Strain Sensitivity of $\mathrm{Li}$-ion Conductivity in β-${\mathrm{Li}}_3{\mathrm{PS}}_4$ Solid Electrolyte

Strain is present at the interfaces of solid electrolytes with the cathode and the anode in solid-state batteries due to interfacial reactions and due to volumetric expansion and contraction of the electrodes during battery charging and discharging cycles. This work quantifies the effect of elastic strain on $\mathrm{Li}$-ion diffusion in a model solid electrolyte, β-${\mathrm{Li}}_3{\mathrm{PS}}_4$, by using ab initio molecular dynamics (AIMD). We find that the strain tensors which compress the c axis (+2% a-b, −2% a-c, −2% b-c, −2% isotropic) increase the $\mathrm{Li}$-ion diffusivity, and the strain tensors which stretch the c axis (−2% a-b, +2% a-c, +2% b-c, +2% isotropic) reduce it. Ionic conductivity increases by 2–14-fold with a reduction in activation energy for c-axis compressive strains and decreases by 1–14-fold with an increase in activation energy for c-axis tensile strains at room temperature. The c-axis compression increases disorder in the lattice and promotes jumps along all migration pathways. In particular, the $\mathrm{Li}$ 4c site occupancy increases from about 3% to 6% (at 500 K), thus creating more vacancies at otherwise fully occupied and bottleneck 8d and 4b sites. The c-axis compression also reduces the distance between the 8d and 4b sites, thus increasing Coulomb repulsion between these sites. Increased Coulomb repulsion can destabilize $\mathrm{Li}$ at the 8d and 4b sites, promoting reduced occupancy and increased diffusivity associated with these sites. The results show that elastic strain can promote $\mathrm{Li}$ disorder and superionic conductivity, with an effect on $\mathrm{Li}$-ion diffusion comparable to that of chemical substitution, and is important to consider for an accurate understanding and prediction of the solid-state $\mathrm{Li}$-ion battery interface properties.

Popular Summary

Solid-state batteries are safer and can achieve higher energy density than typical liquid-electrolyte-based $\mathrm{Li}$-ion batteries, but several challenges limit their attainable performance, including low $\mathrm{Li}$-ion conductivity. Mechanical strain is inevitably present in solid-state batteries due to volumetric changes of the cathode and anode materials during battery charge-discharge cycles as well as interfacial strain due to reactions at the solid-electrolyte interface. Controlling this mechanical strain via strain engineering may provide new degrees of freedom for increasing the ionic conductivity of solids. Therefore, it is important to quantify changes in $\mathrm{Li}$-ion conductivity under strain to understand and optimize the solid-electrolyte performance. Experimentally isolating the effects of strain is challenging, so computational methods provide an opportunity to selectively treat the effects of elastic strain. In this work, the authors quantify the $\mathrm{Li}$-ion conductivity of the solid electrolyte β-${\mathrm{Li}}_3{\mathrm{PS}}_4$ using ab initio molecular dynamics. They find that elastic strain can promote $\mathrm{Li}$ disorder and superionic conductivity, with an effect on $\mathrm{Li}$-ion diffusion comparable to that of chemical substitution. These findings are not only important for the accurate understanding and prediction of solid-state $\mathrm{Li}$-ion battery properties but also provide a design strategy for increasing disorder and promoting superionic conduction in solid electrolytes by strain engineering.

Figure 1

β-${\mathrm{Li}}_3{\mathrm{PS}}_4$ orthorhombic unit cell (Pnma space group, oP32 [64]). ${\mathrm{PS}}_4$ tetrahedra are shown in yellow ($\mathrm{P}$ is black at the center of the tetrahedron). $\mathrm{Li}$ sites: 8d, gray; 4b, green; 4c, violet. Conventional cell shown in this figure contains 4 formula units ($4{\mathrm{Li}}_3{\mathrm{PS}}_4$), with 12 $\mathrm{Li}$ ions distributed over a total of 16 sites (8d, 4b, 4c). 8d and 4b sites are almost fully occupied and the 4c site is almost empty [63]. $\mathrm{Li}$-ion diffusion is especially fast along the facile 4b-4c chain, but other pathways also contribute to overall transport (8d-4c, 8d-4b and 8d-8d) [63]. In this and further figures, we use vesta software for visualization of crystal structures [65].

Figure 2

Three-dimensional (3D) $\mathrm{Li}$-ion density of β-${\mathrm{Li}}_3{\mathrm{PS}}_4$ obtained from AIMD simulations at 500 K: a-c (left) and b-c (right) plane views. ${\mathrm{PS}}_4$ groups are shown as black-and-yellow sticks. 8d and 4b sites are stable, with typical residence times of 80 and 30 ps, respectively. 4c is a transient site with a short 1 ps residence time. 8d-4b-4c sites form two-dimensional continuous layers (b-c layers), which are highlighted with dashed lines. Within the b-c layer, diffusion happens mainly via 4b-4c, 8d-4c, 8d-4b, and 8d-8d nearest-neighbor jumps. Between b-c layers, diffusion happens mainly via 8d-8d interlayer jumps.

Figure 3

$\mathrm{Li}$-ion (tracer) diffusivity in β-${\mathrm{Li}}_3{\mathrm{PS}}_4$ (without strain, ε = 0%) calculated with AIMD. AIMD simulations of diffusivity from the literature are shown for comparison: Yang and Tse et al. [111], Phani Dathar et al. [103], de Klerk et al. [63].

Figure 4

$\mathrm{Li}$-ion diffusivity under ±2% biaxial strain on the a-b, a-c, and b-c planes of β-${\mathrm{Li}}_3{\mathrm{PS}}_4$, deduced from AIMD simulations. (a) Arrhenius plot (650–500 K). Dashed line shows strain-free diffusivity (ε = 0%) as a reference state. (Isotropic strain diffusivities are shown in the Supplemental Material, Sec. G [82].) (b) Relative change in c lattice parameter under biaxial strain at 500 K. (c) $\mathrm{Li}$-ion conductivity extrapolated to room temperature; one standard deviation confidence intervals are highlighted; ε = −2% and ε = +2% label conductivities under isotropic compressive and tensile strain, respectively; text label of each marker provides the relative change in $\mathrm{Li}$-ion conductivity with respect to the unstrained state (${\sigma }_{\epsilon }/{\sigma }_{\epsilon =0}$ ratio).

Figure 5

(a) Activation energy, E_a, and (b) logarithm of the pre-exponential factor (log₁₀ A) of $\mathrm{Li}$-ion diffusivity under ±2% isotropic and biaxial strain on the a-b, a-c, and b-c planes of β-${\mathrm{Li}}_3{\mathrm{PS}}_4$ deduced by AIMD simulations at 500–650 K, presented as a function of the relative change in the c parameter.

Figure 6

Number of jumps observed during AIMD runs (500 K, 1 ns). Number of jumps in the strain-free case is shown in the first column (ε = 0%). Next three columns show detrimental strains (−2% a-b, +2% a-c, +2% b-c), which stretch the c axis. Last three columns show beneficial strains (+2% a-b, −2% a-c, –2% b-c), which compress the c axis. Dashed lines show number of jumps in the strain-free case as a reference. Types of jumps are as described in the main text (“8d-8d short” are jumps between nearest-neighbor sites; “8d-8d long” are jumps between b-c layers). For jumps between different sites (4b-4c, 8d-4c, 8d-4b), the number of backward jumps (4c-4b, 4c-8d, 4b-8d) is not shown (it is almost equal to the number of forward jumps, as expected in equilibrium [63]). For jumps between the same sites (8d-8d), the total number of jumps is shown (forward and backward). We also note that only a portion of jumps contribute to a net displacement of $\mathrm{Li}$ ions (see the Supplemental Material, Sec. H [82]; cf. Refs. [116, 117]).

Figure 7

Occupancy of 8d, 4b, and 4c $\mathrm{Li}$-ion sites for ±2% biaxial strains at 500 K, calculated by Bader analysis of the $\mathrm{Li}$-ion density obtained in AIMD simulations. Occupancies of sites in the strain-free case are shown in the first column (ε = 0%). Next three columns show detrimental strains (−2% a-b, +2% a-c, +2% b-c), which stretch the c axis. Last three columns show beneficial strains (+2% a-b, −2% a-c, −2% b-c), which compress the c axis. Dashed lines show occupation in the strain-free case.

Figure 8

Radial distribution function of $\mathrm{P}$-$\mathrm{P}$ distances in β-${\mathrm{Li}}_3{\mathrm{PS}}_4$ under biaxial strains, which (a) compress the c axis and (b) expand the c axis. Radial distribution function of (c) $\mathrm{Li}$-$\mathrm{Li}$ distances for all biaxial strains shown together. Black lines (and dark fillings) show the reference state (without strain). Two arrows mark RDF shifts for strains that compress or expand the c axis. Obtained from AIMD simulations at 500 K.