Analysis of Diffusion in Solid-State Electrolytes through MD Simulations, Improvement of the Li-Ion Conductivity in β-Li3PS4 as an Example

Abstract

Molecular dynamics simulations are a powerful tool to study diffusion processes in battery electrolyte and electrode materials. From molecular dynamics simulations, many properties relevant to diffusion can be obtained, including the diffusion path, amplitude of vibrations, jump rates, radial distribution functions, and collective diffusion processes. Here it is shown how the activation energies of different jumps and the attempt frequency can be obtained from a single molecular dynamics simulation. These detailed diffusion properties provide a thorough understanding of diffusion in solid electrolytes, and provide direction for the design of improved solid electrolyte materials. The presently developed analysis methodology is applied to DFT MD simulations of Li-ion diffusion in β-Li₃PS₄. The methodology presented is generally applicable to diffusion in crystalline materials and facilitates the analysis of molecular dynamics simulations. The code used for the analysis is freely available at: https://bitbucket.org/niekdeklerk/md-analysis-with-matlab. The results on β-Li₃PS₄ demonstrate that jumps between bc planes limit the conductivity of this important class of solid electrolyte materials. The simulations indicate that the rate-limiting jump process can be accelerated significantly by adding Li interstitials or Li vacancies, promoting three-dimensional diffusion, which results in increased macroscopic Li-ion diffusivity. Li vacancies can be introduced through Br doping, which is predicted to result in an order of magnitude larger Li-ion conductivity in β-Li₃PS₄. Furthermore, the present simulations rationalize the improved Li-ion diffusivity upon O doping through the change in Li distribution in the crystal. Thus, it is demonstrated how a thorough understanding of diffusion, based on thorough analysis of MD simulations, helps to gain insight and develop strategies to improve the ionic conductivity of solid electrolytes.

Figure 1

Histogram showing the vibrational amplitude of Li ions in β-Li₃PS₄ at 600 K, with the fitted Gaussian (solid red line) and the standard deviation (±0.495 Å, dotted green line).

Figure 2

Vibration frequency spectrum of Li-ions in β-Li₃PS₄ at 600 K, the average frequency of 8.29 (±0.46) × 10¹² Hz is shown by the solid (±dotted) red line.

Figure 3

Energy landscape and the corresponding ion density, with sites A, B, and C.

Figure 4

Schematic pictures of the energy landscape due to the crystal lattice (top) and the Coulomb repulsion of another Li ion (middle) during a collective jump, giving the energy landscape experienced by the gray Li ion (bottom). Step 1: situation before a collective jump. Step 2: the other ion moves to the right and makes the barrier between the gray ion and the next site disappear. Step 3: situation after the collective jump.

Figure 5

Jump diffusion paths at 600 K for (a) β-Li_2.75PS₄, (b) β-Li₃PS₄, and (c) β-Li_3.25PS₄. Li-ion sites are shown by 4b = blue, 4c = green, and 8d = black. The jump types are shown by 4b–4c = red, intralayer = pink, and interlayer = cyan, thicker lines correspond to larger jump rates.

Figure 6

Tracer diffusivity from the current MD simulations, Phani et al. and Yang et al.

Figure 7

Jump rates for the 4b–4c and interplane jumps.

Figure 8

Activation energy at 600 K for (a) 4b–4c and (b) intraplane jumps.

Figure 9

Percentage of collective jumps in the MD simulations

Figure 10

Number of collective jumps versus the time condition (in units of the attempt frequency).

Figure 11

(a) Attempt frequencies and (b) vibration amplitudes from the MD simulations.

Figure 12

Jump diffusion paths at 600 K for (a) β-Li_2.75PS_3.75Br_0.25 and (b) β-Li₃PS_3.75O_0.25. Li-ion sites are shown by 4b = blue, 4c = green, and 8d = black. The jump types are shown by 4b–4c = red, intralayer = pink, and interlayer = cyan, thicker lines correspond to larger jump rates.

Figure 13

Activation energies at 600 K in Br- and O-doped β-Li₃PS₄ for (a) 4b–4c and (b) intraplane jumps.

Figure 14

O–Li and S–Li distribution in β-Li₃PS_3.75O_0.25 at 600 K, calculated using eq 10.