It is known that the Li15Si4−xGex phase is in the fully lithiated state at room temperature, in which all the Si (and Ge) atoms at 16c sites are surrounded by Li atoms while Li atoms are classified into two groups according to the symmetry: Li1 atoms at 12a sites and Li2 atoms at 48e sites (Fig. 1, C and D). To theoretically find out the stable structures of Li15Si4−xGex (x = 0, 0.25, 0.5, and 4.0) alloys, their structure optimizations were first performed in the frame of DFT with the program package CASTEP (54, 55), using the plane-wave (PW) ultrasoft pseudopotential method and the Perdew-Wang (PW91) form of generalized gradient approximation (GGA) exchange-correlation energy functional (56). To quantificationally estimate the covalent interactions on each Li atom in Li15Si4−xGex, the average bond orders (BO) and BLs were calculated by using a projection of PW states onto a molecular orbital basis in the Mulliken population analysis (57).

Then, depending on the type of Li atoms and the distances between them, we chose two sets of pathways for Li migration in Li15Si4−xGex to examine the energy barriers by performing transition state (TS) searches. As seen in Fig. 1E, for the first set of pathways (Path 1), the Li2α vacancy defect moves to Li1, while for the second set of pathway (Path 2), Li2α vacancy defect migrates to Li2β in adjacent groups. The TS searches of Li migration in Li15Si4−xGex were carried out using the program package DMol3 (58, 59) with double numerical with polarization basis sets and the complete linear synchronous transit/quadratic synchronous transit method (60).

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