Synergistic effect of Li–Ti and K–Ti co-doping on the dehydrogenation properties of NaAlH₄: an ab initio study

Abstract

The synergistic effect of Li–Ti and K–Ti dopants on the energy, structure and electronic properties of NaAlH₄ has been investigated using density functional theory and ab initio molecular dynamics. Pair distribution functional analyses show that the substitution of NaAlH₄ by Li₂Ti and K₂Ti favor not only the release of H₂ but also the reductions in the barrier energies of (AlH₄)⁻ units. Density of states analyses suggest that the weakening of Al–H bonds in Li₂Ti- and K₂Ti-doped NaAlH₄ is attributed to the formation of Ti–Al and Ti–H phases. Bader atomic charges analyses imply that the strong interaction of Li–Al prevent the further formation of Ti–Al clusters. The results of H removal energies analyses reveal that both Li₂Ti and K₂Ti are favorable catalysts for NaAlH₄. Thus, that a Li₂Ti dopant, with lighter weight than K₂Ti, can be applied as a favorable catalyst for NaAlH₄ has been given for the first time.

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1. Introduction

NaAlH₄ is a light–metal complex hydride and one of the most promising hydrogen storage materials. These materials are alternative energy sources for on-board vehicular applications.¹ However, commercial applications of NaAlH₄ are still restricted because of the high thermodynamic stability and sluggish re/dehydrogenation kinetics of this compound. Compounds with Ti can significantly reduce the decomposition temperature and enhance the kinetic properties of the re/dehydrogenation of NaAlH₄. The TiF₃ dopant is effective in improving the de-/hydriding performance of NaAlH₄. F⁻ exhibits a remarkable catalytic effect because of the favorable thermodynamic modification caused by the substitution of H⁻ by F⁻.^2–4 Doping KH to Ti–NaAlH₄ system can improve the property of the dehydrogenation/hydrogenation cycles. Moreover, isothermal desorption kinetics of K₂TiF₆-doped NaAlH₄ is much faster than that of TiF₃- or KH-doped samples.⁵ K, Ti and F exhibit strong synergistic effect on the dehydrogenation of NaAlH₄ by forming Al₃Ti, TiH₂, KH and NaF.^6,7 Further studies have shown that, compared with single-doped NaAlH₄, multi-doped NaAlH₄ exhibits more significant effect on the kinetic and thermodynamic properties of NaAlH₄.^8–11 However, the destabilizing mechanism remains ambiguous, although co-doping NaAlH₄ can further reduce the thermodynamic stability and enhance the kinetics effectively. Thus, the theoretical investigation of K and Ti co-doping NaAlH₄ is necessary. Moreover, Li, as the relative light-weight metal among alkali metals, is the most attractive decorating atom. Studies of Li–Ti co-doping to destabilize NaAlH₄ have been conducted to explore for efficient dopants that influence the reversibility of the transition metal Ti and high capacity of the lithium alanates.

In this paper, the structure and catalytic mechanism of Li–Ti and K–Ti co-doped NaAlH₄ were investigated using first-principles calculations. The positions of dopants were determined by minimizing the total electronic energy. The substitution energies were calculated to find out the suitable doping ratio. The structural characteristics were investigated using ab initio molecular dynamics (AIMD). The electronic structures were calculated to reveal the underlying mechanism. The hydrogen removal energies were calculated to examine the co-doping efficiency. All the electronic structures and hydrogen removal energies calculated based on the most stable one after structural optimization at 0 K.

2. Method of calculation

All studies were performed using first-principles method based on density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP).^12,13 The generalized gradient approximation (GGA) of PW91 (ref. 14 and 15) was employed. The kinetic cut-off energy for the plane wave expansion was 400 eV for NaAlH₄. Geometry optimization was performed until the residual forces were within 10⁻² eV Å⁻¹, and the total energy converged to within 10⁻⁴ eV per atom. The co-doping calculations were performed for a 2 × 2 × 1 supercell containing 96 atoms to avoid drastic structural changes in the individual supercells under the periodic boundary conditions. The 6 × 6 × 5 k-points generated using the Monkhorst–Pack scheme¹⁶ were used to sample the surface Brillouin zone during structural optimization.

The occupied sites of Ti in NaAlH₄ were determined in our previous studies, in which the Al site was considered the most thermodynamic site.¹⁷ In the current study, we considered Li or K to occupy the Na sites because of their similar chemical properties, whilst Ti substituted the Al sites. We started by determining which doping ratios of Li–Ti and K–Ti are most energetically favorable. We considered three types of atomic ratios (1 : 1, 2 : 1 and 1 : 2) to simulate the synergistic effect of Li–Ti and K–Ti on the dehydrogenation of NaAlH₄. In addition, the substituted atoms (Na or Al atoms) are most adjacent to each other. The atomic valence electrons are H 1s¹, Li 1s¹2s¹2p⁰, Al 3s²3p¹, Na 2p⁶3s¹3p⁰, K 3p⁶4s¹ and Ti 4s¹3d³. In all the calculations, we adopted the fully optimized structures of doped-NaAlH₄ cell by using DFT method as the AIMD simulation models. We performed AIMD simulations using the constant particle number, volume and temperature (NVT) ensemble at the temperature of 300 K in the cases of co-doped system. The lattice parameters of doped-NaAlH₄ cell would remain constant during MD structural optimization as NVT ensemble was chosen. Nosé–Hoover thermostat method¹⁸ was used to control the different temperatures during the simulations. The AIMD simulations were ran for 10 000 steps containing with equilibration and data sampling procedures and the time step was chosen to be 1.0 fs.

3. Results

3.1 Undoped and Li–Ti and K–Ti co-doped on NaAlH₄ models

Fig. 1 shows the initial geometrical structures of Li–Ti and K–Ti co-doped NaAlH₄. As shown in Fig. 1a, the two adjacent Li or K atoms occupying the Na sites and one Ti atom occupying the Al site. In Fig. 1b, the Li or K atoms are relatively further from each other. In Fig. 1c, one Li or K atom occupying the Na site and two adjacent Ti atoms occupying the Al sites. Li, K and Al5 atoms are the nearest neighboring atoms of the dopant Ti. The substitution energy is the difference in the formation energies of the substituted and original compounds, which can be written as follows:

E_sub = E(Na_16−xM_xAl_16−yTi_yH₆₄) + x × E(Na) + yE(Al) − x × E(M) − yE(Ti) − E(Na₁₆Al₁₆H₆₄). (x = 0, 1, 2; y = 0, 1, 2) (1)

where E(Na_16−xM_xAl_16−yTi_yH₆₄) and E(Na₁₆Al₁₆H₆₄) represent the total energies of the substituted and original compounds. E(Na), E(Al), E(Ti) and E(M) represent the atomic energies of Na, Al, Ti and M, respectively. The calculated lattice parameters and substitution energies of pure and Li–Ti and K–Ti co-substituted Na₁₆Al₁₆H₆₄ are shown in Table 1. The substitution energy for the doped system is positive meaning that it requires energy to achieve this doping resulting less stable of the doped system than the undoped NaAlH₄. Among the dopants, we find that Li₂Ti and K₂Ti with lower substitution energies are energetically more stable than LiTi, LiTi₂, KTi and KTi₂. This result indicates that higher contents of alkali metal ions are likely to facilitate the solubility of transition element Ti in NaAlH₄. The effects of distance between the dopants have been studied. As for Li₂Ti, the dopants are adjacent to each other are the most stable in all systems and can produce better catalytic effect on NaAlH₄. But for K₂Ti, the distance of dopants has no significant influence on the substitution energy. Considering the concentrations of Li or K reach up to 12.5 at% in some doped systems, and therefore, we built a bigger supercell (2 × 2 × 2 supercell in Fig. 1d) to study the interactions between dopant. And we find that the concentrations of Li or K atoms (6.25 at% in 2 × 2 × 2 supercell, 12.5 at% in 2 × 2 × 1 supercell) has no significant influence on the substitution energy. For the convenience of comparison, we adopt the 2 × 2 × 1 supercells as our calculation models, in which the dopants are adjacent to each other.

Fig. 1 Examples of crystal structures of (a) initial Li₂Ti-doped and K₂Ti-doped NaAlH₄ with dopants are adjacent to each other in 2 × 2 × 1 supercell, (b) initial Li₂Ti-doped and K₂Ti-doped NaAlH₄ with dopants are relatively father in 2 × 2 × 1 supercell, (c) initial LiTi₂-doped and KTi₂-doped NaAlH₄ with dopants are adjacent to each other in 2 × 2 × 1 supercell, (d) Li₂Ti-doped and K₂Ti-doped NaAlH₄ with dopants are adjacent to each other in 2 × 2 × 2 supercell. Purple, blue, green, gray and white balls denote Na, Li, K, Ti and H atoms, respectively. The Al atoms are at the center of the tetrahedra.

Table 1 Optimized lattice parameters and substitution energies of the Li–Ti and K–Ti co-doped 2 × 2 × 1 supercells Na₁₆Al₁₆H₆₄

	a	b	c	Substitution energy (eV)
Pure	9.89	9.90	11.02
Li2	9.85	9.84	10.92	0.20
K2	10.03	10.01	11.20	−0.07
Ti2	9.77	10.06	10.92	0.29
LiTi2	9.90	9.69	11.11	1.39
LiTi	9.94	9.82	10.91	1.26
Li2Ti (adjacent)	9.91	9.77	10.82	1.19
Li2Ti (further)	9.93	9.71	10.81	1.54
KTi2	10.03	9.81	11.22	1.52
KTi	9.90	10.07	10.99	1.41
K2Ti (adjacent)	9.92	10.07	11.21	1.13
K2Ti (far)	9.88	10.08	11.25	1.03

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3.2 Structural changes induced by substitution

The radial pair distribution functions (PDFs), g(r), for each pair of atom types at the temperature of 300 K were calculated and shown in Fig. 2. The PDFs allow a comparison of the local order in those of pure, Li₂Ti-doped and K₂Ti-doped NaAlH₄ and reflect the probability of finding an atom of a given type at some distance away from a reference atom. All the PDFs of pure NaAlH₄ show distinct peaks (0–10.0 Å), corresponding to the first few neighbor shells in the compound. Compared with those of the pristine sample NaAlH₄, the PDFs peaks of Al–H of substituted systems, as shown in Fig. 2d, become less prominent and show asymmetric broadening toward longer distances, indicating the bond length of Al–H become longer. As shown in Fig. 2e, comparing to the undoped system, the local order of H in substituted systems are reduced, then they will move closer to each other (the H atoms between adjacent AlH₄ (Al–H ∼ H–Al)), which might facilitate H₂ formation and release. Of note, in Fig. 2a and c, the PDF peaks of substituted compounds also show asymmetric broadening toward longer distances, indicating that the local order of Na–Al and pair-wise (AlH₄)⁻ anionic unit are largely reduced, which will lead directly to the reductions in the barrier energies of (AlH₄)⁻ units. An important effect that we observed is the formation of Ti–Al bonds. In Fig. 2f, the first Ti–Al PDF peak is centered at about 2.65 Å for K₂Ti substituted NaAlH₄ and is approximately 2.88 Å for Li₂Ti substituted NaAlH₄, respectively. Given that the typical Ti–Al distance in TiAl₃ systems is approximately 2.80 Å,¹⁹ we suggest the formation of some kind of TiAl_x (x > 1) clusters in Li₂Ti and K₂Ti substituted NaAlH₄. The catalytic Ti–Al clusters can facilitate the dissociation and recombination of molecular H,^20–22 suggesting that both Li₂Ti and K₂Ti are likely to favor the dehydrogenation of NaAlH₄.

Fig. 2 Radial pair distribution functions, g(r), versus radius for atom types in pure, Li₂Ti-doped and K₂Ti-doped NaAlH₄ at the temperature of 300 K: (a) Na–Al, (b) Na–H, (c) Al–Al, (d) Al–H, (e) H–H and (f) Ti–Al. The insets are the first-order peaks from (d) to (f).

3.3 Density of states (DOSs)

The total and partial DOSs of pure, Li₂Ti-doped and K₂Ti-doped NaAlH₄ were calculated and shown in Fig. 3. The Fermi level (E_f) is set to zero, and the energies are shown relative to E_f. As shown in Fig. 3a, the band gap of pure NaAlH₄ is approximately 4.8 eV, indicating its insulator features. The conduction band is controlled by Na s, p and Al s, p orbital hybridizations from 3.8 eV to 7.5 eV. Thus, Na and Al atoms interact ionically. The valence band is controlled by Al s, p and H s orbital hybridizations from −4.0 eV to −7.0 eV and from −1.0 eV to −4.0 eV, respectively. Thus, Al and H atoms interact covalently. Fig. 3b shows the total and partial DOSs of Li₂Ti-doped NaAlH₄. The total DOS of Li₂Ti-doped NaAlH₄ is very similar to that of pure NaAlH₄ (Fig. 3a), except that the main bonding peaks, from −1.0 eV to −4.0 eV, are shifted by approximately 2.5 eV and there emerge a small peak around −1.0 eV. So doping Ti induces extra electrons (as shown in Fig. 3b a sharp peak of Ti d electron appears around −1.0 eV) and thus promotes the Fermi energy level with respect to the undoped system. Al5 is the nearest neighboring atoms of the dopant Ti. In conduction band, the Al5 p overlapped with Li p from 0.8 eV to 4.2 eV, suggesting that Li–Al interact ionically. In valence band, the hybridization between Ti d and H28 s orbitals in the range of −3.3 eV to −3.8 eV indicates that the formation of Ti–H. The peaks of Al5 p overlaps with Ti d from −1.1 eV to −0.9 eV, suggesting the formation of TiAl_x phases. Fig. 3c shows the total and partial DOSs of K₂Ti-doped NaAlH₄. In the total DOS of K₂Ti-doped NaAlH₄, the main bonding peaks are also shifted by approximately 2.5 eV and there emerge two peaks around −3.5 eV and −1.0 eV, respectively. Separately, around −3.5 eV, the Ti d overlapped with H28 s, indicating the formation of Ti–H. The Ti d overlapped with Al 5p around −1.0 eV, indicating the formation of TiAl_x phases. Thus, Ti–H and Ti–Al phases are both formed in Li₂Ti and K₂Ti doping systems. Differently, the interaction of Ti–H (H28) around −3.5 eV in K₂Ti doping is slightly weaker than that in Li₂Ti doping, by contrast, the interaction of Ti–Al around −1.0 eV in K₂Ti doping is slightly stronger than that in Li₂Ti doping. Similarly, the reduced peaks from −10.0 eV to −3.5 eV in both substituted compounds suggest the weakening of Al–H bonds.

Fig. 3 Total and partial DOSs: (a) pure, (b) Li₂Ti-doped and (c) K₂Ti-doped NaAlH₄.

3.4 Bader atomic charge (BAC)

The BACs of Li₂Ti-doped NaAlH₄ and K₂Ti-doped NaAlH₄ are studied based on the Bader's theory of atoms in molecules.²³ The corresponding results are listed in Table 2. Based on the calculated BAC, one can speculate that Li, Na, K, Al and Ti atoms are electron donors and H atoms are electron acceptors. For the Li₂Ti co-doped system, Al5, Al6 and Al12 atoms are the nearest neighboring atoms of the dopant Li₂Ti and these Al atoms move towards Ti to form TiAl₃. The total BAC of formed TiAl₃ phase is 8.019|e|. Similarly, for the K₂Ti-doped NaAlH₄, Al3, Al5 and Al6 atoms are the nearest neighboring atoms of the dopant K₂Ti and these Al atoms also move towards Ti to form TiAl₃. The total BAC of formed TiAl₃ phase is 7.969|e|. Thus, compared with the original Al₄, BAC of which is 8.608|e|, the TiAl₃ unit contributed fewer electrons than Al₄. As a result, the number of electrons around H atoms (H are bound Ti and Al) in the co-doped systems is decreased compared with pure NaAlH₄, which implies that the electron transfer from Al to H is further weakened. For the K₂Ti-doped system, the BAC for K atoms is in the range of 0.784|e| to 0.794|e|. For Li₂Ti-doped NaAlH₄, the BAC of Li atoms is in the range of 0.895|e| to 0.898|e|. By contrast, for the pure material, the BAC for Na atoms is 0.859|e|, illustrating K atoms contribute fewer electrons than Na but Li atoms contribute more electrons than Na. This fact suggests that the electron transfer from K to Al is slightly weaker than Na to Al but the electron transfer from Li to Al is slightly stronger than Na to Al. Therefore, one can conceive that the stronger interaction of Li–Al will prevent the further formation of Ti–Al cluster.

Table 2 The calculated BAC (in unit of |e|) of some atoms in pure, Li₂Ti-doped NaAlH₄ and K₂Ti-doped NaAlH₄

Pure	BAC	Li2Ti-doped	BAC	K2Ti-doped	BAC
Al3	2.152			Al3	2.170
Al6	2.152	Ti	1.523	Ti	1.471
Al7	2.152	Al6	2.165	Al6	2.163
Al5	2.152	Al5	2.169	Al5	2.165
Al13	2.152	Al12	2.162
H17	−0.752	H17	−0.717	H17	−0.681
H18	−0.752	H18	−0.655	H18	−0.664
H23	−0.752	H23	−0.661	H23	−0.658
H28	−0.752	H28	−0.662	H28	−0.504
H29	−0.752	H29	−0.580	H29	−0.675
H32	−0.753	H32	−0.714	H32	−0.724
H49	−0.752	H49	−0.759
H59	−0.752	H59	−0.729
H6	−0.752			H6	−0.716
H27	−0.752			H27	−0.751
Na7	0.859	Li1	0.898	K1	0.794
Na16	0.859	Li2	0.895	K2	0.784

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3.5 Hydrogen removal energies of Li₂Ti-doped NaAlH₄ and K₂Ti-doped NaAlH₄

We calculated the removal energies of H atoms in the substituted compounds to examine the doping efficiency of Li₂Ti and K₂Ti in NaAlH₄ during dehydrogenation. The corresponding results are listed in Table 3. The hydrogen removal energy is the difference in the total energies between the pure and removed systems, which can be calculated as follows:

E_rem = E(Na₁₄M₂Al₁₅TiH₆₃) + 1/2E(H₂) − E(Na₁₄M₂Al₁₅TiH₆₄). (2)

where E(Na₁₄M₂Al₁₅TiH₆₄) and E(Na₁₄M₂Al₁₅TiH₆₃) represent the total energies before and after removing one H atom, respectively. E(H₂) represents the total energy of an isolated H₂ molecule. The H atoms can be divided into three types according to the coordination of H atoms, namely, the H atoms of Ti–H (H18, H23, H28, H29), the H of bridge Al–H–Ti bonds (H6, H17, H32, H59) and the H atoms of AlH₄ tetrahedra (H49, H27). We can see the H atoms near Ti are easy to release. The average hydrogen removal energies are −0.07 eV for Li₂Ti-doped and −0.31 eV for K₂Ti-doped NaAlH₄, respectively. The small values of H removal energies imply that the removal of H atoms in Li₂Ti and K₂Ti doping is much easier than in pure NaAlH₄ (3.8–4.0 eV).^24,25

Table 3 The removal energies for some H atoms in the substituted compounds

H bonds in Li2Ti-doped NaAlH4	H removal energy Erem (eV)	H bonds in K2Ti-doped NaAlH4	H removal energy Erem (eV)
Ti–H18	−0.18	Ti–H18	−0.82
Ti–H23	0.10	Ti–H23	−0.78
Ti–H28	−0.75	Ti–H28	−0.82
Ti–H29	−0.17	Ti–H29	−0.78
Al–H17	0.10	Al–H17	0.56
Al–H32	0.81	Al–H32	−0.08
Al–H49	−0.24	Al–H6	0.61
Al–H59	−0.19	Al–H27	−0.37

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4. Conclusions

In this study, we investigated the synergistic effect of Li–Ti and K–Ti co-doping on NaAlH₄. Thermodynamic calculations show that Li₂Ti and K₂Ti are suitable catalysts. By contrast, we have provided the structural characterization of NaAlH₄, Li₂Ti and K₂Ti doped NaAlH₄ based on PDFs by the AIMD simulations at 300 K. The PDFs analyses of Na–H, Al–H and H–H indicate that the substitution of NaAlH₄ by Li₂Ti and K₂Ti favor the release of H atoms. The PDFs analyses of Na–Al, Al–Al and Ti–Al reveal that Li₂Ti and K₂Ti dopants can facilitate the dehydrogenation kinetics of the substituted compounds. In addition, the DOSs analytical results indicate that the Al–H phases decreased in Li₂Ti and K₂Ti doping because of the formation of Ti–Al and Ti–H phases. The reasons of Li₂Ti and K₂Ti doping are conducive to the release of H were discussed based on above mentioned BAC analyses. Moreover, Li₂Ti and K₂Ti are favorable catalysts because of the small H removal energies, especially K₂Ti. Li₂Ti is also much lighter than K₂Ti. Thus, Li₂Ti and K₂Ti dopants can be regarded as best catalysts for NaAlH₄ among all the Li–Ti and K–Ti dopants according to my study.

Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities (FRF-BR-14-023A).

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