Helium-induced damage in MAB phase MoAlB and Fe2AlB2: first-principles simulation

Similar to Mn+1AXn (MAX, M: transition metal, A: A group element, X: C or N, n = 1 ∼ 3) phase materials, MAB (M: transition metal, A: A group element, B: B) phases also exhibit excellent comprehensive mechanical and thermal properties that are applicable to future nuclear reactors. The origination and growth conditions of He bubbles under irradiation in MAB phase MoAlB and Fe2AlB2 have been calculated through first-principles theory in this work. In general, Fe2AlB2 may present lower single/di-vacancy formation energies and a consequent higher He bubble number density. The final He bubble shape and comparative average size of MoAlB and Fe2AlB2 have been predicted as well. In MoAlB there will form large platelet-like He bubbles and small spherical ones. In Fe2AlB2 there will form spherical He bubbles with different sizes. These He bubbles can all further link via interlayer vacancies into string-like shape. Fe2AlB2 also possesses higher He-induced embrittlement tendency than MoAlB.

When focused on the defect chemistry and radiation tolerance of these two materials, Lu et al have imaged the atomic structures of tilt boundary in Fe 2 AlB 2 and stacking fault in MoAlB through analytical aberrationcorrected high-resolution scanning transmission electron microscopy [48]. Kim et al have reported in Cr-Al-B MAB phases, homolog of Fe 2 AlB 2 , that the increase of the hexagonal B ring number in the Cr-Al-B structure can help to weaken the strongest Cr-B bond and the related bonds of the Cr atom in middle of the B ring, reduce the formation energy of Cr/B vacancies and Cr interstitials respectively and therefore increase the number density of Frenkel pairs [49]. For the two major problems (antisite defect and He bubble) influencing the radiation resistance of MAX/MAB phase materials, Zhang et al have investigated the antisite defect induced amorphization and cracking behavior of MoAlB and Fe 2 AlB 2 at 150/300°C. They indicated that MoAlB presented anyhow complete amorphization under low/high-dose carbon ion irradiation from room temperature to 300°C, nevertheless, Fe 2 AlB 2 possessed amorphization resistance similar to SiC and performed better to resist irradiation-induced cracking than the MAX phase counterparts (Ti 2 AlC and Ti 3 SiC 2 ) at this temperature range [18]. In recent year the same group and coworkers further surveyed the Si + irradiation of MoAlB from room temperature to 600°C and pointed out that at higher temperatures (>450°C) most disorder domains formed by irradiation can be annealed out to rebuild the crystallinity of MoAlB even though there exist few kinds of defects such as V Mo and Mo Al antisite that cannot be recovered because of the high migration energy. They also revealed in MoAlB at these high temperatures greatly reduced surface cracking when compared with MAX phases due to its low anisotropy inflation during the irradiation process [19].
However, even though the two promising MAB phases (MoAlB and Fe 2 AlB 2 ) presented attractive properties to resist irradiation damage illustrated by these previous studies, their He bubble aggregation condition which usually results in serious sudden brittle rupture is still unknown. Therefore, in this work via first-principles simulation we systematically investigated the origination and growth behaviors of He bubbles in MoAlB and Fe 2 AlB 2 and further compared and evaluated their He bubble resistance based on the different above behaviors.

Methods
First-principles calculations are performed based on the density functional theory (DFT) [50] and via the Vienna Ab-initio Simulation Package (VASP) [51,52]. The projector augmented-wave (PAW) potentials [53] and the generalized gradient approximation with the Perdew-Breke-Ernzerhof (PBE) parameterization [54] are adopted. In all the calculations the plane-wave cut-off energy is set as 625 eV and 3 × 1 × 3 supercells (108 atoms for MoAlB and 90 atoms for Fe 2 AlB 2 ) with a Monkhorst-Pack k-point mesh [55] of 3 × 2 × 3 are used. In the energy minimization calculations both the supercell volume and the atomic positions are allowed to fully relax with the force convergence reached when the force of each atom is less than 0.01 eV Å and the energy convergence reached with the energy tolerance of 0.001 meV. The body-centered cubic Mo and Fe, facecentered cubic Al, regular icosahedron B and isolated atomic He are adopted in the calculation of the elemental chemical potential.

Results and discussion
MoAlB and Fe 2 AlB 2 both have orthorhombic crystal structures with the space group of Cmcm and Cmmm respectively, as displayed in figures 1(a) and (b). For MoAlB and Fe 2 AlB 2 supercells after full relaxation the lattice constants have been obtained as shown in table 1, all in good agreement (difference within 1%) with the lattice constants determined by previous experiments [56].
The potential interstitial sites for MoAlB and Fe 2 AlB 2 are also depicted in figure 1. To determine the most stable position for a single He atom to locate in MoAlB or Fe 2 AlB 2 , the solution energy for a He atom in different interstitial sites are calculated with the definition of solution energy as following: where E is (ref+He) is the energy of the supercell with a single He atom located in an interstitial site, E(ref) is the energy of a perfect supercell and μ(He) is the elemental chemical potential of He. To calculate the He solution energy at different interstitial sites the He atoms are placed with a slight distance (0.15 Å) away from the geometrically symmetric point of the interstitials as the original positions [18]. From the solution energy results of different interstitial sites in MoAlB and Fe 2 AlB 2 as listed in table 2, it can be summarized that for MoAlB the most stable site to accommodate a He atom is the type-1 tetrahedral interstitial site surrounded by four Al atoms and for Fe 2 AlB 2 which is most stable is the type-1 octahedral interstitial site composed of four Al atoms and two Fe atoms. The most stable interstitial sites for MoAlB and Fe 2 AlB 2 are both in the Al layer, which predicts that they may have a high disorder tendency in the Al layer similar to the behaviors of the MAX phase materials as reported before. And these two type-1 interstitial sites will be used as the position of He atoms before they move to neighboring vacancies in further calculations of He trapping energy for single vacancy and primary nearest second vacancy formation energy for He loaded vacancy.
To further determine the potential origination sites for He bubbles in MoAlB and Fe 2 AlB 2 , the formation energy of single vacancy and di-vacancys in these two MAB phases have been calculated. The formation energy of a single vacancy and a di-vacancy are defined as:    therefore a higher tendency than MoAlB to generate vacancies in energetic perspective. Hence, in Fe 2 AlB 2 there is some possibility to finally form a larger number density of He bubbles than in MoAlB. In order to investigate the He bubble growth process, firstly the trapping energy of He atoms by different vacancy sites in MoAlB and Fe 2 AlB 2 have been calculated with the trapping energy of an additional He atom by a vacancy defined as: where E(V+nHe) is the energy of the supercell with n He atoms trapped by a vacancy and E i-type-1 s (ref+He) is the energy of the supercell with a He atom at its lowest energy interstitial position, the type-1 interstitial sites for MoAlB and Fe 2 AlB 2 . The variation trends of the trapping energy as a function of the trapped He atoms have been displayed in figure 2 and the lattice parameter and volume changes resulted from the He atom trapping have been summarized in tables 4 and 5. For Fe 2 AlB 2 the largest number of He atoms that can be trapped by V Fe is 5, V Al is 6 and V B is 5, which is very average among the three types of vacancies and different from that of MoAlB which can trap 6 He atoms by V Mo and 5 He atoms by V Al but only can accommodate 2 atoms in V B . This can be explained through the electronic structure perspective that in MoAlB the strong B-B, Mo-B and Al-B covalent bonds [19] make the electrons around the B vacancy very localized, however, since Fe 2 AlB 2 presents more metallic electronic structure [15] its electron cloud may be more dispersed. Due to the inert electron configuration of the He atom, vacancies with lower neighboring electron density are more possible to attract it and therefore lead to the different He atom accommodation condition of vacancies in Fe 2 AlB 2 and MoAlB.
From analyzing table 4 it can be known that for MoAlB if the number of the He atoms trapped by a vacancy is the same, the corresponding lattice volume change of V B +nHe is much larger than that of V Mo +nHe and V Al +nHe but V Mo +nHe and V Al +nHe systems present similar volume changes with the same n value. This can  help to explain the variation trend of the trapping energy for MoAlB in which V B +nHe also possesses much higher energy and V Mo +nHe and V Al +nHe present similar lower energy when the number of the trapped He atoms is the same. As displaced in table 5, for Fe 2 AlB 2 with the same number of He atoms trapped by a vacancy, the volume changes of the lattice caused by the He trap generally have the trend V B +nHe > V Fe +nHe > V Al +nHe. This also can serve as the explanation for that V Fe and V Al have to some extent lower trapping energy than V B and V Al can trap the maximum number of He atoms. When comparing MoAlB and Fe 2 AlB 2 from the volume change perspective it should also be noted that with the same He atom accommodation condition Fe 2 AlB 2 generally presents much larger lattice parameter variation and more anisotropy than MoAlB and may result in greater strain of the structure and higher possibility of embrittlement during the He bubble growing process.
For further investigation of the He bubble growth condition, the 2nd primary nearest vacancy formation energies have been calculated for MoAlB and Fe 2 AlB 2 with the definition as following:  Table 4. Summary of lattice parameters and volume of MoAlB with trapped He atoms in different vacancy sites.  Table 5. Summary of lattice parameters and volume of Fe 2 AlB 2 with trapped He atoms in different vacancy sites. the chemical potential of the element in V A position. As displaced in figure 3 it can be seen that for the dominant He bubble originating sites V B and V Al in MoAlB, if the He bubble growth starts from V B it will trap one or two He atoms and then induce primary nearest 2nd V Al formation to grow into spherical He bubbles ( figure 4, left). However, if the He bubble originates from the V Al position it can trap up to five He atoms and also attract the 2nd nearest V Al to finally generate platelet-like He bubbles ( figure 4, right). As far as Fe 2 AlB 2 is concerned, V B ,  V B+B and V Fe are its energetically inclined He bubble originating sites. If the He bubble growth starts from V B /V B+B it will further absorb 2nd nearest V Fe or V Al in a He atom loaded condition to develop into spherical He bubbles. There is also some possibility that the He bubble originates from V Fe in Fe 2 AlB 2 and then traps He atoms and absorbs 2nd nearest V Al or V B to form spherical He bubbles as well. When comparing the primary nearest second vacancy forming condition of MoAlB and Fe 2 AlB 2 , it should be mentioned that in MoAlB the second vacancy formation energies of V Al are lower than that of V B , which indicates a higher energetically possibility of the final platelet-like He bubbles in MoAlB to grow into a larger average size than that of the spherical ones. Meanwhile, in Fe 2 AlB 2 the second vacancy formation energies of V B are lower than that of V Fe , which predicts that the spherical He bubbles originate from V B may have larger final sizes than those starting growth from V Fe . In addition, it is worth noting that the 2nd primary nearest vacancy formation energies even though not the most energetically favored are also probable to be negative in MoAlB and Fe 2 AlB 2 , hence there still exists some possibility for the spherical and platelet-like He bubbles to link into string-like shape, which has been previously observed in MAX phase materials by experiments as well [57,58].

Conclusions
The He-induced damage in MAB phases MoAlB and Fe 2 AlB 2 have been investigated through first-principles calculations in this work. The results show that Fe 2 AlB 2 presents lower single/di-vacancy formation energies than MoAlB and He bubbles in Fe 2 AlB 2 may have a larger number density than that in MoAlB. If the He bubble growth can be triggered by the irradiation process in MoAlB and Fe 2 AlB 2 , there will form spherical/platelet-like bubbles and nearly all spherical bubbles respectively, and both then link via interlayer vacancies to form stringlike bubbles. Due to the different 2nd vacancy formation energies of different original vacancies in MoAlB and Fe 2 AlB 2 , besides the final shape difference the He bubbles may also grow into different average sizes. It is revealed that the He bubbles in Fe 2 AlB 2 may lead to a higher possibility of embrittlement as well. In conclusion, Fe 2 AlB 2 possesses better amorphization resistance under irradiation demonstrated by previous experiment but it presents more serious He bubble generating and He-induced embrittlement tendency in our simulation when compared with MoAlB and these two MAB phases exhibit similar He bubble growth inclination. Considering the preeminent comprehensive thermal and mechanical properties of MoAlB and Fe 2 AlB 2 , they are still promising to be applied in the extreme environment of nuclear reactors. The solid-solution modification and defect chemistry theoretical study and spectroscopy analysis may help to further improve the He bubble tolerance of these two materials. This conclusion is obtained at 0 K, and the number of trapped He will decrease at operating temperature of nuclear reactors. The effect of helium migration energy on the He bubble growth should also be considered.