Distribution of relaxation times investigation of $$hbox {Co}^{3+}$$ doping lithium-rich cathode material $$hbox {Li}[hbox {Li}_{0.2} hbox {Ni}_{0.1} hbox {Mn}_{0.5} hbox {Co}_{0.2}]hbox {O}_{2}$$Li[Li0.2Ni0.1Mn0.5Co0.2]O2

The element (hbox {Co}^{3+}) was introduced into lithium-rich material (0.5hbox {Li}_{2}hbox {MnO}_{3} cdot 0.5 hbox {LiNi}_{0.5}hbox {Mn}_{0.5}hbox {O}_{2}) by a polyacrylamide-assisted sol–gel method to form (hbox {Li}[hbox {Li}_{0.2} hbox {Ni}_{0.1} hbox {Mn}_{0.5} hbox {Co}_{0.2}]hbox {O}_{2}) and better electro-chemical performances were observed. Electrochemical impedance spectroscopy spectra were measured on 11 specific open circuit voltage levels on the initial charge profile. Then they were converted to the distribution of relaxation times (DRTs) g((tau )) by self-consistent Tikhonov regularization method. The obtained DRTs offered a higher resolution in the frequency domain and provided the number and the physical origins of loss processes clearly. Through the analysis of DRTs, the rapid augmentation of resistance to electronic conduction and charge transfer within the voltage range 4.46–4.7 V where the removal of (hbox {Li}_{2}hbox {O}) from (hbox {Li}_{2} hbox {MnO}_{3}) component took place was the most remarkable phenomenon and the (hbox {Co}^{3+}) doping greatly reduced the resistance to electronic conduction Re. This gave us more evidence about the complicated ‘structurally integrated’ composite character of the material.