Site Disorder Drives Cyanide Dynamics and Fast Ion Transport in Li6PS5CN

Abstract

Halide argyrodite solid-state electrolytes of the general formula Li₆PS₅ X exhibit complex static and dynamic disorder that plays a crucial role in ion transport processes. Here, we unravel the rich interplay between site disorder and dynamics in the plastic crystal argyrodite Li₆PS₅CN and the impact on ion diffusion processes through a suite of experimental and computational methodologies, including temperature-dependent synchrotron powder X-ray diffraction, AC electrochemical impedance spectroscopy, ⁷Li solid-state NMR, and machine learning-assisted molecular dynamics simulations. Sulfide and (pseudo)halide site disorder between the two anion sublattices unilaterally improves long-range lithium diffusion irrespective of the (pseudo)halide identity, which demonstrates the importance of site disorder in dictating bulk ionic conductivity in the argyrodite family. Furthermore, we find that anion site disorder modulates the presence and time scales of cyanide rotational dynamics. Ordered configurations of anions enable fast, quasi-free rotations of cyanides that occur on time scales of 10¹¹ Hz at T = 300 K. In contrast, we find that cyanide dynamics are slow or frozen in Li₆PS₅CN when site disorder between the cyanide and sulfide sublattices is present at T = 300 K. We rationalize the observed differences in cyanide dynamics in the context of elastic dipole interactions between neighboring cyanide anions and local strain induced by the configurations of site disorder that may impact the energetic landscape for cyanide rotational dynamics. Through this study, we find that anion disorder plays a decisive role in dictating the extent and time scales of both lithium ion and cyanide dynamics in Li₆PS₅CN.

Figure 1

Structure of Li₆PS₅CN, F4̅3m. Partial occupancies (shown as partially shaded spheres) of S, C, and N were determined through Rietveld refinement at T = 300 K. The Li⁺ positions and occupancies were fixed to previously reported values.

Figure 2

Exemplary Rietveld refinements of Li₆PS₅CN from the 11-BM-B beamline. (a) Rietveld refinements at T = 300 K of the sample initially before any temperature changes, after heating from the slow cooled temperature ramp, and after heating from quenching to T = 90 K. (b) Rietveld refinements at T = 90 K of Li₆PS₅CN after slow cooling and quenching.

Figure 3

Color plot representations of the diffraction patterns for Li₆PS₅CN during (a) slow cooling, (b) heating from slow cooling, and (c) heating from quenched cooling. Rietveld refinements are included for the SXRD patterns taken at T = 300 K and T = 90 K before and after temperature cycling.

Figure 4

Cubic lattice parameter for the Li₆PS₅CN as a function of temperature for each of the heating and cooling profiles. Data collected on slow cooling and then slow heating are shown as purple circles and orange squares, respectively. Data collected on slow heating from quenching are shown as pink triangles. The arrows indicate the direction of heating/cooling.

Figure 5

(a) Representative Nyquist plots of temperature-dependent electrochemical impedance spectroscopy measurements of Li₆PS₅CN. Data are shown as circles and fits to the (R₁Q₁) + Q₂ equivalent circuit model are shown as black lines. Data points collected at higher frequencies are found toward lower Z_real. At T = 30 °C, the apex frequency of the R₁Q₁ element occurs at approximately 1.89 × 10⁶ Hz. (b) Representative Arrhenius plot obtained from temperature-dependent electrochemical impedance spectroscopy data shown in (a).

Figure 6

⁷Li SSNMR fwhm analysis of the Li₆PS₅CN argyrodite. (a) shows a waterfall plot demonstrating the motional narrowing of the static ⁷Li peak as a function of temperature. (b) shows the fwhm of the peaks from (a). The solid orange line represents a sigmoidal regression.

Figure 7

⁷Li spin–lattice relaxation data for Li₆PS₅CN. Relaxation rates were collected in the laboratory frame (1/T₁) at a Larmor frequency of 77.76 MHz (yellow circles). Relaxation rates in the rotating frame (1/T_1ρ) were collected at a spin-lock frequency of 45 kHz. The blue circles are calculated from a monoexponential decay fitted according to BPP theory. The (1/T_1ρ) data were also fit to a biexponential decay (light blue triangles and green squares) which results in a fast motional regime (triangles) and a slow motional regime (squares). The solid lines represent a BPP fit according to eq 2, while dashed lines indicate a linear fit to Arrhenius behavior. The activation energies for the high temperature flanks were calculated through the BPP fit, and activation energies for the low temperature flanks were calculated through the Arrhenius fit.

Figure 8

Structural representations of the six disorder configurations used as starting models for molecular dynamics simulations. (Pseudo)halide ions, X^–, are represented by magenta spheres, while sulfur atoms are represented by yellow spheres. The 4a and 4d Wyckoff sites are labeled in Configuration 1 for clarity, and the 4d Wyckoff sites are connected by dashed gray lines as a guide to the eye. The P and S atoms that comprise the PS₄^3– tetrahedra are omitted for clarity, and the tetrahedra are shown as teal polyhedral representations. Lithium ions are also omitted for clarity.

Figure 9

Lithium ion mean squared displacement for each of the six configurations of Li₆PS₅CN at (a) T = 300 K and (b) T = 500 K (see Figure 7). Simulations were performed in triplicate. Lines represent the average MSD from the three runs and the shaded areas represent the standard deviations between replicate runs.

Figure 10

Lithium density distribution determined from molecular dynamics simulations of Li₆PS₅CN for each configuration of S^2–/CN^– site mixing at T = 300 K. The lithium density isosurfaces, shown in green, are overlaid with the argyrodite structure.

Figure 11

Comparison of diffusion coefficients determined by MD simulations, ⁷Li SSNMR relaxometry, and AC electrochemical impedance spectroscopy. Li⁺ diffusion coefficients from MD simulations are shown as filled symbols for each Configuration of site disorder, and dotted lines are provided as a guide to the eye. The magenta star represents the Li⁺ diffusion coefficient determined from SS NMR relaxometry in the rotating frame (R_1ρ, 45 kHz). Li⁺ diffusion coefficients calculated from temperature-dependent AC electrochemical impedance spectroscopy (EIS) are shown as open orange triangles. For all data sets, solid lines represent linear regressions based on the relationship D_Li = D₀ exp(−E_A/k_BT).

Figure 12

(a) A cartoon diagram representing the PSDF calculations for Li₆PS₅CN taken from 12 ns MD trajectories at T = 300 K. Lithium ions were tracked relative to the origin at each time step in the simulation. The radial distance from the Li⁺ to the center of the CN bond (at the origin) was recorded and projected into a 2D color plot shown in (b)–(d) for Configurations 1, 4, and 6 respectively. The frequency of occurrence at a particular radial distance is represented in “counts” in the color map. In each configuration, the lithium ions show a preference for aligning along the C–N axis, particularly near the carbon.

Figure 13

Rotational autocorrelation function for cyanide ions calculated for all Configurations of anion site disorder from MD simulations performed at T = 300 K. The autocorrelation functions were fit to a stretched exponential, , to determine the time constants for cyanide reorientations (τ). Data are shown as colored markers and the fits to the stretched exponential function are shown as black lines.

Figure 14

Depiction of cyanide elastic dipoles arranged on the argyrodite structure for Configurations 1 (a), 4 (b), and 6 (c). Sulfide ions are represented by yellow spheres, and cyanide elastic dipoles and orientations are represented by magenta vector arrows.

Figure 15

Flowchart of the iterative training database preparation and MTP training scheme for halide argyrodites with different configurations of site disorder.