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International audience; Crystal strength and plastic flow are controlled by the motion and interaction of dislocations, the line defects carrying atomic shear increments. Whereas, in most crystals, deformation develops in the crystallographic planes in which the glide force acting on dislocations is maximum, plasticity in body-centred cubic metals is more complex. Slip systems in which the resolved shear stress is not the highest can dominate at low temperature, leading to anomalous slip. Using in situ tensile tests in a transmission electron microscope we show that anomalous slip arises from the high mobility of multi-junctions , that is, junctions between more than two dislocations, which glide at a velocity several orders of magnitude larger than single dislocations. These multi-junctions result from the interaction of a simple binary junction with a gliding dislocation. Although elasticity theory predicts that these binary junctions should be unstable in crystals with a weak elastic anisotropy such as tungsten, both experiments and atomistic simulations reveal that such junctions can be created under dynamic conditions, in agreement with the existence of anomalous slip in almost all body-centred cubic metals, including tungsten .

Plasticity in hexagonal close-packed zirconium is mainly controlled by the glide of dislocations with 1/3 Burgers vectors. As these dislocations cannot accommodate deformation in the [0001] direction , twinning or glide of dislocations, i.e. dislocations with 1/3 Burgers vector, have to be activated. We have performed in situ straining experiments in a transmission electron microscope to study the glide of dislocations in two different zirconium samples, pure zirconium and Zircaloy-4, at room temperature. These experiments show that dislocations exclusively glide in first-order pyramidal planes with cross-slip being activated. A much stronger lattice friction is opposing the glide of dislocations when their orientation corresponds to the direction defined by the intersection of their glide plane with the basal plane. This results in long dislocations straightened along which glide either viscously or jerkily. This direction governs the motion of segments with other orientations, whose shape is merely driven by the minimization of the line tension. The friction due to solute atoms is also discussed.

International audience; The interplay of screw dislocations with carbon atoms is investigated in tungsten at high temperature using in situ straining experiments in a transmission electron microscope (TEM) and through ab initio calculations. When the temperature is high enough to activate carbon diffusion, above 1373 K, carbon segregates in the core of screw dislocations and modifies their mobility, even for a carbon concentration as low as 1 appm. TEM observations reveal the reappearance of a Peierls mechanism at these high temperatures, with screw dislocations gliding viscously through nucleation and propagation of kink-pairs. The mobility of screw dislocations saturated with carbon atoms is then investigated with ab initio calculations to determine kink-pair formation, nucleation and migration energies. These energies are used in kinetic Monte-Carlo simulations and in an analytical model to obtain the velocity of screw dislocations as a function of the temperature, the applied stress and the dislocation length. The obtained mobility law parametrised on ab initio calculations compares well with experiments.

International audience; Plasticity in hexagonal close-packed zirconium is controlled by screw dislocations which easily glide in the prismatic planes where they are dissociated. At high enough temperatures, these dislocations can deviate out of the prism planes to also glide in the first order pyramidal and basal planes. To get a better understanding of these secondary slip systems, we have performed molecular dynamics (MD) simulations of a screw dislocation gliding in a basal plane. The gliding dislocation remains dissociated in the prism plane where it performs a random motion and occasionally cross-slips out of its habit plane by the nucleation and propagation of a kink-pair. Deviation planes are always pyramidal, with an equal probability to cross-slip in the two pyramidal planes on both sides of the basal plane, thus leading to basal slip on average. Basal slip appears therefore as a combination of prismatic and pyramidal slip in the high stress regime explored in MD simulations. This is confirmed by nudged elastic band (NEB) calculations. But NEB calculations also reveal a change of glide mechanism for a decreasing applied stress. At low stress, kinks do not lie anymore in the pyramidal planes. They are now spread in the basal planes, thus fully compatible with a motion of the screw dislocation confined to the basal plane as seen in experiments. Basal slip, which is in competition with pyramidal slip, appears therefore favoured at low stress in pure zirconium.

International audience; The interaction of hydrogen with 2/1 screw dislocations is investigated in body-centered cubic tungsten and iron using ab initio calculations. Different core reconstructions are evidenced, depending on the number of hydrogen atoms introduced inside the dislocation core. Corresponding interaction energies are highly attractive in both metals, with a significant contribution of zero point energy associated with H vibrations, particularly in Fe. The pinning by hydrogen of the dislocation in its reconstructed core remains efficient for a local atomic fraction of hydrogen as low as 1/5. Other octahedral interstitial sites close to the reconstructed core are also attractive, contrary to the perfect bcc crystal where these sites are unstable and where hydrogen lies in the tetrahedral sites. Hydrogen recovers its bulk behavior only beyond the eighteenth neighbor octahedral sites. A simple pair interaction model is parameterized on ab initio calculations and used with a mean-field approximation to predict the concentration profiles of hydrogen segregated in and around the dislocation core. This segregation model predicts that dislocation core-sites remain completely decorated by hydrogen atoms up to at least 750 K and 200 K in W and Fe, respectively.

Basal slip acts as a secondary deformation mode in hexagonal close-packed titanium and becomes one of the primary mechanisms in titanium alloyed with simple metals. As these solute elements also lead to a pronounced reduction of the energy of the basal stacking fault, one can hypothesize that they promote basal dissociation of dislocations which can then easily glide in the basal planes. Here, we verify the validity of this hypothesis using ab initio calculations to model the interaction of a screw dislocation with indium (In) and tin (Sn). These calculations confirm that these simple metals are attracted by the stacking fault existing in the dislocation core when it is dissociated in a basal plane, but this interaction is not strong enough to stabilize a planar configuration, even for a high solute concentration in the core. Energy barrier calculations reveal that basal slip, in the presence of In and Sn, proceeds without any planar dissociation, with the dislocation being spread in pyramidal and prismatic planes during basal slip like in pure Ti. The corresponding energy barrier is higher in presence of solute atoms, showing that In and Sn do not ease basal slip but increase the corresponding lattice friction. This strengthening of basal slip by solute atoms is discussed in view of available experimental data.

International audience; Plasticity of body-centered cubic (bcc) metals is atypical at low temperatures, caused by the important lattice friction of screw dislocations. In this paper, we present a yield criterion that can be used to predict yield stress and active slip systems in all bcc transition metals for any applied stress. The criterion is fully parametrized on ab initio calculations of screw dislocation glide properties, and is applied in the case of uniaxial loading to compare with tension and compression experiments at low temperature. The criterion describes most of the different plastic behaviors observed experimentally in different metals, i.e. the dependence of the yield stress and active slip system on the orientation of the loading axis, as well as the tension/compression asymmetry. We find that plastic yield generally occurs at lower stresses in tension than in compression but for some metals, in particular niobium, there are large regions of the stereographic projection where compression is easier

We show here how density functional theory calculations can be used to predict the temperatureand orientation-dependence of the yield stress of body-centered cubic (BCC) metals in the thermallyactivated regime where plasticity is governed by the glide of screw dislocations with a 1/2 Burgers vector. Our numerical model incorporates non-Schmid effects, both the twinning/antitwinning asymmetry and non-glide effects, characterized through ab initio calculations on straight dislocations. The model uses the stress-dependence of the kink-pair nucleation enthalpy predicted by a line tension model also fully parameterized on ab initio calculations. The methodology is illustrated here on BCC tungsten but is applicable to all BCC metals. Comparison with experimental data allows to highlight both the successes and remaining limitations of our modeling approach., Comptes Rendus Physique, Centre Mersenne, In press

The influence of magnetism on the properties of screw dislocations in body-centered cubic chromium is investigated by means of ab initio calculations. Screw dislocations having Burgers vectors 1/2 ⟨111⟩ and ⟨100⟩ are considered, following experimental observations showing activity for both slip systems. At low temperature, chromium has a magnetic order close to antiferromagnetism along ⟨100⟩ directions, for which 1/2 ⟨111⟩ is not a periodicity vector. Hence, dislocations with Burgers vectors 1/2 ⟨111⟩ generate magnetic faults when shearing the crystal, which constrain them to coexist and move pairwise, leading to dissociated ⟨111⟩ super-dislocations. On the other side, ⟨100⟩ is a periodicity vector of the magnetic order of chromium, and no such magnetic fault are generated when ⟨100⟩ dislocations glide. Dislocation properties are computed in the magnetically ordered and non magnetic phases of chromium for comparison purposes. We report a marginal impact of magnetism on the structural properties and energies of dislocations for both slip systems. The Peierls energy barrier opposing dislocation glide in {110} planes is comparable for both 1/2 ⟨111⟩ {110} and ⟨100⟩ {110} slip systems, with lower Peierls stresses in the magnetically ordered phase of chromium.

International audience; The interaction between carbon and screw dislocations in tungsten is investigated using ab initio calculations. The presence of carbon atoms in the vicinity of the dislocation induces a reconstruction, with the dislocation relaxing to a configuration, the hard core structure, which is unstable in pure tungsten. The reconstruction corresponds to a strong binding of carbon in the prismatic sites created by the dislocation which is perfect for high concentrations of carbon segregated on the dislocation line. However, the reconstruction is only partial for lower atomic fractions, with the dislocation tending to fall back in its easy core ground state. This pinning by carbon atoms of the dislocation in an unstable position is well described by a simple line tension model. A strong carbon-dislocation attraction is also evidenced at larger separation distances, when the solute is in the fourth nearest neighbour octahedral sites of the reconstructed core. The equilibrium concentrations of carbon in these different segregation sites are modelled with an Ising model and using a mean-field approximation. This thermodynamic model evidences that screw dislocations remain fully saturated by carbon atoms and pinned in their hard core configuration up to about 2500 K.

Slip activity in body-centered cubic chromium is modeled by means of ab initio calculation of screw dislocations core properties and Peierls potential. As dislocations having 1 / 2 〈 111 〉 Burgers vector and also 〈 100 〉 , both gliding in { 110 } crystallographic planes have been reported experimentally, both screw dislocations are modeled. A generalized yield criterion incorporating physical ingredients necessary to account for deviations from the Schmid law is obtained for 〈 111 〉 { 110 } and 〈 100 〉 { 110 } slip systems. We report a broad range of crystal orientations for which 〈 100 〉 screw dislocations are easier to activate than the conventional 1 / 2 〈 111 〉 in tension and compression. These results hold for both the non-magnetic and antiferromagnetic phases of body-centered cubic chromium, with only a marginal effect of magnetism.

A hallmark of low-temperature plasticity in body-centered cubic (BCC) metals is its departure from Schmid’s law. One aspect is that non-glide stresses, which do not produce any driving force on the dislocations, may affect the yield stress. We show here that this effect is due to a variation of the relaxation volume of the $$1/2\langle 111\rangle$$1∕2⟨111⟩ screw dislocations during glide. We predict quantitatively non-glide effects by modeling the dislocation core as an Eshelby inclusion, which couples elastically to the applied stress. This model explains the physical origin of the generalized yield criterion classically used to include non-Schmid effects in constitutive models of BCC plasticity. We use first-principles calculations to properly account for dislocation cores and use tungsten as a reference BCC metal. However, the methodology developed here applies to other BCC metals, other energy models and other solids showing non-glide effects.

Plasticity in body-centred cubic (BCC) metals at low temperatures is atypical, marked in particular by an anisotropic elastic limit in clear violation of the famous Schmid law applicable to most other metals. This effect is known to originate from the behaviour of the screw dislocations; however, the underlying physics has so far remained insufficiently understood to predict plastic anisotropy without adjustable parameters. Here we show that deviations from the Schmid law can be quantified from the deviations of the screw dislocation trajectory away from a straight path between equilibrium configurations, a consequence of the asymmetrical and metal-dependent potential energy landscape of the dislocation. We propose a modified parameter-free Schmid law, based on a projection of the applied stress on the curved trajectory, which compares well with experimental variations and first-principles calculations of the dislocation Peierls stress as a function of crystal orientation., Low-temperature plasticity in BCC metals is atypical, marked by an anisotropic elastic limit in violation of the Schmid law. Here, the authors show that these deviations can be quantified from subatomic deviations of the screw dislocation trajectory away from its average glide plane.

Although precipitates’ compositions are theoretically determined by thermodynamics, their formation kinetics can also lead to composition variations that allow further structural evolution, making the precipitation path more complex.

International audience; We investigate the thermally activated glide mobility of dislocations in uranium dioxide (UO 2) from an atomistic point of view using a variable charge many-body empirical potential, the Second Moment Tight-Binding potential with charge equilibration (SMTB-Q). In order to determine the main glide system , we model the dislocation core structures for edge and screw orientations lying in different glide planes. Uncommon core structures with a double periodicity and a charge alternation are obtained. Straight dislocations motion is first considered to obtain the Peierls stress of each dislocation. We then address the thermally activated motion of the dislocations by the nucleation of kink pairs. Atomistic simulations give us the structure as well as the formation and migration energies of kink pairs. This information is finally combined with an elastic interaction model for kink pairs to obtain the dislocation velocities and the evolution of the critical resolved shear stress as a function of temperature. These quantities are compared to experimental data on urania single crystals.

International audience; Basal slip of ⟨a⟩ screw dislocations in hexagonal closed-packed titanium is investigated with ab initio calculations. We show that a basal dissociation is highly unstable and reconfigures to other structures dissociated in a first order pyramidal plane. The obtained mechanism for basal slip corresponds to the migration of the partial dislocations and of the associated stacking fault ribbon in a direction perpendicular to the dissociation plane. Presented results indicate that both basal and pyramidal slip will operate through the Peierls mechanism of double-kink nucleation and will be equally active at high enough temperature.

International audience; The interaction between screw dislocations and oxygen interstitial atoms is studied with ab initio calculations in hexagonal close-packed titanium. Our calculations evidence a strong repulsion when the solute atoms are located in the dislocation glide plane, leading to spontaneous cross-slip, which allows the dislocation to bypass the atomic obstacle. This avoidance process explains several experimental observations in titanium in presence of oxygen: (1) a larger lattice friction against screw dislocation motion, (2) a reduction of the dislocation glide distance in prismatic planes and (3) an enhancement of cross-slip in pyramidal planes.

International audience; Different descriptions used to model a point-defect in an elastic continuum are reviewed. The emphasis is put on the elastic dipole approximation, which is shown to be equivalent to the infinitesimal Eshelby inclusion and to the infinitesimal dislocation loop. Knowing this elastic dipole, a second rank tensor fully characterizing the point-defect, one can directly obtain the long-range elastic field induced by the point-defect and its interaction with other elastic fields. The polarizability of the point-defect, resulting from the elastic dipole dependence with the applied strain, is also introduced. Parameterization of such an elastic model, either from experiments or from atomic simulations, is discussed. Different examples, like elastodiffusion and bias calculations, are finally considered to illustrate the usefulness of such an elastic model to describe the evolution of a point-defect in a external elastic field.

International audience; This chapter reviews the different methodological aspects of the ab ini-tio modeling of dislocations. Such simulations are now frequently used to study the dislocation core, i.e. the region in the immediate vicinity of the line defect where the crystal is so strongly distorted that an atomic description is needed. This core region controls some dislocation fundamental properties, like their ability to glide in different crystallographic planes. Ab initio calculations based on the density functional theory offer a predictive way to model this core region. Because dislocations break the periodicity of the crystal and induce long range elastic fields, several specific approaches relying on different boundary conditions have been developed to allow for the atomistic modeling of these defects in simulation cells having a size compatible with ab initio calculations. We describe these different approaches which can be used to study dislocations with ab initio calculations and introduce the different analyses which are currently performed to characterize the core structure, before discussing how meaningful energy properties can be extracted from such simulations.

International audience; The interaction of point-defects with an external stress eld or with other structural defects is usually well described within continuum elasticity by the elastic dipole approximation. Extraction of the elastic dipoles from atomistic simulations is therefore a fundamental step to connect an atomistic description of the defect with continuum models. This can be done either by a tting of the point-defect displacement eld, by a summation of the Kanzaki's forces or by a linking equation to the residual stress. We perform here a detailed comparison of these dierent available methods to extract elastic dipoles, and show that they all lead to the same values when the supercell of the atomistic simulations is large enough and when the anharmonic region around the point-defect is correctly handled. But for small simulation cells compatible with ab initio calculations, only the denition through the residual stress appears tractable. The approach is illustrated by considering various point-defects (vacancy, self-interstitial and hydrogen solute atom) in zirconium, using both empirical potentials and ab initio calculations.

International audience; The thermodynamic properties of the Zr-Nb alloy are investigated at temperatures below 890 K with ab initio calculations. The solution energies of the bcc Nb-rich and hcp Zr-rich solid solutions obtained within the framework of density functional theory are in good agreement with experimental data, although insufficient for a quantitative description of the miscibility gap, for which non configurational entropy has to be accounted for. Whereas electronic free energies can be neglected, we show, using the harmonic approximation and the density functional perturbation theory, that both solution free energies are strongly modified by the contribution related to atomic vibrations. Considering this vibrational free energy leads to a good description of the phase diagram.

Atomistic simulations, based either on an empirical interatomic potential or on ab initio calculations, are used to study the pyramidal glide of a $$1/3\ \langle 1\bar{2}10\rangle $$ screw dislocation in hexagonal close-packed zirconium. Generalized stacking fault calculations reveal a metastable stacking fault in the first order pyramidal $$\lbrace 10\bar{1}1 \rbrace $$ plane, which corresponds to an elementary pyramidal twin. This fault is at the origin of a metastable configuration of the screw dislocation in zirconium, which spontaneously appears when the dislocation glides in the pyramidal plane.

International audience; The easy, hard and split core configurations of the < 111 > screw dislocation and the energy pathways between them are studied in body-centered cubic (bcc) Fe and W using different density functional theory (DFT) approaches. All approaches indicate that in Fe, the hard core has a low relative energy, close to or even below that of the saddle configuration for a straight path between two easy cores. This surprising result is not a direct consequence of magnetism in bcc Fe. Moreover, the path followed by the dislocation core in the (111) plane between easy cores, identified here using two different methods to locate the dislocation position, is almost straight, while the energy landscape between the hard core position and the saddle configuration for a straight path is found to be very flat. These results in Fe are in contrast with predictions from empirical potentials as well as DFT calculations in W, where the hard core has an energy about twice that of the maximum energy along the Peierls barrier, and where the dislocation trajectory between easy cores is curved. Also, the split core configuration is found to be unstable in DFT and of high energy in both Fe and W, in contrast with predictions from most empirical potentials. (C) 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

International audience; Plasticity in zirconium alloys is mainly controlled by the interaction of 1/3 1210 screw dislocations with oxygen atoms in interstitial octahedral sites of the hexagonal close-packed lattice. This process is studied here using ab initio calculations based on the density functional theory. The atomic simulations show that a strong repulsion exists only when the O atoms lie in the dislocation core and belong to the prismatic dislocation habit plane. This is a consequence of the destruction of the octahedral sites by the stacking fault arising from the dislocation dissociation. Because of the repulsion, the dislocation partially cross-slips to an adjacent prismatic plane, in agreement with experiments where the lattice friction on screw dislocations in Zr-O alloys has been attributed to the presence of jogs on the dislocations due to local cross-slip.

International audience; Dislocation cores, the regions in the immediate vicinity of dislocation lines, control a number of properties such as dislocation mobility, cross-slip and short-range interactions with other defects. The quantitative modeling of dislocation cores requires an electronic-level description of atomic bonding. Ab initio quantum mechanical calculations of dislocation cores based on the density functional theory have progressed rapidly thanks to the steady increase in computing capacities and the development of dedicated numerical methods and codes. Our aim in this overview paper is, after a description of the methodology regarding in particular the boundary conditions, to review the new and unexpected results obtained on dislocation cores from first principles, including the identification of unforeseen stable and metastable cores and the quantitative evaluation of both interaction energies and energy pathways, in pure metals and alloys of different crystallography (FCC, BCC, HCP) as well as semiconductors. We also identify key challenges to be explored in this rapidly growing field.

International audience; Twin growth in hexagonal close-packed zirconium is investigated at the atomic scale by modeling the various disconnections that can exist on twin boundaries. Thanks to a coupling with elasticity theory, core energies are extracted from atomistic simulations and the formation energy of isolated disconnection dipoles is defined. For twin systems where several disconnections can exist, because of this core contribution, the most stable disconnection is not always the one with the smallest Burgers vector. Crystallographic parameters of the disconnection with the lowest formation energy correlate well with twin modes observed experimentally. On the other hand, disconnection migration, characterized here by computing their migration energy and Peierls stress, does not appear critical for twin mode selection.

International audience; Molecular dynamics simulations are performed to investigate the onset of plasticity in zirconium, in conditions associated with the formation of hydrides. These simulations show that plasticity is always initiated by the nucleation and propagation of pyramidal partial dislocations from the surfaces, followed by the formation of basal dislocations in a second step. This result is shown to be weakly dependent on several parameters such as surface orientation and roughness, loading conditions, temperature, and interatomic potential. Our analysis based on generalized stacking fault surfaces suggests that the favored activation of pyramidal slip is related to a surface nucleation effect. Finally, the computed elasticity limits are in agreement with the strains associated with the formation of hydride precipitates.

A cluster dynamics model has been parametrized to quantitatively reproduce results obtained by atomistic kinetic Monte Carlo (AKMC) modeling on the precipitation of Cu in α-Fe under thermal aging. The cluster mobility, highlighted by AKMC, is shown to have a significant effect on the precipitation kinetics and can reconcile the experimentally observed fast kinetics with the relatively low diffusivity of Cu monomers.

We present recent applications of the atomistic diffusion model and of the kinetic Monte Carlo (AKMC) algorithm to alloys of industrial interest or to model systems. These applications include study of homogeneous and heterogeneous precipitation during thermal ageing as well as of phase transformation under irradiation. The AKMC simulations are also used to test the main assumptions and limitations of more simple models and classical theories used in the industry, e.g. the classical nucleation theory.

The motion of [100](010) screw dislocations via a kink-pair mechanism is investigated in high-pressure ${\mathrm{MgSiO}}_{3}$ perovskite by means of atomistic calculations and an elastic interaction model for kink nucleation. Atomistic calculations based on the nudged elastic band method provide the Peierls potential, which is shown to be dynamically asymmetric and stress dependent. The elastic interaction model adjusted to match kink width computed atomistically, is used to evaluate the critical nucleation enthalpy. We demonstrate that the kink-pair mechanism in ${\mathrm{MgSiO}}_{3}$ perovskite is controlled by the nucleation of kinks along the [100] screw dislocation.

The aim of this paper is to give a short review on cluster dynamics modeling in the field of atoms and point defects clustering in materials. It is shown that this method, due to its low computer cost, can handle long term evolution that cannot, in many cases, be obtained by Lattice Kinetic Monte Carlo methods. Indeed, such a possibility is achieved thanks to an important drawback that is the loss of space correlations of the elements of the microstructures. Some examples, in the field of precipitation and irradiation of metallic materials are given. The limitations and difficulties of this method are also discussed. Unsurprisingly, it is shown that it goes in a very satisfactory way when the objects are distributed homogeneously. Conversely, the source term describing the primary damage under irradiation, by nature heterogeneous in space and time, is tricky to introduce especially when displacement cascades are produced.

The effect of solute hydrogen on the stability of vacancy clusters in hexagonal closed packed zirconium is investigated with an ab initio approach, including contributions of H vibrations. Atomistic simulations within the density functional theory evidence a strong binding of H to small vacancy clusters. The hydrogen effect on large vacancy loops is modeled through its interaction with the stacking faults. A thermodynamic modeling of H segregation on the various faults, relying on ab initio binding energies, shows that these faults are enriched in H, leading to a decrease of the stacking fault energies. This is consistent with the trapping of H by vacancy loops observed experimentally. The stronger trapping, and thus the stronger stabilization, is obtained for vacancy loops lying in the basal planes, i.e. the loops responsible for the breakaway growth observed under high irradiation dose., submitted

We present some recent applications of the atomistic diffusion model and of the kinetic Monte Carlo (KMC) algorithm to systems of industrial interest, i.e. Al-Zr-Sc and Fe-Nb-C alloys, or to model systems. These applications include study of homogeneous and heterogeneous precipitation as well as of phase transformation under irradiation. The KMC simulations are also used to test the main assumptions and limitations of more simple models and classical theories used in the industry, e.g. the classical nucleation theory.

Precipitation kinetics of Al3Zr and Al3Sc in aluminum supersaturated solid solutions is studied using cluster dynamics, a mesoscopic modeling technique which describes the various stages of homogeneous precipitation by a single set of rate equations. The only parameters needed are the interface free energy and the diffusion coefficient which are deduced from an atomic model previously developed to study the same alloys. A comparison with kinetic Monte-Carlo simulations based on the vacancy diffusion mechanism shows that cluster dynamics correctly predicts the precipitation kinetics provided a size dependent interface free energy is used. It also manages to reproduce reasonably well existing experimental data.

A self-consistent mean field (SCMF) theory starting from an atomic diffusion model can predict most of the correlation effects induced by the vacancy diffusion mechanism while being coherent with thermodynamics. For that purpose a time dependent effective Hamiltonian is introduced into the non-equilibrium distribution function. Such effective Hamiltonian makes a new hierarchy of approximations to appear in parallel to the thermodynamic mean-field approximations. We explain how each level of approximation is related to correlation effects and how kinetics of phase transformation results from both thermodynamics and diffusion properties. A first example is the radiation induced segregation (RIS) at grain boundary (GB) in austenitic steels where thermodynamics is shown to play an important role under irradiation. In a second example, we demonstrate how mean-field approximations combined with mesoscopic theories like the classical nucleation theory can describe the kinetics of precipitation, leading to a prediction of the cluster size distributions in the solid solution and of the steady state nucleation rates in agreement with kinetic Monte Carlo simulations.

International audience

The ab initio calculation of charged supercells within density-functional theory is a necessary step to access several important properties of matter. The relaxation volume of charged point defects or the partial molar volume of ions in solution are two such examples. However, the total energy and therefore the pressure of charged systems is not uniquely defined when periodic boundary conditions are employed. This problem is tightly related to the origin of the electrostatic potential in periodic systems. This effect can be easily observed by modifying the electrostatic convention or modifying the local ionic potential details. We propose an approach to uniquely define the pressures in charged supercells with the use of the absolute deformation potentials. Only with such a definition could the ab initio calculations provide meaningful values for the relaxation volumes and for the elastic interactions for charged defects in semiconductors or ions in solution. The proposed scheme allows one to calculate sensible data even when charge neutrality is not enforced, thus going beyond the classical force-field-based approaches.

International audience; The relative stability of dislocation core configurations in body-centered-cubic metals is profoundly modified by the presence of solutes. Considering the Fe(C) system, we demonstrate by using density functional theory that carbon atoms destabilize the usual easy core to the benefit of the hard core configuration of the screw dislocation, which is unstable in pure metals. The carbon atom is at the center of a regular prism in a cementitelike local environment. The same dislocation core reconstruction is also found with other solutes (B, N, O) and in W(C). This unexpected low-energy configuration induces a strong solute-dislocation attraction, leading to dislocation core saturation by solute atoms, even for very low bulk solute concentrations. This core reconstruction will constitute an essential factor to account for in solute-segregation related phenomena, such as strain aging.

The stability properties of vacancy clusters in hexagonal close-packed Zr—both cavities and dislocation loops—are investigated at the atomic scale, with a modeling approach based on density functional theory and empirical potentials. By considering the vacancy–vacancy interactions and the stability of small vacancy clusters, we establish how to build larger clusters. A study of extended vacancy clusters is then performed using continuous laws for defect energetics. Once validated with an empirical potential, these laws are parameterized with ab initio data. Our work shows that the easy formation of 〈 a 〉 loops can be explained by their thermodynamic properties.

International audience; A density functional theory (DFT) study of the 1/2⟨111⟩ screw dislocation was performed in the following body-centered cubic transition metals: V, Nb, Ta, Cr, Mo, W, and Fe. The energies of the easy, hard, and split core configurations, as well as the pathways between them, were investigated and used to generate the two-dimensional (2D) Peierls potential, i.e. the energy landscape seen by the dislocation as a function of its position in the (111) plane. In all investigated elements, the nondegenerate easy core is the minimum energy configuration, while the split core configuration, centered in the immediate vicinity of a ⟨111⟩ atomic column, has a high energy near or above that of the hard core. This unexpected result yields 2D Peierls potentials very different from the usually assumed landscapes. The 2D Peierls potential in Fe differs from the other transition metals, with a monkey saddle instead of a local maximum located at the hard core. An estimation of the Peierls stress from the shape of the Peierls barrier is presented in all investigated metals. A strong group dependence of the core energy is also evidenced, related to the position of the Fermi level with respect to the minimum of the pseudogap of the electronic density of states.

Ab initio methods, based on the Density Functional Theory (DFT), have been extensively used to study point defects and defect clusters in materials. Present HPC resources and DFT codes now allow similar investigations to be performed on dislocations. The study of these extended defects requires not only larger simulation cells but also a higher accuracy because the energy differences, which are involved, are rather small, typically 50-to-100 meV for supercells containing 50-to-500 atoms. The topology of the Peierls potential of screw dislocations with 1/2 Burgers vector, i.e. the 2D energy landscape seen by these dislocations, is being completely revisited by DFT calculations. From results obtained in all body-centered cubic (bcc) transition metals, except Cr (V, Nb, Ta, Mo, W and Fe), using the PWSCF code, which is part of the Quantum-Espresso package, we concluded that the 2D Peierls potentials have two common features: the single-hump shape of the barrier between two minima of the potential, and the presence of a maximum – and not a minimum as predicted by most empirical potentials – around the split core. In iron, the topology of the Peierls potential is reversed compared to the classical sinusoidal picture: the location of the saddle point and the maximum are indeed inverted with unexpected flat regions. The first results obtained within the framework of the PRACE project, DIMAIM (DIslocations in Metals using Ab Initio Methods), started at the beginning of 2013, will also be presented. In particular, in order to address the twinning-antitwinning asymmetry often observed in bcc metals and regarded as the major contribution to the breakdown of Schmid's law, we have determined the crystal orientation dependence of the Peierls stress, i.e. the critical stress required for dislocation motion. These computationally most expensive simulations were performed on the PRACE Tier-0 system at Barcelona Supercomputing Center (Marenostrum III). The scalability results using the various parallelization levels of the PWSCF code up to 10 000 cores will be presented.

International audience; Although the favored glide planes in hexagonal close-packed Zr are prismatic, screw dislocations can escape their habit plane to glide in either pyramidal or basal planes. Using abinitio calculations within the nudged elastic band method, we show that, surprisingly, both events share the same thermally activated process with an unusual conservative motion of the prismatic stacking fault perpendicularly to itself. Halfway through the migration, the screw dislocation adopts a nonplanar metastable configuration with stacking faults in adjacent prismatic planes joined by a two-layer pyramidal twin.

International audience; Modeling point defects at an atomic scale requires careful treatment of the long-range atomic relaxations. This elastic field can strongly affect point defect properties calculated in atomistic simulations because of the finite size of the system under study. This is an important restriction for ab initio methods which are limited to a few hundred atoms. We propose an original approach coupling ab initio calculations and linear elasticity theory to obtain the properties of an isolated point defect for reduced supercell sizes. The reliability and benefit of our approach are demonstrated for three problematic cases: the self-interstitial in zirconium, clusters of self-interstitials in iron, and the neutral vacancy in silicon.

Plasticity in zirconium is controlled by $1/3\ensuremath{\langle}1\overline{2}10\ensuremath{\rangle}$ screw dislocations gliding in the prism planes of the hexagonal close-packed structure. This prismatic and not basal glide is observed for a given set of transition metals like zirconium and is known to be related to the number of valence electrons in the d band. We use ab initio calculations based on the density functional theory to study the core structure of screw dislocations in zirconium. Dislocations are found to dissociate in the prism plane in two partial dislocations, each with a pure screw character. Ab initio calculations also show that the dissociation in the basal plane is unstable. We calculate then the Peierls barrier for a screw dislocation gliding in the prism plane and obtain a small barrier. The Peierls stress deduced from this barrier is lower than 21 MPa, which is in agreement with experimental data. The ability of an empirical potential relying on the embedded atom method (EAM) to model dislocations in zirconium is also tested against these ab initio calculations.