Vacancy-Driven Anisotropic Defect Distribution in the Battery-Cathode Material ${\mathrm{LiFePO}}_4$

Li-ion mobility in ${\mathrm{LiFePO}}_4$, a key property for energy applications, is impeded by Fe antisite defects (${\mathrm{Fe}}_{\mathrm{Li}}$) that form in select $b$-axis channels. Here we combine first-principles calculations, statistical mechanics, and scanning transmission electron microscopy to identify the origin of the effect: Li vacancies ($V_{\mathrm{Li}}$) are confined in one-dimensional $b$-axis channels, shuttling between neighboring ${\mathrm{Fe}}_{\mathrm{Li}}$. Segregation in select channels results in shorter ${\mathrm{Fe}}_{\mathrm{Li}}\mathrm{\text{−}}{\mathrm{Fe}}_{\mathrm{Li}}$ spans, whereby the energy is lowered by the $V_{\mathrm{Li}}$’s spending more time bound to end-point ${\mathrm{Fe}}_{\mathrm{Li}}$’s. $V_{\mathrm{Li}}\mathrm{\text{−}}{\mathrm{Fe}}_{\mathrm{Li}}\mathrm{\text{−}}{V}_{\mathrm{Li}}$ complexes also form, accounting for observed electron energy loss spectroscopy features.

Figure 1

(a) Schematic of ${\mathrm{Li}}_{14}{\mathrm{Fe}}_{17}{\mathrm{P}}_{16}{\mathrm{O}}_{64}$ including one ${\mathrm{Fe}}_{\mathrm{Li}}\mathrm{\text{−}}{V}_{\mathrm{Li}}$ pair separated by a distance $d$. (b) Binding energy for ${\mathrm{Fe}}_{\mathrm{Li}}\mathrm{\text{−}}{V}_{\mathrm{Li}}$ pairs as a function of separation $d$. The red points are for ${\mathrm{Fe}}_{\mathrm{Li}}$ and $V_{\mathrm{Li}}$ on the same $b$ axis; green points are for ${\mathrm{Fe}}_{\mathrm{Li}}$ and $V_{\mathrm{Li}}$ on different $b$ axes.

Figure 2

(a) Energy landscape for a $V_{\mathrm{Li}}$ shuttling between two ${\mathrm{Fe}}_{\mathrm{Li}}$’s in a $b$-axis channel combining migration barrier and binding energy variation. (b) Schematic version of the same figure, defining a one-dimensional random walk with absorbing end points. The symbols are defined in the text.

Figure 3

Total energy lowering (a) as a function of separation $L$ between ${\mathrm{Fe}}_{\mathrm{Li}}$’s and (b) as a function of temperature $T$.

Figure 4

Top: Schematic figure of the probable configuration of ${\mathrm{Fe}}_{\mathrm{Li}}$ with a higher Fe oxidation state. Bottom: (Left) EELS data of ${\mathrm{Fe}}_{\mathrm{Li}}$ (shown in the red circle in the inset) and of Fe in bulk positions in ${\mathrm{LiFePO}}_4$. The inset shows an atomically resolved $Z$-contrast image of ${\mathrm{LiFePO}}_4$ oriented along the $b$ axis. The scale bar is 0.5 nm. (Right) Fe $L_3/L_2$ ratios for ${\mathrm{Fe}}_{\mathrm{Li}}$ (red triangle) and ${\mathrm{Fe}}_{\mathrm{bulk}}$ (black triangle) sites of ${\mathrm{LiFePO}}_4$ compared with different iron compounds. ${\mathrm{Fe}}^{+3}$ and ${\mathrm{Fe}}_{\mathrm{metal}}$ correspond to spectra obtained for $\alpha \mathrm{\text{−}}{\mathrm{Fe}}_2{\mathrm{O}}_3$ and metallic iron thin film, respectively. The data point shown as a purple circle corresponds to the Fe $L_3/L_2$ ratio of the FeO spectra, i.e., ${\mathrm{Fe}}^{+2}$, presented in Ref. 22 and calculated by using the second derivative method of Ref. 23. The data point is shown only for comparison purposes.