Unveiling the crystal structure of ‘antimonic acid’: short- and long-range perspectives

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 (H 3 O) 1.20(7) H 0.77(9) Sb 2 O 6 . Some protons belong to heavily delocalized H 3 O + 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 Sb 5+ 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.


INTRODUCTION
One of the long-standing chemical identity issues is that corresponding to the so-called "antimonic acid" (hereafter: AA), also referred to as hydrated antimony pentoxide (HAP), antimony oxide hydrates, and Sb(V) hydroxide. This material has proven useful for a variety of applications due to its distinctive proton-conducting nature [1][2][3][4] , ionic exchangeability [5][6][7][8][9][10] , and radiation resistance 7 , serving as potential candidate for photocatalyst 11,12 , fuel cells electrolyte 13,14 , heavy metals remover 15,16 , and for its application in electrochromic displays 3 or as precursor of several useful derivatives 7,11,[17][18][19] , among others. This enigmatic substance was already described by J.J. Berzelius. In his pioneering work in 1812, Berzelius published 20 the preparation of a "hydrated antimony pentoxide" by treating alkali antimonate with diluted nitric acid, while his disciple H. Rose synthesized it in 1824 by hydrolysis of antimony pentachloride 21 . One of the earliest structural discussions concerning AA salts dates back from the mid-19 th century, where oxygen/metal ratios were elucidated, and six-sided crystals of magnesium, cobalt, and nickel antimonates are successfully synthesized. 22 More than a hundred years later, the atomic arrangement within the crystal of this elusive compound (or more properly speaking, series of compounds) is still being a topic of debate. Perhaps the first modern review gathering all these results is the one presented by J. W. Mellor 17 in 1929. The most accepted formula for AA is Sb2O5·xH2O; depending on the synthesis and water content; water amounts varied from one to six H2O molecules per formula unit. A few years later, L. Pauling suggested the formula HSb(OH)6, equivalent to that of Sb2O5·7H2O, as the most likely composition for the acid phase 23 . This was supported by the water amount in the crystals and the ionic radius and behaviour of the Sb 5+ cation, and it was widely accepted as a base of further compositional and structural determinations 7,[24][25][26][27] . So forth, although researchers took many efforts to define the composition of AA, the crystal structure was totally unknown, perhaps given the difficulty of obtaining well-crystallized samples.
In a big attempt to shed light on the plausible structures adopted by AA-type compounds, Abe and Ito 28 synthesized AA samples from antimony pentachloride under different acidic conditions, temperatures, and aging times, obtaining solids tagged as amorphous, glassy, and crystalline solids 1 . They demonstrated that the crystalline phase can be fostered at higher acid concentrations, longer aging times, and suitable aging temperatures, regardless of the starting phase employed. The crystalline solid, of formula unit Sb2O5·4H2O, was defined in the 3 ̅ 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 six 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 Sb2O5 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 samples from easy-to-handle reactants, namely Sb2O3 and H2O2. 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 microscopic arrangement of AA, in a pyrochlore-type framework containing both H3O + and H + units accounting for the acidic behaviour of this material.

Long-range order structural determinations
Crystalline antimonic acid was obtained by soft-chemistry procedures as described in Methods. The obtained compound of nominal formula (H3O)pH2−pSb2O6 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 3 ̅ (# 227, ℎ 7 ) space group, in agreement with previous reports 3, 28  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 32e (x,x,x) main diagonal (as reported by Slade et al. 30 ), resulted in atomic SOFs close to zero, many times even reaching negative isotropic displacement factors.
This way, tenths of feasible structural alternatives and atomic incorporations were discarded. 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.    Table 1.

Table 1
The crystallographic formula obtained from the structural refinement is 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, there are 1.20(7) hydronium groups within the framework per formula unit, but in reality, only one or two subunits may fit in each cavity, off-centre of the 8a (⅛,⅛,⅛) Wyckoff site and displaced along the 32e (x,x,x) direction. Therefore, about eight cavities hold one single hydronium ion, whereas two H3O + subunits must be contained in two of them. In the latter case, owing to the repulsive electrostatic forces between the two highly electronegative O2 atoms fitting close to each other at a mean 1.752(10) Å distance, the H3O + 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 H3O + 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.  Table 2.
The obtained Rietveld profiles are exhibited in Fig. 1b

Table 2
Water and proton content assessment The SOFs 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 120 °C to eliminate all contributions to the final spectrum that could come from adsorbed water. The resulting deconvolution, shown in Fig 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.

Table 3
In the AA series, moisture is frequently present, and the total water amount they contain seems to vary from zero to six H2O 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 Scanning electron microscope SEM images helped to confirm a tiny and uniform particle size of AA. This is compatible with the soft chemistry procedure here used to synthesize this solid. Fig. 3c,d shows two pictures of the long-term stored sample, displaying smaller than a micron particles. This is in line with the colloidal nature of the sample, and the impossibility of collecting it from its liqueur by a simple filtration process. FeSbO4 (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 FeSbO4 oxide, which also contains Sb 5+ . It is also worth noting that the XANES features of AA increase as compared to that one of Sb2O3, meaning that the coordination number of the first shell Sb−O has also risen.
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 such that , , and 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.

CONCLUSIONS
A compelling study of the so-called antimonic acid structure by robust local-and long-range techniques, together with a bond-valence energy landscape 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 3 ̅ space group. Aided by a combined Rietveld refinement from synchrotron X-ray and neutron powder diffraction data and by a solid-state magic-angle spinning nuclear magnetic resonance spectroscopy study, 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 B2O6 −2 covalent framework within which the hydronium groups percolate. The refined crystallographic formula is (H3O)1.20 (7)H0.77(9)Sb2O6, with 0.703 water molecules from 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 H3O + groups within the same cavity are prone to become two H2O 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 X-ray Absorption Fine Spectroscopy, the nuclear magnetic resonance and thermogravimetric analysis and differential scanning calorimetry 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.

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 Sb2O3 and a 31% H2O2 solution, following previously described procedures. 3,42 The mixture was stirred at 343 K for 24 h, while the hereunder reaction occurs: The white colloidal suspension is centrifuged at 15,000 rpm for 10 min until nearly  respectively), and that they fit in the same conduction path, we tacitly assume that the migration energy Em is equivalent to the threshold energy Eth here determined, defined as the energy at which the proton pathway starts percolating across the unit cell 49 . Hence, undertaking a multiple technique approach, we disclose a detailed and comprehensible structural description of the antimonic acid, which is compatible with their main chemical properties.

Magic-angle Spinning Nuclear Magnetic Resonance Spectroscopy
The chemical shift anisotropy CSA is the interaction between the external magnetic field B0 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 B0, 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 CSA tensor. For nucleus in an axial symmetry site, it is true that δxx = δyy ≠ δzz and η = 0.

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 well-established 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 X-ray absorption spectroscopy 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 51 . 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 Sb2O3 (99.7%) were purchased from Aldrich and Alfa Aesar, respectively.
FeSbO4 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 RT to 700 °C with a rate of 10 K·min −1 for powder samples encapsulated in standard Al 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:

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

Competing interests
The authors declare no competing interests.  (7)H0.77(9)Sb2O6, with cubic space group 3 ̅ (# 227) and Z = 8, from dual SXRD and NPD data refinement collected at 298 K (λSXRD = 0.44271 Å, λNPD = 1.5947 Å, Origin Choice # 2). Table 2. Selected interatomic distance and angles refined from combined SXRD and NPD data. Main interatomic distances and angles for (H3O)1.20 (7)H0.77(9)Sb2O6, with cubic space group 3 ̅ (# 227) and Z = 8, from dual SXRD and NPD data refinement collected at 298 K (λSXRD = 0.44271 Å, λNPD = 1.5947 Å, Origin Choice # 2). Sb2O6 2− covalent framework, H3O + subunit, and non-bonding atoms categories are classified. In the latter, only meaningful distances and angles from atomic pairs and triplets of near non-bonding elements are summarized. Table 3. 1 H MAS NMR chemical shift anisotropy data from spectra recorded at 10 kHz. In spectra analysis, position, linewidth, and integrated area of central components were deduced with non-linear iterative techniques. The analysis of spinning sideband patterns enables a determination of the isotropic chemical shift (δiso), and the axiality (dCS) and asymmetry parameter (η) of the CSA tensor. Table 4. Structural parameters extracted from EXAFS data. is the distance from absorber atom, is the average coordination number, 2 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: Nidp ≈ 2ΔkΔR/π. Nvar, number of variables used during the fitting procedure.  These atoms present high mobility, with prolate anisotropic ellipsoids oriented along the 32 (x,x,x) direction. (e) Close up of the statistical distribution of a single cavity wherein the O2 and H1 are distributed at 32e and 96g Wyckoff positions, respectively, with SOFs close to 0.301 (2), and H2 atoms at 48f sites exhibiting a SOF of 0.129 (15). Only 1.20(7) H3O + groups and 0.77(9) H2 species are statistically present in each cavity. (f) Snapshot of a single octahedra-sharing crown with a hydronium subunit and a H2 proton. In dotted lines: H1 atoms of the H3O + subunit establish H bonds with the O1 atoms at about 1.400(10) Å.

Figure 2.
Proton percolation path and mechanism. Atoms in all six panels are presented as anisotropic displacement ellipsoids at a 95% probability level. The colour reference is the same one used in Fig. 1. (a and b) Close up of the AA final structure; the ionic percolation path is highlighted in blue. The pathway involves both H + species in a 3D interconnected arrangement, generating the 3D percolation isosurface defined for the AA. The ionic percolation begins with a low percolation activation energy barrier of 0.13 eV. (c) Proton percolation pathway in a simplified view of the AA unit cell approximately along the [110] direction. For the sake of clarity, the Sb2O6 2− octahedra-sharing covalent framework is hidden, and only the H3O + 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 H3O + subunits coexist. The repulsive electrostatic forces between the two O2 species would force their shift away from the 8a (⅛,⅛,⅛) along the (x,x,x) main diagonal 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 to c), achieving an electrostatic stability.        Proton percolation path and mechanism. Atoms in all six panels are presented as anisotropic displacement ellipsoids at a 95% probability level. The colour reference is the same one used in direction. For the sake of clarity, the Sb2O62− octahedra sharing covalent framework is hidden, and only the H3O+ acid groups and the H2 species are visible. Statistically, less than a third of the hydronium units here gured are present. (d) Proposed ionic migration mechanism of two H1 atoms from 96g to 48f (H2) Wyckoff sites, for those cages wherein two H3O+ subunits coexist. The repulsive electrostatic forces between the two O2 species would force their shift away from the 8a (⅛,⅛,⅛) along the (x,x,x) main diagonal 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 to c), achieving an electrostatic stability.   Structural short range order studies. Room condition Sb K-edge XANES spectra of AA as compared with reference samples of Sb foil, Sb2O3, and FeSbO4 (a). The k3-weighted EXAFS signals (b) and their corresponding moduli of the Fourier transform (c). The tting was performed using the scattering paths in Table 4: the EXAFS oscillations k3χ(k) (d), moduli of the Fourier transform |χ(R)| (e), and its real part