Oxygen-vacancy-induced Raman softening in the catalyst Fe$_2$(MoO$_4$)$_3$

TL;DR

This work tackles the mechanism behind the Raman intensity reduction observed during methanol-to-formaldehyde catalysis on Fe$_2$(MoO$_4$)$_3$ by linking it to oxygen vacancies in the bulk. Using density functional theory with PAW, PBESol, and a $U=4$ eV for Fe, the authors compute phonons and Raman intensities for both monoclinic and orthorhombic Fe$_2$(MoO$_4$)$_3$, and employ an effective frozen-phonon approach to isolate atomic contributions. They identify oxygen-dominated MoO$_4$ stretching modes around $789$ cm$^{-1}$ as the main Raman-active feature and show that suppressing oxygen vibrations reproduces the observed Raman-intensity decrease, while vacancies alone would distort local symmetry unless the effect is vibrational. Structural relaxation with a single oxygen vacancy reveals a pentagonal FeO$_5$ motif and defect states near $E_F$, suggesting possible oxidation-state changes detectable by Mössbauer spectroscopy; overall, the results support an oxygen-reservoir mechanism with bulk-to-surface diffusion participating in catalysis and explain the Raman observations without measurable peak shifts.

Abstract

Although iron molybdate (Fe$_2$(MoO$_4$)$_3$) has been commercially utilized for the production of formaldehyde from methanol via oxidative dehydrogenation, the detailed mechanism during the catalytic process remains unclear. Recent operando Raman and impedance measurements of the reaction suggested that the bulk region of Fe$_2$(MoO$_4$)$_3$ acts as a reservoir of oxygen atoms that can migrate to the surface to participate in catalysis. This conclusion was drawn from the observed significant reduction in Raman intensity during the catalytic process which implies the formation of atomic defects. However, the microscopic origin of this reduction remains to be clarified. In this work, we performed density functional theory (DFT) calculations to elucidate the origin of the experimentally observed Raman intensity variation. Our phonon analysis reveals that oxygen-dominated vibrational modes, with a small Mo contribution, occur near 782 cm$^{-1}$-the same frequency region where the Raman intensity reduction was measured. Using an effective frozen-phonon approach, we further demonstrate that oxygen vibrations are primarily responsible for the decrease in calculated Raman intensity. Moreover, structural relaxation of Fe$_2$(MoO$_4$)$_3$ including an oxygen vacancy suggests that oxygen diffusion from the bulk to the surface should occur without significant alteration of the local symmetry, consistent with the absence of measurable peak shifts or broadening in the experimental Raman spectra.

Figures (3)

• Figure 1: (a) Crystal structure of high-temperature orthorhombic Fe2(MoO4)3. (b) The corresponding phonon dispersions along the high symmetry points and atom-resolved phonon density of states. (c) Enlarged atom-resolved phonon density of states of the high-frequency range. (d) Calculated Raman intensity ($I$), normalized to the maximum value ($I_{max}$), as a function of frequency for orthorhombic Fe2(MoO4)3. Lorentzian broadening with a width of 10 cm$^{-1}$ is plotted with a black solid line. At 789.68 cm$^{-1}$, asymmetric MoO4 vibrational modes are dominant, while symmetric ones are found at 972.05 cm$^{-1}$. A red (black) arrow represents the O(Mo)-atom vibrations at a given frequency.
• Figure 2: Calculated relative Raman intensity at (a) 790.28 cm$^{-1}$, (b) 789.68 cm$^{-1}$, (c) 786.87 cm$^{-1}$, and (d) 786.18 cm$^{-1}$ by freezing each atom's phonon eigenvectors. Those four frequencies were selected since the calculated Raman intensity is large, contributing dominantly to the major Raman peak, as shown in Fig. \ref{['fig:str_phon_Ram_ortho']} (d).
• Figure A.1: (a) Crystal structure of low-temperature monoclinic Fe2(MoO4)3. (b) The corresponding phonon dispersions along the high symmetry points and atom-resolved phonon density of states. (c) Enlarged atom-resolved phonon density of states of the high-frequency regime. (d) Calculated Raman intensity ($I$), normalized to the maximum value ($I_{max}$), as a function of frequency. Lorentzian broadening with a width of 10 cm$^{-1}$ is plotted with a black solid line. At 789 cm$^{-1}$, asymmetric MoO4 vibrational modes are dominant, while symmetric ones are found at 971 cm$^{-1}$. A red (black) arrow represents the O(Mo)-atom vibrations at a given frequency.