Recent experimental literature reports the solid state electrolyte properties of Li 4 SnS 4 and Li 4 SnSe 4 , identifying interesting questions regarding their structural details and motivating our first principles simulations. Together with Li 4 GeS 4 , these materials are all characterized by the orthorhombic space group Pnma and are found to be isostructural. They have a ground state crystal structure (denoted Li 4 SnS 0 4 ) having interstitial sites in void channels along the c-axis. They also have a meta-stable structure (denoted Li 4 SnS * 4 ) which is formed by moving one fourth of the Li ions from their central sites to the interstitial positions, resulting in a 0.5 Å contraction of the a lattice parameter. Relative to their ground states, the meta-stable structures are found to have energies 0.25 eV, 0.02 eV, and 0.07 eV for Li 4 From this literature, some interesting questions arise regarding crystal structures and mechanisms for ion mobility. In order to address these questions, we use first principles methods to examine the ideal crystal forms and defect structures of Li 4 SnS 4 and the structurally and chemically related materials Li 4 GeS 4 and Li 4 SnSe 4 . For each of these materials, we identify two closely related structures -an ideal ground state structure and an ideal meta-stable structure. The simulations show that the meta-stable structural form is most accessible to Li 4 SnS 4 of the three materials studied. The simulations are extended to study mechanisms of Li ion migration in both Li 4 SnS 4 and Li 4 SnSe 4 and are related to the experimental results reported in the literature.
Computational MethodsThe computational methods used in this work are based on density functional theory (DFT), 8,9 using the projected augmented wave (PAW) 10 formalism. The PAW basis and projector functions were generated by the ATOMPAW 11 code and the crystalline materials were modeled using the QUANTUM ESPRESSO 12 and ABINIT 13 packages. Visualizations were constructed using the XCrySDEN, 14 The exchange correlation function is approximated using the localdensity approximation (LDA). 17 The choice of LDA functional was made based on previous investigations 18-20 of similar materials which showed that, provided that the lattice constants are scaled by a correction factor of 1.02, the simulations are in good agreement with experiment, especially lattice vibrational frequencies and heats of formation. The partial densities of states were calculated as described in previous work, 20,21 using weighting factors based on the charge within the augmentation spheres of each atom with radii r The calculations were well converged with plane wave expansions of the wave function including |k + G| 2 ≤ 64 bohr −2 . Calculations for the conventional unit cells were performed using a Brillouin-zone sampling grid of 4 × 8 × 8. Simulations of Li ion migration were performed at constant volume in supercells constructed from the optimized conventional cells extended by 1 × 2 × 2 and a Brillouin-zone sampling grid of 2 × 2 × 2. In ...