Unraveling the electrolyte properties of ${\mathrm{Na}}_3{\mathrm{SbS}}_4$ through computation and experiment

Solid-state sodium electrolytes are expected to improve next-generation batteries on the basis of favorable energy density and reduced cost. ${\mathrm{Na}}_3{\mathrm{SbS}}_4$ represents a new solid-state ion conductor with high ionic conductivities in the mS/cm range. Here, we explore the tetragonal phase of ${\mathrm{Na}}_3{\mathrm{SbS}}_4$ and its interface with metallic sodium anode using a combination of experiments and first-principles calculations. The computed Na-ion vacancy migration energies of 0.1 eV are smaller than the value inferred from experiment, suggesting that grain boundaries or other factors dominate the experimental systems. Analysis of symmetric cells of the electrolyte—${\mathrm{Na}/\mathrm{Na}}_3{\mathrm{SbS}}_4/\mathrm{Na}$—show that a conductive solid electrolyte interphase forms. Computer simulations infer that the interface is likely to be related to ${\mathrm{Na}}_3{\mathrm{SbS}}_3$, involving the conversion of the tetrahedral ${\mathrm{SbS}}_4^{3-}$ ions of the bulk electrolyte into trigonal pyramidal ${\mathrm{SbS}}_3^{3-}$ ions at the interface.

Figure 1

Ball and stick model of ${\mathrm{Na}}_3{\mathrm{SbS}}_4$ in the tetragonal $P\overline{4}{2}_{1}c$ structure, using black and orange balls to indicate Sb and S sites, respectively. Inequivalent Na sites are indicated with blue and white balls. The red arrows illustrate possible vacancy migration paths between neighboring $a$ and $d$ sites, while the green arrows illustrate possible vacancy migration paths between neighboring $d$ sites.

Figure 2

Comparison of x-ray diffraction measurements and simulations for ${\mathrm{Na}}_3{\mathrm{SbS}}_4$ for the diffraction wavelength of $\lambda =1.54056\AA$. The x-ray patterns were scaled to a maximum amplitude of 2 (arbitrary units) for the peak intensity at $2\theta =17.4^{\circ }$. The calculated results were generated from those reported in Table 1. The neutron results were generated from the lattice parameters and fractional coordinates fit to neutron diffraction data, as reported in Ref. [1].

Figure 3

Ball and stick model of ${\mathrm{Na}}_3{\mathrm{SbS}}_3$ in its $P{2}_{1}3$ crystal structure, using black and orange balls to indicate Sb and S sites, respectively. Inequivalent Na sites are indicated with bright blue, pale blue, and white balls. The violet arrows illustrate possible vacancy migration paths between nearest-neighbor Na ions on alternating $a_1$ and $a_2$ sites.

Figure 4

Partial densities of states for the ground-state structures of ${\mathrm{Na}}_3{\mathrm{SbS}}_4, {\mathrm{Na}}_3{\mathrm{SbS}}_3$, and ${\mathrm{Na}}_2\mathrm{S}$. The zero of energy in these plots is taken as the top of the valence band of each material.

Figure 5

Computed energy path diagram for Na-ion vacancy migrations in ${\mathrm{Na}}_3{\mathrm{SbS}}_4$ corresponding to the nearest-neighbor hops indicated in Fig. 1 for migration along the a or b axis (red symbols and line) and along the c axis (green symbols and line). The symbols represent directly calculated configurations, while the lines are smooth interpolations between NEB images. The zero of energy is set at the energy of a Na-ion vacancy at a ${\mathrm{Na}}_a$ site.

Figure 6

Plot of experimentally measured values of $log\left(\sigma T\right)$ (left, filled symbols and lines) and $log\sigma$ (right, open symbols) versus $1000/T$ where $\sigma$ is given in units of S/cm and $T$ is given in units of Kelvin for ${\mathrm{Na}}_3{\mathrm{SbS}}_4$ (black symbols from present work) and ${\mathrm{Na}}_3{\mathrm{SbS}}_3$ (red symbols from Ref. [13]). Lines represent least-square fits to the $log\left(\sigma T\right)$ data. The values of the activation energies $E_a^{\mathrm{expt}.}$ as determined from the fits are indicated.

Figure 7

Computed energy path diagram for Na-ion vacancy migrations in bulk ${\mathrm{Na}}_3{\mathrm{SbS}}_3$ corresponding to nearest-neighbor hops between ${\mathrm{Na}}_{a1}$ and ${\mathrm{Na}}_{a2}$ sites. The symbols represent directly calculated configurations, while the lines are smooth interpolations between NEB images. The zero of energy is set at the energy of a Na-ion vacancy at a ${\mathrm{Na}}_{a3}$ site.

Figure 8

Experimentally measured voltage versus time plot for a $\mathrm{Na}/{\mathrm{Na}}_3{\mathrm{SbS}}_4/\mathrm{Na}$ symmetric cell cycled 40 times with a current density of $0.1\mathrm{mA}/{\mathrm{cm}}^2$ and holding the positive and negative voltages for 30 min.

Figure 9

(a) SEM image of the interface between a metallic sodium anode and the tetragonal ${\mathrm{Na}}_3{\mathrm{SbS}}_4$ solid electrolyte after 40 cycles in a ${\mathrm{Na}/\mathrm{Na}}_3{\mathrm{SbS}}_4/\mathrm{Na}$ symmetric cell configuration at a current density of $0.1\mathrm{mA}/{\mathrm{cm}}^2$ with the $20\mu \mathrm{m}$ scale indicated. Regions of pure electrolyte, pure anode, and the SEI are indicated. Panels (b), (c), (d), and (e) show the same interface sections of the SEM image as analyzed using the EDS to find elemental mappings of S, Na, Sb, and the three elements together, respectively.

Figure 10

(a) Ball and stick model of the simulated relaxed structure of a ${\mathrm{Na}}_3{\mathrm{SbS}}_4$ surface oriented along the (001) direction and interfaced with Na metal. The ball conventions for Sb and S is the same as in Fig. 1 and light blue balls represent both ionic and metallic Na. The indicated axes reference the ${\mathrm{Na}}_3{\mathrm{SbS}}_4$ lattice. (b) Corresponding partial densities of states analysis of this system, separately indicating the interior of the electrolyte, the interface region, and the metallic region in the bottom, middle, and top panels, respectively.

Figure 11

(a) Ball and stick model of the simulated relaxed structure of a ${\mathrm{Na}}_3{\mathrm{SbS}}_4$ surface oriented along the (110) direction and interfaced with Na metal. The ball conventions for Sb and S are the same as in Fig. 1 and light blue balls represent both ionic and metallic Na. The indicated axes reference the ${\mathrm{Na}}_3{\mathrm{SbS}}_4$ lattice. (b) Corresponding partial densities of states analysis of this system, separately indicating the interior of the electrolyte, the interface region, and the metallic region in the bottom, middle, and top panels, respectively.