Experimental and Computational Study of the Lithiation of Ba 8 Al y Ge 46–y Based Type I Germanium Clathrates

RESULTS AND DISCUSSION

3.1. Structural Characterization. PXRD patterns were taken on the synthesized Ge clathrates samples before and after ball-milling. All of the hand-ground samples displayed crystalline peaks (Figure 2a), matching the reflections for Ba 8 Ge 43 clathrate (PDF 01-073-5638), 34 and in excellent agreement with the simulated PXRD patterns from the refined structures via SCXRD methods. For the Al containing samples, the reflections were shifted to lower angles and least-squares refinement showed the lattice constant increased from 10.653 Å for Al0 to 10.835 Å for Al16 (Table S1). These cell parameters match closely with those previously reported 32 as well as the SCXRD results (Table 1). Crystalline diamond cubic Ge (c-Ge), identified by the (111) reflection, was noticeable in the PXRD patterns for Al0 and Al4, but the phase fraction determined from the refinement showed that the quantity was very small (Table S1). No other crystalline peaks were observed. The powder after ball-milling (Figure S1a) also displayed a crystalline clathrate structure without any change of the cell parameter and impurities, but the PXRD diffraction intensities decreased and the peaks were broader, which is consistent with a smaller particle size in the ball-milled samples.

SCXRD was performed on the as-synthesized clathrate samples by extracting small crystallites from the crushed arcmelted ingots. The lattice parameters and Ge/Al ratios obtained from the SCXRD data are shown in Table 1 and the crystallographic information files can be found in the Supporting Information. Standard deviations on the occupancies were 1% or better. The four samples with the highest Al content (Al8-Al16) showed unit cell parameters in the narrow range of 10.8008(5) to 10.8425(6) Å and refined compositions of Ba 8 Al 11.4(1) Ge 34.6 (1) to Ba 8 Al 15.6(1) Ge 30.4 (1) .

The structure refinements for almost all prepared clathrates showed excellent agreement between the nominal (loading) and final composition, which is indirect proof for the homogeneity of the samples. The unit cell volumes subtly decrease with the decrease of the Al content, corresponding to the small difference in the elemental radii (Al is 1.248 Å while Ge is 1.242 Å), but the variations in the unit cell volume were not monotonic. Because Al and Ge atoms scatter X-rays in a significantly different way, the refinements of the occupancies of Al on the three framework positions was possible and confirmed the preference of Al for the 6c site. This is in contrast to the Ba 8 Al y Si 46-y clathrates, where the exact Al/Si ratios on the individual framework sites cannot be reliably established using X-rays. 43,44 The ratios are in agreement with the literature on other type I clathrates, where the preference for the 6c site is well documented. 45,46 The balance to 100% occupancy is attributed to vacancies.

For the sample with the lowest Al content (Al4), the 24k site appeared to contain no measurable amount of Al; the 16i site was co-occupied by Ge and Al in a ratio of 9:1, and for the first time, the 6c site in a Ba-Al-Ge clathrate system was found to be under-occupiedwhen freed, the site occupation factor of this position was less than 100%, suggesting that the atom(s) located at 6c is almost 1/4 lighter than Al. This, together with the drastic decrease in the unit cell parameter (a = 10.741 Å), is an indicator of vacancies at the 6c site. The diffraction data can then be modeled with ca. 2 vacancies at the 6c site. This results in a refined composition of Ba 8 Al ∼6 Ge ∼38 , which is in good but not excellent agreement with the nominal composition of Ba 8 Al 4 Ge 42 . This structural description is consistent with the interatomic distances within the framework, which for the Al-rich samples show Ge/Al (6c)-Ge/Al (24k) bond lengths exceeding 2.51-2.53 Å (recall that the 6c site is mostly occupied by Al, which is spatially more demanding than Ge), while for Al4, the corresponding bond distance is 2.4660(9) Å.

The anisotropic displacement parameters of the Ge atoms neighboring the vacancies (i.e., in the 24k sites) are also worthy of a mentioninstead of spherical, the mean square atomic displacements (0.0273, 0.0141, and 0.0140 Å 2 ) show that one of the principal directions is nearly twice as large as the other two. This is also readily seen in Figure 2b, where the nearest Ge/Al neighbors at the 24k site are strongly affected by the vacancy, causing the ellipsoid to be elongated in the direction of the Ge/Al (6c)-Ge/Al (24k) bond.

Exactly the same phenomenology concerning the bond distances and anisotropic displacement parameters is also seen in the structure refinements for Al0, Ba 8 Ge 43 . The unit cell parameter decreased sharply to 10.6335(15) Å with the 6c site being vacant nearly 50% of the time. As a result, the unrealistically short Ge-Ge distance of 2.354(1) Å is avoided. The anisotropic displacement parameter of the Ge atoms neighboring the vacancies is also clear indication that these atoms are "vibrating" around their equilibrium positionsthe principal direction is nearly three times as large as the other two, as evident from the principal mean square displacements of 0.0510, 0.0160, and 0.0153 Å 2 . The latter is a sign that the structural description of the Al0 clathrate in the same space group as the others leads to structural deficiencies and alternatives must be sought. Other research teams have shown that using an eight times larger unit cell volume with cell edge in excess of 21 Å and body-centered cubic symmetry might resolve these problems, 34,47,48 although the diffraction patterns of our arc-melted samples did not show reflections that violate the presumed symmetry.

3.2. XPS Characterization. XPS was used to further characterize the surfaces of the hand-ground and ball-milled clathrate electrodes. Deconvolution of the high-resolution Ge 2p spectrum (Figure S2a), showed characteristics typical for GeO 2 , GeO, and Ge-Ge at binding energies of 1220.8, 1219.2, and 1217.8 eV, respectively. 49 From the fitting procedure, the amount of Ge-Ge signal was found to be 9% for Al0 and 15% for Al16 in both HG and BM cases (Table S2). To serve as a reference, c-Ge powder was ball-milled and characterized by XPS; the Ge-Ge contribution was 21% of the total Ge 2p signal (Table S2). This suggests that the oxide layer on the Ge clathrates is thicker than the native oxide layer on c-Ge. A similar observation was made in epitaxially grown Ge clathrate, where only the Ge oxide signals were seen in the Ge 2p XPS spectrum taken from the surface. 50 The high-resolution XPS profile for Al 2p (Figure S2b) showed a single peak at 75.44 and 75.07 eV for BM-Al16 and HG-Al16, respectively. These binding energies are in the range for aluminum oxide. 51 Because of the care taken to minimize oxygen contamination during the arc-melting synthesis, the oxidized surfaces likely formed from the exposure of the germanium clathrates to atmospheric oxygen. 3.3. SEM and TEM Characterization. SEM was used to characterize the morphology of the pristine electrodes prepared from hand-ground (Figure S3) and ball-milled clathrates (Figure S4). The SEM micrographs of the HG samples show large shards (greater than 3 μm) of clathrate particles covered in carbon black. The BM samples contained spherically shaped particles generally around 1 μm or smaller in diameter, demonstrating that ball-milling changed the morphology and particle sizes. No morphological differences were observed between the clathrates of varying Al substitution.

TEM was used to characterize the surfaces and crystallinity of the hand-ground and ball-milled Al0 and Al16 samples (Figure 3). Selected area electron diffraction (SAED) was also used to assess the crystallinity of an entire particle. Similar to our previous work with the Ba 8 Al y Si 46-y clathrates, we find that ball-milling has a considerable effect on the crystallinity of the samples, particularly at the surface. For HG-Al0, distinct lattice fringes and a spot pattern in the fast Fourier transform (FFT, inset) were observed, indicating crystalline clathrate in the center of the particle, although with a thick amorphous layer (up to ∼15 nm) on the surface (Figure 3a). The amorphous layer on the surface of the particles is consistent with the oxide layer observed in the XPS results. From the TEM image, small crystalline regions could be seen in the BM-Al0 particles, but the SAED pattern showed diffuse rings, indicating that the particle lacked long range order and contained large amorphous content (Figure 3b). This indicates that the ballmilling process significantly amorphized the Al0 clathrate particles, which is consistent with the lower and broader intensities from the PXRD patterns of the ball-milled powders (Figure S1a).

For the Al16 samples, a similar trend is seen whereby HG-Al6 (Figure 3c) is more crystalline than BM-Al16 (Figure 3d) based on the SAED patterns of the particles. The BM-Al16 sample appears to have retained more of its crystallinity after the ball-milling based on the decreased amount of amorphous background in the SAED compared with BM-Al0. This is consistent with the XRD pattern (Figure S1a) where BM-Al16 had sharper and more intense reflections than the BM-Al0 pattern, suggesting a higher crystallinity for BM-Al16.

3.4. Galvanostatic Measurements. To study the electrochemical properties of the Ge clathrate samples, galvanostatic cycling was performed between 0.01-2.5 V versus Li/Li + at 25 mA/g. The first charge (lithiation) and discharge (delithiation) voltage curves are shown in Figure 4. As indicated by the voltage plateaus observed during charging, the clathrates undergo two-phase conversion reactions 52 to form Li-rich phases, with a large amount of Li reacted per clathrate formula unit (f.u.), as designated by the numbers next to each voltage profile. For example, HG-Al0 (Ba 8 Ge 43 ) reacted with 173 Li per f.u. in the first charge, which corresponds to 4 Li/Ge (assuming all of the charge went toward the lithiation reaction with the clathrate). However, because of the irreversible capacity loss in the first cycle, there is likely substantial solid electrolyte interphase (SEI) formation from electrolyte reduction and the actual Li/Ge ratio is lower.

It is well known that c-Ge will react with Li to form a series of amorphous and crystalline Li-Ge phases, accompanied by a large volume expansion. 39 In contrast to c-Ge, which reacts at ∼350 mV versus Li/Li + , 39,53,54 we find that the reaction potential for the clathrates occurs at a lower voltage (∼160-200 mV for HG-Al0) and decreases with the increasing amount of Al content. The capacity of the first charge also decreases with the increasing Al content, suggesting that framework substitution of Al alters the properties of the twophase reaction. The voltage profiles are more sloped in the ball-milled samples (Figure 4b) than in the hand-ground ones (Figure 4a), which is consistent with the higher amount of amorphous content in the ball-milled powders because lithium is expected to react with the amorphous clathrate phase in a solid-solution mechanism, similar to lithiation of amorphous Si and Ge. 54,55 The delithiation characteristics for the HG and BM samples are similar and show a gradually sloping voltage profile, indicating a single-phase reaction. The voltage profiles of the subsequent cycles were also sloped (as shown in Figure S5a for HG-Al0). These observations are similar to those found in lithiation of c-Si and c-Ge, whereby amorphous lithium silicide/germanide phases grow at the expense of the unlithiated crystalline phase as the electrochemical reaction proceeds in the first charge, but subsequent cycling involves lithium insertion/deinsertion into the amorphous phases in a solid-solution mechanism. XRD of the electrodes at the end of the first charge (Figure S1b) showed no reflections, which suggests that the phases after lithiation are amorphous. This is different from the lithiation of Ge and type II Na 24 Si 136 clathrates, where the formation of Li containing crystalline phases is observed at low voltages. 23,39 These ex situ XRD results suggest that the presence of Ba and Al seem to impede the formation of these phases in Ge clathrates, although operando studies would be more suitable for detecting the presence or absence of transient Li-Ge phases. 39 The capacities also increase after ball-milling, which can be attributed to enhanced lithiation in the smaller particle sizes due to the decreased diffusion length, as observed in the SEM images (Figures S3 andS4).

The differential capacity (dQ) plots for Al0 and Al16 (Figure 5), derived from galvanostatic cycling, are presented to elucidate the differences between the HG and BM voltage profiles. The reduction peaks are attributed to the two-phase reaction between the unlithiated Ge clathrate and the amorphous Li germanide phases. The HG-Al0 dQ plot (Figure 5a) displayed two sharp reduction peaks at 0.16 and 0.12 V versus Li/Li + , suggesting the formation of a series of Li germanide phases with different compositions. This potentialdependent redox behavior is distinctly different from that in c-Ge, where peaks at ∼0.35 and ∼0.18 V are seen in dQ plots during lithiation. 39,54 The BM-Al0 sample, however, shows a much broader voltage profile with the reactions starting at ∼0.4 V in contrast to ∼0.2 V for HG-Al0. This is consistent with the large amount of amorphous content in BM-Al0, as seen in the TEM results (Figure 3b) and the tendency for amorphous materials to display a much wider reaction window because of a larger distribution of possible Li reaction site energies. 56 Upon delithiation, both BM and HG-Al0 show similar behavior with an oxidation peak at 0.3 V, suggesting that the phases created at the end of lithiation are similar. The dQ plots for HG and BM-Al16 match closely with each other (Figure 5b), indicating that the ball-milling did not significantly affect the electrochemical properties. This is consistent with the TEM and XRD results showing that the BM-Al16 retained more of its crystallinity than BM-Al0. The reaction begins at 0.08 V in the Al16 samples, demonstrating a decrease in the reaction voltage as the Al content increases. The delithiation of Al16 is characterized by a broad peak stretching from 0.15 to 0.6 V, which contrasts with the sharper profile observed in Al0. We attribute this to the distribution of Al over many possible configurations in the amorphous phase, which would result in the reaction voltage to be more spread out, reflecting the different possible chemical environments for Li. The dQ plots of subsequent cycles (Figure S6) showed little change in the potential-dependence behavior, with broad reaction peaks characteristic of the lithiation of amorphous phases.

The capacity retention plots for the HG samples (Figure S5b) showed that the capacity of the Al0, Al4, and Al8 clathrates quickly decreased to less than 5% of their initial lithiation capacity while Al12 and Al16 retained 10 and 20%, respectively, of the initial capacity after 20 cycles. The results also show that Al16 showed the highest capacity retention, but lowest charge capacity in the first cycle. Al12 and Al16 react with the least amount of Li and thus suffer less from the volume expansion induced capacity degradation during cycling.

The Coulombic efficiency (CE) of the first cycle for the BM and HG samples (Figure S5c) decreases with the increasing Al content and is also higher for the ball-milled samples.

This quick capacity fade is typical of unoptimized Si and Ge electrodes and arises due to large volume changes during charge and discharge, which can cause particle decrepitation/ pulverization and detachment from the current collector. 30,57,58 Our electrode preparation (Supporting Information) is not optimized for large volume expansion, as generally more conductive additives are used to maintain electronic contact. 59 Ge powder that was ball-milled was also tested and a similar capacity fade was observed (Figure S7). Therefore, this low capacity retention could be due to the pulverization and particle detachment of the clathrate materials after the amorphization reaction and hence could be improved with subsequent modification of the electrode formulation and particle sizes.

The composition dependence of the capacity can be rationalized by considering the electrochemical behavior of Li with Ge versus Al. Al reacts with 1 Li to form the LiAl phase at room temperature, 60 while Ge can react with up to 4.4 Li. 54 This means that replacing Ge with Al will decrease the capacity of the resulting amorphous phase. In Table S3, the theoretical and observed experimental capacities are compared assuming reaction of 4.4 Li/Ge. Note that to understand the effect of composition to the observed capacities, the contribution of charge to SEI formation is not considered. Al0 shows the closest correspondence to the theoretical values, but as the Al content increases, the difference between theoretical and experimental values increases. Previous studies on amorphous Si-Al-sputtered thin films 61 have suggested that the formation of ternary phases, such as LiAlSi, 62 may trap Li and limit the lithiation. LiAlGe also exists, but its electrochemical properties have not been investigated. The formation of a kinetically trapping phase could also explain the lower CE found for the clathrates with higher Al content (Figure S5c). However, no other crystalline phases are detected after lithiation (Figure S1b), indicating that if present, any crystalline regions are too small to detect via XRD. Different SEI formation properties could also contribute to this trend in the CE. The presence of Ba in these amorphous phases further complicates the analysis and more detailed studies would be needed to understand the properties and formation of the amorphous phases.

3.5. Post-Mortem Characterization. As discussed previously, PXRD of the electrodes after the first charge showed that the reflections associated with the clathrates had all disappeared, suggesting the amorphization of the material and a conversion reaction mechanism (Figure S1b). Comparing the morphology of the clathrate electrodes before and after the first lithiation (Figure S4) showed indication of particle volume expansion and coating of the electrode with an SEI layer, which explains the fast decay of the capacities (Figure S5b) and generally low CE (Figure S5c,d).

These results confirm that the reaction mechanism of Li with the Ge clathrates is a conversion reaction to a Li-rich phase like that seen in the electrochemical lithiation of c-Si and c-Ge. However, the question of whether Li insertion into the crystal structure is possible is still yet to be answered. The voltage region before the start of the voltage plateau is considerably more sloped for the BM samples, indicating a single-phase reaction. 52 Ex situ PXRD was performed for the BM and HG samples before and after the beginning of this region, which corresponds to 40 and 60 Li inserted per f.u. (with the assumption that all the charge went towards Li insertion), to assess the crystallinity at these points in the lithiation process. The voltage profiles and corresponding XRD results from these experiments are shown in Figure 6a,b.

For the pristine (unlithiated) electrodes, the HG-Al0 sample is more crystalline when compared to the BM sample, as seen by the higher intensity and sharper reflections. This is also consistent with the TEM characterization results (Figure 3). After insertion of 40 Li per f.u., the intensities of the clathrate reflections in the XRD decreased in both Al0 samples, but by different amounts. The intensity of the reflections in HG-Al0 decreased by more than half, while that for BM-Al0 decreased to ∼75% of those in the pristine sample. After insertion of 60 Li, the reflections decreased more for both samples. The larger decrease in peak intensity for HG-Al0 suggests that the Li being inserted is participating in the two-phase conversion reaction between the Ge clathrate and the Li-rich amorphous phase, thus decreasing the amount of crystalline clathrate. This is corroborated by the flat voltage profile at this point in the first lithiation step (Figure 6a). The voltage profile for BM-Al0, however, is more sloped indicating a solid-solution insertion into an amorphous phase, 55,63 which in this case is the amorphous clathrate phase that was formed during ball-milling. BM-Al4 was investigated in a similar manner (Figure 6c,d). After insertion of 40 Li per f.u., no decrease in the intensity of the clathrate reflections was detected. This suggests that these Li were not participating in a two-phase conversion of the crystalline clathrate, but a reaction with the amorphous surfaces (i.e., the surface oxides, the amorphous layer formed from ball-milling). As more Li was inserted, the clathrate structure was completely converted to the amorphous phase at around 120 Li per f.u. No significant change in peak positions was seen after the insertion of these different amounts of Li, suggesting that the clathrate structure was maintained without large change in lattice constant until the conversion reaction.

The PXRD results were confirmed with SCXRD measurements on samples after lithiation. Al0 powders were chemically lithiated using direct contact with Li foil, but the refinement results showed no statistically significant differences from the lattice constant and formula of the as-synthesized Al0 (Supporting Information).

3.6. Electrochemical Impedance Spectroscopy. In our previous investigation of Si clathrates, EIS was used to identify the mechanism of lithiation as being confined to the surface of the particles in a pseudocapacitive-faradaic process, primarily by inspection of the Bode plots. 29 The same galvanostatic pulse protocol we used in that study was applied to both the handground and ball-milled Al0 and Al16 Ge clathrate samples (Supporting Information, Figures S8-S11). In the Bode plot, the low-frequency phase angle close to -45°is an indication of Warburg-type, solid-state diffusion of Li into the electrode, while a phase angle close to -90°would indicate a blocking electrode or surface adsorption of Li. 64 As shown in Figure 7, the low-frequency angle moved toward -45°for all samples as the state-of-charge (SOC) increased, which is consistent with the conversion of the crystalline clathrate into amorphous phases that can react with lithium. When comparing the Bode plots for HG-Al0 (Figure 7a) with HG-Al16 (Figure 7b), we see that the phase angles for HG-Al16 remained less than -60°, indicating a more blocking character. This is also consistent with the increased crystallinity of the pristine sample as observed by TEM, as well as the lower lithiation capacities obtained in the galvanostatic cycling. On the other hand, the phase angle at low frequencies remained close to -80°for silicon clathrates lacking an amorphous surface layer, 29 indicating the blocking character of the structure. We attribute the Warburg feature to Li diffusion in the amorphous phases present in the Ge clathrates, which originate from the decreased structural stability of the Ge clathrates to atmospheric oxygen, ball-milling, and also to electrochemically induced amorphization, while the blocking character of the electrodes originate from the crystalline clathrate domains.

The reaction mechanism for the hand-ground and ballmilled Ge clathrate samples can thus be summarized as follows. After reduction (presumably) of the surface oxide species and formation of the SEI layer, the Li reacts with the HG clathrate in a two-phase reaction between the unlithiated crystalline clathrate and a Li-rich amorphous germanide phase. For the BM samples, lithium insertion into the amorphous layer on the outside of the crystalline cores (presumably arising from the damage caused by ball-milling) precedes the two-phase reaction. For both cases, full lithiation results in complete amorphization, with subsequent lithium cycling occurring through a single-phase, amorphous solid-solution.

3.7. Theoretical Calculations. DFT was used to theoretically investigate the lithiation voltages and diffusion barriers (Supporting Information) for the Al0 and Al16 Ge clathrates to rationalize why Li insertion into the clathrate structure is not observed experimentally unless it is amorphous. The framework vacancies can occupy the 6c position in a random or ordered arrangement depending on the synthesis conditions and heat treatment. 6,34 For arc-melted Ba 8 Ge 43 , it has been reported that there is an absence of vacancy ordering 6 and this is consistent with single-crystal refinements of the arc-melted Al0 clathrates synthesized in this work (Supporting Information). For this reason, we chose to model Ba 8 Ge 43 with randomly chosen vacancies at the 6c positions in the conventional unit cell. For the Al16 clathrate, we followed previous calculations showing that the lowest energy configuration consists of 3 Al at the 6c sites, 1 Al at a 16i site, and 12 Al in the 24k sites, with no Al-Al bonds. 32,65 The formation energy and lattice constants for the unlithiated structures are shown in Table 2. The lattice constants match well with the experimental results and show the increase of lattice constant with substitution of 16 Ge with Al.

For Li insertion to occur in a material, there must be favorable positions in the crystal structure for Li to reside and a low-energy pathway between these positions for bulk diffusion. To assess the possibility of Li insertion into the Ge clathrates, S12a) is found to be energetically favorable, resulting in a decrease in the formation energy and a high average lithiation voltage of 0.85 V versus Li/Li + . Filling the three vacancies with Li (i.e., Ba 8 Ge 43 Li 3 , Figure S12b) is also favorable with an average lithiation voltage of 0.77 V. The formation energy of these compounds also decreases with Li incorporation, indicating a stabilization of Li in the clathrate structure with respect to bcc Li. This is consistent with experimental findings that type I clathrates can be synthesized with Li in the framework positions, 35,66 suggesting that Ba 8 Ge 43 could also be synthesized with Li in these positions. Further, according to the results in Table 2, a lattice parameter increase is calculated with framework Li incorporation, which is consistent with experimental results reported by others. For example, the lattice constants of K 8 Ge 44 and K 8 Li 2 Ge 44 are 10.677 and 10.735 Å, respectively. 36 The calculated lattice parameter increase is ∼0.2 Å for Li filling all three vacancies in Ba 8 Ge 43 □ 3 , which should be detectable by XRD. However, no lattice constant increase was observed in our PXRD measurements at different points in lithiation (Figure 6b), suggesting no bulk incorporation of Li into the vacancies. Further, SCXRD measurements of lithiated samples showed no changes in lattice constant or any of the refined metrics (Supporting Information).

Next, the nudged band elastic band (NEB) method was used to assess potential pathways for bulk Li diffusion within the Ba 8 Ge 43 □ 2 Li 1 structure through the estimation of energy barriers for Li migration. The vacancy positions reside on the hexagonal faces of the Ge 24 cages and are rotated by 90°r elative to adjacent hexagonal faces. One possible pathway, denoted as Path 1 in Figure 8a, is for Li to move to the next closest vacancy along the same chain of connected hexagons. This path involves Li moving through the hexagonal face of the Ge 24 cage until it reaches the center position, which is the 6b site; then, the Li traverses through a pentagonal face connecting the Ge 24 cages and follows a symmetrical pathway to the 6c site in the adjacent Ge 24 cage that houses the other vacancy position, also via a 6b site (Video S1). Another pathway, which is more direct and denoted as Path 2 in Figure 9a, is for Li to move within a Ge 24 cage to the vacancy site on the other hexagonal face (Video S2).

The calculated energy barriers for Path 1 and Path 2 are presented in Figures 8b and9b, respectively, with the images for each pathway labeled in Figure S14 according to each respective reaction coordinate number. We find that the highest energy barrier between two Li vacancy sites via Path 1 is 2.1 eV. There is a local energy minimum when Li is at the 6b site; the highest energy barrier is found when Li is moved to a position off a pentagon inside the Ge 24 cage (image 5 in Figure S14a). For Path 2, the energy barrier between the two vacancy sites is 1.6 eV, where the saddle point occurs when the Li is above a Ge-Ge bridge position between two pentagons (image 4 in Figure S14b). Both paths involve the movement of Li around the Ba guest atom inside the Ge 24 cage, and the highest energy positions arise in both when Ba is displaced from its favorable position in the center of the cavity, incurring a high energetic cost. Figure 9c shows a single Ge 24 cage looking down the b-axis (left) and a-axis (right) with Li (red atoms) in the 6c vacancy sites and the arrow indicating Path 2. Figure 9d shows the structure corresponding to the highest energy image from the NEB calculation, where the displacement of the Ba from the center is clearly seen. If, however, the Ba atom is absent from the cage center, the energy barrier for Li movement between the vacancies decreases to 0.5 eV (Figure 9b) and the Li is positioned closer to the cage center (Figure 9e, Video S3). As the Li diffusion barrier in c-Si is 0.47 eV 67,68 and that for c-Ge is 0.35 eV, 68 these results suggest that Li movement through the clathrate structure could be feasible but that guest atoms in the cage cavities impede lithium movement between framework vacancies. Despite lithiation into the vacancies at the 6c positions being energetically favorable, the high-energy barrier between them (1.6 or 2.1 eV, depending on the pathway) would prevent these positions from being occupied through electrochemical lithiation at room temperature.

Other Li positions aside from the framework vacancies in Ba 8 Ge 43 and Ba 8 Al 16 Ge 30 were also considered and shown in Table 2. For the Ba 8 Si 46 clathrates, the most favorable position for Li was found to be the 6b site, where the Li is centered within the hexagonal plane separating two Si 24 cages. 25 This is also found to be the lowest energy position in the Al0 and Al16 Ge clathrates (Figure S13). However, the formation energy relative to the starting structure increased when placing Li in the 6b site, and the calculated lithiation voltages were negative. This indicates that lithiation relative to metallic Li is not energetically favorable. This was also seen in the Ba 8 Si 46 case, 25 but with a lower voltage of -1.23 V compared with -0.48 V for the Al0 Ge clathrate.

Much like the high-energy transition state between two vacancies, the instability of these positions can be rationalized by unfavorable guest atom displacements. When Li is relaxed at the 6b position in Ba 8 Al 16 Ge 30 (Figure S13a), the two Ba atoms in the adjacent cages are pushed 0.35 Å away from the cage center, resulting in a 3.1 Å Ba-Li distance. The other local minimum position found was in the [Ge/Al] 24 cage offplane of the pentagon adjacent to the [Ge/Al] 20 cage (Figure S13b). This configuration had 0.1 eV higher energy than Li in the 6b position and resulted in the Ba atom to be pushed 0.78 Å off center, resulting in a 3.07 Å Ba-Li distance. In contrast, Li in the framework vacancies in Ba 8 Ge 43 results in no Ba displacement from the center and a Ba-Li distance of 3.84 Å. When Li is added to the 6b site in Ba 8 Ge 43 Li 3, the relaxed structure has large distortions in the framework as seen in Figure S12d. The voltage (-0.10 V) is higher when the vacancies are not filled (-0.48 V) suggesting that the framework distortions are more energetically favorable. This Li-induced framework distortion could lead to eventual framework destruction with the introduction of more Li where Ge-Ge bonds are broken to form the phase front of the amorphous transition, similar to what has been predicted in c-Si. 69 It is interesting to note that Li insertion at the 6b site in Ge clathrate does seem to be more favorable than the Si clathrate case as the voltage is higher (-0.48 V vs -1.23 V). This could suggest that the Ge framework more favorably accommodates Ba displacements (resulting from Li insertion) because of the larger cage size or different framework stiffness. Previously, ab initio molecular dynamics studies have shown that Ge atoms migrate significantly during lithiation of diamond cubic Ge, whereas Si atoms remain in a static position during lithiation. 70,71 The structural rigidity of Si frameworks and limited Si migration during lithiation compared to Ge could also explain the significant difference of lithiation between Si clathrates and Ge clathrates. This is consistent with our experimental XPS, XRD, and TEM results showing that Ge clathrates are less structurally stable than the Si analogues. Overall, we find that unfavorable Li positions in the Ge clathrates and high-energy barriers between vacancies suggest that Li insertion into the crystal structure is not feasible, which is consistent with experimental results.