Li-Ion Conductivity of Single-Step Synthesized Glassy-Ceramic Li10GeP2S12 and Post-heated Highly Crystalline Li10GeP2S12

Li10GeP2S12 is a phosphosulfide solid electrolyte that exhibits exceptionally high Li-ion conductivity, reaching a conductivity above 10–3 S cm–1 at room temperature, rivaling that of liquid electrolytes. Herein, a method to produce glassy-ceramic Li10GeP2S12 via a single-step utilizing high-energy ball milling was developed and systematically studied. During the high energy milling process, the precursors experience three different stages, namely, the ‘Vitrification zone’ where the precursors undergo homogenization and amorphization, ‘Intermediary zone’ where Li3PS4 and Li4GeS4 are formed, and the ‘Product stage’ where the desired glassy-ceramic Li10GeP2S12 is formed after 520 min of milling. At room temperature, the as-milled sample achieved a high ionic conductivity of 1.07 × 10–3 S cm–1. It was determined via quantitative phase analyses (QPA) of transmission X-ray diffraction results that the as-milled Li10GeP2S12 possessed a high degree of amorphization (44.4 wt %). To further improve the crystallinity and ionic conductivity of the Li10GeP2S12, heat treatment of the as-milled sample was carried out. The optimal heat-treated Li10GeP2S12 is almost fully crystalline and possesses a room temperature ionic conductivity of 3.27 × 10–3 S cm–1, an over 200% increase compared to the glassy-ceramic Li10GeP2S12. These findings help provide previously lacking insights into the controllable preparation of Li10GeP2S12 material.

For impedance measurements, pellets were prepared according to the processes stated in the main text, with the diameters and thicknesses presented in Table S1. After sputtering, the solid electrolytes are placed into a stainless steel Swagelok cell and sealed. To ensure further protection against atmospheric degradation, all joints are additionally sealed using hot glue.
The sealed cells are placed into an environmental chamber (LabEvent T/20/40/EMC, Vötschtechnik). Depending on the material, two temperature ranges were tested. For the materials that underwent high-energy ball milling (HBM) for 40 min, 160 min, 320 min and 400 min, the temperatures at which impedance spectroscopy was carried out was 0 °C, 10 °C, 20°C, 25 °C, 30 °C, 40 °C and 60 °C. For the materials that underwent HBM for 520 min as well as the heat treated (HT) materials, a wider temperature range was used, that is to say, -20 °C, -15 °C, -10 °C, -5 °C, 0 °C, 10 °C, 20°C, 25 °C, 30 °C, 40 °C and 60 °C. For both temperature ranges, the materials were first bought down to the lowest measurement temperature (0 °C or -20 °C) and held for 4.75 h before potential electrochemical impedance spectroscopy (PEIS) was carried out. For each increase of 5 °C, the cell was stabilized at that temperature for at least 1.75 h, and for each increase of 10 °C, the cell was stabilized at that temperature for at least 2.75 h.
For PEIS, all materials were tested utilizing an excitation potential of 50 mV and a frequency range between 7 MHz and 1 Hz. 20 points were taken per decade with 1 measure per frequency. Table S1. Diameter and thicknesses of polished solid electrolyte pellets produced from cold pressing material that has underwent high-energy ball milling (HBM) or HBM and heat treatment (HT).

Sample
Diameter ( Nyquist plot fitting Due to the complex nature of the material that underwent HBM for 40 min (Fig. S1) and 160 min (Fig. S2), a varied mixture of both extremely poor Li-ion conductors and ionically conductive amorphous phases, the contributions to the resistance cannot be easily modeled. As such only the total resistance, R total , as taken from 0 Ω to the inflection point is given.
Due to the similarities in chemistry as demonstrated by XRD (Fig. 1), for the materials that underwent HBM for 320 min (Fig. S4) and 400 min (Fig. S5)  CPE DP describes the diffuse layer resistance. As measurement temperatures increase, however, the Li-ion transport becomes faster thus leading to lower measured resistances making separation of different contributions difficult thus necessitating the use of multiple, simplified equivalent circuits (Fig S3).
For the materials that underwent HBM for 520 min (Fig. S7), from observation of the XRD and QPA (Fig. 1, Table 1), it is shown that a large minority of the material, ~40 wt. % is amorphous with the majority of the remaining being Li 10 GeP 2 S 12 . Due to the use of HBM we assume the material is nano-crystalline in an amorphous matrix thus R gb , the grain boundary resistance, will be minimal and is ignored. Thus the material is simply modeled with R b , the bulk resistance of the crystalline Li 10 GeP 2 S 12 and R am , the resistance contribution of the amorphous phase. The equivalent circuits are presented in (Fig. S6).
For the material that underwent HBM for 520 min plus an additional heat treatment at 575 °C (Fig. S11) and 600 °C (Fig. S12), XRD and QPA (Fig. 1, Table 1) showed them to be extremely similar, both consisting of relatively pure crystalline Li 10 GeP 2 S 12 with negligible amorphous phase. As such the same model was used for both consisting of the bulk resistance R b and the grain boundary resistance R gb . The equivalent circuits are presented in (Fig. S10).
XRD and QPA (Fig. 1, Table 1) reveal that the material that underwent HBM for 520 min plus an additional heat treatment at 625 °C possesses a small amount of amorphous content (~10 wt. %), a large amount of side products (~ 20 wt. %) with the remaining being crystalline Li 10 GeP 2 S 12 . As the amount of amorphous phase is relatively low, the resistance put up should be negligible. Due to the high crystallinity both the grain boundaries between similar materials (R gb ) as well as when differing crystalline particles are in contact with each other (R cc ) would be the main bottleneck to Li-ion transport and thus the measured resistances. Figure S1. Nyquist plots for temperatures in the range between 0 °C and 60 °C and Arrhenius plot, with activation energy, of sample that has undergone HBM for 40 min.  Table S2. R total and ionic conductivity measured from 0 °C and 60 °C for sample that has undergone HBM for 40 min (Fig. S1) Figure S2. Nyquist plots for temperatures in the range between 0 °C and 60 °C and Arrhenius plot of sample, with activation energy, that has undergone HBM for 160 min.  Table S3. R total and ionic conductivity measured from 0 °C and 60 °C for sample that has undergone HBM for 160 min (Fig. S2) Figure S3. Model of Li-ion transport trough the material that has underwent HBM for 320 min ( Fig. S4) and 400 min (Fig. S5) Figure S4. Nyquist plots of sample that has undergone HBM for 320 min from 0 °C to 10 °C (a), 20 °C to 30 °C (b) and 40 °C to 60 °C (c). Equivalent circuit used are found in Fig. S3.
Arrhenius plot measured from 0 °C to 60 °C along with calculated activation energy (d).  Table S4. Fitting values used for sample that has undergone HBM for 320 min (Fig. S4). Where Q am and a am describe CPE am , S 1 describes the Warburg element, Q gb and a gb describe CPE gb , Q cc and a cc describe CPE cc , Q DP and a DP describe CPE DP , Q 2 and a 2 describe CPE 2 and Q 3 and a 3 describe CPE 3 . R total is the sum of all resistors in the circuit.   Table S5. Fitting values used for sample that has undergone HBM for 400 min (Fig. S5). Where Q am and a am describe CPE am , S 1 describes the Warburg element, Q gb and a gb describe CPE gb , Q cc and a cc describe CPE cc , Q DP and a DP describe CPE DP , Q 2 and a 2 describe CPE 2 and Q 3 and a 3 describe CPE 3 . R total is the sum of all resistors in the circuit.    Table S6. Fitting values used for sample that has undergone HBM for 520 min (Fig. S7). Where Q am and a am describe CPE am , S 1 describes the Warburg element and Q DP and a DP describe CPE DP . R total is the sum of all resistors in the circuit. s^(a -1)) a am R am (Ohm) S 1 (Ohm.s^-1/2) Q DP (F.s^(a -1) Figure S10. Model of Li-ion transport trough the material that has underwent HBM for 520 min with additional heat treatment at 575 °C (Fig. S11) and 600 °C (Fig. S12) (a).
Equivalent circuit used for fitting the impedance spectroscopy (b-c). For the material heat treated to 575 °C (b) was used for -20 °C to 0 °C, and (c) was used for 10 °C to 60 °C. For the material heat treated to 600 °C (b) was used for -20 °C to 0 °C, and (c) was used for 10 °C to 60 °C. Shaded portions of equivalent circuits are represented in the impendence spectroscopy ( Fig. S11 and S12) by semi circles of the same color. Figure S11. Nyquist plots of sample that has undergone HBM for 520 min with additional heat treatment at 575 °C from -20 °C to 0 °C (a), and 10 °C to 60 °C (b). Equivalent circuit used are found in Figure S10. Arrhenius plot measured from -20 °C to 60 °C along with calculated activation energy (c).

CPE DP
and a gb describe CPE gb , S 1 , and Q DP and a DP describe CPE DP . R total is the sum of all resistors in the circuit. s^(a -1)) a gb R gb (Ohm) Q DP (F.s^(a -1) Figure S12. Nyquist plots of sample that has undergone HBM for 520 min with additional heat treatment at 600 °C from -20 °C to 0 °C (a), and 10 °C to 60 °C (b). Equivalent circuit used are found in Figure S10. Arrhenius plot measured from -20 °C to 60 °C along with calculated activation energy (c).  Table S8. Fitting values used for sample that has undergone HBM for 520 min and then a further heat treatment at 600 °C (Fig. S11). Where Q gb and a gb describe CPE gb and Q DP and a DP describe CPE DP . R total is the sum of all resistors in the circuit.
(°C) R b (Ohm) Q gb (F.s^(a -1)) a gb R gb (Ohm) Q DP (F.s^(a -1) Figure S13. Model of Li-ion transport trough the material that has underwent HBM for 520 min with additional heat treatment at 625 °C (Fig. S14) Table S9. Fitting values used for sample that has undergone HBM for 520 min and then a further heat treatment at 625 °C (Fig. S14). Where Q gb and a gb describe CPE gb , Q cc and a cc describe CPE cc , and Q DP and a DP describe CPE DP . R total is the sum of all resistors in the circuit.