Segregation of Cr at tilt grain boundaries in Fe–Cr alloys: A Metropolis Monte Carlo study
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)
- et al.
Scripta Mater.
(2002) - et al.
Acta Metall. Mater.
(1994) - et al.
Acta Mater.
(2002) - et al.
J. Nucl. Mater.
(2004) - et al.
J. Nucl. Mater.
(1981) - et al.
Ultramicroscopy
(1987) - et al.
Scripta Mater.
(2008) - et al.
J. Nucl. Mater.
(2003) - et al.
Comput. Mater. Sci.
(2010) - et al.
J. Nucl. Mater.
(2009)
J. Nucl. Mater.
J. Nucl. Mater.
Acta Mater.
J. Nucl. Mater.
Nucl. Instrum. Methods Phys. Res. B
Comput. Mater. Sci.
Scripta Mater.
Comput. Mater. Sci.
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