Elsevier

Journal of Nuclear Materials

Volume 484, February 2017, Pages 42-50
Journal of Nuclear Materials

Interatomic potential to study the formation of NiCr clusters in high Cr ferritic steels

https://doi.org/10.1016/j.jnucmat.2016.11.017Get rights and content

Abstract

Under irradiation NiSiPCr clusters are formed in high-Cr ferritic martensitic steels as well as in FeCr model alloys. In the literature little is known about the origin and contribution to the hardening of these clusters. In this work we performed density functional theory (DFT) calculations to study the stability of small substitutional NiCr-vacancy clusters and interstitial configurations in bcc Fe. Based on DFT data and experimental considerations a ternary potential for the ferritic FeNiCr system was developed. The potential was applied to study the thermodynamic stability of NiCr clusters by means of Metropolis Monte Carlo (MMC) simulations. The results of our simulations show that Cr and Ni precipitate as separate fractions and suggest only a limited synergetic effect between Ni and Cr. Therefore our results suggest that the NiCrSiP clusters observed in experiments must be the result of other mechanisms than the synergy of Cr and Ni at thermal equilibrium.

Introduction

High-chromium ferritic-martensitic (FM) steels (∼9–12 at% Cr) are the materials of choice for high temperature applications in aggressive environments (e.g. corrosion and/or irradiation). As a consequence, they are the commonly proposed structural materials for advanced nuclear reactors [1], [2], [3]. This choice is supported by their superior thermal, corrosion and radiation resistance compared to austenitic steels [4].

Irradiation campaigns on FeCr alloys – model alloy for FM steels – have shown that the hardening due to neutron irradiation can be attributed to a microstructure containing dislocation loops, α′ precipitates and NiCrSiP clusters [5], [6], [7]. While a lot of both experimental and theoretical research has focused on α′ precipitation [8], [9], [10], [11], [12], [13], [14] and dislocation loops in FeCr alloys [15], [16], [17], not so much is known about NiCrSiP clusters. The latter are observed under both ion and neutron irradiation using tomographic atom probe (TAP) [7], [18], [19], [20]. They are suggested to be irradiation induced and might be associated to small dislocation loops that are below the detection limit of transmission electron microscopy (TEM) [18], [19].

In support of this effort, both small and large-scale atomistic simulations are desirable to clarify the formation mechanisms and role of NiCrSiP clusters in the hardening of FeCr alloys and FM steels. For point defects or small defect configurations, density functional theory (DFT) is the ideal tool. For large-scale atomistic simulations, however, a suitable interatomic potential is necessary. As a first step towards the chemical complexity of high-Cr FM steels, we consider the ternary bcc FeNiCr alloy. For this phase, neither DFT data nor an interatomic potential are available in the literature.

In this work we employ DFT calculations to study the stability of small interstitial solute-containing configurations and small NiCr-vacancy (v) clusters. These results, together with experimental considerations, are then transferred into an interatomic potential that allows large-scale atomistic simulations. As a first application of the potential we investigate the thermal stability of NiCr clusters using Metropolis Monte Carlo (MMC) simulations.

Section snippets

Density functional theory

The DFT calculations were performed using the Vienna ab initio simulation package (VASP) [21], [22]. VASP is a plane-wave DFT code that implements the Projector Augmented Wave (PAW) method [23], [24]. Standard PAW potentials supplied with VASP were used, with exchange and correlation functional described by the Perdew-Wang parameterization [25] of the Generalised Gradient Approximation (GGA), with the Vosko-Wilk-Nusair interpolation correction [26]. The calculations were spin-polarized and Fe,

DFT data set and model validation

In this section the DFT data set for small substitutional NiCr-v clusters and interstitial configurations in bcc Fe is presented and the potential is validated against DFT and experimental data. For completeness the properties related to the L12 FeNi3 and Ni2Cr intermetallics are provided in Appendix B.

In Fig. 1 a comparison of the binding energy of solute-solute and solute-v pairs calculated by both DFT and the potential is presented. Although only the binding energy for Ni-v, Ni-Ni and Cr-Ni

Conclusions

We have performed density functional theory (DFT) calculations to study the stability of small substitutional NiCr-vacancy (v) clusters and interstitial configurations in bcc Fe. Based on DFT data and experimental considerations a ternary potential for the ferritic FeNiCr system was developed. The potential was applied to study the thermodynamic stability of NiCr clusters by means of MMC simulations.

The DFT data show that pure vacancy clusters are the most stable clusters here investigated and

Acknowledgements

The research leading to these results is partly funded by the European Atomic Energy Community's (Euratom) Seventh Framework Programme FP7/2007–2013 under grant agreement No. 604862 (MatISSE project) and in the framework of the EERA (European Energy Research Alliance) Joint Programme on Nuclear Materials (JPNM).

References (81)

  • L.K. Mansur et al.

    J. Nucl. Mater

    (2004)
  • C. Fazio et al.

    Nucl. Eng. Des.

    (2011)
  • Y. Dai et al.

    J. Nucl. Mater

    (2006)
  • M. Matijasevic et al.

    J. Nucl. Mater

    (2008)
  • F. Bergner et al.

    Scr. Mater

    (2009)
  • V. Kuksenko et al.

    J. Nucl. Mater

    (2011)
  • F. Bley

    Acta metall. Mater

    (1992)
  • S. Novy et al.

    J. Nucl. Mater

    (2009)
  • D.A. Terentyev et al.

    Acta Mater

    (2008)
  • C. Pareige et al.

    Acta Mater

    (2011)
  • F. Bergner et al.

    J. Nucl. Mater

    (2013)
  • E.E. Zhurkin et al.

    J. Nucl. Mater

    (2011)
  • D. Terentyev et al.

    Acta Mater

    (2013)
  • V. Kuksenko et al.

    J. Nucl. Mater

    (2012)
  • V. Kuksenko et al.

    J. Nucl. Mater

    (2013)
  • C. Pareige et al.

    J. Nucl. Mater

    (2015)
  • Y. Mishin

    Acta Mater

    (2004)
  • M. Grujicic et al.

    CALPHAD

    (1993)
  • M. Grujicic et al.

    Mat. Sci. Eng.

    (1995)
  • M. Grujicic et al.

    Mat. Sci. Eng.

    (1997)
  • Y. Mishin et al.

    Acta Mater

    (2005)
  • E. del Rio et al.

    J. Nucl. Mater

    (2011)
  • S.M. Eich et al.

    Comp. Mat. Sci.

    (2015)
  • P. Olsson et al.

    J. Nucl. Mater

    (2003)
  • D. Terentyev et al.

    J. Nucl. Mater

    (2011)
  • G. Bonny et al.

    J. Nucl. Mater

    (2011)
  • E.E. Zhurkin et al.

    J. Nucl. Mater

    (2011)
  • N. Castin et al.

    J. Nucl. Mater

    (2011)
  • T.P.C. Klaver et al.

    Comp. Mat. Sci.

    (2016)
  • G. Bonny et al.

    J. Nucl. Mater

    (2013)
  • L. Malerba et al.

    J. Nucl. Mater

    (2010)
  • G. Bonny et al.

    Comp. Mat. Sci.

    (2011)
  • D. Nguyen-Manh et al.

    Comp. Rendus Phys.

    (2008)
  • G. Bonny et al.

    Comp. Mat. Sci.

    (2008)
  • A.T. Al-Motasem et al.

    J. Nucl. Mater

    (2011)
  • P. Franke et al.

    Calphad

    (2011)
  • G. Bonny et al.

    J. Nucl. Mater

    (2014)
  • C. Fazio et al.

    J. Nucl. Mater

    (2009)
  • G. Bonny et al.

    Phys. Rev.

    (2009)
  • D. Terentyev et al.

    Phys. Rev.

    (2010)
  • Cited by (21)

    • On the formation and structure of Mn-Ni-Si Γ<inf>2</inf> precipitates in steels

      2020, Journal of Nuclear Materials
      Citation Excerpt :

      Cr is ubiquitous to stainless steels and is being considered as an addition to future advanced nuclear reactor structural materials as is has been found to lead to much smaller DBTT shifts [61,62]. Significant work has been performed on studying the interaction of Cr with other minor alloying elements, from which it has been found Ni-Cr interactions are repulsive and Si-Cr and Mn-Cr interactions are only marginally attractive (< 0.05 eV) [62,63]. In this study, Cr will not favourably replace any atomic site in any of the Γ2 structures, therefore is not expected to stabilise the Γ2-phase, this is consistent with the observed lack of Cr in Mn-Ni-Si clusters [9,44,64].

    • The effect on the mechanical response of Cr and Ni segregation on dislocation lines in bcc Fe

      2020, Journal of Nuclear Materials
      Citation Excerpt :

      This indicates that there is also some influence of Cr on Ni segregation, although probably weaker, in the presence of a dislocation line. In contrast, in a system without dislocation, it has been shown that, if Ni is present, it has no influence on the Cr solubility [34]. Compared to the equilibrium binary phase diagrams corresponding to the potential, we conclude that the presence of the dislocation raises the solubility curve for Ni, inducing heterogeneous precipitation.

    • Large Scale Integrated Materials Modeling Programs

      2020, Comprehensive Nuclear Materials: Second Edition
    • Interatomic Potential Development

      2020, Comprehensive Nuclear Materials: Second Edition
    View all citing articles on Scopus
    View full text