Comparing Proton Conduction in Potassium and Ammonium Borosulfate—Isostructural Inorganic Polyelectrolytes Exhibiting High Proton Mobility

A scalable new method for the synthesis of borosulfate compounds in sulfuric acid providing control over product crystallite size is reported as an alternative to traditional methods requiring slow growth from oleum. This new synthetic approach is used to prepare three isostructural, 1D borosulfates: one containing only ammonium cations, another containing only potassium cations, and the third sample with a solid solution of 1:1 ammonium–potassium. Proton conduction in polycrystalline pellets of these borosulfate electrolytes is compared by electrochemical impedance spectroscopy (EIS) and ab initio molecular dynamics (AIMD) simulations. For a given cation (e.g., NH4 +), conductivity decreases by three orders of magnitude with decreasing particle size while maintaining constant activation energy, indicating that proton conduction is not primarily a grain‐boundary process. AIMD simulations show that excess proton mobility in K[B(SO4)2] is in line with that of NH4[B(SO4)2], being a backbone (not cation) mediated process. Although K[B(SO4)2] exhibits higher activation energy (60.6 ± 2.0 kJ mol−1) than NH4[B(SO4)2] (33.8 ± 1.0 kJ mol−1), at 200 °C it achieves comparable conductivity to NH4[B(SO4)2] samples, which is attributable to hydrolytic B–O–H defects being the common source of mobile protons in these materials.


Introduction
Hydrogen fuel cells have characteristic temperatures of operation dictated by the properties of the electrolyte material around which the fuel cell is designed. Polymer electrolyte membrane fuel cells (PEMFCs) operate at comparatively low temperatures (≤100°C) due to relying upon liquid water for proton (H þ ) conduction, while solid oxide fuel cells (SOFCs) are limited to high-temperature operation (500-1000°C) due to poor oxide anion (O 2À ) conduction in ceramic oxide electrolytes at lower temperatures. [1] Accessing an intermediate temperature regime (100-400°C) is challenging, as H þ conduction in a dry (i.e., waterless) electrolyte is difficult and O 2À conduction in ceramics has a high activation energy barrier. However, the ability to run a hydrogen fuel cell in this intermediate temperature range is technologically attractive as it has the potential to simplify (or eliminate) water management subsystems (a bulky component of PEMFCs) while still allowing for the use of standard engineering materials in cell construction (whereas SOFCs rely on ceramics and high-temperature sealants). [1] Achieving operation at 100-400°C relies upon an electrolyte exhibiting high ionic conductivity (H þ or O 2À ) and good thermo-oxidative and mechanical stability at these temperatures under fuel cell operating conditions. Solid acids were demonstrated to be effective proton conductors in this temperature range over 20 years ago and were subsequently proposed for use as fuel cell electrolytes. [2][3][4] Since then, the Haile group and others have continued to advance solid acid fuel cell (SAFC) technology. [5][6][7][8][9][10][11][12][13] Of the solid acid electrolytes reported over the past two decades, CsH 2 PO 4 has emerged as the material of choice for highperformance SAFCs. While CsH 2 PO 4 is functional, it possesses characteristics that complicate its use as an electrolyte. One such characteristic, intrinsic to many solid acids, is that good H þ conduction occurs only above a "superprotonic transition," which for most compounds occurs at an elevated temperature where the hydrogen bonding network in the crystal structure is broken and the protic species (e.g., HSO 4 À , H 2 PO 4 À ) becomes rotationally disordered, allowing proton exchange between neighboring units. [2][3][4][5] In the case of CsH 2 PO 4 , its superprotonic transition occurs at %225°C, where the effective proton conductivity improves by three orders of magnitude in the span of just a few degrees. In practice, this means that below the superprotonic transition temperature, a fuel cell utilizing this electrolyte cannot function effectively. Another complicating characteristic of DOI: 10.1002/aesr.202200029 A scalable new method for the synthesis of borosulfate compounds in sulfuric acid providing control over product crystallite size is reported as an alternative to traditional methods requiring slow growth from oleum. This new synthetic approach is used to prepare three isostructural, 1D borosulfates: one containing only ammonium cations, another containing only potassium cations, and the third sample with a solid solution of 1:1 ammonium-potassium. Proton conduction in polycrystalline pellets of these borosulfate electrolytes is compared by electrochemical impedance spectroscopy (EIS) and ab initio molecular dynamics (AIMD) simulations. For a given cation (e.g., NH 4 þ ), conductivity decreases by three orders of magnitude with decreasing particle size while maintaining constant activation energy, indicating that proton conduction is not primarily a grain-boundary process. AIMD simulations show that excess proton mobility in K[B(SO 4  CsH 2 PO 4 is, like many phosphate materials, its tendency to decompose by dehydration in the absence of water. [14] The combination of high superprotonic transition temperature and tendency to dehydrate above 200°C means that CsH 2 PO 4 requires active humidification in a narrow operational temperature window (%225-245°C). Therefore, it presents engineering challenges that, although possible to overcome, make SAFCs utilizing a CsH 2 PO 4 electrolyte more complicated and costly. Significant gains in SAFC performance may be possible with the discovery of electrolyte materials that exhibit effective proton conduction in a wider temperature range with good stability regardless of the presence of water. Recently, we identified ammonium borosulfate (NH 4 [B(SO 4 ) 2 ], Figure 1) as a promising new solid acid proton-conducting polyelectrolyte displaying characteristics that improve some of the properties of CsH 2 PO 4 . [15] We originally identified the potential for NH 4 [15] Determining the origin of mobile H þ concentration in these materials, and whether conduction is predominantly a bulk or a grain-boundary-mediated process, is generally challenging due to the difficulty of controlling for the many variables involved. In this study, we report a new synthetic approach to prepare NH 4  . The originally reported borosulfates were synthesized utilizing 60% oleum (i.e., fuming sulfuric acid) as the solvent, which poses significant challenges in handling. [16] Our new synthetic approach utilizes common reagents (e.g., sulfuric acid, boric acid, sulfate salts) and readily available equipment (e.g., glassware, Schlenk lines, etc.) to prepare these materials safely, on a multi-gram scale, and with access to a range of crystallite sizes. Synthesizing NH 4 [B(SO 4 ) 2 ] of varying crystallite size, its aprotic analog K[B(SO 4 ) 2 ], and a 1:1 solid solution of the two borosulfates (K 0.5 (NH 4 ) 0.5 [B(SO 4 ) 2 ]), we compare the behavior of these materials to identify a common mechanism of proton transport therein. In the process, we find that NH 4 [B(SO 4 ) 2 ] is only one of a family of 1D borosulfate compounds that exhibit excellent proton mobility, expanding the possible set of borosulfate proton-conducting electrolytes available for developing electrochemical devices that operate at intermediate temperatures.

Synthesis and Crystallite Size
This method of synthesizing 1D borosulfates (e.g.,    (1) In the absence of another cation, protons serve to charge balance the borosulfate chains. In this form, products remain soluble in sulfuric acid as a viscous solution. When a suitable source of alternative cations, such as K 2 SO 4 , is added to the reaction mixture, H 2 SO 4 -insoluble products with higher lattice energy, such as K[B(SO 4 ) 2 ], precipitate from the reaction mixture. In this manner, this method of synthesizing borosulfates relies upon the solubility of starting materials and insolubility of products in the concentrated H 2 SO 4 solvent, as well as the ability to remove water formed over the course of the reaction to drive the reaction toward completion.
Viewing the synthesis of borosulfates in terms of Equation (1) also leads us to another innovation: since the reaction is driven in part by precipitation of a poorly soluble, polymeric product, crystallite size can be controlled by changing reaction conditions to affect nucleation and growth. The slow (1-3 day), evaporative process used in the oleum-based synthesis of NH 4 [B(SO 4 ) 2 ] yields millimeters to centimeters long needles, [16] while transitioning to forced, rapid (3-16 h) dehydration with mechanical stirring yielded sub-mm length crystallites (product 1a, see Figure S1, Supporting Information, for optical images) that are more amenable to powder processing. Nucleation can be made even more rapid (and crystallites even smaller) by choosing a cation source that exhibits sparing solubility in H 2 SO 4 , and therefore causing concerted nucleation only once a critical concentration of cation is reached in solution. We found that ammonium sulfamate (NH 4 SO 3 NH 2 ) worked well in this capacity, causing rapid precipitation of NH 4 [B(SO 4 ) 2 ] as a fluffy, white powder (product 1b, see Figure S2, Supporting Information, for optical images) after the dissolution of a critical amount of sulfamate. These three methods of preparing the same material (NH 4 [B(SO 4 ) 2 ]) to give chemically and structurally identical products, as confirmed by IR spectroscopy and powder X-Ray diffraction (PXRD), provided a suitable subset of materials to investigate how grain boundaries affect the conductivity of sintered borosulfate pellets.

Grain Boundary Effects on Conduction
The source of "free" protons in NH 4 [B(SO 4 ) 2 ] was a major unresolved question from the original discovery of proton conductivity in this material. [15] From AIMD simulations, it was determined that excess protons coordinated to the borosulfate chain are exceptionally mobile, while those on NH 4 þ are unlikely to be dissociated as the source of mobile protons; the activation energy found computationally for dissociation of NH 4 þ (%83 kJ mol À1 ) is much higher than the activation energy for conduction measured by impedance spectroscopy (EIS, %35 kJ mol À1 ). [15] This leaves two likely scenarios: 1) charge carriers arise primarily from defects at grain boundaries; or 2) charge carriers originate from defects within the crystal lattice. We postulated that protic defects are likely to be the result of hydrolysis, as depicted schematically in Figure 2. The formation of these defects may be considered the inverse of the dehydration process used to synthesize NH 4 [B(SO 4 ) 2 ]. Due to the ladder structure of the borosulfate chain, single hydrolytic point defects should not destabilize the backbone, although they may interfere with crystallinity.
Sintered pellets of NH 4 [B(SO 4 ) 2 ] were prepared by pressing 100-200 mg of 1a (larger crystallites) or 1b (smaller crystallites) at %240 MPa in a 12.7 mm diameter tungsten carbide die in a Carver press with platens heated to 100°C for 16 h. The resulting pellets were opaque but were measured to be at %95% of the crystal density of NH 4 [B(SO 4 ) 2 ] (2.337 g cm À3 ) and thus relatively well-consolidated. These pellets were subsequently mounted in an aluminum test fixture (illustrated in Figure S10, Supporting Information) between spring-loaded, porous, Au sputter-coated, stainless steel electrodes and heated to 200°C for %16 h under a low flow of dry air to ensure samples were equilibrated prior to performing EIS. Impedance spectra were collected on cooling from 200°C to room temperature under dry airflow over the course of %8 h, from which conductivity was calculated by fitting the data to a modified Randles circuit ( Figure S11, Supporting Information) and dividing the cell constant (κ ¼ thickness/1.228 cm 2 ) by the extracted electrolyte resistance (R) at each temperature. The results are plotted in Figure 3 (full Bode plots in Figure S12 [1a] and S13 [1b], Supporting Information) alongside prior results from a pellet made of large (mm-sized) NH 4 [B(SO 4 ) 2 ] crystallites synthesized by the originally reported synthesis in oleum. [15] If defects are localized primarily at grain boundaries, where access to atmospheric moisture is greatest and the lattice is unconstrained, pellets pressed from materials with smaller crystallites should contain more protic defects and thus exhibit higher conductivity. Instead, conductivity was observed to decrease with decreasing crystallite size, dropping by several orders of magnitude from the largest (several mm length) to smallest (%10 μm length) crystallites. This is excellent evidence that the protic defects providing mobile proton concentration cannot be primarily a grain boundary phenomenon. If either proton transport is primarily grain-boundary-mediated or proton concentration results primarily from grain boundary defects (as in many metal oxides), any increase in the area of grain  To explain the significant decrease in conductivity with decreasing crystallite size, we postulate that the transport of protons across grain boundaries must be the limiting process, thus materials prepared from larger crystallites should exhibit, on average, less interfacial resistance. An important implication of this result is that good sintering is critical to maximizing conductivity in these materials. Prior AIMD simulations on NH 4 [B(SO 4 ) 2 ] showed that H þ transport should occur along all axes of the crystallographic structure, so as long as grainto-grain contact is good, the relative orientation of crystalline facets should not be a major concern.

Role of the Cation in Proton Transport
Knowing that conduction in NH 4 [B(SO 4 ) 2 ] is not a grainboundary-mediated process, our next goal was to determine if the ammonium cation form is unique in promoting proton conduction in borosulfates. Although comparing prior AIMD results with the experimental activation energy for conduction in NH 4 [B(SO 4 ) 2 ] (E a % 34 kJ mol À1 ) showed that dissociation of the NH 4 þ cation (E a % 83 kJ mol À1 ) is unlikely to take part in the generation of charge carriers, the hydrogen bonding of NH 4 þ to the borosulfate chain could still be critical to facilitating proton conduction. To test this, we performed AIMD simulations on NH 4 [B(SO 4 ) 2 ] and the isostructural, aprotic borosulfate K[B(SO 4 ) 2 ] to assess proton mobility in both these structures.
Compared to the AIMD simulations presented in our prior work [15] , the simulation box in this study was enlarged to 8 unit cells (2 Â 2 Â 2) containing a total of 32 cations (NH 4 þ or K þ ).
One to four (1-4) excess protons were added to each super-cell, along with a homogeneous negative background to maintain charge neutrality. By using a variable number of excess protons, it is possible to determine whether results are being affected by Coulombic interactions between nearby protons in the simulation volume. As previously observed in similar calculations for NH 4 4 units such that the distance between two oxygen atoms sufficiently decreases so as to allow a low energy site-to-site hop. In our calculations, hops occur when the O…O distance is <2.5 Å and when the proton rotates around its current "host" atom to reside as close as possible to the next oxygen atom. The change in mean square displacements (msd) of atoms over time can be used to approximate diffusivity (units of m 2 s À1 ) over long times. Tracking msd of the excess protons from their initial, energy minimized positions over 20 ps at 900 K ( Figure 4) shows that the diffusivity of excess protons should be comparable in K[B(SO 4 ) 2 ] to NH 4 [B(SO 4 ) 2 ]. It is useful to compare calculated proton diffusivities (D H þ ) in borosulfates to other proton conductors, such as water, for example. Linear regressions (not shown) to the data in Figure 4 give D H þ at 900 K from which diffusivities at lower temperatures can be calculated per Equation (2), assuming that conduction is an Arrhenius process over the 900 K to 300 K (23°C) interval. Temperature ( C) Figure 3. Conductivity versus inverse temperature plotted for sintered pellets prepared from NH 4 [B(SO 4 ) 2 ] with large crystallites (Oleum synthesis, [15] red circles), intermediate crystallites (1a, blue diamonds), and small crystallites (1b, green squares). Arrhenius fits (colored lines) and the activation energies calculated from these fits are also shown. www.advancedsciencenews.com www.advenergysustres.com From the data in Figure 4, we calculate D H þ at 900 K to be (1.3 AE 0.5) Â 10 À8 m 2 s À1 in NH 4 [B(SO 4 ) 2 ] and (1.6 AE 0.6) Â 10 À8 m 2 s À1 in K[B(SO 4 ) 2 ]. The activation energy for proton hopping in K[B(SO 4 ) 2 ] is unknown, but for NH 4 [B(SO 4 ) 2 ] this value was previously determined by simulations to be %12.5 kJ mol À1 . [15] Therefore, at 25°C in NH 4 [B(SO 4 ) 2 ] (assuming Arrhenius behavior), D H þ % (4.6 AE 1.8) Â 10 À10 m 2 s À1 , which is only one order of magnitude lower than the diffusivity of a proton in water at 25°C (D H þ ¼ 9.8 Â 10 À9 m 2 s À1 ), despite ammonium borosulfate being a crystalline solid! [17] Additionally, protons appear to not interact with each other significantly at these concentrations (0.03-0.12 per formula unit), as msds appear to be independent of proton concentration.
To test whether proton conduction analogous to that exhibited by NH 4 Figure S3, Supporting Information) synthesized using K 2 SO 4 as the potassium source are of comparable size to the smaller NH 4 [B(SO 4 ) 2 ] crystallites (1b, Figure S2, Supporting Information) prepared using the poorly soluble NH 4 SO 3 NH 2 ammonium source. In light of the crystallite size-dependent conductivities illustrated in Figure 3, this makes 1b and 2 well-matched for a direct comparison of proton conductivities between NH 4 [B(SO 4 ) 2 ] versus K[B(SO 4 ) 2 ] ( Figure 5).
The most readily apparent result of comparing conduction in polycrystalline NH 4 2 ] could arise from either a difference in the ease of transport across grain boundaries or from differences in backbone motion resulting from hydrogen bonding (or lack thereof ) to the cation.
We subsequently tested whether this trend holds in mixedcation borosulfates by synthesizing K 0.5 (NH 4 ) 0.5 [B(SO 4 ) 2 ] (3) using a 1:1 mixture of K 2 SO 4 and (NH 4 ) 2 SO 4 as starting materials. The resulting crystallite sizes (see Figure S4, Supporting Information) are in line with both 1b and 2, and PXRD on (see Figure S9, Supporting Information) shows that the product is a solid solution of the two cations, not a mixture of independent NH 4 [B(SO 4 ) 2 ] and K[B(SO 4 ) 2 ] crystallites. Interestingly, the temperature-dependent conductivity of the mixed cation borosulfate is not an average (in either magnitude or activation energy) of the mono-cationic borosulfates. The conductivity of 3 is a factor of 3-4 higher than pure NH 4 [B(SO 4 ) 2 ] with an activation energy (E a ¼ 28.9 AE 0.8 kJ mol À1 ) slightly lower than the pure compound ( Figure 5). Although definitive conclusions cannot be drawn from these data, we believe this is likely due to the mixed compound sintering better than the single cation compounds.

Evidence for Bulk Hydrolytic Defects as the Source of "Free" H þ
We had previously hypothesized that hydrolytic defects (see Figure 2) are the source of the "free" protons that contribute to ionic conduction in borosulfates. [15] As shown by the comparable degrees of conduction measured in NH 4 [B(SO 4 ) 2 ] and K[B(SO 4 ) 2 ] ( Figure 5), this hypothesis remains in line with these experimental results. Such protic defects are unlikely to be confined to surfaces or grain boundaries, as crystallite sizedependent measurements of conductivity ( Figure 3) show decreasing conductivity with increasing surface area of crystallites. Unfortunately, many analytical techniques are limited in their ability to resolve the excess protons resulting from partial hydrolysis, especially at low levels of doping. Direct measurement with X-Ray analytical techniques, while useful for heavier elements, is essentially impossible for hydrogen. Further, the local chemical environments of sulfur and boron are unlikely to be very different between hydrolyzed borosulfate chains and perfect crystals to be resolvable by these methods. However, the IR spectra of ammonium and potassium borosulfate ( Figure 6) do provide critical insight due to the sensitivity of vibrational spectroscopies to the large dipole moment and highly polarizable O─H bond.
As shown in Figure 6, the IR spectra of ammonium (1b) and potassium (2) borosulfate below 1500 cm À1 are almost identical. Above 1500 cm À1 , the only major feature is a peak at 3200-3300 cm À1 that was initially attributed to N-H stretching in NH 4 þ , but clearly must be originating from another species in K[B(SO 4 ) 2 ]. These peaks are present even after samples have   O-H). The acidity of a hydroxyl group and its hydrogen bonding environment affects its stretching frequency quite significantly, [18] however, the frequencies of a prototypical sulfate O-H stretch (3500 cm À1 ) [19] and borate O-H stretch (3200 cm À1 ) [20] are quite far apart. Since the peak in K[B(SO 4 ) 2 ] is so close to the O-H stretch in boric acid, we attribute this stretching mode (in both ammonium and potassium samples) to hydrolytic B-O-H point defects in the crystal lattice, and not to a residual sulfate hydroxyl group. In NH 4 [B(SO 4 ) 2 ], hydrogen bonding with the ammonium cations causes these peaks to overlap and show up closer to 3300 cm À1 with a stronger relative absorbance. The lack of hydroxyl stretching modes corresponding to residual sulfates has caused us to revise our hypothesis of the structure of hydrolytic defects in 1D borosulfates. While the initial steps of hydrolysis probably proceed according to Figure 2, the dangling borosulfate is likely susceptible to either further cleavage by water (and loss of H 2 SO 4 ) or to irreversible loss of gaseous SO 3 , resulting in a structure with two dangling, proximal B-O-H units, illustrated in Figure 7. Based on the observed evidence, these acidic borate units are the most likely a source of mobile protons for conduction without significantly disrupting the overall structure and crystallinity of the borosulfate.

Summary and Conclusions
We present a new, general method of borosulfate synthesis that uses sulfuric acid, rather than oleum, and is, therefore, less hazardous and more amendable to scale-up than syntheses previously reported in the literature. This method provides the means to not only produce a variety of borosulfate salts but also control the product crystallite size. In turn, this has afforded us the materials necessary to elucidate the roles of grain boundaries and hydrolytic defects on proton conduction in 1D borosulfates, which at this point we believe to be a general characteristic of this structural family of compounds.
The ionic conductivity previously observed in NH 4 [B(SO 4 ) 2 ] is demonstrated to also be present in another isostructural 1D borosulfate, K[B(SO 4 ) 2 ], confirming that this phenomenon is not tied to the protic nature of the NH 4 þ cation in ammonium borosulfate, but instead is enabled by the movement of the 1D borosulfate chain, and therefore is likely to be present in other similar compounds. The activation energies for the Arrhenius conduction process (over 50-200°C) vary significantly between the pure ammonium and potassium compounds, increasing from 33.1 AE 1.5 kJ mol À1 for NH 4 þ to 60.6 AE 2.0 kJ mol À1 for K þ . Increased activation energy for conduction in K[B(SO 4 ) 2 ] is likely the result of either differing ease of transport at the grain boundaries or differences in backbone mobility due to hydrogen bonding to the interstitial cations. Further investigations into these phenomena are certainly warranted.
Infrared spectra strongly suggest that B-OH hydrolytic defects in the backbone generate "free" acidic protons enabling proton conductivity in these materials regardless of the identity of the cation. AIMD simulations show high proton mobility for free protons in both NH 4 [B(SO 4 ) 2 ] and K[B(SO 4 ) 2 ], with diffusivity for NH 4 [B(SO 4 ) 2 ] at room temperature of only 1 order of magnitude lower than that of H þ in water. Crystallite size-dependent conductivity studies show that these defects are likely distributed not at grain boundaries, but rather throughout the bulk of the crystallites. In fact, the conductivity of sintered polycrystalline pellets decreases with decreasing powder crystallite size, indicating that grain boundary conduction is likely to be the limiting process in these materials. It is our conclusion that future work focused on the improvement of the performance of borosulfate materials as proton-conducting electrolytes should focus on minimizing the interfacial resistance of these grain-to-grain contacts.

Experimental Section
All reagents were purchased from Fisher Scientific and used as received. Procedures were performed in air, but products were stored in sealed vials under inert (N 2 ) atmosphere to prevent absorption of moisture over time.  . Revised hypothesized structure of hydrolytic defects giving rise to "free" protons in 1D borosulfates. Hydroxyl groups in red should have a stretching mode at %3500 cm À1 , whereas groups in blue should have a stretching mode at %3200 cm À1 .
www.advancedsciencenews.com www.advenergysustres.com General Method: Boric acid was dissolved as a 5-15 wt% solution in concentrated (98%) H 2 SO 4 , to which an approximately equimolar amount of sulfate salt (e.g., (NH 4 ) 2 SO 4 , K 2 SO 4 ) was added. The reaction mixture was attached to a distillation apparatus in which a desiccant (e.g., concentrated H 2 SO 4 ) was added to the receiving flask to aid the removal of water. The reaction mixture was heated to 150-200°C under a dynamic vacuum for several hours, after which the product typically precipitates as a slurry of white solid. The solids were then suction filtered from the sulfuric acid mother liquor/filtrate on a fritted glass funnel, washed with a polar organic solvent (e.g., isopropanol, sulfolane), and dried in vacuo to isolate the borosulfate product.   SO 4 , and a magnetic stir bar were added. The flask was attached to an air-cooled distillation head and a receiving flask containing 50 mL concentrated H 2 SO 4 acting as a desiccant. Dynamic vacuum (%0.15 mmHg) was applied to the system, the reaction vessel was immersed in an oil bath, and the reaction was heated to 200°C with magnetic stirring for 3 h. The clear, colorless reaction mixture slowly became viscous, then rapidly precipitated white solid, becoming a slurry; at this point, heating was ceased and the mixture cooled to room temperature. The fine white solids were suction filtered off the mother liquor on a fritted filter funnel, washed with isopropanol, and dried under vacuum at 230°C for 1 h. The solids were weighed at 36.128 g (91% isolated yield). Crystallites were measured by optical microscopy to be needles averaging 8 μm long by 2 μm wide (see Figure S3 (112 [3]: Solid solutions with varying percentages of ammonium or potassium can be achieved by using a mixture of (NH 4 ) 2 SO 4 and K 2 SO 4 at the desired ratio; a 1:1 ratio was targetted herein. To a 100 mL round-bottom flask, 6.185 g B(OH) 3 (100 mmol), 3.562 g (NH 4 ) 2 SO 4 (27 mmol), 4.706 g K 2 SO 4 (27 mmol), 50 mL concentrated (98%) H 2 SO 4 , and a magnetic stir bar were added. The flask was attached to a water-cooled distillation head and a receiving flask containing 50 mL concentrated H 2 SO 4 acting as a desiccant. Dynamic vacuum (%0.15 mmHg) was applied to the system, the reaction vessel was immersed in an oil bath, and the reaction was heated to 200°C with magnetic stirring for %16 h. The clear, colorless reaction mixture slowly became viscous, followed by a rapid precipitation of a white solid. The fine white solids were diluted with tetramethylenesulfone (sulfolane), suction filtered off with a fritted filter funnel, washed with isopropanol, and dried under vacuum at 60°C for 16 h. The solids were weighed at 11.132 grams (48.1% yield). Crystallite size was too small to successfully perform singlecrystal X-Ray diffraction (XRD) on the product, but PXRD confirms that only a single phase is present, which is isostructural with both NH 4 2 ] are different, if the product were a physical mixture of phase pure ammonium and potassium borosulfates, rather than a solid solution, then two separate, overlapping sets of diffraction peaks would instead be visible. Crystallites were measured by optical microscopy to be needles averaging 15 μm long by 1 μm wide (see Figure S4, Supporting Information). PXRD (see also Figure S9 To confirm the identity and phase purity of the products, PXRD, IR spectroscopy, and X-Ray photoelectron spectroscopy (XPS) were utilized. PXRD was performed on the products of each synthesis using a Rigaku SmartLab diffractometer and Cu K α radiation (λ ¼ 1.5406 Å). These powder diffraction patterns were compared to simulated powder patterns of the known ammonium and potassium species generated from their single crystal structures using the Mercury software package. Full diffraction patterns are provided in Supporting Information ( Figure S6-S9, Supporting Information). Single crystal XRD was not possible on samples synthesized via these methods as the crystallites were not of suitable size. Attenuated total internal reflectance (ATR) IR spectra were acquired from 4000 to 525 cm À1 on a Nicolet iS50 spectrometer using a single-bounce diamond ATR crystal and averaging over 256 scans. A two-point linear baseline was applied to each spectrum after referencing the bare ATR crystal (i.e., air). XPS was performed on a Thermo Scientific Nexsa spectrometer. Samples were prepared for XPS by loading loose powders into a copper well plate www.advancedsciencenews.com www.advenergysustres.com and tamping them down with a clean glass rod to prevent surface contamination. Spectra were collected under flood gun (Ar þ ) irradiation to minimize charging. All spectra were fit with Shirley backgrounds without calibrating binding energies. B1s, N1s, O1s, S2p, and K2p spectra were fit with symmetrical 30% Gaussian-70% Lorentzian (G-L) peaks, where full width at half maximum (FWHM) was constrained to be equal for any peaks for the same element. Elemental compositions are reported as weight percentages converted from the atomic percentages measured by XPS. Full XPS spectra for 1b, 2, and 3 are provided in Supporting Information ( Figure S17 through Figure S19, Supporting Information). Disc-shaped pellets of each sample 300-700 μm thick were prepared by pressing 100-200 mg of each material in a 12.7 mm tungsten carbide die press to %240 MPa between platens of a Carver press heated to 100°C for 16 h. The bulk density of these pellets (1.2668 cm 2 area) was measured using a digital micrometer to determine the thickness of each pellet and an analytical balance to determine its weight. Bulk densities were compared with single crystal densities to determine the fraction of theoretical density/extent of consolidation as ρ Ã ¼ ρ bulk =ρ single crystal .
The ionic conductivity was calculated from electrochemical impedance spectra (EIS) acquired on a Gamry Reference 3000 potentiostat. For EIS, pellets were sandwiched between two 12.7 mm diameter gold-coated (50 nm by sputtering) porous sintered steel discs as electrical contacts allowing gas permeability. The assembly of sample and porous contacts was mounted in a machined aluminum cell ( Figure S10, Supporting Information) through which dry air was passed over both sides of the sample during heating and cooling cycles. Impedance spectra were collected on cooling after holding for %16 h at 200°C under flowing, dry air. Bode plots of the raw impedance data along with fits to a modified Randles circuit ( Figure S11, Supporting Information) are provided in the Supporting Information ( Figure S12-S15, Supporting Information). Conductivities were extracted from these fits by the equation: σ ¼ t RÃA , where t is the pellet thickness, A is its area (1.228 cm 2 ), and R is the electrolyte resistance calculated from the circuit model.
To calculate proton diffusivity, an NRL-developed formulation [21] with input forces and energies imported from the Vienna Ab Initio Simulation Program VASP [22] using the Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation functional was used. [23] All calculations began by creating 2 Â 2 Â 2 supercells of NH 4 [B(SO 4 ) 2 ] and K[B(SO 4 ) 2 ], comprising 32 formula units. 1-4 excess H atoms were added and converted to protons by subtracting an electron and adding a negative uniform background to obtain a charge-neutral cell. Each cell at each proton concentration was fully relaxed at T ¼ 0, with a very high energy cutoff of 670 eV to ensure accurate stresses for lattice relaxation. Subsequently, MD simulations of the initially relaxed cells were run for 100 ps with time steps of 0.5 fs at 900 K to evaluate proton diffusivity. The mean-squared distance moved by the protons was plotted against the time, the slope of which gives a measure of the diffusivity.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.