Structural Water Accommodation in Co₃O₄: A Combined Neutron and Synchrotron Radiation Diffraction and DFT Study

Abstract

Spinels like Co₃O₄ have acquired relevance because of their photocatalytic, electrocatalytic, optical and magnetic properties. In this context, we investigated the defect structure evolution of compounds synthetized using the nitrate precursor method and after annealing cycles at temperatures ranging from 260 to 650 °C by means of thermogravimetric analysis (TGA), neutron powder diffraction (NPD), X-ray powder diffraction (XRPD) coupled to Pair Distribution Function (PDF) analysis, and Density Functional Theory (DFT) calculations. Deuterated and hydrogenated precursors were adopted to produce the samples for NPD and XRPD experiments, respectively. TGA measurements displayed weight losses, the extent of which increased on lowering the preparation annealing temperature, suggesting that the adopted wet synthesis introduces structural water in the sample. Both XRPD and NPD revealed the presence of vacancies in tetrahedral cobalt sites ($V_{Co1}^{″}$) whose concentration at RT decreases on raising the annealing temperatures, while octahedral cobalt and oxygen sites were fully occupied in all the samples. In addition, the $V_{Co1}^{″}$ presence induces a shrinking of the volume of the CoO₄ tetrahedra. The combination of DFT calculation and diffraction revealed that deuterium/hydrogen ions ($D_i^{•}$/$H_i^{•}$), introduced during the synthesis by the nitrate precursor balanced the $V_{Co1}^{″}$. Finally, DFT calculations revealed that ($D_i^{•}$/$H_i^{•}$) in Co₃O₄ forms hydroxyl groups.

1. Introduction

In recent years, cobalt spinel, Co₃O₄, has acquired relevance because of its catalytic [1,2,3,4,5,6,7,8,9], electrocatalytic [9,10,11,12], optical [13,14,15,16], magnetic [17,18,19] and photocatalytic properties [14,20,21]. Moreover, it has promising applications in innovative devices [22].

When coupled with additional phases to form a heterostructure, Co₃O₄ reveals interesting dielectric and electrode properties [11,22,23,24].

Many available preparation routes exist for Co₃O₄, spanning from comparatively simple to complex ones, e.g., the decomposition of many inorganic salts [17,18,25] or organometal complexes [26] that have recently been adopted to produce nanosized compounds [16,17,18,19,20,21,25,27]. Nitrate-based reactions are also widely used to obtain supported and unsupported Co₃O₄ due to the low cobalt nitrate decomposition temperature (T < ~200 °C) and self-sustaining oxidizing atmosphere (from NO₃⁻ decomposition) that simplify operations, also alleviating any concern for thermal substrate stability. The preparation is also of interest for fundamental Co₃O₄ features.

Co₃O₄ is commonly accepted to be anhydrous regardless of preparation, and to contain excess oxygen in amounts that vary by an approximately inverse temperature dependence, from limiting low values at T ≈ 600–800 °C, where the nominal composition (O/Co = 4/3) is approached, to much greater ones (usually unspecified) near ambient temperature. Excess oxygen is believed to be charge-compensated, promoting cobalt ions to higher valence, either Co²⁺ to Co³⁺ [28,29,30] or Co³⁺ to Co⁴⁺ [31,32,33,34,35,36,37], depending on the assumed defect model.

According to other authors, the synthesis method influences composition, the presence of defects and vacancies, and finally the overall properties of synthesized materials [17,18,19,32,34,38,39,40,41]. As an example, Gautier [42] and Formaro [43] have evidenced the presence of “structural water” accommodation in the mixed valence oxide Co₃O₄ prepared using nitrate precursors. Cobalt-coordinated water from the nitrate precursor is likely at the origin of “structural water”, left over in reaction products in spite of the wide variations in preparation conditions reported in the literature.

However, these two different positions in the literature refer to the same oxide, thus highlighting that Co₃O₄ is characterized by a complex defectivity that has not been fully understood yet. Given the importance of defectivity in the electronic properties of Co₃O₄ and, therefore, in the catalytic and electrocatalytic behaviour of this material, which is frequently used as an effective catalyst in both gas–solid and liquid-solid applications [5,8,9,10,12,24,44], it is believed that further investigation is necessary to clarify its defectivity.

Thus, in this paper we report a contribution to the problem of “structural water” accommodation in the mixed valence oxide Co₃O₄. The paper relies on structural investigations by means of both neutron and synchrotron radiation powder diffraction, to take advantage of their complementarity [45], coupled to ab initio DFT calculations to check the structure and the formation energies of different possible defects. Deuterated samples were produced for neutron diffraction to take advantage of the large scattering length of D (and O) and avoid the undesired incoherent scattering of H.

We will show that sizeable water amounts are present in Co₃O₄ produced by the thermal decomposition of Co(NO₃)₂∙6H₂O, in the form of hydroxyl groups which balance cobalt vacancies in tetrahedral sites of the cobalt oxide spinel structure. Thus, H⁺/OH⁻ (with H⁺ binding to a different O ion forming a second OH⁻ group) are actually meant for “structural water”, these ions being presumably distributed in the structure, in some as-yet-unexplored relation with the characteristic O/Co oxide defectivity.

2. Results and Discussion

2.1. Thermogravimetric Measurements

Figure 1 reports the TGA curves on all the deuterated samples. In this figure, samples D550 and D650 show straightforward behaviour, with profiles that are almost flat from room temperature to T ≈ 700 °C where mass loss begins, this being completed at T = 820 °C. The mass loss of both samples (Δw = 6.6 ± 0.01%) reasonably agrees with the calculated value for Co₃O₄→ 3CoO + ½O₂ transformation (Δw = 6.64%). The same process also occurs with the same temperature range and mass loss on samples from lower annealing temperatures T_ann., even though it is shifted to lower initial mass percentage at 700 °C: this becomes smaller with decreasing T_ann. of the samples, due to superposition with other processes taking place at lower temperatures with decreasing T_ann. TGA results on hydrogenated samples produced with the same synthetic path as the present ones are reported in Ref. [43].

2.2. Average Structure

The structure of all the deuterated samples was investigated by means of neutron diffraction. Figure 2a reports the experimental neutron diffraction pattern collected on the D260 sample (black crosses). In addition, high-resolution synchrotron radiation diffraction patterns were also collected on the H260 and H650 samples to reveal complementary structural information at the lowest and highest T_ann. values. The pattern of the H260 sample is reported in Figure 2b, as an example.

For these selected samples, we will take advantage of the different scattering power of the involved atoms using neutrons or X-rays In fact, while the atomic form factor for X-ray scattering at Q = 0 is strictly related to Z (=1, 8 and 27 for H, O and Co, respectively), the neutron scattering lengths for D, O and Co are 6.671, 5.803 and 2.49 fm, respectively. X ray diffraction is mostly sensitive to Co scattering, while information on D and O structures is likely recovered from neutron diffraction.

The Rietveld refinement performed on neutron diffraction patterns revealed the presence of the spinel-like Co₃O₄ phase (cubic system, space group $Fd\overline{3}m$, n. 227). Figure S1 reports, as an example, the structure resulting from the refinement of D260 sample neutron data. In this structure, two non-equivalent Co sites exist; positioning the cell origin at $\overline{3}m$ (choice 2), the tetrahedral Co1 site (Co²⁺ ions, green spheres and tetrahedra in Figure S1) is at 8a (⅛, ⅛, ⅛), while the octahedral Co2 site (Co³⁺ ions, blue spheres and tetrahedra in Figure S1) is at 16d (½, ½, ½); oxygen ions occupy only one non-equivalent position O at 32e (x, x, x), with x ≈ ¼ [hereafter x_O]. x_O is the unique positional degree of freedom of this phase, since all the other ones are fixed by symmetry [46,47]. Tetrahedra share corners with octahedra only, while the latter ones additionally share six edges with nearest neighbour octahedra. Finally, it is worth citing the tetrahedral 8b (3/8, 3/8, 3/8) and 48f (≈3/8, 1/8, 1/8) and the octahedral 16c (0, 0, 0) sites that are empty in the spinel structure but could in principle locate interstitial Co ions [46,48].

In addition to the intense Bragg peaks of the spinel phase, a tiny peak around 53.02° appears which could correspond to the 002 reflection of CoO. Attempts to refine the phase fraction in D260 brought the weight fraction value to around 0.4%.

In preliminary refinements (model_1), the cell constant a, x_O and three isotropic thermal parameters (U_Co1, U_Co2 and U_O for the Co1, Co2 and O sites, respectively) were varied. U_Co1 increased steeply on lowering T_ann., as reported in Figure 3a, despite all the measurements being taken at the same (room) temperature. In addition, in the Fourier Difference Density (FDD) maps for all the samples, intense FDD minima centred on the Co1 site were found, whose intensity lowers on rising T_ann.

Therefore, in the final structural models, the occupancy of the Co1 site (of_Co1) was allowed to vary in the refinements as well as the cell parameter, x_O and the two thermal parameters for Co (U_Co) and O (U_O) sites, respectively (model_2). This brought a noticeable increase in the fit quality, especially when samples annealed at the lowest T_ann. values were involved. Also, Tronel and co-workers detected cobalt vacancies preferentially at the Co1 site in Co₃O₄-containing electrodic materials, detecting a Co/O ratio smaller than 3/4 [31]. Conversely, attempts to change the occupational factors of Co2, as suggested by Ref. [49], brought values larger than 1. The fit according to model_2 relative to the sample annealed at 260 °C (D260) is displayed in Figure 2a as a red curve. The refined parameters for all the samples are reported in

Table 1. Rietveld refinement results and residuals of the neutron diffraction patterns referring to the final model (model_2) for Co₃O₄. Estimated Standard Deviations (ESDs) are in brackets.

Sample	D260	D350	D450	D550	D650
Space Group	$\mathit{F}\mathit{d}\overline{3}\mathit{m}$	$\mathit{F}\mathit{d}\overline{3}\mathit{m}$	$\mathit{F}\mathit{d}\overline{3}\mathit{m}$	$\mathit{F}\mathit{d}\overline{3}\mathit{m}$	$\mathit{F}\mathit{d}\overline{3}\mathit{m}$
a/Å	8.0763(2)	8.0787(1)	8.0792(2)	8.0798(3)	8.0794(3)
xO	0.26352(4)	0.26356(3)	0.26358(4)	0.26364(3)	0.26364(3)
UCo/Å2	0.0017(5)	0.0046(5)	0.0051(5)	0.0035(4)	0.0040(4)
UO/Å2	0.0021(3)	0.0046(5)	0.0049(3)	0.0040(3)	0.0046(2)
ofCo1	0.912(9)	0.937(8)	0.957(8)	0.961(7)	0.980(6)
R(F2)	0.0213	0.0198	0.0195	0.0218	0.0149
Rp	0.0285	0.0306	0.0303	0.0302	0.0292

.

Using this last model, the anomalous trend of the Co thermal parameters is removed (see Figure 3b). The cell parameter a and x_O coordinate increase with the annealing temperature as well as of_Co1, as displayed in Figure 3c and Table 1. In the most defective sample (D260), about 9% of the Co ions are vacant; of_Co1 rises on increasing T_ann. and for the D650 sample of_Co1 = 0.98.

The value of x_O is strictly bound to the geometry and the dimension of the oxygen cages that surround Co ions. When x_O becomes larger than ¼, the O-Co2-O angles bend and the six equivalent Co2-O distances decrease, thus causing a distortion and a shrinkage of the octahedral environment of Co2. At the same time, the tetrahedral environment of Co1 remains undistorted but the Co1-O distances increase, as well as the tetrahedron volume (V_tet), according to the following equation [46]:

$$V_{tet}={\displaystyle \raisebox{1ex}{$8$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{a}^3{\left[x_O-0.125\right]}^3$$

Co1 vacancy formation promotes the shrinkage of the Co1 tetrahedron volume. The tetrahedron volume contraction ΔV_tet revealed by NPD passing from the D650 to the D260 samples was quite small (≈0.4%); however, it is worth supposing that the formation of a Co1 vacancy induces the local distortion of the position of the oxygen ions around it. Since only a fraction of the O1 ions should be involved, both x_O and V_tet values determined by Rietveld analysis should be the weighted mean for Co1-full and Co1-empty tetrahedra; larger “local” x_O and V_tet changes should locally occur around each Co1 vacancy.

The same structural models applied for NPD were also tested for X-ray diffraction, obtaining similar T_ann. evolution. In particular, refined of_Co1 < 1 and of_Co2 ≈>1 are found when they are both allowed to vary; moreover, annealing at larger T values increases a, x_O, and of_Co1 parameters, as well as V_tet. Finally, a small fraction of CoO is revealed in H260 (wf ≈ 0.04), while it disappears in H650. Table S1 of the Supplementary Information reports the refined parameters applying model_2. We note that the small differences in the absolute values of the refined parameters after the NPD and XRPD data refinements could be attributed to slightly different reaction paths using deuterated and hydrogenated precursors.

As Co1 vacancies ($V_{Co1}^{″}$) are negatively charged, they must be compensated by some positive charged defect. The possible candidates are as follows: (1) Co ions in interstitial sites (${Co}_i^{••}$), forming Frenkel defects; (2) electronic defects, which can be represented as positive charges on the Co1 ((${Co}_{Co1}^{•}$), Co2 (${Co}_{Co2}^{•}$), and O ($O_O^{•}$) ions; (3) oxygen vacancies ($V_O^{••}$); and finally (4) interstitial deuterium ions ($D_i^{•}$) in the proximity of the Co1 vacancies. The last mechanism implies that deuterium ions are introduced during the synthesis and, in other words, that structural water is present in the structure, as proposed in Refs. [42,43].

NPD measurements revealed that high T annealing cycles remove most of the Co1 vacancies, and the ideal spinel structure is approached. This process can be described by different equations, depending on the defect that compensates the negative charge induced by Co1 vacancies. Using the Kröger–Vink notation [50], they are:

$$V_{Co1}^{″}+{Co}_i^{••}\rightleftarrows {Co}_{Co1}^x$$

(1)

$$3V_{Co1}^{″}+6{Co}_{Co1}^{•}+18{Co}_{Co2}+36O_O\rightleftarrows 8C{o}_3{O}_4+2O_2$$

(2a)

$$3V_{Co1}^{″}+6{Co}_{Co2}^{•}+12O_O\rightleftarrows 2{Co}_3{O}_4+2O_2$$

(2b)

$$3V_{Co1}^{″}+6{Co}_{Co2}+6O_O^{•}+6O_O\rightleftarrows 2{Co}_3{O}_4+2O_2$$

(2c)

$$3V_{Co1}^{″}+6{Co}_{Co2}+9O_O+3V_{O1}^{••}\rightleftarrows 2{Co}_3{O}_4+{\displaystyle \frac{1}{2}}{O}_2$$

(3)

$$3V_{Co1}^{″}+6D_i^{•}+6{Co}_{Co2}+12O_O\rightleftarrows 2{Co}_3{O}_4+3D_{2}O+{\displaystyle \frac{1}{2}}{O}_2$$

(4)

where Co₃O₄ in the equations indicates a defect-free spinel structural unit (SSU) made up of one Co1 site, two Co2 sites and four O sites.

While Equation (1) does not affect the compound stoichiometry Co₃O₄, in all the remaining cases, the removal of $V_{Co1}^{″}$ implies weight loss due to oxygen (and water) evolution. Independently of the mechanism, this qualitatively agrees with the trends revealed by TGA measurements: the smaller the T_ann., the larger the [$V_{Co1}^{″}$] and the sample weight loss before the Co₃O₄ → CoO transformation. In the case of Equation (2a–c), the correct formula to describe our samples is Co_3-xO₄, while for Equations (3) and (4), it is Co_3-yO_4-y and Co_3-zD_2zO₄, respectively.

Different defects affect the structure in different ways. Equation (1) implies the presence of interstitial Co ions, that is, the partial occupation of 8b, 16c and/or 48f sites. In Equation (2a–c), the negative charge of $V_{Co1}^{″}$ is compensated only by electronic defects, without additional atomic point defects. According to Equation (3), the Co1 vacancies are balanced by oxygen, bringing a decrease in the oxygen occupational factor. Finally, Equation (4) implies the presence of D⁺ ions, which have not been included up to now in the structural models.

To distinguish among different mechanisms of charge compensation, the patterns of the D260 and H260 samples (the most defective ones) were fitted with additional structural models, where ${Co}_i^{••}$, $V_O^{••}$ or $D_i^{•}$ ($H_i^{•}$ for XRPD measurements) are explicitly introduced.

To account for mechanism (1), we also inserted Co ions into the 8b (test_1), the 16c (test_2) or the 48f (test_3) sites, following Ref. [48]. Neutron diffraction detected very small positive site occupations in the 48f site, without any improvement of the fit quality. Conversely, for X-ray diffraction, their refined values were always slightly smaller than zero. Considering that X-ray data are more sensitive to Co scattering with respect to neutrons, this allows us to discard mechanism 1.

Model 2, adopted to refine the NPD and XRPD data, includes all the defect chemistry of mechanism 2, because $V_{Co1}^{″}$ are balanced by electronic defects; as a consequence, no further tests are needed.

To detect possible oxygen under-stoichiometry, the occupational factor of the O site (of_O) was varied, obtaining refined values larger than 1 both for neutron and X-rays. This finding agrees with previous investigations on the defect chemistry of the Co₃O₄ compound as a function of temperature and oxygen partial pressure: the disorder affects mainly the cation structure [51]. As a consequence, we will not consider Equation (3) in the following analysis.

To test mechanism 4, we individuated the position of the highest positive maximum in the Fourier Density Difference (FDD) maps of model_2. In this way, Ammundsen et al. detected structural deuterium in the Li_1+xMn_2−xO₄ spinel after lithium–deuterium ion exchange. They found that deuterium ions were incorporated into the crystal structure as –OD units, with D-O distances in the order of ~1.1 Å with a D concentration of 4.2 D per cell [52]. For each sample, a strong positive maximum appeared in the FDD maps at the ≈0.061, ≈0.061, ≈0.061 sites, with symmetry .3m (site multiplicity = 32) with an intensity that decreases with increasing annealing temperature. In Figure S2 of the Supporting Information, the FDD map relative to the xy, z = 0.061 plane for the sample annealed at 260 °C is shown as an example. However, attempts to include D in the refinements brought about unstable refinements, possibly due to the small D concentration, even in the case where all the $V_{Co1}^{″}$ defects were compensated by $D_i^{•}\mathrm{s}$ (≈1.4 D/cell for the D260 sample). Consequently, the above neutron diffraction findings alone cannot discriminate among different defect models; additional probes are needed.

To obtain an accurate picture of the defect chemistry and structure of defects of Co₃O₄ at the local scale, we adopted the real space analysis of X-ray powder diffraction data and performed DFT calculations.

2.3. Local Structure

Experimental PDF patterns on H260, H350, H450 and H650 samples were collected at the ID22 beamline of the ESRF, as described in the experimental section. The reduced total scattering functions F(Q) = [Q(S(Q)−1)] of all the samples are reported in Figure S3 of the SI, where S(Q) is the total scattering function as defined in [53].

The PDF pattern up to r = 200 Å are reported in Figure 4a. The damping of the amplitude of G(r) peaks has both physical and instrumental origins, the latter deriving from the coarse Q resolution of the 2D detector. Figure 4b displays a small portion of the same G(r) functions at high r values. The smaller G(r) amplitude for samples annealed at T_ann. ≤ 450 °C with respect to H650 points to a reduced structural coherence of the former ones.

In Figure 4, the shortest interatomic distances of the spinel structure are easily identified: the peak around 1.9 Å, labelled A, encompasses all the nearest Co1/Co2-O distances; the one centred at ≈2.85 Å, labelled B, involves only distances between Co2-Co2 ions at the centre of edge-shearing octahedra. Co1-Co2, Co1-Co1 and Co1-O distances contribute to the following peaks around ≈3.35 Å (labelled C) and to its shoulder at its right side (C’) around 3.55 Å; in Figure 4c, the 2.5 < r < 4.0 interval is shown on an enlarged r scale. G(r) peak amplitudes have been slightly rescaled to equalize the height of the B peak, therefore evidencing the raising of the height of the peak C on increasing T_ann.

Peaks A, B, C and C’ at low r values were first fitted using Gaussian functions. An example of fitting in 2.6 ≤ r ≤ 3.8 Å is shown in Figure 5a. The peaks C and C’ were constrained to have the same FWHM in the refinement to minimize correlations among parameters. All the peaks’ positions varied within one standard deviation in the whole T_ann. interval. In the (b) panel of Figure 5, the ratio I_C+C’/I_B between the intensity of peaks around ≈3.35–3.55 Å (I_C+C’) and the one around ≈2.85 Å (I_B) vs. T_ann. is displayed. C and C’ peaks are contributed by interatomic distances involving at least one Co1 ion, while only Co2-Co2 contacts contribute to B. The trend of I_C+C’/I_B on decreasing T_ann. points again to some occupancy depletion of the Co1 site on lowering T_ann.

To quantify this depletion in terms of Co1 site occupancy of_Co1, the same G(r) functions were analyzed using the real-space Rietveld analysis [53], applying model_2. First, we fitted the data in wide r ranges (e.g., 1.5–20 and 1.5–8 Å), allowing a, U_Co, U_O, x_O and of_Co2 parameters to vary. In all cases, the fit quality was not very sensitive to the of_Co1 parameters. Figure 6a reports as an example the fit of the H260 sample in the 1.5–8 Å range.

Despite the acceptable fit quality (Rw = 0.132) and a refined value of_Co1 = 0.94 that confirms the presence of Co1 vacancies in the materials, some mismatch exists between data and refinement. In particular, the intensity of the peak around ≈2.85 Å is underestimated, while the one of the peaks around 3.35 Å is overestimated, suggesting that the occupation factor of Co1 is overestimated in the refined model. This effect is magnified when the full occupation of the Co1 site is imposed (see Figure S4 of the SI). In order to obtain distortions at the very local scale, we limited the fitting r interval to the range including the nearest Co-O and Co-Co distances, that is, 1.5–4 Å. To avoid correlations between x_O and cell a parameters, the latter was fixed to the values refined in the 1.5–20 Å r range. Figure 6b,c shows the refinements for H260 and H650, while the refined parameters are reported in

Table 2. Real-space Rietveld refinement results of the X-ray PDFs, referring to the final model for Co₃O₄. ESDs are in brackets.

Sample	H260	H350	H450	H650
Space Group	$\mathit{F}\mathit{d}\overline{3}\mathit{m}$	$\mathit{F}\mathit{d}\overline{3}\mathit{m}$	$\mathit{F}\mathit{d}\overline{3}\mathit{m}$	$\mathit{F}\mathit{d}\overline{3}\mathit{m}$
a/Å	8.0747	8.0753	8.0761	8.0764
xO	0.3854	0.3858	0.3861	0.3867
UCo/Å2	0.0033	0.0032	0.0032	0.0032
UO/Å2	0.0151	0.0149	0.0148	0.0156
ofCo1	0.90	0.92	0.95	0.96
Rp	0.095	0.090	0.094	0.097

.

All the trends revealed by neutron diffraction are also confirmed by the PDF analysis at the local scale: a, x_O and of_Co1 increase upon raising T_ann. Of_Co1 obtained by X-ray PDF analysis displayed in Figure 7a are in good accord with the NPD findings (see Figure 3c). Finally, the PDF results also indicate the shrinking of the volume of CoO₄ tetrahedron V_tet on depleting of_Co1 (see Figure 7b). More severe effects are revealed by PDF with respect to the reciprocal space NPD analysis, i.e., smaller absolute V_tet values and larger changes upon varying of_Co1. This enforces the idea that Co vacancies heavily affect the structure at the local scale.

As a last comment, in Figure S5 of the SI, the I_C+C’/I_B ratio obtained by a direct analysis of G(r) peaks is plotted against the of_Co1 values refined by real-space Rietveld analysis of G(r)s in the 1.5–4 Å interval using model_2. The good linear correlation between the two quantities reveals that the I_C+C’/I_B ratio can be considered a model-free way to compare the site occupancy of the tetrahedral and octahedral sites in different spinel samples as a function of some coordinates, like, in the present case, T_ann.

Obviously, X-ray PDFs are not sensitive to interatomic distances involving H atoms. To complete this study and distinguish between models (2) and (4), we performed DFT measurements on ideal and defective spinel-like Co₃O₄ compounds.

2.4. DFT Calculations

Firstly, DFT calculations were carried out on the ideally defect-free Co₃O₄ spinel structure. In the Co₃O₄ spinel structure, the Co²⁺ ions are coupled anti-ferromagnetically, as described in Ref. [54]. We found a magnetic moment of 2.41 μ_B on the Co²⁺, in good agreement with previous calculations [55].

Next, we removed one tetrahedral Co atom, corresponding to a vacancy concentration of 1/8 = 12.5%, and relaxed the structure, keeping the cell volume unchanged. This corresponds to defect formation mechanisms 2a–2c. As shown in Figure 8, the V″_Co1 defect has the effect of depleting the valence band, i.e., doping Co₃O₄ with holes. After projecting the density of states (DOS) onto atomic orbitals, we found that hole wave-function is fairly delocalized on the 55-atom cell. At the end of the relaxation, the four oxygen atoms moved away from the vacant site. The volume of the tetrahedron formed by the four O ions increased by 9.5% with respect to pristine geometry. This result is in contrast with both NPD and XRPD outcomes: passing from T_ann. = 650 °C to T_ann. = 260 °C, a decrease in V_tet is apparent in all the refined structures and points against the 2a–2c mechanisms.

Finally, we added two hydrogen atoms to the Co1 vacancy, creating three starting configurations (see Figure 9). In configuration 1, the two hydrogen atoms bind to the two oxygen ions, forming two -OH groups pointing towards the centre of the vacancy. In configuration 2, the two H atoms end up near the centre of the vacancy, without forming any chemical bonds. In configuration 3, we attach two hydrogen atoms to one oxygen (geminal hydroxyls). The minimization of the DFT energies with respect to atomic positions showed that configurations 2 and 3 are not stable, and they all relaxed to configuration 1. In the fully relaxed configuration 1, the OH distance is 0.988 Å, the Co-O-H angle is 132.2° and the H..H distance is 1.812 Å. In Figure S6 of the SI, the fully relaxed configuration 1 is depicted and briefly described, while file Co3O4-vac-8a-2H.zip of the SI reports the input/output files and atomic parameters of all configurations.

It is worth noting that in configuration 1, the volume of the tetrahedron formed by the O ions decreases by 4.3% with respect to the ideal spinel structure. Since just 1/8 of the tetrahedral sites are involved, the average tetrahedron volume shrinking ΔV_tet should be ≈0.54%. This result matches reasonably well with the experimental NPD analysis, which detected ΔV_tet ≈ 0.4% passing from the D650 to the D260 sample.

The PDF experimental data of the H260 sample in the 1.5–4.0 Å interval were fitted against the final structure of configuration 1 without changing the relaxed atomic coordinates and varying only the scale factor, the cell parameter and two U parameters for cobalt and oxygen ions, respectively. The fit results are shown in Figure 10. The residuals (Rw = 0.099) were quite close to the ones obtained on the same data applying model_2 (see Table 2), confirming the reliability of mechanism 4, that is, the defect model implying the presence of structural water in the samples annealed at low temperature values.

Thus, DFT calculations contributed to the shedding of light on the defect chemistry of the spinel-like cobalt oxide materials produced through nitrate-based reactions, allowing to exclude the conclusion that ${Co}_{Co1}^{•}$, ${Co}_{Co2}^{•}$, and/or $O_O^{•}$ positively charged species compensate the negatively charged $V_{Co1}^{″}$ ones, as proposed by several authors (Refs. [28,29,30,31,32,33,34,35,36,37]) and indicating the presence of structural water, as inferred by Refs. [42,43]. Each hydrogen (or deuterium) ion is bonded to one oxygen ion, forming hydroxylic groups and indicating Co1 vacancy.

The DOS of configuration 1 is shown in Figure 11.

Configuration 1 is characterized by a narrow defect band, 0.3–0.4 eV, above the top of the valence band. The band is fully occupied and spin-polarized (the resulting net magnetic moment is 3.0 μ_B).

Therefore, if every Co1 vacancy is “passivated” by deuterium, the electric transport properties of Co₃O₄ would not be affected appreciably by the presence of defects. On the contrary, in the presence of Co₁ vacancies without deuterium passivation, the defects band would become partially filled, and magnetic order would develop (at low enough temperatures), meaning that electric conduction can be fully spin-polarized.

3. Materials and Methods

3.1. Synthesis

Deuterated Co(NO₃)₂·xD₂O was used as a Co₃O₄ precursor. Reactant handling, manipulations and reactions were performed using oven-dried glassware kept in flowing dry N₂ (5–9 N₂, Sapio) and O₂ (5–9 O₂, Sapio) as required. Pure Co metal powder (≈15 g, Aldrich) was suspended in D₂O (18 mL, 99.9%, Aldrich) by stirring in N₂. Deuterated nitric acid (65% DNO₃ in D₂O, Aldrich) was added dropwise and left to react in N₂ at room temperature until complete metal dissolution. The solution was evaporated to a minimum liquid content (T = 55 °C, N₂), separating a pink salt that was decomposed to Co₃O₄ through the two-stage procedure reported in [43,56]. Briefly, cobalt nitrate was first decomposed for 18 h in a rotary tube heated at T = 200 °C under continuously flowing O₂ (10 Nl/h) to remove most NO_x and D₂O. This sample was annealed further in portions in O₂ at T_ann. = 260, 350, 450, 550, 650 °C for 4 + 4 h with overnight intermediate cooling in flowing O₂ to obtain end Co₃O₄ samples. Immediately after room temperature cooling, samples were put in tightly stoppered glass vials and stored in a room temperature desiccator. These “deuterated” samples were labelled D260, D350, D450, D550 and D650. Also, not-deuterated (“hydrogenated”) materials were synthetized using the same preparation route, using Co(NO₃)₂·× H₂O, H₂O and HNO₃ instead of D-containing compounds. These samples will be referred to in the following as H260, H350, H450, and H650.

Samples were characterized using the experimental probes described below a few days after their synthesis, because their water content evolves with time [43].

3.2. Sample Characterization

Thermal Gravimetric Analyses were performed on all the deuterated samples by means of a Universal V3 TA instrument at 10 °C/min from room temperature up to 985 °C in dry, high purity N₂.

Neutron powder diffraction (NPD) measurements were recorded on the deuterated samples at room temperature on the Debye–Sherrer D1A high-resolution diffractometer at the Institut Laue–Langevin (Grenoble, France) in the 10° < 2θ < 157° 2θ range (Δ2θ = 0.05°). A wavelength of λ = 1.911 Å was selected with a Ge(115) monochromator. In this way, diffraction data were collected up to Q_max = 4πsin θ _max/λ = 6.45 Å⁻¹. The powder samples were contained in thin-walled vanadium cans.

XRPD patterns were collected at the ID22 beamline of the European Synchrotron (ESRF) in Grenoble at RT. To this purpose, the powdered deuterium-free samples were loaded into 1.0 mm diameter Kapton^® capillaries; samples H260 and H650 were investigated for Rietveld Refinement and line profile analysis using the crystal analyzer setup [57,58], at incident wavelength λ = 0.35438 Å up to 2θ = 48°, reaching Q_max = 14.4 Å⁻¹. A 2D CCD detector (Perkin Elmer XRD 1611CP3) was adopted for PDF quality measurements on samples H 260, H350, H450, and H650. Wavelength (λ 0.177125 Å), sample–detector distance, and azimuthal integration parameters were calibrated on a CeO₂ reference that was sintered for 4 h at 1673 K. Calibration and azimuthal integration were all performed using the program pyFAI [59]. PDF data up to Q_max = 27.5 Å⁻¹ were reduced using pdfgetX3 [60] and real-space refinements were carried out by PDFgui [61]. The PDF peak position and integrated intensity were determined via direct analysis using Gaussian functions [62].

NPD and high-resolution synchrotron powder diffraction patterns were analyzed via the Rietveld using the GSAS software suite [63] and its graphical interface EXPGUI [64]. The background was fitted using shifted Chebyshev polynomial. The diffraction peak profiles were fitted with a pseudo-Voight profile function [65]. Absorption correction was performed through the Lobanov empirical formula implemented for the Debye–Scherrer geometry.

3.3. Density-Functional Theory Analysis

DFT calculations were performed with the planewave pseudopotential code Quantum-Espresso [66]. We employed the PBE functional [67] for the exchange and correlation energy and optimized ultrasoft pseudopotentials [68]. The semicore 3s and 3p states of Co were treated as valence electrons. We used a planewave cutoff of 45 Ry, 2 × 2 × 2 k-points in the Brillouin zone. We modelled the system starting from a 56-atom spinel structure, composed of 8 tetrahedral-coordinated Co²⁺ ions, and 16 octahedral-coordinated Co³⁺ ions. We applied a Hubbard U of 4.4 eV and 6.7 eV on the Co²⁺ and Co³⁺ sites, respectively.

4. Conclusions

We investigated the defect structure evolution of spinel-like cobalt oxide compounds synthetized using the nitrate precursor method and after annealing cycles at temperatures from 260 to 650 °C. To this purpose, a batch of samples produced using deuterated reactants was investigated by means of neutron powder diffraction. Another batch was synthetized using hydrogenated precursors and investigated by means of X-ray pair distribution function analysis. The structural analysis was coupled to DFT calculation.

Both X-ray and neutron diffraction revealed the presence of vacancies in the tetrahedral cobalt sites ($V_{Co1}^{″}$) whose concentration decreased on heating the samples at higher temperatures, while octahedral cobalt and oxygen sites were fully occupied in all the samples. The evidence of [$V_{Co1}^{″}$] presence and of its change on varying T_ann. came from refinement, but were also easily identified by the visual inspection of the experimental PDFs, observing the changes in the relative intensity of peak B around 2.85 Å, that involved only Co2-Co2 distances, and peaks C and C’ between 3.3 and 3.6 Å, which involved distances including at least one Co1 site.

The good linear correlation between the I_C+C’/I_B ratio and the of_Co1 values refined by the real-space Rietveld analysis of G(r)s suggests that I_C+C’/I_B can be considered a model-free way to compare the site occupancy of the tetrahedral and octahedral sites in different spinel samples.

Last but not least, both NPD and X-ray PDFs revealed that $V_{Co1}^{″}$ presence induces a shrinking in the volume of CoO₄ tetrahedra.

In principle, $V_{Co1}^{″}$ may be balanced by different counter-defects, which are as follows: (1) Co ions in interstitial sites (${Co}_i^{••}$), forming Frenkel defects; (2) holes in the valence band, which could also be expressed as (${Co}_{Co1}^{•}$), (${Co}_{Co2}^{•}$) or O ($O_O^{•}$); (3) oxygen vacancies ($V_O^{••}$); and finally (4) interstitial deuterium/hydrogen ions ($D_i^{•}$/$H_i^{•}$). $D_i^{•}$/$H_i^{•}$ defects would be introduced during the synthesis by the nitrate precursor. While the first mechanism does not affect the sample stoichiometry, in the remaining three cases, the compound chemical formulae would be Co_3-xO₄, Co_3-yO_4-y and Co_3-zO₄D_2z, respectively.

Neutron and X-ray diffraction allowed the exclusion of mechanisms (1) and (3) because of the negligible occupation of interstitial Co sites and the full occupation of the O site, but they barely distinguished between mechanisms (2) and (4) due to the uncertain experimental evidence of D presence in the structure.

DFT calculations allowed the exclusion of compensation mechanism (2), which should bring an increase in V_tet. Conversely, mechanism (4) caused the experimentally observed shrinking of V_tet. For this reason, we believe that in spinel-like cobalt oxide produced using the nitrate precursor method, Co vacancies are balanced by $D_i^{•}$/$H_i^{•}$, giving rise to compounds of formula Co_3-zO₄D_2z (or Co_3-zO₄H_2z), with the z value depending on the annealing temperature T_ann.

Finally, DFT calculations suggest a model for the insertion of structural water in Co₃O₄. Water is not present in the structure as D₂O molecules, but oxygen ions enter into O1 sites, while deuterium ions enter interstitial sites, so forming two hydroxyl groups. The good fit of the PDF of the H260 sample with the relaxed DFT structure confirms the reliability of mechanism 4 and the presence of structural water in Co_3-zO₄H_2z compounds.