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First-principles studies of the effects of impurities on the ionic and electronic conduction in LiFePO$_{4}$

Olivine-type LiFePO$_{4}$ is widely considered as a candidate for Li-ion battery electrodes, yet its applicability in the pristine state is limited due to poor ionic and electronic conduction. Doping can be employed to enhance the material's electrical conductivity. However, this should be understood as incorporating electrically active impurities to manipulate the concentration of native point defects such as lithium vacancies and small hole polarons which are responsible for ionic and electronic conduction, respectively, and {\it not} as generating band-like carriers. Possible effects of monovalent (Na, K, Cu, and Ag), divalent (Mg and Zn), trivalent (Al), tetravalent (Zr, C, and Si), and pentavalent (V and Nb) impurities on the ionic and electronic conductivities of LiFePO$_{4}$ are analyzed based on results from first-principles density-functional theory calculations. We identify impurities that are effective (or ineffective) at enhancing the concentration of lithium vacancies or small hole polarons. Based on our studies, we discuss specific strategies for enhancing the electrical conductivity in LiFePO$_{4}$ and provide suggestions for further experimental studies.