Internship for M2 students / PhD thesis :
"Modeling cavities in crystals at the nanoscale : atomic and meso scale simulations"
Keywords: crystalline defects, atomic scale simulations, meso-scale dislocation dynamics
Cavities are often at the origin of the damage of materials. Examples include : ductile fracture initiation in metals [1, 2], fatigue, damage related to hydrogen storage, dewetting of thin films, cavitation by electromigration in microelectronics... Modeling the first stages of cavity formation is key to the development of more resistant materials.
In this research project, we propose to study crack nucleation in metals by the formation of nanoscale cavities originating from the condensation of vacancies. It is a methodological challenge which combines the diffusion of vacancies, their aggregation on pre-existing defects in the crystal (grain boundaries and dislocations) and the local mechanical stresses which originate from specific dislocations arrangements which are not well known. Therefore, two length scales and long timescales have to be dealt with. The elementary vacancy jumps on the crystal lattice are at the atomic scale and over long time scales (several µs at the temperature considered), i.e. way beyond the capabilities of Molecular Dynamics. Dislocation structures, on the other hand, have micrometer dimensions. We plan to develop an interconnection between two different simulation codes dealing with each of these aspects.
We have recently developed an atomic scale Monte Carlo (MC) method [5] capable of sampling the vacancy clusters configurations, within the framework of classical statistical mechanics, in complex crystalline structures, such as grain boundaries and including the effect of mechanical stresses. Preliminary results reveal that the interaction of the vacancy with the other defects, prior to the application of stress is of primary importance. Therefore, the code needs to be extended to more realistic defect configurations, for example, a dislocation impinged on a grain boundary. The second aspect of the problem will be explored by producing and analyzing three dimensional dislocation arrangements by a meso scale discrete dislocation dynamics code [6]. The idea will be to transfer the local stress levels from the dislocation scale to the atomic scale within the MC code.
The project will start by an M2 internship and could be extended by a PhD thesis (funding already obtained). The PhD subject will be the continuation of the master, with the main goal of finding the specific arrangements of defects that could lead to the formation of cavities at stress levels compatible with experiments, but with some flexibility depending on the interests and skills of the candidate. The focus will be put either on the simulation methodology, or the subject could be opened to experiments.
The first route could explore another important aspect of simulations, with the use of Machine-Learning Interatomic Potentials (MLIPs) to assess the reliability of atomic interactions. Using those efficient and highly accurate tools [7, 8] in the Monte-Carlo simulations will require thoughtful implementation work, including the interfacing with the LAMMPS software to use existing and efficient (CPU/GPU) MLIP frameworks, finding clever algorithmic optimization tricks to speed up calculations and an extensive exploration of state-of-the-art MLIP solutions. Ideally, MC could be used for active learning using well chosen configurations for Density Functional Theory (DFT) calculations.
The second route will consist in performing in situ tensile tests within an electron microscope and nano scale deformation field measurements (at iLM). The idea will be to observe experimentally the location where the nano scale cavities appear, in particular their position with respect to intense slip bands (Fig. 1b). For this, brand new experimental facilities at our partner in Paris (https://pimm.artsetmetiers.fr/) will be used : a Plasma Focused Ion Beam coupled to high resolution Electron Back Scattered Diffraction.
The team will be composed of : Döme Tanguy (CNRS, Monte Carlo / experiments), Ronan Madec (CEA, Dislocation Dynamics), Dylan Bissuel (engineer U Claude Bernard Lyon1, Machine Learning) and Thomas Niehaus (professor U Claude Bernard Lyon 1, Density Functional Theory).
Technical skills: The candidate should have an appetite for code development (C/C++…), for production/analyses of large sets of numerical simulations (Linux) and for microscopic physics. Nevertheless, the initial programming skills can be limited (C and python) and will be extended during the project.
Location : Institut Lumière Matière (iLM), université Lyon 1 [
ilm.univ-lyon1.fr]
Contact:
dome.tanguy@univ-lyon1.fr
Bibliography:
[1] "Do voids nucleate at grain boundaries during ductile rupture?" P. Noell et al. acta mater. 137 103-114 (2017)
[2] “Void nucleation during ductile rupture of metals: A review” P. J. Noell et al. Prog. Mat. Sci. 135 101085 (2023)
[3] “Fatigue damage of ultrafine-grain copper in very-high cycle fatigue region” P. Lukáš et al. Mat. Sci. Eng. A 528 (2011) pp. 7036-7040
[4] "Slip band-grain boundary interactions in commercial-purity titanium" Y. Guo et al. acta mater. 76 1-12 (2014)
[5] “Sampling vacancy configurations with large relaxations using Smart Darting” D. Tanguy Phys. Rev. Mat. 8 033604 (2024)
[6] “On the role of cross-slip and collinear annihilation in dynamic recovery annihilation” R. Madec, B. Devincre and L. Kubin, Modelling Simul. Mater. Sci. Eng. 33 015010 (2025)
[7] "Machine-learning interatomic potentials for materials science" Y. Mishin Acta Mater 214 116980 (2021)
[8] "Machine Learning Force Fields" O. T. Unke et al. Chem Rev 121 10142–10186 (2021)
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