Fast fluoride ion conduction of NH4(Mg1-xLix)F3-x and (NH4)2(Mg1-xLix)F4-x assisted by molecular cations

Aiming development of the fast anion conductors, we proposed a new material design using flexible molecular cation as a host cation, and demonstrated it with fluoride ion conduction in NH4MgF3 and (NH4)2MgF4 based materials. Dominant fluoride ion conduction with relatively high conductivities of 4.8 × 10–5 S cm−1 and 8.4 × 10–6 S cm−1 were achieved at 323 K in (NH4)2(Mg0.85Li0.15)F3.85 and NH4(Mg0.9Li0.1)F2.9, respectively. It is implied that the molecular cation in the host lattice can assist the anion conduction. Our findings suggest molecular cation-containing compounds can be attractive material groups for fast anion conductors.

Developing high energy density batteries are an urgent issue for establishing environmentally-friendly and sustainable society. All-solid-state fluoride ion batteries (ASSFIBs) are one of promising batteries because of their potential of high energy density [1][2][3][4] . The energy density of ASSFIBs is theoretically expected to reach 5000 Wh L −1 . However, state-of-the-art ASSFIBs still have many problems, for instance, the gap between theoretical and practical discharge/charge capacities, the poor cycling performance, the high operating temperature, the insufficient operating voltage, and so on 5,6 . One major reason for such poor performances of the present ASSFIBs is the lack of suitable solid electrolytes having high ionic conductivity and thermochemical stability. PbSnF 4 shows the highest ionic conductivity, 1.6 × 10 -3 S cm −1 at room temperature, among already-known solid-state fluoride ion conductors. However, this material is unstable under the high operating voltage due to the narrow potential window.
There are several strategies for development of solid electrolytes. One is the use of highly disordered structure advantageous for high ionic conduction. Another is the introduction of the mobile ionic defects (such as vacancies or interstitial ions) by doping aliovalent ions. Among fluoride ion conductors, PbSnF 4 , RbSnF 3 , and β-PbF 2 are the materials developed based on the former strategy [7][8][9][10] . On the other hand, the tysonite-type La 1-x Ba x F 3-x and Sm 1-x Ca x F 3-x and the fluorite-type Sn 1-x K x F 2-x and Ba 1-x La x F 2+x are the materials based on the latter one [11][12][13][14] . Although various fluoride ion conductors are previously reported 15,16 , further material explorations for sufficiently high fluoride ion conductivity are required to realize ASSFIBs.
Excellent cation conduction has been reported in some materials containing molecular anions such as PO 4 [17][18][19][20] . High cation conductivity in these materials is considered to be caused by unique size, structure, and dynamics of molecular ions, resulting in extension of the bottleneck for ion conduction, reduction of the interaction between the host and carrier ions, and assistance of the ion conduction by the rotation of the molecular ions 21  www.nature.com/scientificreports/ examined. It is therefore interesting to systematically investigate the potential of materials containing molecular cations as fast anion conductors. In this study, perovskite and layered perovskite fluorides containing NH 4 + as a molecular cation, NH 4 MgF 3 and (NH 4 ) 2 MgF 4 , are selected as targets of materials 23 . NH 4 (Mg 1-x Li x )F 3-x and (NH 4 ) 2 (Mg 1-x Li x )F 4-x were prepared with the intention of introducing fluoride ion vacancies by the substitution of Li + for Mg 2+ , and their electrical conduction properties were studied. In comparison, the conductivities of perovskite and layered perovskite containing K + as the A-site cation, K(Mg 0.9 Li 0.1 )F 2.9 and K 2 (Mg 0.9 Li 0.1 )F 3.9 , were examined. Since the ionic radius of K + (1.64 Å) is similar to the effective radius of NH 4 + (1.46 Å) 24 , the influence of the molecular ions on the ionic conductivity can be discussed. NH 4 (Mg 1-x Li x )F 3-x and (NH 4 ) 2 (Mg 1-x Li x )F 4-x were synthesized by solid state reaction methods. The obtained powders and pressed samples were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM) observation, electron probe micro analyzer (EPMA), and nuclear magnetic resonance (NMR) spectroscopy. The thermal stabilities of NH 4 MgF 3 and (NH 4 ) 2 MgF 4 were examined by thermogravimetry (TG). The electrical conductivities of the pellets were measured by AC electrochemical impedance spectroscopy (EIS). To confirm the dominant fluoride ion conduction, AC EIS and DC polarization measurements were performed with the fluoride ion conducting cell. In order to cross-check the dominant fluoride ion conduction, electromotive force (emf) measurements of the fluorine concentration cell, : metal fluoride), were performed. Details are given in the supplementary information. Figure 1a,b show the XRD patterns of (a) NH 4

Results
The most of XRD peaks could be indexed with the cubic (Pm 3 m) symmetry for NH 4 (Mg 1-x Li x )F 3-x and the tetragonal symmetry (I4/mmm) for (NH 4 ) 2 (Mg 1-x Li x )F 4-x . In NH 4 (Mg 1-x Li x )F 3-x , the diffraction peaks of the cubic phase gradually shifted to lower angle with increasing the Li content. This indicated that larger Li + (0.76 Å) was substituted into the smaller Mg 2+ (0.72 Å) sites. The lattice parameters of NH 4 (Mg 1-x Li x )F 3-x and (NH 4 ) 2 (Mg 1-x Li x )F 4-x were calculated from the diffraction angles and were plotted in Fig. 1c,d as a function of the Li content. Except for the c-axis of (NH 4 ) 2 (Mg 1-x Li x )F 4-x , the lattice parameters changed monotonically with the Li content in NH 4 (Mg 1-x Li x )F 3-x and (NH 4 ) 2 (Mg 1-x Li x )F 4-x phases, suggesting that solid solution is formed at least within the compositional range of 0 < x < 0.3 in NH 4 (Mg 1-x Li x )F 3-x and 0 < x < 0.2 in (NH 4 ) 2 (Mg 1-x Li x )F 4-x and the solubility limit of Li is higher than 30 mol% in NH 4 (Mg 1-x Li x )F 3-x and 20 mol% in (NH 4 ) 2 (Mg 1-x Li x )F 4-x . Small diffraction peaks of NH 4 NO 3 could be found in some compositions, especially in NH 4 (Mg 0.8 Li 0.2 )F 2.8 . In order to investigate the state and location of the impurity, the SEM observation and EPMA analysis were carried out. The results for NH 4 (Mg 0.8 Li 0.2 ) F 2.8 were presented in Figs. S1. The impurity, possibly NH 4 NO 3 , was observed as indicated by the yellow circles in Fig. S1. However, since the impurity particles seemed to exist sparsely from the main compound and their amount was not significant, the influences of the impurity on the observed ionic conductivities were supposed as negligibly small.
The SEM images of the cross sections of the pressed samples of NH 4 (Mg 0.8 Li 0.2 )F 2.8 and (NH 4 ) 2 (Mg 0.85 Li 0.15 ) F 3.85 were shown in Fig. S2. The pellets seemed dense as just pressed, and the relative densities of all the pellets were approximately 75%. Figure S3 Figure 2 show Nyquist plots observed with (a) NH 4 (Mg 1-x Li x )F 3-x and (b) (NH 4 ) 2 (Mg 1-x Li x )F 4-x at 323 K. Although the results are not given in Fig. 2, only scattered signals were observed in EIS measurements with nondoped NH 4 MgF 3 , indicating its extremely low electrical conductivity. On the other hand, the Li-doped samples showed typical impedance responses of an ionic conductor with blocking electrodes, e.g. a semicircle in the high frequency region and a sharp spike in the low frequency region. These impedance behaviours suggested ionic conductivity in these samples. The total resistance of the sample including the bulk and grain boundary resistances was determined from the semicircle in high frequency region. Figure 3 shows temperature dependences of the electrical conductivities of NH 4 (Mg 1-x Li x )F 3-x and (NH 4 ) 2 (Mg 1-x Li x )F 4-x . The conductivities were enhanced by Li-doping, but they showed the maximum and decreased with further increasing the Li content. At 323 K, the maximum conductivity was observed at x = 0.1 for NH 4 (Mg 1-x Li x )F 3-x (8.4 × 10 -6 S cm −1 ) and at x = 0.15 for (NH 4 ) 2 (Mg 1-x Li x )F 4-x (4.8 × 10 -5 S cm −1 ). The decrease in electrical conductivity in highly doped samples is considered to be caused by cluster formation or ordering of fluoride ions and vacancies, and etc. 25,26 . The fact that the conductivities showed the maximum at a certain Li concentration also indicated that the presence of the impurities did not affect the conductivity enhancement of NH 4 (Mg 1-x Li x )F 3-x and (NH 4 ) 2 (Mg 1-x Li x )F 4-x , because the amount of the impurities monotonically increased with increasing the Li concentration.
In order to confirm dominant fluoride ion conduction in the investigated materials, we prepared a block-  In the case of the layered perovskite structure, interstitial anions sometimes can be mobile, as interstitial oxygens in Ln 2 NiO 4+d (Ln = rare earth) 30 . Based on this idea, the introduction of interstitial fluoride ions was tried for the layered perovskite (NH 4 ) 2 MgF 4 by partially substituting trivalent cation Sc 3+ for Mg 2+ . However, as shown in Fig. S6, this trial was not effective for improving the ionic conductivity of (NH 4 ) 2 MgF 4 .
In order to demonstrate the influence of the molecular cations on the anionic conductivity, K(Mg 0.9 Li 0.1 )F 2.9 having the same crystal structures was prepared. The lattice constant of K(Mg 0.9 Li 0.1 )F 2.9 was 3.989 Å which was comparable with NH 4 (Mg 0.9 Li 0.1 )F 2.9 , 4.072 Å. The electrical conductivities of K(Mg 0.9 Li 0.1 )F 2.9 and K 2 (Mg 0.9 Li 0.1 ) F 3.9 were considerably low, 5.2 × 10 -6 S cm −1 at 789 K and 7.3 × 10 -5 S cm −1 at 717 K, respectively (Fig. S7). This demonstrated that NH 4 + in the host lattice can assist the fluoride ion conduction. At this moment, the reason for the conductivity enhancement by the substitution of K + for NH 4+ is not clear. One likely hypothesis is that the rotational motion of NH 4 + assists the fluoride ion conduction. Figure 5 presents 1 H NMR spectra of NH 4 (Mg 0.8 Li 0.2 )F 2.8 and (NH 4 ) 2 (Mg 0.8 Li 0.2 )F 3.8 at various temperatures. A peak was observed at 9 ppm for both NH 4 (Mg 0.8 Li 0.2 )F 2.8 and (NH 4 ) 2 (Mg 0.8 Li 0.2 )F 3.8 . This peak gradually narrowed as temperature increased. As already  www.nature.com/scientificreports/ discussed, the dominant charge carrier in both of NH 4 (Mg 0.8 Li 0.2 )F 2.8 and (NH 4 ) 2 (Mg 0.8 Li 0.2 )F 3.8 is confirmed to be fluoride ion, meaning the conduction of NH 4 + or proton is negligible. Thus, the narrowing of the 1 H NMR peak seen in Fig. 5 is considered due to the rotational or reorientational motions of NH 4 + . Actually, in (NH 4 ) 2 MgF 4 , the rotational motion of NH 4 + was suggested in literature 31 . The rotation of NH 4 + can induce extension of the bottleneck for anion conduction, reduction of the interaction between the host and carrier ions, or assistance of anion hopping, as happened in cation conductors containing molecular anions 17,32 . Such influences by the molecular cation might enhance the fluoride ion conduction in NH 4 MgF 3 and (NH 4 ) 2 MgF 4 based materials.
In this work, we succeeded to achieve relatively high fluoride ion conductivity in compounds containing molecular cations, NH 4 (Mg 1-x Li x )F 3-x and (NH 4 ) 2 (Mg 1-x Li x )F 4-x , by introducing fluoride ion vacancies. It was suggested that the molecular cation in the host lattice might assist anion conduction. The findings of this works suggested that compounds containing molecular cations can be new host materials for fast anion conductors.

Conclusion
NH 4 (Mg 1-x Li x )F 3-x and (NH 4 ) 2 (Mg 1-x Li x )F 4-x were found to exhibit relatively high fluoride ion conductivities of 8.4 × 10 -6 (x = 0.1) and 4.8 × 10 -5 (x = 0.15) S cm −1 at 323 K, respectively. The major conduction carrier was identified as fluoride ion. This work demonstrated that compounds containing molecular cations, like hybrid organic-inorganic perovskites, can be a promising material group for noble anion-conducting materials.    Figure S8 shows the products obtained with different molar ratios of NH 4 MgF 3 . When the mixing ratio was 1:7, the single phase of the perovskite NH 4 MgF 3 was obtained, while impurities including MgF 2 were observed with the mixing ratios below 1 : 6, suggesting the lack of NH 4 + . Considering these results, raw material powders were mixed with a molar ratio of Mg : Li : F = (1-x) : x : 7. The mixture was calcined at 453 K for NH 4 (Mg 1-x Li x )F 3-x and 433 K for (NH 4 ) 2 (Mg 1-x Li x )F 4-x for 2-8 h under Ar gas flow. In order to remove remaining NH 4 F, the mixtures were additionally calcined at 433 K for NH 4 (Mg 1-x Li x )F 3-x and 413 K for (NH 4 ) 2 (Mg 1-x Li x )F 4-x for 1-5 h.
Electrical conductivity measurements. The obtained NH 4 (Mg 1-x Li x )F 3-x and (NH 4 ) 2 (Mg 1-x Li x )F 4-x powders were pelletized at 200 MPa by a cold isostatic pressing method. Au thin film electrodes were sputtered on the both sides of the dense pellets. Electrical conductivities were evaluated from AC electrochemical impedance spectroscopy (EIS) at 303-343 K in N 2 gas with 30-50 mV of amplitude with frequency of 4.0 × 10 7 to 1 Hz by using the impedance analyzer (Alpha-A, Novocontrol Technologies GmbH & Co. KG, Germany).
The powders of K(Mg 0.9 Li 0.1 )F 2.9 and K 2 (Mg 0.9 Li 0.1 )F 3.9 were pelletized at 200 MPa by a uniaxial pressure, and sintered at 1073 or 873 K for 10 h. Electrical conductivities of K(Mg 0.9 Li 0.1 )F 2.9 and K 2 (Mg 0.9 Li 0.1 )F 3.9 were evaluated from AC EIS at room temperature − 788 K in Ar atmosphere by using a potentiostat (VersaSTAT, Princeton Applied Research, USA).
To confirm the dominant fluoride ion conduction, DC polarization measurements were performed by using the blocking cell consisting of Pb/PbSnF 4 /sample/PbSnF 4 /Pb at room temperature − 423 K under vacuum. Schematic illustration of the blocking cell was given in Fig. S9. The current for DC polarization measurements was 10 or 20 mA.