# Topotactic Reduction-Induced Stabilization of *β*-La 2 Mo 2 O 8.68 Phase: Structure, Static Oxygen Disorder, and Electrical Properties

Xueting Zhang, Cecile Genevois, Cheng Li, Xiaoyan Yang, Michael J Pitcher, Mathieu Allix, Xiaojun Kuang, Alberto Fernández-Carrión

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Xueting Zhang, Cecile Genevois, Cheng Li, Xiaoyan Yang, Michael J Pitcher, et al.. Topotactic Reduction-Induced Stabilization of *β*-La 2 Mo 2 O 8.68 Phase: Structure, Static Oxygen Disorder, and Electrical Properties. Inorganic Chemistry, 2024, 10.1021/acs.inorgchem.4c02151 . hal-04807217

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Topotactic Reduction-Induced Stabilization of β-La<sub>2</sub>Mo<sub>2</sub>O<sub>8.68</sub> Phase: Structure, Static Oxygen Disorder, and Electrical Properties

Xueting Zhang<sup>1</sup>, Cecile Genevois<sup>2</sup>, Cheng Li<sup>3</sup>, Xiaoyan Yang<sup>1,4</sup>, Michael J. Pitcher<sup>2</sup>, Mathieu Allix<sup>2</sup>, Xiaojun Kuang<sup>1,4*</sup>, Alberto J. Fernández-Carrión<sup>†*1,5,6</sup>

<sup>1</sup>MOE Key Laboratory of New Processing Technology for Nonferrous Metals and Materials, Guangxi Universities Key Laboratory of Non-ferrous Metal Oxide Electronic Functional Materials and Devices, College of Materials Science and Engineering, Guilin University of Technology, Guilin 541004, P. R. China.

<sup>2</sup>CNRS, CEMHTI, UPR 3079, Université Orléans, Orléans F-45071, France.

<sup>3</sup>Neutron Scattering Division, Oak Ridge National Laboratory, 1 Bethel Valley Rd, Oak Ridge, TN 37830, USA.

<sup>4</sup>Guangxi Key Laboratory of Electrochemical and Magnetochemical Functional Materials, College of Chemistry and Bioengineering, Guilin University of Technology, Guilin 541004, P. R. China.

<sup>5</sup>Departamento de Química Inorgánica and Instituto de Ciencia de Materiales de Sevilla (ICMS), Centro Mixto CSIC-Universidad de Sevilla, Av. Américo Vespucio, 49, 41092 Sevilla, Spain.

<sup>6</sup>LE STUDIUM Loire Valley Institute for Advanced Studies, Centre-Val de Loire region, 45000 Orleans, France.
**ABSTRACT:** La₂Mo₂O₉ is acknowledged as an exceptional oxide ion conductor. It undergoes a reversible phase transition around 580°C from the non-conductive low-temperature monoclinic α-La₂Mo₂O₉ phase to the highly conductive high-temperature cubic β-La₂Mo₂O₉ phase. In addition, La₂Mo₂O₉ demonstrates complex chemistry under reducing conditions. This study reports, for the first time, the stabilization at ambient temperature of a novel cubic phase through a topotactic reduction of α-La₂Mo₂O₉ employing CaH₂. This phase contains approximately ~3 at% oxygen vacancies relative to the nominal composition (La₂Mo₂O₈.₆₈(1)). The cubic symmetry is associated with a static distribution of these vacancies, in contrast to the dynamic distribution observed in the high temperature cubic β-La₂Mo₂O₉ phase reported previously. Additionally, the material exhibits mixed ion-electronic conduction, which expands its potential use in applications requiring both ionic and electronic transport.

# 1. Introduction

Oxide ion conductors containing tetrahedral moieties can exhibit high oxide ion conductivity.¹ Among them, La₂Mo₂O₉ spawned great attention as an oxide ion conductor for solid oxide fuel cells (SOFCs) technology.² It undergoes a reversible phase transition from the stable monoclinic phase (α-polymorph, S.G. P2₁, with lattice parameters *a* = 14.325(3) Å, *b* = 21.482(4) Å, *c* = 28.585(6) Å, β = 90.40(3)°)³ at room temperature to a cubic phase (β-form, S.G. P2₁3, with lattice parameter *a* = 7.2014(7) Å)⁴ at 580 °C, accompanied by a rise in conductivity of almost two orders of magnitude, reaching as high as σ = 6 × 10⁻² S cm⁻¹ at 1073 K.² This phase transition is rather subtle, during which the oxide sublattice changes from a static oxygen distribution (α-phase) to a dynamically disordered oxygen distribution (β-phase), inferring native oxygen vacancies that boost oxide ion conduction.
Given the high oxide ion conductivity exhibited by the β-phase, numerous efforts have focused on stabilizing this high-temperature form at room temperature.⁵ This has led to the development of a wide variety of compounds, collectively referred to as the LAMOX family. The main strategy has been based on either isovalent or aliovalent substitution on both the La site⁶⁻¹¹ and Mo site.¹¹⁻¹³ Anionic substitution has been also explored by replacing oxygen with fluorine.¹⁴ Yet, this latter strategy has resulted in the formation of La₂Mo₂O₉ superstructures which remain poorly understood. Overall, most of these substitutions suppress the phase transition and stabilize the β-form at room temperature. Although stabilization and enhancements in conductivity at low temperatures have been achieved, improvements in high-temperature conductivity remain a challenge. Alternatively, different thermal treatments have been applied pursuing the β-phase. Thus, Voronkova et al. and Alekseeva et al. isolated single-crystals of the β phase from the incongruent crystallization of 31 mol % of La₂O₃ and 69 mol % of MoO₃ mixture through controlling the cooling process from the melt.¹⁵,¹⁶

The application of LAMOX-based compounds as solid-state electrolytes is limited due to their high tendency to be reduced under typical reduction conditions at the anode side of SOFC devices. This leads to the formation of intermediate phases with different structures and oxygen contents, and in some cases, partial or complete amorphization occurs, causing an increase in n-type electronic conduction instead of the desired oxide ion mechanism. Still, some studies have demonstrated the potential interest in using the amorphous phase for implementation as anode material in SOFCs.¹⁷,¹⁸ The introduction of W⁶⁺ improves the resistance against reduction, although it leads to a decrease in ionic conductivity.

The early study of chemical reduction in La₂Mo₂O₉ can be traced back to the experiment carried out by Goutenoire et al. in 1999,¹⁹ in which the reduction was conducted at constant temperature
of 1033 K, under a flow of 6% H₂ and 94% N₂. The process led to the formation of a perovskite
derivative compound with chemical formula La<sub>7</sub>Mo<sub>7</sub>O<sub>30</sub> (or La<sub>2</sub>Mo<sub>2</sub>O<sub>8.57</sub>). Subsequent
investigations by Marrero Lopez et al. identified the formation of La<sub>2.4</sub>Mo<sub>1.6</sub>O<sub>8</sub>, La<sub>7</sub>Mo<sub>7</sub>O<sub>30</sub>, α-
La<sub>2</sub>Mo<sub>2</sub>O<sub>9</sub> upon reduction at 1173, 1073 and 973 K overnight, respectively, under 5% H₂ and 95%
N₂ atmosphere.<sup>20</sup> Studies into the La<sub>2</sub>Mo<sub>2-x</sub>W<sub>x</sub>O<sub>9</sub> system (x = 0-2)<sup>13</sup> revealed the influence of
tungsten doping on the reduction products upon using a gas mixture of dry 5% H₂ and 95% Ar at
973 K for 24 h, that rendered an amorphous compound for the x = 0 compound, while W doping
resulted in the formation of isostructural La<sub>7</sub>Mo<sub>7</sub>O<sub>30</sub> phase (0.25 < x < 0.75). Alternatively,
aliovalent doping at La sites were found to enhance redox stability at lower temperatures, although
not significantly more than with high tungsten content.<sup>21</sup> The characterization of the amorphous
phase formed during these reduction processes was then a focal point of recent studies. Vega-
Castillo et al. proposed a non-stoichiometric range, with general formula La<sub>2</sub>Mo<sub>2</sub>O<sub>7-y</sub>.<sup>22</sup> In
addition, they stabilized La<sub>2</sub>Mo<sub>2</sub>O<sub>8.96</sub> during the reoxidation of La<sub>2</sub>Mo<sub>2</sub>O<sub>7-y</sub> at 881 K within the
10<sup>-25</sup> < pO<sub>2</sub> < 10<sup>-23</sup> atm range. This compound is isostructural with α-La<sub>2</sub>Mo<sub>2</sub>O<sub>9</sub> and behaves as
mixed ionic and electronic conductor. Buvat et al.<sup>23</sup> used laboratory XRD coupled to
thermogravimetric analysis to observe the phase evolution, noting a direct reduction to La<sub>2</sub>Mo<sub>2</sub>O<sub>7-
</sub>y at 973 K. At 1033 K, reduction progressed through the crystallization of La<sub>7</sub>Mo<sub>7</sub>O<sub>30</sub> as
intermediate phase before amorphization, with further reduction leading to metallic molybdenum
exsolution and a molybdenum-deficient amorphous phase. The significance of the amorphous
phase was also emphasized by Liu et al.,<sup>24</sup> who synthesized La<sub>2</sub>Mo<sub>2</sub>O<sub>9</sub> nanowires featuring an
amorphous nanolayer on their surface, identified chemically as La<sub>2</sub>Mo<sub>2</sub>O<sub>8.50</sub>. This layer is
responsible for suppressing the β→α transformation, as well as significantly enhancing the ionic
conductivity. Collectively, these studies reveal the nuanced interplay between reduction
conditions, doping strategies, and the structural transformations of La₂Mo₂O₉, highlighting its complex reduction behavior and its impact on ionic and electronic conductivity.

Due to the high tendency of La₂Mo₂O₉ to undergo reduction and yield different compounds, further exploration using different reducing chemical synthesis routes is advisable. In this regard, alkaline and alkaline earth hydrides as reducing agents have proven highly useful in stabilizing novel metastable compounds with oxygen deficiency and oxyhydrides.²⁵⁻³¹ In this contribution, controlled reduction processes were performed on α-La₂Mo₂O₉ by employing CaH₂ at different temperatures and durations, resulting in the stabilization of the high temperature polymorph, i.e. the cubic phase, at room temperature. The crystal structure at both local and long-range levels was investigated using high-resolution synchrotron powder diffraction (SPD), neutron powder diffraction (NPD) coupled to neutron pair distribution function (n-PDF), in addition to high resolution transmission electron microscopy (HRTEM).

## 2. Experimental

### 2.1. Synthesis

The preparation of the raw α-La₂Mo₂O₉ ceramic was undertaken by means of classic solid-state reaction. Stoichiometric amounts of La₂O₃ (99.99%, Aladdin) and MoO₃ (99.0%, Aladdin) were weighed and mixed in ethanol in an agate mortar and pestle. La₂O₃ was dried at 1273 K overnight prior to weighing. The dried powder was pressed into pellets (uniaxial pressure of 330 MPa) and calcined in air at 773 K for 12 h in order to avoid MoO₃ sublimation.³² The obtained product was ground and pressed into pellets that were subsequently fired in air at 1173 K for 12 h. The obtained resulting products were ground into powder for chemical reduction.
Controlled reduction reactions were carefully conducted by grinding α-La₂Mo₂O₉ together with 2-3 molar excess of CaH₂ (98.5%, Aladdin) in a glovebox (Ar atmosphere). The resulting powder mixture was pelletized. The pellet was then flame-sealed in an evacuated silica tube at a pressure below 1×10⁻⁴ MPa and heated at temperatures ranging from 673 K to 723 K for 3 days. The products were then washed with 0.1 M NH₄Cl/methanol in air to remove unreacted CaH₂ and CaO/Ca(OH)₂, and finally with methanol to remove residual NH₄Cl. The resulting dark powder was dried and stored in an Ar-filled glovebox. In this study, the optimal reductive conditions were determined to be 723 K for three days with a 2-molar excess of CaH₂ resulting in β-La₂Mo₂O₉·δ, where δ = 0.22(1).

## 2.2 Characterization

Powder X-ray diffraction (XRD) was performed on a Panalytical X'Pert Pro diffractometer using CuKα radiation over the angular range of 10° ≥ 2θ ≥ 80° with step size of 0.008°. Variable temperature X-ray diffraction (VTXRD) data were acquired over the 15–100° 2θ range with a step size of 0.012° at an interval of 20 K from room temperature to 938 K on heating, allowing 3 min for temperature equilibration before collecting the data sets for 40 min at each set point. High resolution synchrotron powder diffraction (SPD) data were acquired at room temperature on the 11BM beamline at the Advanced Photon Source, Argonne National Laboratory, US, over the 1° to 50° (2θ) range, with a 0.001° step using a λ = 0.45961 nm wavelength. Time-of-flight neutron diffraction experiments were recorded at room temperature at the nanoscale-ordered materials diffractometer, NOMAD,³³,³⁴ at the Spallation Neutron Source (SNS), Oak Ridge Laboratory, USA. All the structure analysis was performed using the Rietveld method with the *JANA2006* software.³⁵ Neutron total scattering data were also acquired at NOMAD station. The PDF data were modeled using the PDFgui software.³⁶
High Resolution Transmission Electron Microscopy was employed to explore the cation distributions at the atomic scale via high-resolution High Angle Annular Dark Field-Scanning Transmission Electron Microscopy (HAADF-STEM) imaging on a JEOL ARM200CF (JEOL Ltd.) Cold FEG operating at 200 kV and equipped with a double spherical aberration corrector. The inner-outer collection angles were 68-174.5 mrad respectively and the probe size was 0.1nm. The sample was first prepared by finely grinding powder which was then dispersed in ethanol and subsequently one droplet of the resulting suspension was deposited on a TEM amorphous holey carbon-coated copper grid and left to dry.

Differential scanning calorimetry (DSC) was performed on a Setaram MULTI HTC 1600 instrument to determine content of oxygen vacancies. A~300 mg powder sample was used, contained within a platinum crucible, under an atmosphere of O₂ and a heating rate of 10 K min⁻¹, samples were heated up to 973 K. The measured temperatures have an incertitude of ±2°K.

Mass spectrometry was carried out using an STA 449C-QMS 403C quadrupole mass spectrometer. The decomposition/detection of volatile elements was performed by heating the reduced La₂Mo₂O₉ sample under an O₂ or N₂ flow at 10 K min⁻¹ in the temperature range of 313–1073 K while using the mass spectrometer to monitor the formation of gaseous products.

X-Ray photoelectron spectroscopy (XPS) data were collected on an ESCALAB 250Xi X-ray photoelectron spectrometer and monochromatic Al Kα X-rays (1486.6 eV) at a power of 75 W under 5 × 10⁻¹⁰ mbar. The binding energies were corrected based on the C 1s peak (284.8 eV).

Alternating-current impedance spectroscopy measurements were carried out with a solartron 1260 frequency analyzer over a frequency range of 10⁻¹-10⁷ Hz within the RT-1073 K in 10% H₂/90% N₂ gas flowing at 90 mL min⁻¹. Prior to impedance spectroscopy measurements,
silver paste was coated in the upper and lower surfaces of the pellets (87% relative density) and dried at room temperature. The ZView software was used to analyze the impedance data.³⁷

# 3. Results and discussion

## 3.1. Average and local crystal structure

The XRD pattern of the as-prepared La₂Mo₂O₉ (Supplementary Figure 1a) matches well with the monoclinic phase (S.G. P2₁) reported by Evans et al. (ICSD number 172479).³ The α-La₂Mo₂O₉ reduction was conducted at temperatures ranging from 673 K to 773 K with 2 or 3 molar excesses of CaH₂ over three days. It was observed that shorter durations or smaller molar excesses of CaH₂ did not significantly reduce α-La₂Mo₂O₉. Elevated temperatures or increased CaH₂ contents gradually caused the powder to darken (Figure 1a-b) and led to its transformation towards the β-phase (ICSD number 98871).⁷ This transformation was evidenced by the merging of reflections around 47° (2θ) into a single reflection (321) cubic characteristic of the cubic phase, which is better visualized in the SPD patterns (13.9° (2θ)) recorded for the sample reduced at 723 K with a 2-molar excess of CaH₂, labeled as β-La₂Mo₂O₉-δ (Figure 1a-b). In addition, the diffraction patterns display a peak shift towards higher angles for the main peaks, while most of the low intensity peaks vanish in the reduced samples. It is noteworthy that a progressive amorphization of the sample occurred, as evidenced by bumps in the background of the XRD patterns (Supplementary Figure 1d). Specifically, the SPD pattern of the sample reduced at 723 K for three days with a two-molar excess of CaH₂, was successfully fitted using Rietveld refinement using the cubic phase as starting structure model. In addition, this sample exhibited the smaller proportion of the amorphous phase. Consequently, this sample was chosen for further characterization.
<figure><img src="image_2.png" /><figcaption>**Figure 1.** SPD patterns and Rietveld refinements of La₂Mo₂O₉ (a) and (b) La₂Mo₂O₉-δ (reduced at 723 K with an excess of 2 mol of CaH₂) samples. The insets depict the color of the samples as well as an enlargement of the (321) cubic reflection that is distinctive from the α to β polymorph. (c) Average structure of α-La₂Mo₂O₉ and (d) β-La₂Mo₂O₉-δ.</figcaption></figure>

The structure and microstructure of the as-reduced sample were further examined using high-resolution transmission electron microscopy (HRTEM) (Figure 2). An amorphous layer of approximately 3 nm in thickness (Supplementary Figure 2b) is observed on the grains. Electron nanodiffraction, using a condenser aperture, performed on the interior of a nanodomain oriented along the [100] direction allowed for indexing according to a cubic cell with a = 7.23 Å (Figure 2a), which aligns well with the P2₁3 structure. No additional spots were visible on the electron
nanodiffraction pattern, indicating the absence of any remaining monoclinic phase (note that the selected area electron diffraction (SAED) for the α-La₂Mo₂O₉ precursor features a more complex electron diffraction pattern, as shown in Figure 2b). To investigate the possibility of local deviation in the underlying structure, atomic scale HAADF-STEM imaging was performed on the as-reduced β-La₂Mo₂O₉-δ sample oriented along the [100] direction. The image (Figure 2c) shows the dumbbells composed of a La site (brighter) and a Mo site (darker) that matches well with the cationic sublattice reported for β-La₂Mo₂O₉ (Figure 1c-d) as confirmed by its associated FFT pattern (Figure 2c inset).

<figure><img src="image_3.png" /><figcaption>**Figure 2.** (a) Electron nanodiffraction pattern recorded for β-La₂Mo₂O₉-δ (diameter of the selected area ~ 50 nm) and (b) SAED pattern for α-La₂Mo₂O₉. (c) HAADF-STEM micrograph at the atomic resolution displaying the microstructure of β-La₂Mo₂O₉-δ oriented along the [100] zone axis. The</figcaption></figure>
corresponding FFT pattern has been inserted in the bottom left, as well as the structure in the bottom right (La in blue and Mo in orange).

Although an amorphous phase with a probably similar La₂Mo₂O₇-y composition exist as a by-product,²² the XRD patterns of the resulting products do not exhibit any peaks resembling the other reduction products of α-La₂Mo₂O₉ reported previously in the literature, i.e., La₂Mo₂O₈.₉₆ or La₂Mo₂O₈.₅₇. Additionally, the color of the initial compound gradually changed from white to black with an increase in reduction temperature, as observed in the inset of Figure 1(a-b). This observed color change is attributed to the presence of oxygen vacancies and/or a variation in the oxidation state of Mo. The existence of oxygen vacancies was confirmed by DSC-TG data, which clearly show a mass increase of 0.88% (Supplementary Figure 3). This mass change corresponds to the chemical formula La₂Mo₂O₈.₆₉ in the as-reduced compound. The oxygen defects are stabilized by the partial reduction of Mo⁶⁺, as inferred from the XPS data analysis (Supplementary Figure 4a and Supplementary Table 1). The 3d₅/₂ spectral lines at 232.72 and 235.74 eV in the Mo spectrum are assigned to the Mo⁶⁺ oxidation state in La₂Mo₂O₉,³⁸ whereas the presence of additional low-energy lines around 230.33 eV in the spectrum of β-La₂Mo₂O₉-δ indicates the presence of low oxidation state, specifically assigned to Mo⁴⁺ (15.87 at% that leads to La₂Mo₂O₈.₆₈ chemical formula, similar to the one observed by TG data).³⁹,⁴⁰ Additional evidence supporting the presence of oxygen vacancies can be inferred from the O1s XPS spectrum. The O1s spectra recorded for La₂Mo₂O₉ before reduction exhibit two distinct peaks at around 530.43 eV and 532.26 eV (Supplementary Figure 4b). The peak with lower binding energy is commonly assigned to lattice oxygen types (O_L), while the peak at about 532.26 eV may be linked to the surface oxygen stemming from a diverse range of species, including adsorbed oxygen O²⁻ and/or OH⁻ like species, such as hydroxyl, and carbonate groups (O_A).⁴¹ Indeed, mass-spectrometry data detected the
existence of these species, including the volatilization of O₂ (Supplementary Figure 5). When La₂Mo₂O₉ is reduced, the amount of OA increases, indicating the existence of oxygen vacancies in the structure. This increase suggests that the powder surface of La₂Mo₂O₉-δ, when exposed to an air atmosphere, adsorbs adventitious hydroxyls from water under ambient conditions. A similar phenomenon was observed in the chemical reduction of LaCrO₃ by CaH₂.²⁷ Last, no significant differences were detected in the La 3d spectra, and the peaks around 834.9 eV (3d₅/₂) and 851.6eV (3d₃/₂) confirm the existence of the La³⁺-O network (Supplementary Figure 4c).

The existence of oxygen vacancies was further supported by time-of-flight neutron powder diffraction experiments (NOMAD station, ORNL, USA). Rietveld refinement of the time-of-flight neutron diffraction patterns (Supplementary Figure 6, banks 1 to 4) with high sensibility to the oxygen positions yielded a good agreement with the P2₁3 reported by Georges et al. (ICSD 98459).⁷ Finally, a combined refinement including the SPD data was performed and Supplementary Table 2 gathers the refined atomic parameters. The refinement of the atomic position for O1, which is fully occupied in the starting model, led to occupancy values larger than one, and thereby its occupancy was fixed to 1. Then, the occupancies for O2 and O3 were refined, but constraining the number of vacancies according to the chemical formula calculated from TG and XPS. Both positions possess similar number of vacancies compared to the initial cubic structure model,⁷ although the variation was larger for O3 (decreases from 0.38(2) to 0.352(3), while the oxygen content at the O2 site slightly decreases from 0.78(2) to 0.761(3). Supplementary table 3 summarizes the main bond distances. Compared with the cubic structure model reported at high temperature, the as-reduced sample exhibits slightly longer Mo-O distances which agrees with the existence of Mo in oxidation states smaller than six, even when the data were recorded at room temperature.
**Local structure analysis by n-PDF.** Supplementary Figure 7a shows the PDF data of La₂Mo₂O₉ before and after reduction (registered at 293 K). Overall, both datasets exhibit similar set of pair distribution functions, although some minor differences can be distinguished. The PDF pattern of the sample after reduction exhibits a marginal shift towards shorter radial distances (*r*), better evidenced at larger *r*, that may indicate a contraction of the unit cell. In both cases, the first peak, centered at 1.78 Å, is attributed to the Mo-O pair and exhibits a shoulder at 2.01 Å, which also indicates Mo-O pairs (Supplementary Figure 7b). This suggests a variable coordination environment surrounding Mo. The broader second peak centered at 2.57 Å is mainly assigned to La-O pairs. The interatomic distances mostly remain constant at local scale. More interestingly, the relative intensity for the peaks arising from the Mo-O pairs changes; the intensity of the first peak diminishes, while that of the shoulder slightly increases. This phenomenon aligns with the lowering of the oxidation state of Mo that results in an elongation of Mo-O bond lengths. Considering that Mo⁶⁺ tends to adopt tetrahedral coordination with Mo-O bond lengths around 1.78 Å, and that Mo⁵⁺ and Mo⁴⁺ usually exhibits longer Mo-O bond lengths,⁴² it can be inferred that the reduction process subtly alters the Mo coordination polyhedra.

Each structure model underwent initial fitting in PDFgui, employing both monoclinic and cubic phases within the 0.5-30 Å range, the upper limit encompassing the larger lattice parameter according the monoclinic structure model (c ~ 29 Å).⁴³ Initially, the scale factor, lattice parameters, and the quadratic atomic correlation factor (*delta*2) were refined, while the PDF Gaussian dampening envelope (*Qdamp*) and PDF peak broadening (*Qbroad*) were fixed to 0.0181 Å and 0.0254 Å, respectively. Subsequently, the fittings improved upon refining the isotropic thermal parameters and the atomic positions. Monoclinic model employment resulted in satisfactory fittings (*R*<sub>w</sub> ~ 6.2%); however, the cubic model failed to accurately describe the observed shoulders
(R<sub>w</sub> ~ 31.7%), such as the one at around 2.0 Å, which cannot be modulated based on the cubic structure model (Figure 3a-b). This is not surprising given that the calculated PDF patterns from the reported structure model displays remarkable differences that are not observed experimentally (Supplementary Figure 8). On the other hand, the fittings of the PDF patterns for r > 10 Å improved using the cubic model, and a clear reduction in the R<sub>w</sub> values was observed as a function of the analyzed r range, i.e., lower values were noted when local to medium scales were not considered (see Supplementary Figure 10).

Given that the monoclinic model accurately fits the components of the PDF patterns, it was
utilized to reveal distinctive structural features of the compounds before and after reduction; The
monoclinic cell appears to contract upon reduction, although the change is anisotropic, where the
*a* and *b* lattice parameters expand while *c* parameter shrinks from 28.61(1) Å to 28.137(1) Å. The
monoclinic angle also decreases upon reduction (from 89.8(3)° to 89.4(1)°). Nevertheless,
unveiling the distribution of the oxygen vacancies is challenging owing to the elevated number of
O atomic positions. An important aspect emerging from our investigation is the notable increase
in Mo-O pairs with bond lengths around 2 Å (Supplementary Figure 9a), which exceeds the typical
range for tetrahedral coordination, traditionally between 1.7 and 1.85 Å.<sup>44</sup> This observation
suggests a significant variation in the coordination environment surrounding certain Mo cations.
Indeed, the refined unit cell data indicates a reduction in the number of Mo cations in tetrahedral
coordination from 15 to 10.<sup>3</sup> This shift correlates with changes in the oxidation state from Mo<sup>6+</sup> to
Mo<sup>4+</sup>, as observed by XPS analysis. Mo<sup>4+</sup> and Mo<sup>5+</sup> have a lower tendency to stabilize in
tetrahedral environments, favoring trigonal bipyramid and/or octahedral coordination
geometries.<sup>42</sup>
It is worth noting that Malavasi et al.⁴⁵ conducted qualitative analysis of n-PDF data for both α-La₂Mo₂O₉ (recorded at 773 K) and β-La₂Mo₂O₉ (acquired at 873 K), finding no significant differences between the PDF patterns at the local scale. Both patterns were successfully refined using the monoclinic structure model, focusing solely on refining lattice parameters, scale factor, and dynamic correlation factor. Similarly to this study, the cubic model did not provide satisfactory fits at the short range (< 10 Å),⁴³ even for the phase identified as cubic by neutron diffraction. The authors concluded that the local structure of β-La₂Mo₂O₉ closely resembles its lower temperature monoclinic phase, proposing that the long-range cubic symmetry is a dynamic average of local monoclinic arrangements in the oxygen sublattice. This finding suggested that the structural phase transition in La₂Mo₂O₉ is not a change in structure per se but a transition from a static to a dynamic distribution of oxygen vacancies.

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Fits of n-PDF data obtained at 300 K for β-La₂Mo₂O₈.₆₈ with the average monoclinic (a) and cubic (b) structure models. The pink circles correspond to the experimental data, while the blue and green lines represent the calculated data and difference curves, respectively.</figcaption></figure>

There are numerous examples in the literature where the local structure significantly differs from the average structure. For instance, the discrepancy is evident in oxygen-deficient perovskites such
as Sr₂ScGaO₅⁴⁶ and SrSc₀.₃Zn₀.₂Ga₀.₅O₂,⁴⁷ the hexagonal perovskite Ba₃NbMoO₈.₅, lithium orthosilicate cathode materials Li₂MSiO₄ (M = Mn, Fe and Co),⁴⁸ RE₃TaO₇ weberite-type compounds, or non-oxide based compounds such as GeBi₂Te₄.⁴⁹ Similarly, our PDF data analysis, like that of Malavasi et al., suggests that our cubic β-La₂Mo₂O₈.₆₈(1) is better described using the monoclinic model, especially at the local scale. Nevertheless, the significantly lower oxygen motion in our sample (the PDF data were recorded at 293 K, unlike Malavasi et al.⁴⁵ who conducted their measurements at 773 K and 873 K for the monoclinic and cubic phases, respectively), suggests that the observed features cannot be attributed to a dynamic average distribution of oxygen vacancies in the oxygen sublattice. In the specific case of β-La₂Mo₂O₈.₆₈, the apparent cubic symmetry encompasses a static distribution of oxygen vacancies, with 'randomness' only evident when viewed on a larger scale, as observed by SAED and NPD/SPD data. At the scale of a single unit cell, the distribution is not random, leading to the manifestation of monoclinic symmetry. Therefore, the monoclinic model is necessary to accurately describe the local structural details that the average cubic structure overlooks.

## Thermal stability by VTXRD.

The crystal phase evolution was monitored in air using VTXRD. Figure 4 displays the (321) pseudo-cubic peak evolution. What was first noticed is a better resolution of the diffraction peak at around 538 K, which is attributed to the elimination water molecules and derivate chemical species absorbed in the powder. In any case, the as-reduced powder retained its cubic structure until 638 K, at which point a transition to the monoclinic form was observed and indicated the oxidation of the powder. Subsequently, the transformation from the monoclinic to the cubic phase occurred within the temperature range of 838-858 K temperature range, as expected. The β-phase was then maintained up to the highest recorded temperature of 938 K.
The phase reverted to monoclinic at 798 K upon cooling, remaining stable down to room
temperature. Notably, the color of the powder changed from blue dark to pale yellow during the
experiment).

<figure><img src="image_5.png" /><figcaption>**Figure 4.** (a) Visualization of the splitting of the (123) pseudo-cubic peak of β-La₂Mo₂O₈.₆₈(1) upon heating and cooling, recorded in air. The data were recorded in air. (b) The main phase transition events and temperatures through the variation of the (123) pseudo-cubic peak. The XRD patterns shown in red correspond to those recorded during heating, while the patterns shown in blue were recorded during cooling</figcaption></figure>

**Electrical conduction properties - AC Impedance spectroscopy**

A critical aspect of this study was investigating the impact of the reduction process on the electrical properties of La₂Mo₂O₉. To minimize re-oxidation of β-La₂Mo₂O₈.₆₈(1), AC impedance measurements were conducted in an atmosphere consisting of 90% Ar and 10% H₂. The same conditions were applied for La₂Mo₂O₉ sample (before reduction). Figure 5a shows the complex impedance spectrum of La₂Mo₂O₈.₆₈(1) at 673 K, which comprises one large semicircular arc in the
high frequency region and a curved inclined spike at low frequencies within the middle to low
frequency region. The large semicircular arc can be modeled with an equivalent circuit consisting
of parallel resistor (R) and a constant phase element (CPE) as shown in Supplementary Figure 11.
The intercept of the semicircular arc in the low frequency was extracted as resistivity, and the
associated capacitance estimated by 2πfmaxRC = 1 (where fmax is the frequency in hertz at the
arc maximum) is ~9 pF cm⁻¹ (see inset of Figure 5a), indicating the bulk response.⁵⁰ This is further
confirmed by the existence of one single imaginary electrical modulus M'' peak from the
imaginary electrical modulus as a function of frequency that matches with the peak maxima in the
imaginary part of the complex impedance Z'' vs frequency plot (Supplementary Figure 12).⁵¹ The
electrode response observed in the low frequency region has capacitance with a magnitude of ~10⁻⁸–10⁻⁷ F cm⁻¹ within 10–1 Hz is attributed to ion blocking at the electrodes, suggesting the
occurrence of ionic conduction in the sample, although the apparent curvature of the spike
indicates that the capacitance is not completely blocking. This behavior likely reflects the existence
of electronic conduction through the sample involved in the charge transfer of oxygen across the
electrode-sample interfaces.⁵² No apparent grain-boundary response arc was observed due to the
grain boundary overlaps significantly with the electrode response arcs. With increasing the
temperature, the bulk response arc gradually disappears, resulting in a well-resolved grain-
boundary response arc and a partially collapsed electrode response arc at 1073K (Supplementary
Figure 13). The transformation of the electrode response from an inclined spike to a semicircular
form is primarily attributed to the diminishing influence of the oxide ion charge transfer
component, and the increasing contribution of electronic conduction to the total conductivity due
to the partial reduction of Mo (Supplementary Figure 4a and Table 1).⁵⁰,⁵³ Figure 5b shows the
comparison of conductivity for β-La₂Mo₂O₈.₆₈(1) and as-made α-La₂Mo₂O₉ composition under 5%
H₂-95% Ar atmosphere. The total conductivity (σt) of β-La₂Mo₂O₉.₆₈(1) is two order of magnitude smaller than the observed value for La₂Mo₂O₉ at 1073 K (σt = ~5.4 × 10⁻⁴ and ~2.8 × 10⁻² S cm⁻¹, respectively). The trend of the conductivity values for the reduced sample did not display any conductivity jump attributed to the α-β phase transition, in contrast with what is observed for the non-reduced sample. This fact further supports the stabilization of the cubic phase by chemical reduction with CaH₂. The activation energy, calculated from the slope of the Arrhenius plot, is 0.72 eV within the 523–1073 K temperature range, which is lower than the value of 1.2 eV calculated in the pioneering work by Lacorre et al.²

<figure><img src="image_6.png" /><figcaption>**Figure 5.** (a) Typical complex impedance plots and related fitted curves (red) for β-La₂Mo₂O₉.₆₈(1) at 673K (relative density (ρrel) of ~73% alongside for α-La₂Mo₂O₉ (ρrel ~87%). The inset (a) illustrates the dependence of capacitance with frequency. Rb and Rt donate the bulk and total resistivities, respectively, while the numbers denote the logarithms of the selected frequencies marked by filled circles. (b) Arrhenius plots of the conductivities for β-La₂Mo₂O₉.₆₈(1) and the as-made α-La₂Mo₂O₉ ceramic.</figcaption></figure>
According to the collected data, the ionic conductivity was not enhanced following reduction; instead, it diminished, even though a cubic phase was stabilized. Upon reduction, the shortest O-O interatomic distances increased from ~2.69 Å to ~2.84 Å upon reduction (values obtained from the peak maxima observed in the simulated O-O PDF partials, Supplementary Figure 9b). These distances are still within the typical range for other good oxide ion conductors (e.g., ~2.8 Å in LaGaO₃,⁵⁴ ~2.9 Å in LaBaGaO₄,⁵⁵ or shorter than 2.7 Å found in La₁.₅₄Sr₀.₄₆Ga₃O₇.₂₇⁵⁶). Consequently, direct conclusions cannot solely rely on analyzing the O-O interatomic distances in β-La₂Mo₂O₈.₆₈. Consideration of other differences between the cubic phase observed here and those explored at higher temperatures should be considered.

High conductivity in β-La₂Mo₂O₉ is typically assigned to oxygen disorder associated with high oxygen mobility, a phenomenon identified by Malavasi et al.⁵⁷ as a dynamic disorder of oxygen defects. Nevertheless, in our case, the cubic phase was stabilized at a low temperature where oxygen motion is limited, and therefore, the premise of Malavasi et al. does not apply. In β-La₂Mo₂O₈.₆₁(1) the oxygen vacancy distribution remains static, and that could explain the low conductivity observed. Additional factors affecting the ionic conduction include an increased number of oxygen vacancies that can induce structural distortions and increase defect interactions, mobility of oxide ion defects as observed in other oxide ion conductors such as in melilite family,⁵⁸ cation-deficient apatites⁵⁹ or scheelite.⁶⁰ In addition, there is an overall reduction of the unit cell, which could lead to a less open space for oxygen migration. Last, the partial reduction of Mo could also limit oxygen vacancy migration, as Mo⁴⁺ and Mo⁵⁺ exhibit less flexibility to adapt to different coordination environments.⁴²

Considering other scenarios where the cubic phase was stabilized via aliovalent doping acceptor strategy, the content of oxygen vacancies was not altered but regulated through changes in the
valence state of Mo. In addition, the stabilization of the cubic phase in those cases did not consistently result in enhanced ion conductivity. For instance, conductivities at 1073 K are almost one order of magnitude lower than that of the non-reduced $\beta$-La$_2$Mo$_2$O$_9$ for substitutions of Ba (10%), K (5%) and Sr (5%) at the lanthanum site.¹¹ The greater values were reported when isovalent substitution took place, probably due to the lower crystal structure distortion at low temperature. Still, those substitutions did not result in better conductivities within 873-1073 K temperature range.

## Conclusions

The controlled reduction of $\alpha$-La$_2$Mo$_2$O$_9$ using CaH$_2$ as a reducing agent result in the formation of cubic phase $\beta$-La$_2$Mo$_2$O$_{8.68(1)}$ not previously reported. In the specific instance of $\beta$-La$_2$Mo$_2$O$_9$ stabilized at low temperatures, the oxygen vacancies are statically distributed, which differs from the dynamic distribution necessary for higher conductivity observed at elevated temperatures. This static but random distribution of vacancies, combined with a reduced unit cell size, likely impedes oxygen migration, thus reducing ionic conductivity despite the stabilization of the cubic phase. This analysis highlights the crucial role of temperature and defect dynamics in determining the electrical properties of oxide ion conductors. The present work represents a fascinating example of solid-state chemistry where manipulating the oxygen content can lead to different crystal structures and phases with unique properties.

## ASSOCIATED CONTENT

XRD patterns of La$_2$Mo$_2$O$_{9-δ}$ reduced at different temperatures and with different amounts of CaH$_2$. Representation of the cationic sublattices of $\alpha$-La$_2$Mo$_2$O$_9$ and $\beta$-La$_2$Mo$_2$O$_9$. DSC-TG data of reduced La$_2$Mo$_2$O$_9$. XPS spectra comparison of La$_2$Mo$_2$O$_9$ and La$_2$Mo$_2$O$_{9-δ}$. Mass-
spectrometry of gas species during heating of La₂Mo₂O₉·₈ under flowing O₂ gas. Combined Rietveld refinement against time-of-flight neutron and X-ray synchrotron powder diffraction data collected on La₂Mo₂O₉·₈ from Banks 1 to 4. Comparison between the experimental PDFs of La₂Mo₂O₉ before and after reduction. Comparison between the calculated PDFs of La₂Mo₂O₉ from the monoclinic and cubic models. Mo-O (a) and O-O (b) partial PDFs. R<sub>w</sub> evolution of the PDF fittings as a function on the radial distances obtained for La₂Mo₂O₉ reduced sample.

Equivalent circuit. Binding energies and relative percentages for the different elements in La₂Mo₂O₉ and La₂Mo₂O₉·₈. Weighted residual (R<sub>w</sub>) of the PDF fittings. Imaginary impedance Z'' and modulus M'' as function of frequency at 673 K for the La₂Mo₂O₈·₆₈(1) pellet.

Refined atomic parameters and main bond distances for β-La₂Mo₂O₉ from room temperature neutron total scattering. (PDF)

AUTHOR INFORMATION

**Corresponding Author**

* kuangxj@glut.edu.cn and alberto@glut.edu.cn

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval
to the final version of the manuscript.

ACKNOWLEDGMENT

The authors thank the National Science Foundation of China (Nos. 21850410458, 22365011, 22090043), Guangxi Natural Science Foundation (No. 2019GXNSFGA245006, 2020GXNSFAA297050) for the financial support, and the EMERGIA program from Junta de
Andalucía [No. 2022/00001043]. AJFC is extremely grateful to LE STUDIUM for the financial support. Use of the Advanced Photon Source at Argonne National Laboratory was supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. A portion of this research used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory. The beam time was allocated to NOMAD on proposal number IPTS-28909. The project benefitted from the microscopy facilities of the Platform MACLE-CVL which was co-funded by the European Union and Centre-Val de Loire Region (FEDER). We thank Dr. Emmanuel Veron and Sandra Ory (CEMHTI laboratory) for the VT-XRD and DSC-TG data acquisition.

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