Overscreening and Underscreening in Solid-Electrolyte Grain Boundary Space-Charge Layers

Polycrystalline solids can exhibit material properties that differ significantly from those of equivalent single-crystal samples, in part, because of a spontaneous redistribution of mobile point defects into so-called space-charge regions adjacent to grain boundaries. The general analytical form of these space-charge regions is known only in the dilute limit, where defect-defect correlations can be neglected. Using kinetic Monte Carlo simulations of a three-dimensional Coulomb lattice gas, we show that grain boundary space-charge regions in nondilute solid electrolytes exhibit overscreening—damped oscillatory space-charge profiles—and underscreening—decay lengths that are longer than the corresponding Debye length and that increase with increasing defect-defect interaction strength. Overscreening and underscreening are known phenomena in concentrated liquid electrolytes, and the observation of functionally analogous behavior in solid electrolyte space-charge regions suggests that the same underlying physics drives behavior in both classes of systems. We therefore expect theoretical approaches developed to study nondilute liquid electrolytes to be equally applicable to future studies of solid electrolytes.

Figure 1

Two-dimensional schematic of the kinetic Monte Carlo model used in this work. Lattice sites (circles) are either vacant (dashed circles) or occupied by positively charged “defects” (solid green circles). Arrows indicate allowed site-site moves. Interstitial positions are assigned partial negative charges. All lattice sites in the central plane (yellow) are assigned an on-site occupation energy of $-E_{\mathrm{gb}}$.

Figure 2

One-dimensional time-averaged mobile-defect distributions for $n_{\infty }=0.005$ and relative permittivities (a) ${ϵ}_r=100$, (b) ${ϵ}_r=10$, and (c) ${ϵ}_r=1$. On each plot, $x=0$ corresponds to the grain boundary plane. For each set of simulation data, we also plot the maximum likelihood exponential and oscillatory models (Eqs. (2) and (3), respectively). Error bars show a 95% confidence interval around each point (errors are smaller than the symbols). Plots showing these data on a semilogarithmic scale are provided in the Supplemental Material [27]. Source: Raw simulation data and scripts to generate this figure are available under CC BY 4.0/MIT licenses as Ref. [29].

Figure 3

Log-log plot of scaled simulated decay length ${\lambda }_{\mathrm{sys}}/{\lambda }_D=1/(\alpha {\lambda }_D)$ versus $\mathrm{\Gamma }={\lambda }_B/a$ for simulations performed at four different defect concentrations. The diagonal dashed line shows the maximum likelihood estimate for Eq. (4) in the underscreening regime. Open and closed circles correspond to space-charge profiles that best support the pure exponential decay model [Eq. (2)] or the oscillatory decay model [Eq. (3)], respectively, as determined through Bayesian model selection (see the Supplemental Material [27] for details). Error bars show 95% confidence intervals for ${\lambda }_{\mathrm{sys}}/{\lambda }_D$. Source: Raw simulation data and scripts to generate this figure are available under CC BY 4.0/MIT licenses as Ref. [29].