Joint Experimental and Computational 17O and 1H Solid State NMR Study of Ba2In2O4(OH)2 Structure and Dynamics.

A structural characterization of the hydrated form of the brownmillerite-type phase Ba2In2O5, Ba2In2O4(OH)2, is reported using experimental multinuclear NMR spectroscopy and density functional theory (DFT) energy and GIPAW NMR calculations. When the oxygen ions from H2O fill the inherent O vacancies of the brownmillerite structure, one of the water protons remains in the same layer (O3) while the second proton is located in the neighboring layer (O2) in sites with partial occupancies, as previously demonstrated by Jayaraman et al. (Solid State Ionics2004, 170, 25-32) using X-ray and neutron studies. Calculations of possible proton arrangements within the partially occupied layer of Ba2In2O4(OH)2 yield a set of low energy structures; GIPAW NMR calculations on these configurations yield 1H and 17O chemical shifts and peak intensity ratios, which are then used to help assign the experimental MAS NMR spectra. Three distinct 1H resonances in a 2:1:1 ratio are obtained experimentally, the most intense resonance being assigned to the proton in the O3 layer. The two weaker signals are due to O2 layer protons, one set hydrogen bonding to the O3 layer and the other hydrogen bonding alternately toward the O3 and O1 layers. 1H magnetization exchange experiments reveal that all three resonances originate from protons in the same crystallographic phase, the protons exchanging with each other above approximately 150 °C. Three distinct types of oxygen atoms are evident from the DFT GIPAW calculations bare oxygens (O), oxygens directly bonded to a proton (H-donor O), and oxygen ions that are hydrogen bonded to a proton (H-acceptor O). The 17O calculated shifts and quadrupolar parameters are used to assign the experimental spectra, the assignments being confirmed by 1H-17O double resonance experiments.

Introduction

Perovskites display a wide range of properties due to their ability to accommodate varying cations, substitutions, nonstoichiometry, and structural defects. They are consequently used in a widespread variety of applications. Of specific interest to this work is their application, when hydrated, as proton conductors at intermediate to high temperatures (above ca. 200 °C).[1,2] Initial studies by Iwahara et al. and Nowick et al. led to the discovery that perovskites such as LaYO3,[3] SrZrO3,[3] SrCeO3,[4,5] BaCeO3,[6,7] KTaO3,[8] Sr2GaNbO6[9] and Ba3CaNb2O9[10] have high proton conductivities under humid conditions. All of these materials require cation substitution in order to create oxygen vacancies and, upon hydration, the hydroxyl defects responsible for their proton conductivities. In contrast, Ba2In2O5 is an inherently oxygen deficient perovskite, and hence cation substitution is not required to allow water uptake.

Compensation of the Ba2+ and In3+ cation charges in Ba2In2O5 requires the removal of one-sixth of the O atoms in the perovskite structure, yielding a high intrinsic concentration of O vacancies along with both tetrahedrally and octahedrally coordinated In3+ ions. The vacancies order at room temperature into an orthorhombic structure, resulting in three crystallographically distinct O sites (Figure 1a). The labeling used here has O1 sites at the equatorial positions of In octahedra, O2 sites bridging In octahedra and tetrahedra and O3 sites within the In tetrahedral layer. We use this labeling scheme for both the dry and hydrated structures in contrast to some earlier work.[11,12] The structure type is named brownmillerite after the original Ca2FeAlO5 mineral which has a similar arrangement of O vacancies.[13] An understanding of the water uptake and protonic conduction processes in this system is of particular interest as the extremely large number of vacancies in the brownmillerite structure facilitates a level of hydration rarely possible in related materials.[14,15]

Figure 1

(a) Room temperature crystal structure of the brownmillerite Ba2In2O5 structure in space group Ibm2[13,21] with an ···OctTetOctTet′··· staggered O vacancy pattern. (Reproduced from reference (24) by permission of the PCCP Owner Societies.) (b) Room temperature crystal structure of tetragonal Ba2In2O4(OH)2 in space group P4/mbm,[11] showing the partially occupied H1 and fully occupied H2 positions. Schematic representations of the O3 layer of (c) Ba2In2O5 and (d) Ba2In2O4(OH)2. The interlayer Ba atoms in b, c, and d have been omitted for clarity. Sector filling of atoms in (b) denotes partial site occupancy.

A TGA study of Ba2In2O5 under wet air by Jayaraman et al.[11] found a maximum weight gain at around 200 °C, indicating the formation of the Ba2In2O4(OH)2 phase. Further heating results in weight reduction due to H2O loss, and a neutron powder diffraction study under controlled humid air by Yildirim et al.[16] showed that only Ba2In2O5 is present above 350 °C. Studies by Schober et al.[17−19] and by Yildirim et al.[16] indicate that there is a metastable, partially hydrated Ba2In2O5 phase (ca. 0.5 mol of H2O per formula unit) with a slight deviation from the brownmillerite structure with the Ima2 space group. Complete hydration of Ba2In2O5 results in a tetragonal structure with space group P4/mbm where the intrinsic O vacancies of Ba2In2O5 in the O3 layer are fully occupied by the water O atoms, yielding the composition Ba2In2O5.H2O (or Ba2In2O4(OH)2).[11,20] The 2c positions (in the O3 plane) are fully occupied by one of the water protons (H2) while the second proton (H1) partially occupies (12.5%) the 16l positions (in the O2 plane) according to the combined X-ray and neutron diffraction analyses of Jayaraman et al.[11] (Figure 1b). This model should be contrasted with that proposed in the earlier studies of Zhang and Smyth[22] where the water was believed to react with (O1) vacancies in the perovskite slabs, the vacancies resulting from p-doping and/or Frenkel defects created by occupancy of vacant O3 sites.

Early force field calculations of the energetics of defect formation by Fisher and Islam[20] questioned the role of the O1 vacancies proposed in the Zhang and Smyth model[22] and confirmed that the water oxygen atoms occupy the vacant O3 sites. They suggested, however, that the lowest energy site for the protons were the O1 sites. A subsequent DFT based, explicit full optimization of a large number of possible proton arrangements of the hydrated material Ba2In2O4(OH)2 (two formula units, i.e., 24 ions per unit cell) by Martinez et al.[12] identified a set of low energy structures with two protons (H2) in the O3 layer occupying half of the 4h (x, x̅ + 0.5, 0.5) positions, and two other protons (H1) in one of the two O2 layers occupying one-16th of the 32y positions. The 32y positions are defined by Martinez et al.[12] and are derived from the 4e positions of the O2 site in the P4/mbm space group by the eight displacements (±0.4 Å, ±0.4 Å, ±0.4 Å). Note that this 32y position is not found in the International Tables for Crystallography[23] for the P4/mbm space group (No. 127) but it is nevertheless useful for visualization of the proton positions.

Zhang and Smyth[22] reported protonic conductivity of Ba2In2O4(OH)2 under humid air, where three regions of protonic conduction were observed corresponding broadly to temperatures below 400 °C, between 400 and 925 °C, and above 925 °C. These authors proposed both Grotthuss (H-hopping) and vehicle (OH-hopping) mechanisms as being involved in protonic conductivity: the Grotthuss mechanism dominating at low temperature; the vehicle mechanism or a combination of vehicle and Grotthuss mechanisms dominating at elevated temperatures.[22]

A study of Ba2In2O4(OH)2 and of its Ti-doped derivatives[11] using 1H and 2H solid state NMR experiments under magic angle spinning (MAS) identified three distinct proton sites (giving rise to a higher frequency split resonance and a lower frequency broad resonance), while only two proton sites are anticipated based upon the tetragonal crystal structure obtained by Jayaraman et al.[11] (Figure 1b). The increased splitting of proton sublattices in the NMR data as compared with the number of crystallographic sites found by neutron diffraction was interpreted as a result of a further ordering of proton sites with respect to the average structure. The authors postulated that this arises from the actual unit cell being larger than the average unit cell of the P4/mbm space group used in the refinement of the diffraction data (a larger cell having been observed in their electron diffraction studies), NMR being sensitive enough to distinguish between variations of different ordering schemes for at least one of the two environments. However, no clear assignments of these three proton resonances were given.

Our previous paper on Ba2In2O5 focused on the dry material and used DFT methods to rationalize the 17O spectra seen in this system.[24] The current work examines hydrated Ba2In2O5 [i.e., Ba2In2O4(OH)2] using both current solid state 17O and 1H NMR spectroscopy techniques and DFT calculations. The DFT energetics and GIPAW calculations are first presented to describe the various configurations investigated in this work. We reproduce the general results of the DFT study by Martinez et al.,[12] although differences in the ground state structure and the energies of the other low energy structures are observed. First-principles periodic DFT NMR calculations within the gauge-including projector augmented wave (GIPAW) approach[25] are then performed to help interpret the NMR spectra. High magnetic field strengths are used to obtain NMR spectra of the hydrated material. This approach allows high resolution solid state NMR spectra of quadrupolar nuclei (such as 17O, spin I = 5/2) to be obtained. The individual 17O and 1H NMR shifts are assigned to specific oxygen and proton environments, the DFT results allowing us to assign the three 1H NMR signals seen at room temperature to specific local environments. We show that multiple low energy structural configurations are responsible for the experimental 1H NMR spectra. The 17O NMR spectra well reproduced with these multiple configurations, allowing us to assign the proton donor and acceptor oxygens. Variable temperature 1H NMR spectroscopy is then used to probe proton motion.

Materials and Methods

Experimental Methods

Sample Preparation

Ba2In2O5 was prepared according to a literature procedure.[24] Ba2In2O4(OH)2 was prepared by slow cooling of Ba2In2O5 (dried at 400 °C under a flow of dry N2 for 12 h) from 350 °C to room temperature (at a rate of 0.1 °C.min–1) under a flow of wet N2 gas. The water vapor pressure corresponds to ∼20–30 mbar PH (∼2.3% (w/v) H2O) and was controlled by bubbling N2 through water at room temperature.[17]17O enriched Ba2In2O4(OH)2 was synthesized by heating previously synthesized Ba2In2O4(OH)2 in a 50% 17O enriched O2 gas (Isotec, used as received) atmosphere with ∼2.3% (w/v) H2O (nonenriched) in a closed quartz tube, at 1000 °C for 24 h. During 17O enrichment with the closed quartz tube, the initial air inside the tube was removed by vacuum while concurrently freezing the H2O inside the tube with liquid N2.

Powder X-ray diffraction patterns were obtained on either a Panalytical Empyrean or Bruker D8-Focus X-ray diffractometer using Cu Kα radiation (λ = 1.5418 Å; Figure S1 in the Supporting Information). Thermogravimetric analyses (TGA) were performed on a Mettler Toledo TGA/SDTA851 thermobalance using an alumina crucible (Supporting Information Figure S2). All measurements were performed under flowing dry nitrogen, in a temperature range of 30–800 °C and at a heating rate of 10 °C·min–1. TGA showed that both Ba2In2O4(OH)2 and 17O enriched Ba2In2O4(OH)2 contain 1 mol of water per formula unit, as anticipated.

Solid State NMR Spectroscopy

Solid state 17O MAS NMR experiments on Ba2In2O4(OH)2 were performed on 9.4 T Bruker Avance 400 MHz and 16.4 T Bruker Avance III 700 MHz spectrometers using Bruker 2.5 mm HX probe and Bruker 3.2 mm HXY (in double resonance mode) probe, respectively. Unless otherwise stated, spectra were recorded using a solid ∼π/2 pulse length of 1 μs, corresponding to a radio frequency (rf) field amplitude of ∼83 kHz, and a MAS frequency of 30 kHz at 9.4 T, and a solid ∼π/2 pulse length of ∼1.7 μs, corresponding to a rf field amplitude of ∼50 kHz, and a MAS frequency of 20 kHz at 16.4 T. The 17O 3QMAS experiment was performed at 9.4 T with 128 t1 increments of 1320 scans each. Hard and soft pulses are performed at rf fields of 150 and ∼10 kHz, respectively. The 1H–17O cross-polarization (CP) and heteronuclear correlation (HETCOR)[26−29] spectra were obtained at 16.4 T with a 17O rf field amplitude of ∼50 kHz, while the 1H rf field amplitude was ramped to obtain maximum signal at ∼83 kHz. Small phase incremental alternation with 64 steps (SPINAL64)[30]1H heteronuclear decoupling was applied during the acquisition. Contact times for the CP experiments ranged between 5 and 5120 μs. All 17O NMR data were collected on a freshly 17O enriched Ba2In2O4(OH)2 sample packed in a ZrO2 rotor. A recycle delay of 10 s was used for all experiments, with 20480 scans for 17O Hahn-echo experiments and 48 t1 increments of 256 scans for the HETCOR spectra.

1H MAS NMR experiments were performed on a 16.4 T Bruker Avance III 700 MHz spectrometer equipped with a Bruker 4 mm HXY probe (in double resonance mode). One dimensional (1D) spectra were recorded under MAS using a rotor-synchronized spin echo sequence to suppress the proton background of the probe.[31] All 1H spectra were recorded at a rf field amplitude of 100 kHz and a MAS frequency of 12.5 kHz with recycle delays ranging from 4 to 60 s depending on the T1 relaxation times. Temperature calibration was performed using the 207Pb resonance of Pb(NO3)2 as a chemical shift thermometer.[32,33] The sample temperatures quoted subsequently have all been corrected and have an accuracy of ±10 °C. Additional fast MAS 1H NMR experiments were recorded on the same spectrometer with a Bruker 1.3 mm HX probe spinning at 60 kHz, using a rotor-synchronized spin echo sequence, an rf field amplitude of 115 kHz, and recycle delay of 8 s.

17O and 1H chemical shifts were externally referenced to water at 0.0 and 4.8 ppm, respectively, at 20 °C. NMR data were processed using TopSpin 3.0[34] and MatNMR,[35] the latter running within the MATLAB package. Simulations and deconvolutions were performed using the same software and SIMPSON.[36]

Computational Methods

Energetics and Configurations

The first-principles solid state electronic structure calculations used here are similar to those reported in our previous work on Ba2In2O5 and in related studies[37−43] and were all performed within the CASTEP code.[44] Structural models of Ba2In2O4(OH)2 were derived, as described later, from the experimental neutron diffraction model by Jayaraman et al.[11] following the approach of Martinez et al.[12] Full structural optimizations (both cell and atomic positions) of Ba2In2O4(OH)2 (two formula units) were performed in the absence of any symmetry operators (i.e., in space group P1), using a plane wave kinetic energy cutoff of 40 Ry and a linear spacing of 0.04 Å–1 or smaller for the reciprocal space sampling mesh, yielding Monkhorst–Pack meshes of dimension 6 × 6 × 4 for the Ba4In4O8(OH)4 supercell. Full details of all of these structures are presented in the Supporting Information (SI). The Perdew–Burke–Ernzerhof GGA-type exchange-correlation functional has been used throughout.[45] Convergence of total energy with respect to numerical parameters was estimated at 0.2 kJ·mol–1 per atom or better. Structural optimizations (both cell parameters and atomic positions) pursued until the energy difference, maximum atomic force, maximum atomic displacement, and maximum stress tensor component fell below tolerances of 1 × 10–6 eV, 1 × 10–3 eV·Å–1, 1 × 10–3 Å, and 5 × 10–3 GPa, respectively. The effect of decreasing these listed tolerances by a further order of magnitude was investigated, yielding only minimal changes in geometry and computed NMR parameters. To facilitate our exploration of the complex energy landscape, vibrational free energy contributions were not included in this analysis. However, given the relatively similar bonding sites being considered for the H, we assume that these contributions will largely cancel when comparing the relative energies. Previous work on a series of iron- and aluminum-oxyhydroxides calculated a less than 1.5 kJ/(mol of H) variation in vibrational free energies at room (25 °C) and synthesis (350 °C) temperatures for H across three compounds with both Fe and Al cations.[46,47] This error is as small or smaller than that found later between different DFT approaches, justifying exclusion of these contributions.

The hydration enthalpy of formation for the ground state configuration was calculated for the theoretical reaction of Ba2In2O5 (staggered configuration)[24] with one isolated water molecule H2O (calculated in a large unit cell with volume of 332 Å3). DFT total energies of geometry-optimized structures were used in this calculation. The experimental enthalpy of hydration is reported to be −0.65 ± 0.08 eV (∼−63 kJ·mol–1) with the Zhang–Smyth model and −0.76 eV (∼−74 kJ·mol–1) (trapped) and −0.3 eV (∼−29 kJ·mol–1) (untrapped) with the trapping model by Schober and Friedrich[18] at temperatures of 623–1073 K.

Boltzmann distribution weights at 350 °C were calculated according to weight = (exp(ΔE/RT))/(Σ exp(ΔE/RT)) where ΔE is the relative energy of a configuration from the ground state configuration, per mole of hydrogen. Structural models were visualized with the VESTA[48] and CrystalMaker packages.

NMR Calculations

Fully periodic calculations of NMR parameters within the gauge-including projector augmented wave (GIPAW) approach[25,49] have been performed using the CASTEP code, including determination of electric field gradient tensors and associated quadrupolar interaction parameters for 17O sites.[50] The NMR parameters are obtained from single point calculations within the optimized geometry, differing only from the prior optimization runs in that a larger basis set cutoff of 60 Ry was applied. The isotropic shielding was obtained as σiso = (σ + σ + σ)/3, where σ, σ, and σ are the principal components of the shielding tensor, ordered such that |σ – σiso| ≥ |σ – σiso| ≥ |σ – σiso|. The chemical shift δiso is then derived from the computed site shielding σiso by application of a shielding reference σref with the expression δiso = σref + mσiso. Both σref and the scaling factor m for 17O are taken unmodified from previous work by the current authors which obtained σref = 223.70 ± 3.03 ppm and m = −0.888 ± 0.014 with a mean absolute error (MAE) in computed shifts relative to experiment of 12.1 ppm across a range of phases.[37] Meanwhile, σref and m for 1H are determined from a fit of the results of NMR CASTEP calculations on Mg(OH)2 (σiso = 30.89 ppm; δiso = 0.5 ppm)[51] in combination with 55 different proton sites in four separate organic molecules as computed recently by Yates et al.,[52] Webber et al.,[53] and Sardo et al.,[54] yielding σref = 28.45 ± 0.51 ppm and m = −0.930 ± 0.020 with a MAE (defined similarly to those given earlier) of 0.29 ppm (SI Figure S3). We note that all but one of the proton sites used in deriving the shielding reference arise within organic molecules, and thus we might expect some discrepancy between experimental and calculated 1H chemical shifts in Ba2In2O4(OH)2 as discussed later. Chemical shift anisotropies and asymmetries are also computed, defined as σaniso = σ – (1/2)(σ – σ) and ηCS = (σ – σ)/(σ – σiso), respectively. The quadrupole coupling constant for 17O is obtained as CQ = eQV/h and the asymmetry as ηQ = (V – V)/V, where an ordering |V| ≥ |V| ≥ |V| of the principal components of the traceless electric field gradient tensor is assumed. The experimental value Q = −0.02558 barns has been used for the 17O nuclear electric quadrupole moment.[55]

Unless otherwise specified, all of the corresponding simulated 17O NMR spectra were obtained by simulation of each individual O site using SIMPSON[36] and summation of these spectra, resulting in the final spectra. No attempts were made to include 17O–1H dipolar couplings given that the spectra were acquired under MAS.

Results and Discussion

DFT Energetics and Configurations

The structural optimization of Ba2In2O4(OH)2 was performed with the same approach as that used for Ba2In2O5 in our previous work[24] taking the P4/mbm structure (Figure 1b) of Jayaraman et al. as the starting point.[11] The cell lengths of the P4/mbm cell are given by √2ap × √2ap × 2ap (where ap is the notional perovskite unit cell length).[19,56] Sixteen arrangements of protons are considered. All structures feature full occupancy of the O3 layer proton positions (2c site) but have various proton configurations in the O2 (16l site with fractional occupancy of one-eigth; 14 arrangements) and O1 (two arrangements) layers, O1 occupancy not being observed by Jayaraman et al.[11] but identified theoretically by Fisher and Islam.[20] This results in configurations that are similar to those found in the study by Martinez et al.[12] The configurations are then ranked in terms of the calculated total energies (Figures 2 and 3 and Table 1). As was also shown by Martinez et al.,[12] all configurations undergo significant relaxations from the average positions suggested by Jayaraman et al.[11] The O2 layer protons (H1) move off the 16l positions [with fractional coordinates (x, y, 0.25)] suggested by neutron diffraction[11] into the “32y” positions (with values close to x ± 0.07, y ± 0.07, 0.25 ± 0.04, e.g., with x = 0.10, y = 0.13) retaining the nomenclature previously used by Martinez et al.[12] The computationally relaxed ground state forms alternating layers of ···O2–O3–O2–O1··· oxygens, partially occupied, fully occupied, nonoccupied, and nonoccupied by protons, respectively (Figure 2b). Thus, the O3 layer O vacancies of Ba2In2O5 are fully occupied by a hydroxyl group (Figures 1c and 2d), while the second water proton occupies one of the two nearby O2 layers. However, only one of the O2 layers is protonated, while the other remains empty (Figure 2b). The optimized In–O3–In bond angles differ significantly from In–O1–In and In–O2–In, and thus O3 oxygen atoms are in a significantly different electronic environment (Table 1). Moreover, the bond length asymmetry of In–O2–In is substantial which may have implications for the 17O NMR spectra of this phase (Table 1). The optimized structures also indicate that hydrogen bonding constitutes the main interaction driving the formation of a range of distinct chemical environments for both protons and oxygen ions.

Figure 2

(a) Room temperature crystal structure of tetragonal Ba2In2O4(OH)2 in space group P4/mbm[11] showing full occupancy of the protons in the O3 layer (2c site) and partial occupancy in the O2 layer (16l site) (denoted, as in Figure 1b, by partially filled white balls). The interlayer Ba cations have been omitted for clarity. (b) Schematic representation of the 14 proton H1 configurations considered, differing in terms of the arrangement of protons in the O2 layers (16l site). Full and empty circles represent the O atoms and protons, respectively. Eight configurations (A–H) correspond to two-layer hydroxyl (TLH) forms; four configurations (I–L), to one-layer hydroxyl (OLH) forms; and two configurations (M–N), to one-layer water (OLW) forms. H1 protons were placed initially in the 16l positions with fractional occupancy of one-eighth determined by neutron diffraction,[11] and subsequently moved to the 32y positions on geometry optimization as in the previous study of Martinez et al.[12] The calculated energy per formula unit (containing two H atoms) of each configuration, relative to the ground state structure I, is also shown on the right-hand side of each configuration. A hydration enthalpy (ΔHh) of −79.3 kJ·mol–1 to form the ground state configuration I from dry Ba2In2O5 and a single molecule of H2O was calculated. The hydration enthalpies of other configurations can be achieved by adding the relative energies to −79.3 kJ·mol–1.

Figure 3

DFT optimized geometries of (a) configuration I (ground state), (b) configuration L, (c) configuration J, and (d) configuration K showing the O3 and O2 (z ≈ 0.25 and 0.75) layer protons. The interlayer Ba atoms have been omitted for clarity.

Table 1

Cell Constants (a, b, and c, Å; α, β, and γ, deg), In–O and O–H Bond Distances (Å) and In–O–In and O–H···H Bond Angles (deg) for O1, O2, and O3 Environments Obtained from Optimizations of the Initial Perturbed P1 Symmetry Ba4In4O8(HO)4 Cells, in the Lowest Energy I, J, K, and L Configurations (Figure 2b), As Compared with Corresponding Experimental and Calculated Literature Valuesa

	present calculations
	I struct (P1)	J struct (P1)	K struct (P1)	L struct (P1)	average of I, J, K, and L structures	calculations Martinez et al.[12]	experimental Jayaraman et al.[11] (P4/mbm)
cell
a (Å)	5.975	5.951	5.929	5.966	5.955(0.017)		5.915
b (Å)	5.992	6.029	5.984	5.979	5.996(0.020)		5.915
c (Å)	9.308	9.225	9.324	9.247	9.276(0.041)		8.999
α (deg)	93.3	87.9	93.7	89.7	91.2(2.4)		90
β (deg)	93.1	90.2	90.0	90.0	90.8(1.3)		90
γ (deg)	90.3	91.0	90.0	92.1	90.8(0.8)		90
In–O1–In
distance (Å)	2.120 (0.006)	2.138 (0.014)	2.112 (0.006)	2.160 (0.023)	2.133 (0.028)		2.092*
	2.132 (0.008)	2.162 (0.008)	2.121 (0.001)	2.162 (0.024)	2.144 (0.026)		2.092*
angle (deg)	169.1 (2.5)	164.0 (11.0)	168.5 (1.3)	160.4 (14.8)	165.5 (18.7)		178.4
In–O2–In
distance (Å)	2.274 (0.162)	2.251 (0.138)	2.299 (0.183)	2.213 (0.076)	2.259 (0.290)		2.192*
	2.411 (0.231)	2.391 (0.235)	2.378 (0.172)	2.428 (0.250)	2.402 (0.448)		2.307*
angle (deg)	173.9 (4.1)	169.6 (5.9)	175.6 (3.1)	170.9 (1.7)	172.5 (8.0)		180.0
In–O3–In
distance (Å)	2.231 (0.067)	2.245 (0.085)	2.250 (0.053)	2.253 (0.080)	2.244 (0.145)		2.201
	2.293 (0.108)	2.297 (0.128)	2.274 (0.064)	2.262 (0.087)	2.282 (0.199)		2.201
angle (deg)	139.0 (4.4)	138.1 (1.2)	137.5 (3.7)	139.2 (6.0)	138.4 (8.4)		143.6
O3–H···O
distance (Å)	1.011 (0.005)	1.013 (0.001)	1.022 (0.000)	1.018 (0.002)	1.016 (0.006)		1.404
	1.750 (0.035)	1.720 (0.020)	1.676 (0.000)	1.680 (0.037)	1.707 (0.055)	1.7	1.404
angle (deg)	173.3 (5.3)	175.3 (0.2)	177.8 (0.0)	176.7 (0.5)	175.8 (5.3)		180.0
O2–H···O
distance (Å)	0.993 (0.003)	0.983 (0.001)	0.995 (0.000)	0.982 (0.001)	0.988 (0.003)	1.00*	0.991 (0.000)*
	1.819 (0.005)	1.969 (0.005)	1.844 (0.000)	1.957 (0.014)	1.897 (0.016)	1.90	2.542 (0.051)
angle (deg)	153.5 (1.8)	151.0 (1.7)	154.5 (0.0)	150.0 (1.7)	152.2 (3.0)		116.4 (4.2)

Means and standard deviations (in parentheses) of the values are shown. For values marked with an asterisk (*), note that the O1 and O2 labels of the Jayaraman et al. structure are switched in order to match this work and the previous publication on the Ba2In2O5 phase.[24]

The configurations were grouped into three different types. In the two-formula-units cell of Ba4In4O8(OH)4, two out of four protons are always in the O3 layer (H2) and the other two are each either in a different O2 layer (H1) [two-layer hydroxyl (TLH), configurations A–H], in the same O2 layer (H1) [one-layer hydroxyl (OLH), configurations I–L], or present as one water molecule (two protons attached to one oxygen) per layer [one-layer water (OLW), configurations M and N] (Figure 2). OLH configuration I represents the ground state structure (with hydration enthalpy, ΔHh = −79.3 kJ·mol–1) in which the protons in the O2 layer (H1) point toward two different O3 acceptors. Configurations in which the protons are located within one O2 layer (H1) (OLH, Eref = 0–8.8 kJ·mol–1) are systematically lower in energy than the OLW (Eref 17.8 and 35.8 kJ·mol–1) and TLH (Eref = 10.2–48.8 kJ·mol–1) arrangements. Here all energies are given as Eref to denote their being referenced to the energy of the ground state structure I. All of the OLW configurations considered are unstable, configuration M relaxing to a mixed O1 and O2 layer protonation and configuration N to an OLH configuration. Structures where a proton is located in the O1 plane are noticeably higher in energy. For example, two configurations were also considered where the O3 layer is fully protonated and one O2 site and one O1 site are also protonated, the two structures differing in the relative orientations of the O1 and O2/O3 protons. Both of these structures are much higher in energy, occurring at 34.6 and 48.3 kJ·mol–1 above the ground state structure. The protons in both of these structures are located within the plane of the O1/In layers, in contrast with the structures proposed by Fisher and Islam[20] in which the O1–H bonds were oriented perpendicular to the plane.

Note that the previous study of Martinez suggested the present configuration L as the ground state structure (first low energy state), in which the O2 layer protons point toward the O1 oxygen site (Figures 2b and 3); a structure close to configuration I represented their first excited state.[12] The fact that the present and the Martinez et al. studies[12] disagree on the energy ordering of structures at the ∼6 kJ·mol–1 (or just ∼3 kJ/(mol of H)) level suggests that the DFT approach used cannot be regarded as yielding energies any more accurately than to within a few kJ/(mol of H). Thus, it is clear that we should consider more than just the ground state structure when analyzing our NMR data. Bielecki et al.,[57] in an inelastic neutron scattering (INS) study of hydrogen bonding in this material, suggested that the second lowest energy structure of Martinez et al.[12] should not exist due to its strong hydrogen bonds, which would result in higher frequency O–H wag modes than observed experimentally. However, our related structure (ground state structure I) has a longer hydrogen bond distance (1.819 Å; see Table 1) than that obtained by Martinez et al.[12] (1.7 Å). Hence, structure I is likely consistent with the lower frequency O–H wag modes observed experimentally and cannot be ruled out on the basis of the INS data.

The thermal energy kBTNA (or RT) at a typical hydration synthesis temperature (350 °C) is ∼5 kJ. Assuming fast cooling (equilibrium of atomic motion is not reached in the given time frame and temperature), this suggests that configurations with up to ∼5 kJ/(mol of H) may be present at significant concentrations at room temperature. We note that H is quite mobile in this system. A previous thermogravimetric study of hydrated Ba2In2O5 by Schober and Friedrich[18] suggests an activation energy of 0.3 eV (∼30 kJ·mol–1) for trapping effects in the hydration, as well as a hydrogen diffusion enthalpy (ΔH*) of 0.34 eV with diffusion coefficient prefactor (D0) of 0.34 × 10–5 cm2/s. These values all suggest that at least some H can readily diffuse at room temperature (as will be explored later by 1H NMR spectroscopy). However, we propose that either some of the H+ ions are significantly less mobile or that the cooperative motion of the H needed to reorder is inhibited, despite the good mobility of individual H+ ions. We therefore consider GIPAW calculations on the first four lowest energy structures I, J, K, and L, all of which are of OLH-type and have relative energies in the range of 0–8.8 kJ·mol–1 (or 0−4.4 kJ/(mol of H)), consistent with the possibility of thermal excitations being trapped in the system and the uncertainty in DFT energies and neglected vibrational energies mentioned earlier. We also limit ourselves to these four structures as they are clearly distinct in character from the next highest energy structures C, A, and B [at 10.2, 12.5, and 13.0 kJ·mol–1, respectively (or ∼6 kJ/(mol of H))], which all have protons in both O2 layers (z = 0.25 and 0.75).

Assuming all of the structures occur with a Boltzmann distribution established at 350 °C, the relative amounts of each configuration are given by the Boltzmann weights 0.25, 0.11, 0.11, and 0.15 for I, J, K, and L, respectively, and 0.09, 0.08, 0.07, 0.06, and 0.05 for the configurations C, A, B, D, and N, respectively; the remaining seven configurations have weights of less than 0.01 contributing total weights of approximately 0.02. We discuss the preceding assumptions in the context of the NMR experiments.

Experimental and GIPAW Calculations Results

X-ray Powder Diffraction

The X-ray powder diffraction pattern of Ba2In2O4(OH)2 samples and the 17O enriched counterpart prepared in this study are consistent with previous reports[11,19] (Figure S1 in the Supporting Information) and indicate that the structure has tetragonal P4/mbm symmetry.[11]

17O NMR Spectroscopy

The 1D 17O MAS NMR spectrum of 17O enriched Ba2In2O4(OH)2 obtained at 9.4 T under conditions where the line shape distortion is minimal (i.e., with short pulse length)[58] shows a complicated pattern characteristic of multiple overlapping 17O resonances (Figure 4). Four sites could be resolved in the 17O 3QMAS experiment (Figure 5), which could be satisfactorily fit with the NMR parameters given in Table 2. Fitting of the 1D 17O MAS NMR spectra with these parameters yields an intensity ratio of 4:1:6:4 for the resonances with chemical shifts of 188, 173, 152, and 97 ppm, respectively (Figure 4). In addition to these resonances there is a fifth peak at 220 ppm which nutates at the same frequency as water (i.e., it must be associated with a very small or zero quadrupolar coupling) and is tentatively attributed to either a possible H2O molecule on the surface of the material as also discussed in our previous paper,[24] or to an impurity phase. The 17O signals in the 3QMAS show a broadening along the +1 direction (positive slope diagonal), which is attributed to a distribution of chemical shifts arising from a distribution of different local environments.

Figure 4

17O MAS NMR spectra of 17O enriched Ba2In2O4(OH)2 obtained at 9.4 and 16.4 T. Experimental spectra are shown with full lines and total best-fit simulations in black dashed lines. The individual site components are shown as dashed lines in red (site A, O1), blue (site B, acceptor O1), orange (site C, combination of acceptor O2 and acceptor O3), pink (site D, donor O2 and donor O3), and green (small quadrupole coupling impurity site) (see Table 2). Assignments of the O sites are made by comparison with parameters derived from DFT GIPAW calculations (see Figure 6).

Figure 5

Two-dimensional 17O 3QMAS spectrum of 17O enriched Ba2In2O4(OH)2 obtained at 9.4 T. Right: experimental cross-sections (full lines) obtained at δ1 = 140 (pink), 174 (orange), 192 (blue), and 207 ppm (red) along with best-fit simulations (dashed lines) using the parameters given in Table 2. The weaker high frequency component in the δ1 = 140 (pink) slice results from an overlap with the more intense resonances with larger δ1 values (as explained in the main text) and has thus not been included in the line-shape simulation.

Table 2

Experimental and Calculated 1H and 17O Isotropic Shift (δ1, ppm), Isotropic Chemical Shift (δiso, ppm), Quadrupolar Coupling Constant (CQ, MHz), and Quadrupolar Asymmetry Parameter (ηQ) for Ba2In2O4(OH)2

structure	nucleus	environmenta	δ1 (ppm)	δiso (ppm)	CQ (MHz)	ηQb	Nc
Experimentald
Ba2In2O4 (OH)2	17O	O-site A (O1)a	140	188(4)	4.5(2)	0.0(1)	0.25
	17O	O-site B (H-acc. O1)a	174	173(4)	4.1(2)	0.7(1)	0.0625
	17O	O-site C (H-acc. O2 and O3)a	192	152(4)	4.2(2)	0.5(1)	0.375
	17O	O-site D (H-donor O2 and O3)a	207	97(4)	4.8(2)	0.7(1)	0.25
	17O	O-site E (no match)		223(4)	1.0(2)	0.0(1)	0.0625
	1H	H-site A (H2, O3 plane)a		7.3(1)			0.5
	1H	H-site B (H1, O2 plane I,K)a		3.3(1)			0.25
	1H	H-site C (H1, O2 plane J,L)a		1.7(1)			0.25
Calculatedb
I	17O	O1	200.6 (11.1)	170.4 (7.0)	–5.0	0.2	0.33
	17O	donor O2	168.7 (5.2)	114.4 (3.3)	–6.0	0.8	0.167
	17O	O2	193.4 (1.1)	159.6 (0.7)	–5.3	0.1	0.167
	17O	donor O3	136.9 (1.6)	94.5 (1.0)	5.3	0.8	0.167
	17O	acceptor O3	180.0 (19.7)	156.4 (12.4)	–4.3	0.5	0.167
	1H	H2, O3 plane		8.5 (0.7)			0.5
	1H	H1, O2 plane		5.3 (0.1)			0.5
J	17O	O1	217.7 (11.3)	185.1 (7.1)	–5.2	0.2	0.25
	17O	acceptor O1	204.6 (0.0)	175.4 (0.0)	–4.4	0.8	0.083
	17O	donor O2	167.0 (10.2)	103.6 (6.4)	–6.9	0.6	0.167
	17O	O2	204.2 (9.8)	169.1 (6.2)	–5.4	0.1	0.167
	17O	donor O3	149.6 (3.2)	107.0 (2.0)	5.1	0.9	0.167
	17O	acceptor O3	185.7 (0.5)	158.5 (0.3)	–4.4	0.7	0.167
	1H	H2, O3 plane		8.8 (0.3)			0.5
	1H	H1, O2 plane		4.0 (0.2)			0.5
K	17O	O1	197.5 (1.7)	168.5 (1.1)	–4.9	0.2	0.33
	17O	donor O2	171.2 (0.0)	117.1 (0.0)	–6.2	0.7	0.167
	17O	O2	200.2 (0.0)	166.5 (0.0)	–5.3	0.0	0.167
	17O	donor O3	146.8 (0.0)	103.5 (0.0)	5.7	0.6	0.167
	17O	acceptor O3	169.8 (0.0)	151.9 (0.0)	–3.8	0.4	0.167
	1H	H2, O3 plane		9.7 (0.0)			0.5
	1H	H1, O2 plane		5.1 (0.0)			0.5
L	17O	O1	223.8 (19.1)	188.6 (12.0)	–5.4	0.2	0.25
	17O	acceptor O1	225.4 (0.0)	196.9 (0.0)	4.5	0.7	0.083
	17O	donor O2	166.7 (1.3)	105.1 (0.8)	–6.8	0.6	0.167
	17O	O2	207.2 (5.6)	170.8 (3.5)	–5.5	0.1	0.167
	17O	donor O3	142.8 (11.9)	98.8 (7.5)	5.4	0.8	0.167
	17O	acceptor O3	178.1 (16.4)	154.0 (10.3)	–4.0	0.8	0.167
	1H	H2, O3 plane		9.5 (0.4)			0.5
	1H	H1, O2 plane		3.8 (0.1)			0.5

An asterisk denotes the most plausible O and H environments from four hydrated models. Standard deviations are also given in parentheses; deviations of quadrupolar parameters CQ and ηQ are less than 0.01 and are therefore omitted.

Obtained from the averaged DFT calculated NMR parameters of the four low energy structures I, J, K, and L. The calculated values of δ1 are obtained with δ1 = (27δiso – 10δ2)/17 with δ2 = δiso – (3/500)((CQ2(1 + ηQ2/3))/ν02) for 17O (I = 5/2) (see ref (58)), the errors arising from the range of δiso values.

Molar fraction of the site in the structure specified.

Obtained from the 3QMAS and 1H–17O HETCOR experiments. δiso was determined from the center of gravity of each peak in F2 (δ2) and F1 (δ1) as δiso = (10/27)δ2 + (17/27)δ1 and CQ from the fit of the δ2 cross-sections through the ridge line shapes.

Figure 6

(a) Simulation of the GIPAW calculated 17O NMR spectra of the 12 sublattice O sites occurring in the lowest energy optimized structure I of Ba2In2O4(OH)2. All of the spectra were simulated at 9.4 T. (b) Comparison of the experimental 17O NMR spectra of 17O enriched Ba2In2O4(OH)2 (black lines) and the sum of the simulation of the GIPAW calculated 17O NMR spectra (dashed red lines) of all O sites of the four lower energy structures Ba2In2O4(OH)2 (I, J, K and L, combined with relative weights of 0.25, 0.11, 0.11 and 0.15) at 9.4 and 16.4 T.

The 17O isotropic chemical shifts, δiso, obtained by GIPAW calculations of the lower energy I, J, K, and L structures of Ba2In2O4(OH)2 are also given in Table 2 and are found to span a wide range of values for each O sublattice O1, O2, and O3 (Figure 6). Nevertheless, we may divide the sites into three general types of oxygen atoms, namely, bare oxygens (O), oxygens directly bonded to a proton (H-donor O), and oxygen ions that are hydrogen bonded to a proton (H-acceptor O).

More specifically, we note that O1, H-acceptor O1, O2, H-donor O2, H-donor O3, and H-acceptor O3 local environments occur in all of the low energy structures I, J, K, and L (see Table 2). A range of CQ are also observed, where CQ for the H-acceptor O sites ranges from 3.8 to 4.5 MHz, the H-donor O sites from 5.3 to 6.9 MHz, and the bare O sites from 4.9 to 5.5 MHz. Two distinct ranges for the quadrupolar asymmetry parameter ηQ are obtained: those for bare O sites are approximately 0.1, while those for H-donor and -acceptor O sites are approximately 0.7. Taking the ground state structure I as an example, the O1 (sites 1–4 in Figure 6a, δiso = 170.4 ppm), O2 (sites 5 and 8 in Figure 6a, δiso = 159.6 ppm), and H-acceptor O3 (sites 9 and 12 in Figure 6a, δiso = 156.4 ppm) all contribute to the high frequency resonances in the experimental spectrum (mean, 164 ppm), while the H-donor O2 (sites 6 and 7 in Figure 6a, δiso = 114.4 ppm) and H-donor O3 (sites 10 and 11 in Figure 6a, δiso = 94.5 ppm) contribute to the lower frequency resonances (mean, 104 ppm) (see Table 2).

1H–17O double resonance experiments probe the 1H–17O heteronuclear dipolar coupling (and hence the 1H–17O heteronuclear distance) and were therefore carried out to investigate the spatial proximities between the 17O sites and protons. The 17O cross-polarization (CP) spectrum of 17O enriched Ba2In2O4(OH)2 recorded with a very short contact time (τCP = 40 μs) is given in SI Figure S4b and reveals a single resonance corresponding to the low frequency signal at δiso = 97 ppm, confirming its assignment to H-donor oxygens. Additionally, a two-dimensional 1H–17O heteronuclear correlation (HETCOR) spectrum, also recorded with τCP = 40 μs, shows that this 97 ppm resonance correlates with all of the 1H signals (see SI Figure S4a and section 3.2.3). The 17O CP spectrum obtained with a longer contact time of 2.5 ms (SI Figure S4b) still does not contain the signals observed at high frequencies (δiso = 188 and 173 ppm) in the 17O MAS spectrum (Figure 4), indicating that the O sites that give rise to these resonances are not in close proximity to the protons (or that the associated protons are too mobile). Instead a weak resonance at δiso = 152 ppm is observed which is tentatively assigned to an H-acceptor oxygen. The 17O CP kinetics curve (SI Figure S5) shows the slower CP dynamics associated with the 152 ppm compared to the 97 ppm resonance, consistent with our assignment of the 152 ppm resonance to a H-acceptor O site.

Assuming that all of the low energy configurations, I, J, K, and L contribute to the spectrum with weights from the Bolztmann distribution at 350 °C (given by 0.25, 0.11, 0.11, and 0.15, respectively), we combined all of the oxygen resonances obtained from the GIPAW calculations to yield the simulated spectra shown in Figure 6b. A peak intensity ratio of 4.3:1:6.3:4.3 (from high to low frequency) is derived, which is remarkably close to the experimentally derived 4:1:6:4 ratio. On the basis of this reasonable agreement, the experimentally observed high frequency resonance at δiso = ∼188 ppm is, therefore, assigned to the bare O1 sites; the other high frequency weaker resonance at 173 ppm, to the acceptor O1 sites; the next resonance at δiso = ∼152 ppm, to the bare O2 sites and H-acceptor O3 sites; and finally the lowest frequency resonance at δiso = ∼97 ppm, to the H-donor O2 and H-donor O3 sites, in agreement with the 17O CP experiments, all of these sites corresponding to the 48 O sites in the four Ba4In4O8(OH)4 configurations, I, J, K, and L (Figure 3 and Table 2). In summary, the present first-principles calculations permit the assignment of the 17O MAS NMR spectrum of Ba2In2O5(OH)2, yielding chemical shifts and quadrupolar parameters in reasonable agreement with the experimental trends, albeit with some minor differences in the chemical shifts, quadrupolar parameters, and relative resonance intensities. A likely source of error in the intensities is the assumption that only structures I, J, K, and L contribute to the experimental spectra in proportions governed by their relative energies and the synthesis temperature. However, the assignment of the “high” and “low” shift peaks in the 17O MAS NMR experimental spectra is consistent; i.e., we expect nondonor oxygen resonances to occur in the high frequency region and a donor oxygen to occur in the low frequency region. Overall, while relative intensities of the experimental peaks may vary, their assignment to these chemical environments is sound.

1H NMR Spectroscpy

The room temperature 1H MAS NMR spectrum of Ba2In2O4(OH)2 obtained at 16.4 T clearly shows three distinct proton sites at shifts of 7.3, 3.3, and 1.7 ppm in a 2:1:1 intensity ratio (Figure 7). 1H/2H NMR resonances in approximately the same chemical shift range were observed by Jayaraman et al.[11] in their study of this material; however, these authors observed a splitting of the higher frequency resonance (of approximately 1–2 ppm), a broader resonance being observed at lower frequencies (at approximately 2.5 ppm) and the high (split) and low frequency resonances occurring with intensity ratios of 1:1. No assignment was given in that study. The three resonances observed in our study are fairly broad, and we assign this to inhomogeneous broadening (i.e., a chemical shift distribution) rather than to the effects of strong homogeneous dipolar interactions between protons, as similar 1H line widths were obtained in spectra acquired under fast MAS conditions (SI Figure S6).[59]

Figure 7

1H NMR spectrum of Ba2In2O4(OH)2: (a) experimental data, (b) simulation of combined GIPAW calculated parameters of structures I and L, (c) all structures with Eref < 20 kJ·mol–1, and (d) structures I, J, K, and L. The blue dashed line with double arrows indicates the 2–6 ppm region corresponding to the H1 protons in the O2 plane, and the red dashed line with double arrows indicates the 7–11 ppm region corresponding to the H2 protons in the O3 plane. Simulations are carried with a 0.8 ppm Lorentzian line broadening summing the spectra using the respective 350 °C Boltzmann weights for structures I and L in b; I, J, K, L, C, A, B, D, and N in c; and I, J, K and L in d.

In order to assign all three resonances observed in the experimental 1H MAS NMR spectrum of Ba2In2O4(OH)2, we computed the 1H site shielding tensors in the proton arrangements discussed earlier (Table 2 and Figure 7 and SI Figure S7). A simulation of the 1H spectrum using the calculated NMR parameters (SI Figure S7) of the lowest energy structure I contains three peaks with a 1:1:2 ratio (∼9, ∼8, and ∼5 ppm), providing a poor match with the experimental spectrum (Figure 7a). Thus, in order to generate a spectrum that is closer to the experimental one, other low energy structures were also considered. Inclusion of the first high energy configuration (L; with Boltzmann weights of 0.25 and 0.11 for I and L) improves the fit to the spectrum in the low part per million region but worsens it in the higher frequency region (Figure 7b). When all of the low energy configurations, with respective weights, are considered (Eref < 20 kJ·mol–1), we do not observe a narrow peak at the high shift region in the spectrum (Figure 7c). Concentrating on NMR parameters obtained in the four most stable configurations (structures I, J, K, and L), the calculations yield O3 layer proton resonances at δiso of 7.8–9.3 ppm (due to configuration I), 8.6–9.1 (configuration J), 9.7 (configuration K), and 9.1–9.9 ppm (configuration L) (Figure 7d; spectrum shown with 350 °C Boltzmann weights). In some proportion, all of these O3 layer 1H signals are likely to contribute to the broad signal (Δν1/2 = 800 Hz (∼1.5 ppm on 16.4 T magnet)) observed experimentally at approximately 7.3 ppm for Ba2In2O4(OH)2 (Figure 7a). Two distinct sets of shifts are observed, at 5.2 ± 0.2 ppm from the O2 layer protons (H1) in structures I and K and at 3.9 ± 0.2 ppm arising from structures J and L (Figure 7, Table 2), which are reasonably close to the two experimental resonances observed at 3.3 and 1.7 ppm.

Of note, the spectrum simulated with structure I resembles that obtained by Jayaraman et al.,[11] predicting the small splitting at higher frequency and the absence of a splitting at lower frequency. This may suggest that the sample prepared by these authors is more ordered than ours (i.e., contains fewer proton configurations), with a structure that is closer to that of the thermodynamic ground state.

The apparent offset in δiso between the calculated and experimental values for all of the structures and sites is relatively constant at approximately 2 ppm, a value larger than the 1H calculated standard deviation of 0.29 ppm (see Computational Methods and SI Figure S3) and may be due to a systematic error in the 1H shielding reference, arising out of the use of primarily organic phases in deriving σref. More work is required to obtain a reliable set of reference parameters for protons in inorganic materials, preferably considering hydrated oxides and simple hydrous phases. In addition, proton motion and, likely, systematic deviation in calculated to experimental lattice constants may also play a role in the 1H chemical shift. The fact that the protons are involved in chains of hydrogen bonding in the Ba2In2O4(OH)2 system means that the 1H chemical shift will be very sensitive to lattice dilation/contraction. Nonetheless, the relative chemical shifts and relative intensities of the calculated resonances are in good agreement with experiment. Of note, the results show that configurations in which the O2 protons are involved in hydrogen bonds with both the O3 and O1 sublattices must be included in order to account for the split H1 (O2) resonance observed in our sample.

It is evident from the H···O (hydrogen bond) distances in Table 1 and the 1H chemical shifts in Table 2 that longer hydrogen bonds result in a lower 1H chemical shift. A study by Yesinowski et al.[60] on a series of hydrated silicates yielded an inverse correlation between donor O to acceptor O distance and 1H chemical shift characterized by the following equation.Applying this equation to the O–O distances from the I, J, K, and L structures, we calculate 1H shifts of 7.4 and 9.7 ppm for O2 and O3 layer protons, respectively. Slightly better fits to experiment were obtained by using the empirical equations derived by Xue and Kanzaki for a wider range of hydrous silicates and related inorganic materials (yielding 5.5 and 8.0 ppm for the O2 and O3 layer protons).[61] These simple calculations provide trends and allow us to distinguish the O3 and O2 layer protons from each other, but do not provide the ability to further separate the two types of O2 layer protons. The predicted shifts are noticeably larger than those observed experimentally, particularly for the O2 coordinated protons, most likely due the very different systems studied here than used to derive the empirical correlations.

Variable temperature 1H solid state MAS NMR experiments up to 195 °C show that all of the protons in Ba2In2O4(OH)2 are mobile on the NMR time scale, the resonances first broadening and then completely coalescing at around 150 °C, yielding a single site with an isotropic chemical shift of 4.4 ppm. Such a coalescence process occurs when the proton-hopping frequency k equals πΔν/√2 (where Δν is the frequency separation between the peaks) indicating that the hopping rate between the two O2 environments (1.7 and 3.3 ppm) must be greater than k ∼ 2.2 kHz, while that between the O1 and O2 sites is ∼7 kHz (where shifts of 7.3 and 2.5 ppm are used in this calculation, 2.5 ppm being the predicted shift following coalescence of the 1.7 and 3.3 ppm resonances). As the temperature is increased further, the peak height of the new resonance increases as the line width narrows, due to an increase in proton motion. A weak resonance at 1.7 ppm persists even at 195 °C, this being assigned to both structures L (containing O2–H2 protons pointing to the O1 (bare) oxygens) and J (containing O2–H2 protons alternatively pointing to both O1 and O3 sites J). We suggest the O2–H1···O1 protons are more strongly trapped, while the O2–H1···O3 protons undergo more rapid exchange with the O3–H (H2) protons.

Two dimensional exchange NMR experiments were performed to explore motion on a longer time scale (Figure 9). Both chemical exchange and magnetization exchange (due to spin-diffusion) will result in cross-peaks situated off the 1H vs 1H diagonal. At 42 °C, cross-peaks are observed between the two distinct protons assigned to the O2 layer (H1; sites at 1.7 and 3.3 ppm) at a mixing time of 1 ms, indicating that these sites occur within a single particle. The cross-peaks are most likely generated from a combination of slow motion and spin diffusion. Longer mixing times reveal cross-peaks between all of the resonances, most likely as a result of spin diffusion. The observation of H1–H1 and H1–H2 cross-peaks at short mixing times (0.1 and 1 ms, respectively) at 80 °C is ascribed to the onset of motion, since the spin diffusion rates are unlikely to increase with temperature. At a temperature of 150 °C, all protons exchange rapidly at a rate in excess of 10 kHz, in agreement with the variable temperature 1H spectra (Figure 8).

Figure 9

Variable temperature two-dimensional 1H chemical exchange experiments as a function of mixing time, obtained at a MAS rate of 20 kHz and at 16.4 T. Only the isotropic region is shown. Single pulse 1D 1H spectra (from Figure 8) are shown above the 2D plots.

Figure 8

Variable temperature 1H MAS NMR spectra of Ba2In2O4(OH)2 obtained at a MAS rate of 20 kHz and at 16.4 T. (a) Full spectral width showing the isotropic region and the spinning sideband manifold marked with asterisks. (b) Magnified view highlighting the coalescence of the 1.7 and 3.3 ppm resonances and coalescence of all the resonances above 150 °C.

The relatively rapid exchange between different proton sites at room temperature may seem inconsistent with the presence of multiple proton environments associated with excited states. However, the existence of some mobile protons does not necessarily imply that all of the protons can reorder into the unique ground state. Local orderings, even ones that allow significant H transport, could still be effectively locked in place as a cooperative ordering transition to the ground state could be inhibited, or some of the H could be immobile. The 2D spectra indicate that some of the proton configurations are present within the same particle. We indicated earlier that, within the errors of the DFT, no unique ground state structure emerges (ours differing from that of Martinez et al.[12]). Thus, it is likely that the lower energy structures reflect the different possible H-bonding configurations within one particle and that the four lowest structures identified in this study represent the more probable configurations. A future study treating the H ordering with a more complete thermodynamics and kinetic model would be valuable, but this is beyond the scope of this current work.

Conclusions

In summary, we have performed a comprehensive structural analysis of the hydrated form of brownmillerite, Ba2In2O4(OH)2, using multinuclear solid state NMR spectroscopy in combination with solid state DFT calculations. We reproduce the structural analysis of a large number of possible proton positions of Martinez et al.,[12] identifying multiple configurations that may exist concurrently at room temperature. Three different proton sites were observed by 1H MAS NMR spectroscopy, which were found to exchange at 150 °C on the NMR time scale with hopping rates in excess of 10 kHz. Assignment of these resonances make use of extensive total energy DFT calculations of a wide range of proton configurations, which yielded four chemically similar low energy configurations, the simulated 1H GIPAW NMR spectra of which are in relatively good agreement with the experimental data. The three resonances can be assigned as follows: the high frequency shift corresponds to O3 layer protons (H2), while the two lower frequency shifts arise due to two types of configurations of O2 layer protons (H1) with shorter and longer H···O (hydrogen bond) distances and a difference in O–H···O angles. Distinct O2 layer proton (H1) configurations are observed in four low energy structures that perhaps coexist at room temperature. The 17O NMR spectrum of Ba2In2O4(OH)2 is dominated by four O sites, which can be rationalized by the DFT GIPAW calculations, which reveal that H-donor oxygens appear at lower shift while the nonhydroxyl oxygens and H-acceptor O are visible at higher shifts. We suggest that all the lower energy proton sites should be considered in any proposed proton conduction mechanism within the Ba2In2O4(OH)2 phase.

The joint experimental and theoretical approach presented in this work can be readily applied to investigate H-bonding and local structure in other hydrated perovskites. The current work suggests that multiple H-bonding motifs are likely present in related structures, the relative energies of these strongly affecting proton trapping and conductivity.