1. Introduction
The Fe–V–O system has attracted huge interest for decades due to the variety of the iron vanadate oxides formed in this system and the diverse applications of the oxides [
1,
2]. For instance, more than twenty oxides of iron vanadate such as Fe
0.1V
2O
5.15, Fe
0.33V
2O
5, Fe
0.83V
1.17O
4, Fe
2V
2O
5, Fe
2V
4O
12.29, Fe
2V
4O
13, FeV
2O
6, FeV
3O
8, FeVO
3, Fe
2VO
4, FeV
2O
4, FeVO
4, and Fe
4V
6O
21. have been reported [
3,
4,
5,
6], and their potential application in rechargeable batteries, electrical and optical switching devices, and heterogeneous catalysis fields have also been investigated [
7,
8].
Among the reported iron vanadate oxides, the oxides Fe
2VO
4 and FeV
2O
4 have been the focus of special attention [
9,
10] because they possess a spinel structure and key structural-related magnetic or electrical properties [
11,
12]. Fe
2VO
4 has the inverse spinel structure of Fe
3+[Fe
2+V
3+]O
4, like magnetite Fe
3+[Fe
2+Fe
3+]O
4. However, FeV
2O
4 changes to the normal spinel structure of Fe
2+[V
3+]
2O
4 with divalent iron (Fe
2+) occupying tetrahedral sites and trivalent vanadium (V
3+) occupying octahedral sites due to the strong affinity of V
3+ ions for octahedral sites.
In addition to the stoichiometric compounds Fe
2VO
4 and FeV
2O
4, a complete solid solution Fe
3–xV
xO
4 can be formed by Fe
3+[Fe
2+Fe
3+]O
4 and Fe
2+[V
3+]
2O
4. The cation distribution in the spinel solid solution Fe
3–xV
xO
4 has been determined by Mössbauer spectroscopy [
13]. For 0 < x < 1.0, the solid solution remains an inverse spinel structure as Fe
3+[Fe
2+Fe
3+1-xV
3+x]O
4. For 1.64 < x < 2.0, the solid solution remains a normal spinel structure as Fe
2+[Fe
3+1–x/2V
3+x/2]
2O
4. The transition from normal to inverse is observed for 1.0 < x < 1.64.
Due to the similar structure to magnetite Fe
3O
4, great consideration has been given to the magnetic properties of Fe
3–xV
xO
4. Wakihara et al. [
14] synthesized the spinel solid solution with stoichiometric composition at 1500 K under controlled CO
2–H
2 atmospheres, measured the Curie temperature and the magnetization behaviors of a series of solid-solution compounds, and proposed a magnetic structure model. Jin et al. [
15] fabricated epitaxial Fe
3–xV
xO
4 (0 ≤ x ≤ 0.6) films by using reactive co-sputtering from pure Fe and V in a gas mixture of Ar and O
2, and the magnetic and magnetotransport properties of the film spinels were studied at room temperature. Pool et al. [
16] synthesized nanoparticles of Fe
3–xV
xO
4 with up to 33% vanadium substitution (x = 0 to 1) by mixing appropriate ratios of solutions of 0.5 mmol V(acac)
3 and Fe(acac)
3, 1,2-hexadecanediol with benzyl ether, oleic acid(1.5 mmol), and oleylamine (1.5 mmol) under evacuated conditions. The site preference of the vanadium and the magnetic behavior of the nanoparticles were investigated through L23edge X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (MCD) spectra.
Research on the optical absorption properties as well as the catalytic and stable properties of Fe
3–xV
xO
4 have also been reported. Kim et al. [
17] prepared the Fe
3–xV
xO
4 thin film on Si (100) substrates by using a sol–gel method. The valence and occupying sites of V ions in the Fe
3–xV
xO
4 (x < 1.0) compounds were revealed by using X-ray diffraction, X-ray photoelectron spectroscopy, and Mössbauer spectroscopy, while the optical absorption properties of the films were measured by spectroscopic ellipsometry (SE). Häggblad et al. [
18] investigated the catalytic effect of Fe
3–xV
xO
4 (x < 1.37) on the oxidation of methanol to produce formaldehyde, and the valence change of V ion was revealed by in and ex situ analyses of the samples with X-ray absorption near edge structure (XANES) spectroscopy.
Apart from the research on the physical properties of Fe
3–xV
xO
4, a number of works relating to the phase equilibria of Fe
3–xV
xO
4 have been carried out. Coetsee et al. [
19] determined the existing phases with the change of Fe/V molar ratio in the V
2O
3–FeO system from 1673 K to 1873 K by using CO/CO
2 = 3 gas mixture to control the oxygen partial pressure. Wakihara et al. [
20] determined the phase equilibria in FeO–Fe
2O
3–V
2O
3 system at 1500 K by varying the oxygen partial pressure and proposed the phase boundaries of Fe
3–xV
xO
4. In our previous publication [
21], the phase equilibria of the FeO–V
2O
3 system at 1473 K under various oxygen partial pressures were determined, and a phase diagram of
vs. the molar ratio of V/(Fe + V) was presented. Based on the available phase equilibria and thermodynamic data, the Fe–V–O system was assessed and optimized through the CALPHAD method. Xie et al. [
2] performed the assessment by adopting the modified quasichemical model to describe the liquid phase in the system and the sublattice model based on the compound energy formalism to describe the spinel solid solution Fe
3–xV
xO
4. Du et al. [
22] also performed an evaluation and modeling of the system by using the modified quasichemical model to describe the liquid oxide solution and the two sublattice spinel solution model within the framework of the compound energy formalism to the spinel solid solution Fe
3–xV
xO
4. In addition, the modeling works of some more complex systems, such as the Fe–Ti–V–O system [
23] and CaO–FeO–Fe
2O
3–MgO–SiO
2-containing V
2O
3 and V
2O
5 system [
24], were reported.
However, regarding the elementary thermodynamic data, i.e., the standard Gibbs energy of Fe
3–xV
xO
4, only the data of FeV
2O
4 was reported. The first Gibbs energy measurement was performed by Chipman and Dastur [
25] by the equilibration of FeV
2O
4 with liquid Fe–V solution under a controlled H
2–H
2O gas atmosphere at 1873 K. Wakihara et al. [
20] determined the standard Gibbs energy of the reaction of Fe + V
2O
3 + 0.5O
2 = FeV
2O
4 and 0.05Fe + V
2O
3 + Fe
0.95O = FeV
2O
4 at 1500 K, according to the equilibrated oxygen partial pressure. And even in the database of commercial thermodynamic software FactSage [
26], only the data of FeV
2O
4 can be retrieved. Therefore, the present study aimed at providing the fundamental thermodynamic data of Fe
3–xV
xO
4 and understanding the effect of V substituting on the thermodynamic property of the spinel phase; the standard Gibbs energy of formation of Fe
3–xV
xO
4 was determined by combining theoretical derivation with experimental measurements.