Diffusion processes in solids are relevant for the kinetics of many microstructural changes that occur during preparation, processing, and heat treatment of materials. Typical examples are nucleation of new phases, diffusive phase transformations, precipitation of a second phase, recrystallisation, high-temperature creep, and thermal oxidation. To reach a deep understanding of diffusion in solids, one needs information on the position of atoms and how they move in solids. The atomic mechanisms of diffusion in crystalline solids are closely connected with defects. Point defects such as vacancies or interstitials are the simplest defects and often mediate diffusion in crystals. Ab initio methods as DFT (Density Functional Theory) can provide fundamental information, such as the stable positions of atoms in a crystal lattice and their jumping rates between two neighour sites. However, it is not trivial to obtain diffusion coefficients from these fundamental properties because, in complex solid crystals, there are usually various point defects (vacancy and interstitial positions) and hence several diffusion paths are possible for the diffusing atom. Analytical solutions of multi-state diffusion problems are generally complex. A good alternative is to resource to Kinetic Monte Carlo (KMC), which is a particular Monte Carlo method used for processes with known rates such as atom migration. It consists of mapping N possible events that can occur from a given state. Each event is defined by jump frequency, displacement and cumulative function of the jump frequency: all these input quantites can be obtained from the DFT calculations.
The main aim of this project is to develop a Kinetic Monte Carlo code for studying diffusion of atoms in crystals. The code will receive as input data the results of DFT calculations, which will be performed with the VASP code. The first applications will address the diffusion of interstitial atoms (B, O, N, C) in Ti-Al alloys. The code will be validated by comparison with the analytical solution of the simplest crystal lattices (as the tetragonal TiAl) and then it will be applied for the study of diffusion in more complex geometries (as the hexagonal Ti3Al).
The control of the composition and morphology of materials at the nanoscale allowed to disclose novel structural, electronic and chemical properties which are fundamental for many recent technological advances. Amongst nanostructures, 2D materials are a class formed of materials which cryistallise as atomically-thin layers. Since the discovery of graphene in the early 2000s, the family of 2D materials grew larger, with the emergence of new systems alike the hexagonal boron nitride (hBN) or the black phosphorus (BP).
Because of their extreme thinness, 2D materials often display electronic properties sizeably different from those of their bulk equivalent. Moreover, their characteristics are strongly influenced by the interaction with the near surroundings: for instance by modifications of the substrate, or changes of their thickness. Van der Waals heterostructures are based on this principle. They are built by stacking layers of different 2D materials on top of each other, so that several properties are combined in the same system and tuned in a controlled fashion. This allows to engineer specific properties aimed for technological development or fundamental research.
In this context, we will consider heterostructures based on hBN and/or BP layers. In order to study these systems from a theoretical perspective, we will elaborate a mixed approach combining analytical and numerical developments in the tight-binding formalism, with ab-initio simulations. The latter will be done on simple reference systems, with the intent to establish a quantitative basis for the parametrization of tight-binding models. This will make possible the investigation of extended systems like realistic heterostructures. More precisely, the objectif will be that of studying the influence of the environment (substrate, stacking …) on the electronic and optical properties of van der Waals heterostructures based on hBN and BP.
Another specificity of this work will consist on coupling the theoretical study with diverse experimental techniques, namely thanks to our rich collaboration network.
Georges Saada was born on August 10, 1932 in Sfax, Tunisia. He left Tunisia at the age of seventeen, after high school and obtaining his baccalaureate. In Paris, he prepared the Grandes Ecoles at the Louis-le-Grand and Buffon high schools. He joined the École Polytechnique in 1952 and then prepared a thesis in metal physics. He also graduated at the École Nationale Supérieure des Télécommunications.
After military service, his career began in the army, which he left in 1960. Indeed his skills led him to scientific research. After five years at the Institut de Recherche de la Sidérurgie, as a research engineer, he chose to focus his career on university teaching. First a lecturer at the University of Lille, he participated in 1969 in the creation of the University of Paris XIII Villetaneuse where he became a professor in 1971. From 1973 to 1981, he was at the head of the Laboratoire des Propriétés Mécaniques et Thermodynamiques des Matériaux.
In 1981, he was appointed Head of Mission for Higher Education at the Ministry of National Education, Alain Savary.
He returned to the University of Paris XIII and joined the Laboratoire d’Etude des Microstructures in 1990.
Georges Saada played a pioneering role in the field of plasticity of materials. His work has had a major impact on the development of this discipline, with seminal contributions to the understanding of the physical mechanisms that cause deformation of metal alloys. His work has been recognized by the award of the Grande Médaille de la Société Française de Métallurgie et de Matériaux in 2008.
Dislocation Dynamics (DD) simulations are used to investigate the Hall-Petch (HP) effect and back stresses induced by grain boundaries (GB) in polycrystalline materials.
The HP effect is successfully
reproduced with DD simulations in simple periodic polycrystalline aggregates
composed of 1 or 4 grains. In addition, the influence of grain shape was
explored by simulating grains with different aspect ratios. A generalized HP
law is proposed to quantify the influence of the grain morphology by defining
an effective grain size. The average
value of the HP constant K calculated
with different crystal orientations at low strain is close to the experimental
The dislocations stored during
deformation are mainly located at GB and can be dealt with as a surface
distribution of Geometrically Necessary Dislocations (GNDs). We used DD
simulations to compute the back stresses induced by finite dislocation walls of
different height, width, density and character. In all cases, back stresses are
found proportional to the surface density and their spatial variations can be
captured using a set of simple empirical equations. The back stress calculation
inside grains is achieved by adding the contributions of GNDs accumulated at
each GB facet.
These back stresses are found to increase linearly with plastic strain and are independent of the grain size. The observed size effect in DD simulations is attributed to the threshold of plastic deformation, controlled by two competing mechanisms: the activation of dislocation sources and forest strengthening. Due to strain localization in coarse-grained materials, the pile-up model is used to predict the critical stress. By superposing such property to the analysis we made from DD simulations in the case of homogeneous deformation, the HP effect is justified for a wide range of grain sizes.