Lithium Ion Disorder and Conduction Mechanism in LiCe(BH4)3Cl

Article pubs.acs.org/JPCC

Lithium Ion Disorder and Conduction Mechanism in LiCe(BH4)3Cl Young-Su Lee,*,† Morten B. Ley,‡,§ Torben R. Jensen,‡ and Young Whan Cho† †

High Temperature Energy Materials Research Center, Korea Institute of Science and Technology, Seoul 02792, Republic of Korea Center for Materials Crystallography (CMC), Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Århus C, Denmark § Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany ‡

S Supporting Information *

ABSTRACT: We investigate the diffusion mechanism of Li ions in LiCe(BH4)3Cl, which exhibits fast Li ion conduction. It was previously shown that eight Li ions partially occupy the 12d Wyckoff sites in the I4̅3m structure and the Li ion diffusion takes place via jumping through the three-dimensional network of the 12d sites. In this study, we employ firstprinciples nudged elastic band simulation to elucidate the diffusion mechanism and discover that the Li ion does not directly jump to the neighboring 12d site, but instead passes through the closest 6b site. Moreover, the 6b site turns out to be another stable Li ion site, not just a transient point during a jump event. The occupation of the 6b site and the Li ion diffusion mechanism were assured by first-principles molecular dynamics simulations. The partial occupancy of the 12d site and 6b site at 500 K is approximately 1/2 and 1/3, respectively. The experimental diffraction data can be consistently interpreted. The peculiar crystal structure of LiCe(BH4)3Cl allowing efficient and fast Li ion diffusion is again highlighted together with the role of [BH4]− ion in thermodynamically stabilizing LiCe(BH4)3Cl. [BH4]−.18 However, the exact diffusion path of the Li ions remains unknown. Here, in order to better understand how the crystal structure of LiM(BH4)3Cl supports fast Li ion conduction, we elucidate the diffusion mechanism from firstprinciples calculations. Both static calculation and molecular dynamics simulation have been carried out to investigate the occupation of the Li sites, the energy minimum path for Li ion diffusion, and the accompanying activation energy. The simulation results suggest another plausible Li site (6b Wyckoff site) and Li ion diffusion through this site. The X-ray and neutron diffraction data were analyzed to confirm the simulation result.

1. INTRODUCTION Complex metal borohydrides, M(BH4)n, have been drawing attention owing to their potential as reversible, high-capacity, solid state hydrogen storage materials.1−5 In addition to their technical importance as energy carriers, their structural diversity and unique bonding characteristics inspire us to explore their utility other than for hydrogen storage, such as in electrical, optical, and magnetic applications.6−10 The directional and mixed ionic and covalent bonding created by the complex anion, [BH4]−, can produce energetically similar polymorphs with a variety of crystal structures and functionalities.11 Further versatility in structural and physicochemical properties is brought by a plethora of multication and multianion borohydride derivatives: Li2(BH4)(NH2),12 CsEu(BH4)3,8 LiCe(BH4)3Cl,13,14 and Rb2Li[Y(BH4)6−xClx],15 to list a few. One of the promising applications of metal borohydrides and their derivatives is as solid electrolytes. High Li ion conductivity in hexagonal LiBH4 was discovered by Matsuo et al.,16 and from then on numerous reports on the Li ion conduction in the borohydride-based compounds have appeared.6,12,17−20 Among the materials studied, the family of LiM(BH4)3Cl (M = Ce, La, Gd) exhibits some of the highest Li ion conductivities, on the order of 10−4 S cm−1 at room temperature.14,17 The fast Li ion conduction relies on LiM(BH4)3Cl’s unique crystal structure that provides 12 Li occupation sites per unit cell (12d Wyckoff site in I4̅3m space group), out of which only two-thirds are randomly occupied.14 Such inherent disorder and relatively low activation energy for Li ion diffusion explains the high Li ion conductivity.17 A recent NMR study revealed correlated motion between the jump of a Li ion and the reorientational motion of © XXXX American Chemical Society

2. THEORETICAL AND EXPERIMENTAL METHODS 2.1. First-Principles Calculation. The energetics and diffusion mechanism of Li ions were investigated by firstprinciples calculations. The calculations were performed within the framework of density functional theory (DFT),21,22 as implemented in the Vienna ab-Initio Simulation Package.23,24 The generalized-gradient approximation by Perdew, Burke, and Ernzerhof25 was adopted for exchange-correlation functional. Projector augmented wave potential26 with a planewave cutoff energy of 600 eV was used. The simulation cell is a cubic unit cell with a = 11.72 Å containing eight formula units of LiCe(BH4)3Cl (144 atoms). Since the unit cell is rather large, Γ-point sampling was used for efficiency; the total energy is Received: June 30, 2016 Revised: August 4, 2016

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DOI: 10.1021/acs.jpcc.6b06564 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C converged to within 1 meV/atom. Atomic coordinates were optimized until the force on each atom became smaller than 0.005 eV/Å. For location of an energy minimum path for Li ion diffusion and estimation of the activation energy, the nudged elastic band method (NEB) was employed.27 In addition to the static calculation at 0 K, Li ion motion at finite temperature was tracked by the Born−Oppenheimer molecular dynamics simulation. The simulations were performed in a canonical ensemble (NVT) with the Nosé−Hoover thermostat fixed at 500 K, and four different starting configurations were simulated. A time step of 1 fs was used, and the total energy was converged to within 10−8 eV/unit cell at each time step. The temperature was raised to 500 K for 1 ps, and the system was equilibrated for 10 ps; the simulation ran for 100 ps. 2.2. Structural Data and Refinement. LiCe(BH4)3Cl was prepared via a mechanochemical reaction between LiBH4 and CeCl3 (similarly for LiCe(11BD4)3Cl). The details are provided in the Supporting Information. The crystal structure was analyzed by powder neutron diffraction and synchrotron radiation powder X-ray diffraction. Powder neutron diffraction (PND) data were collected at the high-resolution powder neutron diffractometer HRPT at the spallation neutron source SINQ at the Paul Scherrer Institute in Villigen, Switzerland.28 The sample was enclosed in a vanadium can (8 mm diameter), and data were collected with a neutron wavelength of λ = 1.494 Å in the high-intensity mode using the standard ILL-type Orange cryostat at −271 °C. Synchrotron radiation powder Xray diffraction (SR-PXD) data were obtained at the SwissNorwegian Beamlines (BM01A, SNBL) at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. The data were collected using a MAR345 image plate detector at T = 160 °C at a sample to detector distance of 250 mm and a selected X-ray wavelength of λ = 0.709637 Å. The capillary was oscillated 30° during X-ray exposure of the sample for 30 s. The sample was packed in a glovebox in a 0.5 mm boron silicate capillary sealed with glue. All obtained raw images were transformed to powder patterns using the FIT2D program,29 which was also used for calibration of the X-ray wavelength and the sample−detector distance using SR-PXD measurements of the standard NIST LaB6. Uncertainties of the integrated intensities were calculated at each 2θ point by applying Poisson statistics to the intensity data, considering the geometry of the detector.30 The crystal structure of LiCe(BH4)3Cl/LiCe(11BD4)3Cl was refined from both SR-PXD and PND data. The X-ray scattering powers differ significantly between the heavy atoms, cerium and chlorine, and the lighter ones, lithium, boron, and hydrogen, which means that the refinement of the X-ray is mainly dependent on cerium and chlorine. The structural model was refined by the Rietveld method using the program Fullprof with structural coordinates from a previous study.14 However, different Li positions, 2a, 6b, 12d, and 24g and their combinations were attempted in the refinements according to the models suggested from the DFT calculations.

Figure 1. (a) Crystal structure of LiCe(BH4)3Cl. Li, Ce, and Cl are colored in blue, yellow, and green, respectively. Gray tetrahedrons are [BH4]− groups. (b) 12d Wyckoff sites and their three-dimensional network. (c) Combination of 12d (in blue) and 6b (in magenta) sites and their three-dimensional network.

Figure 1b was speculated to be responsible for the high Li ion conductivity.18 The network is identical to that of tetrahedral interstitial sites in bcc metals, which serves as a fast diffusion path for H interstitial atoms in vanadium or niobium. However, the distance between the neighboring sites is relatively large being 4.144 Å compared to 1.06 Å in vanadium, so the simple analogy requires a validation. The exact diffusion mechanism has never been theoretically explored yet. We employ the NEB method to elucidate the energy minimum path of Li ion diffusion. Two combinations of Li occupation were chosen as initial and final states (Li occupation sites are shown in Figure S1). Although the Li distribution is different, the energy is almost degenerate with a difference of less than 1 meV/unit cell. The energy diagram along the energy minimum path of a Li jump is presented in Figure 2. The

Figure 2. Energy diagram of a Li ion jump calculated by the nudged elastic band method. The dashed line is a guide to the eye. The inserts show positions of two Li ions located on the xy plane. The Li ion in magenta jumps to the nearest 12d site passing through the nearest 6b site.

inserts show the positions of the Li ions on the xy plane, and the magenta-colored Li ion moves from a T1 site to the nearest T1 site. To our surprise, it turned out that the Li ion does not move along the path directly connecting the two nearby T1 sites (diagonal direction in Figure 2). Instead, it passes through the 6b site located at the center. We hereafter refer to the 6b sites as T2 sites, since they are also tetrahedrally coordinated by four [BH4]− groups. Even more intriguing is the fact that the T2 site is not just a saddle point but a stable position, as is clearly seen in the energy diagram in Figure 2. The result in Figure 2 is a combination of two separate NEB calculations: from image number 0 to 9, and from 9 to 18. Actually, the relative ease of the T1 ↔ T2 jump can be captured in the

3. RESULTS AND DISCUSSION 3.1. Diffusion Mechanism and Stable Positions of Li Ions. Figure 1a presents the crystal structure of LiCe(BH4)3Cl in the I4̅3m space group. The blue spheres are the 12d Wyckoff sites, previously proposed to be a partially occupied Li position.14 We will refer to the 12d Wyckoff site as the T1 site, since Li ion is tetrahedrally coordinated by four [BH4]− groups. The three-dimensional network of T1 sites shown in B


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valid upon changing the Li distribution, we tested a different set of initial and final configurations for the Li ion diffusion (full configurations in Figure S3). Figure 4 shows the energy and

polyhedral structure model in Figure S2: the neighboring T1 and T2 tetrahedrons share an edge whereas the neighboring T1 tetrahedrons are connected by a corner. The activation energy for the Li ion diffusion is about 0.3 eV, which is similar to 0.38 eV determined for LiGd(BH4)3Cl and smaller than 0.59 eV for LiLa(BH4)3Cl.17 Previously, the T2 site was excluded from the possible Li positions due to the unfavorable energy.14 However, only the case of fully occupied 2a + 6b sites was tested, which was the originally proposed Li position when the compound was first identified.13 Judging from the stability of the 6b site revealed by the present NEB calculation, the energy rise upon the 2a + 6b occupation is probably caused by the Li ion at the 2a site, which is surrounded by Ce3+ ions without proper shielding of their positive charges. Unfortunately, the 6b sites could not be treated independently, since there are eight Li ions and only six 6b sites (or T2 sites). To confirm the stability of the T2 site in a different condition, we fully populate the T2 site with six Li ions and place the remaining two Li ions at the T1 site. The configuration is shown in Figure 3g. The total energy is

Figure 4. (a) Energy diagram of a Li ion jump for LiCe(BH4)3Cl (●) and LiCeBr3Cl (△) calculated by the nudged elastic band method. The dashed lines are guides to the eye. (b) The atomic configurations of LiCe(BH4)3Cl at the selected image numbers. Ce, Cl, B, and H are colored in yellow, green, gray, and pink, respectively, and Li1 and Li2 are drawn in magenta and blue.

geometry variation upon two consecutive jumps made by Li1 and then Li2. The result is a combination of two separate NEB calculations−from image number 0 to 9 (Li1 jump), and from 9 to 18 (Li2 jump). The activation energy for Li ion diffusion is again approximately 0.3 eV. Additionally, the T2 site is confirmed to be stable in agreement with the previous NEB result. To detect any changes in the bonding character during the Li ion diffusion, we performed the Bader charge analysis31 for Li1 and Li2 along the diffusion path for the Li1 jump and present the result in Figure S4. The charges on Li1 and Li2 are about +0.9e, and only a minor variation within 0.01e is found for Li1 going from T2 to T1 site. Therefore, the ionic character of the Li ions is preserved irrespective of the position of a Li ion. It is clearly illustrated in Figure 4b that the Li ion diffusion accompanies and is assisted by a reorientational motion of the coordinated [BH4]− ions, in line with the previous experimental finding that Li ion diffusion and reorientational motion of [BH4]− ions occur at the same frequency scale.18 We were curious to know how the activation energy is affected when a spherical halide ion Br− replaces the [BH4]− ion and performed the same calculation using a hypothetical “LiCeBr3Cl” structure. The energy diagram for LiCeBr3Cl is coplotted in Figure 4a. Interestingly, the activation energy for Li ion diffusion in

Figure 3. Total energy and the position of the Li ions (magenta and blue spheres) in LiCe(BH4)3Cl for seven different combinations of Li occupation site, from part a to part g. The energy is expressed as the excess energy per formula unit with respect to the lowest energy configuration in part a.

compared with several combinations of an exclusive T1 occupation. Out of the 17 independent configurations, in which eight Li ions are distributed in combinations of (4, 2, 2) or (2, 3, 3) on the (001), (010), (100) planes, the six lowest energy structures are illustrated in Figure 3a−f together with the relative energy (per formula unit) with respect to that of Figure 3a. The energy of the six T2 + two T1 combination (Figure 3g) is comparable to the exclusive T1 populations, and the structure is locally stable. This result is consistent with the NEB result that the T2 site is a stable Li position and Li diffusion takes place through the network comprising both T1 and T2 sites as drawn in Figure 1c instead of Figure 1b. As can be immediately noticed in Figure 1b,c, the combined T1 + T2 network reduces the jumping distance by a factor of 1/√2 with respect to that of the exclusive T1 network (from 4.14 to 2.93 Å). 3.2. Li Ion Diffusion in LiCe(BH4)3Cl and LiCeBr3Cl. In order to check whether the aforementioned NEB result remains C


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The Journal of Physical Chemistry C LiCeBr3Cl appears to be lower than in LiCe(BH4)3Cl by ca. 0.1 eV. A close inspection on the crystal structure is necessary to understand the difference. The calculated lattice parameter of LiCeBr3Cl is 11.95 Å, being larger than 11.72 Å of LiCe(BH4)3Cl. This is unexpected, since the ionic radius of Br− (1.96 Å) is smaller than that of [BH4]− (2.05 Å) and the solid solution of LiBH4−LiBr has a smaller cell volume than pure LiBH4.32,33 We repeated DFT optimization of the cell parameter employing a different exchange-correlation functional that includes van der Waals energy,34 but the trend is not affected, giving slightly reduced cell parameters of 11.89 and 11.67 Å for LiCeBr3Cl and LiCe(BH4)3Cl, respectively. The crystal structure of LiCe(BH4)3Cl can be viewed as a bcc stacking of anionic clusters [Ce4Cl4(BH4)12]4− connected by disordered Li+ cations.14 An analogous example is the hightemperature cubic Na2B12H12, where large [B12H12]2− polyanions make a bcc sublattice and disordered Na+ ions allow for superionic conductivity.35,36 The relative size of a cation with respect to a polyanion and the bonding characteristics between them must be the important factors in making this kind of structure such a good ionic conductor. We therefore focus on the intercluster distance and the size of the anion cluster to figure out what contributes mainly to the lower activation energy and the larger cell parameter of LiCeBr3Cl. The distance between the two B atoms (or Br atoms) that belong to different anionic clusters is chosen as a criterion to compare the intercluster distance. The average intercluster B−B and Br−Br distance for the Li distribution in Figure 3a is 4.231 and 4.225 Å, respectively, very similar to each other considering the difference in the ionic radius between [BH4]− and Br−. On the other hand, the average Ce−B distance inside the cluster is 2.664 Å, which is significantly shorter than the Ce−Br distance of 2.850 Å. The short Ce−B distance can be attributed to a tridentate coordination of [BH4]− to Ce3+. The tight tridentate coordination is possible because there are only three, not six, [BH4]− groups in the octahedral coordination shell of Ce3+ (the rest three are Cl− ions), and they are all terminal groups. The [BH4]− terminal groups can form a stable large anionic cluster as evidenced by a number of compounds composed of [M(BH4)4]− (M = Sc, Y, Yb).10,15,37−39 In addition, the similar intercluster B−B and Br−Br distances indicate that the [BH4]− terminal groups may suppress the repulsion among the anionic clusters. Summarizing the structural analysis, the anionic clusters in LiCeBr3Cl are relatively large and loosely bound compared to those in LiCe(BH4)3Cl. Since Li ions diffuse through the space between the anionic clusters, a smaller ionic radius of Br− would allow larger space for the Li ion diffusion, and the lower activation energy in LiCeBr3Cl can be understood in this regard. It is noteworthy in Figure 4a that, in the case of LiCeBr3Cl, there are additional local energy minima at images 4 and 15. In order to locate the position of Li ions at those minima, the coordinates of Li1 and Li2 along the diffusion path in Figure 4a are plotted in Figure 5a. The ordinate denotes the deviation in y and z coordinates from the (y, z) = (0.5, 1) line, which is a straight line that connects the initial to the final Li position. It is found that another stable Li site is an octahedral position (henceforth referred to as O site) surrounded by five Br− (or [BH4]−) and Cl− ions as illustrated in Figure 5b. The ideal O site would have deviation of −1.4 to −1.5 Å both for y and z coordinates if plotted in Figure 5a. The evolution of Li coordinates in Figure 5a clearly demonstrates that Li ions move toward the O site located between T1 and T2 sites (Figure 5b)

Figure 5. (a) Variation of y and z coordinates of Li1 and Li2 in LiCe(BH4)3Cl and LiCeBr3Cl during the jump event illustrated in Figure 4. The solid and open symbols in the same color are the y and corresponding z coordinates, respectively. The displacement is with respect to y = 1/2 and z = 1 (in fractional coordinates). (b) Octahedral position (O) coordinated by five [BH4]− (or Br−) groups and one Cl−. Upon jumping from T2 to T1 (or vice versa) site, the Li ion approaches this O site.

and Li ions in LiCeBr3Cl approach the O site more closely, probably due to the favorable energetics. The lower activation energy in LiCeBr3Cl can also be explained by the existence of such stable O sites, which are absent in LiCe(BH4)3Cl. The inclusion of O sites in the Li ion diffusion path would further decrease the jumping distance by ∼0.4 Å compared to that of the T1 ↔ T2 jump (see Figure S5). The approximate T1−O− T2 pathway is hinted in the polyhedral structure model in Figure S2. The O and T1/T2 polyhedrons are closely connected via a face. We note that such a Li ion diffusion pathway is typical of the structures with an fcc stacking of anions,40 and in our case, [BH4]− (or Br−) and Cl− ions together make an fcc sublattice. The O site is the 24g Wyckoff site and was also discussed originally as a possibly occupied Li position in LiCe(BH4)3Cl but rejected because of the unfavorable energetics.14 The stability of the O site in LiCeBr3Cl can be interpreted in analogy with the octahedral coordination of Br− to Li+ in LiBr in contrast to the tetrahedral coordination of [BH4]− to Li+ in LiBH4. The comparison between LiCe(BH4)3Cl and LiCeBr3Cl overall suggests that the hypothetical LiCeBr3Cl may be an even better Li ion conductor, and in this regard we tried to synthesize it. However, the synthesis starting from LiCl and CeBr3 was unsuccessful (details in the Supporting Information). DFT total energy calculation predicts that the formation of LiCeBr3Cl would increase the total energy: LiCl + CeBr3 → LiCeBr3Cl

ΔE = 0.40 eV/f. u.

(1)

Actually, the formation energy for LiCe(BH4)3Cl from LiCl and Ce(BH4)3 was also predicted to be endothermic with an energy D


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The Journal of Physical Chemistry C increase by 0.14 eV/f.u.14 While such an energy barrier can be overcome by entropy in the case of LiCe(BH4)3Cl, the larger energy barrier for the formation of LiCeBr3Cl may not be compensated by entropy. Indeed, the thermodynamic instability of LiCeBr3Cl is somewhat expected, since the intercluster binding is rather loose as we have dicussed. Therefore, we highlight that [BH 4 ] − groups play a critical role in thermodynamically stabilizing LiCe(BH4)3Cl whose unique crystal structure provides partially occupied Li ion sites that enable fast Li ion diffusion. Tailoring the Li site stability by making a solid solution of LiCe(Brx(BH4)1−x)3Cl would be worthwhile, and further studies in this direction are underway. 3.3. Molecular Dynamics Simulation. We performed MD simulations to follow the Li ion motion at a finite temperature. Four different starting configurations as shown in Figure 3a,b,c,g were used. The temperature was maintained at 500 K to facilitate Li ion diffusion. First of all, the site occupation was checked throughout the simulation time. It is clearly found that Li ions always stay at either T1 (12d site) or T2 (6b site) site, and the 24g site is never populated: the difference between LiCeBr3Cl and LiCe(BH4)3Cl is confirmed again. The occupancy of T1 and T2 is quantitatively analyzed, and the result is summarized in Figure 6. For the identification

500 K. With the assumption that the activation energy is 0.3 eV, the room temperature (298 K) diffusion coefficient is estimated to be 4.2 × 10−8 cm2/s, which is in the same order of magnitude as 5.2 × 10−8 cm2/s for LiLa(BH4)3Cl.18 Another important result from MD simulations is the time evolution of the Li ion positions. Figure 7 shows a typical

Figure 7. Trajectory of one Li ion during the MD simulation. Three jump events (marked with red arrows) are captured; the last one transmits the Li ion directly from a T1 to a neighboring T1 site.

trajectory of a Li ion undergoing diffusion. As anticipated from the NEB result, the diffusion mainly occurs between the T1 and T2 sites, but a few percent of the jumps turned out to be directly between T1 ↔ T1 sites like the third jump event in Figure 7. One can easily differentiate between the two kinds of jumps: the T1 ↔ T2 jump involves a change in only one of the x, y, and z coordinates whereas the T1 ↔ T1 jump involves two of them. Closer inspection of the Li coordinates and Li−B coordination confirms that the third jump event transmits a Li ion directly from a T1 site to the neighboring T1 site without passing through a T2 site. Figure 8a shows the variation of the Li−B distances over time for the third jump event, and Figure 8b illustrates selected snapshots among the seven cases annotated in Figure 8a (see Figure S7 for the full description). The Li ion jump is initiated when one [BH4]− (B1) is expelled from the coordination shell, which leaves three coordinated [BH4]− groups (B2, B3, and B4). As time progresses the coordination number (C.N., annotated in Figure 8) reduces to 2 (B3 and B4), and there is a brief moment where only one [BH4]− (B4) is closely bonded to the Li ion. This [BH4]− group belongs to the coordination shell of both the initial and final T1 sites. Eventually, the Li ion moves toward the final T1 site undergoing a reverse process; i.e., the coordination number increases one by one (B5, B6, and B7 are sequentially incorporated). Figure 8 provides a rough idea on the procedure of the T1 ↔ T1 jump; the detail will depend on the Li distribution around the jumping Li ion since that determines the orientation of the nearby [BH4]− groups. As in the case of the T1 ↔ T2 jump shown in Figure 4b, [BH4]− groups reorient themselves during the jump and also after the jump to stabilize the new Li position. We expect that the contribution by the direct T1 ↔ T1 jump will increase as temperature increases. 3.4. Rietveld Refinement of the PND and SR-PXD data. In a previous NMR study on LiLa(BH4)3Cl,17 the onset of Li ion diffusion occurred at T ∼ −73 °C.18 This indicates that, below T = −73 °C, the Li ions are located on the positions with the lowest energy, 12d.14 The PND data were collected at

Figure 6. Number of Li ions sitting at the T1 sites obtained from the MD simulation for 100 ps. The number at a time period = n is the averaged value within the time period from (n − 1) × 10 ps to n × 10 ps containing 10000 time steps. Different starting configurations are noted with different symbols: up triangle (orange), circle (blue), square (red), and down triangle (olive) for Figure 3a,b,c,g, respectively. Black solid circle represents the value averaged from the four configurations.

of which site a Li ion is sitting in, among all the available T1 and T2 sites in the simulation cell, whichever is closest to that Li ion is chosen to be the occupied site. Each data point is the number of Li ions at the T1 site averaged over a 10 ps time period for each configuration. We would like to mention that although the simulation cell has 144 atoms, the number of Li ions is only eight. Therefore, the size is rather limited to get well-converged statistics, and a large fluctuation appears among the data points. However, when an average is taken over four configurations (black circles in Figure 6), the fluctuation is reduced, and we can see that approximately 5−6 Li ions stay at the T1 site, and the remaining go to the T2 site. We calculate the diffusion coefficient of a Li ion from the averaged mean square displacement of the Li ions over time (see Figure S6). The diffusion coefficient thus obtained is 4.7 × 10−6 cm2/s at E


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models. The lowest R values are found for 24g and 6b/12d models. However, DFT calculations have previously shown that the occupation of the 24g position is not possible due to the high energy of the resulting structure,14 and this is again confirmed by the present MD simulations. Additionally, refinement of the neutron diffraction data also revealed Li−D distances that are too short, when Li ions are located on the 24g position.14 The determined occupancies and B factors for lithium from the refinements of the PND data using both the 24g and 6b/12d models also give values which indicate that the 24g and 6b/12d models are not correct. Physically realistic values are found for the 12d model where lithium is only located on the 12d site. The refined occupancy (5.5) of the 12d site is still too low according to the idealized occupancy of 8 Li ions necessary for a charge neutral compound. However, at low temperatures the 12d site is still the most likely position for the Li ions. The refinement results of the SR-PXD data in Table 2 show that at higher temperatures the 6b site is indeed a possible Table 2. Refinement Parameters from the Rietveld Refinements of the SR-PXD Data Using Different Lithium Positions Collected for the Ball Milled CeCl3−LiBH4 1:3 Sample at T = 160 °C Figure 8. (a) Time evolution of the Li−B distance for the third jump event in Figure 7. The coordinated [BH4]− groups change as B1, B2, B3, B4 to B4, B5, B6, and B7 as time progresses. The number of coordinated [BH4]− groups (C.N.) at several representative moments is annotated. (b) The atomic configurations of C.N. = 3, 1, and 3 as annotated in part a according to the time sequence.

model Rpa/% Rwpa/% Rpb/% Rwpb/% RBragg LiCe(BH4)3Cl/% RBragg LiCl/% RBragg CeCl3/% χ2 Li Positions occupancy 2a Biso 2a occupancy 6b Biso 6b occupancy 12d Biso 12d occupancy 24g Biso 24g

−271 °C. The refinement parameters of all the different models are summarized in Table 1. The Rietveld refinement of the PND data indicates that at this temperature the Li ions are most likely also located on the 12d position. The refinement parameters do not vary considerably between the different Table 1. Refinement Parameters from the Rietveld Refinements of the PND Data Using Different Lithium Positions Collected for the Ball Milled CeCl3−Li11BD4 1:3 Sample at T = −271 °C model

2a/6b

12d

24g

2.92 2.71 2.62 Rpa/% Rwpa/% 3.85 3.57 3.50 Rpb/% 10.5 9.75 9.36 Rwpb/% 11.5 10.6 10.3 RBragg LiCe(BH4)3Cl/% 7.20 5.97 5.28 RBragg LiCl/% 2.76 2.34 2.27 RBragg CeCl3/% 13.0 11.0 10.5 χ2 11.8 10.3 9.85 Li Positions in the LiCe(11BD4)3Cl Model occupancy 2a 2c Biso 2a 2c occupancy 6b 6c Biso 6b 2c occupancy 12d 5.5(7) Biso 12d 1.8(2) occupancy 24g 21.8(9) Biso 24g 37.1(9)

6b/12d

a

2.70 3.57 9.71 10.6 5.87 2.30 10.8 10.2

c

12d

24g

6b/12d 3.15 4.52 5.94 7.85 2.24 2.10 6.72 7240

4.7(8) 11.1(9) 3.3(8) 8.3(9)

Not corrected for background. bConventional Rietveld R-factors. Not refined.

position for the Li ions. The 24g model again gives reasonble parameters, but according to the same argumentation as for the PND data, it is rejected. Lower refinement parameters are found for the 6b/12d model compared to the 12d model. Additionally, both the occupancies and B factors give realisic values. A higher value is found for the occupantion of the 6b site compared to the 12d site in the 6b/12d model, which is opposite compared to the results from the DFT calculations. However, because of the difference in scattering factors between the heavy cerium ions and the much lighter lithium ions, DFT calculations are more reliable in the determination of the occupancies. Finally, the refinements of both the PND and SR-PXD corroborate the findings from the first-principles MD simulations, which shows that the 6b site is a stable position for the Li ions and that the 2a site may be responsible for the high energy of the 2a/6b model previously suggested.13,14

−1.9(5) 3c 7.4(7) 2.3(9)

a c

2a/6b

3.36 3.16 2.99 4.66 4.55 4.42 6.31 5.95 5.64 8.08 7.89 7.67 3.45 2.46 2.20 2.27 2.11 2.29 6.79 6.69 6.81 7670 7310 6900 in the LiCe(BH4)3Cl Model 2c 14.9(9) 6c 14.9(9) 7.1(9) 9.4(9) 8.6(9) 3.6(9)

Not corrected for background. bConventional Rietveld R-factors. Not refined. F


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(6) Maekawa, H.; Matsuo, M.; Takamura, H.; Ando, M.; Noda, Y.; Karahashi, T.; Orimo, S. I. Halide-Stabilized LiBH4, a RoomTemperature Lithium Fast-Ion Conductor. J. Am. Chem. Soc. 2009, 131, 894−895. (7) de Jongh, P. E.; Blanchard, D.; Matsuo, M.; Udovic, T. J.; Orimo, S. Complex Hydrides as Room-Temperature Solid Electrolytes for Rechargeable Batteries. Appl. Phys. A: Mater. Sci. Process. 2016, 122, 1− 6. (8) Schouwink, P.; Ley, M. B.; Tissot, A.; Hagemann, H.; Jensen, T. R.; Smrčok, L.; Č erný, R. Structure and Properties of Complex Hydride Perovskite Materials. Nat. Commun. 2014, 5, 5706. (9) Schouwink, P.; Didelot, E.; Lee, Y.-S.; Mazet, T.; Č erný, R. Structural and Magnetocaloric Properties of Novel Gadolinium Borohydrides. J. Alloys Compd. 2016, 664, 378−384. (10) Roedern, E.; Lee, Y.-S.; Ley, M. B.; Park, K.; Cho, Y. W.; Skibsted, J.; Jensen, T. R. Solid State Synthesis, Structural Characterization and Ionic Conductivity of Bimetallic Alkali-Metal Yttrium Borohydrides MY(BH4)4 (M = Li and Na). J. Mater. Chem. A 2016, 4, 8793−8802. (11) Filinchuk, Y.; Chernyshov, D.; Dmitriev, V. Light Metal Borohydrides: Crystal Structures and Beyond. Z. Kristallogr. 2008, 223, 649−659. (12) Matsuo, M.; Remhof, A.; Martelli, P.; Caputo, R.; Ernst, M.; Miura, Y.; Sato, T.; Oguchi, H.; Maekawa, H.; Takamura, H.; et al. Complex Hydrides with (BH4)¯ and (NH2)¯ Anions as New Lithium Fast-Ion Conductors. J. Am. Chem. Soc. 2009, 131, 16389−16391. (13) Frommen, C.; Sørby, M. H.; Ravindran, P.; Vajeeston, P.; Fjellvåg, H.; Hauback, B. C. Synthesis, Crystal Structure, and Thermal Properties of the First Mixed-Metal and Anion-Substituted Rare Earth Borohydride LiCe(BH4)3Cl. J. Phys. Chem. C 2011, 115, 23591− 23602. (14) Ley, M. B.; Ravnsbæk, D. B.; Filinchuk, Y.; Lee, Y.-S.; Janot, R.; Cho, Y. W.; Skibsted, J.; Jensen, T. R. LiCe(BH4)3Cl, a New LithiumIon Conductor and Hydrogen Storage Material with Isolated Tetranuclear Anionic Clusters. Chem. Mater. 2012, 24, 1654−1663. (15) Jaroń, T.; Wegner, W.; Grochala, W. M[Y(BH4)4] and M2Li[Y(BH4)6‑xClx] (M = Rb, Cs): New Borohydride Derivatives of Yttrium and Their Hydrogen Storage Properties. Dalton Trans. 2013, 42, 6886−6893. (16) Matsuo, M.; Nakamori, Y.; Orimo, S.; Maekawa, H.; Takamura, H. Lithium Superionic Conduction in Lithium Borohydride Accompanied by Structural Transition. Appl. Phys. Lett. 2007, 91, 224103. (17) Ley, M. B.; Boulineau, S.; Janot, R. l.; Filinchuk, Y.; Jensen, T. R. New Li Ion Conductors and Solid State Hydrogen Storage Materials: LiM(BH4)3Cl, M= La, Gd. J. Phys. Chem. C 2012, 116, 21267−21276. (18) Skripov, A. V.; Soloninin, A. V.; Ley, M. B.; Jensen, T. R.; Filinchuk, Y. Nuclear Magnetic Resonance Studies of BH 4 Reorientations and Li Diffusion in LiLa(BH4)3Cl. J. Phys. Chem. C 2013, 117, 14965−14972. (19) Unemoto, A.; Matsuo, M.; Orimo, S.-i. Complex Hydrides for Electrochemical Energy Storage. Adv. Funct. Mater. 2014, 24, 2267− 2279. (20) Blanchard, D.; Nale, A.; Sveinbjörnsson, D.; Eggenhuisen, T. M.; Verkuijlen, M. H. W.; Suwarno; Vegge, T.; Kentgens, A. P. M.; de Jongh, P. E. Nanoconfined LiBH4 as a Fast Lithium Ion Conductor. Adv. Funct. Mater. 2015, 25, 184−192. (21) Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Phys. Rev. 1964, 136, B864−B871. (22) Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133− A1138. (23) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169−11186. (24) Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50.

4. CONCLUSIONS We elucidated the diffusion path of a Li ion in LiCe(BH4)3Cl from first-principles simulations. The previously discarded 6b site is unveiled to be a stable Li site and at the same time shown to participate in the network of the Li ion diffusion path. Simulation results suggest that most of the Li ion jumps take place between the 12d and 6b site, but the contribution of a direct jump between the two 12d sites would increase as temperature increases. Activation energy for Li diffusion is as low as 0.3 eV, and comparison with a hypothetical LiCeBr3Cl demonstrates the critical role of [BH4]− in stabilizing the complex compound LiCe(BH4)3Cl. Rietveld refinement results also support the population of a 6b site, consistent with the finding in DFT simulations. This study again highlights the importance of the unique crystal structure of LiCe(BH4)3Cl that accommodates inherent Li ion disorder and an efficient diffusion path: such a crystal structure can be further exploited to design even faster Li ion conductors.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b06564. Details of the synthesis of LiCe(BH4)3Cl, LiCe(11BD4)3Cl, and CeBr3−LiCl samples, and Figures S1− S7 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Phone: +82-2-958-5412. Fax: +82-2-958-5449. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by The Innovation Fund Denmark via the research project HyFill-Fast and by Convergence Agenda Program (CAP) of the Korea Research Council of Fundamental Science and Technology. The authors acknowledge Dr. Denis Sheptyakov, Paul Scherrer Institut, PSI, Switzerland, for the powder neutron diffraction measurement and the Swiss-Norwegian Beamlines, European Synchrotron Radiation Facility (ESRF), Grenoble, France, for the allocated beam time.

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REFERENCES

(1) Züttel, A.; Wenger, P.; Rentsch, S.; Sudan, P.; Mauron, P.; Emmenegger, C. LiBH4 a New Hydrogen Storage Material. J. Power Sources 2003, 118, 1−7. (2) Orimo, S.; Nakamori, Y.; Eliseo, J. R.; Züttel, A.; Jensen, C. M. Complex Hydrides for Hydrogen Storage. Chem. Rev. 2007, 107, 4111−4132. (3) Graetz, J. New Approaches to Hydrogen Storage. Chem. Soc. Rev. 2009, 38, 73−82. (4) Ley, M. B.; Jepsen, L. H.; Lee, Y.-S.; Cho, Y. W.; Bellosta von Colbe, J. M.; Dornheim, M.; Rokni, M.; Jensen, J. O.; Sloth, M.; Filinchuk, Y.; et al. Complex Hydrides for Hydrogen Storage − New Perspectives. Mater. Today 2014, 17, 122−128. (5) Jepsen, L. H.; Ley, M. B.; Lee, Y.-S.; Cho, Y. W.; Dornheim, M.; Jensen, J. O.; Filinchuk, Y.; Jørgensen, J. E.; Besenbacher, F.; Jensen, T. R. Boron−Nitrogen Based Hydrides and Reactive Composites for Hydrogen Storage. Mater. Today 2014, 17, 129−135. G


Article

The Journal of Physical Chemistry C (25) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (26) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953−17979. (27) Mills, G.; Jónsson, H.; Schenter, G. K. Reversible Work Transition State Theory: Application to Dissociative Adsorption of Hydrogen. Surf. Sci. 1995, 324, 305−337. (28) Fischer, P.; Frey, G.; Koch, M.; Könnecke, M.; Pomjakushin, V.; Schefer, J.; Thut, R.; Schlumpf, N.; Bürge, R.; Greuter, U.; et al. HighResolution Powder Diffractometer HRPT for Thermal Neutrons at SINQ. Phys. B 2000, 276, 146−147. (29) Hammersley, A. P.; Svensson, S. O.; Hanfland, M.; Fitch, A. N.; Häusermann, D. Two-Dimensional Detector Software: From Real Detector to Idealised Image or Two-Theta Scan. High Pressure Res. 1996, 14, 235−248. (30) Vogel, S.; Ehm, L.; Knorr, K.; Braun, G. Automated Processing of 2D Powder Diffraction Data. Adv. X-Ray Anal. 2002, 45, 31−33. (31) Tang, W.; Sanville, E.; Henkelman, G. A Grid-Based Bader Analysis Algorithm without Lattice Bias. J. Phys.: Condens. Matter 2009, 21, 084204. (32) Rude, L. H.; Zavorotynska, O.; Arnbjerg, L. M.; Ravnsbæk, D. B.; Malmkjær, R. A.; Grove, H.; Hauback, B. C.; Baricco, M.; Filinchuk, Y.; Besenbacher, F.; et al. Bromide Substitution in Lithium Borohydride, LiBH4−LiBr. Int. J. Hydrogen Energy 2011, 36, 15664− 15672. (33) Cascallana-Matias, I.; Keen, D. A.; Cussen, E. J.; Gregory, D. H. Phase Behavior in the LiBH4−LiBr System and Structure of the AnionStabilized Fast Ionic, High Temperature Phase. Chem. Mater. 2015, 27, 7780−7787. (34) Lee, K.; Murray, É. D.; Kong, L. Z.; Lundqvist, B. I.; Langreth, D. C. Higher-Accuracy van der Waals Density Functional. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 081101. (35) Udovic, T. J.; Matsuo, M.; Unemoto, A.; Verdal, N.; Stavila, V.; Skripov, A. V.; Rush, J. J.; Takamura, H.; Orimo, S.-i. Sodium Superionic Conduction in Na2B12H12. Chem. Commun. 2014, 50, 3750−3752. (36) Skripov, A. V.; Babanova, O. A.; Soloninin, A. V.; Stavila, V.; Verdal, N.; Udovic, T. J.; Rush, J. J. Nuclear Magnetic Resonance Study of Atomic Motion in A2B12H12 (A = Na, K, Rb, Cs): Anion Reorientations and Na+ Mobility. J. Phys. Chem. C 2013, 117, 25961− 25968. (37) Hagemann, H.; Longhini, M.; Kaminski, J. W.; Wesolowski, T. A.; Č erný, R.; Penin, N.; Sørby, M. H.; Hauback, B. C.; Severa, G.; Jensen, C. M. LiSc(BH4)4: A Novel Salt of Li+ and Discrete Sc(BH4)4− Complex Anions. J. Phys. Chem. A 2008, 112, 7551−7555. (38) Č erný, R.; Severa, G.; Ravnsbæk, D. B.; Filinchuk, Y.; D’Anna, V.; Hagemann, H.; Haase, D.; Jensen, C. M.; Jensen, T. R. NaSc(BH4)4: A Novel Scandium-Based Borohydride. J. Phys. Chem. C 2010, 114, 1357−1364. (39) Wegner, W.; Jaroń, T.; Grochala, W. MYb(BH4)4 (M = K, Na) from Laboratory X-Ray Powder Data. Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 2013, C69, 1289−1291. (40) Wang, Y.; Richards, W. D.; Ong, S. P.; Miara, L. J.; Kim, J. C.; Mo, Y.; Ceder, G. Design Principles for Solid-State Lithium Superionic Conductors. Nat. Mater. 2015, 14, 1026−1031.

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Lithium Ion Disorder and Conduction Mechanism in LiCe(BH4)3Cl

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