Diffusion and retention of hydrogen in vanadium in presence of Ti and Cr: First-principles investigations

Accepted Manuscript Diffusion and retention of hydrogen in vanadium in presence of Ti and Cr: Firstprinciples investigations Pengbo Zhang, Tingting Zou, Jijun Zhao, Pengfei Zheng, Jiming Chen PII:

S0022-3115(16)31277-6

DOI:

10.1016/j.jnucmat.2016.12.013

Reference:

NUMA 50032

To appear in:

Journal of Nuclear Materials

Received Date: 22 April 2016 Revised Date:

27 October 2016

Accepted Date: 15 December 2016

Please cite this article as: P. Zhang, T. Zou, J. Zhao, P. Zheng, J. Chen, Diffusion and retention of hydrogen in vanadium in presence of Ti and Cr: First-principles investigations, Journal of Nuclear Materials (2017), doi: 10.1016/j.jnucmat.2016.12.013. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Diffusion and retention of hydrogen in vanadium in presence of Ti and Cr: First-principles investigations Pengbo Zhang1, 3*, Tingting Zou2, Jijun Zhao3, Pengfei Zheng4, Jiming Chen4

2

Department of physics, Dalian Maritime University, Dalian 116026, China.

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1

Information Science and Technology College, Dalian Maritime University, Dalian 116026, China

3

Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Dalian University of Technology), Ministry of Education, Dalian 116024, China. 4

Abstract

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Southwestern Institute of Physics, Chengdu 610041, China.

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We systemically investigated diffusion and retention of hydrogen (H) in vanadium (V) in presence of Ti/Cr and determined the stability of Hn clusters and Hn-vacancy clusters (n=1-6) near Cr/Ti using first-principles calculations. H prefers a tetrahedral site near Ti than other interstitial sites. H-Cr interactions have a weak repulsion contrarily H-Ti interactions have a weak attraction. Kinetically, H diffusion barrier decreases towards Ti, while it increases towards Cr. Ti and Cr block H

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mobility in V alloys. Moreover, Hn Ti clusters are quite stable while HnCr clusters are less stable. Ti enhances H retention by acting as a trapping site for multiple H atoms in similar with vacancy, and a Ti atom can trap at least six H atoms. The stability of

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H-vacancy-Cr/Ti complexes and vacancy-Cr/Ti trapping for multiple H atoms are discussed. The findings are valuable for understanding the mechanism of H bubble

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nucleation and H embrittlement under irradiation.

Keywords: H retention; diffusion; vanadium alloys; first principles

*

Corresponding authors. Tel.: +86 411 84724335; E–mail: [email protected]. 1

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1. Introduction Hydrogen (H) retention has significant impacts on the physical and mechanical properties of metals and alloys [1-3], especially fission and fusion reactor materials.

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Under 14 MeV neutrons irradiation in the fusion reactors, large amounts of H impurities and vacancy defects would be produced continually in the structural materials [4, 5], H bubble and H embrittlement are extremely serious problem.

Low-activation V-Cr-Ti alloys are regarded as promising structural materials in future

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fusion reactors owing to their excellent resistance to neutron irradiation, superior high-temperature mechanical properties, and high compatibility with liquid lithium blanket [5-7]. To elucidate H effects on the properties of V-Cr-Ti alloys under

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irradiation, knowledge about the atomistic mechanism of H-metal interactions is of great importance.

Previous observations from neutron/ion irradiation and implanted H experiments [1-3, 8-14] that H atoms are trapped by vacancies, dislocations, and grain boundaries, forming complex clusters (like H-vacancy) and blocking the mobility of these defects

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within the host lattices, finally cause H embrittlement and swellings of pure V and V alloys. For instance, Neutron irradiation experiments [8] demonstrated H in the V alloys caused solid solution hardening in correlation with H diffusion, and the alloys have strong sensitivity to hydrogen embrittlement. The tensile experiments from Chen

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et al. [10] observed that the alloy could stands high level H concentration of more than 215 wppm without significant loss in the ductility in V-4Cr-4Ti alloy. Tensile

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experiments from Aoyagi et al. [3] demonstrated that H embrittlement is more serious in pure V than its alloys and this effect was attributed to H diffusion and hydride formation. Therefore, the alloying elements play an important role in H diffusion and H embrittlement. In fact, the fundamental science underlying the mechanisms of H embrittlement and H bubbles are still poorly understood. First-principles calculations have been devoted to investigate the behavior of H in metals and alloys. Recent studies [15, 16] show that H atoms in bulk V favor the tetrahedral interstitial sites and can diffuse rapidly between the tetrahedral interstitial sites due to very low migration barrier (about 0.07-0.08 eV), in similar with many bcc 2

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metals (like Fe [17] and W [18]). Interaction between H and vacancy are a strong attraction while H-H interactions have weak attractions. A monovacancy can accumulate six H atoms and not form H2 molecule [19-21], thus vacancies can act as a

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trapping site for multiple H atoms. The theoretically predictions show that the formation of H bubbles occur under sufficiently high internal pressure (in the magnitude of GPa) in well agreement with the DFT results of H in other metals [13,

22]. Recent studies of H in V alloys show that single H atoms prefer to occupy a

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tetrahedral interstitial site surrounded by Ti atoms [23-25], indicating that the retention and diffusion of H in the alloys are different from H in pure V. However, the

studies of the interaction between H and alloying elements and its relationship with H

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embrittlement in pure V and V-Cr-Ti alloys with vacancy defects are rare in the literature.

To explain the role of alloying elements in H retention and H embrittlement, it is important to understand how H diffusion and H bubble formation are affected by the presence of Cr or Ti. This rather complex problem is difficult to address both

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experimentally and theoretically. Of course, He effects are still very important on the fusion materials under irradiation. we also investigated the effect of alloying elements of Cr or Ti on He diffusion and segregation in V alloys, which has been already reported in a parallel paper [26]. Thus, in this work, using first-principles calculations

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we systemically investigated the diffusion and retention of hydrogen in V in presence of Ti/Cr and the stability of Hn clusters and Hn-vacancy clusters (n=1-6) near Cr and

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Ti. We first calculated the H-Cr/ H-Ti interaction as a function of the distance and migration barrier for H moving to Cr or Ti via optimal diffusion paths. The stability and atomic structures of small Hn-Cr and Hn-Ti clusters (n=1-6) are determined by calculating solution energies in comparison with Hn clusters in pure V. We finally investigated effect of Cr/Ti addition vacancy trapping for multiple H atoms and the stability of H-vacancy complexes. The findings show that Ti can act as a trapping site for multiple H atoms similar with vacancy from thermodynamically and kinetically, which give a reference to elucidate the mechanism of H bubble nucleation and H embrittlement under irradiation. 3

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2. Computational methods and models All calculations were performed using density functional theory (DFT) and the plane-wave pseudopotential approach [27, 28], as implemented in the Vienna Ab

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initio Simulation Package (VASP) [29, 30]. We adopted the generalized gradient approximation (GGA) with the Perdew and Wang (PW91) functional [31] for the

exchange-correlation interaction and the projector-augmented wave (PAW) potentials

[30, 31] for the ion-electron interaction. A 128-atom bcc supercell (4×4×4 unit cells

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containing a Cr or Ti atom) of vanadium solid was used and the cutoff energy of the

planewave was set as 500 eV. The Brillouin zones were sampled with 3×3×3 k points by Monkhorst-Pack scheme [32]. The smearing set used the method of

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Methfessel-Paxton order 1 and the width of the smearing is 0.1 eV. All geometries and atomic positions at constant volume were fully relaxed until the force on each atom is less than 0.005 eV/Å. The climbing image nudged elastic-band (CI-NEB) method [33, 34] is used to determine the minimum energy paths and diffusion barriers of H in bulk. Five intermediate structures (images) between the initial and final configurations are

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constructed by linear interpolation. All images are relaxed until the force on each atom in each image is less than 0.01 eV/Å.

The solubility of H in V bulk containing a X atom (X = Cr, Ti) can be characterized by the solution energy, Esol, defined as

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Esol (H) = E(1X,nH) − E[1X] − nE(H2)/2,

(1)

where E(1X,mH) are the energies of the supercell with nH atoms and a X atom; E[1X]

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is the energy of the supercell with 1X atom; E(H2) is the energy of a H2 molecules in vacuum (−3.4 eV from our calculations). Similarly, for a hydrogen-vacancy-X

complex, solution energy of multiple H trapped in the presence of a vacancy in V-X system is defined as:

Esol (H) = E(VA+X,nH) − E[VA+X] − nE(H2)/2,

(2)

where E(VA+X,nH) or E[VA+X] is the energy of simulation supercell with a vacancy and n H atoms or no H. By definition, positive solution energy denotes endothermic process, while negative energy denotes exothermic. Binding energy between A and B can be obtained by, 4

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Eb (A,B) = E(A+B) + E(bulk) − [E(A) + E(B)]

(3)

By definition, a negative binding energy means an attractive interaction of two defects and a positive binding energy means a repulsive interaction.

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For the light elements like H, zero-point energy (ZPE) effect plays a significant role in the dissolution behavior inside host lattice. Our test calculations yield the ZPE

values of 0.233 eV and 0.213 eV for H atom at the T-site and O-site, respectively.

Therefore, ZPE has a significant effect on the absolute solution energies of H in bulk

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V, however, the energy difference between ZPEs at both sites is quite small about 0.02 eV, so that the preferential site for H remains unchanged after ZPE correction.

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3. Results and discussion

First, we briefly compare typical point-defects with experimental and theoretical results in the literature. The most stable site for a single H atom is the tetrahedral interstitial (T-site) with solution energy with Esol=−0.384 eV in pure V from our calculations, and followed by the octahedral interstitial site (O-site) with Esol=−0.260

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eV, which is in good agreement with the heat of solution of −0.36±0.3 eV from early experimental measurements [35-37] and previous DFT calculations (−0.38 eV and −0.26 eV [21], −0.37 eV and −0.23 eV [15], respectively). The minor differences are due to different energy cutoffs (500eV versus 350 eV) in the respective calculations.

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Calculated formation energy of monovacancy (VA) and divacancy is 2.139 eV and 4.123 eV, which is in satisfactorily consistent with the experimental data of 2.2±0.4

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eV and 3.7±0.8 eV [38].

3.1. H interaction with Cr and Ti in vanadium To elucidate H retention and segregation in the presence of Cr and Ti in V, we

investigated H solution at different sites in the V-Cr system (V127Cr1) and V-Ti system (V127Ti1). We put one H atom into at a T-site or a O site near Cr or Ti, and various T-site with increasing distances of H-Cr or H-Ti (from 2.5 Å to 8.0 Å). Calculated H solution energies with the distances are shown in Fig. 1. Apparently, the

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addition of Cr enhances H solution energy contrarily Ti reduces H solution energy, here all negative solution energies indicate that H is energetically favorable to enter both V-Cr and V-Ti systems from the external environment.

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In the V-Cr system, by looking at the distances of the incorporated H atom to Cr, one clearly observes that H at the T-site near Cr has significantly higher solution energy (with Esol= −0.318 eV) than any far away T-sites (Esol=−0.352 to −0.395 eV),

which also is larger than −0.384 eV for H in pure V. The O-site near Cr for H

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(Esol=−0.241 eV) is less favorable than far O-site due to its energy increasing about

0.10 eV. Thus, H solution near Cr is unfavorable in the V-Cr system energetically. Fig. 1 shows H solution energy basically decreases as a function of H-Cr distance in the

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V-Cr system. We observed that the solution energy decreases about 0.07 eV when H-Cr distance increases from 1.7 Å to 5.0 Å. With greater than 5.0 Å, the magnitude of solution energy basically keeps unchanged (about 0.003-0.008 eV ) and is close to the value of H in pure V. From the viewpoint of thermodynamics, H solution becomes more difficult in the region of Cr due to higher the heat of solution.

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In the V-Ti system, the first nearest-neighbor T-site near Ti for H is the lowest energy configuration with solution energy of −0.446 eV and equilibrium H-Ti distance of 1.860 Å, and followed by the second, third and fourth nearest-neighbor T-site with solution energies of −0.438, −0.406, and −0.398 eV, respectively. Above

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the four configurations are more energetically favorable than far away from T-site (or T-site in pure V). And, H at the O-site near Ti is more slightly favorable than far

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O-site by 0.045 eV. In Fig. 1, we clearly observed that H in Ti region is always more stable than far away from T-site when H-Ti distances keep in the order of 1.7 Å to 4.0 Å. With greater than 4.0 Å, the magnitudes of solution energy are gradually close to the value of H at T-site in pure V. Namely, the space of about diameter 8 Å (Ti as center,) can attract H atoms. From the thermodynamics point of view, H solution is more favorable in the region of Ti in the dilute V-Ti alloy. In general, the H solution energy decreases with decreasing distance in the V-Ti system, showing that H segregation towards the region of Ti is energetically favored. With respect to the T site in pure V, about 0.062 eV is gained by H atoms at the T site 6

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near Ti. In contrast, the H solution energy increases with decreasing distance in the V-Cr system, indicating that H tends to keep away from the region of Cr. To compare interaction strength between H and Cr/Ti, we also calculated binding energy

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according to equation 3. The results show there is a weak attraction of H-Ti with their distances in the order of 1.7-4.0 Å, while H-Cr interaction has a weak repulsion. Thus,

we suggested that Ti addition enhances H retention while Cr addition blocks H retention in the V-Cr-Ti alloys.

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We now consider H solution properties for the systems containing more than one

Cr or Ti alloy atom because the real alloy behavior may depend on the situations involving (many) more alloy atoms. When there is one/two/three Cr or Ti atoms

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surrounding the interstitial H, H solution energies at the T-sites and O-sites are determined, as shown in Fig.2. Apparently, as Cr concentration increases, H solution energy at both T-sites and O-sites overall increases from -0.318 eV for H near one Cr atom to 0.227 eV for H near three Cr atoms. Contrarily, as Ti concentration increases, H solution energy basically decreases from -0.446 eV for H near one Ti atom to 0.495

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eV for H near three Ti atoms. Thus, H impurities prefer to occupy in the Ti region. This proves that Ti can attract H impurities energetically whereas Cr results in a repulsion interaction of H impurities in the V-Cr-Ti alloys.

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3.2.H diffusion in vanadium with Cr or Ti

As discussed in the previous section, H is favorable to segregate to Ti region and

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keep away from Cr region thermodynamically. To clarify how H diffusion is affected in the presence of Cr or Ti kinetically? We determined H diffusion barrier towards a Cr/Ti atom via possible paths of H from a far fifth nearest-neighbor T-site (5NN site as site A) gradually diffusing to a first nearest-neighbor T-site (1NN site as site F) near Cr or Ti using the CI-NEB method, here seven sites are stable T-sites, as displayed in Fig.3 and Fig. 4. For H diffusing to Cr in Fig. 3, it is found that H migration barrier sharply increases to 0.162 eV via diffusion path D→E, while the magnitude of energy barrier is close for H diffusing via path A→B→C→D, corresponding to 0.087, 0.085, and 7

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0.076 eV, respectively. A second high barrier of 0.102 eV is observed for H diffusing from site E to site F near Cr (as two 1NN T-sites near Cr). By contrast, for H diffusing to Ti in Fig. 4, H migration barrier sharply decreases to 0.004 eV for H diffusing from

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site D to site E near Ti, and a second low barrier is 0.040 eV for H diffusion near Ti via path E→F. Such low barrier near Ti means H can diffuse toward Ti region from far T-site speedily. For H diffusing from site A to site D, the energy barriers are quite close via path A → B → C → D, corresponding to 0.063, 0.069, and 0.075 eV,

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respectively. Besides, if H escapes from Ti region via path E→D→C, H will

overcome a quite high barrier about 0.116 eV. From the kinetics point of view, Cr significantly increases H migration barrier, contrarily Ti reduces H migration barrier.

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Thus, we concluded that H prefers to diffuse toward Ti region, while Cr blocks the mobility of H by diffusion kinetically. In summary, H retention will tend to accumulate in the region of Ti in V-Cr-Ti alloys. 3.3.Stability of H clusters near Cr or Ti

We turn to investigate the stability of H clusters in presence of Cr and Ti, H is

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placed into T-site in the vicinity of Cr/Ti from one to six one by one, a series of possible structures are considered. We calculated solution energies of small Hn clusters (n=1-6) near Cr /Ti in dilute Ti-V /Cr-V alloy in comparison with Hn clusters

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in pure V. Total solution energies and the nth H solution energies of the most (type I) and second (type II) stable Hn clusters as a function of H numbers (n=1 to 6) are

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summarized in Fig. 5. Generally speaking, the Hn clusters residing in Ti region are energetically more stable than in the Cr region and pure V. It also shows that there are two different modes of type I and type II in H clustering processes. We specifically discuss the most stable Hn clusters (type I) as follows. In the Ti region, it is found that

the nth H solution energy keeps in the order of -0.446 ~ -0.422 eV with n=1 to 6, which is always lower than single H at the T-site in pure V (-0.384 eV). In other words, the aggregation of multiple H in the Ti region is more stable than separated H atoms in bulk and Hn clusters in pure V. This means that a Ti atom can trap at least six H atoms, forming stable H6Ti cluster. By contrast, the nth H solution energy in the Cr 8

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region (-0.337~-0.286 eV) are always higher than single H at the T-site in pure V (see Fig.5), indicating that all Hn clusters are unfavorable in the Cr region. In pure V, the Hn clusters with n=2-4 are slightly more stable than separated H at the T-sites

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energetically. With n＞4, the Hn clusters will be unfavorable. The analysis of atomic structures shows the bond lengths of H-Ti are slightly larger than H-Cr for all the

cases. Local expansion induced by H6 clusters near Ti is about 9% while it is about 7% for H6 clusters near Cr.

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Furthermore, we explore Ti trapping mechanism for multiple H atoms. Fig. 6 plots the most (type I) and second (type II) stable configurations of HnTi1clusters with n=1-6 after relaxations. For the two types of H clustering, all type I configurations are

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slightly more stable type II, the energy difference is very small and less than 0.052 eV. Such small energy differences indicate that both configurations are coexistence in the actual materials. The combination of the energetic and diffusion properties of H in bulk above, we concluded that Ti can act as a trapping site for H impurities and further form stable HnTi clusters in V-Cr-Ti alloys, while the formation of Hn clusters

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in the Cr region is almost impossible. These findings indicate that Ti addition enhances the capability of H retention in Cr-Ti-V alloys, in well agreement with experimental observations [10] that the Cr-Ti-V alloy could stands high H concentration of more than 215 wppm without significant loss in the ductility. From

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both theoretical and experimental points of view, H retention can weaken the bonding strength of V-V in bulk, and further lead to H embrittlement under certain H

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concentration. In Cr-Ti-V alloys, since many H impurities are attracted in the Ti region, the weakening of the V-V bonding by H atoms would be reduced markedly, thus keeping the ductility of the V alloys basically. 3.4.Stability of H-vacancy-Cr/Ti complex Irradiation induced vacancies can nonetheless exist and trap multiple H atoms under irradiation. The presence of vacancies in V materials plays a significant role in H embrittlement and H bubble formation. The calculations above show Cr/Ti addition cause a certain effect on solution properties of H in the dilute V alloys. To understand 9

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the effect of Cr/Ti on stability of H-vacancy complex in the configurations V-Cr-Ti alloys, we created a vacancy near Cr or Ti by removing a V atom. More H atoms are placed into the vacancy space one by one (up to eight) and relaxed the system to find

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the optimal position for every H atom, including a series of possible T-sites and O-sites near the vacancy and vacancy center.

Fig. 7 and Fig. 8 present representative atomic configurations and corresponding

solution energies of HnVa (n=1-6) clusters in the Cr region and Ti region after full

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relaxation, respectively. By comparison, we observed that the most stable configurations of HnVa clusters with n=3-5 are different for Cr or Ti addition. Single

H and double H trapped in the vacancy possess same stable structures, corresponding

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to solution energies of -0.708 eV and -1.437 eV near Cr (-0.684 eV and -1.418 eV near Ti), respectively. Upon optimization, single H atom at any T-site near vacancy-Cr/Ti is unstable and move into close O-site, in accordance with H in vacancy. Meanwhile, we determined the stability of a H2 molecule placed at the vacancy near Cr/Ti. Energetically, the H2 molecule in a vacancy is unstable and would

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dissociate into two separated H atoms with the equilibrium distance of about 2.5 Å (much longer than ~0.75 Å for gaseous H2 molecule in vacuum). Moreover, the equilibrium H-H distances are in the orders of 1.92~2.52 Å in the vacancy space of V within a Cr or Ti, while the distances of H-metal (Cr/Ti/V) are about 2.05~2.14 Å.

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This indicates that two H atoms cannot form a H2 molecule in small H-vacancy clusters even if Cr or Ti existence.

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To further understand the effect of Cr/Ti on vacancy trapping for multiple H atoms, we define a trapping energy Etrap to characterize the energy required for

moving an H atom into the monovacancy space from a remote T-site. For the first H atom (n=1) trapped in the vacancy and in the case of multiple H atoms (n>1). The trapping energy is obtained by [39]: Etrap (1) = E(VA,H) − [E(VA,HT),

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and Etrap (n) = E(VA,nH) − E[VA,(n−1)H)] − [E(VA,HT) − E(VA)],

(5)

respectively. Here E(VA,H) is the energy of the supercell with a vacancy and a H 10

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atom; E(VA,nH) is the energy of the supercell with a vacancy and n H atom; [E(VA,HT) is the energy of the supercell with a vacancy and a tetrahedral H far from the vacancy; E(VA) is the energy of the supercell with a vacancy. By definition, a

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negative trapping energy indicates exothermic process. Fig. 9 shows the trapping energy for each H atom placed into the monovacancy near Cr or Ti in comparison with H in a monovacancy of pure V. We observed that the trend of vacancy trapping for H impurities is unchanged in the presence of Ti or

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Cr. Only trapping energy per H has some small changes (less than 0.15 eV). A monovacancy-Cr/Ti can accommodate six H atoms in same with H in a monovacancy of pure V, corresponding to negative trapping energy in order of -0.351~ -0.081 eV.

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More than six H atoms, the trapping energy sharply increases and becomes positive values (about 0.601~0.858 eV) for these three cases, indicating that these Hn-vacancy clusters (with n>6) are always less favorable energetically even if Cr and Ti addition. 4. Conclusions

First-principles calculations have been carried out to investigate diffusion and

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retention of hydrogen in V in presence of Ti/Cr and the stability of Hn clusters and Hn-vacancy clusters (n=1-6) near Cr or Ti in a dilute V alloy. We first calculated H solution energy and binding energy with the H-Cr/H-Ti distances. Energetically, H

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prefers to reside in the tetrahedral sites near Ti with solution energy of −0.446 eV. The H-Cr interactions have a weak repulsion (0.066 eV) contrarily H-Ti interactions

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have a weak attraction (-0.062 eV). Kinetically, CI-NEB calculations show that H migration barrier sharply decreases to 0.004 eV from 0.063 for H diffusing to Ti, while it increases to 0.162 eV from 0.085 eV for H diffusing to Cr. This indicates that Cr and Ti addition hinder H mobility in the V alloys. In the other hand, we determined the effect of the alloying elements Cr and Ti on

H clustering in the bulk. The Hn Ti clusters are quite stable while HnCr clusters are less stable with respect to Hn clusters energetically. Importantly, Ti can act as a trapping site for multiple H atoms in similar with vacancy, but the trapping capability for H is weaker than vacancy defects. A Ti atom can trap at least six H atoms alone 11

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with exothermic process. This indicates Ti enhances the capability of H retention in V-Cr-Ti alloys in well agreement with experimental observations. The stability of H-vacancy-Cr/Ti complexes shows small change compared with Hn clusters in pure V.

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A monovacancy near Cr/Ti still traps six H atoms, only the values of trapping energy have some small fluctuations. The findings give a reference for understanding the mechanism of H bubble nucleation and H embrittlement under irradiation.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (11305022), the Liaoning Province Doctor Scientific Research Foundation of China

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(201501189), the China Postdoctoral Science Foundation (2015M581325), the National Magnetic Confinement Fusion Energy Research Project of China (2015GB118001), and the Fundamental Research Funds for the Central Universities

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of China (3132016126).

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[27] P. Hohenberg and W. Kohn, Phys. Rev. 136 (1964) B864. [28] W. Kohn and L. J. Sham, Phys. Rev. 140 (1965) A1133. [29] G. Kresse and J. Hafner, Phys. Rev. B 47 (1993) 558. [30] G. Kresse and D. Joubert, Phys. Rev. B 59 (1999) 1758.

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[31] P. E. Blöchl, Phys. Rev. B 50 (1994) 17953. [32] H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13 (1976) 5188.

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Captions Fig. 1. (Color online) H solution energies with the H-Cr and H-Ti distances in V-Cr and V-Ti systems. The dashed line denotes H solution energy at T- site in pure V.

Cr or Ti atoms in comparison with the data of H in pure V.

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Fig. 2. (Color online) H solution energies at the T-sites and O-sites near one/two/three

Fig. 3. (Color online) Migration barrier and diffusion path for H moving towards a Cr atom from a 5NN T-site to a 1NN T-site near Cr. Sites E and F are two equivalent

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1NN T-sites near Cr. Site A, B, C and D are the 5NN, 4NN, 3NN, and 2NN T-site of the Cr, respectively.

Fig. 4. (Color online) Migration barrier and diffusion path for H moving towards a Ti

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atom from a 5NN T-site to a 1NN T-site near Ti. Sites E and F are two equivalent 1NN T-sites near Ti. Site A, B, C and D are the 5NN, 4NN, 3NN, and 2NN T-site of the Ti, respectively.

Fig. 5 (Color online) Total solution energies and the nth H solution energies of the (a) most and (b) second stable Hn clusters with n =1-6 in the Cr and Ti region in

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comparison with Hn clusters in pure V, respectively. The insert graphics present H clustering by both type I (a) and type II (b). The dashed line denotes H solution energy at T- site in pure V.

Fig. 6. (Color online) Atomic configurations of HnTi clusters with n=1-6 after

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relaxation: the (a) most and (b) second stable configurations. Blue, green and small red balls denote V, Ti and H atoms, respectively.

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Fig. 7. (Color online) Atomic configurations of HnVa clusters near Cr with n=1-6 after relaxations. Blue, orange and small red balls denote V, Cr and H atoms, respectively.

Fig. 8. (Color online) Atomic configurations of HnVa clusters near Ti with n=1-6 after relaxation. Blue, green and small red balls denote V, Ti and H atoms, respectively. Fig. 9. (Color online) Trapping energy for each H atom added to the monovacancy near Cr or Ti in comparison with H in a monovacancy of pure V. The dashed line of zero energy denotes H solution energy at T- site in pure V as reference.

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Highlights

1. Ti enhances H retention by trapping for multiple H atoms in similar with vacancy.

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2. H prefers the tetrahedral sites near Ti than other interstitial sites.

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3. H diffusion barrier decreases towards Ti, while it increases towards Cr.