Computationally Guided Discovery of the Sulfide Li3AlS3 in the Li–Al–S Phase Field: Structure and Lithium Conductivity

With the goal of finding new lithium solid electrolytes by a combined computational–experimental method, the exploration of the Li–Al–O–S phase field resulted in the discovery of a new sulfide Li3AlS3. The structure of the new phase was determined through an approach combining synchrotron X-ray and neutron diffraction with 6Li and 27Al magic-angle spinning nuclear magnetic resonance spectroscopy and revealed to be a highly ordered cationic polyhedral network within a sulfide anion hcp-type sublattice. The originality of the structure relies on the presence of Al2S6 repeating dimer units consisting of two edge-shared Al tetrahedra. We find that, in this structure type consisting of alternating tetrahedral layers with Li-only polyhedra layers, the formation of these dimers is constrained by the Al/S ratio of 1/3. Moreover, by comparing this structure to similar phases such as Li5AlS4 and Li4.4Al0.2Ge0.3S4 ((Al + Ge)/S = 1/4), we discovered that the AlS4 dimers not only influence atomic displacements and Li polyhedral distortions but also determine the overall Li polyhedral arrangement within the hcp lattice, leading to the presence of highly ordered vacancies in both the tetrahedral and Li-only layer. AC impedance measurements revealed a low lithium mobility, which is strongly impacted by the presence of ordered vacancies. Finally, a composition–structure–property relationship understanding was developed to explain the extent of lithium mobility in this structure type.


Exploration of the Li-Al-O-S phase field
1.1. Synthesis of LiAlO 2 First, LiAlO 2 was synthesized for use as a precursor according to the procedure described by Gao et al. 1 Li 2 CO 3 (1.681 g, 22.7 mmol) and Al(OH) 3 (3.

Synthesis attempt of Li 3 AlO 3
Attempts to synthesize Li 3 AlO 3 was carried out using the combustion method. 2 LiNO 3 (2.757 g, 40.0 mmol), Al(NO 3 ) 3 , 9 H 2 O (5.0 g, 13.3 mmol) and urea (4.803 g, 80.0 mmol) were weighted according to the stoichiometry 3:1:1/4, in order to keep a molar ratio of nitrate:urea of 1:1. In a 400 mL beaker, the powders were dissolved in distilled water under magnetic agitation, and the solution was then dried overnight at 100 °C. The combustion reaction was then performed by placing the beaker on a hot plate at 500 °C. After the reaction took place, the beaker was left to cool down naturally. The powder was manually ground and analysed with X-Ray diffraction, which revealed the presence of both crystalline phases LiAlO 2 and Li 2 CO 3 , but no peaks corresponding to unknown phases. In order to further attempt in the stabilization of a Li 3 AlO 3 phase, the powder was placed in an alumina crucible and annealed in air at 900 °C or 1200 °C for 10 h, with a ramp rate of 5 °C·min -1 , followed by quenching in air. The two different temperatures were chosen for being below and above the melting point of composition Li 3 AlO 3 according to the phase diagram. However, the X-ray diffraction patterns of the two different samples only revealed the presence of crystalline LiAlO 2 and Li 5 AlO 4 in different ratios.

Refinement
3.1. Comparison between fits with and without the use of the spherical harmonics expansion in the peak shape function Figure

Occupancy refinement details
The occupancy of each site was determined by first refining the site occupancy during independent runs. The refinement of the sof of aluminium with the SXRD dataset indicated an electron density deficiency at this position. This was confirmed when refining the site occupancy of this site by considering the occupation with both aluminium and lithium atoms.
The lithium antisite defect (Li Al , Table S5), was found to occupy 6.7(4)% of the aluminium site.
No aluminium antisite defects were found by refining the sof of Al atoms in the Li1 site.
Moreover, a careful examination of the Fourier difference maps, and especially of the vacant tetrahedral and octahedral interstices did not show any obvious location for any Al or other Li antisite defects. On the other hand, the occupancy of the other atoms, when refined individually, were found to be 0.99(1) for S1, 0.97(1) for S2, 0.95(2) for S3, 1.04(1) for Li1, 1.02(2) for Li4, 0.521 (9) for the sum of Li2 and Li2b, and 0.496 (9) for Li3 each during independent refinements. Therefore in the final refinement, the occupancy of S1, Li1 and the sum of Li2 and Li2b were remained fixed to their ideal values so that their sof does exceed the maximum value. In the meantime, the sof of S2, S3, Al, Li4, and Li3 were refined simultaneously while constraining the overall composition to be charge neutral. Results of the final refinement are presented in Table S4.   Figure S4).  Li4 S1 2.440(12) S1 Li4 S1 102.6(5) Li4 S1 2.629(11) S1 Li4 S1 118.7(6) Li4 S1 2.361(12) S1 Li4 S1 94.

Calculation and conversion of NMR parameters
For comparison with experiment, NMR parameters were calculated for the experimentally refined crystal structure of Li 3 AlS 3 considering occupancy of the high symmetry sites for Li2 and Li3 atoms instead of the split sites due the results found in phonon calculation stated above. For this model, both sites are in the 4e Wyckoff position along the two fold axis. Following geometry optimisation in VASP, the geometry was optimised again using GIPAW 3,4 in CASTEP 5 with the same parameters as VASP, except for a higher plane wave cut-off of 800 eV. On-the-fly generated pseudopotentials were used to treat core electrons in CASTEP. NMR parameters were then calculated using the GIPAW method as implemented in CASTEP. The method used for conversion of the chemical shieldings to the calculated isotropic chemical shifts is presented in the supplementary information.
Conversion of the chemical shieldings, σ iso , directly obtained from the calculations, to the isotropic chemical shifts, δ iso,cs , is obtained with the expression: 4 where m ref and σ iso,ref are a gradient close to -1 and a reference shielding, respectively.   (Figure 3b).

Results
The calculations predict a resonance at 1.5 ppm linked to Li3, a resonance at 1.7 ppm associated with Li2 and two resonances at 3.1 and 3.5 ppm each with double the intensity (4 times Li1 and 4 times Li4).

Analysis of the Impedance data
The electrical admittance for the constant phase element (CPE) can be calculated with the expression: where is the impedance of the CPE, is a dimensionless factor which value lies CPE between 0 and 1 and has the numerical value of the admittance at = 1 rad·s -1 0 and its unit is S·s n . In the ideal case where = 1, the CPE represent a capacitor.
The impedance data were fitted with the equivalent circuit represented in Figure   S 9, where R bulk is the resistance of the semicircle at high frequency, R GB the resistance of the semicircle at low frequency, and the admittance of both CPE being: and respectively.   the frequency at the top of the first and second semicircles respectively.