Cation Distribution and Anion Transport in the La3Ga5–xGe1+xO14+0.5x Langasite Structure

Exploration of compositional disorder using conventional diffraction-based techniques is challenging for systems containing isoelectronic ions possessing similar coherent neutron scattering lengths. Here, we show that a multinuclear solid-state Nuclear Magnetic Resonance (NMR) approach provides compelling insight into the Ga3+/Ge4+ cation distribution and oxygen anion transport in a family of solid electrolytes with langasite structure and La3Ga5–xGe1+xO14+0.5x composition. Ultrahigh field 71Ga Magic Angle Spinning (MAS) NMR experiments acquired at 35.2 T offer striking resolution enhancement, thereby enabling clear detection of Ga sites in different coordination environments. Three-connected GaO4, four-connected GaO4 and GaO6 polyhedra are probed for the parent La3Ga5GeO14 structure, while one additional spectral feature corresponding to the key (Ga,Ge)2O8 structural unit which forms to accommodate the interstitial oxide ions is detected for the Ge4+-doped La3Ga3.5Ge2.5O14.75 phase. The complex spectral line shapes observed in the MAS NMR spectra are reproduced very accurately by the NMR parameters computed for a symmetry-adapted configurational ensemble that comprehensively models site disorder. This approach further reveals a Ga3+/Ge4+ distribution across all Ga/Ge sites that is controlled by a kinetically governed cation diffusion process. Variable temperature 17O MAS NMR experiments up to 700 °C importantly indicate that the presence of interstitial oxide ions triggers chemical exchange between all oxygen sites, thereby enabling atomic-scale understanding of the anion diffusion mechanism underpinning the transport properties of these materials.


INTRODUCTION
Solid Oxide Fuel Cells (SOFCs) are promising all-solid-state power generation devices enabling the electrochemical conversion of chemical energy into electric energy and represent one of the key technologies which are being considered to address the rapidly increasing global energy demand.One of the main advantages of SOFCs compared to other types of fuel cells is the ability of this device to operate on a wide range of fuels, including but not limited to hydrogen. 1 Nevertheless, the further development of SOFCs relies on the reduction of their operating temperature to intermediate (650 °C−800 °C) or even lower (below 650 °C) ranges, 1 and research effort has been undertaken to identify suitable solid electrolytes that exhibit elevated oxide ion conductivity at these temperatures. 2he presence of chemical defects in the lattice is associated with increased ionic conductivity, and oxide materials are commonly doped with aliovalent cations to form oxygen vacancies or interstitials that lead to enhanced transport properties.−10 The La 3 Ga 5 GeO 14 langasite structure (general formula A 3 BC 3 D 2 O 14 ) consists of layers of three-connected DO 4 tetrahedra distinguished by the presence of one nonbridging oxide ion and four-connected CO 4 tetrahedra containing four bridging oxide ions (Figure 1a and 1c).These layers are connected to form a three-dimensional framework by BO 6 octahedra which bridge four-connected CO 4 tetrahedra belonging to adjacent layers.The void space between the tetrahedral layers is occupied by eight-coordinate La 3+ cations (A sites) located in hexagonal channels formed by the edges of one BO 6 octahedron, three four-connected CO 4 tetrahedra and two three-connected DO 4 tetrahedra.−13 Contrasting results were obtained in further work on a multicell model of La 3 Ga 5 GeO 14 , wherein it was concluded that Ge 4+ cations partially occupy both B and D sites. 14nterstitial oxide ions introduced in the lattice upon Ge 4+doping to form La 3 Ga 5−x Ge 1+x O 14+0.5x are accommodated in a (Ga,Ge) 2 O 8 structural unit consisting of a pair of edge-sharing five-coordinate Ga/Ge square pyramidal sites connected via one interstitial oxide ion O4 and one framework oxide ion which is displaced from its original O2 position to the O2b site (Figure 1b, 1d, and 1e). 7It has been reported that B, C, and D sites in La 3 Ga 5−x Ge 1+x O 14+0.5x with x > 0 exhibit Ga 3+ /Ge 4+ mixed site occupancies. 7mportantly, the maximum amount of excess oxygen that can be incorporated in the La 3 Ga 5−x Ge 1+x O 14+0.5x langasite structure (i.e., up to 5.4 mol % in La 3 Ga 3.5 Ge 2.5 O 14.75 with respect to the amount of oxygen in La 3 Ga 5 GeO 14 ) exceeds the concentration of interstitial defects in the related tetragonal La 1+y Sr 1−y Ga 3 O 7+0.5y melilite phase with highest concentration of dopant (i.e., up to 3.8 mol % in La 1.54 Sr 0.46 Ga 3 O 7.27 versus LaSrGa 3 O 7 while preserving tetragonal structure).Nevertheless, a comparison of the transport properties in La 3 Ga 5−x Ge 1+x O 14+0.5x and La 1+y Sr 1−y Ga 3 O 7+0.5y at 500 °C shows that the oxide ion conductivity is 2 orders of magnitude higher in La 1.54 Sr 0.46 Ga 3 O 7.27 than in the most highly conductive langasite phase. 7Furthermore, the ionic conductivity as a function of excess oxygen concentration increases less significantly in the langasites than in the melilites and is observed to decrease in La 3 Ga 5−x Ge 1+x O 14+0.5x with x > 0.45. 7hese observations suggest that the incorporation of interstitial oxide ions in La 3 Ga 5−x Ge 1+x O 14+0.5x leads to a substantial structural rearrangement, and the formation of (Ga,Ge) 2 O 8 units effectively traps the interstitial ions, thereby limiting the enhancement in ionic conductivity occurring upon Ge 4+ doping. 7lthough the ionic conductivity in La 3 Ga 5−x Ge 1+x O 14+0.5x is lower than that measured for state-of-the-art solid oxide electrolytes, the langasite family offers great flexibility with regards to the range of cations that can occupy the lattice sites. 15The distribution of cations among the distinct polyhedra can be tuned to reduce the structural rearrangements which occur upon Ge 4+ doping and limit the excessive stabilization of the interstitial defects in the (Ga,Ge) 2 O 8 units.This motivates further examination of the compositional disorder in the site-disordered langasite family and highlights the need to investigate Ga 3+ /Ge 4+ cation distribution in the Ge 4+ -doped phase to identify possible relations between the local structure and the oxide ion conduction mechanism.1][12][13][14]16,17 Solid-state Nuclear Magnetic Resonance (NMR) spectroscopy is element-specific, thus offering an alternative approach to investigate compositional disorder in La 3 Ga 5−x Ge 1+x O 14+0.5x .
Solid-state NMR spectroscopy is highly sensitive to changes in the local environment around the nuclei being probed, making this technique ideal to access the local structure in La 3 Ga 5−x Ge 1+x O 14+0.5x . 17−24 Importantly, oxide ion conductors can be readily 17 O enriched via a post synthetic exchange procedure based on high  7 O, Ga, Ge and La atoms are shown in red, green, blue and gray.Three-connected DO 4 tetrahedra (red) with one nonbridging oxide ion O1 are connected to three four-connected CO 4 tetrahedra (gray) via O2 ions, and BO 6 octahedra (blue) bridge four-connected CO 4 tetrahedra belonging to adjacent layers via O3 ions.In La 3 Ga 5 GeO 14 , B and C sites are fully occupied by Ga 3+ cations, while the D site exhibits Ga 3+ /Ge 4+ mixed site occupancy, as reported in refs 11−13.In La 3 Ga 3.5 Ge 2.5 O 14.75 , Ga 3+ /Ge 4+ cations are distributed across the B, C, and D sites. 7(e) An example of (Ga,Ge) 2 O 8 structural unit which forms upon Ge 4+ doping.Ga 3+ /Ge 4+ cations are randomly distributed within the (Ga,Ge) 2 O 8 unit.
temperature annealing with 17 O enriched O 2 gas to overcome the limitations of the low natural abundance (0.037%) of the only NMR active isotope of oxygen, 17 O. 25 71 Ga (spin quantum number = I 3 2 ) MAS NMR spectroscopy is well suited for structural elucidation by virtue of the established relation between the 71 Ga isotropic chemical shift and the Ga coordination environment 26−28 but requires high external magnetic field strengths and rapid sample spinning rates owing to relatively large nuclear electric quadrupole moment of 71 Ga (NMR properties listed in Table S1 in the Supporting I n f o r m a t i o n ) .P r e v i o u s 7 1 G a N M R w o r k o n La 3 Ga 5−x Ge 1+x O 14+0.5x at 20 T and under MAS rates ν r = 65 kHz revealed the presence of GaB octahedra and GaD tetrahedra in the parent phase, while one additional 71 Ga signal tentatively assigned to five-coordinate GaD centers was detected upon Ge 4+ -doping. 7Nevertheless, the relative area of the signals in the 71 Ga MAS NMR spectrum of La 3 Ga 5 GeO 14 diverges from the 1:1 ratio expected based on the percentage of GaB and GaD sites in the average unit cell, and GaC polyhedra were not detected owing to the large quadrupolar coupling constant C Q predicted for this site. 7,11139La (spin quantum number = I 7 2 ) is another NMR-active nucleus suitable to examine structural details, 26 although 139 La NMR spectroscopy is less frequently exploited due to the typically large 139 La quadrupolar coupling constants that lead to extremely broad line shapes (Table S1).
−31 The computational prediction of NMR parameters for site-disordered solids such as La 3 Ga 5−x Ge 1+x O 14+0.5x is challenged by the presence of fractional site occupancies in the average unit cell that are not effectively modeled in a single configuration.Such systems require computations to be carried out for a configurational ensemble, and the Site Occupancy Disorder (SOD) method, 32 recently introduced to the field of NMR, 33 enables the identification of all symmetrically inequivalent configurations for a given average unit cell.
Here, we explore the local structure and coordination environments of the ions in the undoped La 3 Ga 5 GeO 14 and Ge 4+ -doped La 3 Ga 3.5 Ge 2.5 O 14.75 langasites and tackle the compositional disorder of the Ga 3+ and Ge 4+ cations using solid-state NMR spectroscopy, thereby addressing the debated results obtained with diffraction-based methodologies.The inherent resolution limitations of half-integer quadrupolar nuclear spins such as 71 Ga and 139 La are overcome by performing the NMR experiments at ultrahigh magnetic fields with the Series Connected Hybrid (SCH) magnet operating at 35.2 T, thereby enabling the acquisition of highly resolved NMR spectra. 34The Ga 3+ /Ge 4+ cation distribution is subsequently captured by comparing the experimental NMR data with the NMR spectra simulated for an ensemble of configurations which effectively models the possible distributions of the ions in the average unit cell.The results are exploited to interpret the evolution of the 17 O MAS NMR spectra as a function of temperature up to 700 °C, establishing that the oxide ion diffusion involves all oxide ions and is mediated by the concerted rotation of the (Ga,Ge)O n units.

EXPERIMENTAL SECTION
2.1.Materials Synthesis.La 3 Ga 5 GeO 14 was synthesized using a standard procedure based on annealing at 1300 °C of a mixture of the binary oxide starting materials (La 2 O 3 , Ga 2 O 3 , and GeO 2 ), and Ge 4+doped La 3 Ga 3.5 Ge 2.5 O 14.75 was prepared using a sol−gel method which expands the chemical space and enables the incorporation of large concentrations of dopant (x ≥ 0.30) while preventing the formation of secondary phases, as described in detail elsewhere. 7To enable the acquisition of 17 O MAS NMR experiments, the samples were 17 O enriched using a standard method based on hightemperature, postsynthetic exchange with 17 O 2 gas. 25In particular, the samples were heated at 750 °C for 24 h in an atmosphere of 60% 17 O enriched O 2 gas (Isotec) using heating and cooling rates of 5 K min −1 .The 17 O level is expected to be ∼9% in La 3 Ga 5 GeO 14 and ∼8% in La 3 Ga 3.5 Ge 2.5 O 14.75 based on mass balance analysis between the langasite sample and the 17 O enriched O 2 gas used in the enrichment procedure.This assumes an equal mole fraction of the oxygen isotopes in the 17 O enriched sample and in the 17 O enriched atmosphere at the end of the labeling process.
2.2.Solid-State NMR Experiments.2.2.1. 71Ga MAS NMR Experiments. 71Ga MAS NMR experiments at 23.5 T were performed on a Bruker Avance Neo NMR spectrometer equipped with a double resonance 1.3 mm HX MAS probe tuned to X = 71 Ga at a Larmor frequency ν 0 = 305.11MHz.One-dimensional spectra of La 3 Ga 5 GeO 14 and La 3 Ga 3.5 Ge 2.5 O 14.75 were acquired under MAS rates ν r of 60 kHz with the rotor-synchronized Hahn echo pulse sequence, using Central Transition (CT)-selective pulses at a radio frequency (rf) field amplitude of 20 kHz and recycle delays of 2 s. 71 Ga MAS NMR spectra at 23.5 T are reported relative to the 71 Ga signal of a 1 M solution of Ga(NO 3 ) 3 in H 2 O at 0 ppm, also used to measure nutation frequencies.
Ultrahigh field 71 Ga MAS NMR experiments were performed on the 36 T SCH magnet available at the National High Magnetic Field Laboratory (NHMFL) NHMFL in Tallahassee (Florida, USA) operating at 35.2 T. 34 A Bruker Avance Neo console and a solidstate 1.3 mm HXY MAS NMR probe tuned to 71 Ga at ν 0 = 457.48MHz were used to acquire the data, and samples were spun at ν r = 60 kHz.One-dimensional 71 Ga MAS NMR spectra were acquired with the rotor-synchronized Quadrupolar Carr−Purcell−Meiboom−Gill (QCPMG) pulse sequence 35−38 combined with an initial Wideband Uniform Rate Smooth Truncation (WURST) shaped pulse 39 for signal enhancement.The duration of the excitation and refocusing pulses was set to experimentally optimized values, respectively 1.25 and 2.5 μs for La 3 Ga 5 GeO 14 and 1.5 and 3 μs for La 3 Ga 3.5 Ge 2.5 O 14.75 .The 1 ms WURST pulse was placed at an experimentally optimized frequency offset of 600 kHz, and the power of the frequency sweep was set to approximately 30 kHz.The envelope of the QCPMG spikelet pattern was obtained via Fourier transform of the coadded echoes.Truncating the QCPMG echo train did not lead do changes in the relative area of the signals, thereby revealing that the different Ga sites exhibit similar transverse relaxation time constants T 2 ′ and confirming that the QCPMG spectra are quantitative.
5][36][37]39,40 The QMAT spectrum was recorded using CT-selective π/2 and π pulses of length equal to 1.25 and 2.5 μs, respectively. A totl of 16 t 1 increments were recorded, and the experimental conditions of the initial WURST pulse were kept the same as those in the corresponding one-dimensional spectrum.All 71 Ga MAS NMR spectra recorded at 35.2 T were obtained with recycle delays suitable to obtain quantitative spectra (i.e., 2 s for La 3 Ga 5 GeO 14 and 0.4 s for La 3 Ga 3.5 Ge 2.5 O 14.75 ).NMR experiments at 35.2 T were externally calibrated to the 1 H chemical shift of alanine at 1.46 ppm (indirectly referenced to tetramethylsilane at 0 ppm) using the IUPAC frequency ratios.41 2.2.2.73 Ge NMR Experiments.73 Ge NMR experiments were performed on a 20 T Bruker Neo Avance spectrometer equipped with a low-gamma 4 mm HX probe tuned to X = 73 Ge at ν 0 = 29.66MHz.
One-dimensional NMR spectra were acquired under static conditions using the WURST-QCPMG and Double Frequency Sweeps (DFS) DFS spin echo pulse sequences, 42−44 and the experimental parameters were varied in an attempt to detect signal.The unfavorable NMR properties of 73 Ge (see Table S1) precluded the observation of 73 Ge resonances.
2.2.3. 17O MAS NMR Experiments.Room-temperature 17 O MAS NMR spectra at 20 T and under a MAS rate ν r = 22 kHz were recorded using the experimental settings already detailed in previous work. 7 17  VT MAS NMR experiments were performed on a 20 T Bruker Neo Avance spectrometer equipped with a 7 mm laser-heated single resonance X MAS probe 45 tuned to X = 17 O at a Larmor frequency ν 0 = 115.28MHz and under ν r = 4 kHz.17 O MAS NMR experiments in the 19 °C−300 °C temperature range were additionally performed using a 4 mm high temperature double resonance HX MAS probe spinning at ν r = 10 kHz for La 3 Ga 5 Ge 17 O 14 and ν r = 12.5 kHz for La 3 Ga 3.5 Ge 2.5 17 O 14.75 owing to the enhanced spectral resolution attainable with this probe.Unless otherwise specified, 17 O VT NMR spectra were recorded with the pulse-acquire sequence using experimentally optimized 30°flip angle pulses at a rf field amplitude of either 20 kHz (7 mm probe) or 42 kHz (4 mm probe) and suitable recycle delays to obtain quantitative data.17 O MAS NMR spectra of La 3 Ga 5 Ge 17 O 14 above 300 °C were acquired with experimentally optimized 90°flip angle pulses and recycle delays of approximately 1.3 times the spin−lattice relaxation time constant in the laboratory frame (T 1 ) owing to the long T 1 values determined for La 3 Ga 5 Ge 17 O 14 and the need for an increased number of transients to obtain a satisfactory signal-to-noise ratio when using the laserheated 7 mm probe as opposed to the 4 mm probe.17 O T 1 values were determined from saturation recovery experiments performed with a saturation block consisting of a train of 90°fl ip angle pulses (100 for La 3 Ga 5 GeO 14 and from 100 at room temperature to 10 at 700 °C for La 3 Ga 3.5 Ge 2.5 O 14.75 ) with an rf field amplitude of 20 kHz separated by short, rotor-asynchronized (where applicable) time intervals δ (1.125 ms for La 3 Ga 5 GeO 14 and from 0.875 ms at room temperature to 60 μs at 700 °C for La 3 Ga 3.5 Ge 2.5 O 14.75 ) to ensure complete saturation of the spin system at each temperature and considering the probe safety. 46Suitable delays τ (e.g., at room temperature from 1 ms to 110 s for La 3 Ga 5 GeO 14 and from 0.6 ms to 22 s for La 3 Ga 3.5 Ge 2.5 O 14.75 ) were chosen at each temperature to fully capture the magnetization buildup.This build-up as a function of τ was fitted to the stretch exponential function shown in eq 1 to account for (i) the presence of overlapping signals which results in a distribution of T 1 relaxation time constants and (ii) the temperature gradient across the sample where A(τ) and A ∞ are the normalized area of the 17 O overlapping signals respectively at delay τ and infinity, T 1 * is the characteristic time constant, and c is the stretch exponent.c was constrained to the 0−1 range and was observed to take values between 0.472 and 0.994.Equation 2 enabled the determination of the mean T 1 value from T 1 * and c where Γ is the gamma function.Since the τ values were not equally spaced, weights ω yielded from kernel density estimation were included in the fitting procedure as in eq 3 where s represents the sum of the squared error which was minimized in the fit.
Temperature calibrations were performed using standard procedures based on the detection of the 207 Pb chemical shift thermometer of Pb(NO 3 ) 2 47 for the 4 mm high temperature HX MAS probe and the 79 Br chemical shift thermometer of KBr 48 for the 7 mm laserheated X MAS probe.Variations in temperature across the rotor of up to ∼50 °C at 700 °C for the 7 mm probe and ∼7 °C at 280 °C for the 4 mm probe were detected from the corresponding temperature calibrations.All 17 O experiments were acquired on 17 O enriched samples and are referenced to the 17 O signal of H 2 O at 0 ppm, also used to measure nutation frequencies.
2.2.4. 139La NMR and MAS NMR Experiments. 139La NMR experiments were performed at 35.2 T using the SCH magnet available at the NHMFL.A 1.3 mm HXY MAS NMR probe tuned to X = 139 La at ν 0 = 211.95MHz was used throughout.All 139 La NMR spectra were acquired using recycle delays of 0.5 s for La 3 Ga 5 GeO 14 and 70 ms for La 3 Ga 3.5 Ge 2.5 O 14.75 .One-dimensional NMR spectra were recorded with the QCPMG pulse sequence 35−37 both under static conditions and spinning the samples at ν r = 60 kHz.Excitation and refocusing pulses of duration equal to 1.5 μs were used.QCPMG spectra recorded under MAS conditions were rotor-synchronized.Two-dimensional 139 La QMAT spectra were recorded while spinning the samples at a MAS rate of 60 kHz and using the QCPMG acquisition mode for signal enhancement.CT-selective π/2 and π pulses of 1 and 2 μs in duration were used, and 16 t 1 increments were recorded. 139La spectra were externally calibrated to the 1 H chemical shift of alanine at 1.46 ppm (indirectly referenced to tetramethylsilane at 0 ppm) using the IUPAC frequency ratios. 41.3.Computations.The complete set of symmetrically inequivalent configurations (i.e., not interconvertible via isometric transformations) from a La 3 Ga 5 GeO 14 unit cell and a La 3 Ga 4 Ge 2 O 14.5 1 × 1 × 2 supercell (on the basis of the cell parameters of the La 3 Ga 4 Ge 2 O 14.5 average unit cell obtained from diffraction measurements) 7 was generated using the SOD method. 32A total of three symmetrically inequivalent configurations was obtained for La 3 Ga 5 GeO 14 assuming Ga 3+ /Ge 4+ mixed site occupancies for the three-connected DO 4 tetrahedra, four-connected CO 4 tetrahedra, and BO 6 octahedra.495 symmetrically inequivalent configurations were generated for La 3 Ga 4 Ge 2 O 14.5 taking into account additional mixed site occupancy of the Ga 3+ /Ge 4+ sites in the (Ga,Ge) 2 O 8 structural unit and the partial site occupancy of the O2, O2b, and O4 sites depicted in Figure 1b and 1d, while forcing the oxide ion originally located in the O2 site of the undoped phase to occupy the O2b site in the presence of an interstitial oxide ion O4 nearby.The La 3 Ga 4 Ge 2 O 14.5 1 × 1 × 2 supercell expansion contains one (Ga,Ge) 2 O 8 structural unit and resembles the La 3 Ga 3.5 Ge 2.5 O 14.75 experimental composition, while maintaining the computational cost of the calculations relatively low as opposed to the La 3 Ga 3.5 Ge 2.5 O 14.75 composition which would require larger supercell expansions.
All calculations were performed using plane-wave DFT 29 with periodic boundary conditions, as implemented in the CASTEP (version 20.11) code. 49On-the-fly generated ultrasoft pseudopotentials 50 and the Perdew−Burke−Ernzerhof (PBE) exchange-correlation functional 51 were used.The plane-wave cutoff energy was set to 850 eV, and the Brillouin zone was sampled with either a 2 × 2 × 3 Monkhorst−Pack k-point grid for La 3 Ga 5 GeO 14 or a 2 × 2 × 2 Monkhorst−Pack k-point grid for La 3 Ga 4 Ge 2 O 14.5 . 52A further increase in the cutoff energy and k-point density resulted in changes in energy smaller than 1 meV atom −1 .The Zeroth-Order Regular Approximation (ZORA) approach 53 was selected to account for relativistic effects, and the electronic energy was optimized selfconsistently with a threshold of 1 × 10 −9 eV atom −1 .The atomic coordinates and unit cell parameters of all symmetrically inequivalent configurations were optimized setting the convergence threshold for the maximum energy to 1 × 10 −5 eV atom −1 , for the maximum force to 3 × 10 −2 eV Å −1 , for the maximum stress to 3 × 10 −2 GPa and for the maximum displacement to 1 × 10 −3 Å.During the geometry optimization step, five La 3 Ga 4 Ge 2 O 14.5 configurations exhibited thermodynamic instability by converging to one of the other structural models already contained in the symmetry-adapted configurational ensemble and were therefore excluded, leaving a total of 490 configurations.
The NMR parameters were computed for the optimized geometries using the GIPAW approach 30,31 and applying the same parameters as in the geometry optimizations.The absolute shielding tensor σ in the crystal frame generated in the calculations can be expressed in terms of the isotropic chemical shielding To facilitate comparison between the experimental and computational data, the isotropic and anisotropic chemical shifts, respectively δ iso,cs and δ aniso,cs , were determined from the computed σ iso,cs and σ aniso,cs terms using δ iso,cs = σ ref + m σ iso,cs and δ aniso,cs = m σ aniso,cs with σ ref  S1).

Numerical Simulations.
NMR spectra for the different symmetry-adapted configurational ensembles were simulated from the computed NMR parameters (i.e., δ iso,cs , reduced anisotropic shift δ aniso,red,cs = δ zz − δ iso,cs , η, C Q , and η Q ) using the SIMPSON package. 57AS NMR spectra were simulated with the gcompute method, while the direct method was used for NMR spectra under static conditions.NMR spectra simulated for each structural model in the symmetry-adapted configurational ensemble were multiplied by a statistical weight and subsequently summed to obtain the total NMR spectrum.The statistical weights take into account the configurational degeneracy of the structural model and, in some cases, its relative energy.

RESULTS AND DISCUSSION
3.1.Configurational Disorder.Figure 2 shows the 71 Ga MAS NMR spectra of La 3 Ga 5 GeO 14 and La 3 Ga 3.5 Ge 2.5 O 14.75 recorded at 23.5 T and 35.2 T while spinning the samples at ν r = 60 kHz.Ultrahigh field NMR spectroscopy is particularly critical for the detection of half-integer quadrupolar nuclei such as 71 Ga because strong quadrupolar interactions result in a fourth-rank second-order quadrupolar broadening of the NMR resonances (in Hz) that remains even under MAS but is inversely proportional to the external magnetic field strength B 0 .While the 71 Ga MAS NMR spectra at 23.5 T are dominated by broad, overlapped resonances and show limited gain in resolution with respect to data acquired at 20 T under ν r = 65 kHz, 7 further increasing the external magnetic field strength by 50% considerably enhances the spectral resolution, thereby enabling the detection of several distinct 71 Ga resonances at 35.2 T for both La 3 Ga 5 GeO 14 and La 3 Ga 3.5 Ge 2.5 O 14.75 , as previously observed for the related La 1+x Sr 1−x Ga 3 O 7+0.5x melilite family of fast oxide ion conductors. 58ne relatively sharp signal at a shift δ of ∼5 ppm and one broader spectral feature in the 190 ppm−270 ppm region are clearly observed for La 3 Ga 5 GeO 14 .Although overshadowed by partial overlap with the spinning sideband manifold, one additional resonance that is unresolved at lower magnetic field strengths is detected at intermediate shifts 50 ppm < δ < 150 ppm.In order to prevent the interference of the spinning sidebands, a two-dimensional 71 Ga QMAT experiment was performed for La 3 Ga 5 GeO 14 at 35.2 T (Figure 3). 40The QMAT pulse sequence enables complete separation of the spinning sidebands by their order, as shown in Figure 3a.The "infinite MAS" representation of the QMAT data presented in Figure 3b shows the spectrum without spinning sidebands as if acquired under infinitely high MAS rates, and the observed spectral line shape is clear evidence for the presence of three distinct signals in the 71 Ga MAS NMR data of La 3 Ga 5 GeO 14 .The 71 Ga MAS NMR spectrum of La 3 Ga 3.5 Ge 2.5 O 14.75 acquired at 35.2 T, albeit presenting spectral features resembling those observed for La 3 Ga 5 GeO 14 , exhibits broader resonances, reflective of the enhanced structural disorder in the Ge 4+doped langasite phase.Furthermore, it is importantly observed that the relative area of the signal at 50 ppm < δ < 150 ppm increases upon Ge 4+ -doping of La 3 Ga 5 GeO 14 to form La 3 Ga 3.5 Ge 2.5 O 14.75 .0][31][32]59 Restricting the Ga 3+ /Ge 4+ mixed site disorder to the D site in La 3 Ga 5 GeO 14 , 11 only one symmetrically inequivalent configuration is generated starting from a 1 × 1 × 1 average unit cell (Configuration 3 in Figure 4a). Th computed 71 Ga NMR parameters are on the order of those previously predicted for a La 24 Ga 40 Ge 8 O 112 supercell corresponding to the La 3 Ga 5 GeO 14 structure, with GaB, GaC, and GaD sites presenting increasing isotropic chemical shifts from ∼18 ppm to ∼253 ppm and GaC exhibiting an extremely large quadrupolar coupling constants of ∼24.6 MHz (Figure S1).7 The 71 Ga MAS NMR spectrum of La 3 Ga 5 GeO 14 simulated at 35.2 T from the computed NMR parameters and shown in Figure 4e suggests that the relatively sharp resonance at δ of ∼5 ppm and the broader signal in the 190 ppm−270 ppm region correspond to octahedral GaB and tetrahedral GaD sites, respectively, in agreement with the relation between Ga coordination environment and 71 Ga isotropic chemical shift which indicates that higher coordination numbers yield lower δ iso,cs values.26−28 Nevertheless, poor agreement between the experimental and simulated spectra is clearly observed, especially for the signal detected in the 50 ppm−150 ppm spectral region which is assigned to GaC (Figure 4b,e).The particularly large C Q constant computed for GaC leads to a severe anisotropic broadening which is considerably greater than that observed experimentally for the GaC signal.Furthermore, the relative area of the GaD signal in the experimental spectrum is larger than that observed for GaB, in contrast with the 1:1 ratio in the computational data obtained for an average unit cell containing equal percentage of GaB and GaD sites.
To address the discrepancies between the experimental and simulated spectra, La 3 Ga 5 GeO 14 was modeled with additional Ga 3+ /Ge 4+ mixed site occupancy for the B and C sites, as proposed for the Ge 4+ -doped phase based on neutron powder diffraction. 7The three symmetrically inequivalent configurations generated with the SOD approach from the 1 × 1 × 1 average unit cell assuming chemical disorder for B, C, and D sites are shown in Figure 4a, where Configuration 3 corresponds to the structural model previously generated when constraining Ge 4+ cations to D sites.The NMR parameters were computed for the three symmetrically inequivalent configurations and are shown in Figure S1.While the isotropic chemical shifts are largely unaffected by the Ga 3+ /Ge 4+ cation distribution, the C Q constants computed for GaC sites in Configurations 1 and 2 (15 MHz−20 MHz) are significantly smaller than those obtained for Configuration 3 (∼24.6MHz).Furthermore, the six-coordinate GaB site exhibits larger C Q values in Configuration 2 than in Configuration 3, as expected based on the presence of chemical disorder in the nearby four-coordinate GaC sites for Configuration 2 that results in enhanced structural distortion and electrostatic asymmetry at the octahedral sites.
The simulated 71 Ga MAS NMR spectrum of La 3 Ga 5 GeO 14 was obtained as a sum of the spectra computed for each individual configuration weighted by a statistical term which accounts for (i) the degeneracy and (ii) the relative energy of the configurations, the latter expressed by a temperaturedependent Boltzmann factor (e E k T / B ).The set of statistical weights were determined both at room temperature, assuming that the configurational ensemble is in thermodynamic equilibrium, and in the high temperature limit e 1 , implying an energetically unbiased distribution of the Ga 3+ / Ge 4+ cations in the disordered material (Table 1). 71Ga MAS NMR spectra simulated using statistical weights determined at ambient and infinite temperatures are shown in Figure 4d and Figure 4c, respectively.First, closer agreement between the experimental and computed 71 Ga MAS NMR spectra of La 3 Ga 5 GeO 14 is obtained if Ge 4+ cations are not constrained to the D site (Configuration 3 in Figure 4a), indicating that B, C, and D sites exhibit Ga 3+ /Ge 4+ mixed site disorder.Second, the predicted spectrum more accurately resembles the experimental data in the high-temperature limit, especially for the GaB resonance owing to the larger statistical weight determined at infinite temperature for the energetically disfavored Configuration 3.This is an indication that the Ga 3+ /Ge 4+ cation distribution is controlled by the degeneracy of the configurations rather than by their relative energy, implying the occurrence of a kinetically governed cation diffusion process that does not lead to thermodynamic equilibrium.
The La 3 Ga 4 Ge 2 O 14.5 composition was chosen to model the Ge 4+ -doped langasite phase because the La 3 Ga 3.5 Ge 2.5 O 14.75 composition requires a larger supercell expansion that would lead to a prohibitive increase in the computational cost of the calculations.The computed NMR spectrum of La 3 Ga 4 Ge 2 O 14.5 can be compared with the experimental NMR spectrum of La 3 Ga 3.5 Ge 2.5 O 14.75 owing to the subtle differences in the 17 O and 71 Ga MAS NMR spectra of La 3 Ga 4 Ge 2 O 14.5 and La 3 Ga 3.5 Ge 2.5 O 14.75 previously observed. 7A symmetry-adapted configurational ensemble consisting of 495 configurations was generated from a 1 × 1 × 2 super cell corresponding to the La 3 Ga 4 Ge 2 O 14.5 structure (additional details are provided in the Experimental Section).The large amount of structural models arises from the presence of several sites with mixed or partial site occupancy in the average unit cell of the Ge 4+doped langasite phase, including Ga 3+ /Ge 4+ chemical disorder for B, C, D and five-coordinate C V and D V sites and partial site occupancy for the interstitial site O4. 7he 71 Ga NMR parameters computed for La 3 Ga 4 Ge 2 O 14.5 are reported in Figure 5a.Although distributed over a wider range due to the presence of enhanced disorder in the Ge 4+doped phase, the NMR parameters computed for the four-and six-coordinate Ga sites in La 3 Ga 4 Ge 2 O 14.5 are of comparable magnitude to those obtained for La 3 Ga 5 GeO 14 .Additional sites are present in La 3 Ga 4 Ge 2 O 14.5 due to the presence of two edgesharing, square-based pyramids C V O 5 and D V O 5 which form from the original tetrahedra to accommodate the interstitial oxide ion O4 (Figure 1b). 7 71Ga isotropic chemical shifts predicted for GaD V reveal that the incremented coordination number of this site leads to a reduction in the corresponding δ iso,cs value.On the other hand, the isotropic chemical shift computed for five-coordinate GaC V is on the same order of magnitude as δ iso,cs obtained for four-coordinate GaC.While a clear distinction between the 71 Ga isotropic chemical shifts predicted for GaC V and GaD V is observed, the range of 71 Ga quadrupolar coupling constants predicted for these sites very significantly overlap (Figure 5a).
The 71 Ga MAS NMR spectrum of La 3 Ga 4 Ge 2 O 14.5 was simulated from the NMR parameters in the high temperature limit (Figure 5b), and the computed data are in outstanding agreement with the experimental spectra.Figure 5b indicates that the increase in the relative area of the signal at 50 ppm < δ < 150 ppm experimentally observed upon Ge 4+ -doping originates from the presence of resonances assigned to five-  The three configurations are shown in Figure 4a.The weights consider the configurational degeneracy and an additional temperature-dependent Boltzmann factor (e E k T / B ) determined at 298 K and in the high temperature limit T → ∞ (corresponding to e 1

E k T / B
).The temperature dependence of the statistical weights arises from the fact that the configurations possess distinct energies.coordinate GaC V O 5 and GaD V O 5 sites that overlap with the GaC signal.These results confirm that the interstitial ions in La 3 Ga 5−x Ge 1+x O 14+0.5x are hosted in the (Ga,Ge) 2 O 8 unit consisting of edge-sharing five-coordinate Ga/Ge square pyramidal sites.While structural models with all B sites occupied by Ge 4+ cations exhibit a dominant Boltzmann factor at ambient temperature due to their favorable relative energy, the six-coordinate 71 Ga signal is clearly resolved in the experimental spectrum.In the high temperature limit, however, the symmetry-adapted configurational ensemble accurately models the experimental data, implying that the synthesis procedure leads to kinetically controlled Ga 3+ /Ge 4+ cation distribution (i.e., the Ga 3+ /Ge 4+ cation distribution does not reach thermodynamic equilibrium when the samples are cooled to ambient conditions after the synthesis procedure), similarly to what was observed for the parent structure.
Due to the sensitivity of this isotope to the local environment, 73 Ge ( = I 9 2 ) NMR spectroscopy is, in principle, ideal to confirm the presence of chemical disorder in the B, C, and D sites for both La 3 Ga 5 GeO 14 and La 3 Ga 3.5 Ge 2.5 O 14.75 . 60evertheless, this only NMR active isotope of Ge possesses a large nuclear electric quadrupole moment of (−0.196 ± 0.001) × 10 −28 m 2 and suffers from a low natural abundance of 7.76% and a low Larmor frequency of 29.66 MHz at 20 T (resulting in a receptivity R ( 13 C) of only 1 order of magnitude higher than that of 17 O at natural abundance, see Table S1).We attempted to record one-dimensional 73 Ge NMR spectra for La 3 Ga 5 GeO 14 and La 3 Ga 3.5 Ge 2.5 O 14.75 at 20 T under static conditions, but the unfavorable NMR properties of 73 Ge combined with the small Ge content in the samples and the large computed C Q values (Figures S2 and S3) prevented the detection of any signal with the available equipment. 17O is another key isotope with the potential of providing compelling insight into the local environment of the langasite structure, as demonstrated by the 17 O MAS NMR spectra recorded at room temperature in previous work. 7The 17 O NMR parameters predicted for La 3 Ga 5 GeO 14 and La 3 Ga 4 Ge 2 O 14.5 using the computational approach described above are presented in Figure 6a and 6b, respectively.The 17 O isotropic shifts predicted for the different O sites in La 3 Ga 5 GeO 14 are scattered over distinct ranges.In particular, O2 ions connecting CO 4 and DO 4 tetrahedra and O3 ions bridging BO 6 and CO 4 polyhedra exhibit the lowest and highest δ iso,cs values, respectively.Interestingly, the NMR parameters calculated for the apical O1 ions bound to D sites are strongly affected by the nature of the cation occupying this site, with O1 bound to GeD exhibiting lower isotropic chemical shifts and higher quadrupolar coupling constants than O1 connected to GaD.The 17 O MAS NMR spectrum simulated from the NMR parameters in the high temperature limit is in excellent agreement with the experimental spectrum previously acquired at 20 T and under MAS rates of 22 kHz (Figure 6c). 7Comparison between the experimental and computational data reveals that the spectral feature detected at approximately 200 ppm corresponds to significantly overlapped O3 and O1−GaD resonances, while the signal at lower shifts arises from O2 and O1−GeD sites.
The NMR parameters computed for La 3 Ga 4 Ge 2 O 14.5 are of comparable magnitude to those predicted for La 3 Ga 5 GeO 14 , but they are distributed over a wider range, as observed for the 71 Ga NMR parameters (Figure 6b).The pair of five-coordinate C V and D V sites that forms upon Ge 4+ doping is connected by one interstitial oxide ion O4 and one largely displaced framework oxide ion O2b which give rise to a strongly deshielded signal with higher δ iso,cs and lower C Q values compared to those obtained for the other oxygen sites.Furthermore, it is observed that O1 ions connected to D V sites show higher δ iso,cs and lower C Q values than those bound to four-coordinate D sites.Similarly, O2 sites in the (Ga,Ge) 2 O 8 structural unit present overall higher δ iso,cs and slightly lower C Q than those obtained for O2 oxygens bridging two four-  71 Ga isotropic chemical shifts and quadrupolar coupling constants computed with the GIPAW approach 30,31 for a set of symmetrically inequivalent configurations generated with the SOD program 32 starting from a 1 × 1 × 2 supercell of La 3 Ga 4 Ge 2 O 14.5 .The NMR parameters are grouped according to their site, with sixcoordinate GaB, four-coordinate GaC, four-coordinate GaD, fivecoordinate GaC V , and five-coordinate GaD V sites in blue, gray, red, orange, and green, respectively.(b) Experimental (top) and simulated (bottom) 71 Ga MAS NMR spectrum of the Ge 4+ -doped langasite phase obtained at 35.2 T and under ν r = 60 kHz (black lines).The simulated spectra are presented in the high temperature limit.The colored lines indicate the contribution of each site to the simulated spectrum and are color-coded with the data presented above.The experimental data were acquired with the QCPMG pulse sequence processed with coadded echoes.The asterisk (*) symbol denotes experimental spinning sidebands.
connected Ga/Ge sites.Compared to the line shape observed for La 3 Ga 5 Ge 17 O 14 , the presence of the (Ga,Ge) 2 O 8 structural unit in the Ge 4+ -doped phase leads to broader and more significantly overlapped resonances in the corresponding 17 O MAS NMR spectrum (Figure 6d).Notably, the computed spectral line shape resembles the experimental spectrum remarkably well, thereby validating (i) the complex defect structure proposed by diffraction methods 7 and (ii) the accuracy of the symmetry-adapted configurational ensemble in the high temperature limit.Furthermore, the relative area of the computed signals is consistent with that observed in the experimental spectra for both La 3 Ga 5 Ge 17 O 14 and La 3 Ga 3.5 Ge 2.5 17 O 14.75 , and this is strong evidence for the attainment of homogeneous 17 O enrichment.
Further information on the La 3 Ga 5−x Ge 1+x O 14+0.5x local structure can be provided by solid-state 139 La NMR spectroscopy.−56 Static 1 3 9 La NMR spectra of La 3 Ga 5 GeO 1 4 and La 3 Ga 3.5 Ge 2.5 O 14.75 recorded at 35.2 T are shown in Figure 7.One relatively broad signal in the region of the spectrum between −800 and 1200 ppm is observed for both La 3 Ga 5 GeO 14 and La 3 Ga 3.5 Ge 2.5 O 14.75 , with the signal obtained for La 3 Ga 5 GeO 14 also exhibiting one shoulder at high frequencies.The absence of spectral features in the 139 La Figure 6. 17 O isotropic chemical shifts and quadrupolar coupling constants computed with the GIPAW approach 30,31 for a set of symmetrically inequivalent configurations generated with the SOD program 32 starting from (a) a 1 × 1 × 1 unit cell of La 3 Ga 5 GeO 14 and (b) a 1 × 1 × 2 supercell of La 3 Ga 4 Ge 2 O 14.5 .The NMR parameters are grouped according to their site as noted in the figure, where O1−GaD/O1−GeD and O1− GaD V /O1−GeD V correspond to O1 bound to four-and five-coordinate D sites occupied by Ga/Ge, respectively, and O2 [(Ga,Ge) 2 O 8 ] denotes O2 sites in the (Ga,Ge) 2 O 8 structural unit.Experimental (top) and simulated (bottom) 17 O MAS NMR spectra of the (c) undoped and (d) Ge 4+doped langasite phases obtained at 20 T and under ν r = 22 kHz (black lines). 7The simulated spectra are presented in the high temperature limit.The colored lines (color-coded with the NMR parameters) indicate the contribution of each site to the simulated spectrum.Dashed lines are used to identify O1−Ga/GeD V and O2[(Ga,Ge) 2 O 8 ] signals.Asterisks (*) denote the experimental spinning sidebands, and the hash symbols (#) mark the sharp signal at approximately 70 ppm assigned to adsorbed H 2 O. NMR spectrum for La 3 Ga 3.5 Ge 2.5 O 14.75 clearly indicates that doping La 3 Ga 5 GeO 14 with Ge 4+ leads to enhanced disorder.
Static 139 La NMR spectra were simulated using the computational approach discussed above (Figure 7).The computed NMR parameters presented in Figure S4 reveal δ iso , C Q , and η Q values scattered over wide ranges for La 3 Ga 4 Ge 2 O 14.5 , while reduced variance is observed for La 3 Ga 5 GeO 14 , reflective of the detected enhanced disorder brought about by Ge 4+ doping.While the line shapes experimentally observed for La 3 Ga 3.5 Ge 2.5 O 14.75 are well captured by the computational modeling, close reproduction of the La 3 Ga 5 GeO 14 experimental spectrum is challenged by contradistinctive features being described by NMR parameters that differ by an amount which is comparable with the accuracy threshold of the calculations (Figure 7).This effect is not observed for La 3 Ga 4 Ge 2 O 14.5 due to averaging.
139 La NMR spectra were additionally recorded under fast MAS, resulting in the appearance of a set of spinning sidebands separated by the MAS frequency (ν r = 60 kHz), as shown in Figure S5."Infinite" MAS spectra were acquired using the QMAT sequence coupled with QCPMG acquisition mode and are presented in Figure S6.While poor signal-to-noise ratio is observed for La 3 Ga 3.5 Ge 2.5 O 14.75 due to the large magnitude of the corresponding 139 La quadrupolar coupling constants, the asymmetric line shape detected for La 3 Ga 5 GeO 14 features a low-frequency tail which is attributed to a Czjzek-like  distribution of quadrupolar parameters. 61This is further captured in the 139 La MAS NMR spectra of both La 3 Ga 5 GeO 14 and La 3 Ga 3.5 Ge 2.5 O 14.75 , which also reveal a distribution of isotropic chemical shifts (Figure S3).
3.2.Oxygen Dynamics. 17O VT MAS NMR spectra of La 3 Ga 5 Ge 17 O 14 (Figure 8a) and La 3 Ga 3.5 Ge 2.5 17 O 14.75 (Figure 8b) were recorded to gain insight into differences in the local oxide ion dynamics between the undoped and Ge 4+ -doped langasite phases. 17O MAS NMR spectra at T < 300 °C were recorded with a 4 mm high temperature probe under ν r = 10 kHz for La 3 Ga 5 Ge 17 O 14 and ν r = 12.5 kHz for La 3 Ga 3.5 Ge 2.5 17 O 14.75 , while a 7 mm laser-heated probe spinning at ν r = 4 kHz was employed to acquire data in the 300 °C−700 °C temperature range.Only subtle changes are observed in the 17 O MAS NMR spectra of La 3 Ga 5 Ge 17 O 14 as the temperature is increased up to 700 °C.While the center of mass of the spectra is observed to shift to slightly higher chemical shifts at a rate of approximately 0.015 ppm/°C, likely reflecting a small increase in the unit cell parameters and/or a reduction of the quadrupolar coupling constant at high temperatures, the line shape of the resonances is largely not altered by the increase in temperature.The absence of radical changes in the line shape and position of the signals as the temperature is increased is reflective of the poor ionic conductivity known for La 3 Ga 5 GeO 14 . 7triking different behavior is observed for the more highly conductive La 3 Ga 3.5 Ge 2.5 O 14.75 phase.The 17 O variable temperature MAS NMR spectra of La 3 Ga 3.5 Ge 2.5 17 O 14.75 reveal coalescence of all the 17 O resonances as the temperature is increased from 20 to 700 °C.The overlapping resonances in the 150 ppm−230 ppm region corresponding to O3 sites, apical O1 sites bound to four-and five-coordinate Ga, apical O1 sites bound to five-coordinate Ge, and O2 sites in the (Ga,Ge) 2 O 8 structural unit coalesce with the interstitial signal already below 300 °C, while at 450 °C all spectral features coalesce into a single resonance which narrows as the temperature is further increased.This indicates the occurrence of chemical exchange between all oxide ions and supports the involvement of all oxide ions in the conduction mechanism, while also demonstrating that the introduction of interstitial ions in the langasite framework leads to increased ionic motion, in agreement with the enhanced transport properties of La 3 Ga 3.5 Ge 2.5 O 14.75 compared to La 3 Ga 5 GeO 14 .At the coalescence temperature, the rate τ −1 of the detected motion is = 1 2 where Δν is the frequency separation between the resonances in the absence of chemical exchange, yielding values of τ −1 up to ∼56 kHz at ∼450 °C.
Comparison of the high temperature 17 O MAS NMR spectra recorded for the more highly conductive La  17 O resonances in the latter coalesce at higher temperatures. 24onsidering that the frequency separation of the spectral features in the absence of chemical exchange is comparable for the two compounds, this suggests that the oxide ions are more mobile in the melilite phase, in agreement with the impedance data. 6,7This is further supported by the NMR line width of the coalesced signal at 700 °C which is broader for La 3 Ga 3.5 Ge 2.5 O 14.75 (∼3.2 kHz) than for La 1.54 Sr 0.46 Ga 3 O 7.27 (∼1.8 kHz).While the small percentage of interstitial defects in La 1.54 Sr 0.46 Ga 3 O 7.27 hinders the detection of the corresponding signal at high temperatures, the La 3 Ga 3.5 Ge 2.5 17 O 14.75 data clearly reveal that the resonance assigned to O4 and O2b ions coalesces with the remaining signals as the temperature is increased, confirming that also the interstitial oxide ions are involved in the detected motional process, as expected. 17O spin−lattice relaxation time constants in the laboratory frame of motion T 1 were determined to gain insight into ionic dynamics on the MHz time scale in the langasite phases (fits shown in Figures S7 and S8).The logarithmic T 1 −1 rates determined for La 3 Ga 5 Ge 17 O 14 only reveal moderate dependence on the reciprocal temperature and are overall smaller than those obtained for La 3 Ga 3.5 Ge 2.5 17 O 14.75 , as expected based on the enhanced structural disorder in the Ge 4+ -doped phase (Figure S9).In contrast, the La 3 Ga 3.5 Ge 2.5 17 O 14.75 logarithmic T 1 −1 rates linearly increase with reciprocal temperature above 400 °C (i.e., in the temperature range in which conductivity measurements capture O 2− transport), 7 indicative of the occurrence of thermally activated short-range motion on the MHz time scale (Figure 8c), while below 400 °C the data diverge from a linear trend and show weaker dependence on the temperature.Fitting the linear data to Arrhenius behavior yields an activation energy for the short-range motion equal to (0.75 ± 0.08) eV which, as expected, is lower than the longrange activation energy determined from impedance measurements (∼1.1 eV). 7−64 The (0.315 ± 0.006) eV activation energy determined for La 1.54 Sr 0.46 Ga 3 O 7.27 is lower than that determined for La 3 Ga 3.5 Ge 2.5 O 14.75 , further demonstrating the superior ionic transport properties of the melilite phase. 24verall, the high temperature 17 O MAS NMR experiments confirm that doping La 3 Ga 5 GeO 14 with Ge 4+ to form La 3 Ga 3.5 Ge 2.5 O 14.75 enhances the mobility of the oxide ions by triggering exchange between all oxygen sites.Nevertheless, the oxide ions in La 3 Ga 3.5 Ge 2.5 O 14.75 are observed to be less mobile than those in La 1.54 Sr 0.46 Ga 3 O 7.27 melilite.The coalescence of all 17 O NMR resonances at high temperature importantly indicates the participation of both interstitial and framework oxide ions in the ionic motional process.The ionic diffusion mechanism likely involves the concerted rotation of the polyhedra containing leading to randomization of all oxide ions.

CONCLUSIONS
In this work, a combination of experimental and computational multinuclear solid-state NMR approaches are used to investigate the Ga 3+ /Ge 4+ cation distribution and the ionic diffusion mechanism in the La 3 Ga 5−x Ge 1+x O 14+0.5x langasite family of oxide ion conductors, the former being particularly challenging to identify using conventional X-ray and neutron diffraction methods.The unique 36 T SCH magnet operating at 35.2 T enables the unambiguous detection of 71 Ga NMR resonances assigned to Ga sites in four-, five-and sixfold coordination environments, thereby overcoming the resolution limitations encountered at lower magnetic field strengths.The complex spectral line shapes observed in the 17 O and 71 Ga experimental MAS NMR spectra are very well reproduced by the NMR parameters computed for a symmetry-adapted configurational ensemble, confirming that excess oxygen in La 3 Ga 3.5 Ge 2.5 O 14.75 is stabilized by the formation of a (Ga,Ge) 2 O 8 structural unit, as opposed to the interstitial oxide ions in the La 1.54 Sr 0.46 Ga 3 O 7.27 melilite which are Journal of the American Chemical Society accommodated in a GaO 5 structural unit.Comparison of the experimental and simulated NMR spectra reveals that the synthesis procedure results in a kinetically controlled Ga 3+ / Ge 4+ cation diffusion across the B, C, D, C V , and D V sites.This work illustrates that compositional disorder of isoelectronic cations with similar coherent neutron scattering lengths can be unravelled using a combined experimental and computational solid-state NMR approach that does not rely on diffractionbased methodologies. 17O MAS NMR spectra at variable temperature up to 700 °C provide insight into the oxygen dynamics.As also concluded for the La 1.54 Sr 0.46 Ga 3 O 7.27 melilite structure, the coalescence of all 17 O NMR resonances observed for La 3 Ga 3.5 Ge 2.5 17 O 14.75 indicates that (i) the incorporation of interstitial defects in the langasite structure triggers exchange between all oxygen sites and (ii) both framework and interstitial oxide ions play an important role in the conduction mechanism.These results demonstrate the potential of solid-state NMR spectroscopy to capture the relation between short-range structure and anionic conductivity in site-disordered materials.

Figure 1 .
Figure 1.Structures viewed along the (a, b) c-axis and the (c, d) a-axis of (a, c) La 3 Ga 5 GeO 14 and (b, d) La 3 Ga 3.5 Ge 2.5 O 14.75 .7 O, Ga, Ge and La atoms are shown in red, green, blue and gray.Three-connected DO 4 tetrahedra (red) with one nonbridging oxide ion O1 are connected to three four-connected CO 4 tetrahedra (gray) via O2 ions, and BO 6 octahedra (blue) bridge four-connected CO 4 tetrahedra belonging to adjacent layers via O3 ions.In La 3 Ga 5 GeO 14 , B and C sites are fully occupied by Ga 3+ cations, while the D site exhibits Ga 3+ /Ge 4+ mixed site occupancy, as reported in refs 11−13.In La 3 Ga 3.5 Ge 2.5 O 14.75 , Ga 3+ /Ge 4+ cations are distributed across the B, C, and D sites. 7(e) An example of (Ga,Ge) 2 O 8 structural unit which forms upon Ge 4+ doping.Ga 3+ /Ge 4+ cations are randomly distributed within the (Ga,Ge) 2 O 8 unit.
( 17 O) = 222.02ppm, m ( 17 O) = −0.872,σ ref ( 71 Ga) = 1442.22ppm, m ( 71 Ga) = −0.8206,σ ref ( 139 La) = 3460.92ppm, and m ( 139 La) = −0.6811for 139 La.The σ ref and m values were determined using a standard procedure 27 which also minimizes the systematic errors in the calculations.The calculations yield the traceless electric field gradient tensor V and its three principal components V xx , V yy , V zz ordered such that |V zz | ≥ | V yy | ≥ |V xx |.The quadrupolar coupling constant = to express V, where Q is the nuclear electric quadrupole moment, h is the Planck constant, and e is the electron charge.The C Q values for 139 La were calculated using Q( 139 La) = (0.206 ± 0.004) × 10 −28 m 2 , 54−56 while C Q values for the other spins were calculated using the Q values implemented in CASTEP 20.11 (see Table

Figure 2 .
Figure 2. One-dimensional 71 Ga MAS NMR spectra of (a) La 3 Ga 5 GeO 14 and (b) La 3 Ga 3.5 Ge 2.5 O 14.75 recorded at 23.5 T and 35.2 T under ν r = 60 kHz.Data at 35.2 T were recorded with the rotor-synchronized QCPMG sequence processed with coadded echoes.The asterisks (*) denote the spinning sidebands.

Figure 3 .
Figure 3. Two-dimensional 71 Ga QMAT spectrum of La 3 Ga 5 GeO 14 recorded at 35.2 T under ν r = 60 kHz presented in (a) the Phase-Adjusted Sideband Separation (PASS) representation after shearing the f 1 dimension and (b) the "infinite MAS" representation after shearing (a) along f 2 .MATLAB was used to process and shear the data.

Figure 4 .
Figure 4. (a) Three symmetrically inequivalent configurations generated with the SOD program from a 1 × 1 × 1 average unit cell of La 3 Ga 5 GeO 14 with chemical disorder in the B, C and D sites, highlighting three-connected DO 4 tetrahedra in red, four-connected CO 4 tetrahedra in gray and BO 6 octahedra in blue.O, Ga, Ge and La atoms are shown in red, green, blue and gray.(b) Experimental 71 Ga rotor-synchronized QCPMG spectrum of La 3 Ga 5 GeO 14 recorded at 35.2 T and processed with coadded echoes.The asterisk symbols (*) denote experimental spinning sidebands.The signal assigned to four-connected CO 4 tetrahedra overlaps with the spinning sideband at ∼100 ppm.Simulated 71 Ga MAS NMR spectra of La 3 Ga 5 GeO 14 (c−d) assuming chemical disorder of the B, C and D sites and (e) constraining Ge 4+ cations to D sites.The 71 Ga simulated MAS NMR spectrum was simulated taking into account (c) the configurational degeneracy (high temperature limit) and (d) an additional Boltzmann factor at 298 K.The colored lines indicate the contribution of each site to the simulated spectrum and are color-coded with the polyhedra shown above.

Figure 5 .
Figure 5. (a)71  Ga isotropic chemical shifts and quadrupolar coupling constants computed with the GIPAW approach30,31 for a set of symmetrically inequivalent configurations generated with the SOD program32 starting from a 1 × 1 × 2 supercell of La 3 Ga 4 Ge 2 O 14.5 .The NMR parameters are grouped according to their site, with sixcoordinate GaB, four-coordinate GaC, four-coordinate GaD, fivecoordinate GaC V , and five-coordinate GaD V sites in blue, gray, red, orange, and green, respectively.(b) Experimental (top) and simulated (bottom)71  Ga MAS NMR spectrum of the Ge 4+ -doped langasite phase obtained at 35.2 T and under ν r = 60 kHz (black lines).The simulated spectra are presented in the high temperature limit.The colored lines indicate the contribution of each site to the simulated spectrum and are color-coded with the data presented above.The experimental data were acquired with the QCPMG pulse sequence processed with coadded echoes.The asterisk (*) symbol denotes experimental spinning sidebands.

Figure 7 .
Figure 7. Static 139 La NMR spectra acquired at 35.2 T with the QCPMG sequence processed with coadded echoes for (a) La 3 Ga 5 GeO 14 and (b) La 3 Ga 3.5 Ge 2.5 O 14.75 .Spectra simulated in the high temperature limit from the computed NMR parameters are shown below the corresponding experimental data.The NMR parameters computed using the GIPAW approach on a symmetry-adapted configurational ensemble generated from a 1 × 1 × 1 unit cell of La 3 Ga 5 GeO 14 and a 1 × 1 × 2 supercell of La 3 Ga 4 Ge 2 O 14.5 are presented in FigureS4.

Figure 8 . 17 O 14 . 17 O 14 .
Figure 8. 17 O variable temperature MAS NMR spectra of (a) La 3 Ga 5 Ge 17 O 14 and (b) La 3 Ga 3.5 Ge 2.5 17 O 14.75 recorded at 20 T under a MAS rate ν r of either 10 kHz for La 3 Ga 5 Ge 17 O 14 and 12.5 kHz La 3 Ga 3.5 Ge 2.5 17 O 14.75 (4 mm probe) or 4 kHz (7 mm probe).The asterisk symbols (*) denote spinning sidebands, and the dashed line at 183 ppm in (b) is a guide to the eye.The adsorbed H 2 O signal marked with the hash (#) symbol is observed to move to lower shifts above 400 °C.Magnified views (×2 intensity) of the 220 ppm−350 ppm region containing the O4/O2b signal are shown above the corresponding La 3 Ga 3.5 Ge 2.5 17 O 14.75 spectra.In the La 3 Ga 3.5 Ge 2.5 17 O 14.75 spectrum at room temperature, the signal centered at ∼183 ppm corresponds to O3 sites, apical O1 sites bound to four-and five-coordinate Ga, apical O1 sites bound to five-coordinate Ge and O2 sites in the (Ga,Ge) 2 O 8 structural unit, while the resonance at lower shifts is assigned to apical O1 sites bound to five-coordinate Ge and O2 sites.(c) 17 O spin−lattice relaxation rates of La 3 Ga 3.5 Ge 2.5 17 O 14.75 as a function of reciprocal temperature T acquired at 20 T under a MAS rate ν r = 4 kHz.The orange dashed line indicates the activation energy E A for the short-range motion determined from data recorded at T > 400 °C.

Table 1 .
Statistical Weights for the Three Symmetrically Inequivalent Configurations Generated from a La 3 Ga 5 GeO 14 Unit Cell with Chemical Disorder in the B, C, and D Sites a