Atomic scale modeling of the plasticity of body-centered cubic transition metals

Baptiste Bienvenu, Chu Chun Fu and Emmanuel Clouet

Université Paris-Saclay, CEA, Service de Recherches de Métallurgie Physique, 91191 Gif-sur-Yvette

At low temperature, plasticity of body-centered cubic (BCC) transition metals is governed by the glide in compact {110} planes of screw dislocations with a ½<111> Burgers vector, experiencing a high friction with the crystal lattice. The aim of this work is to build laws to predict the plastic flow stress based on atomic scale modeling of the core properties and mobility of these dislocations (using ab initio calculations and molecular dynamics), allowing to link them to macroscopic mechanical properties (yield stress, slip system activity).
In this context, a special care is given to the case of chromium (Cr), the only BCC transition metal having a structure close to antiferromagnetism, a spin-density wave, below ambient temperature. To qualify the impact of magnetism on the plasticity of Cr, ab initio calculations at zero temperature were coupled to Monte Carlo simulations at finite temperature. This allowed to conclude that magnetism has only a marginal influence, except at very low temperature where the ½<111> Burgers vector of these dislocations generates magnetic faults given that it does not respect the magnetic order of Cr.
In the following, a systematic study across all seven BCC transition metals (vanadium, niobium, tantalum, chromium, molybdenum, tungsten and iron) helped develop a yield criterion reproducing the experimental features of the so-called “non-Schmid” effects, characteristic of these metals at low temperature. However, some effects cannot be captured by this criterion, accounting for the motion of isolated dislocations only. This is for instance the case of anomalous slip, observed in all BCC transition metals except iron, and characterized by slip activity of ½<111> dislocations in low-stressed {110} planes. Through in situ observations in a transmission electron microscope performed by Daniel Caillard (CEMES-CNRS, Toulouse), coupled with atomistic simulations, a new mechanism explaining this phenomenon in all BCC metals has been evidenced, based on the high mobility of multi-junctions. Finally, the mobility of dislocations with a <100> Burgers vector, most often observed as junctions between ½<111> dislocations but rarely considered as possible slip systems, is studied using atomistic simulations. It was evidenced that, even if the mobility of <100> screw dislocations is competitive with the conventional ½<111> in {110} planes, <100> dislocations are locked at low temperature along a mixed orientation requiring a very high stress to start moving, thus explaining their low slip activity.

Data-driven models of atomic simulations in discrete and continuous state spaces

Thomas Swinburne
CINaM, Marseille

Building models for the plasticity, thermodynamics and kinetics of metals is challenging as subtle aspects of atomic cohesion must be faithfully reproduced, and predictions often require averaging over large, complex configuration ensembles. I will discuss how the energy landscapes of atomic systems can be rapidly explored at scale and “coarse-grained” when the dynamics are thermally activated thus thus scale separated[1,2] and how data-driven techniques, typically used to regress energies for modern cohesive models, can be used to capture a much wider range of properties such as defect entropics[3] or dislocation properties. When the dynamics do not have a clear timescale separation, coarse graining is much more challenging. I will discuss how a data-driven approach can provide a solution, producing efficient surrogate models which can predict the evolution of nanoparticle ensembles and the yielding of complex microstructures, offering new perspectives for multiscale modelling approaches[4].

[1]  TD Swinburne and D Perez, NPJ Comp. Mat 2020, MSMSE 2022
[2]  TD Swinburne and DJ Wales JCTC 2020, 2022
[3]  C Lapointe et al. PRMat 2020
[4]  TD Swinburne, In Prep.

Dislocation-free plasticity in small-grained metals

Marc Legros, Romain Gauthier, Armin Rajabzadeh, Frédéric Mompiou et Nicolas Combe

CEMES-CNRS, Toulouse

Most crystalline materials around us (metals, alloys, ceramics) are polycrystalline, made of “grains”, separated by “grain boundaries”. These boundaries between domains of different orientation determine certain physical properties and especially their mechanical behavior. For example, we can make a ceramic malleable or on the contrary harden a metal by reducing the size of its crystallites through the famous Hall-Petch law [1,2], established in a phenomenological way for steels 70 years ago. Physically, this relationship can be explained by the obstacle effect that grain boundaries have on dislocations, which are the main vectors of plastic deformation. When grains become nanometric, the plasticity threshold saturates or decreases, which is generally attributed to plastic processes carried by the grain boundaries themselves, such as rotation, intergranular slip and/or migration/shear coupling. These mechanisms are mostly observed in small-grained metals, but rarely quantified experimentally, except in experiments on bicrystals [3]. The Cahn & Mishin (C&M) model [4,5], which popularized the migration-shear coupling, predicts that the coupling factor increases with the disorientation of the joint. In other words, when a joint migrates, it produces more shear the higher its disorientation. The rare measurements made on polycrystals, experimentally more complex to realize, do not seem to attest this trend. And metallic nanocrystals are not known for their deformability.

To be sure, we have been studying the deformation mechanisms related to grain boundary migration for the last ten years, both by in situ transmission electron microscopy (TEM), using atomic simulations by molecular dynamics and more recently by atomic force microscopy (AFM), all coupled with crystal orientation mapping techniques. It is thus possible to follow the motion of the identified boundaries and even to statistically quantify the shear produced in ultra-fine-grained aluminum. In the absence of dislocation, this migration-shear coupling is the main driver of plastic deformation [6]. However, this coupling is much weaker than that predicted by the C&M model, which explains the low yield of grain boundary plasticity mechanisms, and thus the low ductility of metallic nanocrystals.

[1]   EO Hall. The deformation and ageing of mild steel: III Discussion of results. Proceedings of the Physical Society Section B 1951;64:747–53.
[2]   NJ Petch. The cleavage strength of polycrystals: Journal of the Iron and Steel Institute, v. 174. 1953
[3]   T Gorkaya, DA Molodov, G Gottstein. Stress-driven migration of symmetrical 〈100〉 tilt grain boundaries in Al bicrystals. Acta Materialia 2009;57:5396–405.
[4]   JW Cahn, JE Taylor. A unified approach to motion of grain boundaries, relative tangential translation along grain boundaries, and grain rotation. Acta Materialia 2004;52:4887–98.
[5]   JW Cahn, Y Mishin, A Suzuki. Coupling grain boundary motion to shear deformation. Acta Materialia 2006;54:4953–75.
[6]   R Gautier, A Rajabzadeh, M Larranaga, N Combe, F Mompiou, M Legros. Shear-coupled migration of grain boundaries: the key missing link in the mechanical behavior of small-grained metals. Comptes Rendus Physique 2021;22:1–16.

Combining X-ray Tomography and Diffraction modalities to study in situ the mechanics of polycrystalline materials

Clément Ribart, Henry Proudhon

Centre des Matériaux, MINES Paristech, CNRS UMR 7633

Diffraction Contrast Tomography remains the fastest 3D grain mapping characterization method and allows further characterization of specific crystallographic locations. Coupled to in situ mechanical testing, something we have developed for a few years at CDM, it provides a unique way to probe deformation and fracture mechanisms of structural materials. Correlative experiments at higher resolution can now be performed to achieve “zoom-in” observation in selected grains. We will review several technique that can be used at the European synchrotron, such as X-ray topo-tomography, scanning 3DXRD or Dark Field X-ray Microscopy. Example to characterize plastic strain localization in metals will be presented. As the method becomes more and more automated, it allows both quantitative and statistical measurements in the bulk of the microstructure. Finally, coupling experiments with crystal plasticity finite element computations at the grain scale will be discussed as a key to unlock microstructure-deformation mechanisms.

Contact to attend the conference :

Thursday 31st Mars 2022 at 14h00

Contensou conference room, ONERA Châtillon

Impact of thermal strain hardening on the precipitation of hardening phases during SLM manufacture of an aluminium alloy

Frederico Orlacchio


Additive Manufacturing is arousing great interest in both academic and industrial communities, in particular with a view to reducing raw material waste and optimising manufactured components. During the internship carried out between the SIAM unit of DMAS/ONERA and the LEM (CNRS/ONERA), particular attention was paid to the impact of thermal hardening on the precipitation of intermetallic phases in the aluminum alloy Al-4Fe, manufactured by Laser Powder Bed Fusion (L-PBF). First, an experimental study at different scales was carried out in order to characterise the microstructure of the Al-4Fe material in its metallurgical state after fabrication. Various manufacturing conditions were studied. The grain microstructure as well as the precipitation of iron-rich phases were studied by different microscopy techniques (optical, SEM, TEM). Secondly, the evolution of the hardness and the modifications of the microstructure induced by various post-manufacturing heat treatments were characterised. The small disorientations inside the grains were measured by EBSD in order to obtain information on the strain hardening of the material during these treatments. Finally, the various contributions necessary for the development of a model of the hardness of these alloys were discussed.

Tuesday 28th September 2021 at 9h30

videoconference at the followink link:

Investigation of the solid-liquid transition of Ag-Pt nanoparticles

Djahid Oucheriah


At the nanoscale, nanomaterials possess unique properties that differ strongly from those of the bulk material. In the case of AgPt nanoparticles, we aimed to study the solid-liquid transition of nanoparticles of different sizes and compositions. For this purpose, we performed atomic scale simulations using a semi-empirical potential integrated in a Monte Carlo code to relax the structures. In doing so, we observed that the melting temperature decreases with the size of the nanoparticles (pure systems and alloys). However, our detailed analysis shows that the melting of the nanoparticle systematically passes through an intermediate stage with a crystalline core (pure Pt or AgPt depending on the composition) and a layer of liquid Ag.

Thursday 29th July 2021 at 11h00

videoconference at the following link:

First-principle studies of light atom diffusion in γ-TiAl and experimental investigation on MAX phase oxidation

Dr.  Enrica Epifano

CIRIMAT, UMR 5085, toulouse France


In this talk, E. Epifano will present the results of her postdoctoral research conducted at the ONERA. The presentation will comprise two parts. In the first part, solubility and diffusion of light atoms (B, C, N, O) in the γ-TiAl intermetallic phase are investigated by first-principle calculations. The accommodation of the light atoms in the various interstitial positions is studied by density functional theory. Barrier energies for their diffusion among the different interstitial sites are computed using the Nudged Elastic Band (NEB) method and atomic jumping rates are obtained from the Transitional State Theory. Diffusion coefficients are obtained from the solution of the transport equation in the infinite time limit, using the analytical Multi-State Diffusion method.

In the second part, experimental studies of the oxidation resistance of MAX phases are shown. The MAX phases are a new class of materials that have an extraordinary combination of both metallic and ceramic features. Some of the MAXes are alumin-forming and they hence exhibit excellent oxidation resistance. The results herein shown concern a study on the quaternary (Tix,Ga1-x)3AlC2 phase, realized in collaboration with the Drexel University of Philadelphia.

Friday 25 June 2021 14h00

videoconference at the following link:

Contribution of the Electron Channeling Contrast Imaging in polycrystal plasticity

Dr. Antoine GUITTON1,2

1Université de Lorraine – CNRS – Arts et Métiers – LEM3, Metz, France
2LabEx Damas – Université de Lorraine, Metz, France


The full potential of ECCI for multiscale comparisons between experiments and simulations.

Although mechanics of materials is aged by more than one century, it still faces many conceptual challenges. One must relate two extreme scales: the sample scale (i.e. Macroscopic) and the scale of fundamental mech- anisms (i.e. Microscopic). In addition, statistics of observations are generally extremely low so that, on one hand the uncertainty is high and on the other hand the representativeness of mechanisms is very questionable.

The Transmission Electron Microscope (TEM) is one of the most well-known techniques for observing and characterizing dislocations in electron transparent thin foils (thickness of ≈ 100nm with a useful field of view of few μm) (1–4). Comprehensive dislocation studies at microscopic scale bring valuable information for extrapolating to the macroscopic mechanical response of materials and they can feed numerical advanced multiscale crystal plasticity models (4). However, fundamental questions on the representativeness of observed phenomenon must be raised, when extrapolating discussions to a millimeter-size specimen.

In this framework, we have successfully combined mechanical testing (nanoindentation and in-situ tensile tests) of bulk specimens with a dislocation-scale characterization technique: Accurate Electron Channeling Contrast Imaging (A-ECCI) (5). A-ECCI is a non-destructive procedure offering the ability to provide, inside a Scanning Electron Microscope (SEM), TEM-like diffraction contrast imaging of sub-surface defects (at a depth of about 100 nm) on centimetric bulk specimen with still unsurpassed resolutions (6).

First, physics of defect contrasts and experimental procedures will be presented (5; 7; 8). Second, the full potentiality of A-ECCI for following the evolution of deformation microstructures will be detailed (9–11). Finally, statistical comparisons between crystal plasticity models and experiences will be highlighted in the framework of a first step towards feature engineering (12–14).

Thursday 27 May 2021 14h00

videoconference at the following link:


[1]  G.P. Bei, A. Guitton, A. Joulain, V. Brunet, S. Dubois, L. Thilly, and C. Tromas. Pressure-enforced plasticity in MAX phases: from single grain to polycrystal investigation. Philosophical Magazine, 93(15):1784–1801, may 2013, doi: 10.1080/14786435.2012.755272, hal-hal-01501851.

[2]  A. Guitton, A. Joulain, L. Thilly, and C. Tromas. Dislocation analysis of Ti2AlN deformed at room temperature under confining pressure. Philosophical Magazine, 92(36):4536–4546, dec 2012, doi: 10.1080/14786435.2012.715250, hal-03041046.

[3]  A. Guitton, A. Joulain, L. Thilly, and C. Tromas. Evidence of dislocation cross-slip in MAX phase deformed at high temperature. Scientific Reports, 4(1):6358, may 2015, doi:, hal-01503720.

[4]  K. Gouriet, P. Carrez, P. Cordier, A. Guitton, A. Joulain, L. Thilly, and C. Tromas. Dislocation modelling in Ti2AlN MAX phase based on the Peierls–Nabarro model. Philosophical Magazine, 95(23):2539–2552, aug 2015, doi: 10.1080/14786435.2015.1066938, hal-01515323.

[5]  H. Kriaa, A. Guitton, and N. Maloufi. Fundamental and experimental aspects of diffraction for characterizing dislocations by electron channeling contrast imaging in scanning electron microscope. Scientific Reports, 7(1):9742, aug 2017, hal-02392256.

[6]  J. Guyon, H. Mansour, N. Gey, M.A. Crimp, S. Chalal, and N. Maloufi. Sub-micron resolution selected area electron channeling patterns. Ultramicroscopy, 149:34–44, feb 2015, doi: 10.1016/j.ultramic.2014.11.004, hal-01514962.

[7]  H. Kriaa, A. Guitton, and N. Maloufi. Modeling dislocation contrasts obtained by Accurate-Electron Channeling Contrast Imaging for characterizing deformation mechanisms in bulk materials. Materials, 12(10):1587, may 2019, doi: 10.3390/ma12101587, hal-02392249.

[8]  H. Kriaa, A. Guitton, and N. Maloufi. Modelling Electron Channeling Contrast intensity of stacking fault and twin boundary using crystal thickness effect. Materials, 14(7):1696, mar 2021, doi: 10.3390/ma14071696, hal-03118996.

[9]  A. Guitton, H. Kriaa, E. Bouzy, J. Guyon, and N. Maloufi. A dislocation-scale characterization of the evolution of deformation microstructures around nanoindentation imprints in a TiAl alloy. Materials, 11(2):305, feb 2018, doi: 10.3390/ma11020305, hal- 02392252.

[10]  M. Ben Haj Slama, N. Maloufi, J. Guyon, S. Bahi, L. Weiss, and A. Guitton. In situ macroscopic tensile testing in SEM and Electron Channeling Contrast Imaging: pencil glide evidenced in a bulk β-Ti21S polycrystal. Materials, 12(15):2479, aug 2019, doi: 10.3390/ma12152479, hal-02392248.

[11]  F. Habiyaremye, A. Guitton, F. Sch ̈afer, F. Scholz, M. Schneider, J. Frenzel, G. Laplanche, and N. Maloufi. Plasticity induced by nanoindentation in CrCoNi medium-entropy alloy studied by accurate electron channeling contrast imaging revealing dislocation-low angle grain boundary interactions. Accepted in Materials Science and Engineering: A, 2021, hal-03118990.

[12]  M. Ben Haj Slama, V. Taupin, N. Maloufi, K. Venkatraman, A.D. Rollett, R.A. Lebensohn, S. Berbenni, B. Beausir, and A. Guitton. Electron channeling contrast imaging characterization and crystal plasticity modelling of dislocation activity in Ti21S BCC material. Materialia, page 100996, mar, doi: 10.1016/j.mtla.2020.100996, hal-03094460.

[13]  K. Venkatraman, M. Ben Haj Slama, V. Taupin, N. Maloufi, and A. Guitton. Tuning critical resolved shear stress ratios for BCC- Titanium Ti21S via an automated data analysis approach. 2021, hal-03119000.

[14]  F. Habiyaremye, A. Guitton, X. Lei, T. Richeton, S. Berbenni, G. Laplanche, and N. Maloufi. Influence of the local dislocation density and configuration on the first pop-in load during instrumented nanoindentation. 2021.

Characterisation of shear bands and plasticity in model glasses at the atomic scale

First synthesised in the 60’s, the metallic glasses are a very promising class of material thanks to their very high yield strength. Yet, these materials are also very brittle due to the formation of persistent shear bands which concentrate plastic deformation.

In this thesis, we perform atomistic simulations with a simple two-dimensional binary Lennard-Jones model glass. To link plasticity and the material structure, we use a novel structural indicator, the local yield stress. 

Through this measure, the material average local yield stress is shown to increase as the degree of relaxation increases. We also find the existence of a unique post-yield shear threshold distribution, independent on the initial state of the material.

By the mean of an elementary model, the origin of the Bauschinger effect in amorphous solids (a plasticity-induced  asymmetry of the mechanical behaviour) is found to arise from the inversion of the low yield barriers population anisotropy during the unloading.

Then, by considering systems of different sizes and degrees of relaxation the persistence of plasticity, and thus the formation of shear-bands, is shown to mostly depend on the degree of relaxation of the system.

Finally, in well relaxed glasses, a correlation between the location of the shear band and the initial soft regions is shown. As further loading is applied on the material, a diffusive broadening of the shear band is observed.

Modeling of platinum-based nano-alloys: Co-Pt, emblematic system of the order, and Pt-Ag, hybrid system between order and demixtion.

Due to the strong correlation between chemical order and physical properties, nanoalloys with a tendency to order are particularly interesting in the field of catalysis, magnetism, or optics. By reducing the size of the system, i.e. from a solid alloy to a nanoalloy, many questions arise: Is the chemical order preserved? What is the morphology of nanoparticles? What is the composition and chemical order on the surface? What is the evolution of properties with size? This presentation is devoted to the study of two systems, both similar and different in their behavior: Co-Pt, a system emblematic of the chemical order, and Pt-Ag, a hybrid system presenting both a chemical order and a tendency to demix, as well as a strong tendency to segregation. In order to answer these various questions, we adopt a semi-empirical approach through an N-body potential, allowing atomic relaxations, in the approximation of the second moment of state density (SMA), coupled with Monte Carlo simulations in different ensembles. The SMA potential is adjusted, in order to reproduce the volume and surface properties, on calculations derived from the theory of density functional theory (DFT) or on experimental data. In a first step, the volume phase diagram of the two systems is determined by the model and compared to the experiment. Then the low index surfaces (111), (100) and (110) are studied in order to verify the segregation inversion observed for the Co-Pt system, where Pt segregates weakly on the dense surfaces (111) and (100) but where we observe a pure Co plane on the surface (110). On the contrary, the Pt-Ag system shows strong Ag segregation on surfaces (111) and (100). In a second step, aggregates of truncated octahedral morphology of different sizes (ranging from 1000 to 10000 atoms) will be analyzed in terms of chemical composition on the different unequal sites (top, edge, facets (100) and (111) and core) and then compared to the reference systems (surfaces, volume) over the whole concentration range. For the Co-Pt system, we observe ordered structures similar to those of the volume for the core and similar to those of the surfaces for the facets. The impact of the two-dimensional phase (√3 × √3)R30◦ specific to the surface, is all the more important on the chemical order at the core as the nanoparticle is small. For the Pt-Ag system, we observe an important segregation of Ag at the surface, as well as a Pt enrichment at the subsurface, and the stabilization of the L11 ordered phase at the core. This structure can appear in a single variant or by adopting all possible variants, leading to an onion peel structure.


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