Borohydride Ammoniate Solid Electrolyte Design for All‐Solid‐State Mg Batteries

Searching for novel solid electrolytes is of great importance and challenge for all‐solid‐state Mg batteries. In this work, we develop an amorphous Mg borohydride ammoniate, Mg(BH4)2·2NH3, as a solid Mg electrolyte that prepared by a NH3 redistribution between 3D framework‐γ‐Mg(BH4)2 and Mg(BH4)2·6NH3. Amorphous Mg(BH4)2·2NH3 exhibits a high Mg‐ion conductivity of 5 × 10−4 S cm−1 at 75 °C, which is attributed to the fast migration of abundant Mg vacancies according to the theoretical calculations. Moreover, amorphous Mg(BH4)2·2NH3 shows an apparent electrochemical stability window of 0–1.4 V with the help of in‐situ formed interphases, which can prevent further side reactions without hindering the Mg‐ion transfer. Based on the above superiorities, amorphous Mg(BH4)2·2NH3 enables the stable cycling of all‐solid‐state Mg cells, as the critical current density reaches 3.2 mA cm−2 for Mg symmetrical cells and the reversible specific capacity reaches 141 mAh g−1 with a coulombic efficiency of 91.7% (first cycle) for Mg||TiS2 cells.


Introduction
Rechargeable Mg batteries have been considered as promising energy storage devices due to its high theoretical energy densities and abundant earth reserves. [1]Mg possesses two charges per ion, indicating that 1/12 mol electron can be transferred by 1 g Mg, which is close to that of Li (1/7 mol electron by 1 g Li).In addition, the negative redox potential of Mg is À2.36 V (vs SHE), also close to that of Li (À3.05 V). [2,3] More importantly, the reserves of Mg in earth's crust is 2.3 wt%, much higher than that of Li (0.0065 wt%). [4]lectrolytes are the key component in rechargeable Mg batteries, since their Mg-ion conductivity, the electrochemical stability window and the electrode compatibility of the electrolytes all significantly affect the overall performance of the rechargeable Mg batteries. [5]Different from rechargeable Li batteries, the interphase in the Mg anode side is non-ion-conductive when using carbonatebased electrolytes. [6]Meanwhile, ether-based electrolytes, such as Grignard reagents (or derivations) [7] and simple Mg salt (MgCl 2 , Mg (CB 11 H 12 ) 2 ) [8,9] solutions can enable reversible Mg stripping and plating, however, at least one of the following key issues still exists for these electrolytes: incompatibility to electrode, corrosivity against stainless steel, and difficulty for synthesis. [10,11]he application of solid Mg electrolytes can potentially avoid the drawbacks of liquid Mg electrolytes by providing an intrinsically different ion conducting mechanism.For example, 1) solid Mg electrolytes are much safer due to their nonvolatility, noninflammability and noncorrosivity; 2) solid Mg electrolytes can suppress the dendritic Mg growth during fast plating; 3) solid Mg electrolytes can simplify the large-scale battery packaging. [12,13]On the other hand, the solid-state diffusion of high-valence Mg ions is usually difficulty due to the strong bonds with counter anions. [14]Therefore, investigations on solid Mg electrolytes are mainly focused on the improvement in Mg-ion conductivity. [15]Many classes of materials, such as oxides (MgZr 4 (PO 4 ) 6 [16]   ), sulfides (MgS-P 2 S 5 -MgI 2 [17]   ), and selenides (MgSc 2 Se 4 [18]   ), have been investigated as solid Mg electrolytes and significant improvements have been achieved.[22] Le Ruyet et al. [23] proposed that Mg 3 (BH 4 ) 4 (NH 2 ) 2 exhibits higher Mg-ion conductivity of 4.1 9 10 À5 S cm À1 at 100 °C.Roedern et al. [24] found that Mg (BH 4 ) 2 (NH 2 CH 2 CH 2 NH 2 ) possesses higher Mg-ion conductivity of 5 9 10 À8 S cm À1 at 30 °C.Kisu et al. [25] developed Mg (BH 4 ) 2 Á(NH 3 BH 3 ) 2 as solid Mg electrolyte, which exhibits a Mg-ion conductivity of 10 À5 S cm À1 at 30 °C.More recently, Yan et al. [26] investigated Mg borohydride ammoniates as solid Mg electrolytes, in which Mg(BH 4 )ÁNH 3 was reported to show a Mg-ion conductivity of 2 9 10 À9 S cm À1 at 30 °C.29] However, further exploration is still highly needed for pushing the complex hydride electrolytes toward practical applications in Searching for novel solid electrolytes is of great importance and challenge for all-solid-state Mg batteries.In this work, we develop an amorphous Mg borohydride ammoniate, Mg(BH 4 ) 2 Á2NH 3 , as a solid Mg electrolyte that prepared by a NH 3 redistribution between 3D framework-c-Mg(BH 4 ) 2 and Mg(BH 4 ) 2 Á6NH 3 .Amorphous Mg(BH 4 ) 2 Á2NH 3 exhibits a high Mg-ion conductivity of 5 3 10 À4 S cm À1 at 75 °C, which is attributed to the fast migration of abundant Mg vacancies according to the theoretical calculations.Moreover, amorphous Mg(BH 4 ) 2 Á2NH 3 shows an apparent electrochemical stability window of 0-1.4 V with the help of in-situ formed interphases, which can prevent further side reactions without hindering the Mg-ion transfer.Based on the above superiorities, amorphous Mg(BH 4 ) 2 Á2NH 3 enables the stable cycling of all-solid-state Mg cells, as the critical current density reaches 3.2 mA cm À2 for Mg symmetrical cells and the reversible specific capacity reaches 141 mAh g À1 with a coulombic efficiency of 91.7% (first cycle) for Mg||TiS 2 cells.
all-solid-state Mg batteries.First, the Mg-ion conduction mechanism has not been clearly identified, especially in terms of Mg vacancy migration mechanism, which hinders the future improvement in Mgion conductivity.Second, the corresponding physical and chemical interactions on the electrode/electrolyte interfaces in all-solid-state batteries have not been clarified, which generates a huge gap between the Mg-ion conduction properties of the electrolytes and the electrochemical performances of the all-solid-state batteries. [30,31]n this work, an amorphous Mg borohydride ammoniate, Mg (BH 4 ) 2 Á2NH 3 , is prepared through a NH 3 redistribution between 3D framework c-Mg(BH 4 ) 2 and Mg(BH 4 ) 2 Á6NH 3 .Amorphous Mg (BH 4 ) 2 Á2NH 3 shows excellent Mg-ion conduction properties, as a Mgion conductivity of 1 9 10 À7 S cm À1 at 35 °C and 5 9 10 À4 S cm À1 at 75 °C can be obtained.Density functional theory calculations reveal that the Mg vacancy migration play an important role in the Mg-ion conduction, and Mg(BH 4 ) 2 Á2NH 3 has lower energy barriers than those of c-Mg(BH 4 ) 2 and Mg(BH 4 ) 2 ÁNH 3 .The apparent electrochemical stability window of amorphous Mg(BH 4 ) 2 Á2NH 3 reaches 0-1.4 V accompanying with interphases formation.Moreover, the excellent conductivity and stability of amorphous Mg(BH 4 ) 2 Á2NH 3 enables cycling of all-solid-state Mg symmetrical cells and Mg|TiS 2 cells.

Results and Discussion
Figure 1a schematically illustrates the material design principle, in which NH 3 redistribution occurs between unique 3D microporous structured c-Mg(BH 4 ) 2 and Mg(BH 4 ) 2 Á6NH 3 to form amorphous Mg (BH 4 ) 2 Á2NH 3 during high-energy ball milling, benefitting the fast Mgion transfer.Then, the structural characterizations of the as-prepared Mg (BH 4 ) 2 ÁxNH 3 (x = 1, 2, 3), c-Mg(BH 4 ) 2 , and Mg(BH 4 ) 2 Á6NH 3 are performed.X-ray diffraction patterns (Figure 1b) show that c-Mg(BH 4 ) 2 and Mg(BH 4 ) 2 Á6NH 3 exhibit typical diffraction peaks without any impurity signal.As for Mg(BH 4 ) 2 ÁxNH 3 (x = 1, 2, 3), no apparent diffraction peak can be observed, indicating they are mainly amorphous.Some minor peaks in these samples correspond to the small amount of a-Mg(BH 4 ) 2 impurity in c-Mg(BH 4 ) 2 .Raman measurements (Figure 1c) demonstrate that apparent N-H vibration signals can be found at 3178, 3270, and 3346 cm À1 for Mg (BH 4 ) 2 ÁxNH 3 , implying that all N atoms are in the NH 3 group.In addition, B-H bonds can be detected in the wavenumber range of 2000-2600 cm À1 for all samples.The B-H vibration signal is different for each sample and their characteristic peaks fit well with the previous works, indicating a successful preparation of single phase Mg(BH 4 ) 2 ÁxNH 3 (x = 1, 2, 3). [32,33]igure 1d presents the transmission electron microscope (TEM) results of a representative Mg(BH 4 ) 2 Á2NH 3 sample, in which irregular particles with a diameter of 200 nm can be observed in the image and broad and vague rings can be detected in the selected area electron diffraction pattern, further confirming that the as prepared Mg(BH 4 ) 2 Á2NH 3 is composed of amorphous submicron particles.It should be noted that low dose and short time electron beam irradiation should be used to avoid the melting of Mg(BH 4 ) 2 Á2NH 3 .
The thermal stability of Mg(BH 4 ) 2 ÁxNH 3 (x = 1, 2, 3) and reference samples are evaluated using differential scanning calorimetry (DSC, Figure 1e).Endothermic peaks at above 182 °C can be found for c-Mg(BH 4 ) 2 , corresponding to the c to b phase transformation and dehydrogenation. [34]For Mg(BH 4 ) 2 Á6NH 3 , complex heat flows are detected at above 172 °C, corresponding to the successive NH 3 and H 2 desorption. [35]The endothermic peaks at 92 °C and 100 °C (starts at above 85 °C, Figure S1, Supporting Information) are the melting of Mg(BH 4 ) 2 ÁNH 3 and Mg (BH 4 ) 2 Á2NH 3 , respectively, and the following exothermic signals reflect the dehydrogenation. [26]Moreover, Mg(BH 4 ) 2 Á3NH 3 successively releases NH 3 , melts and desorbs H 2 in the temperature range of 120-250 °C. [35]The apparent differences in melting temperature and enthalpy change further confirm the occurrence of NH 3 redistribution reaction.
The above results reveal that amorphous Mg(BH 4 ) 2 ÁxNH 3 (x = 1, 2, 3), that is am-Mg(BH 4 ) 2 ÁxNH 3 , can be successfully prepared by highenergy ball milling c-Mg(BH 4 ) 2 and Mg(BH 4 ) 2 Á6NH 3 with certain ratios and they can maintain physically and chemically stable at below 85 °C.It should be noted here that this amorphization is closely related to the unique microporous structure of c-Mg(BH 4 ) 2 , [36] which is liable to adsorb molecules and collapse into amorphous phase in only several hours (Figure S2, Supporting Information), and Mg(BH 4 ) 2 ÁxNH 3 prepared via a same procedure using b-Mg(BH 4 ) 2 is crystalline, not amorphous (Figure S3, Supporting Information).
The Mg-ion conduction properties of am-Mg(BH 4 ) 2 ÁxNH 3 (x = 1, 2, 3) and reference samples are measured in terms of conductivities and transference numbers.The conductivity of the electrolyte is calculated from the electrochemical impedance spectroscopy (EIS) of blocking cells (Figure S4, Supporting Information).Figure 2a shows the temperature-dependent conductivities of am-Mg(BH 4 ) 2 ÁxNH 3 (x = 1, 2, 3), in which am-Mg(BH 4 ) 2 ÁxNH 3 (x = 1, 2, 3) all exhibit much higher conductivities in the temperature range of 35-85 °C than those of c-Mg(BH 4 ) 2 and Mg(BH 4 ) 2 Á6NH 3 .Among them, am-Mg (BH 4 ) 2 Á2NH 3 shows the highest conductivity, as 1 9 10 À7 S cm À1 at 35 °C and 5 9 10 À4 S cm À1 at 75 °C can be achieved, which are already acceptable for all-solid-state Mg battery cycling.It is noteworthy that the conductivity of am-Mg(BH 4 ) 2 ÁNH 3 is only slightly lower than that of am-Mg(BH 4 ) 2 Á2NH 3 , so the following investigations are mainly focused on these two samples.The activation energies of Mg-ion migration (E a ) for am-Mg(BH 4 ) 2 Á2NH 3 and am-Mg(BH 4 ) 2 ÁNH 3 are calculated to be 1.99 and 2.15 eV, respectively (Figure S5, Supporting Information).
Direct current (DC) polarization and EIS tests are then performed on blocking cells and Mg symmetric cells at 75 °C to show the transference numbers of am-Mg(BH 4 ) 2 ÁxNH 3 (x = 1, 2). Figure 2b presents that the electronic conductivity is 3 9 10 À9 S cm À1 for am-Mg (BH 4 ) 2 Á2NH 3 , corresponding to an electronic transference number of close to 0. In addition, the Mg-ion transference number is calculated to be 0.95 according to the currents and resistances (Figure 2c) at the initial and steady polarization states of Mg symmetric cells, suggesting that it is a single Mg-ion conductor.As for am-Mg(BH 4 ) 2 ÁNH 3 , the transference numbers are similar (Figure S6, Supporting Information).
Based on the above results, we know that am-Mg(BH 4 ) 2 Á2NH 3 exhibits much improved conductivities with high Mg-ion transference numbers, which is a very promising solid electrolyte candidate for solid-state Mg batteries.
To elucidate the mechanism of fast Mg-ion conduction in am-Mg (BH 4 ) 2 Á2NH 3 , density functional theory (DFT) calculations are carried out with c-Mg(BH 4 ) 2 and am-Mg(BH 4 ) 2 ÁNH 3 as reference samples.Crystal Mg(BH 4 ) 2 Á2NH 3 exhibits a space group of orthorhombic Pcab with unit cell parameters of a = 17.482A, b = 9.4132 A, c = 8.7304A and Z = 8, which is built by layered packing of pseudo tetrahedral Mg(BH 4 ) 2 Á2NH 3 molecules. [37]t is known that Mg-ion conduction can be achieved by vacancy migration and/or interstitial migration.We therefore paid special attention to the calculations on the point defects.The Mg vacancy formation energy (E vf ) for Mg(BH 4 ) 2 Á2NH 3 is calculated to be 1.92 eV, which is lower than the Mg interstitial formation energy (2.21 eV).We thus believe that the Mg vacancy migration is the main contributor to the Mg-ion conduction in Mg(BH 4 ) 2 Á2NH 3 .Similar results can also be obtained for c-Mg(BH 4 ) 2 and Mg(BH 4 ) 2 ÁNH 3 (Table S1, Supporting Information).
As shown in Figure 3a-c, the optimized Mg vacancy migration paths to equivalent sites along different axes involve zigzag routes through intermediate sites.For the migration along a, b and c axes, 3, 1, and 1 intermediate site is needed, and the energy barriers for migration (E vm ) are 1.02, 0.96, and 0.83 eV, respectively (Figure 3d).As a comparison (Figure 3e), c-Mg(BH 4 ) 2 , and Mg(BH 4 ) 2 ÁNH 3 possess higher energy barriers for Mg vacancy migration (respectively 1.32 and 0.91 eV, Figure S7).It should be noted that am-Mg(BH 4 ) 2 Á2NH 3 and am-Mg(BH 4 ) 2 ÁNH 3 are amorphous (shortrange ordered but long-range disordered) in this work, which have similar but distinct Mg-ion conduction behaviors to crystalline counterparts that are investigated by DFT calculations.It has been reported that the amorphization can generally lead to the decrease in E vf and E vm . [38,39]Here, we confirm this by both experiments and calculations.Theoretically, E a equals to the sum of E vf and E vm . [40]owever, E a of am-Mg(BH 4 ) 2 Á2NH 3 and am-Mg(BH 4 ) 2 ÁNH 3 (1.99 and 2.15 eV) are smaller than calculated values (2.75 and 2.58 eV), which is one evidence for the decrease in E vf and E vm by amorphization.In addition, we recrystallize am-Mg(BH 4 ) 2 Á2NH 3 by heat treatment under different temperatures and measure their Mg-ion conduction properties (Figures S8 and S9, Supporting Information).The conductivity decreases and E a increases after recrystallization, which can further prove the effect of amorphization on E vf and E vm .The above results show that the apparently reduced E vf and E vm by amorphization are mainly responsible for the super Mg-ion conduction in am-Mg(BH 4 ) 2 Á2NH 3 .
Electrochemical stability is another key parameter that determines the overall performances of electrolytes.Figure 4a presents the cyclic voltammetry (CV) curves of Mg|am-Mg(BH 4 ) 2 Á2NH 3 |Mo cell at 75 °C in the potential range of À0.2 to 1.4 V (vs Mg 2+ /Mg), in which only symmetric current peaks (more than 90 lA) near 0 V is observed, corresponding to the Mg plating and stripping on the Mo electrode (Figure S10, Supporting Information).This result indicates that the apparent electrochemical stability window reaches 0-1.4 V.In addition, the result (Figure S11, Supporting Information) for am-Mg (BH 4 ) 2 ÁNH 3 shows that its electrochemical stability window is narrower, ranging in 0-1.3 V, agreeing well with reference. [26]o reveal the exact electrochemical behaviors of am-Mg (BH 4 ) 2 Á2NH 3 at limiting potentials, we repeatedly scan the Mg|am-Mg (BH 4 ) 2 Á2NH 3 |Mo cells from open circuit voltage to 0 and 1.4 V, respectively (Figure 4b,c).Small current signals (<4 lA) can be observed in the first scans when the potential is smaller than 0.6 V and larger than 0.9 V, and the current signals reduce significantly to close to 0 in the following scans, which suggest that 1) interphases, that is solid electrolyte interphase (SEI) and cathodic electrolyte interphase (CEI), are formed at the Mo/am-Mg(BH 4 ) 2 Á2NH 3 interface and 2) the interphases stabilize the interface by hindering further side reactions (Figure S12, Supporting Information). [41,42]he results for the cells with carbon additives (Figure S13, Supporting Information) also support this conclusion.
In addition, EIS measurements (Figure 4d) before and after scanning are performed to evaluate the resistances of the SEI and CEI.The fresh Mg|am-Mg(BH 4 ) 2 Á2NH 3 |Mo cell has only a SEI at the Mg/electrolyte interface, and its resistance is 1338 Ω.After scanning, the newly formed SEI and CEI at the cathode/electrolyte interface lead to resistance increases, as the chord lengths of the semicircles reach 2575 and 1910 Ω, respectively, indicating that the SEI and CEI possess lower (compared with that of am-Mg (BH 4 ) 2 Á2NH 3 ) but still acceptable Mg-ion conductivity.The above results reveal that am-Mg (BH 4 ) 2 Á2NH 3 possesses an apparent electrochemical stability window of 0-1.4 V with the help of protective in-situ formed SEI and CEI.][22][23][24][25][26][27][28] The cycling stability of am-Mg(BH 4 ) 2 Á2NH 3based Mg symmetric cells is then assessed to identify its long-term compatibility to Mg anode at 75 °C.As shown in Figure 5a, the Mg symmetric cell cycling at 0.05 mA cm À2 (14.13 lA) shows a flat over potential of 20-30 mV in the initial 250 h, and gradually becomes higher after 250 h, indicating a thickening of SEI.For the Mg symmetric cell cycling at 0.1 mA cm À2 (28.26 lA), the galvanostatic charge/discharge (GCD) curve is similar, but the over potential is higher (30-50 mV).No short circuit is found after more than 600 h cycling, suggesting that no apparent Mg dendrite forms during cycling at low current densities (Figure S14, Supporting Information).
Furthermore, after increasing the current density to 1 mA cm À2 , the Mg symmetric cell encounters short circuit after 140 h (Figure S15, Supporting Information).This implies that Mg dendrites can nucleate and grow when the cycling current is enough high, which agrees with literatures. [43]To determine the critical current density for dendrite growth, we test the Mg symmetric cell at increasing current densities (0.1 mA cm À2 increasement per cycle).As seen in Figure 5b, the over potential rises with current density and short circuit occurs at 3.3 mA cm À2 , corresponding to a critical current density of 3.2 mA cm À2 for am-Mg(BH 4 ) 2 Á2NH 3 .This value is higher than those for liquid electrolytes, confirming the effective suppression of Mg dendrites by solid electrolytes with higher shear modulus.TiS 2 is selected as the cathode material of am-Mg(BH 4 ) 2 Á2NH 3 based all-solid-state Mg cells by taking the electrochemical stability Energy Environ.Mater.2024, 7, e12527 into consideration. [44]Figure 6a shows the GCD curves of Mg|am-Mg(BH 4 ) 2 Á2NH 3 |TiS 2 cell in the voltage range of 0.2-1.4V at 0.05 C (1 C = 250 mA g À1 ) and 75 °C.Three plateaus can be observed in the discharge and charge profiles, corresponding to the typical stepwise Mg-ion insertion into and extraction from the cathode.The initial reversible specific capacity is 141 mAh g À1 with a coulombic efficiency of 91.7%, already comparable with that of liquid electrolyte-based cells.This high coulombic efficiency can be attributed to the controllable irreversible Mg-ion insertion/extraction and formation of protective interphases.In the following cycles, the specific capacity decreases with the coulombic efficiency further increases.The cycling performance of Mg|am-Mg(BH 4 ) 2 Á2NH 3 |TiS 2 cell at 0.05 C and 75 °C is shown in Figure 6b.The reversible specific capacity fades from 141 to 70 mAh g À1 quickly in the initial 10 cycles, and then maintains at above 50 mAh g À1 in the following 15 cycles with coulombic efficiencies of close to 100%.The capacity decay may be ascribed to the structural degradation of the cathode, [45] and we will further improve the cycling stability by rational design of electrodes in future works.
Figure 6c shows the EIS spectra of Mg|am-Mg(BH 4 ) 2 Á2NH 3 |TiS 2 cell before and after cycling, which can be well fitted using equivalent circuit and parameters shown in Table S3, Supporting Information.The interphase resistance increases from 1843 to 3457 Ω after the first cycle and then slightly increases to 4032 Ω after the following nine cycles, indicating that interphase forms in the first cycle and prevents the further degradation of the electrode/electrolyte interface. [46]Figure 6d shows the GCD curves of am-Mg(BH 4 ) 2 Á2NH 3 based Mg||TiS 2 cell at 0.05, 0.2, 0.5 C, and 75 °C.The voltage hysteresis increases with current density, resulting in an apparent reduction in reversible specific capacity.The above results prove that the high conductivity and excellent electrochemical stability of Mg(BH 4 ) 2 Á2NH 3 can enable the cycling of all-solid-state Mg||TiS 2 cells at 75 °C.

Conclusion
In conclusion, am-Mg(BH 4 ) 2 ÁxNH 3 (x = 1, 2, 3) are successfully prepared by high-energy ball milling of c-Mg(BH 4 ) 2 and Mg(BH 4 ) 2 Á6NH 3 .Among them, am-Mg(BH 4 ) 2 Á2NH 3 is found to exhibit the best Mg-ion conduction properties, as a high conductivity of 5 9 10 À4 S cm À1 at 75 °C with a Mg-ion transference number of 0.95 can be obtained.DFT calculations reveal that Mg vacancy migration is the main contributor to the Mg-ion conduction, and the migration energy barriers for Mg(BH 4 ) 2 Á2NH 3 are lower than those of c-Mg(BH 4 ) 2 and Mg(BH 4 ) 2 ÁNH 3 .The apparent electrochemical stability window of am-Mg(BH 4 ) 2 Á2NH 3 reaches 0-1.4 V with the help of protective and conductive SEI and CEI.The Mg symmetrical cells based on am-Mg(BH 4 ) 2 Á2NH 3 can cycled at 0.05 mA cm À2 for 710 h, and the critical current density is 3.2 mA cm À2 .Moreover, am-Mg(BH 4 ) 2 Á2NH 3 enables the cycling of all-solid-state Mg||TiS 2 cells, which shows a reversible specific capacity

Experimental Section
Preparation of materials: Mg(BH 4 ) 2 (c phase, 95%; Sigma-Aldrich) and NH 3 (99.9%;Sinopharm) was used as received without further purification.Mg (BH 4 ) 2 Á6NH 3 was synthesized by heating Mg(BH 4 ) 2 under 6 bar NH 3 at 105 °C for 12 h.Mg(BH 4 ) 2 ÁxNH 3 (x = 1, 2 and 3) samples were prepared by high-energy ball milling the mixtures of Mg(BH 4 ) 2 and Mg(BH 4 ) 2 Á6NH 3 with molar ratios of 5:1, 2:1, and 1:1 at 500 rpm for 24 h, respectively (Nanda Instrument QM-3SP2 mill, ZrO 2 jar and ball, ball-to power ratio of 80:1).All sample handling is performed in a glovebox (MBRAUN 200B) with H 2 O and O 2 amount <0.1 ppm.Characterizations: X-ray diffraction measurements were performed on Rigaku Ultima IV at a scan rate of 5°min À1 using a sealed sample holder.Raman spectra were achieved by Bruker Optics Senterra R200-L with a laser wavelength of 532 nm using a sealed quartz holder.TEM observations were performed on JEOL JEM-2100HR.The sample was dispersed on a carbon-coated Cu grid after handgrinding and then transferred under Ar atmosphere.The phase transition was investigated by using DSC (Netzsch Polyma 214) from 50 °C to 350 °C with a scan rate 10 °C min À1 under Ar atmosphere.Measurements: All-solid-state cells were assembled using homemade Swagelok type dies, which can work under 100 MPa stack pressure (Figure S16, Supporting Information).The electrolyte pellets with a diameter of 10 mm and a thickness of 0.5 mm were made by pressing the target materials under 100 MPa (Figure S17, Supporting Information).For different measurements, different electrodes were used, that is Mo foil (ThermoFisher, 10 mm diameter), Mg foil (99.9%,Sinopharm, 6 mm diameter, 0.2 mm thickness, 5 mg), and TiS 2 -based cathode (10 mm diameter, 1 mg, 40 wt% TiS 2 , 99.9%, Sigma-Aldrich, 60 wt% am-Mg(BH 4 ) 2 Á2NH 3 ).
Electrochemical impedance spectroscopy, DC polarization, and CV were conducted on Gamry Interface 1000E.GCD measurements were performed using Arbin BT2000.The conductivities and activation energy were calculated from the EIS of Mo|elec-trolyte|Mo cells (Equations S1 and S2, Supporting Information).The electronic transference number was calculated according to the DC polarization of Mo|electrolyte|Mo cells at 1 V.The Mg-ion transference number was calculated according to the DC polarization of Mg|electrolyte|Mg cells at 10 mV and EIS before and after polarization (Equation S3, Supporting Information).First-principle calculations: Density functional theory calculations were implemented in the Vienna ab initio simulation package with the projector-augmented wave construction for the pseudopotential. [47,48]Exchange and correlation were treated in the generalized gradient approximation of Perdew-Burke-Ernzerhof. [49] The cutoff energy was set to 500 eV to attain sufficient accuracy.A 3 9 3 9 3 k point mesh and the k-point sampling scheme of Monkhorst-Pack were applied in all calculations.The convergence criterion of self-consistent total energy was <10 À5 eV per cell, and forces on each atom converged to be below 0.01 eV A À1 .The lattice volume and shape were allowed to change.The climbing-image nudged elastic band method was applied for the ion migration pathways, and all atoms were allowed to fully relax. [50]The vacancy formation energy and interstitial formation energy were calculated from the total energies of the simulation cell with and without vacancy and interstitial. [51]