Cation Distribution and Anion Transport in the La₃Ga_5–xGe_1+xO_14+0.5x Langasite Structure

Abstract

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 La₃Ga_5–xGe_1+xO_14+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 La₃Ga_3.5Ge_2.5O_14.75 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.

1. 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.²

The 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. While the most widely used solid oxide electrolytes adopt fluorite^3,4 or perovskite⁵ structure with oxygen vacancies driving the ionic diffusion, there has been a growing interest in the development of solid electrolytes with a flexible framework that are able to accommodate interstitial oxygens, and this has led to the discovery of oxide ion transport materials with melilite⁶ and langasite⁷ structures among others.⁸⁻¹⁰

The La₃Ga₅GeO₁₄ langasite structure (general formula A₃BC₃D₂O₁₄) consists of layers of three-connected DO₄ tetrahedra distinguished by the presence of one nonbridging oxide ion and four-connected CO₄ tetrahedra containing four bridging oxide ions (Figure 1a and 1c). These layers are connected to form a three-dimensional framework by BO₆ octahedra which bridge four-connected CO₄ tetrahedra belonging to adjacent layers. The void space between the tetrahedral layers is occupied by eight-coordinate La³⁺ cations (A sites) located in hexagonal channels formed by the edges of one BO₆ octahedron, three four-connected CO₄ tetrahedra and two three-connected DO₄ tetrahedra. It has been reported that B and C sites in La₃Ga₅GeO₁₄ are fully occupied by Ga³⁺, while a 50/50 mixture of Ga³⁺/Ge⁴⁺ occupies the D site.¹¹⁻¹³ Contrasting results were obtained in further work on a multicell model of La₃Ga₅GeO₁₄, wherein it was concluded that Ge⁴⁺ cations partially occupy both B and D sites.¹⁴ Interstitial oxide ions introduced in the lattice upon Ge⁴⁺-doping to form La₃Ga_5–xGe_1+xO_14+0.5x are accommodated in a (Ga,Ge)₂O₈ 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).⁷ It has been reported that B, C, and D sites in La₃Ga_5–xGe_1+xO_14+0.5x with x > 0 exhibit Ga³⁺/Ge⁴⁺ mixed site occupancies.⁷

Figure 1.

Structures viewed along the (a, b) c-axis and the (c, d) a-axis of (a, c) La₃Ga₅GeO₁₄ and (b, d) La₃Ga_3.5Ge_2.5O_14.75.⁷ O, Ga, Ge and La atoms are shown in red, green, blue and gray. Three-connected DO₄ tetrahedra (red) with one nonbridging oxide ion O1 are connected to three four-connected CO₄ tetrahedra (gray) via O2 ions, and BO₆ octahedra (blue) bridge four-connected CO₄ tetrahedra belonging to adjacent layers via O3 ions. In La₃Ga₅GeO₁₄, B and C sites are fully occupied by Ga³⁺ cations, while the D site exhibits Ga³⁺/Ge⁴⁺ mixed site occupancy, as reported in refs (11−13). In La₃Ga_3.5Ge_2.5O_14.75, Ga³⁺/Ge⁴⁺ cations are distributed across the B, C, and D sites.⁷ (e) An example of (Ga,Ge)₂O₈ structural unit which forms upon Ge⁴⁺ doping. Ga³⁺/Ge⁴⁺ cations are randomly distributed within the (Ga,Ge)₂O₈ unit.

Importantly, the maximum amount of excess oxygen that can be incorporated in the La₃Ga_5–xGe_1+xO_14+0.5x langasite structure (i.e., up to 5.4 mol % in La₃Ga_3.5Ge_2.5O_14.75 with respect to the amount of oxygen in La₃Ga₅GeO₁₄) exceeds the concentration of interstitial defects in the related tetragonal La_1+ySr_1–yGa₃O_7+0.5y melilite phase with highest concentration of dopant (i.e., up to 3.8 mol % in La_1.54Sr_0.46Ga₃O_7.27 versus LaSrGa₃O₇ while preserving tetragonal structure). Nevertheless, a comparison of the transport properties in La₃Ga_5–xGe_1+xO_14+0.5x and La_1+ySr_1–yGa₃O_7+0.5y at 500 °C shows that the oxide ion conductivity is 2 orders of magnitude higher in La_1.54Sr_0.46Ga₃O_7.27 than in the most highly conductive langasite phase.⁷ Furthermore, 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 La₃Ga_5–xGe_1+xO_14+0.5x with x > 0.45.⁷ These observations suggest that the incorporation of interstitial oxide ions in La₃Ga_5–xGe_1+xO_14+0.5x leads to a substantial structural rearrangement, and the formation of (Ga,Ge)₂O₈ units effectively traps the interstitial ions, thereby limiting the enhancement in ionic conductivity occurring upon Ge⁴⁺ doping.⁷

Although the ionic conductivity in La₃Ga_5–xGe_1+xO_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.¹⁵ The distribution of cations among the distinct polyhedra can be tuned to reduce the structural rearrangements which occur upon Ge⁴⁺ doping and limit the excessive stabilization of the interstitial defects in the (Ga,Ge)₂O₈ units. This motivates further examination of the compositional disorder in the site-disordered langasite family and highlights the need to investigate Ga³⁺/Ge⁴⁺ cation distribution in the Ge⁴⁺-doped phase to identify possible relations between the local structure and the oxide ion conduction mechanism. As exemplified by previous work, it is very challenging to resolve the Ga³⁺/Ge⁴⁺ cation distribution across the B, C, and D sites in langasite structures using conventional X-ray and neutron diffraction methods due to the absence of X-ray scattering contrast for this isoelectronic pair and the similar coherent neutron scattering lengths of Ga (7.3 fm) and Ge (8.2 fm).^{7,11−14,16,17} Solid-state Nuclear Magnetic Resonance (NMR) spectroscopy is element-specific, thus offering an alternative approach to investigate compositional disorder in La₃Ga_5–xGe_1+xO_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 La₃Ga_5–xGe_1+xO_14+0.5x. ¹⁷O (spin quantum number ) Magic Angle Spinning (MAS) NMR spectroscopy represents a crucial technique to unravel the local structure around the oxygen sites, the key element in oxide ion conductors, and ¹⁷O Variable Temperature (VT) MAS NMR experiments have proven to be extremely powerful to gain insight into the local dynamics across a wide range of time scales and identify the oxide ion diffusion mechanism in solid electrolytes.¹⁸⁻²⁴ Importantly, oxide ion conductors can be readily ¹⁷O enriched via a post synthetic exchange procedure based on high temperature annealing with ¹⁷O enriched O₂ gas to overcome the limitations of the low natural abundance (0.037%) of the only NMR active isotope of oxygen, ¹⁷O.²⁵⁷¹Ga (spin quantum number ) MAS NMR spectroscopy is well suited for structural elucidation by virtue of the established relation between the ⁷¹Ga isotropic chemical shift and the Ga coordination environment²⁶⁻²⁸ but requires high external magnetic field strengths and rapid sample spinning rates owing to relatively large nuclear electric quadrupole moment of ⁷¹Ga (NMR properties listed in Table S1 in the Supporting Information). Previous ⁷¹Ga NMR work on La₃Ga_5–xGe_1+xO_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 ⁷¹Ga signal tentatively assigned to five-coordinate GaD centers was detected upon Ge⁴⁺-doping.⁷ Nevertheless, the relative area of the signals in the ⁷¹Ga MAS NMR spectrum of La₃Ga₅GeO₁₄ 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 ) is another NMR-active nucleus suitable to examine structural details,²⁶ although ¹³⁹La NMR spectroscopy is less frequently exploited due to the typically large ¹³⁹La quadrupolar coupling constants that lead to extremely broad line shapes (Table S1).

The notoriously nontrivial interpretation of solid-state NMR spectra has fuelled growing interest in the computational prediction of the NMR parameters to aid spectral assignment of complex line shapes, and the Gauge Including Projector Augmented Waves (GIPAW)-Density Functional Theory (DFT) method is now commonly employed for periodic solids.²⁹⁻³¹ The computational prediction of NMR parameters for site-disordered solids such as La₃Ga_5–xGe_1+xO_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 La₃Ga₅GeO₁₄ and Ge⁴⁺-doped La₃Ga_3.5Ge_2.5O_14.75 langasites and tackle the compositional disorder of the Ga³⁺ and Ge⁴⁺ 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 ⁷¹Ga and ¹³⁹La 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.³⁴ The Ga³⁺/Ge⁴⁺ 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 ¹⁷O 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.

2. Experimental Section

2.1. Materials Synthesis

La₃Ga₅GeO₁₄ was synthesized using a standard procedure based on annealing at 1300 °C of a mixture of the binary oxide starting materials (La₂O₃, Ga₂O₃, and GeO₂), and Ge⁴⁺-doped La₃Ga_3.5Ge_2.5O_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.⁷ To enable the acquisition of ¹⁷O MAS NMR experiments, the samples were ¹⁷O enriched using a standard method based on high-temperature, postsynthetic exchange with ¹⁷O₂ gas.²⁵ In particular, the samples were heated at 750 °C for 24 h in an atmosphere of 60% ¹⁷O enriched O₂ gas (Isotec) using heating and cooling rates of 5 K min^–1. The ¹⁷O level is expected to be ∼9% in La₃Ga₅GeO₁₄ and ∼8% in La₃Ga_3.5Ge_2.5O_14.75 based on mass balance analysis between the langasite sample and the ¹⁷O enriched O₂ gas used in the enrichment procedure. This assumes an equal mole fraction of the oxygen isotopes in the ¹⁷O enriched sample and in the ¹⁷O 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 = ⁷¹Ga at a Larmor frequency ν₀ = 305.11 MHz. One-dimensional spectra of La₃Ga₅GeO₁₄ and La₃Ga_3.5Ge_2.5O_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. ⁷¹Ga MAS NMR spectra at 23.5 T are reported relative to the ⁷¹Ga signal of a 1 M solution of Ga(NO₃)₃ in H₂O at 0 ppm, also used to measure nutation frequencies.

Ultrahigh field ⁷¹Ga 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 solid-state 1.3 mm HXY MAS NMR probe tuned to ⁷¹Ga at ν₀ = 457.48 MHz were used to acquire the data, and samples were spun at ν_r = 60 kHz. One-dimensional ⁷¹Ga MAS NMR spectra were acquired with the rotor-synchronized Quadrupolar Carr–Purcell–Meiboom–Gill (QCPMG) pulse sequence³⁵⁻³⁸ combined with an initial Wideband Uniform Rate Smooth Truncation (WURST) shaped pulse³⁹ 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 La₃Ga₅GeO₁₄ and 1.5 and 3 μs for La₃Ga_3.5Ge_2.5O_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.

A two-dimensional ⁷¹Ga spectrum of La₃Ga₅GeO₁₄ was recorded with the Quadrupolar Magic-Angle Turning (QMAT) pulse sequence in combination with an initial WURST pulse and QCPMG acquisition mode for signal enhancement.^{35−37,39,40} 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 total of 16 t₁ 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 ⁷¹Ga MAS NMR spectra recorded at 35.2 T were obtained with recycle delays suitable to obtain quantitative spectra (i.e., 2 s for La₃Ga₅GeO₁₄ and 0.4 s for La₃Ga_3.5Ge_2.5O_14.75). NMR experiments at 35.2 T were externally calibrated to the ¹H chemical shift of alanine at 1.46 ppm (indirectly referenced to tetramethylsilane at 0 ppm) using the IUPAC frequency ratios.⁴¹

2.2.2. ⁷³Ge NMR Experiments

⁷³Ge NMR experiments were performed on a 20 T Bruker Neo Avance spectrometer equipped with a low-gamma 4 mm HX probe tuned to X = ⁷³Ge at ν₀ = 29.66 MHz. 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 ⁷³Ge (see Table S1) precluded the observation of ⁷³Ge resonances.

2.2.3. ¹⁷O MAS NMR Experiments

Room-temperature ¹⁷O 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

¹⁷O 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 probe⁴⁵ tuned to X = ¹⁷O at a Larmor frequency ν₀ = 115.28 MHz and under ν_r = 4 kHz. ¹⁷O 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 La₃Ga₅Ge¹⁷O₁₄ and ν_r = 12.5 kHz for La₃Ga_3.5Ge_2.5¹⁷O_14.75 owing to the enhanced spectral resolution attainable with this probe. Unless otherwise specified, ¹⁷O 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. ¹⁷O MAS NMR spectra of La₃Ga₅Ge¹⁷O₁₄ 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 (T₁) owing to the long T₁ values determined for La₃Ga₅Ge¹⁷O₁₄ and the need for an increased number of transients to obtain a satisfactory signal-to-noise ratio when using the laser-heated 7 mm probe as opposed to the 4 mm probe.

¹⁷O T₁ values were determined from saturation recovery experiments performed with a saturation block consisting of a train of 90° flip angle pulses (100 for La₃Ga₅GeO₁₄ and from 100 at room temperature to 10 at 700 °C for La₃Ga_3.5Ge_2.5O_14.75) with an rf field amplitude of 20 kHz separated by short, rotor-asynchronized (where applicable) time intervals δ (1.125 ms for La₃Ga₅GeO₁₄ and from 0.875 ms at room temperature to 60 μs at 700 °C for La₃Ga_3.5Ge_2.5O_14.75) to ensure complete saturation of the spin system at each temperature and considering the probe safety.⁴⁶ Suitable delays τ (e.g., at room temperature from 1 ms to 110 s for La₃Ga₅GeO₁₄ and from 0.6 ms to 22 s for La₃Ga_3.5Ge_2.5O_14.75) were chosen at each temperature to fully capture the magnetization build-up. 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 T₁ relaxation time constants and (ii) the temperature gradient across the sample

1

where A(τ) and A_∞ are the normalized area of the ¹⁷O 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 T₁ value from T^*₁ and c

2

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

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 ²⁰⁷Pb chemical shift thermometer of Pb(NO₃)₂⁴⁷ for the 4 mm high temperature HX MAS probe and the ⁷⁹Br chemical shift thermometer of KBr⁴⁸ for the 7 mm laser-heated 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 ¹⁷O experiments were acquired on ¹⁷O enriched samples and are referenced to the ¹⁷O signal of H₂O 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 = ¹³⁹La at ν₀ = 211.95 MHz was used throughout. All ¹³⁹La NMR spectra were acquired using recycle delays of 0.5 s for La₃Ga₅GeO₁₄ and 70 ms for La₃Ga_3.5Ge_2.5O_14.75. One-dimensional NMR spectra were recorded with the QCPMG pulse sequence³⁵⁻³⁷ 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 ¹³⁹La 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 t₁ increments were recorded. ¹³⁹La spectra were externally calibrated to the ¹H chemical shift of alanine at 1.46 ppm (indirectly referenced to tetramethylsilane at 0 ppm) using the IUPAC frequency ratios.⁴¹

2.3. Computations

The complete set of symmetrically inequivalent configurations (i.e., not interconvertible via isometric transformations) from a La₃Ga₅GeO₁₄ unit cell and a La₃Ga₄Ge₂O_14.5 1 × 1 × 2 supercell (on the basis of the cell parameters of the La₃Ga₄Ge₂O_14.5 average unit cell obtained from diffraction measurements)⁷ was generated using the SOD method.³² A total of three symmetrically inequivalent configurations was obtained for La₃Ga₅GeO₁₄ assuming Ga³⁺/Ge⁴⁺ mixed site occupancies for the three-connected DO₄ tetrahedra, four-connected CO₄ tetrahedra, and BO₆ octahedra. 495 symmetrically inequivalent configurations were generated for La₃Ga₄Ge₂O_14.5 taking into account additional mixed site occupancy of the Ga³⁺/Ge⁴⁺ sites in the (Ga,Ge)₂O₈ 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 La₃Ga₄Ge₂O_14.5 1 × 1 × 2 supercell expansion contains one (Ga,Ge)₂O₈ structural unit and resembles the La₃Ga_3.5Ge_2.5O_14.75 experimental composition, while maintaining the computational cost of the calculations relatively low as opposed to the La₃Ga_3.5Ge_2.5O_14.75 composition which would require larger supercell expansions.

All calculations were performed using plane-wave DFT²⁹ with periodic boundary conditions, as implemented in the CASTEP (version 20.11) code.⁴⁹ On-the-fly generated ultrasoft pseudopotentials⁵⁰ and the Perdew–Burke–Ernzerhof (PBE) exchange-correlation functional⁵¹ 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 La₃Ga₅GeO₁₄ or a 2 × 2 × 2 Monkhorst–Pack k-point grid for La₃Ga₄Ge₂O_14.5.⁵² A 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) approach⁵³ was selected to account for relativistic effects, and the electronic energy was optimized self-consistently 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 La₃Ga₄Ge₂O_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 , the anisotropic chemical shielding , and the asymmetry parameter , where σ_xx, σ_yy, and σ_zz are the principal components obtained upon diagolization of the symmetric part of σ ordered such that |σ_zz – σ_iso| ≥ |σ_xx – σ_iso | ≥ |σ_yy – σ_iso|. 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 (¹⁷O) = 222.02 ppm, m (¹⁷O) = −0.872, σ_ref (⁷¹Ga) = 1442.22 ppm, m (⁷¹Ga) = −0.8206, σ_ref (¹³⁹La) = 3460.92 ppm, and m (¹³⁹La) = −0.6811 for ¹³⁹La. The σ_ref and m values were determined using a standard procedure²⁷ 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 and quadrupolar asymmetry parameter are commonly used 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 ¹³⁹La were calculated using Q(¹³⁹La) = (0.206 ± 0.004) × 10^–28 m²,⁵⁴⁻⁵⁶ while C_Q values for the other spins were calculated using the Q values implemented in CASTEP 20.11 (see Table S1).

2.4. 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.⁵⁷ MAS 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.

3. Results and Discussion

3.1. Configurational Disorder

Figure 2 shows the ⁷¹Ga MAS NMR spectra of La₃Ga₅GeO₁₄ and La₃Ga_3.5Ge_2.5O_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 ⁷¹Ga 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 B₀. While the ⁷¹Ga 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 ⁷¹Ga resonances at 35.2 T for both La₃Ga₅GeO₁₄ and La₃Ga_3.5Ge_2.5O_14.75, as previously observed for the related La_1+xSr_1–xGa₃O_7+0.5x melilite family of fast oxide ion conductors.⁵⁸

Figure 2.

One-dimensional ⁷¹Ga MAS NMR spectra of (a) La₃Ga₅GeO₁₄ and (b) La₃Ga_3.5Ge_2.5O_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.

One 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 La₃Ga₅GeO₁₄. 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 ⁷¹Ga QMAT experiment was performed for La₃Ga₅GeO₁₄ at 35.2 T (Figure 3).⁴⁰ The 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 ⁷¹Ga MAS NMR data of La₃Ga₅GeO₁₄. The ⁷¹Ga MAS NMR spectrum of La₃Ga_3.5Ge_2.5O_14.75 acquired at 35.2 T, albeit presenting spectral features resembling those observed for La₃Ga₅GeO₁₄, exhibits broader resonances, reflective of the enhanced structural disorder in the Ge⁴⁺-doped langasite phase. Furthermore, it is importantly observed that the relative area of the signal at 50 ppm < δ < 150 ppm increases upon Ge⁴⁺-doping of La₃Ga₅GeO₁₄ to form La₃Ga_3.5Ge_2.5O_14.75.

Figure 3.

Two-dimensional ⁷¹Ga QMAT spectrum of La₃Ga₅GeO₁₄ recorded at 35.2 T under ν_r = 60 kHz presented in (a) the Phase-Adjusted Sideband Separation (PASS) representation after shearing the f₁ dimension and (b) the “infinite MAS” representation after shearing (a) along f₂. MATLAB was used to process and shear the data.

To facilitate the spectral assignment of the ⁷¹Ga resonances observed for La₃Ga_5–xGe_1+xO_14+0.5x, NMR parameters were computed with the GIPAW-DFT method for a symmetry-adapted configurational ensemble generated using the SOD approach.^30−32,59 Restricting the Ga³⁺/Ge⁴⁺ mixed site disorder to the D site in La₃Ga₅GeO₁₄,¹¹ only one symmetrically inequivalent configuration is generated starting from a 1 × 1 × 1 average unit cell (Configuration 3 in Figure 4a). The computed ⁷¹Ga NMR parameters are on the order of those previously predicted for a La₂₄Ga₄₀Ge₈O₁₁₂ supercell corresponding to the La₃Ga₅GeO₁₄ 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 ⁷¹Ga MAS NMR spectrum of La₃Ga₅GeO₁₄ 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 ⁷¹Ga 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.

Figure 4.

(a) Three symmetrically inequivalent configurations generated with the SOD program from a 1 × 1 × 1 average unit cell of La₃Ga₅GeO₁₄ with chemical disorder in the B, C and D sites, highlighting three-connected DO₄ tetrahedra in red, four-connected CO₄ tetrahedra in gray and BO₆ octahedra in blue. O, Ga, Ge and La atoms are shown in red, green, blue and gray. (b) Experimental ⁷¹Ga rotor-synchronized QCPMG spectrum of La₃Ga₅GeO₁₄ recorded at 35.2 T and processed with coadded echoes. The asterisk symbols (*) denote experimental spinning sidebands. The signal assigned to four-connected CO₄ tetrahedra overlaps with the spinning sideband at ∼100 ppm. Simulated ⁷¹Ga MAS NMR spectra of La₃Ga₅GeO₁₄ (c–d) assuming chemical disorder of the B, C and D sites and (e) constraining Ge⁴⁺ cations to D sites. The ⁷¹Ga 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.

To address the discrepancies between the experimental and simulated spectra, La₃Ga₅GeO₁₄ was modeled with additional Ga³⁺/Ge⁴⁺ mixed site occupancy for the B and C sites, as proposed for the Ge⁴⁺-doped phase based on neutron powder diffraction.⁷ The 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 Ge⁴⁺ 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 Ga³⁺/Ge⁴⁺ 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 (∼24.6 MHz). 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 ⁷¹Ga MAS NMR spectrum of La₃Ga₅GeO₁₄ 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 temperature-dependent Boltzmann factor (). 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 , implying an energetically unbiased distribution of the Ga³⁺/Ge⁴⁺ 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 ⁷¹Ga MAS NMR spectra of La₃Ga₅GeO₁₄ is obtained if Ge⁴⁺ cations are not constrained to the D site (Configuration 3 in Figure 4a), indicating that B, C, and D sites exhibit Ga³⁺/Ge⁴⁺ 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 Ga³⁺/Ge⁴⁺ 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.

Table 1. Statistical Weights for the Three Symmetrically Inequivalent Configurations Generated from a La₃Ga₅GeO₁₄ Unit Cell with Chemical Disorder in the B, C, and D Sites^a.

Configuration	p (T = 298 K)	p (T → ∞)
1	0.4795	0.1667
2	0.4668	0.5000
3	0.0537	0.3333

^aThe three configurations are shown in Figure 4a. The weights consider the configurational degeneracy and an additional temperature-dependent Boltzmann factor () determined at 298 K and in the high temperature limit T → ∞ (corresponding to ). The temperature dependence of the statistical weights arises from the fact that the configurations possess distinct energies.

The La₃Ga₄Ge₂O_14.5 composition was chosen to model the Ge⁴⁺-doped langasite phase because the La₃Ga_3.5Ge_2.5O_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 La₃Ga₄Ge₂O_14.5 can be compared with the experimental NMR spectrum of La₃Ga_3.5Ge_2.5O_14.75 owing to the subtle differences in the ¹⁷O and ⁷¹Ga MAS NMR spectra of La₃Ga₄Ge₂O_14.5 and La₃Ga_3.5Ge_2.5O_14.75 previously observed.⁷ A symmetry-adapted configurational ensemble consisting of 495 configurations was generated from a 1 × 1 × 2 super cell corresponding to the La₃Ga₄Ge₂O_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 Ge⁴⁺-doped langasite phase, including Ga³⁺/Ge⁴⁺ chemical disorder for B, C, D and five-coordinate C^V and D^V sites and partial site occupancy for the interstitial site O4.⁷

The ⁷¹Ga NMR parameters computed for La₃Ga₄Ge₂O_14.5 are reported in Figure 5a. Although distributed over a wider range due to the presence of enhanced disorder in the Ge⁴⁺-doped phase, the NMR parameters computed for the four- and six-coordinate Ga sites in La₃Ga₄Ge₂O_14.5 are of comparable magnitude to those obtained for La₃Ga₅GeO₁₄. Additional sites are present in La₃Ga₄Ge₂O_14.5 due to the presence of two edge-sharing, square-based pyramids C^VO₅ and D^VO₅ which form from the original tetrahedra to accommodate the interstitial oxide ion O4 (Figure 1b).⁷⁷¹Ga 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 ⁷¹Ga isotropic chemical shifts predicted for GaC^V and GaD^V is observed, the range of ⁷¹Ga quadrupolar coupling constants predicted for these sites very significantly overlap (Figure 5a).

Figure 5.

(a) ⁷¹Ga 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 program³² starting from a 1 × 1 × 2 supercell of La₃Ga₄Ge₂O_14.5. The NMR parameters are grouped according to their site, with six-coordinate GaB, four-coordinate GaC, four-coordinate GaD, five-coordinate GaC^V, and five-coordinate GaD^V sites in blue, gray, red, orange, and green, respectively. (b) Experimental (top) and simulated (bottom) ⁷¹Ga MAS NMR spectrum of the Ge⁴⁺-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.

The ⁷¹Ga MAS NMR spectrum of La₃Ga₄Ge₂O_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 Ge⁴⁺-doping originates from the presence of resonances assigned to five-coordinate GaC^VO₅ and GaD^VO₅ sites that overlap with the GaC signal. These results confirm that the interstitial ions in La₃Ga_5–xGe_1+xO_14+0.5x are hosted in the (Ga,Ge)₂O₈ unit consisting of edge-sharing five-coordinate Ga/Ge square pyramidal sites. While structural models with all B sites occupied by Ge⁴⁺ cations exhibit a dominant Boltzmann factor at ambient temperature due to their favorable relative energy, the six-coordinate ⁷¹Ga 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 Ga³⁺/Ge⁴⁺ cation distribution (i.e., the Ga³⁺/Ge⁴⁺ 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, ⁷³Ge () NMR spectroscopy is, in principle, ideal to confirm the presence of chemical disorder in the B, C, and D sites for both La₃Ga₅GeO₁₄ and La₃Ga_3.5Ge_2.5O_14.75.⁶⁰ Nevertheless, this only NMR active isotope of Ge possesses a large nuclear electric quadrupole moment of (−0.196 ± 0.001) × 10^–28 m² 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 (¹³C) of only 1 order of magnitude higher than that of ¹⁷O at natural abundance, see Table S1). We attempted to record one-dimensional ⁷³Ge NMR spectra for La₃Ga₅GeO₁₄ and La₃Ga_3.5Ge_2.5O_14.75 at 20 T under static conditions, but the unfavorable NMR properties of ⁷³Ge 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 ¹⁷O MAS NMR spectra recorded at room temperature in previous work.⁷ The ¹⁷O NMR parameters predicted for La₃Ga₅GeO₁₄ and La₃Ga₄Ge₂O_14.5 using the computational approach described above are presented in Figure 6a and 6b, respectively. The ¹⁷O isotropic shifts predicted for the different O sites in La₃Ga₅GeO₁₄ are scattered over distinct ranges. In particular, O2 ions connecting CO₄ and DO₄ tetrahedra and O3 ions bridging BO₆ and CO₄ 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 ¹⁷O 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).⁷ Comparison 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.

Figure 6.

¹⁷O 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 program³² starting from (a) a 1 × 1 × 1 unit cell of La₃Ga₅GeO₁₄ and (b) a 1 × 1 × 2 supercell of La₃Ga₄Ge₂O_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)₂O₈] denotes O2 sites in the (Ga,Ge)₂O₈ structural unit. Experimental (top) and simulated (bottom) ¹⁷O MAS NMR spectra of the (c) undoped and (d) Ge⁴⁺-doped langasite phases obtained at 20 T and under ν_r = 22 kHz (black lines).⁷ The 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)₂O₈] signals. Asterisks (*) denote the experimental spinning sidebands, and the hash symbols (#) mark the sharp signal at approximately 70 ppm assigned to adsorbed H₂O.

The NMR parameters computed for La₃Ga₄Ge₂O_14.5 are of comparable magnitude to those predicted for La₃Ga₅GeO₁₄, but they are distributed over a wider range, as observed for the ⁷¹Ga NMR parameters (Figure 6b). The pair of five-coordinate C^V and D^V sites that forms upon Ge⁴⁺ 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)₂O₈ structural unit present overall higher δ_iso,cs and slightly lower C_Q than those obtained for O2 oxygens bridging two four-connected Ga/Ge sites. Compared to the line shape observed for La₃Ga₅Ge¹⁷O₁₄, the presence of the (Ga,Ge)₂O₈ structural unit in the Ge⁴⁺-doped phase leads to broader and more significantly overlapped resonances in the corresponding ¹⁷O 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 methods⁷ 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 La₃Ga₅Ge¹⁷O₁₄ and La₃Ga_3.5Ge_2.5¹⁷O_14.75, and this is strong evidence for the attainment of homogeneous ¹⁷O enrichment.

Further information on the La₃Ga_5–xGe_1+xO_14+0.5x local structure can be provided by solid-state ¹³⁹La NMR spectroscopy. Owing to its large nuclear electric quadrupole moment of (0.206 ± 0.004) × 10^–28 m², ¹³⁹La is usually subject to strong quadrupolar interactions which result in anisotropically broadened NMR resonances, thereby motivating the use of the highest available fields to achieve enhanced resolution.⁵⁴⁻⁵⁶ Static ¹³⁹La NMR spectra of La₃Ga₅GeO₁₄ and La₃Ga_3.5Ge_2.5O_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 La₃Ga₅GeO₁₄ and La₃Ga_3.5Ge_2.5O_14.75, with the signal obtained for La₃Ga₅GeO₁₄ also exhibiting one shoulder at high frequencies. The absence of spectral features in the ¹³⁹La NMR spectrum for La₃Ga_3.5Ge_2.5O_14.75 clearly indicates that doping La₃Ga₅GeO₁₄ with Ge⁴⁺ leads to enhanced disorder.

Figure 7.

Static ¹³⁹La NMR spectra acquired at 35.2 T with the QCPMG sequence processed with coadded echoes for (a) La₃Ga₅GeO₁₄ and (b) La₃Ga_3.5Ge_2.5O_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 La₃Ga₅GeO₁₄ and a 1 × 1 × 2 supercell of La₃Ga₄Ge₂O_14.5 are presented in Figure S4.

Static ¹³⁹La 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 La₃Ga₄Ge₂O_14.5, while reduced variance is observed for La₃Ga₅GeO₁₄, reflective of the detected enhanced disorder brought about by Ge⁴⁺ doping. While the line shapes experimentally observed for La₃Ga_3.5Ge_2.5O_14.75 are well captured by the computational modeling, close reproduction of the La₃Ga₅GeO₁₄ 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 La₃Ga₄Ge₂O_14.5 due to averaging.

¹³⁹La 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 La₃Ga_3.5Ge_2.5O_14.75 due to the large magnitude of the corresponding ¹³⁹La quadrupolar coupling constants, the asymmetric line shape detected for La₃Ga₅GeO₁₄ features a low-frequency tail which is attributed to a Czjzek-like distribution of quadrupolar parameters.⁶¹ This is further captured in the ¹³⁹La MAS NMR spectra of both La₃Ga₅GeO₁₄ and La₃Ga_3.5Ge_2.5O_14.75, which also reveal a distribution of isotropic chemical shifts (Figure S3).

3.2. Oxygen Dynamics

¹⁷O VT MAS NMR spectra of La₃Ga₅Ge¹⁷O₁₄ (Figure 8a) and La₃Ga_3.5Ge_2.5¹⁷O_14.75 (Figure 8b) were recorded to gain insight into differences in the local oxide ion dynamics between the undoped and Ge⁴⁺-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 La₃Ga₅Ge¹⁷O₁₄ and ν_r = 12.5 kHz for La₃Ga_3.5Ge_2.5¹⁷O_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 ¹⁷O MAS NMR spectra of La₃Ga₅Ge¹⁷O₁₄ 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 La₃Ga₅GeO₁₄.⁷

Figure 8.

¹⁷O variable temperature MAS NMR spectra of (a) La₃Ga₅Ge¹⁷O₁₄ and (b) La₃Ga_3.5Ge_2.5¹⁷O_14.75 recorded at 20 T under a MAS rate ν_r of either 10 kHz for La₃Ga₅Ge¹⁷O₁₄ and 12.5 kHz La₃Ga_3.5Ge_2.5¹⁷O_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 H₂O 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 La₃Ga_3.5Ge_2.5¹⁷O_14.75 spectra. In the La₃Ga_3.5Ge_2.5¹⁷O_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)₂O₈ structural unit, while the resonance at lower shifts is assigned to apical O1 sites bound to five-coordinate Ge and O2 sites. (c) ¹⁷O spin–lattice relaxation rates of La₃Ga_3.5Ge_2.5¹⁷O_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.

Striking different behavior is observed for the more highly conductive La₃Ga_3.5Ge_2.5O_14.75 phase. The ¹⁷O variable temperature MAS NMR spectra of La₃Ga_3.5Ge_2.5¹⁷O_14.75 reveal coalescence of all the ¹⁷O 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)₂O₈ 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 La₃Ga_3.5Ge_2.5O_14.75 compared to La₃Ga₅GeO₁₄. At the coalescence temperature, the rate τ^–1 of the detected motion is 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 ¹⁷O MAS NMR spectra recorded for the more highly conductive La_1.54Sr_0.46Ga₃¹⁷O_7.27 melilite phase and for La₃Ga_3.5Ge_2.5¹⁷O_14.75 reveals that the ¹⁷O resonances in the latter coalesce at higher temperatures.²⁴ Considering 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.^6,7 This is further supported by the NMR line width of the coalesced signal at 700 °C which is broader for La₃Ga_3.5Ge_2.5O_14.75 (∼3.2 kHz) than for La_1.54Sr_0.46Ga₃O_7.27 (∼1.8 kHz). While the small percentage of interstitial defects in La_1.54Sr_0.46Ga₃O_7.27 hinders the detection of the corresponding signal at high temperatures, the La₃Ga_3.5Ge_2.5¹⁷O_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 T₁ 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^–1₁ rates determined for La₃Ga₅Ge¹⁷O₁₄ only reveal moderate dependence on the reciprocal temperature and are overall smaller than those obtained for La₃Ga_3.5Ge_2.5¹⁷O_14.75, as expected based on the enhanced structural disorder in the Ge⁴⁺-doped phase (Figure S9). In contrast, the La₃Ga_3.5Ge_2.5¹⁷O_14.75 logarithmic T^–1₁ 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 long-range activation energy determined from impedance measurements (∼1.1 eV).⁷ In fact, the short-range oxide ion motion probed with solid-state NMR spectroscopy also captures unsuccessful (i.e., forward and backward) jumps which do not promote the macroscopic anionic diffusion detected in conductivity measurements.⁶²⁻⁶⁴ The (0.315 ± 0.006) eV activation energy determined for La_1.54Sr_0.46Ga₃O_7.27 is lower than that determined for La₃Ga_3.5Ge_2.5O_14.75, further demonstrating the superior ionic transport properties of the melilite phase.²⁴

Overall, the high temperature ¹⁷O MAS NMR experiments confirm that doping La₃Ga₅GeO₁₄ with Ge⁴⁺ to form La₃Ga_3.5Ge_2.5O_14.75 enhances the mobility of the oxide ions by triggering exchange between all oxygen sites. Nevertheless, the oxide ions in La₃Ga_3.5Ge_2.5O_14.75 are observed to be less mobile than those in La_1.54Sr_0.46Ga₃O_7.27 melilite. The coalescence of all ¹⁷O 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 Ga/Ge, leading to randomization of all oxide ions.

4. Conclusions

In this work, a combination of experimental and computational multinuclear solid-state NMR approaches are used to investigate the Ga³⁺/Ge⁴⁺ cation distribution and the ionic diffusion mechanism in the La₃Ga_5–xGe_1+xO_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 ⁷¹Ga 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 ¹⁷O and ⁷¹Ga experimental MAS NMR spectra are very well reproduced by the NMR parameters computed for a symmetry-adapted configurational ensemble, confirming that excess oxygen in La₃Ga_3.5Ge_2.5O_14.75 is stabilized by the formation of a (Ga,Ge)₂O₈ structural unit, as opposed to the interstitial oxide ions in the La_1.54Sr_0.46Ga₃O_7.27 melilite which are accommodated in a GaO₅ structural unit. Comparison of the experimental and simulated NMR spectra reveals that the synthesis procedure results in a kinetically controlled Ga³⁺/Ge⁴⁺ 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 diffraction-based methodologies.

¹⁷O MAS NMR spectra at variable temperature up to 700 °C provide insight into the oxygen dynamics. As also concluded for the La_1.54Sr_0.46Ga₃O_7.27 melilite structure, the coalescence of all ¹⁷O NMR resonances observed for La₃Ga_3.5Ge_2.5¹⁷O_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.

Data Availability Statement

Reserach data supporting this work are accessible from the University of Liverpool Research Data Catalogue: https://doi.org/10.17638/datacat.liverpool.ac.uk/2658.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.4c02324.

• Additional ⁷¹Ga, ⁷³Ge and ¹³⁹La computed NMR parameters, ¹³⁹La NMR spectra, and ¹⁷O NMR T₁ relaxation data. (PDF)

L.C. thanks the Leverhulme Trust for support from the Leverhulme Research Centre for Functional Materials Design for a PhD studentship, also partially supported by the University of Liverpool. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by National Science Foundation Cooperative Agreement No. DMR-2128556 and the State of Florida. Research reported in this publication was supported by the National Institute of General Medical Sciences of the National Institutes of Health under Award Number P41GM122698 and RM1GM148766. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The UK High-Field Solid-State NMR Facility used in this research was funderd by EPSRC and BBSRC (EP/T015063/1), as well as the University of Warwick including via part funding through Birmingham Science City Advanced Materials Projects 1 and 2 supported by Advantage West Midlands (AWM) and the European Regional Development Fund (ERDF) as well as, for the 1 GHz instrument, EP/R029946/1. Collaborative assistance from the Facility Manager Team (Dinu Iuga and Trent Franks, University of Warwick) is acknowledged. F.B. thanks the EPSRC for funding the purchase of ¹⁷O enriched O₂ gas used in this work (EP/K031511/1), also supported by a Royal Society of Chemistry Research Fund Grant (R21-2293948533). M.J.R. thanks the Royal Society for a Research Professorship.

The authors declare no competing financial interest.