Fast charging sodium-ion batteries based on Te-P-C composites and insights to low-frequency limits of four common equivalent impedance circuits

Various tellurium-red phosphorus-carbon (Te-P-C) composites with different Te to P ratios were prepared via high-energy mechanical milling for application as anode materials in sodium-ion batteries. Highly conductive Te was added to increase the electrical conductivity and improve the mechanical strength of the P-C composite. The optimized Te-P-C (1:2) composite exhibited a reversible capacity of 593 mAh g(-1), demonstrating a capacity retention of 82% at the 100th cycle in the fast recharge test (3 A g(-1)). This performance is related to the electrochemical impedance of each composite. Te-P-C composites are sufficiently simple, such that new constraints for the composites, provided by electrochemical impedance spectroscopy (EIS) results, can be examined. Four mathematical constraints for four frequently applied equivalent circuits at low-frequency limits were declared for batteries. The linear dependence of the sum of the real and imaginary parts of the impedance (Z(real) + Z(imag)) on the frequency was used to interpret the systems. The newly proposed restrictions significantly reduced the uncertainty of the charge-transfer resistance (R-ct) for the Te-P-C composites; the corrected nominal value (158 Omega to 188 Omega) of R-ct was more reliable than the uncorrected one (125 Omega to 560 k Omega from commercial fitting software). Therefore, it is believed that the four proposed constraints could provide a simple and convenient way (linear regression) for electrochemical engineers to control the reliability of the interpretation of EIS data in battery systems.