Insight into the Fergusonite–Scheelite Phase Transition of ABO₄-Type Oxides by Density Functional Theory: A Case Study of the Subtleties of the Ground State of BiVO₄

Abstract

BiVO 4 (BVO) is an important photocatalytic and ferroelastic material. It has been extensively studied using density functional theory (DFT). However, on optimization, at a commonly employed level of theory using the Perdew−Burke−Ernzerhof (PBE) exchange− correlation functional, the monoclinic scheelite (ms-BVO) structure transforms into a highersymmetry tetragonal scheelite (ts-BVO) phase spontaneously, which has also been confirmed by other groups. Such a transformation is highly unusual, as one would expect the transition to a lower symmetry structure to be modeled well at this level of theory, as is the case with, for example, the perovskite BaTiO 3 , and hints at a subtle interplay between structural and electronic properties. In this work, we demonstrate that this phase transition nevertheless can be described accurately with DFT but only using a hybrid density functional with ∼60% Hartree−Fock (HF) exchange. We find a soft phonon mode in ts-BVO, which corresponds to the phase transition from ts-BVO to ms-BVO associated with a double-well potential characterizing this phase transition, implying that the transition is of the second order. We find two key factors that can explain this surprising behavior. First, the polarizability of the Bi 3+ ion, with an on-site contribution from the hybridization of its 6s and 6p states, is notably underestimated by DFT. Moreover, the effective radius of the Bi 3+ ion proves to be too large. With the 60% HF exchange hybrid functional, the description of the polarizability of Bi 3+ does not improve but the radii of the Bi 3+ ions approach more realistic values. The polarizability of the O and V ions are reasonably described already by PBE. To gain further insight into the problem, we investigated the structural stability of other ABO 4 oxides, including ScVO 4 , LaNbO 4 , YTaO 4 , and CaWO 4 , and related materials. Some of them have similar behavior to BVO, whose ground-state monoclinic structure proves to be unstable using commonly employed DFT approaches. In particular, for ScVO 4 , we found that the scheelite tetragonal and fergusonite monoclinic structures cannot be distinguished using the PBEsol functional. But the fergusonite monoclinic structure becomes stable using the hybrid functionals with high fractions of HF exchange, which points to the crucial role of the accurate ionic size reproduction by the method of choice as the on-site Sc 3+ polarizability is too low to have a significant effect. Our findings would be of high interest for the study of other problematic materials with subtle size and polarization properties, especially ABO 4 oxides that undergo similar phase transitions.

Performance of the r2SCAN Functional in Transition Metal Oxides

“…Additionally, BiVO 4 possesses a band gap of 2.4−2.48 eV 96 and is a candidate photocatalyst. 94 Both r 2 SCAN and r 2 SCAN+U provide similar band gap predictions (2.01−1.98 eV), which is in good qualitative agreement with experiment. Surprisingly, r 2 SCAN +U evaluates a marginally lower band gap than r 2 SCAN (see panels a and b in Figure 4).…”

“…We benchmark both structural and electronic properties of BiVO 4 as a transferability check for V-based systems. Note that BiVO 4 transforms from tetragonal ( I 41/ a ) to a monoclinic ( I 2/ b ) “scheelite” phase below ∼528 K, , which is a reversible second order ferroelastic transition driven by soft optical phonon modes. The BiVO 4 unit cell possesses four formula units, with tetrahedrally coordinated V ions, which is different from the coordination environments of V in VO, V 2 O 3 , VO 2 , and V 2 O 5 .…”

Tetrahedral Displacive Disorder in the Scheelite-Type Oxide RbReO4

“…In theory, it should be possible to use first-principles density functional theory methods to establish the ground state of RbReO 4 and to understand the importance of the Rb cation in the valence band of this oxide. However, as recently demonstrated for BiVO 4 , establishing an appropriate strategy to calculate the ground state of scheelite materials containing heavy cations such as Rb or Re is not trivial …”

“…However, as recently demonstrated for BiVO 4 , establishing an appropriate strategy to calculate the ground state of scheelite materials containing heavy cations such as Rb or Re is not trivial. 37 ■ CONCLUSIONS A detailed investigation of the long-range and local structure of RbReO 4 was conducted using variable-temperature XRD and the X-ray PDF. Overall, the temperature-dependent structural behavior of RbReO 4 is much more complicated than initially anticipated.…”

Cation and Lone Pair Order–Disorder in the Polymorphic Mixed Metal Bismuth Scheelite Bi3FeMo2O12

“…This structure supports a large variety of atomic radii and charge combinations of the cations, making it a versatile structure that can exhibit a diverse range of physical and electronic properties. In addition to their uses as heterogeneous catalysts, scheelite-type oxides, including CaWO 4 , BiVO 4 , and NaLa(MoO 4 ) 2 , have been extensively studied for a range of applications exploiting properties such as luminescence, , ferroelectricity, and ionic conductivity. , Bi 3+ -containing scheelites have also been shown to be efficient photocatalysts due to the strong repulsive force of the 6s 2 lone pair of Bi 3+ , resulting in the distortion of the BO 4 tetrahedra and alteration of the band gap. − …”