Structural and Electrochemical Properties of Type VIII Ba8Ga16−δSn30+δ Clathrate (δ ≈ 1) during Lithiation

Clathrates of the tetrel (Tt = Si, Ge, Sn) elements are host–guest structures that can undergo Li alloying reactions with high capacities. However, little is known about how the cage structure affects the phase transformations that take place during lithiation. To further this understanding, the structural changes of the type VIII clathrate Ba8Ga16−δSn30+δ (δ ≈ 1) during lithiation are investigated and compared to those in β-Sn with ex situ X-ray total scattering measurements and pair distribution function (PDF) analysis. The results show that the type VIII clathrate undergoes an alloying reaction to form Li-rich amorphous phases (LixBa0.17Ga0.33Sn0.67, x = 2–3) with local structures similar to those in the crystalline binary Li–Sn phases that form during the lithiation of β-Sn. As a result of the amorphous phase transition, the type VIII clathrate reacts at a lower voltage (0.25 V vs Li/Li+) compared to β-Sn (0.45 V) and goes through a solid-solution reaction after the initial conversion of the crystalline clathrate phase. Cycling experiments suggest that the amorphous phase persists after the first lithiation and results in considerably better cycling than in β-Sn. Density functional theory (DFT) calculations suggest that topotactic Li insertion into the clathrate lattice is not favorable due to the high energy of the Li sites, which is consistent with the experimentally observed amorphous phase transformation. The local structure in the clathrate featuring Ba atoms surrounded by a cage of Ga and Sn atoms is hypothesized to kinetically circumvent the formation of Li–Sn or Li–Ga crystalline phases, which results in better cycling and a lower reaction voltage. Based on the improved electrochemical performance, clathrates could act as tunable precursors to form amorphous Li alloying phases with novel electrochemical properties.

. Crystallographic data for Ba8Ga14.9Sn31.1 from single crystal XRD Table S2. Atomic coordinates, occupancies, and equivalent isotropic displacement parameters (Ueq) of Ba8Ga14.9Sn31.1 from single crystal XRD refinement Table S3. PDFgui refinement parameters for pristine Ba8Ga15Sn31. Table S4. The measured voltages and capacity for each sample after electrochemical lithiation. Table S5. PDFgui refinement parameters for pristine β-Sn and LixSn samples fit to different phase combinations. Table S6. PDFgui refinement parameters for LixBa0.17Ga0.33Sn0.67 samples fit to different phase combinations. Table S7. Lattice constants from the DFT calculated structures (LiBa8Ga15Sn31). Figure S1. SEM images and EDS spectra of two Ba8Ga15Sn31 single crystal particles and PXRD of the type VIII clathrate powder. Figure S2. SEM images of Ba8Ga15Sn31 and β-Sn electrodes prior to electrochemical lithiation. Figure S3. Calculated total and partial PDF patterns for LiSn, Li7Sn3, Li7Sn2. Crystal model schematics of LiSn and Li7Sn3. Figure S4. Calculated total and partial PDF pattern for type VIII clathrate Ba8Ga15Sn31. Figure S5. PDF refinement and crystal structure of pristine β-Sn. Figure S6. PDF refinements for lithiated β-Sn (LixSn) samples. Figure S7. PDF refinements for lithiated Ba8Ga15Sn31 (LixBa0.17Ga0.33Sn0.67) samples. Figure S8. Crystal model view of Li7Sn3 showing only Sn atoms to demonstrate certain Sn-Sn distances. Figure S9. Variable temperature PDF during in situ heating from 310 -420 K for Li3.2Ba0.17Ga0.33Sn0.67 Figure S10. Capacity and Coulombic efficiency vs cycle number for β-Sn and the type VIII Ba8Ga15Sn31 clathrate for 30 cycles. Figure S11. Comparison of the crystal structures of β-Sn, Li2Sn5, and LiSn, which show a common square Sn unit. Figure S12. Voltage profile, dQ/dE plot, PXRD and SEM of electrodes before and after full lithiation for the type I K8LixGe44-x clathrate electrode.

Synthesis of Type VIII Clathrate Ba8Ga15Sn31
The synthesis was done in a manner, similar to a previous work. 1 Large crystals of the type VIII clathrate with refined composition Ba8Ga~15Sn~31 were grown by Ga/Sn flux reaction. Elemental Ba, Ga, and Sn (commercial grade materials with stated purity 99.9% wt or greater) were combined in a 8:40:65 molar ratio to a 2 cm 3 alumina crucible that was subsequently flamed-sealed in an evacuated fused silica tube. The sample was heated to 500 ºC (20 ºC/hr) then held at 500 ºC for 500 hrs. After cooling to 400 ºC (-5 ºC/hr), the Ga/Sn flux was removed by centrifugation. The large crystals were then hand ground prior to electrochemical testing.

Single Crystal X-ray Diffraction
Single-crystal X-ray diffraction measurements were performed on a Bruker APEX-II CCD diffractometer stocked with a sealed-tube Mo Kα (λ = 0.71073 Å) source. Proper single crystals were selected under an optical microscope, covered in Paratone-N oil and placed onto a holder loop made of low-background plastic. The holder was transported to the goniometer head, where a cold stream of nitrogen gas was used to harden the oil and to prevent oxidation/decomposition over the span of the data collection. The temperature was kept at 200(2) K throughout the experiment. Data acquisition was performed with Bruker-provided software. Measurements were collected in batch runs with a frame width of 0.8° in ɷ and θ. Data reduction and scaling were managed using SAINT. 2 Absorption correction was implemented using SADABS software program. 3 The structure was solved using ShelXT 4 in Olex2 5 and refined with the full-matrix least squares method on F 2 , as implemented in SHELXL 6 . Atomic coordinates were standardized using STRUCTURE TIDY 7 and tables were generated using ReportPlus. The CIF from this refinement is available as a supporting information file.

Electrochemical Measurements
The clathrate powder was prepared into slurries by mixing the clathrate sample with 10 wt% carbon black (to serve as conducting additive) and 10 wt% polyvinylidene difluoride (PVDF) (to serve as Two to three repeats of a single electrochemical experiment were conducted to provide enough lithiated powder for structural characterization. After the electrochemical lithiation was complete, the pouch cell was taken into an argon-filled glovebox and opened. The electrode was then immersed in 10 mL of dimethyl carbonate for 30 seconds to wash off any excess battery electrolyte. After the electrode was dry, the lithiated powder was scraped off the copper current collector using a knife. The extracted powder was then crushed in a mortar with a pestle to break up any agglomeration. The powder was sealed in a 2 mL centrifuge tube and then sealed under argon in a polyfoil bag before shipping to the synchrotron facility.

Pair Distribution Function (PDF) Analysis
Lithiated powders were loaded into 0.8 mm diameter borosilicate capillaries and sealed with wax and superglue inside an argon-filled glovebox, while pristine powders were loaded into the capillaries in ambient conditions. PDF measurements were performed at Diamond Light Source (Didcot, United Kingdom) at the I15-I dedicated PDF beamline with 76 keV X-rays (wavelength of 0.161669 Å) and 2D PerkinElmer image plate detectors. The detector geometry allowed collection of total scattering data to Q S5 = 30 Å -1 . Ex situ PDF measurements were carried out at room temperature. The in situ PDF heating measurements were carried out from 300 -450 K (temperature interval of 10 K) using an Oxford Instruments Cryojet 5. After reaching each hold temperature, there was a 1.5 min equilibration period and then the scattering data were collected with a 5 minute collection time. The heating temperature was limited to 450 K to avoid decomposition of the PVDF binder in the composite electrodes.
PDFs were generated from the total scattering data using PDFgetx3 8 within the xPDFsuite software package, 9 wherein the measured total scattering intensities, ( ), are corrected to obtain the coherent scattering, ( ), and transformed into the structure function, ( ), according to equation 1, 8 where ( ) is the atomic scattering factor, which is averaged over all atom types in the sample. The PDF, ( ), is obtained from the Fourier transform of ( ) as shown in equation 2: To generate the PDFs, the following parameters were used: Qmin = 0.5 Å -1 , Qmax = 25 Å, -1 rstep = 0.1 Å, and rpoly = 0.9. The nominal composition for lithiated samples was obtained from the charge passed during the electrochemical measurements.
PDF refinements were carried out using PDFgui. 10 No attempts were made to consider the presence of binder, carbon black, or solid electrolyte interphase (SEI) components in the samples.
Previous reports have shown that these components add negligible contribution to the PDF data. 11 PDF refinements were performed using Qdamp = 0.0247 and Qbroad = 0.0151 (obtained from refinement of a NIST Si standard). To refine a PDF pattern, the major phase of the pattern was first selected and then scale factor and lattice parameter were refined. Then the isotropic displacement parameters for each element (initially set to 0.03 Å 2 ) and the linear atomic scale factor (delta1) were allowed to be refined. If this resulted in an insufficient fit, possible secondary phases were added and refined in a similar way. In some cases, the Li isotropic displacement parameters refined to very large values (0.5 -1 Å 2 ). If this S6 occurred, the Li isotropic displacement parameters were fixed to a lower value. Unphysical isotropic displacement parameters for Li have been reported previously and are an indication of disorder/partial occupancy or atomic substitution. 12 The refinements were conducted using the following structures for the fittings: Ba8Ga14.9Sn31.1 ( 4 ̅ 3 , Table S1-2), β-Sn ( 4 1 / , ICSD-252800), 13 , LiSn (P2/m, ICSD-104782), 14 Li7Sn3 (P21/m, ICSD-104785), 15 and Li7Sn2 (Cmmm, ISCD-104784). 16 The relative phase content determined from the PDFgui refinement is calculated by normalizing the percentage of each phase, with the phase written in whole atom compositions. For example, the refinement results for the data shown in Figure S6a were 70% of Li0.5Sn0.5 and 30% of Li0.7Sn0.3, which we designate as 70% of LiSn and 30% of Li7Sn3.

Powder X-ray Diffraction (XRD)
Powder X-ray diffraction was performed using a Bruker D8 diffractometer with Cu X-ray source with Jana2006. 17 The peak shapes were described by the pseudo-Voigt function background fit with Legendre polynomials.

Scanning Electron Microscopy
Scanning electron microscopy (SEM) imaging was performed using an XL30 ESEM-FEG microscope and a 20 kV electron beam. The electrodes were cut from copper foil and mounted on SEM stubs with carbon tape. Energy dispersive X-ray spectroscopy (EDS) measurements were taken at 20 kV with a 2.4 nA spot size S7

Density Functional Theory (DFT) Calculations
The first-principles DFT calculations were performed to explore Li insertion and migration in the type VIII clathrate using a similar manner as in our previous work [18][19][20] . The calculations were carried out using the VASP code 21,22 , the PBE functional 23 , and projector augmented wave (PAW) potentials with a plane wave basis set 22 . In the PAW potentials, the Sn 5p and 4d, Ba 5s, 5p, and 6s, Ga 4p and 3d and Li The formation energy was calculated as described previously. 19,24 The elemental energies of Ba, Sn, and Ga were -1.923 eV/atom, -3.972 eV/atom, and -3.0281 eV/atom, respectively. The elemental energies of bcc Ba and β-Sn were calculated with a 400 eV energy cutoff and a 12 x 12 x 12 Kpoint grid.
The energy of elemental Ga was taken from the Materials Project (mp-142). 25 The formation energy was determined using equation 3: where ( ) is the calculated energy of the Ba-Ga-Sn clathrate, ( ), ( ) and ( ) are the total energy per atom of bulk Ba, Ga, and Sn, respectively. The Gibbs free energy change of reaction (ΔGr) and the average voltage were calculated as described previously. [18][19][20] The formulas used for calculating the Gibbs free energy change and average voltage for insertion of a single Li atom into 8 15 31 are shown in equation (4) and (5)

Synthesis and Characterization of Type I Clathrate K8LixGe46-x
The K8LixGe46-x clathrate was synthesized using Liang's method. 27 The as-made sample was ground by hand and then washed three times with water. After heating overnight at 50 °C under vacuum to remove the moisture, the powder was prepared into slurries with 10 wt% carbon black and 10 wt% S9 PVDF in NMP solvent. The slurries were stirred overnight and coated onto Cu foil current collectors using a Meyer rod, and then heated at 120 o C to remove the solvent. Half-cells were assembled using Li metal as the counter electrode in the glovebox. Electrochemical testing was performed using a Biologic VMP3 galvanostat/potentiostat. Galvanostatic measurements were performed from 0.01 -2.5 V vs. Li/Li + range using a current density of 25 mA/g, while potentiostatic measurements were performed within the same voltage range using a current density of 100 mA/g. S10   (8) a Ueq is defined as one third of the trace of the orthogonalized Uij tensor. Table S3. Refinement parameters for PDF refinement of pristine clathrate sample fit to type VIII Ba8Ga15Sn31 and β-Sn. The refinement plot is presented in Figure 2c.

Pristine Ba8Ga15Sn31
Phase Type VIII Ba8Ga15Sn31 β-Sn0.93Ga0.07  Table S4. The voltage and capacity corresponding to the lithiated type VIII Ba8Ga15Sn31 and β-Sn samples used for PDF measurements (corresponding to the points indicated in Figure 3). The number of Li inserted was normalized to the amount of Sn or (Ga + Sn) in the starting compound.