First principles study on the segregation of metallic solutes and non-metallic impurities in Cu grain boundary

Metallic dopants have the potential to increase the mechanical strength of polycrystalline metals. These elements are expected to aggregate in regions of lower coordination, such as grain boundaries. At the grain boundaries, they can have a beneficial (toughening) or detrimental effect (e.g. grain boundary embrittlement). In this study, we employ Density Functional Theory (DFT) to compute the segregation energies of various metallic and other non-metallic elements to determine their effect when introduced in a symmetric Cu grain boundary. The study results may be used to qualitatively rank the beneficial effect of certain metallic elements, such as V, Zr, and Ag, as well as the strong weakening effect of non-metallic impurities like O, S, F and P. Furthermore, the induced local distortion is found to be proportional to the weakening effect of the elements

First principles study on the segregation of metallic solutes and non-metallic impurities in Cu grain boundary

Metallic dopants have the potential to increase the mechanical strength of polycrystalline metals. These elements are expected to aggregate in regions of lower coordination, such as grain boundaries. At the grain boundaries, they can have a beneficial (toughening) or detrimental effect (e.g. grain boundary embrittlement). In this study, we employ Density Functional Theory (DFT) to compute the segregation energies of various metallic and other non-metallic elements to determine their effect when introduced in a symmetric Cu grain boundary. The study results may be used to qualitatively rank the beneficial effect of certain metallic elements, such as V, Zr, and Ag, as well as the strong weakening effect of non-metallic impurities like O, S, F and P. Furthermore, the induced local distortion is found to be proportional to the weakening effect of the elements

Relations cristallographie-microstructure de la martensite hiérarchique du point de vue micromécanique

Highly dislocated lath martensite is an essential microstructure component of many multi-phase advanced high-strength steels (AHSS) such as dual-phase-, transformation / twinning induced plasticity and precipitation hardened steels. In the last decade novel experimental microstructure characterization methods based on lattice diffraction phenomena enabled to obtain a clearer picture of the overall microstructural state of lath martensite, revealing that under certain circumstances it forms a hierarchical microstructural arrangement where the smallest units (laths) group to definite blocks that again assemble definite packets. Beside this general trend, the exact microstructure formation during transformation is highly sensitive on the materials processing history as well as temperature rates and external loadings during transformation. Modelling of the transformation necessitates a multi-scale description and a multitude of experimental data for the model verification. Since transformation induced plasticity results from accommodation processes of the highly anisotropic transformation strains at the microscale, the morphological aspects, i.e. the crystallographic variants related to the lattice change of the transformation must be taken into account.This work is motivated by experimental data obtained from electron backscattering diffraction measurements necessary to calibrate stress sensitive constitutive relations formulated at the microscale for their use in finite element models. In order to be able to accomplish such a goal (i) there must be a definite link between the experimental data and variables of the model and (ii) the model must comprise microstructurally and micromechanics motivated relations. However, for none of these two problems a generally accepted strategy exists up to date. Based on the requirements for the microstructure of a thermally cycled and mechanically loaded maraging steel forming a lath martensitic microstructure, first a unification of crystal plasticity and the crystallographic theory of martensite formation is proposed for point (i). For point (ii) phenomenological scaling relations for non-local effects as well as constitutive laws for the stress dependence of the transformation, dislocation plasticity, nucleation and coupling effects fitting this framework are advised.La martensite à haut degré des dislocation présentant une structure en lattes est un composant essentiel de la microstructure de nombreux aciers multi-phase à très haute résistance dont propriétés sont à côté d'autres facteurs, tels que le durcissement par précipitation, pour une large part en raison du effet d’écrouissage induit par une changement de phase. Dans la dernière décennie, de nouvelles méthodes expérimentales de caractérisation microstructurale, basées sur des phénomènes de diffraction en réseau cristallin, on a découvert que dans certaines circonstances, la martensite forme un arrangement microstructural hiérarchique, où les plus petites unités (des lattes) se regroupent en blocs qui, à leur tour, s’assemblent en paquets définis. En plus de cette tendance générale, la structure définitive de la microstructure au cours de la transformation est très sensible au traitement des matériaux avant la transformation ainsi qu'aux vitesses de changement température et de contraintes externes pendant la transformation. La modélisation de la transformation nécessite une description à plusieurs échelles et une variété de données expérimentales pour la vérification du modèle. Puisque la plasticité induite par la transformation résulte des processus d'accommodation des souches de transformation hautement anisotropes à l'échelle microscopique, les aspects morphologiques, c'est-à-dire les variations cristallographiques liées au changement de réseau pendant la transformation, doivent être pris en compte à cette échelle. Le but de ce travail est d'utiliser des données provenant d'expériences de rétrodiffusion électronique pour calibrer différents modèles théoriques. Deux aspects sont essentiels pour la mise en œuvre : (i) Il doit y avoir un lien précis entre les données expérimentales et les variables du modèle et (ii) le modèle doit être basé sur les relations microstructurales (géométriques et micromécaniques). A ce jour, il n'existe pas encore de stratégie générale pour ces deux points. A partie d’un modèle de microstructure d'un acier maraging formant une microstructure martensitique à lattes, thermo-cyclé et chargé mécaniquement, on propose d'abord une unification de la plasticité cristalline et de la théorie cristallographique de la martensite, ce qui résout le point (i). Pour le point (ii), les relations de transition d'échelle phénoménologiques pour tenir compte du effet non local caractéristique des contraintes et des lois de comportement pour la dépendance à l’intensité de la transformation, la plasticité de dislocation, la nucléation et les effets de couplage adaptés à ce cadre sont développés

Special cases of martensite compatibility: A near single-variant habit-plane and the martensite of nanocrystalline NiTi

Lattice parameters measured near the high temperature (~1000°C) bcc α to hcp β transformation in an intermetallic Mo-containing γ-TiAl based alloy indicate a middle valued eigenvalue of the corresponding deformation gradient near 1. Habit-planes calculated under the assumption of a simple slip as lattice invariant shear, agree with experimentally determined orientations of the lens like plates recorded via electron backscattering. By contrast, twinning as invariant lattice shear has been investigated in nanocrystalline NiTi. Here the grain size causes the formation mechanism of the martensite to change from a “herring-bone” morphology faciliting a habit-plane between two twinned laminates and the austenite to a single laminate, which in the nonlinear theory formally cannot form a habit-plane with the austenite. Since this might cause high accommodation strains, the effectiveness of stress accommodation of martensite formed in neighboring grains of a polycrystal is investigated. Subsequent numerical microstructural modeling is outlined. The resulting energetically most favorable transformation sequence yields the transformation kinetics

Special cases of martensite compatibility: A near single-variant habit-plane and the martensite of nanocrystalline NiTi

Lattice parameters measured near the high temperature (~1000°C) bcc α to hcp β transformation in an intermetallic Mo-containing γ-TiAl based alloy indicate a middle valued eigenvalue of the corresponding deformation gradient near 1. Habit-planes calculated under the assumption of a simple slip as lattice invariant shear, agree with experimentally determined orientations of the lens like plates recorded via electron backscattering. By contrast, twinning as invariant lattice shear has been investigated in nanocrystalline NiTi. Here the grain size causes the formation mechanism of the martensite to change from a “herring-bone” morphology faciliting a habit-plane between two twinned laminates and the austenite to a single laminate, which in the nonlinear theory formally cannot form a habit-plane with the austenite. Since this might cause high accommodation strains, the effectiveness of stress accommodation of martensite formed in neighboring grains of a polycrystal is investigated. Subsequent numerical microstructural modeling is outlined. The resulting energetically most favorable transformation sequence yields the transformation kinetics

Experimental and theoretical evidence of displacive martensite in an intermetallic Mo-containing γ\gamma-TiAl based alloy

In this study the martensitic transformation behavior of a Mo-bearing γ-TiAl based alloy was investigated. Therefore, a homogenization treatment within the single β-phase field region followed by water quenching has been carried out, whereby the majority of the disordered β-phase transforms into hexagonal α$_2$′-martensite during cooling. Since the β to α transformation in the intermetallic β-solidifying Ti–44Al–3Mo–0.1B alloy (at%) occurs at very high temperatures causing enhanced diffusional processes, a very locally diffusion-controlled transformation together with a displacive, hence purely martensitic transformation take place. This work investigates the displacive martensite formation in the high-temperature regime using state-of-the-art experimental methods as well as modelling concepts from the phenomenological theory of martensite crystallography. The high temperature at which the transformation takes place suggests the preference of plastic slip over twinning. This fact has also been verified by transmission electron microscopy, as no twinning has been observed after generation of single martensite variants forming an invariant interface plane with the initial β-lattice. Such invariant interfaces are formally possible according to the phenomenological theory of martensite crystallography, if the Bain strains of the martensite variants are superimposed by additional simple shear

Deformation-induced phase transformation in a Co-Cr-W-Mo alloy studied by high-energy X-ray diffraction during in-situ compression tests

ickel-free Co-Cr-W-Mo alloys exhibit a very low or even negative stacking fault energy, and therefore a pronounced tendency towards a deformation-induced phase transformation of the metastable face-centered cubic (fcc) γ-phase to the hexagonal close-packed (hcp) low-temperature ε-phase. In order to analyze the phase transformation in-situ and to correlate it to an external strain, compression tests between 30 °C and 400 °C were performed in a deformation dilatometer simultaneously to high-energy X-ray diffraction. Hence, the elastic strains of the fcc unit cell during compression, the external loads for the onset of the phase transformation and the temperature-dependency could be determined. In the parent fcc γ-phase, the evolution of an $$ fiber texture as well as texture inheritance effects and a distinct variant selection could be observed. Further, for the investigated alloy composition it is demonstrated that the continuum concepts of i) a structural stretch tensor and ii) an invariant plane strain perfectly agree with the widely-accepted nucleation theory of ε-martensite formation in Co-Cr alloys via Shockley partial dislocations on every second {$111$}$_\gamma$ plane. Both, the observed transformation texture as well as crystallographic transformation strains reveal the importance of shear stresses in this system