First-principles study on the dehydrogenation characteristics of LiBH4 modified by Ti

Accepted Manuscript First-principles study on the dehydrogenation characteristics of LiBH4 modified by Ti Xiaohua Mo, Weiqing Jiang, Shilong Cao PII: DOI: Reference:

S2211-3797(17)30487-4 http://dx.doi.org/10.1016/j.rinp.2017.08.053 RINP 903

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Results in Physics

Received Date: Revised Date: Accepted Date:

23 March 2017 3 August 2017 28 August 2017

Please cite this article as: Mo, X., Jiang, W., Cao, S., First-principles study on the dehydrogenation characteristics of LiBH4 modified by Ti, Results in Physics (2017), doi: http://dx.doi.org/10.1016/j.rinp.2017.08.053

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First-principles study on the dehydrogenation characteristics of LiBH4 modified by Ti Xiaohua Mob Weiqing Jianga∗ a

Shilong Caoa

Guangxi Key Laboratory for Relativistic Astrophysics, School of Physical Science & Technology, Guangxi University, Nanning 530004, China b

College of Science, Guangxi University for Nationalities, Nanning 530006, China

Abstract The dehydrogenation characteristics of LiBH4 modified by Ti are investigated by first-principles calculations. Ti doping is shown to kinetically favor H-desorption, by reducing the energy cost that H atom needs to release from the bulk. This improvement in H-desorption may be ascribed to the weaker bonding interaction among Li, B and H atoms, the formation of Ti-H bond as well as the metal-like/metallic character of LiBH4 -Ti systems. Ti is considered to be a good candidate to improve the dehydrogenation properties of LiBH4 in the case of energy cost for H-desorption, but the occupation energy for Ti dopant should be reduced for practical application. Keywords: LiBH4; Ti doping; First-principles calculations; Dehydrogenation

1 Introduction Lithium borohydride (LiBH4) has recently attracted extensive attention as a solid-state hydrogen storage material due to its high gravimetric hydrogen density [1]. This material can desorb about 14 wt% hydrogen via the following thermal decomposition: 3 LiBH 4 → LiH + B + H 2 2

(1)

However, LiBH4 decomposed at temperature above 400 ℃, and then recombined at extremely elevated conditions of 600 ℃ and 35 MPa H2 pressure [2, 3]. It is essential to destabilize LiBH4 thermodynamically as well as enhance dehydrogenation kinetically in order to develop a practical H-storage material. Doping is known to be an effective method for improving the H-exchange thermodynamics and kinetics of LiBH4 . For example, Vajo et al. [4, 5] obtained an enhanced reversibility of H2 sorption when MgH2 was added into LiBH4, which was ascribed to the formation of MgB2 on dehydrogenation that stabilized the dehydrogenated state and, thereby, destabilized LiBH4. Fang et al. [6] mixed LiBH4 with Ti

*

Corresponding author, E-mail address: [email protected] (Weiqing Jiang) 1

halides (TiF3 or TiCl3) by mechanical milling, and found that Ti halides could markedly improve the reversibility of dehydrogenation. The in situ formation of the catalytically active Ti hydride in the reaction of halide additives with LiBH4 was the common reason. Liu et al. [7] systematically studied the dehydrogenation/hydrogenation properties of LiBH4 -xMg(OH)2 composites with x=0, 0.1, 0.2, 0.3, 0.5, 1.0 and 2.0, and reported that LiBH4-0.3Mg(OH)2 composite exhibited optimal dehydrogenation properties and good cycling stability, releasing ~9.6 wt% hydrogen in total with an onset temperature of 100 ℃ and recharging ~4.7 wt% hydrogen into dehydrogenated sample at 450 ℃ and 100 bar of hydrogen. Ma et al. [8] had improved the hydrogen storage properties of LiBH4 by doping with a porous Li3 BO3 additive. They reported that LiBH4-33 wt% Li3 BO3 composite exhibited an acceptable hydrogenation/dehydrogenation rate, high hydrogen storage capacity and superior reversibility, which was attributed to the active sites of Li + and B3+ from Li3 BO3, thus exhibiting a catalytic effect in the decomposition and formation of [BH4]-. Although an enhanced hydrogenation/dehydrogenation capability of LiBH4 has been achieved by doping with appropriate additives, its performance has not yet satisfied the requirements for practical applications. To further improve the performances of LiBH4, understanding the electronic structure mechanisms of LiBH4 with dopant should be of great interest. Recently, Nakamori et al. [9, 10] had systematically investigated the thermodynamical stabilities for series of metal borohydrides M(BH4 )n, and proposed that the hydrogen desorption temperature of M(BH4)n was inversely proportional to the Pauling electronegativity of metal M. According to this viewpoint, a series of double-cation borohydrides Lim-nM(BH4)m, in which M had larger electronegativity than Li, had been produced experimentally and theoretically to precisely tailor the thermodynamic stability of LiBH4 [11-14]. In the present work, Ti as a dopant is added into LiBH4 bulk by occupation of Li atom, B atom and interstitial sites, producing double-cation Ti-containing borohydrides. We expect LiBH4-Ti compounds can exhibit enhanced hydrogen desorption capability compared to pristine LiBH4, since Ti has larger Pauling electronegativity (1.54) than Li (0.98) [15], furthermore, metal Ti and Ti-containing compounds are reported to have a positive impact on the dehydrogenation of LiBH4 [6, 16-20]. We will investigate the hydrogen-metal interactions and the stability of Ti-doped LiBH4 in detail by first-principles density-functional theory calculations, aiming at clarification of the dehydrogenation mechanisms of LiBH4-Ti systems. 2 Computational details First-principles calculations were performed using the Cambridge Serial Total Energy Package (CASTEP) code based on density functional theory (DFT) with ultrasoft pseudopotentials [21]. The generalized gradient approximation of Perdew-Wang 91 (GGA-PW91) was introduced to describe the exchange-correlation energy [22]. The configurations Li 1s22s1 , B 2s22p1, H 1s1 and Ti 3s23p63d24s2 were treated as valence electrons. A series of test calculations using different cutoff energy and k-point sampling were performed, and finally, a high cutoff energy of 800 eV and a fine k-point sampling of 2×3×2 were chosen to 2

make the total energy converge less than 3 meV/atom. Structure relaxations of lattice constants and atomic positions were carried out using the Broyden Fletcher Goldfarb Shanno (BFGS) method [23] until the residual force, stress and displacement were below 0.05 eV/Å, 0.1 GPa and 0.002 Å, respectively. The calculations of single-point energy and electronic structure were followed by cell optimization with self-consistent-field (SCF) tolerance 2.0×10-5 eV/tom. Spin polarization is used only for the systems with transition metal Ti. At ambient conditions, LiBH4 is agreed to crystallize orthorhombic structure with space group Pnma [24]. In this LiBH4 crystal, one Li atom, one B atom and three symmetry-independent H atoms (H1, H2 and H3) occupy the 4c (Li) (0.157, 0.25, 0.102), 4c (B) (0.304, 0.25, 0.431), 4c (H1) (0.9, 0.25, 0.956), 4c (H2) (0.404, 0.25, 0.28) and 8d (H3) (0.172, 0.05, 0.428) sites [24]. Full relaxations of pure LiBH4 gave lattice parameters as a=7.255 Å, b=4.398 Å, c=6.727 Å. These values were comparable to the experimental findings (a=7.179 Å, b=4.437 Å, c=6.803 Å [24]) within the deviation of less than 1.2%. Using the available optimized structural data, a 1×2×1 supercell was built by stacking the LiBH4 unit cell along b-axis. The 1×2×1 supercell with lattice parameters of a=7.255 Å, b=8.795 Å and c=6.727 Å (Table 1) contains 8 LiBH4 formula units (8 Li atoms, 8 B atoms and 32 H atoms), and can be represented as Li8B8H32 (M0), as shown in Fig. 1. In this figure, there exists a [BH4] group, in which the four H atoms surrounding a B atom are labeled with HA, HB, HC and HD. Ti-containing systems were introduced by substituting one Li atom at (0.338, 0.375, 0.613) (marked with S1, Fig. 1), one B atom at (0.689, 0.375, 0.573) (marked with S2, Fig. 1) and one interstitial site at (0.5, 0.5, 0.5) (marked with S3, Fig. 1) with one Ti atom. These Li-, B- and interstitial site-substituted systems were represented as Li7 TiB8H32 (M1), Li8 B7TiH32 (M2) and Li8B8TiH32 (M3), respectively. 3 Results and discussion 3.1 Geometry optimization In the present work, Ti as a dopant is designed to add into LiBH4 by substitution for Li atom, B atom and interstitial site, producing Li-, B- and interstitial site-substituted systems, respectively. Geometry optimization was performed for all Ti-doped systems with the optimized lattice parameters (Rop) shown in Table 1. Ti addition breaks the symmetry of LiBH4, leading to the expansion in lattice parameters, and subsequently in cell volume. This may originate from the larger atomic radius of Ti (1.32 Å) compared to that of Li (1.23 Å), B (0.82 Å) and interstitial site (a point without a size, 0 Å), and can provide more sites for H diffusion. Generally, the lattice parameters will become either smaller or larger as spin polarization calculation is performed [25, 26]. Referring to the B-substituted compound (M2) in our works, spin polarization calculation leads to the decrease in lattice parameters, and subsequently the contraction in cell volume from 462.986 Å3 (without spin polarization) to 457.526 Å3 (with spin polarization). 3.2 Occupation energy and dehydrogenation energy To estimate how much energy is required (energy cost) for Ti dopant in LiBH4, the occupation energy, Eocc, is calculated 3

by the following reaction: Eocc = E ( Li8−x B8− yTix + y + z H 32 ) − E ( Li8 B8 H 32 ) − [( x + y + z ) E (Ti) − xE ( Li) − yE ( B )]

(2)

where Li8-xB8-yTix+y+zH32 are the studied systems, Li8B8H32 (x=0, y=0, z=0), Li7TiB8 H32 (x=1, y=0, z=0), Li8B7TiH32 (x=0, y=1, z=0) and Li8B8TiH32 (x=0, y=0, z=1). E is the total energy of corresponding relaxed-system. Bcc-Li, α-B and hcp-Ti are considered to calculate the total energy, which are -190.14 eV (Li atom), -77.301 eV (B atom) and -1603.89 (Ti atom). Table 1 lists the calculated Eocc for Ti-doped systems. As can be seen, the energy costs to occupy Li atom, B atom and interstitial sites are 3.875, 4.006 and 3.99 eV without spin polarization, and are 3.864, 3.868 and 3.881 eV with spin polarization, respectively. Ti considered here tends to occupy Li atom site relative to B atom and interstitial sites, and this trend is relatively evident without spin polarization, along with the data in Table 1. The occupation energy is reduced slightly when spin polarization calculation is performed, due to a slight decrease in total energy of relaxed-Li8-xB8-yTi x+y+zH32 systems (M1, M2 and M3) from -4076.06 eV (M1), -4188.768 eV (M2) and -4266.085 eV (M3) without spin polarization to -4076.071 eV (M1), -4188.906 eV (M2) and -4266.194 eV (M3) with spin polarization. Whether or not spin polarization is considered, the incorporation of Ti into LiBH4 bulk, unfortunately, is energetically unfavorable due to high occupation energy (>3.8 eV). The energy cost for Ti dopant in LiBH4 needs to be reduced for practical application. The dehydrogenation energy, Ed , is characterized as the energy cost to quickly remove one H atom from the system [27]. The analysis of dehydrogenation energy is helpful to understand the dehydrogenation behavior of LiBH4 modified by Ti. The dehydrogenation energy is defined as below: Ed = [E ( Li8− x B8− yTix+ y + z H 31 ) +

1 E ( H 2 )] − E( Li8− x B8− yTix+ y+ z H 32 ) 2

(3)

where E(Li8-xB8-yTix+y+zH32) is the same as the previous definition. The energy of H2 molecule, E(H2), is estimated as -31.79 eV using a 10 Å3 cubic unit cell containing two H atoms 0.741 Å apart [28]. This result is very close to the literature values, -31.292 eV [25] and -31.617 eV [29]. Li8-xB8-yTix+y+zH31 is a pseudo-structure in which an H atom is taken away from relaxed-Li8-xB8-yTix+y+zH32 to introduce an H vacancy in bulk. Generally, for a system with a vacancy, the total energy will be minimized as atoms around the vacancy move from their original positions in the vacancy free system [30]. To estimate the lowest energy cost for dehydrogenation, H vacancy-containing Li8-xB8-yTix+y+zH31 should be fully relaxed. Considering the fact that in LiBH4 model (Fig. 1), a B atom is surrounded by four H atoms (labeled with HA, HB, HC and HD) to form [BH4] group, in this work, we will remove each one of the four H atoms from the mother system Li8-xB8-yTix+y+zH32 to introduce HA, HB, HC and HD vacancies. The dehydrogenation energies with different H vacancy (Ed-HA, -HB, -HC and -HD) are listed in Table 1. As can be seen, for LiBH4 alone, whichever H atom (HA, HB, HC and HD) is removed from the bulk, the dehydrogenation energies (Ed-HA=2.429 eV, Ed-HB=2.447 eV, Ed-HC=2.387 eV and Ed-HD=2.383 eV) are similar to each other. However, when Ti is 4

added, a different dehydrogenation energy for HA, HB, HC and HD appears due to the symmetry is broken (as described above), for example, for M1 compound without spin polarization, the dehydrogenation energies are Ed-HA=0.074 eV, Ed -HB=-0.002 eV, Ed-HC=0.46 eV and Ed-HD=0.02 eV. Additionally, the dehydrogenation energies are significantly reduced by adding Ti, especially as B is substituted by Ti without spin polarization, the dehydrogenation energies drop down to be Ed-HA, -HB, -HC and -HD=-0.303, -0.009, -0.005, and -0.791 eV, respectively. B-substituted compound (M2) with negative dehydrogenation energies is expected to show a spontaneous dissociation of H atom [30]. It is verified experimentally that Ti additive can serve as a catalyst for self-decomposition of LiBH4 [16]. Here, the lower dehydrogenation energies with Ti doped in LiBH4 bulk may kinetically favor H-desorption. Similar result also can be obtained as Ti atom locates on LiBH4 surface [18]. It is worth noting that spin polarization significantly alters the dehydrogenation energy, especially as Ti substitutes for B atom, for example, from -0.303 eV (without spin polarization) to 1.221 eV (with spin polarization) for the release of HA atom. The B-substituted compound exhibits lower dehydrogenation energy before spin polarization as compared to that after spin polarization. One reason may be that the larger cell volume of 462.986 Å3 without spin polarization (relative to 457.526 Å3 with spin polarization) can provide more sites for H diffusion. Referring to Ti-doped compounds (M1, M2 and M3), the minimum dehydrogenation energy of -0.002 eV (Ed-HB for M1), -0.791 eV (Ed-HD for M2) and 0.41 eV (Ed-HA for M3) are all obtained without spin polarization (Table 1). 3.3 Electronic structure As described above, for relaxed Ti-doped systems (M1, M2 and M3), the total energy changes slightly before and after spin polarization calculation, and the lowest dehydrogenation energy can be obtained without spin polarization. Thus, spin polarization effect is not obvious on relaxed LiBH4-Ti systems. Here, we will take relaxed-Li8-xB8-yTix+y+zH32 (M0, M1, M2 and M3) without spin polarization as representative systems to investigate their electronic structure, with the aim of understanding the dehydrogenation performances of LiBH4 modified by Ti. Fig. 2 shows the total and partial density of states (TDOS and PDOS) of Li8-xB8-yTix+y+z H32 systems (M0, M1, M2 and M3). The Fermi level (EF) is set at zero energy. Here, density pictures for pure LiBH4 shown in Fig. 2 are very similar to those calculated using the same CASTEP code [31, 32]. As seen in Fig. 2, the two main peaks below the Fermi level are mainly contributed by B s, B p, H1 s, H2 s and H3 s states, exhibiting a strong covalent hybridization between B and H atomic orbits. Li s orbit above the Fermi level overlaps with B s/H s orbits forming Li-B/Li-H bond. Considering the small value of DOS at Li site shown in Fig. 2, the bonding between Li and [BH] exhibits an ionic nature. Noticeably, Ti doping causes the peaks values of TDOS contributed by B s and H s states decrease from 18.735 electrons/eV (M0) to 17.910 electrons/eV (M1), 15.644 electrons/eV (M2) and 16.138 electrons/eV (M3), and by B p and H s states from 29.124 electrons/eV (M0) to 26.531 electrons/eV (M1), 25.547 electrons/eV (M2) and 28.144 electrons/eV (M3). The reduction in the peaks values of TDOS 5

originated from B and H atoms suggests a decreased covalent interaction between B-H. Generally, B-H covalent interaction is believed to be dominant the structural stability of LiBH4 compound. In our work, Ti modifies LiBH4 by reducing B-H bond interaction, which may decreases the stability of LiBH4 , and is undoubtedly beneficial for the decomposition of LiBH4 [30]. As shown in Table 1, Ti-doped compounds are found to exhibit lower dehydrogenation energy than that of un-doped compound. It is also seen from Fig. 2 that Ti tends to interact with its neighboring H and B atoms to form Ti-H and Ti-B bond as Ti p and d electrons overlap with the p electron of B atom and the s electron of H atom near Fermi level. However, in the case of B-substituted system (M2), Ti and B atoms exist in different formula unit with Ti-B bonding length obtained from relaxed-M2 model reaching 4.245-6.768 Å. This long distance between Ti and B (>4.2 Å) will make Ti atom unlikely to interact with its neighboring B atom, so that Ti-B bonding interaction in M2 system can be ignored. Fig. 3 depicts the electronic density contours for Li8-xB8-yTix+y+zH32 systems (M0, M1, M2 and M3) containing Li, B, H or/and Ti atoms. The contour lines shown in Fig. 3 are plotted from 0.003 to 0.3 electrons/Å3 . Obviously, there exist a strong polarized covalent bond between B and H atoms due to a directional feature of charge density distribution around [BH] group, and an ionic bond between Li and B/H atoms owing to a spherical charge distribution around Li atom. With Ti adding, the overlap charge density between Ti and H appears, i.e., Ti-H bond forms. The bonding interaction between Ti and B can be detected in M1 and M3 system, not in M2 system, since an obvious overlap electron cloud between Ti and B is shown in the former, instead of the latter. The absence of Ti-B bond in M2 system may be ascribed to a long distance between Ti and B (>4.2 Å), as described above. These bonding characteristics among Li, B, H or/and Ti atoms described in electronic density contours are in good agreement with DOS analysis. To further understand the bonding interactions among Li, B, H or/and Ti atoms, Mulliken charge analysis of Li8-xB8-yTix+y+zH32 systems (M0, M1, M2 and M3) is carried out on the one hand, and the results are tabulated in Table 2. As can be seen, the average Mulliken charges of Li and Ti are positive, whereas those of B and H are negative. Therefore, Li and Ti play the roles of electron donors, while B and H act as electron acceptors. Although the average gaining charge of H atoms shown in Table 1 increases slightly with the addition of Ti, a decreased gaining charge of H atoms still can be obtained, as noted from the Mulliken charge of H atoms in the range -0.13 to -0.19 e for M0, -0.12 to -0.22 e for M1, -0.11 to -0.44 e for M2 and -0.03 to -0.21 e for M3. The decrease in the gaining charge of H atoms coupled with the average losing charge of Li atoms and the average gaining charge of B atoms will lead to weaker bonding interactions among Li, B and H atoms. In general, the bond order (BO) between atoms is another intuitive way to investigate the bonding feature. Thus, Mulliken population analysis is applied to Li8-xB8-yTix+y+zH32 systems (M0, M1, M2 and M3) on the other hand, including the average bond order (BO), the average bond length (BL) and the scaled bond order (BOs) between atoms. Here, BOs, the average bond order per unit bond length, is a measure of the relative bonding strength between atoms, and can be calculated by the equation BOs=BO/BL [33, 34]. 6

Taking scaled bond order between Li-H (BOsLi-H) in M0 system for an example, BOsLi-H=BOLi-H/BLLi-H, here BOLi-H (the average bond order between Li-H, -0.104 shown in Table 3) and BLLi-H (the average bond length between Li-H, 2.167 Å shown in Table 3) are obtained by averaging bond orders between Li-H from -0.08 to -0.14 in M0 system and corresponding bond lengths from 1.976 to 2.353 Å, respectively. Table 3 lists the BO, BL and BOs between B-H, Li-H, Li-B, Ti-H and Ti-B for Li8-xB8-yTix+y+zH32 systems (M0, M1, M2 and M3). As can be seen, for all studied systems, the average bond order between B-H (BOB-H) is positive, but between Li-H and Li-B (BOLi-H and BOLi-B) is negative, exhibiting a covalent nature between B-H and an ionic nature between Li-H and Li-B [35]. Ti makes a bonding with its neighboring H and B atoms, except the absence of Ti-B bond in M2 system, as noted from the bond order listed in Table 3. The long distance between Ti and B (>4.2 Å) may be one reason for the absence of Ti-B bond in M2 system. Mulliken population analysis supports the density pictures for Li, B, H and Ti atoms described in Figs. 2 and 3. It is worth noting that the scaled bond order between B-H, Li-H and Li-B (BOsB-H, BOsLi-H and BOsLi-B) all decrease with Ti doping due to a decrease in bond order followed with an increase in bond length, suggesting that Ti addition weakens the bonding interaction of B-H, Li-H and Li-B. This may help to explain why the dehydrogenation energy is dramatically reduced with Ti addition (Table 1). As generally accepted, the variation in B-H bond interaction agrees with the dehydrogenation energy calculated via Eq. (3) [14]. In the present case, compared to M1 (BOsB-H=0.651 Å-1, Ed-HB=-0.002 eV) and M3 systems (BOsB-H=0.793 Å-1 , Ed-HA=0.41 eV), the dehydrogenation energy of M2 system (Ed-HD=-0.791 eV) decreases in spite of an increased scaled bond order between B-H (BOsB-H=0.819 Å-1). This is believed attributable to the formation of Ti-H bond, being advantageous to the dehydrogenation of LiBH4 -Ti system, since Ti hydride with catalytic activity is reported to have a positive impact on the reversible H-desorption of LiBH4 [6]. In our work, for M2 system, the relatively stronger is Ti-H bond strength with BOsTi-H=0.387 Å-1, the rather lower is dehydrogenation energy with Ed-HD=-0.791 eV, when compared with those of BOsTi-H=-0.034 Å-1 and Ed-HB=-0.002 eV for M1 system, and BOsTi-H=0.008 Å-1 and Ed -HA=0.41 eV for M3 system (Tables 1 and 3). Fig. 4 illustrates the band structure of Li8-xB8-yTix+y+zH32 systems (M0, M1, M2 and M3). The amplified band structure from -0.2 to 0.2 eV is shown in the inset of Fig. 4. The Fermi level is set to zero. The band gap (Eg), characterized as the gap between the lowest energy of conduction band and the highest energy of valence band, can be obtained from Fig. 4 and is also shown in Fig. 4. Obviously, pure LiBH4 has a nonmetallic character with calculated band gap of 7.019 eV. This result is in good agreement with the previous reports [32]. As Ti occupies Li atom and interstitial sites, the band gap becomes narrower, reaching 0.794 eV for M1 compound and 0.314 eV for M3 compound. These values are within 0-3 eV range (the band gap for a semiconductor) [36], indicating that M1 and M3 compounds have metal-like character. M1 and M3 compounds with metal-like nature will consume less energy for H-desorption compared to M0 compound with nonmetallic nature [31]. Additionally, when Ti substitutes for B atom, the valence and conduction bands overlap considerably and there is no band gap at the Fermi level, as 7

illustrated by the amplified band structure from -0.2-0.2 eV. As a result, B-substituted compound (M2) will exhibit metallic properties, which is also favorable for the improvement of dehydrogenation kinetic of LiBH4 [31]. 4 Conclusions In the present study, Ti is designed to add into LiBH4 by substitution for Li atom, B atom and interstitial site, producing LiBH4-Ti systems. We investigate the effect of Ti on the dehydrogenation of LiBH4 by first-principles calculations using GGA-PW91 method within CASTEP. The properties of LiBH4 have been modified by Ti resulting in favorable H-desorption, which may be ascribed to three facts: (1) the decrease in bonding strength of B-H, Li-H and Li-B tailors the structural stability of LiBH4; (2) the formation of Ti-H bond has a positive effect on the H-desorption of LiBH4-Ti system; (3) the translation from nonmetallic character to metal-like/metallic character with Ti doping is favorable for the decomposition of LiBH4, since Ti-doped compounds with metal-like/metallic character exhibit lower dehydrogenation energy as compared to that in Ti-free compound with nonmetallic character. Ti considered here costs rather high energy to occupy Li atom, B atom and interstitial sites, and this occupation energy should be reduced for practical application. Acknowledgments This work was supported by the National Natural Science Foundation of China (51401056, 51661002), the Natural Science Foundation of Guangxi (2014GXNSFAA118282, 2015GXNSFAA139259), and the high-performance computing platform of Guangxi University.

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Tables:

Table 1 Optimized lattice parameters (Rop), occupation energy (Eocc) and dehydrogenation energy (Ed) of Li8-xB8-yTix+y+zH32 systems (M0, M1, M2 and M3). Dehydrogenation energy with HA, HB, HC and HD vacancies is represented as Ed-HA, -HB, -HC and -HD, respectively. Numbers in brackets are obtained with spin polarization calculations. Rop (Å)

Ed (eV)

System

Eocc (eV) a

b

c

-HA

-HB

-HC

-HD

M0

7.255

8.795

6.727

…

2.429

2.447

2.387

2.383

M1

7.398(7.419)

8.811(8.839)

6.653(6.649)

3.821(3.81)

0.074(0.015)

-0.002(0.047)

0.46(0.126)

0.02(0.186)

M2

7.187(7.181)

9.240(9.153)

6.986(6.973)

4.006(3.848)

-0.303(1.221)

-0.009(1.646)

-0.005(1.646)

-0.791(-0.462)

M3

7.398(7.757)

9.552(9.392)

6.802(6.67)

3.99(3.881)

0.41(0.48)

0.571(0.711)

0.502(0.554)

0.988(1.139)

Table 2 Mulliken charges of Li8-xB8-yTix+y+zH32 systems (M0, M1, M2 and M3) in terms of e. Atoms

Systems

Li

Electron orbital occupation

Charge

s

p

d

Total

M0 M1 M2 M3

1.51 1.53 1.57 1.65

0 0 0 0

0 0 0 0

1.51 1.53 1.57 1.65

1.49 1.47 1.43 1.36

B

M0 M1 M2 M3

1 1.01 0.99 1.01

2.9 2.88 2.85 2.83

0 0 0 0

3.9 3.89 3.84 3.84

-0.9 -0.89 -0.84 -0.84

H

M0 M1 M2 M3

1.15 1.16 1.19 1.15

0 0 0 0

0 0 0 0

1.15 1.16 1.19 1.15

-0.15 -0.16 -0.19 -0.15

Ti

M0 M1 M2 M3

0 1.83 2.5 2.58

0 5.47 6.44 5.63

0 2.93 2.61 3.16

0 10.23 11.55 11.38

0 1.77 0.45 0.62

11

Table 3 The average bond order (BO), average bond length (BL, in unit of Å) and scaled bond order (BOs, in unit of Å-1) between B-H, Li-H, Li-B, Ti-H and Ti-B for Li8-xB8-yTix+y+zH32 systems (M0, M1, M2 and M3) according to Mulliken population analysis. B-H

Li-H

Li-B

Ti-H

Ti-B

System BO

BL

BO s

BO

BL

BO s

M0

1.020

1.224

M1

0.899

M2 M3

BO

BL

BOs

0.833

-0.104

2.167

1.38

0.651

-0.099

1.003

1.225

0.819

0.978

1.234

0.793

BL

BOs

-0.048

-0.153

2.502

-0.061

…

…

…

2.18

-0.045

-0.148

2.516

-0.059

-0.074

2.169

-0.091

2.206

-0.041

-0.142

2.537

-0.056

0.685

-0.095

2.239

-0.042

-0.153

2.547

-0.06

0.015

12

BO

BL

BOs

…

…

…

-0.034

-0.265

2.448

-0.108

1.77

0.387

…

…

…

1.951

0.008

-0.6

2.087

-0.287

BO

Figures:

Fig.1 Model of LiBH4 with 1×2×1 supercell. Red, green, white (large), white (middle) and white (small) spheres denote Li, B, H1, H2 and H3 atoms, respectively. Orange, yellow and blue spheres show the substitution positions of Li atom site (0.338, 0.375, 0.613) (marked with S1), B atom site (0.689, 0.375, 0.573) (marked with S2) and interstitial site (0.5, 0.5, 0.5) (marked with S3), respectively. In [BH4] group, the four H atoms surrounding a B atom are labeled with HA, HB, HC and HD.

13

EF

M0

Density of states (electrons/eV)

0.5

H3-s

0.0 1.0

H2-s

0.5 0.0 1.0

Density of states (electrons/eV)

1.0

H1-s

0.5 0.0 2

B-s B-p

1 0 1.0

Li-s

0.5 0.0 40

Total

20 0 -15

-10

-5

0

5

10

15

1.0 0.5 0.0 1.0 0.5 0.0 1.0 0.5 0.0 2 1 0 8 4 0 1.0 0.5 0.0 40 20 0 -15

EF

M1

H2-s H1-s B-s B-p Ti-p Ti-d Li-s Total -10

-5

H3-s H2-s

Density of states (electrons/eV)

Density of states (electrons/eV)

EF

M2

H1-s B-s B-p Ti-p Ti-d Li-s Total -10

-5

0

0

5

10

Energy(eV)

Energy(eV)

1.0 0.5 0.0 1.0 0.5 0.0 1.0 0.5 0.0 2 1 0 8 4 0 1.0 0.5 0.0 40 20 0 -15

H3-s

5

10

1.0 0.5 0.0 1.0 0.5 0.0 1.0 0.5 0.0 2 1 0 8 4 0 1.0 0.5 0.0 40 20 0 -15

EF

M3

H3-s H2-s H1-s B-s B-p Ti-p Ti-d Li-s Total

-10

-5

0

5

10

Energy(eV)

Energy(eV)

Fig. 2 Total and partial density of states for Li8-xB8-yTix+y+zH32 systems (M0, M1, M2 and M3). The Femi level is set at zero energy and marked by the vertical dotted line.

14

Fig. 3 Electronic density contours for Li8-xB8-yTix+y+zH32 systems (M0, M1, M2 and M3) containing Li, B, H or/and Ti atoms in the range 0.003 to 0.3 electrons/Å3.

15

8

16

M0

0.2

M1

0.2

Eg=0.794 eV

Eg=7.019 eV

0.0

0.0

12 Q Z

Q Z

G

G

Energy (eV)

G F

Energy (eV)

-0.2 G F

4

-0.2

8

4

0

-4 0

-4

F

G

Q

8

Z

-8

G

G

F

Q

Z

Eg=0.314eV

0.0 -0.2 G F

4

Energy (eV)

Energy (eV)

G

G

4

0

-4

G

Z

0.2

M3

0.0

-8

Q

8

0.2

M2 -0.2 G

F

Q Z

G

0

-4

F

Q

Z

-8

G

G

F

Q

Z

G

Fig. 4 The band structure of Li8-xB8-yTix+y+zH32 systems (M0, M1, M2 and M3). The bad gap and the amplified band structure from -0.2 to 0.2 eV are shown in the inset of this figure. The Femi level is set at zero energy and shown as dotted line.

16