High-Pressure X-ray Diffraction and DFT Studies on Spinel FeV2O4

“We have studied the behaviour of the cubic spinel structure of FeV2O4 under high-pressure by means of powder X-ray diffraction measurements and density-functional theory calculations. The sample was characterized at ambient conditions by energy-dispersive X-ray spectroscopy, Raman spectroscopy, and X-ray diffraction experiments. One of the main findings of this work is that spinel FeV2O4 exhibits pressure-induced chemical decomposition into V2O3 and FeO around 12 GPa. Upon pressure release, the pressure-induced chemical decomposition appears to be partially reversible. Additionally, in combination with density-functional theory calculations, we have calculated the pressure dependence of the unit-cell volumes of both the spinel and orthorhombic FeV2O4 crystal structures, whose bulk moduli are B0 = 123(9) and 154(2) GPa, respectively, finding the spinel FeV2O4 to exhibit the lowest bulk modulus amongst the spinel oxides. From experimental results, the same information is herein obtained for the cubic structure only. The Raman modes and elastic constants of spinel FeV2O4 have also obtained the ambient conditions.”

2.1. Experimental Details

Simple solvothermal synthesis was used to obtain cubic FeV2O4. 1.2120 g of iron nitrate nonahydrate (Fe(NO3)2·9H2O), 0.7019 g of ammonium vanadate (NH4VO3), and 0.2521 g of oxalic acid monohydrate were combined in 40 millilitres of methanol under vigorous stirring at room temperature. The mixture was then moved to a 100 mL Teflon-lined stainless-steel autoclave and kept in an oven at 200 °C for 24 h. The obtained powder was then repeatedly rinsed with ethanol and acetone and dried overnight. In order to ensure the synthesis of spinel compounds, the precipitates were calcined for four hours at 400–500 °C in an H2/N2 reducing environment [15].
Ambient conditions powder XRD measurements were carried out at Servicio Central de Soporte a la Investigación Experimental (SCSIE) in the University of Valencia using a Bruker D8 Advance A25 powder diffractometer with a Bragg-Brentano geometry and Cu Kα1 radiation (λ = 1.54059 Å).

The final part of this section relates to the sample characterisation via ambient conditions X-ray diffraction. The cubic structure of S-FeVO (space group Fd-3m, number 227) was successfully refined against the observed XRD pattern shown in Figure 2, which also showed small contributions from hexagonal V2O3 (space group R-3c, number 167) and cubic FeO (space group Fm-3m, number 225). Additionally, a detectable contribution from orthorhombic O-FeVO (space group Cmcm, number 63) reported by Ishii et al. [20] is also observed. For example, the reflections observed at 26° and 46° can only be explained with the (002) and (132) reflections of O-FeVO. We also used the HP XRD data (Figure 3) to support this phase identification. The multi-phase Rietveld refinement at ambient conditions, along with phase percentages and goodness parameters, is presented in Figure 2. In the refinement, the background was fitted with a Chebyshev polynomial function of the first kind with eight coefficients, and the overall displacement factor, B, was fixed to 0.5 Å2 [43]. The unit-cell parameter of the spinel phase is 8.335(8) Å. Fe and V atoms are fixed by symmetry at (0,0,0) 8a Wyckoff position and (5/8,5/8,5/8) 16d Wyckoff position, respectively. Oxygen atoms are at (u,u,u) 32e Wyckoff position, with u = 0.386(3). The bond distances are V-O = 1.993(3) Å and Fe-O = 1.961(3) Å and the bond angles are V-O-Fe = 121.5(4)°, V-O-V = 95.1(3)°, O-Fe-O = 109.4(4)°, and O-V-O = 95.4(3)°.
Figure 2. Multi-phase Rietveld refinement at ambient conditions of S-FeVO including the additional minor phases. Black dots are the measured pattern. The solid cyan line is the overall calculated Rietveld profile. The difference between the observed and calculated data is shown with a red line. Tick marks indicate the calculated Bragg peak positions. Relevant reflections are labelled with their corresponding Miller indices.
Figure 3. XRD patterns from FeV2O4 sample at selected pressures. (a) Increasing pressure from 0.8(1) to 18.0(1) GPa. (b) Increasing pressure from 23.1(1) GPa to the maximum pressure, 29.3(1) GPa, followed by decompression to 0.6(1) GPa. Observed data are shown with black symbols. Le Bail profiles and residuals are shown with blue and red lines, respectively. Relevant reflections are indicated with their Miller indices, with the colour of the text matching with the phases as indicated in the legend. Pressures are indicated in the figure. The letter ‘d’ after the labelled pressure corresponds to data acquired on sample decompression. The asterisk ‘*’ marks the unindexed reflection which begins to emerge at 18 GPa.

3.2. High-Pressure Powder X-ray Diffraction Analysis

Figure 3 shows integrated polycrystalline XRD data acquired on compression and decompression for S-FeVO and the corresponding Rietveld profiles. Measurements were performed on various sample locations to prevent the appearance of Cu reflections in these patterns. All minor phases are observed up to the maximum pressure of 29.3(1) GPa and on recovery to ambient conditions. The highest intensity reflection in the data shown in Figure 3 originates from the (311) reflection in the S-FeVO structure. This reflection starts to develop a left shoulder contribution at 12.1(1) GPa (see the reflection marked *(111) in Figure 3a). As pressure further increases, this shoulder contribution gradually gains intensity when compared to the rest of the pattern. This phenomenon observed in the experimental data is consistent with the DFT calculations, which find that the S-FeVO structure becomes mechanically unstable at 11.1 GPa. In addition, above 12 GPa, the calculations predict imaginary phonons and elastic constants (see Table 2). We found that at pressures larger or equal to 11.1 GPa the calculated elastic constants violate the generalised Born criteria of stability under pressure (P) (M1 = (C11 + 2C12)/3 + P/3 > 0, M2 = C44 − P > 0, M3 = (C11 − C12)/2 − P > 0) [44]. This can be seen in Figure 4 where we represent the Born criteria conditions Mi versus pressure. At 11.1 GPa, only M2 is violated. The failure through M2 < 0, called the Born instability, is characterized by symmetry breaking with a coupling of shear modes under volume conservation [45]. At 12.5 GPa, M3 is also violated, which implies a pure shear instability. In the same pressure range, M1 abruptly changes decreasing with pressure beyond 11.1 GPa. This behaviour implies a decrease of the bulk modulus when pressure increases, which means a decohesion of the crystal structure, supporting the notion that the crystal structure becomes destabilised at high pressures [45,46].
Figure 4. Generalized Born stability criteria (Mi) versus pressure for S-FeVO. In the figure M2 and M3 become negative at the conditions described in the text.
One possible explanation for the appearance of the peak marked as *(111) in Figure 3a and the broadening of peaks of cubic FeV2O4 could be related to a structural phase transition. The changes in the patterns are typical of phase transitions involving a symmetry decrease. We tested possible HP structures by applying group-subgroup relationships to spinel FeV2O4. We have tested the tetragonal post-spinel structure proposed by Yong et al. [47]. However, following this method we could not successfully explain the changes observed in the XRD patterns because the candidate HP structures all exhibited unit volumes larger than that of the low-pressure phase, which cannot be possible. We have also tested the known high-pressure post-spinel phases (CaFe2O4-, CaMn2O4-, and CaTi2O4-type [48]) and found that these post-spinel structures also could not explain the changes observed in the XRD patterns. We did not consider cation inversion between Fe and V, because these elements have a similar atomic number, which does not allow us to determine the amount of element substitution from the present experiments. However, we are fully aware that cation substitution could influence the phase stability and bulk modulus [49]. A second-possible explanation for changes in XRD is pressure-induced decomposition, which is known to occur at pressures below 10 GPa in vanadates [50,51]. In our case, the reflection which appears at 12 GPa can be interpreted as an indication of pressure-induced chemical decomposition of the sample because the reflection corresponds to the (111) reflection of FeO. The reflections assigned to V2O3 also become more intense with increasing pressure. In the ambient pressure XRD data shown in Figure 2, the Rietveld refinement suggests that the V2O3 and FeO each constitute around 2% of the total sample. Therefore, by comparison with the intensity of their most recognizable reflections ((012) for V2O3 and (111) for FeO) with the highest one of S-FeVO, (311), it is possible to quantify the decomposition. The amounts of V2O3 and FeO in the sample gradually increase with compression up to 14% each, whereas S-FeVO reduces to 61%. Upon decompression, the decomposition products partially recombine into the original state, ultimately constituting only around 8% of the sample at 0.6(1)d GPa. The O-FeVO contribution remains constant throughout the experiment, indicating that it does not chemically decompose or transition to another phase in the studied pressure range. The phenomenon of reversal of the pressure-induced chemical decomposition has previously been observed in other systems, including vanadates [51,52].
At 18.0(1) GPa, a new reflection emerges around 8° which shifts very little in 2θ up to the maximum pressure studied, 29.3(1) GPa, and remains in the pattern even upon recovery to ambient pressure. This suggests that an irreversible phase transition might have occurred in one of the sample phases (see asterisks in Figure 3). Attempts were made to index this reflection using a known high pressure monoclinic structure of V2O3 [53], since this is the only compound in our sample known to undergo a phase transition in this pressure range. However, this was not possible, and regrettably, the peak remains to be indexed.

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