Elsevier

Journal of Nuclear Materials

Volume 408, Issue 2, 15 January 2011, Pages 161-170
Journal of Nuclear Materials

Segregation of Cr at tilt grain boundaries in Fe–Cr alloys: A Metropolis Monte Carlo study

https://doi.org/10.1016/j.jnucmat.2010.11.024Get rights and content

Abstract

In this work, the Metropolis Monte Carlo (MMC) method employing the isothermal–isobaric statistical ensemble is applied to investigate segregation at grain boundaries in bcc Fe–Cr alloys with varying Cr content from 5 to 14 at.%. Several different 〈1 1 0〉 tilt grain boundaries, namely: Σ19{3 3 1}, Σ9{2 2 1}, Σ3{1 1 1}, Σ3{1 1 2}, Σ11{1 1 3}, Σ9{1 1 4} with misorientation angle varying in the range 26–141° were considered. Systematic MMC simulations were performed employing a two band empirical many-body potential in the temperature range 300–900 K. It was found that the binding energy of substitutional Cr to the GB core is essentially determined by the structure of the GB interface and varies in the range 0.05–0.35 eV. At this, the binding energy increases with the GB excess volume. MMC simulations revealed that either a local atomic rearrangement or segregation of Cr at the considered GBs occurs depending on the combination of temperature, alloy composition and GB structure. Influence of temperature and GB structure on the local atomic rearrangement and precipitation of α′ particles is demonstrated.

Introduction

Segregation of alloying elements to grain boundaries in binary alloys or complex compounds may alter their structure and local chemical composition, which in turn changes mechanical properties of the material, for instance its fracture behavior [1]. Segregation can be induced by thermal annealing or/and irradiation, which offers additional means for the mass transport and can cause non-equilibrium segregation [2]. This is why grain boundary (GB) segregation has been extensively studied over the last few decades both experimentally and theoretically. Recently, a significant part of theoretical investigations was focused on atomistic computer simulations, which is a powerful tool to gain knowledge about GB structure, cohesive and mechanical properties at the atomic level. However, the segregation in concentrated alloys was mainly studied in face centered cubic (FCC) systems such as Cu–Ag and Ni–Al (see e.g., [3], [4]). Little work has been done so far in body centered cubic (BCC) concentrated alloys.

The present work focuses on the study of tilt grain boundaries in bcc Fe–Cr disordered alloys with Cr content in the range 5–14 at.% Cr. The latter alloys are often considered as model alloys for ferritic/martensitic (F/M) steels (including reduced activation steels [5]), which are commonly used as structural materials for gas turbines and nuclear power systems. This choice was made based on superior mechanical properties and good resistance to neutron irradiation. The segregation/precipitation of Cr in bcc Fe–Cr alloys and steels containing more than 13 at.% Cr is long known to cause embrittlement during thermal ageing in the temperature range 400–550 °C. For instance, enrichment of Cr at grain boundaries under thermal ageing of Fe–Cr alloys containing more that 13 at.% Cr was reported by Lagneborg [6]. Experiments involving irradiation in Fe–13Cr [7] and Fe–10Cr [8] alloys show that Cr depletion takes place after electron irradiation at 400° and 500 °C, respectively. Whereas, in Fe–2.8Cr, a strong enrichment was observed under electron irradiation at 600 °C [9]. Finally, neither enrichment nor depletion of Cr was seen in Fe–5Cr alloy irradiated at 400 °C [7]. Summary of other experimental works involving irradiation can be found in Ref. [10], which points out that there is no clear indication for radiation induced segregation or depletion of Cr. It is important to note that the sign of the heat of mixing of Fe–Cr changes from negative to positive at about 9% Cr [11]. As a result, Cr atoms in the alloys containing more than 10% Cr tend to precipitate (see e.g., [6], [12], [13]), and otherwise tend to order [14]. Up to now very little is known about how the presence of the GB region may locally alter phase separation or ordering in Fe–Cr alloys, depending on temperature and GB structure. These issues are the subject of the current work.

One of the common numerical methods to study equilibrium GB segregation is the Metropolis Monte Carlo (MMC) method [15], which allows a variation of the volume, pressure and chemical potential, and to include atomic relaxations, while approaching the equilibrium state [16]. Another advantage of this method is that it can handle relatively large systems containing up to few hundred thousands of atoms. In the present work we apply the MMC method to study rearrangement of Cr atoms near different 〈1 1 0〉 tilt GBs in Fe–xCr alloys at thermodynamic equilibrium. The concentration of Cr, x = 5, 10, 14 at.%, was chosen to cover a typical range of Cr content in the F/M steels for nuclear application. GBs selected were intended to span a wide range of structures with essential variation in GB energy, structure and excess volume.

Section snippets

MMC simulations

MMC sampling was realized within the isobaric–isothermal (NPT) statistical ensemble where N is the number of particles, P is the pressure and T is the temperature, which are kept constant during simulation runs. Three different types of trials were considered, namely: (i) random displacement of any atom from its position (by this trial, lattice relaxation and vibrational entropy are accounted for); (ii) swapping of atoms of different kinds, selected at random; (iii) overall volume change of the

Static calculations

The binding energy for a substitutional Cr atom versus distance from the GB interface in pure Fe is shown in Fig. 2 and the maximum binding energy is reported in Table 1 for each GB. The binding energy shown in Fig. 2 was calculated for all lines shown in Fig. 1 and then sorted by the distance between a Cr atom and GB interface. We can see that Cr is strongly attracted to all GBs except for the 112 GB, for which the maximum binding energy is only ∼0.05 eV. In general, the maximum binding energy

Summary

In this work, we have carried out an atomistic study of rearrangement in Fe–Cr alloys considering several different tilt symmetric grain boundaries. The calculations have been performed using MS and MMC techniques by applying a set of recently developed interatomic potentials for Fe–Cr, partially fitted to ab initio data.

Results of the static simulations suggest that all considered GBs have energetically preferential sites for substitutional Cr atoms, but the actual binding energy depends

Conclusions

Based on the results presented above we can draw the following conclusions:

  • (1)

    The binding energy of a substitutional Cr to the GB core is essentially determined by the structure of the GB interface. The strongest binding energy (∼0.3 eV) is found for GBs with the largest excess volume, such as Σ9{2 2 1} and Σ9{1 1 4} GBs. The weakest interaction takes place in the Σ3{1 1 2} GB.

  • (2)

    All considered GBs contain both energetically preferential and unfavourable sites for the segregation of Cr. At this, the most

Acknowledgements

This work was performed in the framework of the seventh Framework Programme collaborative project GETMAT, partially supported by the European Commission, Grant agreement number 212175. XH acknowledges National Natural Science Foundation of China, Grant number 10975194; National Basic Research Program of China, Grant number 2007CD209801. Part of the calculations was performed at the supercomputer facilities JUROPA within the APM project.

References (37)

  • B. Kempshall et al.

    Scripta Mater.

    (2002)
  • M. Menyhard et al.

    Acta Metall. Mater.

    (1994)
  • X. Xie et al.

    Acta Mater.

    (2002)
  • S. Jitsukawa et al.

    J. Nucl. Mater.

    (2004)
  • H. Takahashi et al.

    J. Nucl. Mater.

    (1981)
  • T. Muroga et al.

    Ultramicroscopy

    (1987)
  • Z. Lu et al.

    Scripta Mater.

    (2008)
  • P. Olsson et al.

    J. Nucl. Mater.

    (2003)
  • D. Terentyev et al.

    Comput. Mater. Sci.

    (2010)
  • D. Terentyev et al.

    J. Nucl. Mater.

    (2009)
  • K. Vörtler et al.

    J. Nucl. Mater.

    (2008)
  • C. Björkas et al.

    J. Nucl. Mater.

    (2008)
  • D. Terentyev et al.

    Acta Mater.

    (2008)
  • D. Terentyev et al.

    J. Nucl. Mater.

    (2009)
  • F. Willaime et al.

    Nucl. Instrum. Methods Phys. Res. B

    (2005)
  • D. Terentyev et al.

    Comput. Mater. Sci.

    (2008)
  • G. Bonny et al.

    Scripta Mater.

    (2008)
  • Y. Shibuta et al.

    Comput. Mater. Sci.

    (2009)
  • Cited by (27)

    • Interfacial nanophases stabilize nanotwins in high-entropy alloys

      2020, Acta Materialia
      Citation Excerpt :

      Subsequently, elongated M23C6 nano-carbide zones form at the incoherent segments of the twin interfaces upon annealing as captured by high-resolution STEM/TEM analysis. Energetically, incoherent twin boundary portions are less stable than coherent twin boundaries [54,55]. Upon cold-rolling, the 9R structure initially forms at {112} incoherent twin boundary segments and then grows along the {111} coherent twin boundary (Fig. 13a, b, d1 and d2), as confirmed by the fast Fourier transform (FFT) analysis shown in Fig. 13a and b. Growth of the 9R structure is promoted by the motion of b1 edge partial dislocations [17,18] without chemical diffusion.

    • Historical review of computer simulation of radiation effects in materials

      2019, Journal of Nuclear Materials
      Citation Excerpt :

      MMC simulations have been used to examine this phase stability for different interatomic potentials [105,106] (for a more detailed discussion of this specific case, see Ref. [107]). MMC has also been used to study the stable atom configurations on sputtered surfaces [108], the balance of Cr atoms and vacancies in FeCr alloys [109], and segregation of atoms at grain boundaries [110]. Molecular dynamics simulations are a way to simulate the motion of atoms in molecules or solids [111–113].

    • Study the grain boundary triple junction segregation of phosphorus in a nickel-base alloy using energy dispersive X-ray spectroscopy on a transmission electron microscope

      2019, Materials Characterization
      Citation Excerpt :

      This can also be verified by the width of the segregation area measured. Equilibrium segregation width is typically only several atomic layers [28], while the non-equilibrium segregation can be several nanometres wide [29], consistent with the line scan results currently obtained. As shown in Table 1, the P concentrations at different GBs are different in that GB3 has obviously lower value than GB1 and GB2, in both cases.

    View all citing articles on Scopus
    View full text