The voltage curve reflects the battery performances and is one of the most fundamental electrochemical properties. The voltage curves are calculated according to equation (2) using the convex hull of each formation energy curve. The experimental studies show that the deviation of the first voltage plateau between c-Si and a-Si is due to the different phase transformation paths, resulting in a thermodynamic voltage hysteresis. A higher charging rate leads to a larger hysteresis loop. The concentration polarization and impedance effects related to charging rates can lead to kinetic hysteresis, and this part of energy loss is not included in the simulations. Figure shows the calculated voltage curves compared with experimental results from references . For lithiation, the predicted voltage curves (Figure ) agree well with experimental results (Figure ). With the increase of Li content x, the lithiation voltage curve jumps abruptly from a high voltage to a stable plateau, and then the voltage decreases slowly to zero. The abrupt jump of the voltage curve is associated with the solid solution of Li in c-Si or a-Si. The plateau region is associated with the two-phase process. One phase is the c-Si or a-Si phase, while the other is a-LixSi phase. The c-Si or a-Si phase and the a-LixSi phase are two stable phases at the initial stage of the lithiation, which can be obtained in the formation energy curve. As displayed in Figure and, our results exhibit two-phase coexistence indicated by the voltage plateau in L-c or L-a. The simulation result not only reproduces the experimental voltage curve, but also agrees well with experimental observations by TEM . As reported by McDowell and Liu et al. , the initial lithiation mechanism of either c-Si or a-Si should follow a two-phase process. Furthermore, the plateau height difference of the lithiation between c-Si and a-Si is also well reproduced by our simulation. In experiments, the plateau of a-Si is 0.22 eV higher compared to that of the c-Si case, while it is 0.17 eV higher in the simulation. This voltage-plateau difference can be attributed to the fact that the initial Li intercalation formation energy of the c-Si (when x is approximately zero in c-LixSi) is lower than that of the a-Si, and both of the c-Si and the a-Si are connected to the same a-LixSi phase in the two-phase region. Therefore, as shown in the formation energy results (Figure ), the phase with a higher Li insertion formation energy at the Li content x ~ 0 would exhibit a larger slope when connected to the endmember phase a-LixSi in the two-phase region, leading to a higher In addition, the atomic force microscope (AFM) result reported that a reversible volume expansion between a-Si and a-LixSi is approximately 300% between 0.0 and 1.2 V in the first and second cycles. We calculated the volume changes ((𝑉 𝐿𝑖 𝑥 𝑆𝑖 -𝑉 𝑆𝑖 ) 𝑉 𝑆𝑖 ⁄ ) 100 ⁄ of the four processes and compared them to experimental result, as listed in suggests that the sampled amorphous structures and computational properties are reliable. For example, the structure of a-Li2.55Si is similar to the Li2.33Si characterized by XRD , which contains Si-Si dumbbells and isolated Si atoms, and the average coordination number of Si-Si is about 1.5. The structure of a-Li3.62Si with 59 mV is similar to that of a-Li3.4Si with 60 mV reported by Grey and Ogata et al. . The a-Li3.62Si contains isolated Si and a few Si-Si bonds (see Figure ), and its Si-Si coordination number is 0.5 (see Figure ). These give us the confidence that we have captured the whole lithiation process of a-Si.