Understanding Ultrafast Rechargeable Aluminum-Ion Battery from

United States. ‡ Department of Chemistry, University of Nebraska—Lincoln, Lincoln, Nebraska 68588, United States. J. Phys. Chem. C , 2017, 121...
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Understanding Ultrafast Rechargeable Aluminum-Ion Battery from First-Principles Yurui Gao,† Chongqin Zhu,‡ ZhengZheng Chen,† and Gang Lu*,† †

Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330-8268, United States Department of Chemistry, University of NebraskaLincoln, Lincoln, Nebraska 68588, United States

‡

S Supporting Information *

ABSTRACT: First-principles calculations are performed to gain fundamental understanding of recently developed Al/graphite battery that exhibits well-defined discharge voltage plateaus, high cycling stability, and ultrafast rate performance. Crucial issues pertaining to the unprecedented performance of the battery are understood, and key controversies in literature with respect to the geometry and gallery height of the intercalant are resolved. The stage and atomic structure of the graphite intercalation compounds (GICs) are elucidated, in line with the experimental finding. It is revealed that the intercalants tend to be inserted at relative high densities with a charging potential profile and theoretical specific capacity that agree well with the experiment. Four stable GIC configurations are identified with essentially the same chemical potential for the intercalant, giving rise to charging potential plateaus. Low diffusion energy barriers of the intercalants are found, which underlie the ultrafast (dis)charging rates of the battery.

1. INTRODUCTION Electrical energy storage technology that is cost-effective, safe, durable, and of high energy density is critical to the operation of modern energy systems, ranging from portable electronic devices to electrical vehicles and energy storage stations, to name but a few.1,2 Al-ion batteries have emerged as promising candidates to meet these stringent requirements thanks to the natural abundance, low flammability, and multielectron redox capability of Al.3−9 However, despite the promise, the development of Albased batteries has encountered numerous roadblocks such as cathode material disintegration, low discharge voltage without clear plateaus, and rapid capacity decay.10−16 To overcome these problems, we need to discover cathode materials that would enable fast ion diffusion and facile (de)intercalation. Recently, a breakthrough was made by Lin17 et al., who developed an Al-ion battery with flexible graphitic foam as the cathode material. The ultrafast Al/graphite battery with AlCl3/ [EMIm]Cl as electrolyte exhibits long-term cycling stability, ultrafast charging/discharging capability, and well-defined discharge voltage plateaus. Fueled by the breakthrough, significant research efforts have been put forward to elucidate the materials science behind the unprecedented performance of the Al/graphite battery;18−22 nonetheless, many important questions remain to be answered. It is believed that the battery operates through electrochemical deposition and dissolution of Al at the anode, and intercalation/deintercalation of AlCl4− in the graphite cathode. However, the atomic geometry of the intercalant AlCl4 in the cathode is still under debate.17,19,20,23,24 On the theory side, first-principles simulations by Wu et al. © XXXX American Chemical Society

revealed that AlCl4 was planar in a single layer between two graphite planes and the intercalant gallery height, i.e., the spacing between two intercalated adjacent graphite layers, di = 6.03 Å.20 On the other hand, based on the similar first-principles calculations, Jung et al. concluded that the preferred geometry of AlCl4 was a doubly stacked tetrahedron and the intercalant gallery height was 12.1 Å.19 On the experimental side, Lin17 et al. reported that the intercalant gallery height was 5.7 Å, derived from X-ray diffraction (XRD) patterns of the fully charged graphite. Based on the doubly stacked tetrahedron model, Jung et al. determined that the graphite intercalation compound (GIC) was at stage 3 (i.e., the intercalant is inserted in every three layers of the graphite),19 in contrast to the experimental result of stage 4. Taking the planar structure of AlCl4, Wu20 et al. determined its diffusion energy barriers between 0.023 and 0.089 eV and its diffusion constants as large as 1.01 × 10−4 cm2 s−1. By contrast, Jung19 et al. estimated the diffusion energy barriers of the doubly stacked tetrahedron in the range of 0.19−0.33 eV and the corresponding diffusion constants between 2.2 × 10−9 and 5.0 × 10−7 cm2 s−1. Since the geometry of the intercalant underlies its diffusion energy barriers in the graphite (thus the rate capability) and the stage of the GICs (thus the specific capacity), the elucidation of the intercalant geometry is of crucial importance to understanding the performance of the Al/graphite battery. Received: January 27, 2017 Revised: March 10, 2017 Published: March 14, 2017 A

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Figure 1. (a) Atomic structure and total energy of the stage-4 GIC with different intercalant geometries, including the planar and tetrahedral (lying and standing) geometries. The energy of the lying tetrahedron geometry is taken as zero. Energy barrier for the structural transformation from the lying tetrahedron geometry to the planar geometry for (b) AlCl4− and (c) neutral AlCl4. (d) Formation energy as a function of the stage number n (left) and the atomic structures of the stage-n GICs (1 ≤ n ≤ 6) with the lying tetrahedron geometry of AlCl4. The density of the intercalant is 3 × 3 (right). di and Ic indicate the intercalant gallery height and the periodic repeat distance of the supercell, respectively.

In this work, we carry out first-principles calculations to address the following issues: geometry of the intercalant, stage of the GICs, density of AlCl4 clusters in the GICs, charging mechanism, charging potential profile, theoretical specific capacity, and diffusion constants of the intercalant. In particular, we resolve the controversies on the geometry and gallery height of the intercalant. We derive the intercalant gallery height from the original XRD data, different from that reported by Lin17 et al. which in turn had led to an inappropriate parametrization in the theoretical calculations by Wu20,24 et al. The doubly stacked tetrahedron geometry is found to be less stable than the singlelayer tetrahedron geometry under normal conditions. We reveal that the intercalants tend to be inserted at relative high densities with a charging potential profile and theoretical specific capacity that agree with the experiment. Four stable GICs are identified with essentially the same chemical potential for the intercalant, which explains the charging voltage plateau. Low diffusion energy barriers of the intercalants are found, responsible for the ultrafast (dis)charging of the battery.

calculations. Due to the distinct graphitic character of the graphite foam and the similarity in the underlying crystal structure between the graphitic foam and the graphite, we choose the graphite as the host structure to examine the intercalation of AlCl4.24 The XRD simulations of the GICs were performed using the DIAMOND package.35 The nudged elastic band (NEB) method36−38 was used to calculate the energy barriers for structural transformation and diffusion of AlCl4 cluster between the graphite layers. The interlayer distance of the pristine graphite (P63/mmc) was determined as 3.340 Å, very close to the experimental value of 3.336 Å,39 indicating that the vdW-DF method was accurate enough to account for the van der Waals interactions in graphite. Once the negative AlCl4¯ ions enter the graphite, the net electrons will be extracted to the external circuit on a very short time scale, leaving behind the neutral AlCl4 clusters in the graphite. This time scale is much shorter than what is required for the system to reach the thermodynamics equilibrium. Therefore, in following DFT calculations, we only consider the neutral AlCl4 clusters within GICs in the equilibrium conditions.

2. COMPUTATIONAL METHODS First-principles calculations were performed based on the density functional theory (DFT)25,26 in conjunction with projectoraugmented-wave pseudopotentials27 and Perdew−Burke−Ernzerhof28 generalized gradient approximation as implemented in the Vienna ab initio simulation package (VASP).29 The dispersion interactions was taken into account by employing the van der Waals density functional (vdW-DF) method (optPBE-vdW).30−34 The energy cutoff was set as 500 eV, and the convergence criterion for the self-consistent-field calculation was 10−5 eV. Atomic geometries were optimized until the force on each atom was less than 0.01 eV Å−1. The Γ-centered K-point meshes with spacing less than 0.07 Å−1 were used in the

3. RESULTS AND DISCUSSION Geometry of the Intercalant. We first address the important issue on the geometry of AlCl4 between the graphite layers. To this end, we assume that the GIC is of stage 4 as observed in the experiment. As shown later, our DFT calculations confirm that the charged graphite cathode in the Al-battery is indeed at stage 4. A number of plausible geometries of AlCl4 cluster have been considered between two graphite layers, and among them, three are examined in detail via DFT calculations. Specifically, AlCl4 can take either a planar or a tetrahedral geometry, as shown in Figure 1a. For the tetrahedral geometry, AlCl4 can be either standing with one Cl atom B

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energetically most stable, consistent with the experimental finding of Lin et al. based on the XRD analysis.17 In addition, we have also examined stage-n GICs with different intercalant densities, such as 2 × 2, 4 × 4, 5 × 5, and 6 × 6, and found that the stage-4 GIC remains to be the most stable one. However, as shown in Figure 1d, the energy differences between different stages are rather small, suggesting that GICs with mixed stages (n = 4, 5, 6) may coexist. Since both the experiment and our calculations find the stage-4 GIC to be most stable, we will focus on it in the following analysis. Simulated XRD Patterns and Intercalant Gallery Height. We next simulate XRD patterns based on the relaxed atomic coordinates obtained from the DFT calculations. The stage-n GICs (n = 1−6) with the intercalant density of 3 × 3 on the ab plane are included in the simulations. For all the stages between n = 1 and 6, we find two dominant peaks indicated by the pink bars in Figure 2. The experimental XRD peaks are

pointing up and the other three down or lying with two Cl atoms pointing up and the other two down. Between the two tetrahedral geometries, the lying configuration is 0.08 eV lower than the standing one. On the other hand, the planar geometry has a much higher energy (0.69 eV) than the tetrahedral geometries. Therefore, the AlCl4 intercalant prefers to take the lying tetrahedral geometry inside the graphite. We next examine the energetics of AlCl4 in vacuum, before it is inserted into the graphite. As shown in Figure 1b and c, the planar geometry of both neutral and negatively charged molecule yields a much higher energy than the tetrahedral geometry, 1.74 eV for AlCl4− and 0.77 eV for AlCl4. More importantly, if AlCl4− (or AlCl4) were transformed from the tetrahedral to the planar geometry before the intercalation, the energy barrier would be 1.74 eV (or 0.77 eV), determined from DFT-NEB calculations (Figure 1b and Figure 1c). Such a high energy cost would render the transformation unlikely. Therefore, we conclude that the intercalant cannot exist in the graphite in the planar geometry. Wu et al. reported that the planar geometry was energetically more favorable,20 opposite to our result. We believe that the contradiction stems from an incorrect parametrization of the van der Waals (vdW) interaction in their DFT-D2 calculations, which in turn was misinformed by an underestimated experimental value. More specifically, Lin et al. reported the intercalant gallery height (see Figure 1 for definition) as di = 5.7 Å derived from their XRD data.17 Instead of using parameter-free vdW-DF calculations, Wu et al. fitted the vdW parameters in their DFT-D2 calculations to reproduce this experimental value.20,24 However, Lin et al. actually underestimated the intercalant gallery height. As shown later, based on the same experimental XRD data, we determine that di should be 8.80−8.85 Å, much larger than value reported by Lin et al. Hence, we believe that the vdW parameters used by Wu20,24 et al. yielded overbinding between the graphite layers, which in turn “flattened” the AlCl4 cluster. There are three reasons supporting our conclusion: (1) Both our parameter-f ree vdW-DF calculations and Jung’s DFTD2 calculation19,23 reveal that AlCl4 should take the tetrahedral as opposed to planar geometry in the graphite and the intercalant gallery height should be above 8 Å. Previous study19 has shown that the distance between Cl in AlCl4 and C in the graphite should be greater than 3 Å. Thus, it makes sense that the intercalant gallery height should be larger than 8 Å. (2) The energy cost is too high (>0.77 eV) to transform the geometry of AlCl4 from a tetrahedron in vacuum to a planar structure in the graphite. (3) Our estimate of di yields a stage-4 GIC, which is consistent with the experimental finding. The Stage of GIC. The second important question to be addressed is the stage number n of GICs, which is a key parameter of the Al/graphite battery, partially responsible for its theoretical capacity. Based on the results discussed above, we can calculate the formation energy of a stage-n GIC as Ef (n) = En(G + AlCl4) − En(G) − E(AlCl4)

Figure 2. Simulated XRD patterns of stage-n GICs (1 ≤ n ≤ 6) with the intercalant density of 3 × 3, compared with the experimental peaks (Exp.) taken from Lin’s paper.17 The last diffraction pattern is for the stage-4 GIC with the intercalant density of 4 × 4.

represented by the two red bars, located at 23.56° and 28.25°. Apparently, the simulated XRD patterns for the stage-4 GIC match very well to the experiment data for the intercalant density of 3 × 3 and 4 × 4. This suggests that the XRD measurements alone may not distinguish the two intercalation densities for the stage-4 GICs. On the other hand, the excellent agreement between the simulated and the experimental XRD patterns provides further validation of our results in terms of the intercalant gallery height (di = 8.81 Å) and the preferred stage (n = 4) of the GIC. In the following, we demonstrate that the intercalant gallery height reported by Lin et al.17 was actually underestimated. It is well-known that for a stage-n GIC, the two most dominant XRD peaks correspond to (0 0 n+1) and (0 0 n+2).17,40,41 As reported in Lin’s paper,17 the corresponding d spacing values are d(n+2) = 3.15 Å and d(n+1) = 3.77 Å. The ratio d(n+1)/d(n+2) = 1.197 reflects the stage number of the GIC and is very close to the ratio (1.200) for an ideal stage-4 GIC.40,41 Therefore, it was concluded that n = 4 in Lin’s paper. The periodic repeat distance in the stacking direction Ic, the intercalant gallery height di and the average interlayer expansion Δd can be obtained according to the following equation: Ic = di + 3.35 × (n − 1) = (Δd + 3.35) × n = l × dobs. The interlayer spacing of the pristine graphite is 3.35 Å; l and dobs are the index of (00l) planes and their d spacing of the stage-n GIC, respectively. dobs values of the two dominant peaks (005) and (006) are 3.77 and 3.15 Å as mentioned before, and

(1)

Here En(G + AlCl4), En(G), and E(AlCl4) are the energies of the stage-n GIC, a n-layer pristine graphite, and a neutral AlCl4 cluster, respectively. The stage-n GIC is modeled by a 3 × 3 repetition of the graphite primitive unit cell on the ab plane and n layers in the c direction. Importantly, each GIC unit cell contains only one AlCl4 cluster. The intercalant density is denoted as 3 × 3 in the following. We have calculated the formation energies of the stage-n GICs with n ranging from 1 to 6, and results are summarized in Figure 1d. We find that the formation energy reaches a minimum at n = 4, indicating that the stage-4 GIC is C

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The Journal of Physical Chemistry C from them we can derive the corresponding intercalant gallery height di. For (005) peak, di = (n + 1) × d(n+1) − 3.35 × (n − 1) = 5 × 3.77−3.35 × 3 = 8.80 Å. For the (006) peak, di = (n + 2) × d(n+2) − 3.35 × (n − 1) = 6 × 3.15−3.35 × 3 = 8.85 Å. Therefore, the intercalant gallery height di should range between 8.80 and 8.85 Å, much larger than the reported value of 5.7 Å. Once again, the derived value from XRD agrees very well to the direct DFT result of 8.81 Å. In this case, the interlayer expansion is 163% upon the intercalation, and the overall lattice expansion of the graphite is 41% in the c direction. Graphite Stacking. It is known that graphite is stabilized by AB stacking where two adjacent graphite sheets displace relative to each other so that the vertices of the honeycomb in the A layer are atop the center of the honeycomb in the B layer. However, this relative displacement vanishes (AA stacking) in fully charged Li-ion batteries. Interestingly, we find that the graphite maintains AB stacking in the charged Al battery, in contrast to Li-ion batteries. The energy of the most stable GIC configuration with the AB stacking is 0.79 eV (with one AlCl4 intercalant in a 6 × 6 × 2 supercell of the graphite) lower than that with the AA stacking. In particular, the most stable GIC configuration consists of AlCl4 tetrahedrons lying between two adjacent graphite layers and with the Al ion lining up with a C atom from each layer (Figure S1). We have also considered ABC stacking and found its energy slightly (0.037 eV) higher than that of the AB stacking. Overall, we find that the energy difference between the configurations with AlCl4 at different sites is rather small, indicating that the relevant potential energy surfaces are essentially flat, consistent with Wu’s observation.20 Intercalant Density in GIC. We next examine the energetics of the stage-4 GIC when AlCl4 is gradually inserted into the graphite with a uniform distribution (Figure S2). The intercalant density is represented by one AlCl4 cluster in every u × u (u = 6, 5, 4, 3, and 2) repetition of the graphite primitive unit cell on the ab plane; thus, a larger u yields a lower density of the intercalants. By inspecting the atomic structure of AlCl4, we realize that the highest possible density is u = 2 (e.g., if u = √3 or 1, the adjacent AlCl4 clusters would be too close to each other). To identify the most favorable density, we calculate the formation energy of the GIC as a function of u Ef (u) = Eu(G + AlCl4) − Eu(G) − E(AlCl4)

Figure 3. Formation energy and various energy contributions as a function of the intercalant density u. Formation energy Ef(u) = Eu(G + AlCl4) − Eu(G) − E(AlCl4) is divided into three parts: Ebind(u) = Eu(G + AlCl4) − Eru(G) − Eru(AlCl4), Elatt(u) = Eru(G) − Eu(G), and Einter(u) = Eru(AlCl4) − E(AlCl4).

Cl and C atoms due to their large interatomic distance (3 Å),19 there may exist long-range ionic and/or van der Waals interactions between them. As u and the volume of the computational cell increase, the total binding energy decreases as shown in Figure 3. The second contribution is of mechanical nature and defined as the elastic energy of the graphite upon charging, i.e., the energy difference between the deformed and the perfect graphite lattice: E latt(u) = Eur(G) − Eu(G)

Clearly, the elastic energy is always positive, and as u or the volume of the computational cell increases, the total elastic energy increases. On the other hand, the elastic energy volume density does not change significantly as a function of u. The third contribution is the interaction energy between the AlCl4 clusters: E inter(u) = Eur(AlCl4) − E(AlCl4)

(5)

The interaction energy is negative implying an attraction between the intercalants. As u or the volume of the computational cell increases, the interaction energy increases. The interaction energy in magnitude is much smaller than the binding energy or the elastic energy. The formation energy of the GIC is thus dominated by the competition between the elastic energy and the binding energy, with the former greater than the latter in magnitude. Hence the trend of the formation energy generally follows the trend of the elastic energy, decreasing with an increasing density of the intercalants. Figure 3 reveals an interesting prediction of the Al/graphite battery. The formation energy of the GIC is a decreasing function of the intercalant density u, as opposed to an increasing function. This suggests that in equilibrium the intercalants prefer to stay together with a higher density (u = 2 or 3) as opposed to being widely separated with a lower density (u = 6 or 5). Since the lower density “phases” (u = ..., 6, 5) are not stable, the charging process has to involve the higher density “phases”, as shown schematically in Figure 4. As the intercalants enter the graphite, they stay close to each other, forming a two-phase mixturethe high intercalant density phase (u = 2 or 3) and pure graphite phase. As more intercalants are inserted, the intercalated phase retains its high density, but the phase boundary moves toward the graphite, with the intercalated phase growing and the graphite phase receding. Similar two-phase mixtures are known to exist in Li-ion batteries, and the presence of phase boundaries has been observed experimentally. Note that the above analysis is

(2)

where Eu(G + AlCl4), Eu(G), and E(AlCl4) are the total energies for the stage-4 GIC with the intercalant density of u × u, the pristine graphite modeled by u × u × 2 supercell, and an isolated AlCl4 cluster, respectively. The results of the formation energy are summarized in Figure 3, and we find that u = 3, i.e., one AlCl4 cluster in every 3 × 3 unit cells on the ab plane is energetically most favorable. u = 2 is the second most favorable, only 0.01 eV higher than u = 3. To understand the trend of the formation energy, we divide Ef(u) into three contributions, the binding energy between the intercalant and the graphite, the elastic energy of the graphite, and the interaction energy among the intercalants. The first contribution is of chemical nature and can be expressed by E bind(u) = Eu(G + AlCl4) − Eur(G) − Eur(A lCl4)

(4)

(3)

where Eru(G) and Eru(AlCl4) are the total energies of the rigid graphite and AlCl4 cluster with their geometries taken from the optimized stage-4 GIC configuration with the intercalant density of u × u. The negative Ebind for all densities signifies the chemical bonding between the graphite and AlCl4 despite the large di (=8.81 Å). Although there appears no covalent bonding between D

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Figure 4. Schematic picture for the charging process: (a) the low density phase with widely separated AlCl4 is unstable. (b, c) Proposed intercalation mechanism involving the mixture of a high-density phase and graphite. The moving phase boundary is represented by the curvy line.

Figure 5. Two typical double-layer configurations: (a) lying and (b) standing tetrahedral geometry of AlCl4. The energy of the latter is 0.018 eV lower than the former.

pertinent to thermodynamic equilibrium. The actual dynamical process, however, could be far from equilibrium and is thus beyond the scope of the present study. Single-Layer vs Double-Layer Intercalation. We next examine whether the intercalation takes place in a manner of single-layer or double-layer. The double-layer intercalation is proposed by Jung19 et al. whereby doubly stacked AlCl4 ions are inserted into the graphite or few-layer graphene (Figure 5). In contrast, the single-layer intercalation means that a single layer of AlCl4 ions is inserted between the graphite layers (Figure 1). To be specific, we focus on the stage-4 GIC with the intercalant density of 2 × 2. Several possible double-layer intercalant configurations are considered with both lying and standing tetrahedral geometries of AlCl4 (Figure 5). We find that in general the double-layer configurations have higher energies than the single-layer configuration. For example, the energy of the most stable double-layer configuration (standing) is 0.27 eV per C32[AlCl4] formula unit higher than the corresponding singlelayer configuration. Thus, we believe that under normal charging conditions, single-layer intercalation is preferred. Moreover, the theoretical capacity derived from the single-layer intercalation is ∼70 mAhg−1, very close to the experimental value of 65−70 mAhg−1, thus confirming the single-layer intercalation mechanism in the Al/graphite battery. Charging Potential Profile. We next evaluate the convex hull in the formation energy of GICs with the chemical formula of C32[AlCl4]x. Because the construction of the convex hull takes V (x1, x 2) =

into consideration stage n, density u, and intercalating layers simultaneously, it provides a more comprehensive and accurate description for the stability of the GICs. The formation energy of the GICs is defined as Ef(x) = E(C32[AlCl4]x) − EG(C32) − xE(AlCl4), where E(C32[AlCl4]x) represents the total energy of the GICs and EG(C32) is the energy of the pristine graphite. A number of intercalant densities and molecular arrangements for the stage-2, stage-3, and stage-4 GICs are included in the construction of the convex hull, and the results are displayed in Figure 6a. Four stable GICs are identified by red symbols on the convex hull: (1) GIC with n = 2, x = 2, and u = 2; (2) GIC with n = 3, x = 1.33, and u = 2; (3) GIC with n = 4, x = 0.44, and u = 3, and (4) GIC with n = 4, x = 1, and u = 2. The molecular structures of the last two GICs are shown in Figure 6b and c, and they are the same ones determined in the previous section. Interestingly, the convex hull can be very well approximated by a straight line whose physical implication is discussed below. In the following, we calculate the charging potential profile. The total electrochemical reaction during the charging of the Al/ graphite battery from x1 to x2 can be expressed as 3C32[AlCl4]x1 + 4(x 2 − x1)Al 2Cl 7− charging

⎯⎯⎯⎯⎯⎯⎯→ (x 2 − x1)Al + 4(x 2 − x1)AlCl4 − + 3C32[AlCl4]x2

(6)

The charging potential can be computed as

(x 2 − x1)E(Al) + 4(x 2 − x1)E(AlCl4 −) + 3E(C32[AlCl4]x2 ) − 3E(C32[AlCl4]x1 ) − 4(x 2 − x1)E(Al 2Cl 7−) 3(x 2 − x1)e

Here E(C32[AlCl4]x1) and E(C32[AlCl4]x2) represent the total energies of the two stable GICs with different x values; E(Al), E(AlCl4−), and E(Al2Cl7−) denote the total energies of the metallic Al and the charged clusters of AlCl4−and Al2Cl7−, respectively. The charging potential can be rewritten as V(x1,x2) = C1 + C2k, where

(0 ≤ x1 < x 2)

(7)

Clearly, C1 and C2 are constants independent of the GICs, and k is the slope of the formation energy or the convex hull. Since the convex hull is a straight line, the charging potential is approximately a constant independent of x, i.e., V(0, 0.44) ≈ V(0.44, 1) ≈ V(1, 1.33) ≈ V(1.33, 2) ≈ 2.06 V, shown schematically in Figure 6d. As mentioned earlier, the stage-4 GIC is the most stable among others in the initial charging process. Since the charging potential is the same among the four stable GICs, we expect that the stage-4 GIC remains dominant during the charging process, consistent with the experimental observation. The theoretical specific capacity corresponding to

1 1 [E(Al) + 4E(AlCl4−) − 4E(Al 2Cl 7−) + 3E(AlCl4)], C2 = 3e e Ef (x 2) − Ef (x1) and k = x 2 − x1

C1 =

E

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Figure 6. (a) Formation energy (symbols) and its convex hull (line) for various GICs, including single- and double-layer stage-4 GICs, single-layer stage2, and stage-3 GICs. The stable GICs are identified in red color. The atomic structure for two stable stage-4 GICs: (b) C32[AlCl4]0.44 with the intercalant density of 3 × 3 and (c) C32[AlCl4] with the intercalant density of 2 × 2. (d) The charging potential profile. The solid line corresponds to capacity from the stage 4 GICs while the dashed line corresponds to the possible stage 3 and stage 2 GICs.

the stage-4 GIC is calculated as 70 mAh g−1. Overall, our results are in excellent agreement with the experimental observations that the Al/graphite battery exhibits well-defined charging voltage plateaus near 2 V and a specific capacity of about 70 mAh g−1. The two theoretical charging plateaus are not as widely separated as in the experiments,17,42 probably due to many factors that the calculations fail to capture, including the presence of lattice defects, effect of voltage polarization, and possible surface absorption. We note that the slope of the formation energy corresponds to the chemical potential of the intercalant in the GICs; thus, the charging potential plateau is the result of a constant chemical potential among these stable GICs. Owing to their bulky sizes, the intercalants tend to be inserted at relative high densities (u = 3 or 2) to lower the dominant elastic energy. Given the large interlayer expansion, the interaction between the intercalant and the remote graphite layers is negligible; thus, the chemical potential of the intercalant in the stable GICs is independent of their stages. AlCl4 Diffusion in Graphite. Lastly, we examine the diffusion of AlCl4 in the graphite. The diffusion energy barriers of AlCl4 along four elementary pathways in the graphite are calculated using the NEB method. Figure 7 shows these four pathways between two graphite layers with the Al ions lined up with two C atoms at the T site. There are two nonequivalent nearest-neighbor sites to T, labeled by T1 and H, and there are two other nonequivalent nearest-neighbor sites to H, labeled by H1 and H2. Here “T” stands for atop site and “H” stands for hollow site. Other pathways can be regarded as combinations of these four elementary pathways. The energy barriers along these pathways are listed in Table 1, ranging from 0.012 to 0.029 eV, much smaller than those (∼0.2 eV) in the Li/graphite batteries. Thus, the AlCl4 cluster diffuses much faster than Li ions, thanks to the large (163%) interlayer expansion of the graphite. We can also estimate the diffusion constant (D) of the intercalant using

Figure 7. Four elementary diffusion pathways for AlCl4 in the graphite denoted by arrows connecting two sites.

Table 1. Diffusion Energy Barrier (Ed) and Diffusion Coefficient (D) of AlCl4 along the Four Elementary Pathways as Shown in Figure 7 pathway

T→H

T → T1

H → H1

H → H2

Ed (eV) D (cm2 s−1)

0.012 2.045 × 10−4

0.029 3.16 × 10−4

0.012 2.12 × 10−4

0.012 6.37 × 10−4

1

( ) E

the equation: D = 6 l 2v0exp − k Td , where l is the hopping b

distance between the initial and the final sites along each pathway; v0 is the attempt frequency (1013 Hz); Ed is the diffusion energy barrier; kb is the Boltzmann constant; and T is the temperature. The diffusion constants of AlCl4 in the graphite are in the order of 10−4 cm2 s−1 (Table 1), comparable to those reported by Wu20 et al., but much higher than those from Jung19 et al. The much lower diffusion constants from Jung et al. are mainly due to the interaction between the doubly stacked AlCl4 clusters across the adjacent graphene layers. The fast diffusion of AlCl4 is responsible for the ultrafast (dis)charging of the Al battery. Although not studied, the micropore structure in the F

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The Journal of Physical Chemistry C

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graphite foam is expected to accommodate large volume changes and to shorten the diffusion length of AlCl4 in the electrode material.

4. CONCLUSION To summarize, we have carried out first-principles calculations to provide a comprehensive understanding of the Al/graphite battery. We have addressed key questions pertaining to its unprecedented performance and resolved the controversies in literature regarding the geometry and gallery height of the intercalant. We reveal that the intercalant prefers to take the single-layer tetrahedron geometry in the graphite with the gallery height of 8.81 Å, consistent with the experimental XRD patterns. The AB stacking of the graphite is retained after the intercalation. The stage-4 GIC is found to be most favorable, consistent with the experimental finding. Due to its bulky size, AlCl4 tends to be intercalated at relative high densities (3 × 3 and 2 × 2) with an average potential at 2.06 V vs Al3+/Al. Four stable GICs are identified with the same intercalant chemical potential, explaining the observed charging voltage plateaus. Diffusion energy barriers of the intercalants are determined as between 0.012 and 0.029 eV, leading to ultrafast (dis)charging of the battery. These findings shed light on the storage mechanism of Al/graphite battery and pave the way for its further development.

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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.7b00888. Atomic structure of the stage-4 GICs with different stacking and with different intercalant densities (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Yurui Gao: 0000-0001-7486-8134 ZhengZheng Chen: 0000-0002-4911-9649 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Army Research Office through the grant W911NF-15-1-0449. REFERENCES

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DOI: 10.1021/acs.jpcc.7b00888 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcc.7b00888 J. Phys. Chem. C XXXX, XXX, XXX−XXX