Mechanisms of alkali ionic transport in amorphous oxyhalides solid state conductors

TL;DR

This work addresses why amorphous oxyhalide solid-state conductors exhibit high, chemistry-insensitive alkali diffusion. It uses a finely tuned CHGNet interatomic potential to perform long, large-scale MD on AMX$_{2.5}$O$_{0.75}$ to extract diffusion properties via Green-Kubo and Einstein formalisms, including ionic correlations. The study reveals an amorphous network of interconnected metal–anion tetrahedra through which alkali ions diffuse by standard hopping, with diffusion largely governed by self-diffusion and Haven ratios near unity, and identifies oxygen content as a key bottleneck to diffusion. The results offer mechanistic insight and design guidelines—such as aliovalent substitutions or reduced oxygen content—for achieving higher conductivities in amorphous solid electrolytes, with implications for scalable, non-lithium all-solid-state batteries.

Abstract

Amorphous oxyhalides have attracted significant attention due to their relatively high ionic conductivity ($>$1 mS cm$^{-1}$), excellent chemical stability, mechanical softness, and facile synthesis routes via standard solid-state reactions. These materials exhibit an ionic conductivity that is almost independent of the underlying chemistry, in stark contrast to what occurs in crystalline conductors. In this work, we employ an accurately fine-tuned machine learning interatomic potential to construct large-scale molecular dynamics trajectories encompassing hundreds of nanoseconds to obtain statistically converged transport properties. We find that the amorphous state consists of chain fragments of metal-anion tetrahedra of various lenght. By analyzing the residence time of alkali cations migrating around tetrahedrally-coordinated trivalent metal ions, we find that oxygen anions on the metal-anion tetrahedra limit alkali diffusion. By computing the full Einstein expression of the ionic conductivity, we demonstrate that the alkali transference number of these materials is strongly influenced by distinct-particles correlations, while at the same time they are characterized by an alkali Haven ratio close to one, implying that ionic transport is largely dictated by uncorrelated self-diffusion. Finally, by extending this analysis to chemical compositions $AMX_{2.5}\textsf{O}_{0.75}$, spanning different alkaline ($A$ = Li, Na, K), metallic ($M$ = Al, Ga, In), and halogen ($X$ = Cl, Br, I) species, we clarify why the diffusion properties of these materials remain largely insensitive to variations in atomic chemistry.

Figures (15)

• Figure 1: (a--c) Radial distribution function (RDF) $g_{A-B}(r)$ (left scale, solid line) and coordination number $N_{A-B}(r)$ (right scale, dashed line) as a function of the distance of the alkali $A=$ Li (a), Na (b), K (c) from the $B$ atom ($B=$ O [pink], Cl [purple], Al [light blue]). (d) Snapshot of the equilibrated MD trajectory of LiAlCl$_{2.5}$O$_{0.75}$; inset shows examples of [Al$_m$Cl$_n$O$_\ell$]$^{3m-n-2\ell}$ complexes. (e--g) Distribution of tetrahedral cluster sizes, where cluster size is defined as the number of tetrahedra contained in each cluster. The y-axis reports the population fraction (in %). Results are shown for Li$M$Cl$_{2.5}$O$_{0.75}$ ($M=$ Al, Ga, In). Error bars represent the standard deviation $\Delta_m$ (defined in the main text).
• Figure 2: (a) Mean square displacement (MSD) of Li atoms in LiAlCl$_{2.5}$O$_{0.75}$ at different temperatures: 500 K (turquoise), 600 K (blue), 700 K (pink) and 800 K (purple). (b) MSD of the different species (Li [purple], Al [pink], Cl [blue], O [turquoise]) of LiAlCl$_{2.5}$O$_{0.75}$; the insets report the associated (tracer) diffusion coefficients $D$ at $T=500$ K in a color-coded manner. (c) Arrhenius plot of $D$ as a function of the inverse temperature for LiAlCl$_{2.5}$O$_{0.75}$; the dashed line is the linear fit used to extract the activation energy. (a) Barplot displaying the extracted activation energies ($E_\textsf{a}$) (left scale, purple) the and calculated conductivities of alkali cations at 300 K using the Nernst-Einstein relation ($\sigma^A_{300\textsf{K}}$) (right scale, blue) of the $AMX_{2.5}$O$_{0.75}$ family of conductors.
• Figure 3: (a--c): Histograms of the alkali ion displacements after 4 ns simulation time for Li (a), Na (b), and K (c). Highlighted areas define the 5% fastest- and 5% slowest-moving ions, respectively. (d--f): radial distribution functions between alkali (Li [d], Na [e], K [f]) and Cl (pink) or O (purple), for the fast- (continuous lines) and the slow-moving (dashed lines) ions.
• Figure 4: (a--c) Residence times $\tau$ extracted from the exponential fit of $P(t)$ as a function of the inverse temperature for Li (a), Na (b) and K (c); dashed lines are linear fits, and the corresponding slope is proportional to the corresponding activation energies $\varepsilon_\textsf{a}$, which are reported in a color-coded manner. (d) Radial distribution function (continuous lines, left axis) and coordination number (dashed lines, right axis) as a function of distance for Al-Cl pair (light blue) and Al-O pair (purple) in LiAlCl$_{2.5}$O$_{0.75}$. (e) calculated $P(t)$ as a function of time for an MD simulation at $T=500$ K of LiAlCl$_{2.5}$O$_{0.75}$ for Li near different Al-anion tetrahedra; dashed grey lines are the corresponding exponential fits.
• Figure 5: (a) Alkali transference numbers $\mathcal{T}^{A+}$ calculated with Nernst-Einstein (NE) approximation (light blue), cluster NE (purple) and from the Einstein expression (pink) for the $AMX_{2.5}\textsf{O}_{0.75}$ family of compounds, together with alkali the Haven ratio $H^{A+}$ (orange) extracted from MD simulation at $T=750$ K. (b) Displacement-displacement correlation function (DDCF) of LiAlCl$_{2.5}$O$_{0.75}$ between Li-anions and Al-anions. (c) Li-Li DDCF (purple line), mean square displacement (MSD) multiplied by $N^\textsf{Li}$ (pink line), and distinct part of Li-Li DDCF (light blue line) in LiAlCl$_{2.5}$O$_{0.75}$; the distinct part represents the off-diagonal elements of the Li-Li DDCF. (d) Conductivities (multiplied by their corresponding temperatures) as a function of the inverse temperature of Li ions, calculated with the NE approximation, and of [Al$_m$Cl$_n$O$_\ell$]$^{3m-n-2\ell}$ clusters, evaluated within the cNE approximation.