# Reaction Intermediates and Oxygen Ordering Explored by In Situ Neutron Powder Diffraction during Thermal Oxidation of La2CoO4.00

Ruben de Barros, Monica Ceretti, Anna Marsicano, Vivian Nassif, Clemens Ritter, Werner Paulus

► To cite this version:

Ruben de Barros, Monica Ceretti, Anna Marsicano, Vivian Nassif, Clemens Ritter, et al. Re-action Intermediates and Oxygen Ordering Explored by In Situ Neutron Powder Diffraction during Thermal Oxidation of La2CoO4.00. Inorganic Chemistry, 2026, 65 (2), pp.1142-1150. 10.1021/acs.inorgchem.5c04240 . hal-05441946

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Reaction intermediates and oxygen ordering
explored by *in situ* neutron powder diffraction
during the thermal oxidation of La<sub>2</sub>CoO<sub>4.00</sub>

Ruben De Barros<sup>a</sup>, Monica Ceretti<sup>a*</sup>, Anna Marsicano<sup>a†</sup>, Vivian Nassif<sup>b</sup>, Clemens Ritter<sup>c</sup>,
Werner Paulus<sup>a</sup>.

a ICGM, Univ Montpellier, CNRS, ENSCM, 34293 Montpellier, France

b Université Grenoble Alpes, CNRS, Institut Néel, 38000 Grenoble, France

c Institut Laue-Langevin, 38042 Grenoble, France

*Corresponding author: monica.ceretti@umontpellier.fr

KEYWORDS. Non-stoichiometric oxides, La<sub>2</sub>CoO<sub>4+δ</sub>, *in situ* neutron diffraction, oxygen ordering.
ABSTRACT. The thermal oxidation of stoichiometric La₂CoO₄₀.₀₀ was investigated using *in situ* neutron and X-ray powder diffraction in air, complemented by thermogravimetric analysis (TGA). The process involves the topotactic insertion of extra oxygen atoms into interstitial lattice sites, forming La₂CoO₄+δ. Oxygen uptake initiates above 320 K, leading to a sequence of phase transitions as a function of temperature (T) and oxygen excess (δ). The structural evolution starts from an orthorhombic phase at δ = 0, transitions to a tetragonal phase for 0.05 ≤ δ ≤ 0.17, and proceeds through two distinct orthorhombic phases, both exhibiting long-range oxygen ordering above 525 K. The maximum oxygen concentration, observed above 680 K, corresponds to La₂CoO₄·263.

The resulting phase diagram reveals rapid oxygen diffusion and ordering kinetics, accompanied
by subtle structural modifications as a function of δ. Notably, the long-range oxygen order
remains stable over a wide temperature range. Each phase was structurally characterized using
Rietveld refinement.

INTRODUCTION

Ruddlesden-Popper (RP) oxides, with the general formula A₂BO₄, are a class of materials known for their unique electronic and physical properties, which arise from the intricate interactions between lattice, orbital, charge, and spin degrees of freedom.¹⁻³ These materials also demonstrate excellent oxygen ion conductivity at moderate temperatures, rendering them promising candidates for applications in oxygen membranes and electrodes for solid oxide fuel cells (SOFCs) and Solid Oxide Electrolysis Cells (SOECs).⁴,⁵ The structure of RP oxides features an alternating arrangement of A₂O₂ rock-salt layers and infinite BO₂ layers along the c-axis, as shown in Figure 1a. The mechanism of ionic conductivity is closely tied to the presence of excess interstitial oxygen (δ) within the rock-salt layers, resulting in significant
anharmonic displacements of the apical oxygen atoms.⁶,⁷ This gives rise to a shallow one-
dimensional oxygen diffusion pathway between the apical and interstitial oxygen sites, as
described in ⁸,⁹, promoting oxygen conductivity at moderate temperature.

At high oxygen doping levels, long-range oxygen ordering can extend to the mesoscale, a phenomenon observed in several Ruddlesden-Popper oxides, which exhibit remarkable thermal stability. For instance, in Nd₂NiO₄+δ, five distinct first-order phase transitions have been detected between 296 K and 800 K.¹⁰ Each of these transitions is characterized by long-range oxygen ordering with varying modulation vectors and fast ordering kinetics. This behavior points to high oxygen mobility and a relatively narrow energy landscape for the associated ordering processes. Similarly, in the case of the Pr₂NiO₄ homologue, diffraction studies have revealed a three-dimensional, long-range organization of oxygen, with an unprecedented level of complexity at room temperature, featuring superstructural periodicities reaching up to 94 Å.¹¹,¹²

In this context, La₂CoO₄+δ (LCO) is particularly noteworthy, showing a remarkable oxygen
uptake capacity with 0 ≤ δ ≤ 0.25 and reaching δ ≈ 0.32 under high-pressure O₂ treatment. ¹³
In addition, it appears to be the only nonstoichiometric transition metal oxide so far that has
reported to show spontaneous oxygen uptake at ambient conditions, resulting in remarkably
high diffusion coefficients and unexpectedly low activation energies. ¹⁴,¹⁵ Depending on
oxygen content (δ) and temperature, La₂CoO₄+δ presents a complex phase diagram, revealing
several structural phase transitions between orthorhombic and tetragonal symmetries as a
function of δ and temperature. ¹³,¹⁶

At room temperature, the stoichiometric La₂CoO₄.₀₀ phase adopts the Low Temperature Orthorhombic (LTO) structure (space group *Bmab*), whereas the over-stoichiometric phase with δ ≥ 0.12 transitions to an orthorhombic structure with the space group *Fmmm*. A
spontaneous oxidation process of the stoichiometric La₂CoO₄.₀₀ compound at room temperature was reported by Nemudry, following a two-stage kinetic behavior: in the first stage, oxygen uptake is observed to occur rapidly within the first 10–20 minutes.¹⁴ After this first O-uptake, oxidation continues much more slowly over several days and can persist for months under ambient conditions. Qualitative structural analysis by X-ray powder diffraction suggested that the oxidation process proceeds through a series of phase transitions, beginning with a LTO phase at low oxygen content and progressing to a low-temperature tetragonal (LTT) phase at intermediate oxidation levels. Upon further oxidation, a new low-temperature orthorhombic (LTO) phase was observed.

Beside TGA experiments, no quantitative neutron diffraction study was reported on the oxygen uptake of stoichiometric La₂CoO₄.₀₀. The upper oxygen incorporation limit (δ = 0.25), corresponding to one extra oxygen atom per unit cell, is achieved by annealing in an oxygen-rich atmosphere, yielding the orthorhombic *Fmmm* phase of La₂CoO₄.₂₅.¹⁷ For this high oxygen content (δ = 0.25), single-crystal X-ray diffraction reveals the formation of complex superstructures, corresponding to an oxygen ordering scheme with a 4a x 4b cell but also involving Co²⁺/Co³⁺ charge ordering.¹⁵,¹⁷

Characterizing the thermal evolution of La₂CoO₄.₀₀, especially in terms of oxygen-uptake, is essential for understanding the structure-property relationships. Neutron powder diffraction (NPD) is a particularly effective technique for these studies, providing detailed information on atomic positions, interstitial oxygen occupancy, and temperature parameters. Very few studies report the thermal evolution of La₂CoO₄+δ in situ through neutron diffraction.¹³,¹⁶ Nevertheless, *in situ* investigations are essential when considering the tuning of mechanical stability, chemical reactivity, and catalytic solid/gas reactions, particularly in relation to oxygen diffusion and transport properties, as well as identifying potential oxygen ordering.
Consequently, a primary objective of this study is to quantitatively elucidate the structural phase diagram of La₂CoO₄+δ as a function of temperature (T) and oxygen content (δ). To achieve this, we investigated the structural evolution during the oxygen uptake reaction in air by *in situ* neutron powder diffraction at temperatures up to 765 K, starting from the stoichiometric La₂CoO₄.₀₀ compound.

Neutron diffraction offers a significant advantage over X-ray diffraction, as it provides true bulk information, whereas X-ray diffraction is limited to a few micrometers, making it difficult to quantify the volume fractions of phases formed during the reaction. This is particularly important for phase analysis in solid-state reactions. Another advantage of neutron diffraction is that the coherent neutron scattering length of oxygen (5.803 fm) is comparable to that of La (7.69 fm/4.58 fm) and Co (10.3 fm), providing much better contrast for the low-Z oxygen atoms. This enhances the ability to detect oxygen ordering and the identification of reaction intermediates. This approach enabled us to uncover several phase transitions and oxygen ordering during intercalation, enhancing the understanding of oxygen transport and diffusion mechanisms together with the structural stability of La₂CoO₄+δ.

<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>
**Figure 1.** (a) *F*-centered crystallographic unit cell of orthorhombic La₂CoO₄+δ (blue: Co, red: O, grey: La). Interstitial oxygen atoms are located in the La₂O₂ rock salt layer, tetrahedrally coordinated by the apical oxygen as well as La atoms. One out of 8 possible equivalent Oint tetrahedral positions is shown, the average occupation being 1/8. (b) Orthorhombic *Bmab* La₂CoO₄.₀₀. (Reproduced from De Barros R., Ceretti M., Schmidt W., *et al*. Growth and Oxygen Stoichiometry Control of High-Quality La₂CoO₄+δ Single Crystals (δ = 0.25). *Crys. Growth Des.* **2022**, *22* (9), 5542–5551. Copyright 2022, American Chemical Society¹⁷

## EXPERIMENTAL

**Sample preparation.** La₂CoO₄+δ starting material was prepared by classical solid-state reactions at high temperature, beginning from the precursor binary La₂O₃ and Co₃O₄ oxides. Prior to the synthesis, La₂O₃ was heated in dynamic primary vacuum at 1173 K overnight to remove any hydroxide traces. Stoichiometric amounts of La₂O₃ and Co₃O₄ powders (99.99% purity, Alfa Aesar) were then thoroughly ground, and calcinated for 12h at 1173 K in air, with heating and cooling rates of 300 K h⁻¹. The obtained powders were then ground again, pressed in pellets and sintered at 1523 K for 24 h (with heating rate of 500 K h⁻¹, and furnace cooling), in pure argon flux (99,999 %). This step was repeated two times with intermediate grinding and pelletizing, giving rise to the pure La₂CoO₄+δ phase. Subsequent annealing at 723K during 6h in a 5%H₂/95%Ar atmosphere was performed to get the pure stoichiometric δ=0 compound.

Synthesizing La₂CoO₄+δ is quite challenging due to cobalt's mixed valence. The Co²⁺ state is comparatively unstable compared to Co³⁺, and even trace oxygen can oxidize it, forming LaCoO₃ (*Pm-3m*, *a* = 3.82 Å). Phase purity was confirmed by X-ray diffraction (Figure S2),
with no detectable perovskite peaks. The reduced product is fully refined and indexed within the *Bmab* (LTT) structure. For reference, LaCoO₃ would produce diffraction peaks at 2θ = 23.27°, 33.14°, and 40.89° ((100), (110), (111) reflections).

**X-ray diffraction.** Crystalline phase identification and sample purity were assessed from X-ray powder diffraction (XRPD) data collected on a Panalytical diffractometer in Bragg Brentano geometry using Cu<sub>Kα</sub> radiation. Variable temperature X-rays diffraction patterns were collected on a Panalytical Empyrean diffractometer (Co<sub>Kα1</sub>,<sub>Kα2</sub>) equipped with an Anton Paar HTK 1600 furnace. X-rays diffraction measurements were performed on heating from 295 K (RT) up to 723 K for reduction (and 763 K for the oxidation) with 10 K/min ramp, covering a 2θ range between 32° and 40°, in order to monitor the evolution of the (113), (200), and (002) reflections, which are characteristic of the phases being studied.

**Neutron Diffraction.** The room-temperature crystal structure of stoichiometric La₂CoO₄.₀₀ was determined by neutron powder diffraction (NPD) using the high-resolution diffractometer D2B (λ = 1.59 Å up to Q = 7.7 Å⁻¹), at the high-flux reactor of the Laue-Langevin Institute (ILL, France). *In situ* neutron powder diffraction experiments were carried out using the D1B high-intensity two-axis diffractometer at the ILL. The instrument, equipped with a Position Sensitive Detector (PSD) spanning an angular range of 0.8° to 128.8°, provided rapid data acquisition with robust statistical precision. A neutron wavelength of 1.287 Å was selected to access high momentum transfers (up to Q = 8.7 Å⁻¹), enabling a reliable refinement of oxygen site occupancies. The experimental study focused on the oxidation of the stoichiometric phase La₂CoO₄.₀₀ to the oxygen-rich phase La₂CoO₄.₂₅ under ambient air conditions. Approximately 2 grams of synthesized polycrystalline La₂CoO₄.₀₀ were loaded in a quartz tube open to air, and positioned within the isothermal zone of a vanadium. Diffraction patterns were recorded every 5 minutes while the
temperature was ramped from ambient conditions to 765 K. In order to accurately capture the orthorhombic-to-tetragonal transition, the initial heating section up to 550 K was performed at a low rate of 0.2 K/min. Due to neutron beamtime limitations, a slightly higher rate of 0.3-0.4 K/min was used in the subsequent temperature range. In the temperature regions with no observable structural transitions, diffraction patterns over a 12 K range were summed to improve statistical accuracy, yielding a balance between temporal resolution and data quality.

Diffraction data were analyzed using the Rietveld refinement method implemented in the FULLPROF suite.¹⁸ Peak profiles were modelled using a pseudo-Voigt function, and the uneven background arising from the quartz container was extrapolated using reflection-free points.

**Thermogravimetric Analysis.** Thermogravimetric analysis (TGA) measurements were carried out in 33%O₂/67%Ar atmosphere in the temperature range of 300-813K using a Perkin Elmer TG8000 thermobalance (weight accuracy 0.1µg). The same thermal ramp as in the NPD experiments was applied, consisting of 0.2 K/min up to 550 K followed by 0.3–0.4 K/min, allowing a direct comparison between the oxygen content values obtained from TGA and neutron diffraction. A baseline correction with an empty sample holder was applied for all the measurements.

## RESULTS and DISCUSSION

**Thermal behavior.** Prior to the neutron powder diffraction (NPD) studies, we investigated the oxygen uptake kinetics of stoichiometric La₂CoO₄₀₀ by *in situ* X-ray diffraction, as well as by thermogravimetric analysis (TGA).
*In situ* X-ray diffraction measurements were performed using a closed reaction chamber mounted on the powder diffractometer, allowing to switch between H₂ and O₂ gases avoiding possible contaminations e.g., CO₂, which might interfere with the surface creating carbonates and thus inhibiting or at least affecting the O₂ uptake reaction. La₂CoO₄+δ was at first reduced in 5%H₂/N₂ at 723 K (rate 10 K/min) for 6h. This treatment enables the formation and stabilization of the reduced stoichiometric *Bmab* phase, as evidenced by the progressive evolution of the X-ray diffraction patterns (Fig. 2a and 2b). After rapid cooling to room temperature the gas atmosphere was then switched to pure O₂ to probe the oxygen uptake behaviour at room temperature. X-ray diffraction measurements at room temperature over a period of 18 hours did, however, not reveal any structural modifications, i.e., an oxygen uptake (Figure 2c).

The first structural changes were only observed while heating to 320 K, revealing the emergence of a tetragonal intermediate phase, evidenced by the merging of the (020) and (200) peaks (Figures 2d and 2f). These results are supported by thermogravimetric studies under equivalent reaction conditions as applied to the *in-situ* X-ray experiment (Figure 2f and 2g). No measurable weight change was observed over a period of at least 18 hours for a freshly reduced La₂CoO₄.₀₀ sample left at room temperature (Figure 2f) in contrast to ref 14. Oxygen uptake begins to gradually set in between 320 K and 430 K, resulting in a weight increase of ~0.18%. A more pronounced weight uptake occurs only beyond 430 K, continuing up to 600 K, the weight gain being approximately 1%, corresponding to La₂CoO₄.₂₅ (Figure 2d). Upon further heating to 650 K, a slight additional weight uptake is observed, corresponding to La₂CoO₄.₂₆₃. Multiple TGA measurements were performed on independently prepared samples to verify reproducibility (see Supporting Information, Figure S1), all of which show a consistent thermal behaviour.
These findings contrast with earlier reports by Nemudry *et al.* and Girgsdies *et al.* ¹⁴,¹⁹, in which spontaneous oxygen uptake was identified by a significant mass increase after only ~20 minutes after exposure to O₂ at RT.¹⁴ We were, however, unable to reproduce the spontaneous oxygen uptake at room temperature previously reported in [14] on any of several samples studied. X-ray diffraction data reveal that the tetragonal phase forms quantitatively only upon heating in oxygen above 320 °C, which is accompanied by a modest oxygen uptake at that temperature (Figures 2b and 2d). The reported spontaneous oxidation of La₂CoO₄+δ remains thus unclear. The two key studies on this topic are also contradictory: Nemudry [ref] reports spontaneous oxidation of freshly reduced La₂CoO₄·₀₀, while Girgsdies [ref] describes a much slower, barely quantified process under similar synthesis conditions. Our experiments in a close reaction chamber, preventing exposure of the sample to air when switching from reduction to oxidation mode, replicate Girgsdies’ procedure except for minor differences in the sintering and reduction temperatures, do not show spontaneous oxidation either. Small temperature variations (673–723 K) and surface effects such as carbonate or hydroxide formation can therefore be excluded as causes. Despite extensive trials, we were unable to reproduce Nemudry’s observations. At room temperature, the tetragonal phase, indicative of oxygen incorporation, was first observed after 24 h with a volume fraction of about 3%, which increased to 10% after 8 months during which the sample was stored in air at room temperature (Supporting Information Fig. S2).
<figure><img src="image_4.png" /></figure>

Figure 2. (a-b) X-ray diffraction of La₂CoO₄+δ during heating to 723 K in H₂/N₂ and the high-temperature dwell, showing stabilization of the reduced phase. (c) Diffraction of the reduced phase La₂CoO₄.₀₀ at room temperature over 18 h in O₂, confirming structural stability. (d) Structural evolution upon heating in O₂, indicating the onset of a single tetragonal phase at 320 K, followed by the formation of two distinct orthorhombic phases, setting in at 450 K and 600 K respectively. (e) Thermal profile of the reduction/oxidation process. In the inset (f, g) Thermogravimetric analysis of La₂CoO₄.₀₀ with time in flowing O₂: evolution of the weight at room temperature (f), showing no measurable oxygen uptake, and during heating (g), indicating oxygen uptake sets in above 320 K, consistent with the formation of the tetragonal intermediate phase.

**Structural Evolution during oxygen uptake as a function of the temperature followed up by NPD.** The room temperature crystal structure of the stoichiometric starting compound La₂CoO₄.₀₀ was obtained by neutron powder diffraction on D2B at ILL. Rietveld refinement confirms an orthorhombic *Bmab* structure. The occupancy of the oxygen interstitial atoms was also refined, confirming an oxygen stoichiometry of 4.00 within the experimental error. The negligible occupancy of the interstitial sites rendered refinement of the atomic displacement parameters unreliable; consequently, these parameters were kept fixed throughout the
refinement. The refined neutron diffraction pattern is shown in Figure 3, with structural parameters listed in Table 1.

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Rietveld refinement of NPD data at RT of La₂CoO₄.₀₀, corresponding to the orthorhombic *Bmab* symmetry. Data obtained on D2B at ILL (λ = 1.59Å). Red dots are the experimental data while the calculated patterns are represented by continuous black lines. The blue continuous line represents the difference between the experimental and calculated intensities, the short green vertical bars mark the structural Bragg peaks.</figcaption></figure>

<table><caption>**Table 1.** La₂CoO₄.₀₀ structural data obtained at RT from powder neutron diffraction data, collected on the high resolution D2B diffractometer at the ILL, with λ=1.594 Å (up to sinΘ/λ = 0.6Å⁻¹). Refinements were carried out in the space group *Bmab*.ᵃ Crystallographic information file (CIF) has been deposited with the Cambridge Crystallographic Data Centre (CCDC) under deposition number 2501635.</caption><thead><tr><th>Atom</th><th>Wyck.<br>Pos.</th><th>x</th><th>y</th><th>z</th><th>occ.</th><th>U<sub>iso</sub> (Å<sup>2</sup>)</th><th></th></tr></thead><tbody><tr><td>La</td><td>8f</td><td>0</td><td>0.9868(2)</td><td>0.3621(1)</td><td>2.00</td><td>0.0054(3)</td><td></td></tr><tr><td>Co</td><td>4a</td><td>0</td><td>0</td><td>0</td><td>0.976(13)</td><td>0.0064(9)</td><td></td></tr><tr><td>O<sub>apical</sub></td><td>8e</td><td>0.25</td><td>0.25</td><td>0.9868(2)</td><td>1.997(13)</td><td>U<sub>eq</sub>=<br>0.0102(9)</td><td>U<sub>11</sub> = 0.0022(7)<br>U<sub>22</sub> = 0.0132(10)<br>U<sub>33</sub> = 0.0152(11)<br>U<sub>12</sub> = -0.0044(6)</td></tr></tbody></table>
<table><tr><td>O<sub>equatorial</sub></td><td>8f</td><td>0</td><td>0.0547(3)</td><td>0.1798(3)</td><td>1.996(14)</td><td>U<sub>eq</sub>=<br/>0.0133(9)</td><td>U<sub>11</sub> = 0.0165(9)<br/>U<sub>22</sub> = 0.0190(11)<br/>U<sub>33</sub> = 0.0045(8)<br/>U<sub>23</sub> = 0.0025(8)</td></tr><tr><td>O<sub>interstitial</sub></td><td>8e</td><td>0.25</td><td>0.25</td><td>0.25</td><td>0.003(7)</td><td>0.01013</td><td></td></tr></table>

<sup>a</sup>lattice parameters: *a* = 5.46867(14) Å, *b* = 5.60590(15) Å, *c* = 12.6596(3) Å, Vol = 387.859(18)Å³; *R*<sub>p</sub> = 3.95%, *R*<sub>wp</sub> = 5.21%, *R*<sub>Bragg</sub> = 3.4%, *R*<sub>f</sub> = 3.17%, χ<sup>2</sup> = 3.01.

Neutron powder diffraction (NPD) patterns of La<sub>2</sub>CoO<sub>4.00</sub> collected on D1B at ILL during heating (Figure 4b) in air are presented in Figure 4a as a 2D contour plot, covering an angular range of 10–128° in 2θ. To better observe the evolution of weak reflections, the NPD data were corrected for an unbalanced background, resulting essentially from the quartz cell. The background was determined with good counting statistics for the first diffraction pattern, prior to the oxidation, and subsequently subtracted from all following diffractograms.

Figures 4c and 4d display enlarged sections of the complete diffraction pattern, focusing on the evolution of specific reflections that are indicative of the detected phases, while Figure 4e shows the weight change during the oxidation process.

The sequence of diffractograms can be divided into five distinct intervals, each corresponding to the formation of successive phases. Phase identification was performed using Rietveld refinement on NPD patterns acquired at specific temperatures, after transitions, where a monophasic region was confirmed (e.g., T = RT, 475K, 555K, and 765K).

In the first temperature region, from room temperature (RT) to T1 = 320 K, the orthorhombic *Bmab* phase (LTO), corresponding to stoichiometric La<sub>2</sub>CoO<sub>4.00</sub>, is present (Figure S3). As the temperature rises above 320 K, a tetragonal phase starts to emerge. This phase transition is evidenced by the merging of the (040) and (400) reflections into a single (400) reflection at 2θ = 55.5°. Between T1 and T2 = 430 K, a biphasic region is observed where the tetragonal and LTO1 phases coexist. This intermediate region suggests a gradual phase transformation
rather than a discontinuous phase transition. Above 430 K, the orthorhombic LTO phase is no
longer present, also indicated by the complete disappearance of the (212) superstructure
reflection at approximately 32.5° in 2θ (see Figure 6). This intermediate tetragonal phase was
structurally characterized at 455K using Rietveld refinements (Figure S4, Table S1), within
the *F*4/mmm space group (indicated as LTT in the following), which is the non-standard
*I*4/mmm setting. Crystallographic information file (CIF) has been deposited in the Cambridge
Crystallographic Data Centre (CCDC) under deposition number 2501637.

The monophasic LTT region extends over a temperature range of 70 K, up to 500K, where it
further transforms into the orthorhombic *Fmmm* phase with *δ* = 0.22 (which we will refer to
as LTO1 hereafter), indicated by the splitting of the LTT (400) reflection. The crystal
structure of the LTO1 phase was refined from data obtained at 555 K (Figure S5 and Tbla
S2). The oxygen content then increases progressively, attaining *δ* = 0.25 at 600 K.

Another transition occurs at around 630 K, observed by the wider splitting of the (040) and
(400) reflections, reflecting a growing difference between the *a* and *b* lattice parameters, and
thus a significant increase in the deviation from tetragonality. At this temperature, the
transition from the LTO1 phase to a third orthorhombic phase while retaining the *Fmmm*
space group (LTO2 in the following), though the orthorhombicity undergoes a sharp increase.
<figure><img src="image_6.png" /><figcaption>**Figure 4.** (a) 2D contour plot showing the neutron diffraction data during the *in situ* thermal oxidation of the stoichiometric La₂CoO₄.₀₀ in air. (b) temperature ramp used during the *in situ* oxidation (0.2 K/min up to 550K and then 0.3-0.4 K/min); (d) and (c): Zoomed-in sections showing the evolution of some selected reflections, illustrating the symmetry changes of La₂CoO₄+δ as a function of the temperature. (e) Thermogravimetric curve showing weight changes due to the oxygen uptake during the oxidation reaction.</figcaption></figure>

Rietveld refinements of all diffractograms were performed using the FullProf suite.¹⁸ The refinement strategy, and particularly the unambiguous identification of the constituent phases, was quite complex due to the very similar lattice parameters among the coexisting phases in the 430 K - 500 K temperature range. Since the quality of the *in situ* diffractograms does not allow precise determination of thermal displacements within the phase overlapping regions, and to avoid incoherent divergences in the refinements, we kept the structural models in *Bmab*,
F4/mmm and Fmmm fixed, while refining the volume fraction, the lattice parameters and the oxygen occupancies. In this way we could obtain a reasonable approach of the phase relations during the thermal oxidation reaction.

The temperature dependence of the lattice parameters *a*, *b*, *c* is shown in Figure 5a together with the phase volume fractions (Figure 5b) and oxygen stoichiometries derived from thermogravimetric analysis and from the Rietveld refinement of the interstitial oxygen occupancies (Figure 5c). Lattice parameters *a* and *b* show slight, nearly linear variation with temperature, while the *c*-axis exhibits a different trend. Below 500 K (LTT–LTO1 transition), it expands linearly, with both phases showing similar *c* values. Around 500 K, a marked contraction occurs due to oxygen uptake increasing the Co³⁺/Co²⁺ ratio; the smaller Co³⁺ ions cause oxidation-induced lattice contraction that offsets thermal expansion. This competition between thermal expansion and oxygen uptake governs the lattice evolution and explains the slight *c*-axis variation in the LTO1 region. Above 650 K (LTO2 phase), thermal expansion prevails, resulting in further lattice expansion. Corresponding coefficients are given in Table S6.
<figure><img src="image_7.png" /><figcaption>**Figure 5.** (a) Temperature dependence of the unit cell parameters *a*, *b*, and *c*, and (b) of the phases volume fraction. Rietveld refinements were performed using the stoichiometric orthorhombic *Bmab* phase, the intermediate tetragonal *F*4/mmm phase, and the orthorhombic *Fmmm* phase. Error bars are within the size of the data points. The red solid lines in (a) are the linear fits of the thermal evolution of lattice parameters. (c) Temperature dependence of the oxygen over-stoichiometry *δ*, obtained from TGA (black solid line) and from refined interstitial oxygen occupancy (NPD data, pink scattered points). The nearly discontinuous oxygen uptake and its hysteresis, closing at 650 K (inset), suggest that the oxygen-stoichiometry change is associated with the LTO1/LTO2 transition.</figcaption></figure>
Thermogravimetric analysis (TGA) indicates a pronounced acceleration in the oxygen uptake kinetics only above 430 K. This transition aligns with the disappearance of the orthorhombic LTO phase and the formation of a monophasic tetragonal region, which persists up to 500 K and corresponds to an oxygen uptake of $\delta = 0.19$. Upon further oxidation, a phase transformation to an orthorhombic phase with *Fmmm* symmetry occurs, which is characteristic of the over-stoichiometric phases of La₂CoO₄+δ. A progressive increase in oxygen content is observed with rising temperature, attaining stabilization at $\delta \approx 0.25$ around 650 K.

Between 650 K and 690 K, thermogravimetric analysis reveals an almost constant oxygen stoichiometry of $\delta = 0.25$, corresponding approximately to the maximum over-stoichiometry at room temperature. Surprisingly, a slight additional oxygen uptake begins at 680 K, increasing the oxygen content to $\delta = 0.263$ at 730 K. This extra oxygen uptake has no analogue in the homologous nickelates, e.g. (Pr/Nd)₂NiO₄+δ, and occurs not far from the LTO₂ phase transition at 650 K. This nearly discontinuous uptake is accompanied by a hysteresis loop upon cooling, which closes precisely at 650 K (inset Figure 5c). Considering the dynamic nature of the TG measurement, and the associated potential temperature shifts, one may therefore infer that the change in oxygen stoichiometry is linked to the LTO₁/LTO₂ phase transition, despite the small temperature offsets observed in both measurements.

## Oxygen ordering as a function of the temperature

Previous studies on the over-stoichiometric La₂CoO₄.₂₅ have highlighted a modulated structure as a result of the interstitial oxygens ordering. This was demonstrated through X-ray single crystal and neutron powder diffraction, where on top of the main reflection, a huge number of satellites have been identified. These extra reflections, associated with the modulated oxygen ordering, have been indexed with a modulation vector $Q = 0.7535(2)a* + 0.4985(1)b*$.¹⁷
Figure 6a shows a 2D colormap of the evolution of the satellite reflections in the 2θ-range of 31°-34.5° during the oxidation reaction. This section shows no basic reflections, except for the weak (212) reflection at 2θ = 32.5°, which corresponds to the orthorhombic *Bmab* phase up to 430 K. Therefore, it is well-suited for tracking variations in the satellite positions and intensities.

<figure><img src="image_8.png" /></figure>

**Figure 6.** (a) 2D contour plot representing the thermal evolution of oxygen superstructure reflections in the 2θ range of 31-34.5°. The *Bmab* starting $La_2CoO_{4.00}$ (212) reflection at 32.5° is also evident. Satellite reflection are also indexed according to the corresponding modulation vectors. (b) Evolution of the refined modulation vectors *Q* ($q_x$ and $q_y$ are the components along the x and y directions, respectively) as a function of the temperature (error bars are within the size of the data points). (c) Evolution of the satellite reflections intensities as a function of the oxygen over-stoichiometry $\delta$.

Satellite reflections begin to emerge near 500 K, at the onset of the phase transition from the low-temperature tetragonal (LTT) to the orthorhombic LTO1 phase, and become more pronounced at 530 K, where the oxygen content reaches $\delta \approx 0.17$.

At the transition temperature between LTO1 and LTO2, around 630 K, the satellite peaks become sharper and better defined, indicating a significant reorganization of the oxygen
sublattice. This suggests a rapid ordering kinetics and a uniform oxygen stoichiometry across the sample. Remarkably, this ordered state persists up to at least 765 K, as evidenced by well-defined diffraction peaks that indicate stable long-range oxygen order even at such high temperatures.

From the very low intensity of the satellite reflections in powder diffraction patterns, it is quite difficult to fully determine the changes in the modulation vectors. The commensurate modulation vector $Q = \pm 0.75 a^* \pm 0.5 b^*$, obtained from single crystal X-ray diffraction studies of La₂CoO₄.₂₅ at RT¹⁷, could have been applied successfully as starting values, to index the NPD data of LTO1 and LTO2 phases of La₂CoO₄+δ.

Due to the significant intensity reduction from the 1st to 2nd order satellite reflections, the pattern could already be fitted considering 1st order satellite reflections, yielding a refined modulation vector $Q = \pm 0.749(1) a^* \pm 0.497(3) b^*$ for LTO1 at 555 K (Figure S5). In the high-temperature region for LTO2, the refined modulation vector was found to be $Q = \pm 0.791(1) a^* \pm 0.524(1) b^*$ at 765 K (Figure 7). The evolution of the refined modulation vectors as a function of temperature is presented in Figure 6b. Each of the two high-temperature phases (LTO1 and LTO2) is characterized by a quite constant modulation vector, with a sharp discontinuity at the LTO1–LTO2 transition (630 K).

Although we evidenced a gradual increase in the oxygen over-stoichiometry from 0.15 to 0.25 in the temperature range of 500–630 K, the modulation vector remains constant and corresponds to the values observed for single crystals at RT with an oxygen over-stoichiometry $\delta = 0.25$.¹⁷ At higher temperatures, the modulation vector stabilizes around $Q = \pm 0.791(1) a^* \pm 0.521(2) b^*$ while the oxygen content shows a slight increase up to $\delta = 0.263$. This seems to suggest a rapid reorganization of the oxygen sublattice without inducing a phase transition.
<figure><img src="image_9.png" /></figure>

Figure 7: Rietveld refinement of the LCO NPD pattern at 765 K, showing superstructure reflections due to oxygen ordering, with a refined modulation vector $Q = \pm 0.791(1) a^* \pm 0.524(1) b^*$. The inset shows a zoomed view of the shaded blue section highlighting the presence of oxygen superstructure peaks. Average structure has been refined with the space group *Fmmm* (D1B at ILL with 1.287 Å).17,20 Red dots are the experimental data while the calculated patterns are represented by continuous black lines. The lowermost blue continuous line represents the difference between the experimental and calculated intensities and the short green vertical bars mark the structural Bragg peaks and of the satellite reflections.

**Table 2.** La₂CoO₄.263 structural data obtained at 765 K from powder neutron diffraction data, collected on the D1B diffractometer at the ILL, with 1.287 Å. Refinements were carried out in space group *Fmmm*.a
<table><thead><tr><th>Atom</th><th>Wyc. Pos.</th><th>x</th><th>y</th><th>z</th><th>occ.</th><th>U<sub>iso</sub> (Å<sup>2</sup>)</th></tr></thead><tbody><tr><td>La</td><td>8i</td><td>0</td><td>0.0</td><td>0.3581(1)</td><td>2.00</td><td>0.0212(6)</td></tr><tr><td>Co</td><td>4a</td><td>0</td><td>0</td><td>0</td><td>0.976</td><td>0.041(3)</td></tr><tr><td>O<sub>apical</sub></td><td>8e</td><td>0.25</td><td>0.25</td><td>0</td><td>2.0</td><td>0.035(2)</td></tr><tr><td>O<sub>equatorial_1</sub></td><td>8i</td><td>0</td><td>0</td><td>0.1698(3)</td><td>0.79(8)</td><td>0.0260(9)</td></tr><tr><td>O<sub>equatorial_2</sub></td><td>12p</td><td>0.937(3)</td><td>0.915(4)</td><td>0.1698(3)</td><td>1.21(7)</td><td>0.0260(9)</td></tr><tr><td>O<sub>interstitial</sub></td><td>8f</td><td>0.25</td><td>0.25</td><td>0.25</td><td>0.267(10)</td><td>0.0226(8)</td></tr></tbody></table>

a lattice parameters: *a* = 5.4996(5) Å, *b* = 5.5864(4) Å, *c* = 12.8625(13) Å, vol = 395.169(18) Å³; *R*<sub>p</sub> = 9.51%, *R*<sub>wp</sub> = 6.38%, *R*<sub>Bragg</sub> = 2%, *R*<sub>f</sub> = 1.30%. The Co occupancy was fixed to the value determined on D2B.

A comparable trend is observed in the evolution of the satellite intensities with increasing oxygen content, as shown in Figure 6c. In the LTO1 phase (~530–650 K, δ ≈ 0.20–0.24), the satellite intensity remains essentially constant, indicating that oxygen ordering is already established once a threshold δ is reached. In the LTO2 phase (~650–780 K, δ approaching 0.265), the satellite intensity increases noticeably, reflecting further development of ordering. Upon reaching the maximum oxygen content (δ ~ 0.265), the satellite intensity shows only a minor increase. These observations suggest that oxygen ordering is threshold- and phase-dependent, with a nearly constant intensity in LTO1 and significant enhancement in LTO2, rather than a simple linear dependence on δ.

The rapid kinetics of these transitions, along with the sharp peak structures, underscore the strong correlation between oxygen atoms and their collective long-range arrangement. This kinetic stability aligns with the phonon-assisted diffusion model previously reported in Nd<sub>2</sub>NiO<sub>4+δ</sub> and Pr<sub>2</sub>NiO<sub>4+δ</sub>, further supporting the role of lattice dynamics in facilitating oxygen ordering in these materials.

CONCLUSION
The aim of the reported study was to follow up the oxygen uptake with temperature and
respective ordering by *in situ* neutron powder diffraction on a stoichiometric La₂CoO₄.₀₀
polycrystalline sample. Unlike previous studies, no spontaneous oxygen uptake was detected
for La₂CoO₄.₀₀ at room temperature, even over a period of tens of hours under our experimental
conditions. *In-situ* neutron diffraction combined with TG analysis reveals that noticeable
oxidation kinetics emerge only above 320 K, a moderate but clearly higher temperature than
room temperature, confirming a thermally activated process rather than a room-temperature
reaction. Under air, oxygen uptake occurs upon heating, forming first an intermediate phase
La₂CoO₄.₀₅ with tetragonal symmetry, which further evolves successively towards two
different orthorhombic phases, both *Fmmm*. These latter are characterized O-ordering,
resulting into superstructure reflections with modulation vectors of $Q = 0.746(3) a* + 0.493(2) b*$, and $Q = \pm 0.791(1) a* \pm 0.521(2) b*$.

The first modulation vector $Q = 0.746(3) a* + 0.493(2) b*$ appears in the T-range $500 K < T < 630 K$ and closely corresponds to that observed for La$_2$CoO$_4$$_{.}$$_{25}$ at room temperature, where X-ray single crystal diffraction revealed additional reflections, consistent with a 3D $Co^{2+}/Co^{3+}$ checkerboard charge ordering.¹⁸ Above $630 K$, a change towards a new ordering scheme is observed, although the oxygen stoichiometry does not appear to change significantly. Both phase transformation appears to be discontinuous suggesting a facile and fast rearrangement of the interstitial oxygen sub-lattice. It is worthy to note that the modulated phases are well defined and very stable over a wide temperature range.

These findings, together with the well-defined and thermally stable nature of the modulated
phases over a broad temperature range, suggest that oxygen diffusion mechanisms are strongly
correlated and/or cooperative in nature. This supports the idea that long-range ordering induces
dynamic correlations, which in turn lead to phonon softening and lattice instabilities, thereby
localizing oxygen atoms within a shallow diffusion potential landscape.
Further work is underway to determine whether the observed stability arises from the strong
coupling between charge and oxygen ordering, associated with the high stability of Co³⁺, and
to identify structural correlations indicative of Co²⁺/Co³⁺ charge ordering. These studies aim to
clarify its role in driving the modulation of oxygen ordering and to elucidate the underlying
oxygen diffusion mechanisms.

ASSOCIATED CONTENT

The following file is available free of charge (PDF). It contains complementary TGA curves,
Rietveld refinements of the representative structures, as well as temperature-dependent lattice
parameters, oxygen stoichiometry, and thermal expansion coefficients.

AUTHOR INFORMATION

**Corresponding Author**

*monica.ceretti@umontpellier.fr

Present Addresses

†ISIS Neutron and Muon Facility, Rutherford Appleton Laboratory, Chilton, OX11 OQX,
UK.

Author Contributions

All authors have given approval to the final version of the manuscript.

Notes

The authors declare no competing financial interest.

Funding Sources
Financial support from the French National Research Agency (ANR) through the project ExODiff (ANR-19-CE05-0041) is gratefully acknowledged.

ACKNOWLEDGMENT

The authors acknowledge the use of neutron beam time on the diffractometers D1B (DOI:10.5291/ILL-DATA.CRG-2934) and D2B (DOI: 10.5291/ILL-DATA.5-23-719) at the ILL, Grenoble. The support from the “Plateforme d’Analyse et de Caractérisation” of the ICGM Montpellier is gratefully acknowledged.

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SYNOPSIS. *In situ* neutron diffraction during thermal oxidation of La₂CoO₄.₀₀ reveals oxygen-ordering superstructures, corresponding to two discontinuous yet stable modulated phases over a wide temperature range, consistent with a rapid rearrangement of the interstitial oxygen sub-lattice.

<figure><img src="image_10.png" /></figure>