Impact of the energy landscape on the ionic transport of disordered rocksalt cathodes

Traditional approaches to identify ion-transport pathways often presume an equal probability of occupying all hopping sites and focus entirely on finding the lowest migration barrier channels between them. Although this strategy has been applied successfully to solid-state Li battery materials, which historically have mostly been ordered frameworks, in the emerging class of disordered electrode materials some Li sites can be significantly more stable than others due to a varied distribution of transition metal (TM) environments. Using kinetic Monte Carlo simulations, we show that in such cation-disordered compounds only a fraction of the Li sites connected by the so-called low-barrier “0-TM” channels actually participate in Li diffusion. The Li-diffusion behavior through these sites, which are determined primarily by the voltage applied during Li extraction, can be captured using an effective migration barrier larger than that of the 0-TM barrier itself. The suppressed percolation due to cation disorder can decrease the ionic diffusion coefficient at room temperature by over two orders of magnitude.

Figure 1

(a) Three-dimensional (3D) view of 0-TM and 1-TM tetrahedral diffusion channels between adjacent edge sharing Li sites in DRX compounds. The lower-barrier 0-TM channel (black arrow), with no face-sharing transition metals (TMs), forms the basis of the percolating Li pathway [20]. The other 1-TM channel consists of a tetrahedral site which has one face-sharing TM atom (purple). (b) Activation barrier $E_{\text{a}}$ associated with hopping out of an occupied octahedral ($O_{\text{h}}$) site in a DRX system vs a typical ordered compound. Even with the same kinetically resolved activation barrier ($E_{\text{KRA}}$), $E_{\text{a}}$ in DRX systems can be much larger due to a difference in the $O_{\text{h}}$ site energies [21].

Figure 2

(a) Impact of varying $O_{\text{h}}$ site energy distribution (standard deviation $w_{\text{SE}}$) on the calculated Li-diffusion coefficient ($T=300$ K) at different occupancies of the $O_{\text{h}}$ sites. The magnitude of $w_{\text{SE}}$, represented by the shade of the data points, is varied over 11 values in the range [0 eV, 1 eV]. (b) Contour plot of calculated correlation factor (f) at $x_{\text{Li}}=0.3$ in the two-dimensional parameter space ($w_{\text{SE}}, J_{\text{Li-Vac}}^{\text{NN}}$) of the model system. The parameters which best fit the experimentally measured voltage profile of ${\mathrm{Li}}_{1.17-x}{\mathrm{Mn}}_{0.343}{\mathrm{V}}_{0.486}{\mathrm{O}}_{1.8}{\mathrm{F}}_{0.2}$ are given by the solid black line. The region in which the model system becomes ordered at room temperature ($T=300$ K) is shaded in salmon.

Figure 3

Li-site energy distribution (blue histogram) with standard deviation $w_{\text{SE}}=0.8$ eV. Distribution of Li sites involved in Li diffusion at $x_{\text{Li}}=0.2$, 0.5, 0.8 are shown in yellow, orange and green respectively.

Figure 4

Arrhenius plot of calculated tracer diffusion coefficient for model DRX systems at $x_{\text{Li}}=0.3$ with varying $w_{\text{SE}}$ in the range [0, 0.8]. Corresponding high-temperature data are fitted by an increasing effective activation barriers of magnitude $\sim E_{\text{KRA}}+0.45w_{\text{SE}}$.

Figure 5

Calculated Li-site energies for short-ranged ordered (red, $T=1273$ K) and fully disordered (green) ${\mathrm{Li}}_{1.3}{\mathrm{Mn}}_{0.4}{\mathrm{Ti}}_{0.3}{\mathrm{O}}_{1.7}{\mathrm{F}}_{0.3}$. Inset: Calculated voltage profile for the model DRX system ($w_{\text{SE}}=0.6$ eV, $J_{\text{Li-Vac}}^{\text{NN}}=25$ meV) fit to the experimentally measured voltage profile of ${\mathrm{Li}}_{1.17-x}{\mathrm{Mn}}_{0.343}{\mathrm{V}}_{0.486}{\mathrm{O}}_{1.8}{\mathrm{F}}_{0.2}$ (LMVOF).