Readme file for dataset relating to paper Lithium transport in Li4.4M0.4M’0.6S4 (M= Al3+, Ga3+ and M’= Ge4+, Sn4+): Combined crystallographic, conductivity, solid state NMR and computational studies

All file names in the data set refer to sample names in paper

Dataset contains text/ascii data files for powder Xray diffraction, Neutron powder diffraction, AC impedance spectroscopy, MAS NMR spectroscopy, electrochemical cycling, electrochemical plating, Ab initio molecular dynamics simulations.

Sample preparation:
General procedure. All sample handling was carried out in a dry box under a helium atmosphere (O2 < 3 ppm). Compositions were mixed in the appropriate stoichiometric ratio (typically in 500 mg batches), ground thoroughly and sealed as powders in evacuated carbon coated quartz tubes under a pressure of 1 x 10 4 mbar. Lithium sulfide (Li2S, Sigma Aldrich, 99.98%, containing 3 wt% of LiOH), aluminium sulfide (Al2S3, Alfa Aesar, 99+%, containing Al2S3, with Al and S8 as minority phases by PXRD, Figure S2), gallium sulfide (Ga2S3, Alfa Aesar, 99.99%), germanium powder (Alfa Aesar, 99.999%, containing 8.9 wt% GeO2), tin sulfide, (SnS, Sigma Aldrich, ? 99.99%), phosphorous pentasulfide (P2S5, Sigma Aldrich, 99%) and elemental sulfur (Sigma Aldrich, 99.999%) were used as provided, unless otherwise stated. Elemental sulfur develops a high vapour pressure at elevated temperatures, therefore for all first firings the reactions were brought to 673 K at a rate of 5 K min-1, then slowly heated to the final temperature at a rate of 0.3 K min-1, held at the temperature, and subsequently cooled to ambient temperature at a rate of 5 K min-1. When second firings were undertaken, the materials were reground, sealed in evacuated carbon coated quartz tubes as loose powders, and heated/cooled directly to the reaction temperature at a rate of 5 K min 1.
Exploratory synthesis. For the initial exploration of phase formation in the Li5AlS4-Li4GeS4 phase field, the reaction mixtures were subjected to a single firing to 973 K for 12 h, with reagents used as-received. 
Li4.4Al0.4Ge0.6-xSnxS4. To obtain high quality powder samples of Li4.4Al0.4M0.6S4 (M = Ge4+, Sn4+) it was necessary to reduce the Li2S content in the initial reaction composition by 5 mol% in order to remove an Li2S impurity phase, corresponding to a nominal stoichiometry Li4.18Al0.4M0.6S3.89 (M = Ge4+, Sn4+). This was used in all of the reactions described from here onwards, however we refer to the ICP- and Rietveld-validated “ideal” stoichiometry Li4.4Al0.4M0.6S4 for consistency of discussion. Li4.4Al0.4Ge0.6S4 and materials in the Li4.4Al0.4Ge0.6-xSnxS4 (x= 0, 0.2, 0.4, 0.6) series were obtained, as described in the general procedure, by heating reaction mixtures twice to 973 K for 48 h with intermediate grinding. Samples of Li4.4Al0.4Ge0.6S4 using this procedure with commercially sourced reagents were analysed by ICP elemental analysis and used in the solid state NMR data collection.
Additional samples of Li4.4Al0.4Ge0.6S4 and Li4.4Al0.4Sn0.6S4 were synthesised using in-house prepared Li2S and purified Ge and used for synchrotron powder diffraction (SXRD) and AC-impedance experiments. Li2S was synthesised by heating lithium carbonate (Li2CO3, Sigma-Aldrich, ? 99%) under a stream of CS2 vapour to 923 K for 6 h and high purity elemental Ge was generated by heating germanium powder (Ge, Alfa Aesar, 99.999%) in 10% H2 in argon to 873 K for 12 h to remove traces of GeO2. To synthesise Li4.4Al0.4Ge0.6S4 and Li4.4Al0.4Sn0.6S4 reaction mixtures were fired twice to 973 K for 48 h with intermediate grinding. ICP compositional analysis and solid state NMR experiments were conducted on a sample of Li4.4Al0.4Sn0.6S4 prepared in this way.
Due to the large neutron absorption cross section of 6Li, neutron powder diffraction (NPD) experiments were conducted on 7Li-enriched samples of 7Li4.4Al0.4Ge0.6S4 and 7Li4.4Al¬0.4Sn¬0.6S4. 7Li-enriched 7Li2S was synthesised by heating lithium carbonate (7Li2CO3, Sigma-Aldrich, 99% 7Li) under a stream of CS2 vapour to 923 K for 6 h and used as the 7Li2S source, which was found to be phase pure by PXRD. As a one-batch synthesis at 3.5 g led to impurity phases, neutron samples were prepared by mixing a single batch of reactants and subsequently dividing this into five carbon-coated quartz tubes which were fired twice at 973 K for 48 h with intermediate grinding. After completion of the reaction, the individual products were checked for purity by PXRD yielding the same lattice parameters; the powders were combined to give in total ~ 2.5 g of 7Li enriched samples.
Li4.4Ga0.4M’0.6S4. Li4.4Ga0.4M’0.6S4 (M’= Ge4+, Sn4+) phases were prepared using in-house prepared Li2S and purified Ge. Reaction mixtures of the stoichiometry Li4.4Al0.4Ge0.6S4 were heated twice to 973 K for 24 h with intermediate grinding.

Characterisation:
X-ray powder diffraction. All powder X-ray diffraction (PXRD) experiments were carried out at ambient temperature on powders sealed in borosilicate glass capillaries under helium gas. Phase identification was carried out using Bruker D8 diffractometers with either a monochromated Mo source (K?1, ? = 0.7093 Å) or a monochromated Cu source (K?1, ? = 1.5406 Å) in Debye-Scherrer geometry. Structure determination and Rietveld refinements were carried out on synchrotron powder X-ray diffraction (SXRD) data collected from spinning capillaries (0.3mm diameter) at the I11 beamline (Diamond Light Source, UK)  with an incident wavelength of 0.824878(10) Å, using the high resolution multi-analyser crystal (MAC) detectors. Variable-temperature SXRD from 100 – 500 K was carried out at I11 using an Oxford Cryostream Plus with the Mythen position sensitive detector (PSD).
Neutron powder diffraction. Time-of-flight neutron powder diffraction (NPD) data were collected on Li4.4Al0.4Ge0.6S4 and Li4.4Al0.4Sn0.6S4 using the High Resolution Powder Diffractometer (HRPD) instrument (ISIS, UK) both at 10 K and at ambient temperature. Samples were contained in thin-walled vanadium cans of diameter 6 mm, sealed with an indium gasket under 1 atmosphere of helium gas. Low temperature data were collected using an in-situ closed-cycle refrigerator (CCR). Bragg features from the CCR were manually excluded from the Rietveld refinements. Ambient-temperature data were collected with no CCR, in order to minimise background scattering. For all samples, NPD data were collected on 7Li enriched samples to minimise absorption effects.
Densification. For all compositions, pellets for AC-impedance spectroscopy and stability tests against lithium metal were prepared by uniaxial pressing of ~35 mg of the powdered material in a 5mm steel die at a pressure of 2.5 MPa, followed by sintering in evacuated carbon coated quartz tubes at 923 K for 24 h. Densities in the range 75% - 82% were achieved by this method.
AC impedance spectroscopy. Temperature dependent AC-impedance spectroscopy was conducted to obtain the ionic conductivity and activation energy of each composition. Sintered pellets were painted with silver paste (RS silver conductive paint 186-3600) and dried under vacuum at ambient temperature. The measurements were performed from 303 to 398 K under argon (flow rate: 50 mL/min) using a custom-built sample holder (Figure S3) and the Solartron 1296 dielectric interface coupled with the Solartron 1255B frequency response analyser. A sinusoidal amplitude of 50 mV was employed in the frequency range 1 MHz to 100 mHz. The obtained data was analysed with the ZView2 software package (ZView2 Version: 3.5d).25
NMR spectroscopy. 6Li, 27Al and 119Sn magic angle spinning (MAS) NMR spectra were recorded using a 4 mm HXY MAS Probe in double resonance mode on a 9.4 T Bruker DSX solid-state NMR spectrometer. All samples were packed in HRMAS inserts in a He glove box to eliminate air exposure. All data acquisitions were quantitative using recycle delays longer than 5 times the spin-lattice relaxation times T1. 6Li NMR data were obtained with a pulse of length 4 ?s at a radio-frequency (rf) field amplitude of 62.5 kHz and at a MAS rate of ?r = 10 kHz. 27Al NMR data were all obtained with a short 30o pulse flip angle of pulse length 0.33 ?s at rf amplitude of ?1/2?(27Al) = 83 kHz and at a MAS rate of ?r = 8 kHz. Excitation and reconversion pulses for the two dimensional z-filtered triple quantum MAS (3QMAS)26-28 experiments were performed at rf amplitudes of ?1/2?(27Al) = 100 kHz and 833 Hz for the soft pulse, respectively. The 119Sn NMR spectrum was obtained with a 90o pulse of pulse length 3 ?s at rf amplitude of ?1/2?(119Sn) = 83 kHz and at a MAS rate of ?r = 10 kHz. 27Al and 6Li shifts were referenced to 0.1 M Al(NO3)3 in H2O and 10 M in LiCl in D2O at 0 ppm, respectively. 119Sn shifts were referenced to SnO2 at -604.3 ppm (equivalent to trimethyltin at 0.0 ppm).29 
Variable temperature 7Li NMR experiments were recorded on a 4 mm HXY MAS probe in double resonance mode (between 110 K – 400 K) and a 4 mm HX High Temperature MAS Probe (above room temperature), both on a 9.4 T Bruker Avance III HD spectrometer under static conditions with the X channel tuned to 7Li at ?0/2?(7Li) = 156 MHz. All samples were flame sealed in Pyrex inserts under He atmosphere. All 7Li NMR spectra were obtained with a hard 90o pulse of 1.5 ?s at rf amplitude of ?1/2?(7Li) = 83 kHz. Spin-lattice relaxation rates in the laboratory frame (T1-1) were obtained using a saturation recovery pulse sequence and the data was fitted to a stretch exponential function of form 1 – exp[–(?/T1)?] where ? are the variable delays and ? is the stretch exponential (values between 0.3 and 1) . Spin-lattice relaxation rates in the rotating frame (T1?-1) were recorded using a standard spin-lock pulse sequence at frequencies of ?1/2?(7Li) = 20, 33 and 50 kHz and data were fitted to a stretch exponential function of form exp[–(?/T1?-1)?] where ? values are between 0.5 and 1. Temperature calibrations were performed using the chemical shift thermometers Pb(NO3)2 using 207Pb NMR and CuI and CuBr using 63Cu NMR.30-33 7Li NMR shifts were referenced to 10 M LiCl in D2O at 0 ppm.
Electrochemical cycling. The stabilities of Li4.4Al0.4Ge0.6S4 and Li4.4Al0.4Sn0.6S4 were tested against lithium metal electrodes. Symmetric Li|Li4.4Al0.4M0.6S4|Li cells were assembled in Swagelok-type cells using pellets of Li4.4Al0.4M0.6S4. Cells were prepared and sealed inside an Ar-filled glovebox (O2; H2O < 0.1 ppm). Two lithium metal disk electrodes (12 mm diameter) were punched from Li ribbon (0.38 mm thickness, Sigma Aldrich) and then mechanically pressed onto a sintered Li4.4Al0.4M0.6S4 pellet. The sealed cells were allowed to equilibrate to 323 K for 30 minutes in order to increase lithium mobility. The symmetrical cells were then cycled galvanostatically, using a VSP potentiostat/galvanostat (Biologic Science Instruments) for 100 plating and stripping cycles (J= ± 0.01 mA cm-2 for 1 h per half-cycle). 
Plating experiment. Li|solid electrolyte|Cu asymmetrical Swagelok-type cells were likewise prepared wherein one Li disk is replaced with a 12 mm diameter Cu foil (Advent RM) disk working electrode acting as the Li deposition substrate. Prior to use, the Cu disks were soaked in 1 mol dm-3 HCl solution for 15 minutes, subsequently rinsed with ethanol and ultra-pure water and then dried at 373 K under vacuum. Li|SE|Cu cells were prepared and sealed inside the glovebox and then Li was deposited onto the Cu substrate under galvanostatic control for 20 h at 0.01 mA cm-2 (T= 323 K). The resulting cells were dismantled inside an Ar-filled glovebox and the Cu working electrode was photographed.
Ab-initio molecular dynamics simulations. Periodic, plane-wave based, density functional theory (DFT) calculations were performed using VASP34, the PBE functional35 and the projector augmented wave approach.36 Calculations were performed in (a?b, 2a+3b, 2c) supercells of Li4.4Al0.4Ge0.6S4, where the supercells have a total composition of Li88Al8Ge12S80. Crystallographic disorder was taken into account by ranking one hundred different ordered atomic configurations within this supercell by energy. These configurations were generated by randomly distributing atoms in the structure under the following constraints: i) each of the four tetrahedral layers within a supercell contained 2 Al and 3 Ge atoms, ii) one of the two square-pyramidal Li3 sites close to the centre of each octahedron was randomly chosen to be occupied, iii) one octahedral interstice containing Li3 sites in each of the two octahedral layers in a supercell was randomly chosen to be vacant, leading to one vacant Li3 octahedron within each half of a supercell, and iv) one quarter of the face sharing pairs of Li1 and Li2 tetrahedral sites were randomly chosen to be Li2 sites, and three quarters Li1 sites. This generates supercells where neighbouring Li1 and Li2 sites are never simultaneously occupied, and the two nearest Li3 sites are never simultaneously occupied. 
The unit cell and atomic positions of the one hundred generated configurations were optimised using “fast” parameters. Reciprocal space was only sampled at the ? point, an energy cutoff of 600 eV was used, and optimisation was completed once forces fell below 0.02 eV/Å. The configurations were ranked according to the resulting energies, and the lowest five labelled with A-E, starting with the lowest in energy (Table S1). Supercells A and B were chosen to take forward as good representative models for further study. More accurate “slow” parameters were used to reoptimise the structures of the lowest five configurations. Reciprocal space was sampled with a 3×2×3 k-point grid, and forces optimised to a tighter convergence of 0.01 eV/Å. The relative energies of supercells A–C agree well with those calculated with the “fast” parameters (Table S1). Supercell D becomes significantly more stable using the “slow” parameters, and becomes the most stable configuration. This is due to optimisation into a new configuration of cations. Subsequent optimisation using the “fast” parameters and starting from the new configuration, results in a very similar computed stability. Supercell E remains the least stable configuration. These results give us confidence that the “fast” parameters are sufficiently accurate to use for subsequent ab initio molecular dynamics (AIMD) calculations.
AIMD calculations were performed on supercells A and B using the “fast” parameters. A 0.5 fs time step was used throughout using the NVT ensemble. Both AIMD trajectories were initialised by performing a temperature ramp from 0 to 400 K over ~10 ps, and then an equilibration run at 400 K for ~8 ps using velocity rescaling to set the temperature. Production runs of 120 ps were performed at a set temperature of 400 K, using a Nosé thermostat, and resetting the electron density after every 8 ps.
Variations of supercell A were optimised using the “slow” parameters where one of the two Li3 vacancies was occupied by one of the surrounding Li2 atoms, in order to investigate potential Li transport pathways. This was done for each of the four Li2 atoms neighbouring one vacant Li3 site, and the two Li2 atoms neighbouring a second vacant Li3 site. For the first Li3 site, we found that all four of the Li atoms relaxed back from the Li3 site onto their original Li2 sites. It was, however, possible to stabilise Li on the second previously vacant Li3 site, defining one end of a transport pathway, with Li in the Li2 site at the other end. The barrier for the Li3 to Li2 transport along this pathway was determined by performing nudged elastic band (NEB) calculations. We used nine images constructed by placing the Li atom at equal intervals between the Li3 and Li2 positions, with the default VASP settings for the spring constant, and the “slow” parameters for optimisation.
The free energies of Li+ ions along the c axes of supercells A and B were determined by placing a series of Gaussians, each centred on a Li+ ion, in the supercell. All of the Gaussians had a standard deviation of 0.05 Å. For a given point along the c axis, the sum of all of the Gaussians at that point gives the density of Li+ ions. The free energy is then given by F=k_B T ln?W, where W is the density of Li+ ions and the value of T is 400K, from the AIMD calculations