CE08 - Matériaux métalliques et inorganiques et procédés associés

Controlled Computation of Point-Defect Characteristics in High entropy Alloys – CoCoA

CoCoA: Controlled Computation of Point Defect Characteristics in High Entropy Alloys

This project aims at obtaining an improved understanding of point defect (PDs) physics in High Entropy Alloys (HEAs), and at providing methods to precisely characterize their intrinsic properties at the atomic scale. These quantities are then used to inform meso-scale models (of e.g. mechanical properties and diffusion), so as to predict HEAs behavior and guide alloy design.

Chemical complexity and Point Defects

Due to their high number of components at high concentration and to their disordered behavior, HEAs are a challenge for numerical simulations. In particular, point defect properties in these materials are no longer single values but correspond to statistical distributions. Ideally, ab initio calculations should be used for their accurate determinations. <br /><br />This raises convergence problems since this type of calculation is limited to a few hundred atoms: the representativity of the disorder must be ensured while correctly treating the long-range elastic effects. Corrective schemes exist for point defects in pure materials, but a similar approach is needed for materials having finite concentration of chemical species. <br /><br />Furthermore, the precision with which a point defect property distribution must be computed is dictated by its influence on the mesoscopic property modeled next. In other words, models of increasing complexity will require better and better characterized distributions as input data, if they are sensitive parameters of said models at all. <br /><br />The objective of this project is therefore to address these issues, focusing on the properties of point defects that are related to plasticity and diffusion.

In order to achieve these objectives, the approach used:

(i) considers arbitrary compositions - i.e., both dilute and finite concentration materials - on a set of model binary, ternary, etc. alloys of simple crystallographic structure. In particular, the bcc Ti-Zr-Nb and fcc Cu-Ni/Fe-Ni-Cr systems are studied. The point defects considered range from the smallest defects (vacancies, solutes, self-interstitials), to extended defects (dislocation loops, stacking fault tetrahedra, etc.).

(ii) is based on the generation of an atomic scale database on the energetics and elastic dipoles of point defects. Semi-empirical potentials (EAM,..) allow exhaustive calculations, because of their low computational cost. Ab initio calculations, that are more expensive, are used in a more restricted way, and on a real system having very good mechanical properties (Ti-Zr-Nb).

(iii) combines modeling within elastic theory of point defects to treat long-range effects with probabilistic approaches to quantify the uncertainty associated with the representativity of the chemical disorder. The databases generated via the atomistic calculations are used to validate the method and to demonstrate its usefulness on a «real« case.

4) uses and/or develops semi-analytical models of material properties of increasing complexity, to analyze sensitivity to PDs' feature distributions. Yield strength and diffusion are the properties primarily targeted.

(i) A comprehensive EAM potential database was generated for the vacancy and self-interstitial formation energies in cfc model alloys for the Cu-Ni system. The results show a complex convergence with system size. The elastic effects are comparable to those observed in pure materials ; and taking into account the chemical disorder requires a large number of random configurations to reach a significant accuracy, especially for elastic dipoles. In particular, it is shown that the use of unique quasi-random structures can be risky, and that it is accompanied by a loss of information on the uncertainty quantification. Furthermore, developments in elastic theory for point defects in concentrated media have been performed, allowing the generalization of the existing corrective scheme of convergence with the box size for defects in pure materials. Good performances are shown.

(ii) An ab initio study on the cc Ti-Zr-Nb system in the dilute limit has revealed displacive cc?? phase transformations induced by substitutional defects (vacancies and solutes), when starting from metastable Ti and Zr cc structures. The signature of this transformation is characterized at the structural and local electron density levels. This result is surprising, since these single defects do not break the permutation symmetry of the basis set axes. It is explained by an activation of soft phonon modes in eight equivalent directions, generating different ? phase variants. This fact is in agreement with several experimental observations, especially in Zr-Nb and Ti-Nb alloys, where fine ?-phase particles - with somewhat slowed growth - are observed.

(iii) An analytical solid solution strengthening model has been generalized to the anisotropic elastic case, and compared to the isotropic elastic case for a series of model alloys [1]. This will allow to test more accurately the influence of the distributions of the properties of substitutional solutes in HEAs.

(iv) The stability of interstitial and vacancy-type of extended irradiation defects (dislocation loops) has been studied in the dilute limit in a-zirconium, by atomic simulations and continuum modeling. The set of Burgers vectors/stacking sequences considered in the prismatic and basal planes are consistent with experimental observations. Formation energies and structures were determined with two EAM potentials for Zr, for hexagonal and circular loops of increasing sizes. Molecular dynamics annealing of these loops validated the postulated potential energy landscape. Finally, a continuum modeli hybridly calibrated on ab initio calculations and EAM results indicates that the coexistence of vacancy and interstitial < a> loops is supported by stability arguments. We also establish the limitations
of such an approach for quantitative predictions.

Outline for the second part of the project:

• ab initio calculations of the gap properties in Ti-Zr-Nb cc, for finite concentrations. The links between stability, metastability, defect instability and phase transitions will be explored depending on the alloy composition,

• Empirical potential calculations of point and extended defect property distributions on equiatomic ternary and quaternary model alloys. This work will allow to add the variable «number of components« to the difficulty related to disorder within the study,

• Sensitivity analysis to the distribution of PD characteristics, performed on diffusion properties and on solid solution strengthening.

[1] S. Nag, C. Varvenne and W. A. Curtin, Solute-strengthening in elastically anisotropic fcc alloys, Modelling Simul. Mater. Sci. Eng. 28, 025007 (2020)
[2]. C. Dai, C. Varvenne et al., Stability of vacancy and interstitial dislocation loops in a-zirconium: atomistic calculations and continuum modelling , J. Nucl. Mater. 554, 153059 (2021)

High Entropy Alloys (HEAs) are a newly emerged class of metallic alloys, having multi-principal elements and crystallizing as single phase solid solutions, with very simple crystallographic structures. Fabricated HEAs cover a wide range of elements from the periodic table, including transition metals, noble metals, lightweight metals and refractory elements. They exhibit impressive mechanical properties, slow diffusion kinetics – thus impacting subsequent phase transformations – exceptional damage tolerance and resistance to corrosion: this makes them quite attractive for industrial applications.
These materials, having a high number of components and high concentrations, are intrinsically complex, with important disorder (chemical disorder, lattice distortions, eventually magnetic disorder). Therefore, they are extremely difficult to tackle from the theoretical and simulation perspectives, which mainly deal with dilute materials.
Point defects are of prior importance in materials properties: their characteristics must then be computed accurately, preferentially by ab initio methods. However, due to the different possible chemical and structural environments, these characteristics are statistically distributed. This is problematic for ab initio calculations that are limited to a few hundred atoms: the representativity of disorder and the sampling of investigated quantities is highly questionable. Furthermore, the long-range elastic fields of point-defects cause additional finite size effects.
The objective of this project is therefore to establish a well-defined and controlled approach for the ab initio computation of point-defect characteristics in HEAs. This includes the understanding of what dictates the morphology of the distributions of point-defect characterictics, and the modeling, correction and error quantification associated with simulation finite size effects in HEAs. This will be finally coordinated to the understanding of the link between the morphology of the point-defect characteristics distributions, and two main materials properties: the solid solution strengthening effect, and diffusion properties.

Project coordination

Céline VARVENNE (Centre National de la Recherche Scientifique DR12 Centre Indisciplinaire de Nanoscience de Marseille)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.


CINaM Centre National de la Recherche Scientifique DR12 Centre Indisciplinaire de Nanoscience de Marseille

Help of the ANR 222,912 euros
Beginning and duration of the scientific project: - 48 Months

Useful links

Explorez notre base de projets financés



ANR makes available its datasets on funded projects, click here to find more.

Sign up for the latest news:
Subscribe to our newsletter