## 3 Results and Discussion
The relationship between diffusivity and \(b\)-value across the three LFP-based samples reveals how ion transport kinetics and charge storage mechanisms are closely interconnected. In Sample 1, which uses LATP sintered at 900 \({}^{\circ}\)C, the \(b\)-values are close to 0.5 for both anodic and cathodic peaks, indicating a diffusion-controlled charge storage process. This is consistent with the high Li-ion diffusivity measured for this sample (\(\sim\)10\({}^{-9}\) cm\({}^{2}\cdot\)s\({}^{-1}\)), suggesting efficient Li\({}^{+}\) transport through the electrode and across the solid-state interface. The well-sintered LATP structure likely enables good contact and facilitates rapid bulk diffusion, which dominates the electrochemical behavior. In Sample 2, where LATP was sintered at a higher temperature of 1000 \({}^{\circ}\)C, the diffusivity is the lowest among the three samples (\(\sim\)10\({}^{-10}\) cm\({}^{2}\cdot\)s\({}^{-1}\)), reflecting sluggish Li-ion transport. Although the \(b\)-values still hover near 0.5-0.57, indicating primarily diffusion-controlled behavior, the slightly higher cathodic \(b\)-value suggests a minor increase in surface-related contributions, potentially due to the poor interfacial contact that limits bulk diffusion. The degraded diffusivity is likely the result of reduced interface compliance and increased resistance, caused by excessive LATP grain growth or densification at elevated sintering temperatures. Sample 3, which uses a liquid electrolyte (1 M LiPF\({}_{6}\)), shows the highest \(b\)-values (\(\sim\)0.58) for both anodic and cathodic peaks, pointing to a stronger contribution from surface capacitive mechanisms. The liquid electrolyte facilitates faster ion movement at the electrode-electrolyte interface, enhancing pseudocapacitive and non-faradaic processes. Although its diffusivity is not as high as Sample 1, it remains sufficient (\(\sim\)10\({}^{-9}\) cm\({}^{2}\cdot\)s\({}^{-1}\)) to support fast surface redox reactions. The relatively higher \(b\)-values in this case reflect the dominance of interfacial kinetics over bulk diffusion, which is typical in liquid systems. The electrochemical performance of the three LFP-based systems can be comprehensively understood by analyzing the correlation between rate capability, \(b\)-values, and Li-ion diffusivity. Sample 1, which incorporates LATP sintered at 900 \({}^{\circ}\)C, exhibits the highest specific capacity across all tested C-rates, maintaining stable performance even at 5 C. This excellent rate capability is supported by \(b\)-values close to 0.5, indicating a diffusion-controlled charge storage mechanism. The high Li-ion diffusivity (\(\sim\)10\({}^{-9}\) cm\({}^{2}\cdot\)s\({}^{-1}\)) measured in this sample further confirms efficient bulk ion transport and low interfacial resistance, enabling fast and reversible electrochemical reactions during high-rate cycling. In contrast, Sample 2, based on LATP sintered at 1000 \({}^{\circ}\)C, shows significantly poorer rate performance, with lower capacities at all current densities and incomplete capacity recovery when the current returns to 1 C. Although the \(b\)-values (\(\sim\)0.51 anodic, \(\sim\)0.57 cathodic) suggest the process is still largely diffusion-controlled, the much lower diffusivity (\(\sim\)10\({}^{-10}\) cm\({}^{2}\cdot\)s\({}^{-1}\)) indicates sluggish ion transport. The compromised interface due to over-sintering likely results in poor contact between LFP and LATP, which hinders Li-ion movement and reduces the cell's ability to perform under high current conditions. Sample 3, which uses a liquid electrolyte (1 M LiPF\({}_{6}\)), demonstrates intermediate rate performance--better than Sample 2 but slightly inferior to Sample 1 at higher C-rates. This behavior is consistent with its relatively higher \(b\)-values (\(\sim\)0.58), suggesting a greater contribution from surface capacitive processes.