Synthesis, Crystal Structure, and Ionic Conductivity of MgAl 2-x Ga x Cl 8 and MgGa 2 Cl 7 Br

: MgAl 2-x Ga x Cl 8 and MgGa 2 Cl 7 Br was synthesized from MgCl 2 , MgBr 2 , AlCl 3 , and GaCl 3 , and the physical properties were evaluated by XRD, AC conductivity, and X-ray ﬂuorescence. MgAl 2-x Ga x Cl 8 has the same crystal structure as MgAl 2 Cl 8 , belongs to the space group C2 / c, and forms a solid solution in all the synthesized compositions. We attempted to MgGa 2 Cl 8-y Br y synthesize in the same manner as MgAl 2 Cl 8 , but only obtained MgGa 2 Cl 7 Br as a single-phase compound. The AC conductivity of MgAl 2-x Ga x Cl 8 was lowest for MgAl 2 Cl 8 and highest for MgGa 2 Cl 8 . The conductivity of MgGa 2 Cl 8 at 400 K was 1.7 × 10 − 6 S / cm. The conductivity of MgGa 2 Cl 7 Br was higher than that of MgAl 2-x Ga x Cl 8 with a value of 1.6 × 10 − 5 S / cm at 400 K. The formation of Mg metal was observed at the surface of the cathode electrode in an experiment of ﬂowing a direct current using an electrochemical cell, indicating that this compound is a magnesium ion conductor. Author Contributions: Conceptualization, Y.T.; methodology, Y.T. and R.S.; validation, Y.T., and Y.Y.; formal analysis, R.S. and A.N.; investigation, Y.T.; data curation, Y.T., A.N. and Y.Y.; writing—original draft preparation, Y.T.; writing—review and editing, Y.T. and Y.K.; supervision, Y.T.; project administration, Y.T.


Introduction
Among commercially available secondary batteries, lithium-ion secondary batteries have excellent features such as high energy density and high cycle characteristics and are used as batteries for portable devices and electric vehicles [1,2]. In the future, the size and demand of batteries are expected to increase, and the safety and supply of lithium-based batteries are uncertain, so research of alternative secondary batteries is actively conducted. Magnesium ions are the charge carriers in Mg secondary batteries. Magnesium is more stable than alkali metal elements, abundant in nature, and expected to have a high capacity because of the two-electron reaction. Therefore, the Mg secondary batteries are expected as one of the post-lithium ion secondary batteries [3,4]. Acetonitrile and Grignard reagent have been reported as organic electrolytes of Mg secondary batteries, and magnesium metal formation and dissolution reactions on the working electrode have been observed using a magnesium metal sheet as a counter electrode [3,[5][6][7][8]. For magnesium ion conductive solid electrolytes, some oxides and sulfide-based glasses have been reported. Solid oxide electrolytes have low ionic conductivity, and MgHf(WO 4 ) 3 and (Mg 0.1 Hf 0.9 ) 4/3.8 Nb(PO 4 ) 3 have been reported to exhibit a conductivity of 2.5 × 10 −4 S/cm at 873 K and 2.1 × 10 −6 S/cm at 573 K, respectively [9,10]. Sulfide-based glass containing Mg 2+ ion synthesized in a manner similar as lithium-ion conductive glass exhibits magnesium ion conductivity [11]. Some synthesized Mg(BH 4 )-based compounds also show relatively high ionic conductivity (1.3 × 10 −5 S/cm at 303 K) [12,13]. Considering the increase in size of secondary batteries, The electrolyte salt of the abovementioned acetonitrile solution, MgAl 2 Br 8 , is the double salt of MgBr 2 , and the halide of group 13 elements, AlBr 3 , similar to MAlX 4 . So far, only MgAl 2 Cl 8 has been reported as the crystal structure of the compound of MgX 2 and AlX 3 , and its crystal structure is mainly similar to LiAlX 4 and NaAlX 4 [20]. Compared to Li + and Na + ions, Mg 2+ ion has a larger charge and becomes more difficult to diffuse, but the cation conduction is expected to be observable, similar to MAlX 4 . If Mg 2+ ion conductivity is exhibited in MgX 2 -M III X 3 (X = Cl, Br; M III = Al, Ga, etc.) compounds, they may function as solid electrolytes and be applied as electrolyte materials for all-solid-state Mg ion secondary batteries. We researched the synthesis of these compounds and the application as electrolyte materials for all-solid-state batteries. In this study, MgAl 2-x Ga x Cl 8 and MgGa 2 Cl 8-y Br y were synthesized, the crystal structure was analyzed, and the Mg 2+ ion conductivity was evaluated in order to investigate the potential of the Mg secondary battery as an electrolyte.

Materials and Methods
MgAl 2-x Ga x Cl 8 and MgGa 2 Cl 8-y Br y were synthesized from MgCl 2 , MgBr 2 , AlCl 3 , and GaCl 3 as starting materials. MgCl 2 and MgBr 2 were used after vacuum-drying at 473 K and 573 K, respectively, for 24-48 h. AlCl 3 and GaCl 3 were purified by sublimation. The purified raw materials were mixed in a stoichiometric ratio using a mortar and then sealed in a Pyrex glass test tube. The mixed samples were melted in electric furnace at 573 K for 24 h and gradually cooled to room temperature to obtain the target compounds. Since each raw material and the synthesized compound showed hygroscopic properties, all samples were handled in a dry Ar atmosphere using a glovebox. The obtained compounds were evaluated by XRD and X-ray fluorescence, and the diffraction data was analyzed by the Rietveld method [21]. The electrical characteristics of the samples were evaluated by electric conductivity. Powder X-ray diffraction patterns were recorded by a Rigaku Rad-B system with Cu-Kα radiation (40 kV, 40 mA). A handmade cell was used to protect the samples from moisture. The conductivity was determined by a complex impedance method, measured at 35 frequencies between 42 Hz and 5 MHz (3532-80 LCR high tester, HIOKI) in a dry argon atmosphere. The conductivity was measured using a stainless-steel electrode and Mg metal electrode. A two-electrode cell made of stainless-steel was used to measure the conductivity. The cell was sealed with O-ring and measured in an Ar atmosphere. The thickness of the sample was about 1 mm, the diameter was 10 mm, and the conductivity was measured while compressing the sample with a spring (about 20 kgf/cm 2 ). Figure 1 shows the XRD patterns of the synthesized MgAl 2-x Ga x Cl 8 and MgGa 2 Cl 7 Br. The XRD pattern of the MgAl 2 Cl 8 is in good agreement with that of the previous report [20]. The crystal system was monoclinic and the space group was C2/c (No. 15). Although a slight peak of the source material MgCl 2 was observed at 2θ = 15 • , no other starting material peaks were observed, indicating that the target compound was obtained. The change of the peak positions among the XRD pattern of MgAl 2-x Ga x Cl 8 was small, and there was some difference in the intensity ratio of the peaks. The overall patterns of MgAl 2-x Ga x Cl 8 were very similar, and their compounds were presumed to have the same crystal structure. MgGa 2 Cl 8-y Br y (y = 1 to 8) was synthesized but only MgGa 2 Cl 7 Br (y = 1) was obtained. For samples with y > 1, the large diffraction peaks of GaBr 3 were observed in the XRD measurement, and the peaks belonging to MgGa 2 Cl 8-y Br y were not observable or had low intensity. As shown in Figure 1, the diffraction peaks of MgGa 2 Cl 7 Br were shifted to lower angles compared with MgGa 2 Cl 8 , indicating that Cl − ion was partially substituted by Br − ion. On the other hand, even if Al 3+ ion was replaced with Ga 3+ ion as described above, there was almost no change in the angle of diffraction peaks. Comparing the volumes calculated using the lattice constants evaluated from the Rietveld analysis of the diffraction patterns, the volume change in MgAl 2-x Ga x Cl 8 was less than 0.4%. patterns of MgAl2-xGaxCl8 were very similar, and their compounds were presumed to have the same crystal structure. MgGa2Cl8-yBry (y = 1 to 8) was synthesized but only MgGa2Cl7Br (y = 1) was obtained. For samples with y > 1, the large diffraction peaks of GaBr3 were observed in the XRD measurement, and the peaks belonging to MgGa2Cl8-yBry were not observable or had low intensity. As shown in Figure 1, the diffraction peaks of MgGa2Cl7Br were shifted to lower angles compared with MgGa2Cl8, indicating that Cl − ion was partially substituted by Br − ion. On the other hand, even if Al 3+ ion was replaced with Ga 3+ ion as described above, there was almost no change in the angle of diffraction peaks. Comparing the volumes calculated using the lattice constants evaluated from the Rietveld analysis of the diffraction patterns, the volume change in MgAl2-xGaxCl8 was less than 0.4%.

XRD Patterns and Crystal Structure
The Al 3+ (Ga 3+ ) ion occupies a tetrahedral site, and according to Shannon, the ionic radius of Ga 3+ ion (0.47 Å) is 0.08 Å larger than that of Al 3+ ion (0.39 Å) [22]. However, the lattice volumes of MgAl2-xGaxCl8 reflect no difference in the size of their ions. The crystal structure of MgGa2Cl8 is shown in Figure 2 and the results of the structure analysis performed by the Rietveld method in MgAl2-xGaxCl8 are summarized in Table 1. In the Rietveld analysis results of all compounds, Rwp was below 9.5 and S(=Rwp/Re) was below 1.8(See Figure S1, table S1 and S2). Rwp and Re are reliability factors used for Rietveld refinement. The value of S is a scale indicating the reliability of the analysis.  Cl − ions occupy four types of sites crystallographically. The Mg 2+ ion is octahedrally coordinated by six halogen ions, and the Ga 3+ ion is tetrahedrally coordinated by four Cl − ions. Among the four halogen ions, three halogen ions at the sites labeled Cl2, Cl3, and Cl4 in Figure 2 bridge between the Mg 2+ and Ga 3+ ions. The remaining halogen ion labeled Cl1 is bound only to the Ga 3+ ion. Both the The Al 3+ (Ga 3+ ) ion occupies a tetrahedral site, and according to Shannon, the ionic radius of Ga 3+ ion (0.47 Å) is 0.08 Å larger than that of Al 3+ ion (0.39 Å) [22]. However, the lattice volumes of MgAl 2-x Ga x Cl 8 reflect no difference in the size of their ions. The crystal structure of MgGa 2 Cl 8 is shown in Figure 2 and the results of the structure analysis performed by the Rietveld method in MgAl 2-x Ga x Cl 8 are summarized in Table 1. In the Rietveld analysis results of all compounds, R wp was below 9.5 and S(=R wp /R e ) was below 1.8 (See Figure S1, Tables S1 and S2). R wp and R e are reliability factors used for Rietveld refinement. The value of S is a scale indicating the reliability of the analysis.
Cl − ions occupy four types of sites crystallographically. The Mg 2+ ion is octahedrally coordinated by six halogen ions, and the Ga 3+ ion is tetrahedrally coordinated by four Cl − ions. Among the four halogen ions, three halogen ions at the sites labeled Cl2, Cl3, and Cl4 in Figure 2 bridge between the Mg 2+ and Ga 3+ ions. The remaining halogen ion labeled Cl1 is bound only to the Ga 3+ ion. Both the bond lengths of Al (Ga) -Cl and Mg-Cl increased as the amount of Ga 3+ ion increased in MgAl 2-x Ga x Cl 8 as shown in Table 1. Although the change in lattice volume due to the substitution was small, it is considered that the bond length changes depending on the arrangement of cations and anions. In addition, the bond length of Al (Ga) -Cl increased as expected because the ionic radius of the central cation increased in the substitution from Al to Ga. It is interesting that the bond length of Mg-Cl also increased accordingly. As shown in Table 1, β approached 90 • gradually due to the Ga substitution. Although the expansion of the lattice was small, it is considered that the lattice distortion was reduced by increasing the size of the MCl 4 − anion. Rietveld analysis was also performed on MgGa 2 Cl 7 Br.
The occupancy of Cl − and Br − at each of the halogen sites were refined in the analysis. The total Energies 2020, 13, 6687 4 of 9 occupancy of each site was limited to 1, and the ratio of the total amount of each of Cl − and Br − was limited to 7:1 to be equal to the composition ratio of Cl − and Br − . In MgGa 2 Cl 7 Br, the lattice constant increased and the bond length of Mg-X (X = Cl − or Br − ) increased due to the partial substitution from Cl − to Br − . The change in Mg-X bond length due to partial substitution of Cl − was similar to the change due to substitution of all Al 3+ to Ga 3+ in MgAl 2 Cl 8 , indicating that the effects of both on Mg-X bond length were similar. In MgGa 2 Cl 7 Br, no large deviation was confirmed in the occupancy of Cl − and Br − at the Cl1, Cl2, and Cl4 site, and the occupancy of Br − at the Cl3 site was slightly higher than that of the other sites (See Table S3).
considered that the bond length changes depending on the arrangement of cations and anions. In addition, the bond length of Al (Ga) -Cl increased as expected because the ionic radius of the central cation increased in the substitution from Al to Ga. It is interesting that the bond length of Mg-Cl also increased accordingly. As shown in Table 1, β approached 90° gradually due to the Ga substitution. Although the expansion of the lattice was small, it is considered that the lattice distortion was reduced by increasing the size of the MCl4 − anion. Rietveld analysis was also performed on MgGa2Cl7Br. The occupancy of Cl − and Br − at each of the halogen sites were refined in the analysis. The total occupancy of each site was limited to 1, and the ratio of the total amount of each of Cl − and Br − was limited to 7:1 to be equal to the composition ratio of Cl − and Br − . In MgGa2Cl7Br, the lattice constant increased and the bond length of Mg-X (X = Cl − or Br − ) increased due to the partial substitution from Cl − to Br − . The change in Mg-X bond length due to partial substitution of Cl − was similar to the change due to substitution of all Al 3+ to Ga 3+ in MgAl2Cl8, indicating that the effects of both on Mg-X bond length were similar. In MgGa2Cl7Br, no large deviation was confirmed in the occupancy of Cl − and Br − at the Cl1, Cl2, and Cl4 site, and the occupancy of Br − at the Cl3 site was slightly higher than that of the other sites (See Table S3).

AC Conductivity
The temperature dependence of AC conductivity of MgAl2-xGaxCl8 (x = 0, 0.5, 1, 1.5, 2) and MgGa2Cl7Br. MgAl2Cl8 (x = 0) had the lowest conductivity of the synthesized compounds, approximately 10 −7 S/cm even above 400 K. The conductivity increased with the substitution of the Al 3+ ion to Ga 3+ ion. In MgAl2-xGaxCl8, the highest conductivity was observed at MgGa2Cl8 with a value of 1.7 × 10 −6 S/cm at 400 K. In all compositions, the conductivity σ changed monotonously with respect to the reciprocal of temperature. The activation energy, Ea, for the conduction was evaluated by the following equation:

AC Conductivity
The temperature dependence of AC conductivity of MgAl 2-x Ga x Cl 8 (x = 0, 0.5, 1, 1.5, 2) and MgGa 2 Cl 7 Br. MgAl 2 Cl 8 (x = 0) had the lowest conductivity of the synthesized compounds, approximately 10 −7 S/cm even above 400 K. The conductivity increased with the substitution of the Al 3+ ion to Ga 3+ ion. In MgAl 2-x Ga x Cl 8 , the highest conductivity was observed at MgGa 2 Cl 8 with a value of 1.7 × 10 −6 S/cm at 400 K. In all compositions, the conductivity σ changed monotonously with Energies 2020, 13, 6687 5 of 9 respect to the reciprocal of temperature. The activation energy, E a , for the conduction was evaluated by the following equation: where σ and A are the conductivity and the pre-exponential parameter, respectively [23]. The values of E a of MgAl 2-x Ga x Cl 8 were 126, 75.4, 67.6, 69.1, and 59.1 kJ/mol at x = 0, 0.5, 1, 1.5, and 2, respectively (See Figure S2). MgGa 2 Cl 8 had the lowest E a of MgAl 2-x Ga x Cl 8 , indicating that Li-ion conduction becomes easier in this compound. In the XRD measurement, the Mg-Cl bond length of MgAl 2-x Ga x Cl 8 increased with increasing x, suggesting that the diffusion of Mg 2+ ion also becomes easier with the amount of substitution with Ga 3+ . Therefore, it is considered that the E a of MgGa 2 Cl 8 was the smallest among MgAl 2-x Ga x Cl 8 in the conductivity measurement. The conductivity of MgGa 2 Cl 7 Br was 1.6 × 10 −5 S/cm, which was about an order of magnitude higher than that of MgGa 2 Cl 8 as shown in Figure 3. Its E a was 47.7 kJ/mol, which was also lower than MgGa 2 Cl 8 , and it was found that the diffusion of Mg ions became easier. It is considered that longer Mg-X distance due to the partial substitution of Cl − ion improved the Mg 2+ ion conductivity.
Energies 2020, 13, x FOR PEER REVIEW 5 of 9 σT = A exp (-Ea/RT), where σ and A are the conductivity and the pre-exponential parameter, respectively [23]. The values of Ea of MgAl2-xGaxCl8 were 126, 75.4, 67.6, 69.1, and 59.1 kJ/mol at x = 0, 0.5, 1, 1.5, and 2, respectively (See Figure S2). MgGa2Cl8 had the lowest Ea of MgAl2-xGaxCl8, indicating that Li-ion conduction becomes easier in this compound. In the XRD measurement, the Mg-Cl bond length of MgAl2-xGaxCl8 increased with increasing x, suggesting that the diffusion of Mg 2+ ion also becomes easier with the amount of substitution with Ga 3+ . Therefore, it is considered that the Ea of MgGa2Cl8 was the smallest among MgAl2-xGaxCl8 in the conductivity measurement. The conductivity of MgGa2Cl7Br was 1.6 × 10 −5 S/cm, which was about an order of magnitude higher than that of MgGa2Cl8 as shown in Figure  3. Its Ea was 47.7 kJ/mol, which was also lower than MgGa2Cl8, and it was found that the diffusion of Mg ions became easier. It is considered that longer Mg-X distance due to the partial substitution of Cl − ion improved the Mg 2+ ion conductivity. The Nyquist plots of MgGa2Cl7Br at 400 K, obtained using cells with different working electrodes, are shown in Figure 4. When a stainless-steel sheet was used as the working electrode, one arc was observed as shown in Figure 4a. On the other hand, when the working electrode was Mg sheet, another arc appeared on the low-frequency side as shown in Figure 4b, in addition to the arc on the high-frequency side observed in the cell with the stainless working electrode. This arc appeared due to the charge transfer resistance with the Mg electrode, suggesting that MgGa2Cl7Br is an Mg 2+ ion conductor. The new arc shown in Figure 4b was slightly smaller than the arc on the highfrequency side, and the charge transfer resistance was confirmed not to be much different from the bulk resistance.
The activation energy of conductivity in MgGa2Cl7Br was lower than the reported activation energy of Mg 2+ ion conductors at 63.9 kJ/mol of (Mg0.1Hf0.9)4/3.8Nb(PO4)3, 92.0 kJ/mol of Mg0.7(Zr0.85Nb0.15)4(PO4)6, and 80.6kJ/mol of MgHf(WO4)3, indicating that the diffusion of Mg ions is easier [9,10,24]. Higher electric conductivity was obtained at a lower temperature in MgGa2Cl7Br compared with those of the previous compounds, such as 2.1 × 10 −6 S/cm (573 K) of The Nyquist plots of MgGa 2 Cl 7 Br at 400 K, obtained using cells with different working electrodes, are shown in Figure 4. When a stainless-steel sheet was used as the working electrode, one arc was observed as shown in Figure 4a. On the other hand, when the working electrode was Mg sheet, another arc appeared on the low-frequency side as shown in Figure 4b, in addition to the arc on the high-frequency side observed in the cell with the stainless working electrode. This arc appeared due to the charge transfer resistance with the Mg electrode, suggesting that MgGa 2 Cl 7 Br is an Mg 2+ ion conductor. The new arc shown in Figure 4b was slightly smaller than the arc on the high-frequency side, and the charge transfer resistance was confirmed not to be much different from the bulk resistance. Energies 2020, 13, x FOR PEER REVIEW 6 of 9 (Mg0.1Hf0.9)4/3.8Nb(PO4)3, 1.1 × 10 −7 S/cm of Mg0.7(Zr0.85Nb0.15)4(PO4)6, and 2 × 10 −6 S/cm (573 K; extrapolated) of MgHf(WO4)3, indicating that MgGa2Cl7Br is a good Mg 2+ ion conductor.

X-ray Fluorescence
The results of fluorescent X-ray analysis on the surface of the working electrode when a constant current was applied to the fabricated cell are shown in Figure 5. The measured cell was composed of a Ni metal sheet as the working electrode and an Mg metal sheet as the counter electrode, and MgGa2Cl7Br was used as the electrolyte. The spectrum of Figure 5a is that of the working electrode before the current was passed, and the spectrum of Figure 5b is that of the electrode after the current of −50 μA was applied for 36 h. The spectrum of Figure 5c shows the results of the working electrode after a current of −50 μA was applied for 36 h and a current of +50 μA was applied for 36 h. A large peak attributed to Mg Kα was observed in Figure 5b, clarifying that Mg was precipitated on the working electrode. In the spectrum of Figure 5c, after applying the positive current, the peak of Mg in Figure 5b became small, and it was found that the Mg deposited by negative current on the working electrode was consumed in the oxidation reaction. Considering the applied electric quantity, the Mg peak must disappear in Figure 5(c), but the peak was observed, indicating that the current was consumed by other reactions. When a negative current was applied the cell, Mg was precipitated by a reduction reaction on the working electrode, and when a positive current was applied, Mg on the working electrode was oxidized. Therefore, it could be reconfirmed that MgGa2Cl7Br is an Mg ion conductor. The activation energy of conductivity in MgGa 2 Cl 7 Br was lower than the reported activation energy of Mg 2+ ion conductors at 63.9 kJ/mol of (Mg 0.1 Hf 0.9 ) 4/3.8 Nb(PO 4 ) 3 , 92.0 kJ/mol of Mg 0.7 (Zr 0.85 Nb 0.15 ) 4 (PO 4 ) 6 , and 80.6kJ/mol of MgHf(WO 4 ) 3 , indicating that the diffusion of Mg ions is easier [9,10,24]. Higher electric conductivity was obtained at a lower temperature in MgGa 2 Cl 7 Br compared with those of the previous compounds, such as 2.1 × 10 −6 S/cm (573 K) of (Mg 0.1 Hf 0.9 ) 4/3.8 Nb(PO 4 ) 3 , 1.1 × 10 −7 S/cm of Mg 0.7 (Zr 0.85 Nb 0.15 ) 4 (PO 4 ) 6 , and 2 × 10 −6 S/cm (573 K; extrapolated) of MgHf(WO 4 ) 3 , indicating that MgGa 2 Cl 7 Br is a good Mg 2+ ion conductor.

X-ray Fluorescence
The results of fluorescent X-ray analysis on the surface of the working electrode when a constant current was applied to the fabricated cell are shown in Figure 5. The measured cell was composed of a Ni metal sheet as the working electrode and an Mg metal sheet as the counter electrode, and MgGa 2 Cl 7 Br was used as the electrolyte. The spectrum of Figure 5a is that of the working electrode before the current was passed, and the spectrum of Figure 5b is that of the electrode after the current of −50 µA was applied for 36 h. The spectrum of Figure 5c shows the results of the working electrode after a current of −50 µA was applied for 36 h and a current of +50 µA was applied for 36 h. A large peak attributed to Mg K α was observed in Figure 5b, clarifying that Mg was precipitated on the working electrode. In the spectrum of Figure 5c, after applying the positive current, the peak of Mg in Figure 5b became small, and it was found that the Mg deposited by negative current on the working electrode was consumed in the oxidation reaction. Considering the applied electric quantity, the Mg peak must disappear in Figure 5c, but the peak was observed, indicating that the current was consumed by other Energies 2020, 13, 6687 7 of 9 reactions. When a negative current was applied the cell, Mg was precipitated by a reduction reaction on the working electrode, and when a positive current was applied, Mg on the working electrode was oxidized. Therefore, it could be reconfirmed that MgGa 2 Cl 7 Br is an Mg ion conductor.

Conclusions
We attempted to synthesize MgAl2-xGaxCl8 and MgGa2Cl8-yBry and obtained MgAl2-xGaxCl8 (x = 0 to 2) and MgGa2Cl7Br. Their crystal system was monoclinic and the space group was C2/c (No. 15). In XRD measurement of MgAl2-xGaxCl8, as the amount of Ga increased, the diffraction peaks did not shift significantly but the Mg-Cl bond length increased. The lattice constant and volume increased with the partial substitution of Cl with Br between MgGa2Cl8 and MgGa2Cl7Br. The Mg-X bond length also increased with substitution. Rietveld analysis clarified that four kinds of halogen sites in the MgGa2Cl7Br crystal were occupied by both a Br − ion and Cl − ion. There was a site with a relatively high Br − occupancy, but no particular ordering was observed. MgGa2Cl7Br showed the highest conductivity, which was 1.6 × 10 −5 S/cm at 400 K in the measurement of AC conductivity. The behavior of the Nyquist plots and the results of fluorescent X-ray analysis, observed in the cell using Mg as the electrode, suggest that these compounds are magnesium ion conductors. The conductivity value of MgGa2Cl7Br was high as an Mg ion conductor but was slightly insufficient for use as a solid electrolyte in Mg secondary batteries. With this conductivity value, there is concern that voltage drop and energy loss will occur when MgAl2Cl7Br is used as the electrolyte for solid-state batteries and a further increase in conductivity is required. In this study, it was shown that the anion substitution effect can improve Mg 2+ ion conductivity. Further studies are expected to improve the ion conductivity.
Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1, Figure S1: Result of Rietveld analysis of XRD pattern of MgGa2Cl8. The red dotted line, the black line, and the blue line are the observed XRD patterns, the calculated values, and the differences between the observed and the calculated value, respectively. The marks indicate the position of the XRD peaks, Figure S2: Plots of σT against 1/T of MgAl2-xGaxCl8 and MgGa2Cl7Br. The activation energy of the conductivity was evaluated from the linear part over a wide temperature range including the median of the plot of each compound, Table S1: Results of the Rietveld analysis of XRD data for MgAl2-xGaxCl8,

Conclusions
We attempted to synthesize MgAl 2-x Ga x Cl 8 and MgGa 2 Cl 8-y Br y and obtained MgAl 2-x Ga x Cl 8 (x = 0 to 2) and MgGa 2 Cl 7 Br. Their crystal system was monoclinic and the space group was C2/c (No. 15). In XRD measurement of MgAl 2-x Ga x Cl 8 , as the amount of Ga increased, the diffraction peaks did not shift significantly but the Mg-Cl bond length increased. The lattice constant and volume increased with the partial substitution of Cl with Br between MgGa 2 Cl 8 and MgGa 2 Cl 7 Br. The Mg-X bond length also increased with substitution. Rietveld analysis clarified that four kinds of halogen sites in the MgGa 2 Cl 7 Br crystal were occupied by both a Br − ion and Cl − ion. There was a site with a relatively high Br − occupancy, but no particular ordering was observed. MgGa 2 Cl 7 Br showed the highest conductivity, which was 1.6 × 10 −5 S/cm at 400 K in the measurement of AC conductivity. The behavior of the Nyquist plots and the results of fluorescent X-ray analysis, observed in the cell using Mg as the electrode, suggest that these compounds are magnesium ion conductors. The conductivity value of MgGa 2 Cl 7 Br was high as an Mg ion conductor but was slightly insufficient for use as a solid electrolyte in Mg secondary batteries. With this conductivity value, there is concern that voltage drop and energy loss will occur when MgAl 2 Cl 7 Br is used as the electrolyte for solid-state batteries and a further increase in conductivity is required. In this study, it was shown that the anion substitution effect can improve Mg 2+ ion conductivity. Further studies are expected to improve the ion conductivity.
Supplementary Materials: The following are available online at http://www.mdpi.com/1996-1073/13/24/6687/s1, Figure S1: Result of Rietveld analysis of XRD pattern of MgGa 2 Cl 8 . The red dotted line, the black line, and the blue line are the observed XRD patterns, the calculated values, and the differences between the observed and the calculated value, respectively. The marks indicate the position of the XRD peaks, Figure S2: Plots of σT against 1/T of MgAl 2-x Ga x Cl 8 and MgGa 2 Cl 7 Br. The activation energy of the conductivity was evaluated from the linear part over a wide temperature range including the median of the plot of each compound, Table S1: Results of the Rietveld analysis of XRD data for MgAl 2-x Ga x Cl 8 ,