structure. This phenomenon is theoretically quantified introducing an axisymmetric sliding into the Foppl and von-Karman equations that describe the elastic behavior of the film. By extending the analytical investigations to the crack opening, it is shown that dislocation-induced sliding may stabilize the buckling-driven delamination of three-dimensional structures.

Gold single crystals were deformed by uniaxial compression tests with the help of an experimental apparatus that allows one to characterize in situ, by UHV scanning tunneling microscopy, the evolution of surface structures under stress. It is demonstrated that the slip traces resulting from the emergence of moving dislocations at the free surface highly modify the organization of the vicinal steps. A model based on energetic considerations is proposed and discussed to explain the observed phenomenon.

We present a numerical model of dislocation cores in Mg 2 SiO 4 forsterite based on the Peierls-Nabarro model and using generalised stacking faults as an input. The generalised stacking faults have been calculated from ab initio density-functional theory using VASP. Core profiles, atomic models and Peierls stresses are proposed for dislocations from the following slip systems: [100](010), [100](001), [100]{021}, [001](010), [001](100) and [001]{110}. Calculations have been performed at 0 and 10 GPa, to investigate the influence of pressure. We show that [100] dislocations have narrow cores when [001] dislocations tend to spread into (100) and {110} planes. A strong softening effect is found with pressure on the [001](010) slip system. Our study emphasizes the influence of lattice friction on plastic deformation of forsterite with, beyond Peierls stresses, possible effects related to non-planar core structures.

We present ab initio calculations of ideal shear strengths (ISS) in forsterite at zero temperature using pseudopotential density functional theory within the generalized gradient approximation. A localized rigid-body shear is imposed on a given plane of an infinite defect-free crystal. The energy increase associated with this shear (called the generalized stacking fault energy) gives access to the ISS. The goal of this study is to assess the influence of crystal chemistry on the intrinsic resistance of plastic shear of a mineral like forsterite. ISS have been calculated for plastic shear along [100], [010], and [001] in various potential glide planes of forsterite. We show that the [001] slip, which corresponds experimentally to an easy glide at low temperature, exhibits the lowest energy barrier. The [010] glide is precluded because it involves very unfavorable atom impingements.

The {111} surface of niobium single crystals has been investigated by ultra-high vacuum scanning tunneling microscopy. An atomic reconstruction has been experimentally observed and has been characterized by a lattice constant two times larger than that expected for a body-centered cubic structure. Moreover, an upper incipient structure is observed on these (2 × 2) surfaces. The upper unit cell is 2 3 times larger than the bulk one and is also rotated by 30° with respect to the bulk structure. A model is proposed to explain the competition between a covering of the free surface by a non-dense atomic structure and an island formation of niobium atoms in the dense configuration. The experimental results are finally discussed with the help of ab initio calculations used to determine the surface energies of the associated atomic configurations.

International audience; The formation of donut- and croissantlike buckles has been observed onto the free surface of gold thin films deposited on silicon substrates. Numerical simulations clearly evidence that the coupling effect between the atmospheric pressure acting on the free surface and the plastic folding of the ductile film is responsible for the circular blister destabilization and the formation of the donut- and croissantlike buckling patterns

The unilateral buckling of a stressed thin film on a substrate has been investigated theoretically in the framework of the Föppl-von Kármán theory of thin plates when an increasing overpressure is considered onto the upper free surface of the film. It is found that, depending on the initial stress in the film and overpressure, two scenarios of evolution may occur. The snap-through of the one-dimensional buckle leading to the full redeposition should take place for low values of the initial stress. When the initial stress exceeds a critical value, a partial redeposition of the buckle should proceed as the overpressure increases. A snap-through while the redeposition mechanism has taken place should also occur for higher values of the overpressure.

Atomistic simulations of the evolution of a strained thin film on a substrate has been reported and the formation of dislocations has been observed in the film/substrate interface after the film has buckled. In the framework of the linear elasticity theory, an analytical model has been developed to explain the buckle effect on the formation of the dislocations. A stability diagram with respect to the buckling and dislocation emission phenomena is finally presented for the film as a function of the uniaxial strain and the Burgers vector.

The buckling of a Cu thin film deposited on a stiff W substrate is studied by means of molecular static simulations using interatomic potentials. The buckling of a preexisting delaminated part of the film is observed under a uniaxial strain without any further decohesion of the interface. A sliding phenomenon is also observed at the edges of the buckle which can be interpreted in terms of glide of misfit dislocations. Integrating this sliding effect in the Foppl–von Karman theory of thin plates, a modified analytical expression for the deflection of the film has been derived which fits with the deflection obtained from the simulations.

The formation and mobility of point defects in UO 2 have been studied within the framework of the Density Functional Theory. The ab initio Projector Augmented Wave method is used to determine the formation and migration energies of defects. The results relative to intrinsic point defect formation energies using the Generalized Gradient Approximation (GGA) and GGA+U approximations for the exchange-correlation interactions are reported and compared to experimental data. The GGA and GGA+U approximations yield different formation energies for both Frenkel pairs and Schottky trios, showing that the 5 f electron correlations have a strong influence on the defect formation energies. Using GGA, various migration mechanisms were investigated for oxygen and uranium defects. For oxygen defects, the calculations show that both a vacancy and an indirect interstitial mechanism have the lowest associated migration energies, 1.2 and 1.1 eV respectively. As regards uranium defects, a vacancy mechanism appears energetically more favourable with a migration energy of 4.4 eV, confirming that oxygen atoms are much more mobile in UO 2 than uranium atoms. Those results are discussed in the light of experimentally determined activation energies for diffusion.

Buckling phenomena leading to the formation of superimposed blisters have been experimentally observed with the help of a confocal interferometric microscope onto the surface of gold thin films deposited on silicon substrates. Assuming that residual folding effects resulting from plastic deformation mechanisms take place in the film during its morphological evolution, different probable scenarios for the formation of the observed buckling patterns are elaborated in the framework of the Foppl-von Karman's theory of thin plates. Multi-step buckling with growing interface delamination is considered for the first scenario while a single or multi-step buckling at a given delamination width is assumed for the other ones.

With the help of atomic force microscope, ${\text{Y}}_{2}{\text{O}}_{3}$ thin films deposited on GaAs(111) substrates have been evidenced to buckle and to crack at the top side of the wrinkles. This morphological evolution has been explained in the framework of F\"oppl\char21{}von Karman's theory of thin plates integrating two elements: the pre-existing grain and subgrain boundaries in the films leading in the early stage of buckling phenomenon to a first folding effect and in their last stage of evolution; the cracking of the buckles from the previously formed folds.

This work addresses the modeling of dislocation interactions and dynamics in olivine. A 3D dislocation dynamics (DD) simulation developed for cubic and hexagonal metals is adapted to the orthorhombic symmetry of this mineral. Dislocation core effects and mobilities are introduced through available models or phenomenological laws and fitted based on available experimental results on single crystals. The stress dependencies of the mobilities of [100] and [001] dislocations are emphasized. Dislocations interactions are studied through a simple elastic analysis and further using a more realistic approach based on DD simulations. It is shown that no junction formation results from the interaction between [100] and [001] dislocations. The collinear interaction is thus the only potential mechanism for forest hardening although its efficiency is significantly reduced by lattice friction on screw dislocations, which decreases the probability for dislocation reactions. The Taylor relationship is often used to model the dependence of the flow stress with the dislocation density. In the presence of a strong lattice friction, Taylor strengthening is shown here to be only a minor contribution to the flow stress and should not be responsible for it.

We have used a first-principle approach based on the calculation of generalised stacking faults (GSF) to study the influence of pressure on the mechanical properties of forsterite. Six cases corresponding to [100] glide over (010), (021) and (001), and [001] glide over (100), (010) and (110) have been considered. The relaxed energy barriers associated with plastic shear have been calculated by constraining the Si atoms to move perpendicular to the fault plane and allowing Mg and O atoms to move in every direction. These conditions, which preserve dilations as a relaxation process, introduce Si–O tetrahedral tilting as an additional relaxation mechanism. Relaxed GSF show little plastic anisotropy of [100] glide over different planes and confirms that [001] glide is intrinsically easier than [100] glide. The GSF are affected by the application of a 10 GPa confining pressure with a different response for each slip system that cannot be explained by sole elastic effect. In particular, [100](010) is found to harden significantly under pressure compared to [001](010). Our results give the first theoretical framework to understand the pressure-induced change of dominant slip systems observed by Couvy et al. (in Eur J Mineral 16(6):877–889, 2004) and P. Raterron et al. (in GRL, submitted). It appears necessary to account for the influence of pressure on the mechanical properties of silicates in the context of the deep Earth.

M ultiscale m odelling and com putation is becom ing one of the m ost active research areas inm aterials science. T his evolution is driven by the rapid grow th in available com puting pow erand by the developm ent of m any innovative algorithm s and techniques. In m ineral physics, theissue of m antle rheology, controlled by the deform ation of high-pressure m ineral assem blages,can be addressed by this new approach. In contrast w ith therm odynam ic properties like theequation of state, w hich are fully determ ined at the atom ic length scale, m echanical propertiesare inherently m ultiscale: they depend on the interrelationship betw een processes operating atthe scale of the atom , the crystal, the rock and the w hole planet. M oreover, these different scalesare often strongly coupled to each other, w hich m akes the problem even m ore challenging. Fr om the atoms to the EarthO s mantleM echanical properties of real m aterials are controlled by crystal defects such as pointdefects, dislocations, stacking faults and grain boundaries. T aken individually, these defectscan be described at the fundam ental level through their atom ic and electronic structures,w hich can be found by solving the S chršdinger equation. F irst-principles calculations andm olecular dynam ics are used to address such problem s. A t the scale of a grain, them echanical properties are often the result of the collective behaviour of these defects inresponse to the loading conditions. N ew ly developed three-dim ensional dislocation dyna-EMU Notes in Mineralogy , V ol. 7 (2005), Chapter 16, 389Ð415

We report on molecular dynamics simulations of thin film buckling which show that during the buckling phenomena dislocations can be emitted from specific region of the film where the heterogeneous stress was found to be maximum and larger than in the planar adherent part. A scenario of formation of misfit dislocations in the planar interface which lead to stress relaxation is finally proposed.

Molecular dynamics simulations of thin film buckling demonstrate that high compressive stresses are localized in the straight-sided wrinkle leading to the nucleation of dislocations, which are mobile and plastically release a large amount of the strain. As a consequence, the maximum deflection determined in the framework of elasticity theory is found to be overestimated. Finally, the resulting plastic deformation has been estimated and included in the expression of the deflection.

The aim of our studies is to have a better understanding of the buckling phenomenon that generally results in the lost of functional properties that were initially conferred to the coated substrates.

The evolution of the surface reconstruction of the Au(111) under stress-strain has been studied in the context of an experimental approach, both by tunneling microscopy under ultra-vacuum environment coupled to a compression device, and numerically by molecular dynamics simulations. At first, we studied the interaction between atomic steps (vicinal or slip traces) and reconstruction. In particular, we showed experimentally a strong dependence of the length of the reconstruction with the width of the terraces, in very good agreement with the atomistic simulations. We have quantitatively demonstrated that this behavior is originated from the release of surface stress, both along and perpendicular to the atomic steps. Subsequently, we have shown that the appearance of a slip traces, resulting from the emergence of dislocations at the surface, induce a reorganization of the reconstruction, characterized by the formation of a U-shaped pattern. We also observed experimentally the presence of kinks along the trace. The simulations confirmed that these kinks are correlated with the modification of the reconstruction. At last, the study focused on the evolution of the chevron pattern under applied stress-strain. Experimental observations have shown that a macroscopic compressive strain involved a modification of the herringbone structure. Molecular dynamics simulations allowed to analyze the influence of stress orientation on surface threading dislocations. We have shown that an irreversible reorganisation of the herringbone structure takes place, characterized by the annihilation of the surface threading dislocations and the removal of the herringbone structure.; L’évolution de la reconstruction de surface de l’Au(111) sous contrainte-déformation a été étudiée dans le cadre d’une approche, à la fois expérimentale par microscopie à effet tunnel sous environnement ultra-vide couplée à un dispositif en compression, et numériquement par simulations en dynamique moléculaire. Dans un premier temps, nous avons étudié l’interaction entre les marches atomiques (vicinales ou traces de glissement) et la reconstruction. Nous avons notamment montré expérimentalement une forte dépendance de la longueur de la reconstruction avec la largeur des terrasses, en très bon accord avec les simulations atomistiques. Nous avons démontré de manière quantitative que ce comportement provenait de la relaxation des contraintes de surface, à la fois le long et perpendiculairement aux marches atomiques. Par la suite, nous avons montré que l’apparition d’une trace de glissement, résultant de l’émergence d’une dislocation à la surface, induit une réorganisation de la reconstruction, caractérisée par la formation d’un motif en forme de U. Nous avons par ailleurs observé expérimentalement la présence de décrochements le long de la trace. Les simulations ont confirmé que ces décrochements étaient corrélés avec la modification de la reconstruction. Dans un second temps, l’étude s’est axée sur l’évolution de la reconstruction en chevrons sous contrainte-déformation appliquée. Les observations expérimentales ont montré qu’une contrainte de compression macroscopique était à l’origine d’une modification de la structure en chevrons. Les simulations en dynamique moléculaire ont permis d’analyser l’influence de l’orientation de la contrainte sur les dislocations perçant la surface. Nous avons montré qu’une réorganisation irréversible de la structure en chevrons a lieu, se caractérisant par l’annihilation des dislocations perçant la surface et la suppression de la structure en chevrons.

For several decades, the elaboration of nano-structured materials tends to develop more and more. Indeed, these materials often show interesting properties, and in particular surprising mechanical properties when compared to their bulk counterparts. For example, nano-twinned or nano-layered metals are known to have ultra-high mechanical strength, good thermal stability, and very good radiation resistance. As the interface spacing decreases to the nanometer-scale, the density of interfaces increases significantly and subsequently the macroscopic properties become largely governed by the interface-defect interactions. In that context, we have studied deformation twin formation and mechanisms of interaction between a new formed twin and a preexisting interface (a twin boundary or a bimetallic interface), using atomistic simulations and a thin film model configuration. First results show the influence of surface steps on mechanical twinning, for a model system without interface. Then we identify a new mechanism leading to the formation of a Lomer dislocation, following the interaction of a newly formed twin and a preexisting twin boundary. By varying the density of surface defects, we show the particular influence of a preexisting twin boundary on twin size and number. Finally, for the Cu/Ag bimetallic system, our results highlight the role of epitaxial dislocations (at the interface) in twin nucleation and extension as well as a direct influence of the interface type in twin propagation.; Depuis quelques dizaines d'années, l'élaboration de matériaux nanostructurés tend de plus en plus à se développer. En effet, ces matériaux présentent souvent des propriétés intéressantes et en particulier des propriétés mécaniques surprenantes vis-à-vis de leurs homologues sous forme massive. Les métaux nano-maclés ou nano-lamellaires par exemple, sont connus pour avoir une bonne résistance mécanique, une bonne stabilité thermique et une excellente résistance aux radiations. Au fur et à mesure que l'espacement entre les interfaces diminue, leur densité augmente de manière significative et les propriétés macroscopiques du matériau sont de plus en plus dépendantes des interactions défaut-interface. Dans ce contexte, nous avons étudié, via des simulations atomistiques, la formation de macles de déformation et les mécanismes d'interaction d'une macle nouvellement formée avec une interface préexistante (un joint de macle ou une interface entre 2 métaux), pour une configuration modèle de film mince auto-supporté. Des premiers résultats montrent l'influence de marches de surface sur le maclage, pour un cas modèle sans interface. Puis nous avons identifié un mécanisme inédit aboutissant à la formation d'une dislocation de Lomer suite à l’interaction d'une macle en formation avec un joint de macle préexistant. En faisant varier la densité de défauts de surface, nous montrons l'influence particulière d'un joint de macle sur la taille et le nombre de macles formées. Enfin, pour les systèmes bimétalliques Cu/Ag, nos résultats mettent en évidence le rôle des dislocations d'épitaxie (à l'interface) dans la nucléation et l'extension des macles ainsi qu'une influence directe du type d'interface considéré sur la propagation de ces macles.