A. Theoretical analysis of strengthening in Si–Ge solid-solutions

Material fracture occurs when the energy available for the crack growth is sufficient to overcome the fracture resistance of the materials. The fracture toughness of a material represents the resistance of a material (e.g., surface energy and plastic work) to the propagation of defects such as dislocations. A number of mathematical expressions were developed to estimate the critical particle size below which the fracture of the particles could be prevented. Huggins et al. carried out an early attempt to estimate the critical size (d _c) of the anode particles^{Reference Huggins and Nix19}:

(1)$${d_{\rm{c}}} = {{23} \over \pi }{\left( {{{3{K_{{\rm{IC}}}}} \over {B{\varepsilon _{\rm{T}}}}}} \right)^2}\quad ,$$

where K _IC is the fracture toughness of the material, ε_T = (ΔV/V), representing transformation strain, and B is the biaxial elastic modulus. The common parameters for silicon are as follows: ε_T = 3, B = 170 GPa,^{Reference Abel, Chockla, Lin, Holmberg, Harris, Korgel, Heller and Mullins9} K _IC = 1.06 MPa m^1/2.^{Reference Chasiotis, Cho and Jonnalagadda20} The critical size is calculated to be ∼0.28 nm, which is not congruent with the experimental observations for silicon (up to 150 nm).^{Reference Liang, Yang, Fan, Liu, Liu, Huang, Zhu and Zhang6} The selection of proper parameters is a ubiquitous challenge in some mathematic models to predict the critical size.

More than often, the models of lithiation-induced deformation and fracture assumed the elastic behavior of the electrodes. Recently, Zhao et al. argued that the observation of large morphological changes clearly indicates that charge/discharge cycles caused inelastic deformation.^{Reference Zhao21} A new model based on the assumption of inelastic electrodes was developed by considering elastic–plastic deformation and fracture. This model works well for high-capacity materials because of their large volume expansion during lithiation. Center to the development of mathematic models for Si–Ge alloys is the consideration of pre-existing flaws, e.g., constraints at the local solute atoms. For a nonlinear elastic body, the energy release rate can be obtained by J contour integral, defined as the change in the potential energy of the material with respect to the change in crack area. For the lithiation-induced cracks, the mode I fracture (i.e., the tensile stress acts normal to the plane of the crack) may be assumed. The concept of J integral applies equally well to structures failing in elastic conditions and in fully plastic conditions, therefore, K _IC is related to J _IC as^{Reference Zhu and Joyce22}

(2)$$J{}_{{\rm{JC}}} = {{K_{{\rm{IC}}}^2\left( {1 - \nu } \right)} \over E}\quad ,$$

where ν is the Poisson’s ratio and E is the Young’s modulus of the materials. For the inelastic host materials, Zhao et al. proposed a mathematical relation to estimate the critical size of the inelastic hosts as electrodes for the lithium-ion battery by considering diffusion, elastic–plastic deformation, and fracture as^{Reference Zhao, Pharr, Vlassak and Suo7}

(3)$$d{}_{\rm{c}} = {{\Gamma E} \over {Z{\sigma ^2}}}\quad ,$$

where Γ is the fracture energy of the particle, σ is a yield stress, and Z is the dimensionless number of order unity. We now can estimate the critical size of Si_1−xGe_x by considering J _JC = K and using proper values of E, K _IC, and ε. Equation (3) becomes

(4)$${d_{\rm{c}}} = {{\Gamma E} \over {Z{\sigma ^2}}} = {{K_{{\rm{IC}}}^2\left( {1 - \nu } \right)} \over E}{E \over {Z{\sigma ^2}}} = {{K_{{\rm{IC}}}^2\left( {1 - \nu } \right)} \over {Z{E^2}{\varepsilon ^2}}}\quad .$$

Mechanical properties, e.g., Young’s modulus, of Si–Ge alloys have been reported, particularly in Yonenaga’s series of publications for the alloys at high temperatures (>500 °C).^{Reference Yang, Yu, Li, Wang and Wang12,Reference Wang, Yu, Li and Yang13,Reference Yonenaga23–Reference Yonenaga25} The stress–strain for the germanium rich alloy was similar to Ge, likewise silicon-rich alloy similar with Si. The unique behavior occurs in compositions with x ∼ 0.50 at which an athermal stress is in its maximum.^{Reference Yonenaga25} Below the athermal stress, dislocations are pinned due to the dynamic interaction between a solute and surrounding dislocations, thus strengthening Si–Ge alloys. Although much work was done at high temperatures, these results are consistent with our electrochemical measurements.

B. Structure, strain, and critical size of Si–Ge solid solutions

Silicon and germanium are fully miscible to form crystalline alloys due to their similar chemical properties, including valence structure, bonding orbitals (sp ³), crystal structure (diamond FCC), and indirect band gap. Our initial experiment focused on the refinement of diffraction patterns of the Si–Ge alloys. Figure 1 shows XRD patterns of Si_1−xGe_x (x = 0–1), suggesting the formation of single phase solid solutions. To confirm the composition, elemental distribution of Ge and Si in the solid solutions were examined by elemental mapping, which are presented in Fig. 2. Homogenous distribution of Si and Ge in the all solid solutions can be observed. The atomic compositions obtained by quantitative analysis of the elemental mapping results were close to the feed ratio (Table I). Theoretical specific capacities of the alloys based on the weight fractions and theoretical specific capacities of Si^{Reference Mishra, Zheng, Patel, Estevez, Jia, Luo, El-Khoury, Li, Zhou and Zhang26} and Ge^{Reference Ke, Mishra, Jamison, Peng, Ma, Huang, Sun and Zhou27} are also provided in the same table.

FIG. 1.

XRD patterns of Si, Ge, and Si–Ge solid solution series.

FIG. 2.

TEM images and elemental mapping for Si, Ge, and both components for Si_0.25Ge_0.75 (a–d), Si_0.5Ge_0.5 (e–h), and Si_0.75Ge_0.25 (i–l).

TABLE I.

EDS analysis for the chemical composition of Si–Ge solid solutions. The theoretical specific capacity of each alloy is calculated based on the corresponding weight fractions and the theoretical specific capacities of Si (3579 mAh/g) and Ge (1623 mAh/g).

Refinement was carried out to calculate lattice parameters and residual lattice strain. Williamson–Hall plots were used to obtain the residual strain in the solid solution, assuming that the diffraction peaks follow a Lorentzian distribution, as

(5)$${\beta _{{\rm{total}}}} = {\beta _{{\rm{size}}}} + {\beta _{{\rm{strain}}}} = {{0.9\lambda } \over {t\cos \theta }} + {{4\left( {\Delta d} \right)\sin \theta } \over {d\cos \theta }}\quad ,$$

where β_total is the full-width half-maximum of the XRD peak after a subtraction of a systematic broadening, λ is the incident X-ray wave length, θ is the diffraction angle, t is the crystal size, and Δd is the difference of the d spacing corresponding to a typical peak. A plot of β_total versus 4 sin(θ)/cos(θ) yields the crystal size from the intercept value, and the strain (ε = Δd/d) from the slope (Supplementary Material Fig. S1). The lattice parameter was calculated from a linear regression analysis of the measured lattice constant, obtained from each peak, against Nelson–Riley function:

(6)$${{\left( {{{{{\cos }^2}\;\theta } / {\sin \;\theta }} + {{{{\cos }^2}\;\theta } / \theta }} \right)} / 2}\quad .$$

Figure 3 shows the lattice constant and residual strain as a function of germanium content (x). The lattice constant follows Vegard’s law, thus exhibits a tread of linear dependence of x. The subject of the deviation from Vegard’s law in the vicinity of x = 0.50 was extensively studied by the semiconductor physics community.^{Reference Aubry, Tyliszczak, Hitchcock, Baribeau and Jackman28–Reference Yu, Jayanthi, Drabold and Wu31} The residual strain in Si–Ge solid solution was simulated by ab initio molecular dynamics calculation, indicating that the bond lengths between Si–Si, Si–Ge, and Ge–Ge pairs were a function of composition thus resulting in local stress field.^{Reference Martins and Zunger29,Reference Yu, Jayanthi, Drabold and Wu31} X-ray absorption fine structure (XAFS) measurements,^{Reference Aubry, Tyliszczak, Hitchcock, Baribeau and Jackman28} however, found the bond-angle relaxation in the vicinity of Si_0.50Ge_0.50, resulting in a deviation from Vegard’s law. Moreover, XAFS results showed that the Si–Si bond length was only weakly dependent on composition, whereas there was a significant change in the Si–Ge bond length and an even larger change in the Ge–Ge bond length. Hence, the addition of Si into Ge is expected to significantly influence Ge–Ge bond, thus creating greater residual strain, as we observed here, as shown in Fig. 3. The parameters obtained from the literature for germanium are as follows: ν = 0.28, K _IC = 1.004 MPa m^1/2, Z = 0.91, and E = 102 GPa,^{Reference Wortman and Evans32} and its critical size can then be estimated from Eq. (4) ∼400 nm with a measured strain of 1.4%. For a particle of a given size at fixed values of fracture energy and young’s modulus, the critical particle size to avert the fracture is inversely proportional to the square of the lattice mismatch strain as given by Eq. (4). The strain values would be much greater during lithiation. In this research, the average particle size for these electrodes is in the range of 0.3–0.5 micrometers, as shown in Fig. 4.

FIG. 3.

Lattice constant and strain in Si–Ge solid solution series.

FIG. 4.

SEM images of (a) Si, (b) Si_0.25Ge_0.75, (c) Si_0.50Ge_0.50, (d) Si_0.75Ge_0.25, and (e) Ge before cycling.

C. Electrochemical performance of Si–Ge solid solutions

Coin cells were used to evaluate the electrochemical performance of the Si–Ge solid solutions. To embody the unique properties of the solid solutions, control experiments were carried out on Si and Ge electrodes under same conditions. Figure 5 shows the cycling performance of the Si, Ge, and Si–Ge solid solution electrodes at a current density of 500 mA/g after 5 cycles of activation at 100 mA/g. It is worthwhile to note that all of the capacity is based on the total weight of electrodes, which include active materials, binders, and conductive agents. The first discharge (lithiation) capacities of Si, Si_0.75Ge_0.25, Si_0.50Ge_0.50, Si_0.27Ge_0.75, and Ge electrodes were 3197.9, 2715.7, 2228.4, 1968.2, and 1499.8 mAh/g, and their first charge (delithiation) capacities were 2066.3, 2073.4, 1561.1, 1338.9, and 963.6 mAh/g, respectively. The coulombic efficiencies for all the electrodes during the first cycle were less than 80%. Besides the irreversible capacity loss due to the formation of the solid electrolyte interphase (SEI), the coulombic efficiency for first few cycles depend upon the amount of native oxides formed on the electrodes during the synthesis and storage. Therefore, the low coulombic efficiency for the first few cycles may be attributed to the irreversible capacity loss during the formation of the SEI and reduction of native oxides in Si and Ge electrodes.

FIG. 5.

Cyclic capacity performance of (a) Si, (b) Si_0.75Ge_0.25, (c) Si_0.50Ge_0.50, (d) Si_0.25Ge_0.75, and (e) Ge. (f) Voltage profiles of the Ge_0.50Si_0.50 electrode. The first 5 cycles were measured at the current density of 100 mA/g while the rest were obtained at 500 mA/g. Capacity is based on total weight of the electrode.

After five cycles of activation at 100 mA/g, the initial capacity was 417.9, 1869.1, 1425.0, 1277.7, and 844.9 mAh/g for Si_1−xGe_x (x = 0, 0.25, 0.50, 0.75, and 1), corresponding to coulombic efficiencies of 87.1, 98.6, 96.1, 94.9, and 95.4%, at a higher current density of 500 mA/g. Additionally, the cyclic performance and the corresponding coulombic efficiencies of Ge and Ge-rich alloys are more stable compared to Si or Si-rich alloys, suggesting more robust electrode and the SEI. The capacity retentions of the five samples in the 80th cycle are 16.0, 55.2, 84.6, 79.2, and 98.2% for Si_1−xGe_x (x = 0, 0.25, 0.50, 0.75, and 1). As shown in Figure 5(a), a rapid decrease in capacity was observed in silicon (0.3–0.5 micrometers), consistent with the literature reporting the fracture of the silicon electrode with an average particle size >150 nm.^{Reference Liang, Yang, Fan, Liu, Liu, Huang, Zhu and Zhang6} With Ge added into the submicro-sized Si, the capacity retention and cyclic performance are clearly improved. More interestingly, with increasing the composition of Ge, the capacity retention increases at first, then decreases. This indicates that the different component of Si–Ge solid solutions has a different structural stability. As we discussed above, the Si–Ge solid solution with different ratios exhibits a different strain, which is likely the key part to affect the cyclability of Si–Ge solid solutions. According to the strain analysis in Si–Ge solid solutions (Fig. 3), the strain of Si_0.5Ge_0.5 solid solution is the highest. As it is known, the residual strain of the solid solution provides the resistance for the movement of dislocations, due to interaction between the stress field of the solute and the dislocation. Compared to the Ge and Si_0.5Ge_0.5 solid solution electrodes, although the capacity retention of Ge is higher than that of Si_0.5Ge_0.5 solid solution, the capacity of Si_0.5Ge_0.5 solid solution is 1.5 times higher than that of the Ge electrode. Meanwhile, the coulombic efficiency of the solid solution is 99.4%, which is higher than that of Ge (96.2%) at the 80th cycle. It is clear that the Si_0.5Ge_0.5 solid solution electrode exhibited the best cycling performance and the highest capacity amongst the five electrodes, which can be attributed to the highest residual strain.

The selected voltage profile of the Si, Ge, and Si–Ge solid solutions are displayed in Figs. 6(a)–6(d). Compared to the Si electrode [Fig. 6(a)], the Si–Ge solid solutions and Ge electrodes exhibited improved capacity retention, suggesting structural stability of these materials compared to the Si electrode. With an increase in Ge fraction, the length of a small sloping region between 0.125 and 0.02 V versus Li/Li⁺ increases. This sloping region is attributed to the conversion of Li_xGe to Li₁₅Ge₄, which is consistent with in situ XRD studies discussed in later section.

FIG. 6.

Voltage profiles for 1st, 2nd, 20th, 40th, and 50th cycle for (a) Si, (b) Si_0.75Ge_0.25, (c) Si_0.25Ge_0.75, and (d) Ge electrodes.

Further research was carried out to investigate the rate capability of the best performing Si_0.50Ge_0.50 electrode at various current densities, as shown in Fig. 7(a). The rate capability of the solid solution is plotted at the current rates of up to 10 A/g for the voltage range of 0.02–2.0 V versus Li/Li⁺. The specific capacities based on the total electrode mass are ∼1475, 1324, 1171, 982, 789, and 453 mAh/g at 0.1, 0.5, 1, 2, 4, and 10 A/g, respectively. The subsequent cyclic capacity was measured again at 0.5 A/g, which was 1209 mAh/g, indicating that the capacity was recovered 91.3% after rate-performance test. The electrode exhibited highest capacity fading at 10 A/g, with the 15% capacity loss during a five-cycle operation. Such a rapid capacity degradation during charging/discharging at 10 A/g could be explained by the inhomogeneity in Li distribution caused by crowded Li in the outer shell of the particles because of the lithiation rate being faster than diffusion of lithium ions in the active anodes, resulting in large stress in the particle, as reported by Zhao et al.^{Reference Zhao, Pharr, Vlassak and Suo33} Furthermore, it has been reported that such high stress could lead to the growth of pre-existing cracks. The inhomogeneity of Li distribution is higher at greater lithiation rates, resulting in a large lattice mismatch and implying that the charging rate (alloying with lithium) is the driving force for the fracture of materials. The slight loss in capacity when the current rate is brought back to 0.5 A/g compared to previous cycles at the same discharge rate could also be explained by the loss of active materials due to some materials being fractured at a high discharge rate of 10 A/g.

FIG. 7.

(a) Rate capability of the Si_0.50Ge_0.50 solid solution at different current densities (0.1, 0.5, 1, 2, 4, and 10 A/g). (b) Cyclic capacity performance of the Si_0.50Ge_0.50 electrode at the current density of 1600 mA/g, after 5 formation cycles at 200 mA/g.

To further assess the stability of the Si_0.50Ge_0.50 solid solution electrode at high rates, we evaluated the rate dependence of specific capacity of this solid solution, as presented in Fig. 7(b). The discharge capacity of the Si–Ge solid solution electrode is 895 mAh/g after 300 cycles at a current density of 1600 mA/g. The capacity retention of the electrode after 300 cycles is as high as 70%. The specific capacity is still over twice its theoretical value for the graphite electrode. This result illustrates that the Si_0.50Ge_0.50 solid solution electrode has excellent capacity retention and a long cycle life at high rate.

To understand why the Si_0.50Ge_0.50 solid solution electrode exhibits excellent electrochemical performance, we analyzed the differential capacity of the Si, Ge, and Si–Ge solid solution electrodes. Differential capacity analysis was used to study the mechanism of the electrochemical reactions during the lithiation and delithiation processes. Each peak generally represents an electrochemical reaction or phase transition in the active material.^{Reference Ke, Mishra, Jamison, Peng, Ma, Huang, Sun and Zhou27} Figures 8(a)–8(e) show the differential capacity plots for solid solution electrodes. For pure germanium, three peaks are initially observed at 0.14, 0.27, and 0.49 V. After first few cycles, they centered at 0.16 and 0.36 V, suggesting a two-step alloying process. For the delithiation process, the two peaks were initially observed at ∼0.38 and ∼0.51 V. Ultimately, after a few cycles, a single prominent peak was observed at ∼0.39 V, suggesting a single-step delithiation (dealloying) process. Figure 8(a) presents the dQ/dE plots for the silicon anode showing a single lithiation and delithiation peak at ∼0.1 V and ∼0.44 V, respectively, for the 1st cycle. Starting from the 2nd cycle, two lithiation peaks were observed at the ∼0.23 and ∼0.1 V. Similarly, two delithiation peaks were observed at ∼0.27 and ∼0.43 V. Figures 8(b)–8(d) show the dQ/dV plots for the Si_0.75Ge_0.25, Si_0.50Ge_0.50, and Si_0.25Ge_0.75 solid solution electrodes, respectively, corresponding to voltage–capacity relations shown in Figs. 6(a)–6(d). For the Si_0.25Ge_0.75 electrode [Fig. 8(d)], the major lithiation peaks can be observed at ∼0.34 and 0.15 V, and the delithiation process appears to be a two-step process at ∼0.36 and ∼0.5 V. For the Si_0.50Ge_0.50 electrode, apart from the first cycle, the three lithiation peaks are developed at ∼0.42, 0.29, and 0.12 V for rest of the cycles while the delithiation peaks were observed at ∼0.30 and 0.5 V. These results are consistent with the previous work reported by Abel et al. on thin film Si/Ge alloys.^{Reference Abel, Chockla, Lin, Holmberg, Harris, Korgel, Heller and Mullins9} More discussion is provided below. It may be interesting to note that the position of lithiation peaks are found to shift to the slightly lower voltages as the concentration of Si increases in the Ge electrode, indicating the formation of homogeneous solid solutions due to the absence of separate peaks for pure Si and Ge. Furthermore, post cycling TEM and the corresponding elemental mapping of the Si_0.50Ge_0.50 electrode are presented in Fig. S2, which revealed Si and Ge elements in the solid solution still keep uniform distribution, without aggregation after cycling. This result corroborates the stable cyclic performance of the Si_0.05Ge_0.50 solid solution electrode.

FIG. 8.

Differential capacity plots for solid solution electrodes for 1st, 2nd, 20th, 40th, and 50th cycle. (a) Si, (b) Si_0.75Ge_0.25, (c) Si_0.50Ge_0.50, (d) Si_0.25Ge_0.75, and (e) Ge electrodes.

It is commonly known that the ability of metals subject to plastic deformation can be suppressed by reducing the mobility of dislocations. Alloying a metal with solute atoms has been known to restrict the movement of dislocations and ultimately resulting in the increase in tensile and yield strengths. Enhancement of the mechanical strength of silicon by doping with germanium has been reported in semiconductor community, primarily at elevated temperatures >500 °C.^{Reference Yang, Yu, Li, Wang and Wang12,Reference Wang, Yu, Li and Yang13} Yonenaga, in several of his publications, reported that Si/Ge alloys showed a maximum yield stress in Si_0.50Ge_0.50.^{Reference Yonenaga23,Reference Yonenaga25} This finding is consistent with the more stable cyclic capacity observed in Si_0.50Ge_0.50 solid solution in our work. Germanium (atomic radius 122 pm) is larger than silicon (111 pm) in size, hence when the larger solute atoms (Ge) is added to the solvent atoms (Si), a compressive stress is generated near Ge atoms. This additional compressive stress can relieve strain created during lithiation/delithiation, thus enables more stable cyclic performance. From the differential capacity plots, it is apparent that the largest peak during lithiation of Ge is formed ∼0.16 V, suggesting most volume expansion around that voltage. For Si, however, the first peak of lithiation forms at ∼0.1 V, lower than that of Ge. The first peak of lithiation for solid solutions largely overlaps with that of Ge. Hence, the presence of Ge atoms in the Si can prevent from fracturing even at the particle sizes larger than the critical size (<150 nm) reported for Si by several other scholars.^{Reference Liang, Yang, Fan, Liu, Liu, Huang, Zhu and Zhang6,Reference Weker, Liu, Misra, Andrews, Cui and Toney34}

D. Phase evolution investigated by in situ XRD during electrochemical cycling

In situ XRD was used to understand the processes of lithiation and delithiation of the Si–Ge solid solution anode. In this work, a high power (9 kW) diffractometer enabled us to determine structures during the first two cycles between 0.01 and 3.0 V at the current density of 0.15 A/g. In addition to its high power, a significant advantage of this diffractometer is its fast scan rate which allows one to gather sufficient structural details during the electrochemical reaction. In addition, the XRD spectra exhibit higher resolution than those obtained from a synchrotron setup.^{Reference Silberstein, Lowe, Richards, Gao, Hanrath and Abruña35,Reference Misra, Liu, Nelson, Hong, Cui and Toney36} Organic solvent N-methylpyrrolidone-based binder polyvinylidene fluoride was used to reduce the extent of electrode oxidation. As shown in Fig. S3, the peak intensity of Si_0.5Ge_0.5 reflections initially increased during the 1st lithiation cycle, then decreased [Fig. S3(c)]. Such an increase in intensity is attributed to the reaction of the residual Ge or Si oxides with Li ions, which are converted to Ge or Si. When discharging to ∼0.165 V (scan number 20), the intensity of reflection, (220) and (311), is at its maximum; while the intensity of (111) reflection continued to increase until 0.138 V (scan number 40), then decreased again. This observation shows that Li ions react with Si_0.5Ge_0.5 starting from higher index facets, i.e., (220) and (311), which exhibit more open structure than that of (111) facet. With more lithium diffusing into the solid solution, the intensity of all peaks of Si_0.5Ge_0.5 decreases. Further discharge to 0.112 V (scan number 75), a broad peak appeared at 2θ ∼ 41°, corresponding to nanosized or amorphous Li_x(Ge,Si). Another broad peak appeared at 2θ ∼ 23° when discharged to 0.038 V (scan number 120). When the cell was fully discharged (scan number 154), the presence of crystalline Li₁₅(Ge,Si)₄ was observed, along with a few broad reflections, suggesting the presence of cluster-size Li_x(Ge,Si). Interestingly, the (111) peak of Si_0.5Ge_0.5 was still seen after the full discharge which could be due to the high mass loading (∼7 mg/cm²) of the working electrode. Upon charging, the reflections of the lithiated phases began to diminish. When charged to 0.608 V (scan number 249), all peaks of Li₁₅(Ge,Si)₄ disappeared. During the delithiation process, the crystalline phase was converted to nano or amorphous Si_0.5Ge_0.5 solid solution. In the second cycle, a similar phenomenon was observed, in which all of the crystalline Si_0.5Ge_0.5 disappeared at the end of discharge while the intensity of crystalline Li₁₅(Ge,Si)₄ was stronger than that observed during the 1st cycle.

To better understand the function of Si and Ge in the Si_0.5Ge_0.5 solid solution, a comparison of lithiation behavior of Si_0.5Ge_0.5 (Fig. S3) was carried out on the parent Si and Ge anodes, as shown in Figs. S4 and S5, respectively. The Si anode behaved in a similar manner with Si_0.5Ge_0.5, as shown in Fig. S4 with the formation of cluster-type Li_xSi, which is then converted to Li₁₅Si₄ phase, and finally all of the crystalline phases disappeared. It was surprising to observe that the intensity of all Si peaks decreased at the beginning [Fig. S4(a)], indicating that there is no preferential lithiation facet for Si. For the Ge anode (Fig. S5), the first step involved with the conversion of surface GeO₂ to Ge, shown by the increase of the intensity of Ge peaks. The second step was the lithiation process of Ge to form nanosized Li_xGe, and Li₁₅Ge₄ phase, and then the formation of the Li₁₁Ge₆ phase. To the best of our knowledge, the formation of Li₁₁Ge₆ was observed for the first time during the in situ characterization,^{Reference Liu, Huang, Picraux, Li, Zhu and Huang37,Reference Baggetto and Notten38} likely attributed to the use of high power diffractometer. Finally, the Li₁₁Ge₆ phase was converted to cluster-type Ge. According to the selected scan XRD patterns [Fig. S5(b)], the intensity of Ge(111) and (220) peaks increased at the beginning (scan number 80) due to the conversion of GeO₂ to Ge. However, the intensity of the Ge(311) peak decreased, which means that the Li ions react preferentially with Ge at the (311) facet. Based on the in situ XRD of Si and Ge anodes, the addition of Ge into Si changed the direction of lithiation, resulting in improving the stability of the Si anode.

Finally, a comparison of the intensities of XRD reflections of the lithiated phases in Figs. S3(a), S4(a), and S5(a) reveals that the crystallinity of the final lithiated phase in Si is amorphous while it is crystalline in Ge or Si_0.50Ge_0.50. Formation of crystalline Li₁₅Si₄ has been reported to be kinetically slow, often requires current density below C/100.^{Reference Datta and Kumta39,Reference Zhang, Wang, Xiao, Xu, Graff, Yang, Choi, Wang, Li, Liu and Brodd40} Therefore, there appears a relation between the crystallinity of the lithiated phase and the electrochemical stability. Further work may be required to unravel the role of crystallinity on the electrochemical performance of these electrodes.