Synergy of diffraction and spectroscopic techniques to unveil the crystal structure of antimonic acid

The elusive crystal structure of the so-called ‘antimonic acid’ has been investigated by means of robust and state-of-the-art techniques. The synergic results of solid-state magic-angle spinning nuclear magnetic resonance spectroscopy and a combined Rietveld refinement from synchrotron X-ray and neutron powder diffraction data reveal that this compound contains two types of protons, in a pyrochlore-type structure of stoichiometric formula (H3O)1.20(7)H0.77(9)Sb2O6. Some protons belong to heavily delocalized H3O+ subunits, while some H+ are directly bonded to the oxygen atoms of the covalent framework of the pyrochlore structure, with O–H distances close to 1 Å. A proton diffusion mechanism is proposed relying on percolation pathways determined by bond-valence energy landscape analysis. X-ray absorption spectroscopy results corroborate the structural data around Sb5+ ions at short-range order. Thermogravimetric analysis and differential scanning calorimetry endorsed the conclusions on the water content within antimonic acid. Additional 0.7 water molecules per formula were assessed as moisture water by thermal analysis.


Scientific Reports
| (2021) 11:17763 | https://doi.org/10.1038/s41598-021-97147-0 www.nature.com/scientificreports/ regardless of the starting phase employed. The crystalline solid, of formula unit Sb 2 O 5 ·4H 2 O, was defined in the Fd3m space group, with a lattice constant of 10.38 Å. This was the first time that a pyrochlore-type phase was effectively defined for the AA crystalline oxides. With 6 days of difference, Baetsle and Huys announced similar results for AA samples obtained from K and Na antimonates, with similar unit-cell parameters and same compositions 5 , also concomitant with pioneering properties predicted for hydrated Sb 2 O 5 29 . In the present work, we have chosen a straightforward synthesis procedure, to our best knowledge described for the first time by Ozawa et al. 3 , yielding well-crystallized powder samples from easy-to-handle reactants, namely Sb 2 O 3 and H 2 O 2 . It has been characterized by state-of-the-art techniques including neutron and synchrotron X-ray diffraction (NPD and SXRD, respectively), solid-state magic-angle spinning nuclear magnetic resonance spectroscopy (MAS NMR) and local order techniques like X-ray absorption spectroscopy (XAS), in complement with thermogravimetric analysis and differential scanning calorimetry (TGA/DSC), as well as scanning electron microscope (SEM). Our findings agree on a consistent picture of the atom-scale arrangement of AA, in a pyrochlore-type framework containing both H 3 O + and H + units accounting for the acidic behaviour of this material.

Results and discussion
Long-range order structural determinations. Crystalline AA powder was obtained in the form of a colloidal slurry by soft-chemistry procedures as described in "Methods". The obtained compound of nominal formula (H 3 O) p H 2−p Sb 2 O 6 and defect pyrochlore-type crystal structure has been investigated using long-and short-range characterization techniques, in order to determine its composition and atomic arrangement. Firstly, a peak indexing over a laboratory XRD pattern was performed as shown in Fig. 1a, confirming that AA adopts a cubic pyrochlore-type structure belonging to the Fd3m (# 227, O 7 h ) space group, in agreement with previous reports 3, 28 . Briefly, pyrochlore-type oxides present a general formula A 2 B 2 O 6 O′, where A is a voluminous mono-, di-or trivalent cation, B is a smaller metal of higher oxidation state, and O′ is an oxygen atom that can be partially or even entirely absent, giving rise to the so-called defect pyrochlores A 2 B 2 O 6 O′ 1−δ . When O′ is present, two structural groups can be identified within the unit cell: a main covalent framework of B 2 O 6 corner-sharing octahedra, and a sub-lattice A 2 O′, interspersed in a tetrahedral arrangement. Once the XRD data of AA were indexed in the Fd3m space group, the crystalline structure was fully determined by a combined Rietveld refinement from SXRD and NPD data collected at room temperature. Patterns from NPD and SXRD data contained sharp diffraction peaks, consistent with a cubic pyrochlore phase with a = 10.36052(15) Å, as displayed in Fig. 1b,c. An origin choice # 2 at 3m was adopted for this analysis. The in-detail refinement procedure is described in the Supplementary Information, while the refinement parameters can be found in "Methods".
The final refinement includes Sb and O1 atoms located at 16d ( 1 /2, 1 /2, 1 /2 ) and 48f (x, 1 /8, 1 /8 ) Wyckoff sites, constituting the covalent Sb 2 O 6 2− framework of the pyrochlore oxide. Two types of H atoms were identified: H1 located at 96g (x,x,z) sites, constituting together with the O2 atoms at 32e (x,x,x) the hydronium H 3 O + units, and H2 species located at 48f (x, 1 /8, 1 /8 ) positions, directly linked to the Sb 2 O 6 covalent framework. O2 can be considered to be the O′ atoms of the standard pyrochlore structure. Ultimately, the individual atomic anisotropic displacement factors for each non-equivalent atom were determined, with the only exception of the H2 species, which was modelled as an isotropic sphere. This is due to a strong divergence of the model when attempted to be anisotropically determined, probably due to its vicinity to the resonant H1 atom. Attempts to incorporate additional water or hydronium molecules within the structure, as for example centred at 8b sites occupying the empty cages generated by the main framework or along the main diagonal (as reported by Slade et al. 30 ), resulted in atomic site occupation factors (SOFs) close to zero, many times even reaching negative isotropic displacement factors. This way, tens of feasible structural alternatives and atomic incorporations were discarded, many of which containing constrains or restrains varying O-H bond length distances and O2/H1,2 SOF ratios. No preferred orientation is expected to occur due to the isotropy of the cubic structure and the octahedral shape of AA microcrystals, and neither the parameters of preferred orientation nor roughness were refined as they showed no improvement in the reliability factors.
Occupancies of H1, H2, and O2 atoms were constrained to each other according to the MAS NMR analysis, and strongly endorsed by a TGA/DSC study, as explained in the water and proton content assessment section; occupancy constrains partially relied on the electroneutrality of the crystal structure. For the Sb and O1 elements, small displacement ellipsoids were obtained (U eq = 0.98(2) × 10 −2 and 0.83(10) × 10 −2 Å 2 , respectively), denoting small vibrational and delocalization of the scattering contributions. In contrast, although far smaller than those obtained in the 'Case B' scenario described in the Supplementary Information, O2 and H1 atoms belonging to the hydronium units exhibited rather large cigar-shaped (prolate type) displacement ellipsoids of U eq = 5.4(4) × 10 −2 and 6.7(8) × 10 −2 Å 2 , stretched along the (x,x,x) direction. They are reminiscent to those described in the (H 3 O) 1+p Sb 1+p Te 1−p O 6 series 31 . This is expected, considering their high multiplicity and their relatively small occupancy, as well as by the fact that the hydronium units may rattle within the wide cavities generated by the Sb 2 O 6 2− framework, where a high diffusivity of the hydronium units across its channels is expected. Finally, H2 atoms presented somewhat in-between isotropic displacements (U iso = 3.626(1) × 10 −2 Å 2 ), suggesting lower ionic mobility and lower atomic delocalization. The final structure achieved by Rietveld refinement of both SXRD and NPD diffraction data for the AA is exhibited in detail in Fig. 1d (7) H 0.77(9) Sb 2 O 6 , which presents electroneutrality within the standard deviation and is also endorsed by the low Rietveld reliability factors and the reasonable equivalent isotropic displacement factors obtained for each mobile atom. It is interesting to examine the ionic conduction path obtained from a bond-valence energy landscape (BVEL) study of the crystal, illustrated in Fig. 2a-c. The conduction pathway, highlighted with a blue isosurface, involves both types of H atoms and exhibits an isotropic distribution along the three axes. The percolation of the H atoms presents a very low activation energy of 0.13 eV and a noticeably large volume fraction of the unit cell for ion mobility of 72.38% for the given parameters, providing the mechanism for the high ionic intracrystalline proton conduction announced by several authors 3,4,13,32 . The average site-energy computed by bond-valence theory for both mobile protons is − 2.95 eV, differing between both species in only 0.12 eV.
The H2 atom is bonded to the framework in a Sb 5+ -OH fashion, with hydroxyl interatomic distances H2-O1 of 1.13(6) Å. The O2 at 32e Wyckoff sites is coordinated by three H1 species at 96g positions in a tetrahedral arrangement, with internal H1-O2-H1 angles of 104.0(16)°. The lone electron pair of the oxygen atoms belonging to the hydronium groups are oriented in the 8a ( 1 /8, 1 /8, 1 /8 ) direction. The H1 atoms are located about 1.400(10) Å away from the O1 oxygen of the covalent framework, with which a hydrogen bond is likely established. Remarkably, the mean H1-O2 interatomic distance within the hydronium unit is 1.323(11) Å, which might seem rather large for a well-established (coordinated) covalent bond. The reason for this is that, statistically, 20    www.nature.com/scientificreports/ Therefore, when two hydronium groups get close to each other, the central protons become prone to delocalization. Here, it is very likely that one of these in-between protons starts resonating and becomes a shared ion between the two O2 and the O1 oxygens. Such a scheme would entail the bonding of four protons to two O2, the share of a fifth H + between these and one O1 oxygen, and the sixth remaining H + species leaving the H 3 O + groups behind by following the ionic conduction path and bonding to the opposite O1 at a mean O2-H2 distance of 2.811(12) Å. As there are statistically less than 0.8 H2 atoms per cavity, there is room for the proposed mechanism as some of the cages will not present an OH hydroxyl group at all. A schematic representation of this effect is shown in Fig. 2d.
The determined Sb-O1-Sb angle and Sb-O1 distances within the Sb 2 O 6 2− covalent network are 137.33(3)° and 1.9663(12) Å, respectively, which are larger than those of 136.39(2)° and 1.9624(5) Å recently reported for an AA derivative, viz. Sb 6 O 13 , obtained by thermal decomposition of the former 19 . The unit-cell parameter is also longer for AA, about 0.53% more than that of Sb 6 O 13 (10.36052(15) vs 10.30653(11) Å). A wider and bigger cavity for the hydrated sample is consistent with the presence of 1.20(7) voluminous H 3 O + groups per cage, in contrast with the 0.5 Sb 3+ 2 -O′ groups found in the calcined sample. The main interatomic distances and angles obtained are summarized in Table 2.
The obtained Rietveld profiles are exhibited in Fig. 1b,c and in more detail in Supplementary Fig. S1. The domain size assessment, determined by Scherrer's 34,35 equation from SXRD data, yields a crystallite of 42.00(8) nm average apparent size. Instrumental broadening was deconvoluted for Scherrer's apparent domain size determination, see "Methods" for more details.
Water and proton content assessment. The occupancies of O2, H1, and H2 species used on the combined Rietveld refinement were determined by means of MAS NMR applied to dry AA. This is a powerful technique to identify the different 1 H species that may be found within the crystal structure. Prior to this analysis, the sample was dried at 105-107 °C to eliminate all contributions to the final spectrum that could come from adsorbed water. The resulting deconvolution, shown in Fig. 3a, is mainly made up of two components with dif- octahedra-sharing covalent framework is hidden, and only the H 3 O + acid groups and the H2 species are visible. Statistically, less than a third of the hydronium units here figured are present. (d) Proposed ionic migration mechanism of two H1 atoms from 96g to 48f (H2) Wyckoff sites, for those cages wherein two H 3 O + subunits coexist. The repulsive electrostatic forces between the two O2 species would force their shift away from the 8a ( 1 /8, 1 /8, 1 /8 ) along the (x,x,x) direction. One of the in-between protons is shared between the two O2 atoms and the O1 framework oxygen, while the other is relocated at the antipodal position of the cavity by following the percolation path highlighted in panels (a-c), achieving an electrostatic stability. www.nature.com/scientificreports/ ferent widths and intensities, corresponding to the two proton types observed by Rietveld refinement from NPD data. Additionally, a small component has been introduced to the deconvolution at a chemical shift of 1 ppm, corresponding to a parasitic signal from the organic rotor cap. The chemical shift values of the main two contributions are rather similar to each other (8.70 for H1 and 8.46 ppm for H2) and, in both cases, higher than those of the water molecule (5 ppm), indicating a somewhat stronger acidity of the protons. The dependence of the chemical shift or anisotropy with the orientation regarding the external magnetic field B 0 is not pronounced, and the calculated isotropic chemical shift (tabulated in Table 3) coincides with the position of the main components. At the same time, proton contributions (H1 and H2) present similar small chemical shift anisotropy (usually termed CSA) patterns, which are slightly broadened by anisotropic interactions, meaning that the structural environment is slightly distorted in both cases. Signal contribution widths, on the other hand, are noticeably different; in NMR, a higher width may indicate less mobility due to greater interaction with the surface and a higher heterogeneity of structural positions. From the two main deconvoluted signals, the wider and less significant one (6.5 ppm wide, 17.49%) is assigned to the more restrained, short-bonded H2 protons, while the narrow and stronger signal (2.5 ppm, 81.30%) corresponds to the H1 protons constituting the high-mobility hydronium groups. The relationship between the two areas is 4.648, in close agreement with the H1/H2 Rietveld SOFs ratio of 4.674. Principal elements deduced from sideband patterns are given in Table 3, where isotropic chemical shift, anisotropy, and asymmetry parameters corresponding to each site are also included. A brief explanation of the tabulated elements is presented in "Methods". Sb-O2 (× 12) 3.845 (7) Sb-O1-H1 109.0 (7) Sb-H2 (× 6) 2.59 (3) O1-O1-H2 135 (3) Sb-H1 (× 12) 2.760(10) O1-O2-H2 108.7 (6) O1-H1 (× 2) 1.400 (10) O1-H2-O2 149 (3) O1-H1 (× 4) 2.471 (9) O1-H2-O2 92 (2) O1-H1 (× 4) 3.111 (9) O1-H2-H1 129 (2) O1-O2 (× 2) 2.697 (7) O1-H2-H1 88 (2) O1-O2 (× 2) 3.034 (7) O1-H1-O2 164.1 (9) O2-O2 (× 3) 1.752 (10) H1-O1-H2 66 (2) O2-O2 (× 1) 2.340 (10) H1-O2-H2 93.5 (9) O2-H2 (× 2) 1.679 (17)  www.nature.com/scientificreports/ In the AA series, moisture is frequently present, and the total water amount they contain seems to vary from zero to six H 2 O molecules per formula unit 1,5,17,28 , some of which are expected to be adsorbed on the solid surface linked by H bonds to the outmost framework oxygen atoms and exposed acid groups. In order to assess this moisture content and to confirm the crystalline water determined by MAS NMR, a TGA/DSC analysis was performed on both, a dry, and a long-term air-stored sample. The weight and heat flow curves are summarized in Fig. 3b.
The dry sample was used to determine the quantity of hydronium and H2 species, obtaining values in close agreement with those derived from NMR and in agreement with the proposed structural model. It comes to no 40     www.nature.com/scientificreports/ surprise that AA presents some major water affinity, as a small amount of moisture was adsorbed on the dry sample during the TGA/DSC experiment setup, and later degassed in the heating process up to 150 °C. Seamlessly, this extraordinary water affinity was recently identified and reported by our group for a potassium pyrochlorelike niobate and tungstate 33 , probably bound to many series of pyrochlore-like materials as a common behaviour pattern. For the assessment of H content in the dry sample, this last moisture-related contribution was deducted. Scanning electron microscope. SEM images shed light on the microscopic uniformity of the of AA. This landscape is compatible with the soft-chemistry procedure here used to synthesize the solid. Figure 3c,d shows two pictures of the long-term stored sample, displaying particles of a size smaller than a micron. This is in line with the colloidal nature of the sample, and the impossibility of collecting it from the slurry by a simple filtration process.
Structural short-range order studies. XAS is a powerful tool to probe both chemical features of the constituting elements, such as valence and coordination environment around the target atoms, and local structural information, which includes average nearest-neighbour distances and coordination number 39 . XANES (X-ray absorption near-edge structure) part of the XAS spectra provides information on the valence state as the edge position, such that the binding energy of the bound electrons increases with the valence 40 . Figure 4a compares the XANES at Sb K-edge (30.491 keV) of AA with the reference samples, including the Sb foil (Sb 0 ), Sb 2 O 3 (Sb 3+ ) and FeSbO 4 (Sb 5+ ). One may see the blue shift of the edge position when the valence state increases from 0 up to 5+, as indicated by the black arrow. The shift ΔE of the edge energy, from the Sb 0 , is 1.7 eV for valence Sb 3+ , while for valence Sb 5+ of AA is 5.6 eV. Such a result agrees with the edge shift observed for FeSbO 4 oxide, which also contains Sb 5+ . It is also worth noting that the XANES features of AA increase as compared to that one of Sb 2 O 3 , meaning that the coordination number of the first shell Sb-O has also risen.  www.nature.com/scientificreports/ Quantitative information on the local structure was obtained using the extended part of the XAS spectra, the so-called EXAFS (extended X-ray absorption fine structure). Indeed, EXAFS spectra were recorded up to k = 16 Å −1 , as represented in Fig. 4b. Here, the EXAFS oscillations k 3 χ(k) of Sb foil, Sb 2 O 3 , FeSbO 4 , and AA are compared, showing similarities among the oxides. This can be better seen by plotting the moduli of the Fourier transform in R space in Fig. 4c: two main peaks at 1.52 and 3.35 Å (not corrected by photoelectron phase-shift). In order to evaluate the pair-bond distances and the coordination numbers, the standard EXAFS equation was used, which stands for 39 : such that R Ŵ , N Ŵ , and σ Ŵ are the structural parameters to be determined for each photoelectron path: distance from absorber atom to its neighboring ones, coordination number of the shell, and Debye-Waller (DW) factor (it measures the mean square relative displacement), respectively. S 0 stands for the amplitude reduction factor from a previous calibration using a metallic antimony ( S 0 is equal to 0.7802 for all the samples). F Ŵ (k, R Ŵ ) , (k) , and ϕ Ŵ (k) denote the backscattered amplitude, photoelectron mean free path, and phase shift, correspondingly, which are determined by the FEFF-8 code 41 .
The EXAFS signal at room temperature of AA was fitted using three neighbouring shells: one short Sb-O, one Sb-Sb, and a long Sb-O one. All the adjusted parameters of interest in Eq. (1) are listed in Table 4. Figure 4d-f shows the quality of fitting by exhibiting the EXAFS oscillations, moduli of the Fourier transform and its real part in R space, respectively. The first peak in |χ(R)| at 1.52 Å (not phase-shift corrected) denotes the Sb 5+ -O bond with R Sb−O = 1.955(1) Å and coordination number N Sb−O around 6.5(1). Such a shell fully agrees with the pair bond Sb−O1 (× 6) with a distance of 1.9663(12) Å, as obtained from NPD. The second feature in |χ(R)| at 3.35 Å has two components: a metallic-metallic pair with R Sb−Sb = 3.612(1) Å and a metallic-anion one with R Sb−O = 3.898(1) Å. The Sb-Sb pair possesses a coordination environment close to 3, which may be associated with the non-bonding pair Sb-Sb (× 6) with a metal-metal distance of 3.66307(2) Å in Table 2. The second nonbonding pair Sb-O has R Sb−O = 3.898(1) Å and coordination number N Sb−O around 6.0(1), being similar to that obtained for Sb-O2 (× 12) with a distance of 3.845(7) Å. Details on the EXAFS analyses in Sb 2 O 3 and FeSbO 4 samples can be found elsewhere 19 .
Differently from NPD, here it is not possible to identify pair containing this hydrogen by EXAFS, since the atomic number of Hydrogen is 1; therefore, the shortest and longest distances are missing in this study. The DW factors of the shells Sb-O (1.955(1) Å) and Sb-Sb (3.612(1) Å) were derived as 3.4(6) and 2.7(8) × 10 −3 Å 2 , respectively. These values agree well with those reported for cubic Sb 2 O 5 , meaning that AA and the last oxide have a very similar short-range structure 42 , i.e. with a similar covalent framework composed by Sb 5+ -O pair bonds.

Conclusions
A compelling study of the so-called 'antimonic acid' structure by robust local-and long-range techniques, together with a BVEL analysis, shed light on the stoichiometry and atomic distribution in the crystal structure, and provide a plausible ionic diffusion mechanism for its well-established high proton conductivity. The structure can be defined as a defect pyrochlore, belonging to the Fd3m space group. Aided by a combined Rietveld refinement from SXRD and NPD data, and by TGA/DSC and MAS NMR studies, we were capable of identifying two main types of protons in this material, one at 96g Wyckoff sites that belongs to the highly delocalized hydronium subunits and presents lengthened prolate displacement ellipsoids, and another one at 48f positions, directly bonded at 1.12(4) Å to the oxygen atoms constituting the B 2 O 6 −2 covalent framework within which the hydronium groups percolate. The refined crystallographic formula is (H 3 O) 1.20(7) H 0.77(9) Sb 2 O 6 , with 0.703 water molecules from physisorbed moisture per formula unit. We found neither additional H species nor the presence of Sb 3+ remaining from the oxide precursor or generated by reduction of Sb 5+ at A sites. Although no additional crystallization water was found, a plausible mechanism where two H 3 O + groups within the same cavity are prone to become two H 2 O molecules and two H2 protons is proposed, endorsed by the repulsion among hydronium units sharing the same cavity, and by the 48f site availability. Good Rietveld refinement reliability factors were achieved, and the XAS, the MAS NMR, and TGA/DSC results are all consistent with the proposed model. In particular, XANES endorsed the pentavalent state of antimony ion in AA, while EXAFS probed the covalent framework composed by Sb 5+ and O1 atoms. Table 4. Structural parameters extracted from EXAFS data. R Ŵ is the distance from absorber atom, N Ŵ is the average coordination number, σ 2 Ŵ the Debye-Waller factor, and R-factor stands for the quality factor of the fitting. Maximum number of independent variables as imposed by the uncertainty principle: N idp ≈ 2ΔkΔR/π. N var , number of variables used during the fitting procedure.

Sample
Shell

Methods
Sample preparation. All the commercially available ReagentPlus or Analytical-grade reagents were purchased at Sigma Aldrich and Fisher Scientific. Antimonic acid was obtained by an oxidative hydrolysis soft-chemistry reaction. It begins from Sb 2 O 3 and a 31% H 2 O 2 solution, following previously described procedures 3,43 . The mixture was stirred at 343 K for 24 h, while the hereunder reaction occurs: The white colloidal slurry is centrifuged at 15,000 rpm for 10 min until nearly complete sedimentation. The product, a glassy-white solid, is then dried in air at 105-107 °C for 48 h and finally ground.
The (H 3 O) p H 2−p Sb 2 O 6 sample was firstly investigated utilizing X-ray powder diffraction (XRD). Laboratory XRD data were collected with a conventional diffractometer (40 kV, 30 mA) in Bragg-Brentano reflection geometry with Cu K α radiation (λ mean = 1.5418 Å). The SXRD pattern was collected at the CELLS-ALBA facility, Barcelona (Spain), in the MSPD high-angular resolution diffractometer under an incident beam with an energy of 28 keV and a wavelength of λ = 0.44271 Å. For determining the instrumental broadening, the sample was characterized together with a powdered Na 2 Ca 3 Al 2 F 14 fluoride (NAC) standard. The high-angular resolution mode (MAD set-up) was used on the MSPD-diffractometer 44 . The polycrystalline powder was contained in a spinning glass capillary of 0.7 mm diameter. For the NPD experiments, the D2B high-resolution two-axis diffractometer was used, installed at the Institut Laue-Langevin, in Grenoble (France). The sample (about 2-3 g) was contained in a vanadium can. The full diffraction patterns were collected in a 2 h-long analysis time. A wavelength of 1.5947 Å was selected from a Ge monochromator; the measurement temperature was 298 K.
Structural refinement from synchrotron X-ray and neutron diffraction data. FULLPROF 45 software (see "Methods") was used for performing the combined Rietveld refinement 46 from SXRD and NPD data. A relative pattern weight of 0.10/0.90 favouring NPD data was considered, as it presents an absence of form factor and exceptional sensitivity for both hydrogen and oxygen atoms, essential for determining their positions, occupancies and atomic displacement factors (ADPs). Moreover, H + atoms are invisible to X-rays and the atomic weight ratio between Sb and O is large enough for the SXRD to differentiate them even at low pattern weighting. The best ADPs and lowest Rietveld reliability factors were obtained for the announced relationship.
The Thompson-Cox-Hastings 47 pseudo-Voigt convoluted with axial divergence asymmetry over SXRD data were used to determine the crystallite size. A calculated μR = 0.92 absorption correction coefficient determined by adopting a 0.5 packed factor was included in the refinement for compensating transmission and absorption of the X-rays through the irradiated cylindrical volume of the sample. An apparent isotropic crystallite size of 42.00(8) nm and average maximum generalized strain of ε = 6.666(7) × 10 -4 were obtained through microstrainand domain size-determining FULLPROF modules. For the NPD data treatment, a pseudo-Voigt 48 function with the asymmetry correction published by Berar and Baldinozzi 49 were respectively employed for the simulation of the peak shape and the asymmetry assessment.
Both SXRD and NPD backgrounds were linearly interpolated between 68 and 44 individual refined points. The coherent neutron scattering lengths used in the Rietveld refinement are internally tabulated in the program FULLPROF, rated in 5.570, 5.803, and − 3.739 fm for Sb, O, and H atoms, respectively.
BVEL was carried out with BondStr 50 software (see "Methods"), a module embedded in the FULLPROF toolbar. For ensuring a percolation energy convergence of a few hundredths of electron volt, BVEL analysis considering H + as the mobile ion was computed by applying a grid resolution of 0.1 Å and a percolation radius of 8 Å, suiting with the optimal parameters described by Katcho et al. in their high-throughput BVEL calculation of Li and Na ionic conductors 50 . As both mobile ion share almost the same minimum site-energy (− 2.93 and − 3.05 eV for H1 and H2, respectively), and that they fit in the same conduction path, we tacitly assume that the migration energy E m is equivalent to the threshold energy E th here determined, defined as the energy at which the proton pathway starts percolating across the unit cell 50 . Hence, undertaking a multiple-technique approach, we disclose a detailed and comprehensible structural description of the AA, which is compatible with its main chemical properties.
Magic-angle spinning nuclear magnetic resonance spectroscopy. The chemical shift anisotropy is the interaction between the external magnetic field B 0 and the electron density surrounding the nucleus, owing to the magnetic moment coming from its rather ellipsoidal shape. The weak secondary magnetic fields that are generated are added or subtracted to B 0 , modifying the magnetic field around the nucleus, and therefore its resonance frequency in a so-called 'shielding' process that results in a chemical shift. The three main values of the shielding associated tensor are frequently expressed as a function of the isotropic chemical shift (δiso), and the axiality (dCS) and asymmetry parameter (η) of the chemical shift anisotropy tensor. For nucleus in an axial symmetry site, it is true that δxx = δyy ≠ δzz and η = 0. The shape of the powder sample line is very different, depending on the symmetry of both the shielding tensor and the site where the nucleus is located. The MAS experiment ('magic angle spinning' or rotation of the sample around the magic angle) can average the chemical shift anisotropy. Even slow spinning provides very narrow lines, although there may be a substantial number of spinning sidebands. It is interesting to note that the orientation-dependent information of the interaction remains, embedded in the amplitudes of the spinning sidebands. Indeed, a simulation can extract the principal values of the chemical shift anisotropy from slow speed MAS spectra. 1 H MAS NMR spectrum was recorded on a Bruker AVANCE 400 spectrometer. Single pulse sequences were used to irradiate the sample at the 1 H resonance frequency in a 9.4 T (400 MHz) magnetic field. The sample was www.nature.com/scientificreports/ placed on zirconia rotors that rotate inside the probe at an angular frequency of 10 kHz around the magic angle (54° 44′ with respect to the external magnetic field). NMR spectrum was obtained after excitation of the sample with a π/2 pulse duration of 4.7 µs and an interval between successive accumulations of 5 s. The total number of accumulations was 72. To determine the values of the chemical shift, tetramethylsilane was used as internal standard. By adding the components as a combined Lorentzian-Gaussian form, a calculated envelope that reproduces the spectrum is obtained, from which the intensity, position (chemical shift) and width parameters of central components were deduced with non-linear iterative techniques (DMFIT software 51 , see "Methods"). The analysis of spinning sideband patterns enables a determination of chemical shift, dCS and η parameters.
X-ray absorption spectroscopy at the CLAESS beamline of the ALBA synchrotron. The X-ray absorption process was performed by measuring the photon flux through three ionization chambers. This wellestablished technique used in transmission mode provided an exact measurement of the X-ray absorption coefficient. The resulting absorption spectra were then characterized by one or more jumps (absorption edges), whose energy positions are element specific since they coincide with the energy of the corresponding atomic core level. The X-ray transitions are controlled by the dipolar selection rules relating to well-defined atomic symmetry of the involved core hole and the final state angular momenta. XANES spectra show a remarkable site-specific behaviour, because they are sensibly affected by the strong spatial localization of the initial core-shell state. Short-range atomic studies were performed by means of XAS at the BL22-CLAESS beamline of the Spanish synchrotron, CELLS-ALBA, Barcelona, with electron energy and current in the ring of 3 GeV and 200 mA, respectively. Data acquisition was performed with a double crystal monochromator with two Si(311) crystal pairs and three ionization chambers for determining the photon flux before/after the sample and before/after the metal foil employed for energy calibration. In this way, the X-ray absorption coefficient may be exactly measured. Details on the beamline setup can be found elsewhere 52 . Concerning the sample preparation for XAS measurements, the samples were ground in an agate mortar with an inert matrix (boron-nitride, BN), pelletized into disks to optimize the absorption jump of the XANES spectrum, and then protected with Kapton tape. The reference samples such as Sb foil (> 95%) and Sb 2 O 3 (99.7%) were purchased from Aldrich and Alfa Aesar, respectively. FeSbO 4 was synthesized using solid-state reaction method, as detailed elsewhere 19 .
Complementary techniques. The TGA/DSC characterization was performed in a Mettler TA3000 system equipped with a DSC Q-100 unit. The measurements were performed in heating runs from room temperature to 700 °C with a rate of 10 K min −1 for powder samples encapsulated in standard alumina crucibles. About 49 and 56 mg of sample were used for the dry-basis and long-term stored AA experiments, correspondingly. The thermal decomposition reaction of the AA is determined as follows: SEM experiments were conducted with a Hitachi TM1000 (Hitachi High-Technologies Corporation, Minato, Tokyo, Japan) desktop instrument with an acceleration voltage of 1.5 kV and a 90 s acquisition time.

Data availability
The datasets generated during and analysed during the current study are available from the corresponding author on reasonable request.