[en] 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

[en] The effect of solute hydrogen on the stability of vacancy clusters in hexagonal closed packed zirconium is investigated with an ab initioapproach, 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 initiobinding 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.

[en] The interaction between vacancies and edge dislocations in face centered cubic metals (Al, Au, Cu, Ni) is studied at different length scales. Using empirical potentials and static relaxation, atomic simulations give us a precise description of this interaction, mostly in the case when the separation distance between both defects is small. At larger distances, elasticity theory can be used to predict this interaction. From the comparison between both approaches we obtain the minimal separation distance where elasticity applies and we estimate the degree of refinement required in the calculation. In this purpose, isotropic and anisotropic elasticity is used assuming a perfect or a dissociated edge dislocation and considering the size effect as well as the inhomogeneity interaction

[en] 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. (authors)

[en] 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. (authors)

[en] 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.

[en] We report of 3-dimensional discrete dislocation dynamics (DDD) simulations of dislocation loops coarsening by vacancy bulk diffusion. The calculation is based upon a model which couples the diffusion theory of vacancies to the DDD in order to obtain the climb rate of the dislocation segments. Calculation of isolated loops agrees with experimental observations, i.e. loops shrink or expand, depending on their type and vacancy supersaturation. When an array of dislocation loops of various sizes is considered, and the total number of vacancies in the simulation is maintained constant, the largest dislocations are found to increase in size at the expense of small ones, which disappear in a process known as Ostwald ripening.

[en] 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 h(12-bar10) screw dislocation in hexagonal close-packed zirconium. Generalized stacking fault calculations reveal a metastable stacking fault in the first order pyramidal {101-bar1} 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. (authors)

[en] 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 elasto diffusion 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. (authors)

[en] 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 ab initio 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. (authors)