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