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First-principles investigation of hydrogen behavior in different oxides in ODS steels
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 1 7 1 0 5 e1 7 1 1 3
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First-principles investigation of hydrogen behavior in different oxides in ODS steels Dan Sun a, Jianhua Ding a, Yaochun Yang a, Pengbo Zhang b,**, Jijun Zhao a,* a
Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), Dalian University of Technology, Dalian 116024, China b Department of Physics, Dalian Maritime University, Dalian 116026, China
article info
abstract
Article history:
The energetics of single and multiple H atoms inside Y2O3, Y2Ti2O7, Y2TiO5, Y3Al5O12 and
Received 5 February 2019
YAlO3 as well as the migration behavior of H atom have been investigated using first-
Received in revised form
principles calculations. Among these oxide matrixes, single H atom inside Y2TiO5 is most
10 April 2019
energetically stable, followed by Y2O3, Y2Ti2O7, Y3Al5O12 and YAlO3. The migration barrier
Accepted 2 May 2019
of H atom in Y2O3 is lower than that in other oxide crystals. The formation energy and
Available online 25 May 2019
migration barrier of H atom in those oxide crystals are always higher than that in a-Fe. He atom is more stable than H atom inside oxide crystals, contrarily to the trend in a-Fe solid.
Keywords:
Generally, in the cases of Hn (1 n 4) atoms inside oxide crystals, the formation energy of
Hydrogen
even-sized Hn cluster is lower than that of odd-sized Hn clusters, because two H atoms
Oxide crystals
form a hydrogen molecule with strong HeH covalent bond.
Migration
© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Recently, the oxide dispersion strengthened (ODS) steel becomes a candidate structural material for the advanced fission and fusion reactors owing to their superior creep strength and resistance to irradiation [1e6]. The high-density nanosized dispersion particles in the ODS steel act as recombination centers for point defect and pinning sites for dislocation motion and grain boundary movement [3,7e10]. Previous experiments demonstrated that the size, distribution and number density of the oxide particles play a key role in improving the mechanical properties and irradiation tolerance of ODS steels [7,11e15]. Ukai et al. found that addition of titanium (Ti) increases the number density of oxide (Y2TiO5) and then
improves the stability of oxide particles [2]. So far, several types of nanoscale YeTieO particles have been reported, such as Y2Ti2O7 and Y2TiO5 [16e18]. Meanwhile, aluminum (Al) was reported to enhance the corrosion resistance of ODS steel, and YeAleO particles (i.e., Y3Al5O12, YAlO3) instead of Y2O3 particles were incorporated [19e21]. In the environment of a fusion reactor, high temperature, high thermo-mechanical stress and high flux of 14 MeV neutrons have adverse effect on the structural stability of the materials due to formation of high densities of helium (He) and hydrogen (H) along with creation of large amount of vacancies and interstitials, thus affecting the microstructure and eventually degrading the mechanical properties [22e25]. Up to now, numerous experiments have been performed to
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (P. Zhang), [email protected] (J. Zhao). https://doi.org/10.1016/j.ijhydene.2019.05.008 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
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elucidate the microscopic mechanism responsible for the effects of nanosized oxide particles as well as neutron irradiation or H/He implantation [26e29]. Using thermal desorption spectroscopy, Malitckii et al. compared the hydrogen uptake and its effective diffusion activation energy in EUROFER 97, ODS-EUROFER, and PM2000 steels [30]. They found that embedding of nanoparticles leads to hydrogen uptake in ODSEUROFER markedly higher than that in the conventional steels (PM2000 steels). Lee et al. investigated the effects of H on the mechanical properties of ODS steels by means of tensile tests at room temperature [31]. Their experiment data also showed that the ODS steels trapped higher concentration of hydrogen than the conventional steels (9Cre2W martensitic steel) and the critical hydrogen concentration required for the transition from ductile to brittle fracture in ODS steels and 9Cre2W martensitic steel is in the range of 10e12 and 1e2 wppm, respectively. Parallel to the experiments, atomistic simulations can provide key insights into the microscopic mechanism of the formation of He/H bubbles in a structural material. So far, there have been several computational studies on the stability of nanosized oxide clusters, the energetical of He/H in bulk oxides (e.g., Y2Ti2O7), as well as the effect of ferrite/oxide (Fe/ Y2O3, Fe/Y2Ti2O7 and Fe/Y2Hf2O7) interface [32e38]. However, the fundamental mechanism governing the aggregation of H atoms inside the different types of oxide nanoparticles is still unclear. In this study, we performed systematic firstprinciples calculations to illustrate the effect of oxide additions on H behavior inside the ODS steel. We investigated the energetic stability of single H atom and Hn (2 n 4) clusters as well as the migration of H atom in five different oxide host lattices: Y2O3, Y2Ti2O7, Y2TiO5, Y3Al5O12 and YAlO3. Our theoretical results provide a primary picture for understanding the effect of oxide particles on the hydrogen behavior inside the ODS steels.
Computational methods All calculations were performed using density functional theory (DFT) and planewave pseudopotential technique, as implemented in VASP (Vienna Ab initio Simulation Package) [39,40]. The PW91 functional [41] within the generalized gradient approximation (GGA) was used to describe the exchange-correlation interaction and the ion-electron interaction was modeled by the projector-augmented wave (PAW) potentials [42]. An energy cutoff of 500 eV was adopted for the planewave basis. The detailed descriptions of the computational scheme are given in Table 1 [37,38]. We also adopted the GGAþU method to compare with the GGA functional [43]. Ueff values of 2.5 eV and 4.3 eV have been used for the Ti 3d and Y 4f states, respectively [44,45]. Firstly, the supercell parameters of perfect oxide crystals without incorporation of H were fully relaxed. Based on the equilibrium lattice parameters, we added different amounts of H atoms into the supercell by keeping constant volume. All atomic positions were then fully relaxed until the energy change on each atom is less than 1 105 eV and the total force on each atom was less than 0.01 eV/ A, respectively.
The formation energy for interstitial H impurities inside an oxide host lattice is defined as: f
DGHn ¼ Etotal Eperfect nEH þ DZPE TDS Here, n is the number of H atoms inside oxide supercell; Etotal is the total energy of oxide supercell containing n H atoms; Eperfect is the energy of perfect oxide supercell without H, EH is half of the energy for a gas-phase H2 molecule in a large supercell (15 A3); the zero-point energy (DZPE) and the entropy correction (TDS) at T ¼ 298 K were taken from the NIST-JANAF thermodynamics table for H2 molecule [46] and the calculated vibrational frequencies for the adsorbed H atoms, respectively. By definition, a system with positive (negative) formation energy means H incorporation is an endothermic (exothermic) process. Inside the oxide host lattice, the binding energy between two H atoms is defined as [47]: EbHH ¼ EHi þ EHj EHiþj Eperfect where EHi ( EHj ) is the total energy of supercell with only one H atom at interstitial site i (j), EHiþj is the total energy of the supercell with two H atoms at interstitial site i and j, respectively. Here positive (negative) binding energy represents attraction (repulsion) between two interstitial H atoms.
Results and discussion Single H atom inside different oxides Stability of H inside different oxides We start from the incorporation of a single H interstitial atom inside different kinds of oxide lattices (Y2O3, YeTieO, YeAleO) to determine the preferred interstitial site. The main interstitial configurations in those oxide lattices are tetrahedral site (Tet), octahedral site (Oct), pyramid site (Pyr) and hexahedron site (Hex). The structures of five oxide crystals and the possible interstitial configurations are shown in Fig. 1 and the formation energies of single H atom inside different interstitial positions are presented in Fig. 2. The results from GGA and GGAþU method show same trend. The data from GGAþU are described in detail and discussed below. We consider the possible interstitial position of H inside Y2O3, which have the same positions as the cases of He inside Y2O3 [38]: TetO@Y2O3 and TetY@Y2O3 surrounded by four O atoms and Y atoms, respectively, and OctY@Y2O3 surrounded by six Y atoms. The formation energies of one H atom at OctY, TetY and TetO positions from the present DFTþU calculations are 2.37 eV, 2.28 eV and 2.59 eV, respectively, which are systemically higher than those of He atom in Y2O3 (0.92 eV, 0.77 eV and 1.22eV) [38]. One can see that TetY is the most energetically favorable site for both H and He atoms in Y2O3. To account for YeTieO nano-oxides in ODS steel, we consider two complex oxides: Y2Ti2O7 and Y2TiO5. There are two possible interstitial sites of H atom inside Y2Ti2O7: Tet@Y2Ti2O7 surrounded by four Ti atoms, Oct@Y2Ti2O7 surrounded by three Y atoms and three Ti atoms. Different from the case of He inside Y2Ti2O7, the most stable site of H inside Y2Ti2O7 is not octahedral site but tetrahedral site [37]. The
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Table 1 e The computational basic parameters of five different nanoparticles (Y2O3, Y2Ti2O7, Y2TiO5, Y3Al5O12, YAlO3).
Type of supercell Supercell unit K-point sampling Number of atoms Lattice Parameters of unit cell ( A)
PW91
Expt.
PW91
PBE
LDA
a b c a b c a b c a b c a b c
Y2O3
Y2Ti2O7
Y2TiO5
Y3Al5O12
YAlO3
Bixbyite 1*1*1 4*4*4 80 10.61 10.61 10.61 10.602 [58] 10.602 10.602
Pyrochlore 1*1*1 4*4*4 88 10.18 10.18 10.18 10.09 [59] 10.09 10.09 10.18 [63] 10.18 10.18 10.20 [63] 10.20 10.20 10.02 [63] 10.02 10.02
Fluorite 1*3*1 5*7*4 96 10.47 3.72 11.33 10.35 [60] 3.70 11.25 10.47 [63] 3.70 11.34 10.46 [63] 3.73 11.37 10.23 [63] 3.64 11.12
garnet 1*1*1 4*4*4 160 12.00 12.00 12.00 12.01 [61] 12.01 12.01
Perovskite 2*2*2 5*3*5 160 5.33 7.39 5.19 5.33 [62] 7.37 5.18
12.13 [65] 12.13 12.13 11.92 [65] 11.92 11.92
5.39 [65] 7.45 5.27 5.28 [65] 7.31 5.13
10.709 [64] 10.709 10.709
Fig. 1 e The structures of different oxides and the configurations of the possible interstitial sites: (a) Y2O3, (b) Y2Ti2O7, (c) Y2TiO5, (d) Y3Al5O12, and (e) YAlO3.
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Migration barriers of H atom inside different oxides
Fig. 2 e The insertion energy of H at different interstitial sites in five different oxides. formation energy of H atom at Tet@Y2Ti2O7 and Oct@Y2Ti2O7 is 3.04 eV and 3.08 eV, respectively, in line with the previous DFT results of 2.87 eV and 3.01 eV by Tsuchiya et al. [48]. For Y2TiO5 crystal, four possible interstitial sites for H atom are considered: Center@Y2TiO5 is an interstitial site between two layers, Pyr@Y2TiO5 surrounded by four Y atoms and one Ti atom, Oct1@Y2TiO5 surrounded by four Y atoms and two Ti atoms, and Oct2@Y2TiO5 surrounded by three Y atoms and three Ti atoms. The formation energy of Center@Y2TiO5, Pyr@Y2TiO5, Oct1@Y2TiO5 and Oct2@Y2TiO5 is 3.19 eV, 2.30 eV, 2.06 eV and 1.44 eV, respectively. It is clearly that the most stable for an interstitial H atom inside Y2TiO5 is Oct2@Y2TiO5. This is because that H atom inside Oct2@Y2TiO5 forms a hydrogen bond with a nearby O atom with distance of 0.98 A. Similar to Y2O3, formation energies of a single H interstitial atom inside Y2Ti2O7 and Y2TiO5 host lattice are also higher than those of a He atom [37]. The main compositions of YeAleO nano-oxides in ODS steel are Y3Al5O12 and YAlO3 [19]. We consider two possible interstitial sites for H inside Y3Al5O12: Hex@Y3Al5O12 surrounded by three Y atoms and two Al atoms, Oct@Y3Al5O12 surrounded by six O atoms. The most energetically favorable site for H atom in Y3Al5O12 is Hex@Y3Al5O12 with formation energy of 3.16 eV. The formation energy of H atom inside Oct@Y3Al5O12 is slightly higher than that of Hex@Y3Al5O12 by 0.05 eV. There are also two possible interstitial sites in YAlO3: Tet@YAlO3 surrounded by two Y atoms and two Al atoms, Oct@YAlO3 surrounded by two Y atoms and four Al atoms. Tet@YAlO3 is energetically more stable than Oct@YAlO3 by 0.27 eV, and H inside Y3Al5O12 is more stable than that inside YAlO3. Among five oxide crystals considered, H inside Y2TiO5 is most stable with the lowest formation energy (1.44 eV), followed by Y2O3, Y2Ti2O7, Y3Al5O12, and YAlO3. The present results demonstrate that the formation energy of H inside all the considered oxide crystals is higher than that inside a-Fe (0.21 eV), indicating that interstitial H atom prefers to locate in Fe bulk matrix [49]. This behavior is different from the situation of interstitial He atom, which is more stable inside oxide crystals than inside a-Fe [37,38]. Previous DFT study illustrated that the formation energy of H atom is lower than that of He atom in a-Fe [49]. By comparison, He atom is more stable than H inside oxide crystals, which is contrary to the trend of He and H atoms inside a-Fe.
Concerning the diffusion kinetics, we carefully assess the energy barrier for an interstitial H atom diffusing between different interstitials in those five oxide crystals. The energy profile for an H atom migrating between the interstitial locations has been computed using the climbing image nudged elastic Band method (CI-NEB) [50,51]. The calculated migration energies between one interstitial site to an adjacent interstitial site are plotted in Fig. 3. Two diffusion paths of H atom inside Y2O3 are considered: from TetY@Y2O3 to OctY@Y2O3 and to TetO@Y2O3, respectively. As the diffusion path set as from TetO@Y2O3 to an adjacent one or OctY@Y2O3, the diffusion path will change to TetO@Y2O3 to an adjacent TetY@Y2O3 and then to TetO@Y2O3 or OctY@Y2O3 after relaxation. As shown in Fig. 3, there is no barrier for migration from one OctY@Y2O3 to an adjacent TetY@Y2O3, while the migration barrier from TetY@Y2O3 to OctY@Y2O3 is 0.27 eV. A lower migration barrier (0.02 eV) is found along the path from TetO@Y2O3 to TetY@Y2O3. The simulation data suggest easier clustering of H atoms in TetY@Y2O3. The migration path in Y2Ti2O7 is from one Oct@Y2Ti2O7 to an adjacent one. Compared with He diffusion barrier in Y2Ti2O7 (0.72 eV), a slightly lower migration barrier of 0.68 eV is found here. For Y2TiO5, there are four migration paths: one is from one Pyr@Y2TiO5 to Oct1@Y2TiO5, the others are from one Center@Y2TiO5 to Oct1@Y2TiO5, Oct2@Y2TiO5 and Center@Y2TiO5, respectively. As shown in Fig. 3, the migration barrier from Center@Y2TiO5 to adjacent interstitial site (0.10e0.32 eV) is lower than that from other interstitial site to adjacent interstitial site (0.65e1.80 eV). Notably, the migration path between two Center@Y2TiO5 sites has the lowest migration barrier of 0.10 eV. Combined with the high formation energy of H inside Y2TiO5, incorporation of an H atom is difficult inside Center@Y2TiO5 and it tend to escape from Center@Y2TiO5 to other interstitial sites. There are two possible migration paths in Y3Al5O12: from Oct@Y3Al5O12 or Hex@Y3Al5O12 to an adjacent Oct@Y3Al5O12. The lowest diffusion barrier (0.54 eV) is found on the path from Oct@Y3Al5O12 to an adjacent one, while the migration barrier from Hex@Y3Al5O12 to Oct@Y3Al5O12 is 0.79 eV. There is only one possible migration path from Tet@YAlO3 to an adjacent one in YAlO3. The corresponding migration barrier (0.43 eV) is lower than that in Y3Al5O12. To sum up, among five oxide crystals considered, H inside Y2O3 has the lowest migration barrier of 0.02 eV. Regardless the specific diffusion path, the migration barrier of H in oxide crystals except Y2O3 is always higher than that in Fe matrix (0.088 eV) [52]. The higher migration barrier of H atom in oxide crystal means that oxide crystals act as impediment to H diffusion inside Fe matrix. We also consider the strain effect on the H diffusion in the oxide. The insertion energy and migration barrier of H inside Y2O3 under different isotropic strains ((i.e., uniform strain along three crystalline orientations: ε[100] ¼ ε[010] ¼ ε[001]) has been investigated. As shown in Fig. 4(a) and (b), the formation energy of H atom linearly decreases with the increasing tensile strain but increases with the increasing compressive strain. Previous studies about the effect of isotropic strain on
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Fig. 3 e The migration energy of H atom in the five different oxides, (a) Y2O3 and Y2Ti2O7, (b) Y2TiO5, (c)Y3Al5O12 and YAlO3.
Fig. 4 e The insertion energy of H inside Y2O3 under different strain from (a) DFT calculations and (b) DFTþU calculations, (c) the migration energy of H atom in Y2O3 under different strain. the impurity doping in IIIeV semiconductors [53] and H inside bcc metals also present same conclusion [54]. TetY is the most stable interstitial site under all strains. After relaxation, H atom, which was initially placed on the OctY site, removes
to the adjacent TetY site under strain. As mentioned above, there is no barrier for migration from one OctY@Y2O3 to an adjacent TetY@Y2O3 in perfect Y2O3 supercell. Hence, although the formation energy of H atom inside OctY site in
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Fig. 5 e The insertion energy of Hn (2 ≤ n ≤ 4) cluster in five oxides as a function of the number of H atoms (a) Y2O3, (b) Y2Ti2O7, (c) Y2TiO5, (d)Y3Al5O12 and (e) YAlO3.
perfect Y2O3 supercell is intermediate, H atom is easy to escape from this interstitial site to another. Under strain, there is only one diffusion path of H atom inside Y2O3 under strain, i.e., from TetO@Y2O3 to an adjacent TetY@Y2O3. Similar as H atom inside Y2O3 without strain, as the diffusion path set as from TetO@Y2O3 to an adjacent one, the diffusion path will change to TetO@Y2O3 to an adjacent TetY@Y2O3 and then
to TetO@Y2O3 after relaxation. Under different isotropic strains (within ±2%), the diffusion barrier exhibits same trend with the insertion energy of H atom inside Y2O3. The migration barrier from TetY@Y2O3 (OctY@Y2O3) to OctY@Y2O3 (TetY@Y2O3) drops to 0.001 eV (0.03 eV) under 2% tensile strain, while it rises to 0.05 eV (0.40 eV) under 2% compressive strain.
3) of H atom and H2 cluster inside the five different oxides. Blue Fig. 6 e Differential charge density (isovalue: 0.002 e/A contour denotes regions of electron depletion, and yellow contour denotes regions of electron accumulation. For a better clarity, only the atoms around the H1 or H2 are shown. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article).
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Fig. 7 e HeH binding energy as a function of HeH distance in five different oxides (a) Y2O3, (b) Y2Ti2O7, (c) Y2TiO5, (d)Y3Al5O12 and (e) YAlO3.
Stability of Hn cluster inside different oxides To further understand the early stage of nucleation of hydrogen bubbles inside oxides, we also investigated Hn cluster with n ¼ 2e4 inside different oxide crystals. The formation energies of the most stable Hn clusters inside oxide crystals are depicted in Fig. 5 and compared with those of single H atom. For H2 cluster, two H atoms were placed into the same interstitial site or two adjacent interstitial sites, whereas all kinds of possible configurations have been considered. From the energetic point of view, two H atoms staying inside one interstitial site is more stable than those inside two adjacent interstitial sites. On the contrary, He atoms prefer to occupy different interstitial sites according to our previous studies [37,38]. The possible configurations of H3 cluster have also been explored. In all oxide crystals, two H atoms in one interstitial site and the other H atom in the adjacent interstitial site is most stable. As the number of H atoms reaches four, these H atoms are separated into two interstitial sites (two H atoms staying at one interstitial site, another staying at adjacent site) is the most stable configuration. Note that the formation energy of H2 cluster is lower than that of single H atom in all oxide crystals except YAlO3 by about 0.29e0.95 eV. Previous study also presented that the incorporation of H2 cluster costs less energy than that of single H atom in Y2Ti2O7 and Y2TiO5 [55]. The formation energy of H3 cluster is higher than that of H2 cluster in all oxide crystals. Except in Y2Ti2O7, the formation energy of H4 cluster is lower than that of H3 cluster. With the number of H atom increasing, the metal or oxygen atoms surrounding Hn cluster deviate from their initial positions farther.
To gain insight into the physical origin of the high stability of H2 cluster inside oxide crystals, we examined the differential charge density of single H atom and H2 cluster inside the most stable interstitial site in oxide supercell. As shown in Fig. 6, incorporation of an interstitial H atom induces significant distortion on the electron density of the surrounding atoms. Compared with single H atom, the interaction between H2 cluster and the surrounding atoms is weaker, indicating that the HeH interaction is relatively strong. In addition, the distance between HeH pairs is around 0.75 A, namely, an H2 molecule is formed. Furthermore, the binding energy between two interstitial H atoms as a function of HeH distance have also been investigated. As shown in Fig. 7, the binding energy between two H atoms shows the same trend in five different oxide crystals. In general, there is a stronger attraction between two interstitial H atoms. The maximum binding energy between two H atoms is 2.17e5.48 eV at the nearest distance of 0.75 A. With the increase of the distance between two H atoms, the binding energy decreases. Therefore, we attribute the lower formation energy of H2 (or H4) cluster to the formation of hydrogen molecule from two H atoms inside oxide crystals. According to previous simulation results, two H atoms prefer to occupy two interstitial sites in BCC metals like Fe and V [56,57]. Counts et al. investigated the HeH interactions in BCC Fe lattice and found that an HeH pair initially inside 1st nearest neighbor (1NN) interstitial site is unstable and spontaneously forms 3NN defect pair configuration. Zhang et al. reported that the nearest HeH distance is 1.83 A with strong repulsive interaction in prefect BCC vanadium solid and the favorable HeH distances is 2.1 A with weak attractive interaction in two adjacent interstitial sites [57].
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Conclusion The stable configurations and energetics of single hydrogen atom and small Hn clusters with n ¼ 2e4, and the binding energy between two H atoms as well as the migration barrier of single H atom inside five kinds of oxide lattices have been investigated by comprehensive first-principles calculations. Our theoretical findings can be summarized into the following points. (i) H atom inside Y2TiO5 is most stable, followed by Y2O3, Y2Ti2O7, Y3Al5O12, and YAlO3. The formation energy of single H atom is higher than that of He atom in these oxides. (ii) Single H atom in a-Fe is more stable than that in these oxides by 1.23e3.75 eV. Except for Y2O3, the migration barrier of H atom in oxides is higher than that in a-Fe by 0.012e0.592 eV. Therefore, H impurity is more difficult to form and diffuse in oxides than that in Fe matrix. (iii) Generally, the formation energy of even-sized Hn cluster (2 n 4) is lower than that of odd-sized Hn clusters in the considered oxide crystals, suggesting that H atoms tend to gather in pairs. (iv) HeH pair exhibits attractive interaction in these oxides and the maximum binding energy between two H atoms is 2.17e5.48 eV at the nearest distance of 0.75 A, meaning that two H atoms form H2 molecule inside oxide crystals. Finally, it is worth to point out that the present study is only a first step towards understanding the influence of different oxide particles on the growth of hydrogen-filled bubbles in ODS steels under irradiation. In realistic situations, there are many other factors to be considered, such as the finite size of the oxide nanoparticles, grain boundary, and phase boundary. To draw more definitive conclusions, it is thus necessary to investigate the incorporation and migration of H in the Feoxide boundary. Nevertheless, our detailed investigation would stimulate future experimental and theoretical efforts in revealing the hydrogen behavior in ODS steels.
Acknowledgements This work was supported by the Science Challenge Project (TZ2018004), the National Magnetic Confinement Fusion Program of China (2015GB118001), the Fundamental Research Funds for the Central Universities of China (No.3132019185) and the Liaoning Province Natural Science Fund Project of China (20180510053). We thank the computational support from the Supercomputing Center of Dalian University of Technology.
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Available online at www.sciencedirect.com
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First-principles investigation of hydrogen behavior in different oxides in ODS steels Dan Sun a, Jianhua Ding a, Yaochun Yang a, Pengbo Zhang b,**, Jijun Zhao a,* a
Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), Dalian University of Technology, Dalian 116024, China b Department of Physics, Dalian Maritime University, Dalian 116026, China
article info
abstract
Article history:
The energetics of single and multiple H atoms inside Y2O3, Y2Ti2O7, Y2TiO5, Y3Al5O12 and
Received 5 February 2019
YAlO3 as well as the migration behavior of H atom have been investigated using first-
Received in revised form
principles calculations. Among these oxide matrixes, single H atom inside Y2TiO5 is most
10 April 2019
energetically stable, followed by Y2O3, Y2Ti2O7, Y3Al5O12 and YAlO3. The migration barrier
Accepted 2 May 2019
of H atom in Y2O3 is lower than that in other oxide crystals. The formation energy and
Available online 25 May 2019
migration barrier of H atom in those oxide crystals are always higher than that in a-Fe. He atom is more stable than H atom inside oxide crystals, contrarily to the trend in a-Fe solid.
Keywords:
Generally, in the cases of Hn (1 n 4) atoms inside oxide crystals, the formation energy of
Hydrogen
even-sized Hn cluster is lower than that of odd-sized Hn clusters, because two H atoms
Oxide crystals
form a hydrogen molecule with strong HeH covalent bond.
Migration
© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Recently, the oxide dispersion strengthened (ODS) steel becomes a candidate structural material for the advanced fission and fusion reactors owing to their superior creep strength and resistance to irradiation [1e6]. The high-density nanosized dispersion particles in the ODS steel act as recombination centers for point defect and pinning sites for dislocation motion and grain boundary movement [3,7e10]. Previous experiments demonstrated that the size, distribution and number density of the oxide particles play a key role in improving the mechanical properties and irradiation tolerance of ODS steels [7,11e15]. Ukai et al. found that addition of titanium (Ti) increases the number density of oxide (Y2TiO5) and then
improves the stability of oxide particles [2]. So far, several types of nanoscale YeTieO particles have been reported, such as Y2Ti2O7 and Y2TiO5 [16e18]. Meanwhile, aluminum (Al) was reported to enhance the corrosion resistance of ODS steel, and YeAleO particles (i.e., Y3Al5O12, YAlO3) instead of Y2O3 particles were incorporated [19e21]. In the environment of a fusion reactor, high temperature, high thermo-mechanical stress and high flux of 14 MeV neutrons have adverse effect on the structural stability of the materials due to formation of high densities of helium (He) and hydrogen (H) along with creation of large amount of vacancies and interstitials, thus affecting the microstructure and eventually degrading the mechanical properties [22e25]. Up to now, numerous experiments have been performed to
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (P. Zhang), [email protected] (J. Zhao). https://doi.org/10.1016/j.ijhydene.2019.05.008 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
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elucidate the microscopic mechanism responsible for the effects of nanosized oxide particles as well as neutron irradiation or H/He implantation [26e29]. Using thermal desorption spectroscopy, Malitckii et al. compared the hydrogen uptake and its effective diffusion activation energy in EUROFER 97, ODS-EUROFER, and PM2000 steels [30]. They found that embedding of nanoparticles leads to hydrogen uptake in ODSEUROFER markedly higher than that in the conventional steels (PM2000 steels). Lee et al. investigated the effects of H on the mechanical properties of ODS steels by means of tensile tests at room temperature [31]. Their experiment data also showed that the ODS steels trapped higher concentration of hydrogen than the conventional steels (9Cre2W martensitic steel) and the critical hydrogen concentration required for the transition from ductile to brittle fracture in ODS steels and 9Cre2W martensitic steel is in the range of 10e12 and 1e2 wppm, respectively. Parallel to the experiments, atomistic simulations can provide key insights into the microscopic mechanism of the formation of He/H bubbles in a structural material. So far, there have been several computational studies on the stability of nanosized oxide clusters, the energetical of He/H in bulk oxides (e.g., Y2Ti2O7), as well as the effect of ferrite/oxide (Fe/ Y2O3, Fe/Y2Ti2O7 and Fe/Y2Hf2O7) interface [32e38]. However, the fundamental mechanism governing the aggregation of H atoms inside the different types of oxide nanoparticles is still unclear. In this study, we performed systematic firstprinciples calculations to illustrate the effect of oxide additions on H behavior inside the ODS steel. We investigated the energetic stability of single H atom and Hn (2 n 4) clusters as well as the migration of H atom in five different oxide host lattices: Y2O3, Y2Ti2O7, Y2TiO5, Y3Al5O12 and YAlO3. Our theoretical results provide a primary picture for understanding the effect of oxide particles on the hydrogen behavior inside the ODS steels.
Computational methods All calculations were performed using density functional theory (DFT) and planewave pseudopotential technique, as implemented in VASP (Vienna Ab initio Simulation Package) [39,40]. The PW91 functional [41] within the generalized gradient approximation (GGA) was used to describe the exchange-correlation interaction and the ion-electron interaction was modeled by the projector-augmented wave (PAW) potentials [42]. An energy cutoff of 500 eV was adopted for the planewave basis. The detailed descriptions of the computational scheme are given in Table 1 [37,38]. We also adopted the GGAþU method to compare with the GGA functional [43]. Ueff values of 2.5 eV and 4.3 eV have been used for the Ti 3d and Y 4f states, respectively [44,45]. Firstly, the supercell parameters of perfect oxide crystals without incorporation of H were fully relaxed. Based on the equilibrium lattice parameters, we added different amounts of H atoms into the supercell by keeping constant volume. All atomic positions were then fully relaxed until the energy change on each atom is less than 1 105 eV and the total force on each atom was less than 0.01 eV/ A, respectively.
The formation energy for interstitial H impurities inside an oxide host lattice is defined as: f
DGHn ¼ Etotal Eperfect nEH þ DZPE TDS Here, n is the number of H atoms inside oxide supercell; Etotal is the total energy of oxide supercell containing n H atoms; Eperfect is the energy of perfect oxide supercell without H, EH is half of the energy for a gas-phase H2 molecule in a large supercell (15 A3); the zero-point energy (DZPE) and the entropy correction (TDS) at T ¼ 298 K were taken from the NIST-JANAF thermodynamics table for H2 molecule [46] and the calculated vibrational frequencies for the adsorbed H atoms, respectively. By definition, a system with positive (negative) formation energy means H incorporation is an endothermic (exothermic) process. Inside the oxide host lattice, the binding energy between two H atoms is defined as [47]: EbHH ¼ EHi þ EHj EHiþj Eperfect where EHi ( EHj ) is the total energy of supercell with only one H atom at interstitial site i (j), EHiþj is the total energy of the supercell with two H atoms at interstitial site i and j, respectively. Here positive (negative) binding energy represents attraction (repulsion) between two interstitial H atoms.
Results and discussion Single H atom inside different oxides Stability of H inside different oxides We start from the incorporation of a single H interstitial atom inside different kinds of oxide lattices (Y2O3, YeTieO, YeAleO) to determine the preferred interstitial site. The main interstitial configurations in those oxide lattices are tetrahedral site (Tet), octahedral site (Oct), pyramid site (Pyr) and hexahedron site (Hex). The structures of five oxide crystals and the possible interstitial configurations are shown in Fig. 1 and the formation energies of single H atom inside different interstitial positions are presented in Fig. 2. The results from GGA and GGAþU method show same trend. The data from GGAþU are described in detail and discussed below. We consider the possible interstitial position of H inside Y2O3, which have the same positions as the cases of He inside Y2O3 [38]: TetO@Y2O3 and TetY@Y2O3 surrounded by four O atoms and Y atoms, respectively, and OctY@Y2O3 surrounded by six Y atoms. The formation energies of one H atom at OctY, TetY and TetO positions from the present DFTþU calculations are 2.37 eV, 2.28 eV and 2.59 eV, respectively, which are systemically higher than those of He atom in Y2O3 (0.92 eV, 0.77 eV and 1.22eV) [38]. One can see that TetY is the most energetically favorable site for both H and He atoms in Y2O3. To account for YeTieO nano-oxides in ODS steel, we consider two complex oxides: Y2Ti2O7 and Y2TiO5. There are two possible interstitial sites of H atom inside Y2Ti2O7: Tet@Y2Ti2O7 surrounded by four Ti atoms, Oct@Y2Ti2O7 surrounded by three Y atoms and three Ti atoms. Different from the case of He inside Y2Ti2O7, the most stable site of H inside Y2Ti2O7 is not octahedral site but tetrahedral site [37]. The
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Table 1 e The computational basic parameters of five different nanoparticles (Y2O3, Y2Ti2O7, Y2TiO5, Y3Al5O12, YAlO3).
Type of supercell Supercell unit K-point sampling Number of atoms Lattice Parameters of unit cell ( A)
PW91
Expt.
PW91
PBE
LDA
a b c a b c a b c a b c a b c
Y2O3
Y2Ti2O7
Y2TiO5
Y3Al5O12
YAlO3
Bixbyite 1*1*1 4*4*4 80 10.61 10.61 10.61 10.602 [58] 10.602 10.602
Pyrochlore 1*1*1 4*4*4 88 10.18 10.18 10.18 10.09 [59] 10.09 10.09 10.18 [63] 10.18 10.18 10.20 [63] 10.20 10.20 10.02 [63] 10.02 10.02
Fluorite 1*3*1 5*7*4 96 10.47 3.72 11.33 10.35 [60] 3.70 11.25 10.47 [63] 3.70 11.34 10.46 [63] 3.73 11.37 10.23 [63] 3.64 11.12
garnet 1*1*1 4*4*4 160 12.00 12.00 12.00 12.01 [61] 12.01 12.01
Perovskite 2*2*2 5*3*5 160 5.33 7.39 5.19 5.33 [62] 7.37 5.18
12.13 [65] 12.13 12.13 11.92 [65] 11.92 11.92
5.39 [65] 7.45 5.27 5.28 [65] 7.31 5.13
10.709 [64] 10.709 10.709
Fig. 1 e The structures of different oxides and the configurations of the possible interstitial sites: (a) Y2O3, (b) Y2Ti2O7, (c) Y2TiO5, (d) Y3Al5O12, and (e) YAlO3.
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Migration barriers of H atom inside different oxides
Fig. 2 e The insertion energy of H at different interstitial sites in five different oxides. formation energy of H atom at Tet@Y2Ti2O7 and Oct@Y2Ti2O7 is 3.04 eV and 3.08 eV, respectively, in line with the previous DFT results of 2.87 eV and 3.01 eV by Tsuchiya et al. [48]. For Y2TiO5 crystal, four possible interstitial sites for H atom are considered: Center@Y2TiO5 is an interstitial site between two layers, Pyr@Y2TiO5 surrounded by four Y atoms and one Ti atom, Oct1@Y2TiO5 surrounded by four Y atoms and two Ti atoms, and Oct2@Y2TiO5 surrounded by three Y atoms and three Ti atoms. The formation energy of Center@Y2TiO5, Pyr@Y2TiO5, Oct1@Y2TiO5 and Oct2@Y2TiO5 is 3.19 eV, 2.30 eV, 2.06 eV and 1.44 eV, respectively. It is clearly that the most stable for an interstitial H atom inside Y2TiO5 is Oct2@Y2TiO5. This is because that H atom inside Oct2@Y2TiO5 forms a hydrogen bond with a nearby O atom with distance of 0.98 A. Similar to Y2O3, formation energies of a single H interstitial atom inside Y2Ti2O7 and Y2TiO5 host lattice are also higher than those of a He atom [37]. The main compositions of YeAleO nano-oxides in ODS steel are Y3Al5O12 and YAlO3 [19]. We consider two possible interstitial sites for H inside Y3Al5O12: Hex@Y3Al5O12 surrounded by three Y atoms and two Al atoms, Oct@Y3Al5O12 surrounded by six O atoms. The most energetically favorable site for H atom in Y3Al5O12 is Hex@Y3Al5O12 with formation energy of 3.16 eV. The formation energy of H atom inside Oct@Y3Al5O12 is slightly higher than that of Hex@Y3Al5O12 by 0.05 eV. There are also two possible interstitial sites in YAlO3: Tet@YAlO3 surrounded by two Y atoms and two Al atoms, Oct@YAlO3 surrounded by two Y atoms and four Al atoms. Tet@YAlO3 is energetically more stable than Oct@YAlO3 by 0.27 eV, and H inside Y3Al5O12 is more stable than that inside YAlO3. Among five oxide crystals considered, H inside Y2TiO5 is most stable with the lowest formation energy (1.44 eV), followed by Y2O3, Y2Ti2O7, Y3Al5O12, and YAlO3. The present results demonstrate that the formation energy of H inside all the considered oxide crystals is higher than that inside a-Fe (0.21 eV), indicating that interstitial H atom prefers to locate in Fe bulk matrix [49]. This behavior is different from the situation of interstitial He atom, which is more stable inside oxide crystals than inside a-Fe [37,38]. Previous DFT study illustrated that the formation energy of H atom is lower than that of He atom in a-Fe [49]. By comparison, He atom is more stable than H inside oxide crystals, which is contrary to the trend of He and H atoms inside a-Fe.
Concerning the diffusion kinetics, we carefully assess the energy barrier for an interstitial H atom diffusing between different interstitials in those five oxide crystals. The energy profile for an H atom migrating between the interstitial locations has been computed using the climbing image nudged elastic Band method (CI-NEB) [50,51]. The calculated migration energies between one interstitial site to an adjacent interstitial site are plotted in Fig. 3. Two diffusion paths of H atom inside Y2O3 are considered: from TetY@Y2O3 to OctY@Y2O3 and to TetO@Y2O3, respectively. As the diffusion path set as from TetO@Y2O3 to an adjacent one or OctY@Y2O3, the diffusion path will change to TetO@Y2O3 to an adjacent TetY@Y2O3 and then to TetO@Y2O3 or OctY@Y2O3 after relaxation. As shown in Fig. 3, there is no barrier for migration from one OctY@Y2O3 to an adjacent TetY@Y2O3, while the migration barrier from TetY@Y2O3 to OctY@Y2O3 is 0.27 eV. A lower migration barrier (0.02 eV) is found along the path from TetO@Y2O3 to TetY@Y2O3. The simulation data suggest easier clustering of H atoms in TetY@Y2O3. The migration path in Y2Ti2O7 is from one Oct@Y2Ti2O7 to an adjacent one. Compared with He diffusion barrier in Y2Ti2O7 (0.72 eV), a slightly lower migration barrier of 0.68 eV is found here. For Y2TiO5, there are four migration paths: one is from one Pyr@Y2TiO5 to Oct1@Y2TiO5, the others are from one Center@Y2TiO5 to Oct1@Y2TiO5, Oct2@Y2TiO5 and Center@Y2TiO5, respectively. As shown in Fig. 3, the migration barrier from Center@Y2TiO5 to adjacent interstitial site (0.10e0.32 eV) is lower than that from other interstitial site to adjacent interstitial site (0.65e1.80 eV). Notably, the migration path between two Center@Y2TiO5 sites has the lowest migration barrier of 0.10 eV. Combined with the high formation energy of H inside Y2TiO5, incorporation of an H atom is difficult inside Center@Y2TiO5 and it tend to escape from Center@Y2TiO5 to other interstitial sites. There are two possible migration paths in Y3Al5O12: from Oct@Y3Al5O12 or Hex@Y3Al5O12 to an adjacent Oct@Y3Al5O12. The lowest diffusion barrier (0.54 eV) is found on the path from Oct@Y3Al5O12 to an adjacent one, while the migration barrier from Hex@Y3Al5O12 to Oct@Y3Al5O12 is 0.79 eV. There is only one possible migration path from Tet@YAlO3 to an adjacent one in YAlO3. The corresponding migration barrier (0.43 eV) is lower than that in Y3Al5O12. To sum up, among five oxide crystals considered, H inside Y2O3 has the lowest migration barrier of 0.02 eV. Regardless the specific diffusion path, the migration barrier of H in oxide crystals except Y2O3 is always higher than that in Fe matrix (0.088 eV) [52]. The higher migration barrier of H atom in oxide crystal means that oxide crystals act as impediment to H diffusion inside Fe matrix. We also consider the strain effect on the H diffusion in the oxide. The insertion energy and migration barrier of H inside Y2O3 under different isotropic strains ((i.e., uniform strain along three crystalline orientations: ε[100] ¼ ε[010] ¼ ε[001]) has been investigated. As shown in Fig. 4(a) and (b), the formation energy of H atom linearly decreases with the increasing tensile strain but increases with the increasing compressive strain. Previous studies about the effect of isotropic strain on
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Fig. 3 e The migration energy of H atom in the five different oxides, (a) Y2O3 and Y2Ti2O7, (b) Y2TiO5, (c)Y3Al5O12 and YAlO3.
Fig. 4 e The insertion energy of H inside Y2O3 under different strain from (a) DFT calculations and (b) DFTþU calculations, (c) the migration energy of H atom in Y2O3 under different strain. the impurity doping in IIIeV semiconductors [53] and H inside bcc metals also present same conclusion [54]. TetY is the most stable interstitial site under all strains. After relaxation, H atom, which was initially placed on the OctY site, removes
to the adjacent TetY site under strain. As mentioned above, there is no barrier for migration from one OctY@Y2O3 to an adjacent TetY@Y2O3 in perfect Y2O3 supercell. Hence, although the formation energy of H atom inside OctY site in
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Fig. 5 e The insertion energy of Hn (2 ≤ n ≤ 4) cluster in five oxides as a function of the number of H atoms (a) Y2O3, (b) Y2Ti2O7, (c) Y2TiO5, (d)Y3Al5O12 and (e) YAlO3.
perfect Y2O3 supercell is intermediate, H atom is easy to escape from this interstitial site to another. Under strain, there is only one diffusion path of H atom inside Y2O3 under strain, i.e., from TetO@Y2O3 to an adjacent TetY@Y2O3. Similar as H atom inside Y2O3 without strain, as the diffusion path set as from TetO@Y2O3 to an adjacent one, the diffusion path will change to TetO@Y2O3 to an adjacent TetY@Y2O3 and then
to TetO@Y2O3 after relaxation. Under different isotropic strains (within ±2%), the diffusion barrier exhibits same trend with the insertion energy of H atom inside Y2O3. The migration barrier from TetY@Y2O3 (OctY@Y2O3) to OctY@Y2O3 (TetY@Y2O3) drops to 0.001 eV (0.03 eV) under 2% tensile strain, while it rises to 0.05 eV (0.40 eV) under 2% compressive strain.
3) of H atom and H2 cluster inside the five different oxides. Blue Fig. 6 e Differential charge density (isovalue: 0.002 e/A contour denotes regions of electron depletion, and yellow contour denotes regions of electron accumulation. For a better clarity, only the atoms around the H1 or H2 are shown. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article).
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Fig. 7 e HeH binding energy as a function of HeH distance in five different oxides (a) Y2O3, (b) Y2Ti2O7, (c) Y2TiO5, (d)Y3Al5O12 and (e) YAlO3.
Stability of Hn cluster inside different oxides To further understand the early stage of nucleation of hydrogen bubbles inside oxides, we also investigated Hn cluster with n ¼ 2e4 inside different oxide crystals. The formation energies of the most stable Hn clusters inside oxide crystals are depicted in Fig. 5 and compared with those of single H atom. For H2 cluster, two H atoms were placed into the same interstitial site or two adjacent interstitial sites, whereas all kinds of possible configurations have been considered. From the energetic point of view, two H atoms staying inside one interstitial site is more stable than those inside two adjacent interstitial sites. On the contrary, He atoms prefer to occupy different interstitial sites according to our previous studies [37,38]. The possible configurations of H3 cluster have also been explored. In all oxide crystals, two H atoms in one interstitial site and the other H atom in the adjacent interstitial site is most stable. As the number of H atoms reaches four, these H atoms are separated into two interstitial sites (two H atoms staying at one interstitial site, another staying at adjacent site) is the most stable configuration. Note that the formation energy of H2 cluster is lower than that of single H atom in all oxide crystals except YAlO3 by about 0.29e0.95 eV. Previous study also presented that the incorporation of H2 cluster costs less energy than that of single H atom in Y2Ti2O7 and Y2TiO5 [55]. The formation energy of H3 cluster is higher than that of H2 cluster in all oxide crystals. Except in Y2Ti2O7, the formation energy of H4 cluster is lower than that of H3 cluster. With the number of H atom increasing, the metal or oxygen atoms surrounding Hn cluster deviate from their initial positions farther.
To gain insight into the physical origin of the high stability of H2 cluster inside oxide crystals, we examined the differential charge density of single H atom and H2 cluster inside the most stable interstitial site in oxide supercell. As shown in Fig. 6, incorporation of an interstitial H atom induces significant distortion on the electron density of the surrounding atoms. Compared with single H atom, the interaction between H2 cluster and the surrounding atoms is weaker, indicating that the HeH interaction is relatively strong. In addition, the distance between HeH pairs is around 0.75 A, namely, an H2 molecule is formed. Furthermore, the binding energy between two interstitial H atoms as a function of HeH distance have also been investigated. As shown in Fig. 7, the binding energy between two H atoms shows the same trend in five different oxide crystals. In general, there is a stronger attraction between two interstitial H atoms. The maximum binding energy between two H atoms is 2.17e5.48 eV at the nearest distance of 0.75 A. With the increase of the distance between two H atoms, the binding energy decreases. Therefore, we attribute the lower formation energy of H2 (or H4) cluster to the formation of hydrogen molecule from two H atoms inside oxide crystals. According to previous simulation results, two H atoms prefer to occupy two interstitial sites in BCC metals like Fe and V [56,57]. Counts et al. investigated the HeH interactions in BCC Fe lattice and found that an HeH pair initially inside 1st nearest neighbor (1NN) interstitial site is unstable and spontaneously forms 3NN defect pair configuration. Zhang et al. reported that the nearest HeH distance is 1.83 A with strong repulsive interaction in prefect BCC vanadium solid and the favorable HeH distances is 2.1 A with weak attractive interaction in two adjacent interstitial sites [57].
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Conclusion The stable configurations and energetics of single hydrogen atom and small Hn clusters with n ¼ 2e4, and the binding energy between two H atoms as well as the migration barrier of single H atom inside five kinds of oxide lattices have been investigated by comprehensive first-principles calculations. Our theoretical findings can be summarized into the following points. (i) H atom inside Y2TiO5 is most stable, followed by Y2O3, Y2Ti2O7, Y3Al5O12, and YAlO3. The formation energy of single H atom is higher than that of He atom in these oxides. (ii) Single H atom in a-Fe is more stable than that in these oxides by 1.23e3.75 eV. Except for Y2O3, the migration barrier of H atom in oxides is higher than that in a-Fe by 0.012e0.592 eV. Therefore, H impurity is more difficult to form and diffuse in oxides than that in Fe matrix. (iii) Generally, the formation energy of even-sized Hn cluster (2 n 4) is lower than that of odd-sized Hn clusters in the considered oxide crystals, suggesting that H atoms tend to gather in pairs. (iv) HeH pair exhibits attractive interaction in these oxides and the maximum binding energy between two H atoms is 2.17e5.48 eV at the nearest distance of 0.75 A, meaning that two H atoms form H2 molecule inside oxide crystals. Finally, it is worth to point out that the present study is only a first step towards understanding the influence of different oxide particles on the growth of hydrogen-filled bubbles in ODS steels under irradiation. In realistic situations, there are many other factors to be considered, such as the finite size of the oxide nanoparticles, grain boundary, and phase boundary. To draw more definitive conclusions, it is thus necessary to investigate the incorporation and migration of H in the Feoxide boundary. Nevertheless, our detailed investigation would stimulate future experimental and theoretical efforts in revealing the hydrogen behavior in ODS steels.
Acknowledgements This work was supported by the Science Challenge Project (TZ2018004), the National Magnetic Confinement Fusion Program of China (2015GB118001), the Fundamental Research Funds for the Central Universities of China (No.3132019185) and the Liaoning Province Natural Science Fund Project of China (20180510053). We thank the computational support from the Supercomputing Center of Dalian University of Technology.
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