Critical evaluation and thermodynamic modeling of the Fe–V–O (FeO–Fe2O3–VO–V2O3–VO2–V2O5) system

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 67 (2019) 101682

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Critical evaluation and thermodynamic modeling of the Fe–V–O (FeO–Fe2O3–VO–V2O3–VO2–V2O5) system Wei-Tong Du a, b, In-Ho Jung b, * a

Department of Materials Science and Engineering, Chongqing University, No.174 Shazheng Street, Shapingba, Chongqing, 400044, China Department of Materials Science and Engineering, Research Institute of Advanced Materials (RIAM), Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, South Korea

b

A R T I C L E I N F O

A B S T R A C T

Keywords: Fe-V-O system Thermodynamic modeling CALPHAD Phase diagram Thermodynamic properties

Critical evaluation and optimization of the Fe–V–O ternary oxide system was carried out based on all the available phase equilibria and thermodynamic property data at 1 atm total pressure. The Fe3O4–FeV2O4 spinel solid solution was described within the framework of Compound Energy Formalism considering the cation distribution between tetrahedral and octahedral sites. The wüstite phase, corundum phase, and VO2 solid so­ lution were described using a simple random mixing model. The Modified Quasichemical Model was used to describe liquid oxide solution in consideration of all multivalence states of Fe and V (Fe2þ, Fe3þ, V2þ, V3þ, V4þ and V5þ). The variation of phase equilibria depending on the oxygen partial pressures and thermodynamic data in the system were well reproduced in the present study.

1. Introduction The Fe–V–O system has attracted a great deal of interest of ceramists, metallurgist and geochemists. Iron-vanadium catalysts are applied for the water-gas shift reaction [1] and chemo-selective oxidation process [2–4]. The Fe–V–O solid solution thin films [5] are used for photo-electrochemical applications and cathode materials [6] for bat­ teries. FeV2O4 spinel has recently gained increasing attention for multifunctional device because FeV2O4 is a multiferroic material which has orbital degrees of freedom in both V3þ and Fe2þ ions [7–10]. In metallurgy, the Fe–V–O slag and solid oxides are important to under­ stand the refining process for the Fe–V alloys [11], design the process for V-bearing metallurgical slag production [12], and control the process for the high strength low alloy (HSLA) steels containing V alloying element [13,14]. Since iron and vanadium have two and four valence states, respec­ tively, a substantial number of stable compounds and several solid so­ lutions including spinel, wüstite and corundum exist in the Fe–V–O system over a wide range of temperature and oxygen partial pressures The phase diagram of the Fe–V–O system was first reviewed by Raghavan [15], and a literature review was performed later by Lebrun and Perrot [16]. Despite the importance of the Fe–V–O system, the phase equilibria and thermodynamic properties of this system have not been

well investigated because of its complexity. So far, no complete and consistent thermodynamic assessment for the entire Fe–V–O oxide sys­ tem (FeO–Fe2O3-VO-VO2-V2O3–V2O5 system) has been carried out. The only attempt was made by Malan et al. [17], but their work was only limited to the Fe2O3–V2O5 system in air. In the CALPHAD (CALculation of PHAse Diagram) type thermody­ namic “optimization (modeling)” of a system, all available thermody­ namic and phase equilibrium data are critically and simultaneously evaluated to obtain a set of self-consistent model equations for the Gibbs energies of all phases as functions of temperature and composition. From the optimized Gibbs energy functions of phases in the system, the un­ explored phase diagrams and thermodynamic properties can be predicted. In the present study, a critical evaluation and optimization of all available experimental data of the Fe–V–O system in the literature was performed. In particular, the self-consistent Gibbs energy functions of all phases covering temperatures from room temperature to above liquidus and the oxygen partial pressures from metallic saturation to 1 atm pressure were obtained as the results of the optimization. Using the Gibbs energy functions, various types of phase diagrams and thermo­ dynamic properties of the Fe–V–O system could be calculated. This work is the extension from the modeling of the FeO–FeO1.5 [18] and VO-VO2.5 system [19], and it is part of the research project to develop the database

* Corresponding author. E-mail address: [email protected] (I.-H. Jung). https://doi.org/10.1016/j.calphad.2019.101682 Received 7 September 2019; Received in revised form 7 October 2019; Accepted 9 October 2019 Available online 23 October 2019 0364-5916/© 2019 Elsevier Ltd. All rights reserved.

W.-T. Du and I.-H. Jung

Calphad 67 (2019) 101682

for the V oxide containing CaO–MgO–Al2O3–SiO2–FeO–Fe2O3 system which has a wide range of applications in ceramic and metallurgical process. All calculations regarding thermodynamic properties and phase equilibria in this study were performed using the FactSage thermo­ chemical software [20].

Table 1 Optimized model parameters for the compounds and solutions in the Fe–V–O system (J/mol and J/mol-K). Stoichiometric compounds:

2. Phases and thermodynamic models

Wüstite: FeO–FeO1.5–VO1.5 Corundum: (Fe,V)2O3 VO2 solution: VO2–Fe0.5V0.5O2 Cubic spinel: (Fe2þ, Fe3þ, V3þ)T [Fe2þ, Fe3þ,V3þ, Va] O 2 O4 In the case of cubic spinel solution, T and O represent the tetrahedral and octahedral sites, respectively, and Va represents the vacancy in octahedral site. The optimized model parameters for each phase are listed in Table 1. In the present thermodynamic calculations, the Gibbs energy data for metallic Fe–V system and gas phases were taken from FactSage FSStel database and FACTPS database [21]. 2.1. Stoichiometric compounds

Z G

T

CP dT

þ 298K

298 K (J/

Cp (J/mol-K)

118.7990

mol-K) 126.0

q010 FeO; FeO1:5 ; VO1:5 ¼ 119244.0

Corundum: Fe2O3–V2O3 q00 Fe; V ¼ 1861.880–1.213T

The Gibbs energy of all stoichiometric compounds can be expressed

¼ ΔH o298K

mol)

So

129.51 þ 0.0247T - 2160000T 2 (298 K–1173 K) Fe2V4O13 393.4800 389.0 388.83 þ 0.0738T - 6506000T 2 (298 K–973 K) FeV2O6 189.6901 190.04 7.9480 þ 0.0794T 1779137.3370T 2 76767.6092T 1 þ 7354.7027T 0.5 (298 K–943 K) 136.5894 þ 0.0597T 2533299.9943T 2 þ 1500.9000T 0.5 (943 K–1173 K) FeV6O15 4923.1600 414.0 195.9606 þ 0.3570T 322576.0141T 2 115151.4139T 1 þ 8780.7040T 0.5 (298 K–340 K) 292.4685 þ 0.0732T 322576.0141T 2 115151.4139T 1 þ 8780.704T 0.5 (340 K–943 K) 485.4306 þ 0.0437T 1453820T 2 (943 K–1173 K) Spinel: (Fe2þ, Fe3þ, V3þ)T [Fe2þ, Fe3þ,V3þ, Va] O 2 O4 GAG*: ΔHo298 K (kJ/mol) ¼ 1534.4784, So298 K (J/mol-K) ¼ 148.2391, Cp (J/mol-K) ¼ 173.6360 þ 0.0285T - 2594056.0006T 2 (298 K–2000 K) ΔEA:EG ¼ GAG þ GEE - GEG - GAE ¼ 40000-12.0T ΔAG:AG ¼ GAA þ GGG - GAG - GGA ¼ 0 IAG ¼ GGA þ GGG - 2GAG ¼ 69454.4–8.368T ΔAE:GE ¼ GGA þ GEE - GGE - GEA ¼ 0 GGV ¼ 8Go(γ-V2O3) - 5GGG - 2RT(5ln5-6ln6), where Go(γ-V2O3) ¼ Go(V2O3, solid) þ 30.423 þ 4.841T *Notations A, E, G, and V stand for Fe2þ, Fe3þ, V3þ and vacancy, respectively. Wüstite: FeO–FeO1.5– VO1.5 G(VO1.5) ¼ 0.5Go(V2O3, solid) þ 48517.664 q00 76985.60 þ 37.656T FeO; VO1:5 ¼

Molten oxide (Slag): FeO–FeO1.5–VO–VO1.5–VO2–VO2.5

o

298 K (kJ/

FeVO4

Decterov et al. [18] and Kang [19] already performed the optimi­ zations of the FeO–FeO1.5 system and VO-VO2.5 system, respectively. Their optimized model parameters were used in the present study without any change to keep consistency with the already developed thermodynamic database. That is, the present study focused on the expansion of the two binaries to the Fe–V–O ternary system. The calculated phase diagram of the Fe–V–O system at 873 K (600� C) and 1 atm total pressure is presented in Fig. 1. As can be seen, many solid solution phases and binary and ternary stoichiometric phases are found in this system:

as:

ΔHo

� Z T So298K þ

T

CP dT 298K T

q01 Fe; V ¼ 23263.040–2.720T VO2 solution: VO2–Fe0.5V0.5O2 1/2 G(FeVO4) ¼ 1/2 Go(FeVO4, solid) þ 175000.0 q10 VO; Fe0:5V0:5 ¼ 40000.0

� (1)

Molten oxide (Slag): FeO–FeO1.5–VO–VO1.5–VO2–VO2.5 00 q00 35700 þ 17.5T FeO; VO ¼ qFeO; VO1:5 ¼

where ΔHo298K is the standard enthalpy of formation for a given com­

00 q00 FeO; VO2 ¼ qFeO; VO2:5 ¼

30200 þ 17.5T

00 00 00 q00 FeO1:5 ; VO ¼ qFeO1:5 ; VO1:5 ¼ qFeO1:5 ; VO2 ¼ qFeO1:5 ; VO2:5 ¼ 1410.134

01 01 01 q01 FeO1:5 ; VO ¼ qFeO1:5 ; VO1:5 ¼ qFeO1:5 ; VO2 ¼ qFeO1:5 ; VO2:5 ¼ 3692.161

10 10 10 q10 FeO1:5 ; VO ¼ qFeO1:5 ; VO1:5 ¼ qFeO1:5 ; VO2 ¼ qFeO1:5 ; VO2:5 ¼ 3410.134

Gibbs energies of compounds and solution model parameters of the FeO–FeO1.5 and VO-VO2.5 systems were taken from Decterov et al. [18] and Kang [19], respectively.

pound referring to stable element reference at 298 K (25� C), So298K is the standard entropy at 298 K (25� C), and Cp is the heat capacity which is a function of temperature. All available ternary compounds in the Fe–V–O system are listed in Table 1. In the present study, FeVO4, FeV2O6, FeV6O15, and Fe2V4O13 were treated as stoichiometric compounds and their Gibbs energies were described by Eq. (1). The Gibbs energy of these compounds were then determined to reproduce all available and reliable experimental phase diagram data and thermodynamic data. Due to the instability at 1 atm total pressure and lack of their thermodynamic properties, the com­ pounds such as Fe6.5V11.5O35 [22] and Fe0.5V5.5O13 [22,23] were not taken into account in the present study. In addition, the Gibbs energies of various intermediate stoichiometric compounds in the FeO–Fe2O3 system and VO–V2O5 system were taken from Decterov et al. [18] and

Fig. 1. Calculated phase diagram of the Fe–V–O system at 873 K (600� C) and 1 atm total pressure. Solid and dash lines represent phase boundaries and isooxygen lines, respectively. 2

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Calphad 67 (2019) 101682

[26] based on the crystal field theory [26–28] (see Ref. [25]). The details of the optimization of each end-member Gibbs energies will be discussed below in section 3. In the present spinel model, no Gexecss parameter was necessary.

Table 2 Equilibrium oxygen partial pressures for the various three phase assemblages in the Fe2O3–V2O4–V2O5 system at 873 K (600� C) calculated in the present study, compared with experimental data (see Fig. 12) [85]. Regions No.

Oxygen partial pressure, atm. Measurements [85] 6

1 2 3 4 5 6 7 8 9 10 11 12

8.7 � 10 6.76 � 10 6 8.32 � 10 7-1.07 � 10 6 7.41 � 10 8 8.32 � 10 7 1.29 � 10 8 7.76 � 10 15-7.94 � 10 9 – 3.39 � 10 7 8.32 � 10 7 8.10 � 10 7 7.08 � 10 6

2.2.2. Wüstite solid solution Wüstite solid solution has a rocksalt structure in the cubic Fm-3m space group. In order to describe this FeO-rich solid solution with limited solubility of V2O3, a simple random mixing model by Decterov et al. [18] assuming wüstite as a FeO–FeO1.5 solution. In the present study, wüstite solution was structured as FeO–FeO1.5–VO1.5 solid solution. The Gibbs energy of ternary FeO–FeO1.5–VO1.5 solution was calcu­ lated using the symmetric ‘Kohler-like’ approximation [29]. That is, the Gibbs energy per mole of the wüstite solution is expressed as follow: X X Gm ¼ Xi Goi þ RT Xi lnXi

This work 1.409 � 10 2.638 � 10 1.068 � 10 8.746 � 10 7.136 � 10 5.872 � 10 1.046 � 10 1.351 � 10 1.039 � 10 3.066 � 10 4.497 � 10 5.705 � 10

4 5 6 8 7 8 12 6

-1.224 � 10

8

6 6 6 5

i

Kang [19]. 2.2. Solid solutions

gex ternary ¼

2.2.1. Spinel solid solution The crystal structure of cubic spinel belongs to Fd-3m space group, which has two distinctive cation sites, tetrahedral and octahedral sites. In the Fe–V–O system, a complete spinel solution forms between FeV2O4 and Fe3O4, as can be seen in Fig. 1. Both tetrahedral and octahedral sites can be occupied by Fe2þ, Fe3þ, and V3þ, which can be described as: (Fe2þ, Fe3þ, V3þ)T [Fe2þ, Fe3þ,V3þ, Va] O 2 O4 where T and O represent the tetrahedral and octahedral sites, respectively, and Va is a vacancy. Decterov et al. [18] proposed the two sublattice spinel solution model considering the site occupancy of cations between tetrahedral and octahedral sites, and vacancy in octahedral sites to describe oxygen non-stoichiometry. The model has been widely used to describe many different spinel solutions in binary, ternary and high order systems [24, 25]. In the present study, the same model within the framework of the compound energy formalism (CEF) was used to describe the Gibbs en­ ergy of spinel solution. The Gibbs energy expression of the solution per formula unit AB2O4 can be defined as: XX G¼ Y Ti Y Oj Gij TSconfig þ Gexcess (2) i

i

� �m � �n XX Xi Xj ex þ Xi Xj qmn ij þ gternary Xi þ Xj Xi þ Xj i j � XXX Xi Xj Xk i

j

k

Xi Xi þXj þXk

Xj Xi þXj þXk

�n �

Xk Xi þXj þXk

�p qmnp ijk (5)

where Goi is the Gibbs energy of components like FeO, FeO1.5 and VO1.5, and Xi is the mole fraction of the component. The binary model pa­ rameters qmn ij of the FeO–FeO1.5 were taken from previous study [18] without any modification. In the present study, the one binary FeO–VO1.5 parameter and one ternary parameter were optimized to reproduce the phase diagram involving wüstite solution, and oxygen partial pressure data in the wüstite solution. No binary parameter of FeO1.5–VO1.5 was necessary in the wüstite solid solution.

2.2.3. Corundum solid solution Both hematite Fe2O3 and karelianite V2O3 have corundum type structure in the trigonal R-3c space group and form a complete solid solution. The molar Gibbs energy of corundum solution can be expressed as: X � � m n Gm ¼ XA GoA þ XB GoB þ nRTðXA lnXA þ XB lnXB Þ þ qmn AB X A X B XA XB (6)

j

where Yi and Yj represent the site fractions of cation i on the tetrahedral sublattice and cation j on the octahedral sublattice, respectively; Gij is the Gibbs energy of an ‘end-member’, (i)T[j] O 2 O4, of the solid solution; Gexecss is the excess Gibbs energy; Sconfig is the configurational entropy assuming random mixing of cations on the tetrahedral and octahedral sites: ! X X config T T O O S (3) ¼ R Y i ln Y i þ 2 Y j lnY j i

�m �

(4)

where Goi is the molar Gibbs energy of Fe2O3 and V2O3, qmn AB is the interaction energy parameter. As there are 2 mol of Fe and V are mixing in 1 mol of corundum solution, ‘n’ becomes ‘2’ in this solution. 2.2.4. VO2 solid solution There is a solubility of Fe oxide in solid VO2 phase. Inhomogeneity of VO2 phase extends toward FeVO4 composition, but the exact dissolution mechanism of Fe oxide in VO2 phase has not been known. In the present study, therefore, VO2 solution was described using a simple random mixing model similar to corundum solid solution in Eq. (6) by consid­ ering VO2 and hypothetical Fe0.5V0.5O2 as components of the solution. ‘n’ for this solution is ‘1’. The Gibbs energy of the ‘Fe0.5V0.5O2’ was modified from the Gibbs energies of pure FeVO4 (1/2GoFeVO4) to reproduce a proper solubility and oxygen partial pressures involving this phase, which will be discussed later.

j

Among twelve Gij of the present spinel solution, six were already fixed in the previous optimization by Decterov et al. [18] for the magnetite (Fe2þ, Fe3þ)T [Fe2þ, Fe3þ, Va] O 2 O4, and these previous data were taken into account without any modification. Instead of assigning arbitrary value to Gij, certain linear combina­ tions of the Gij parameters having physical significance are used to describe the Gij in the spinel model [18]. I and Δ parameters (see Table 1) which represent the energies related to the inversion of cation distri­ bution and classical site exchange reactions, respectively, were used in the present model. The general description of model and linear combi­ nation expression can be found elsewhere [25]. It should be noted that the inversion parameter ‘I’ is a key parameter to determine the cation distribution of FeV2O4. This parameter can be related to the description of site preference energies in spinel solution by O’Neill and Navrotsky

2.3. Molten oxide phase (slag) Fe and V have two and four valence states in oxide system, respec­ tively, and they all exist in liquid solution (slag), which makes complexity for thermodynamic modeling of liquid solution. In the pre­ sent study, slag phase was described using the Modified Quasichemical Model (MQM) which has been widely used for liquid slag. All liquid 3

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Calphad 67 (2019) 101682

oxide components with six different cations (Fe2þ, Fe3þ, V2þ, V3þ, V4þ, and V5þ) were introduced in the description of liquid oxide solution in order to reproduce the experimental data under various oxygen partial pressures. Details of the model equations and notations can be found elsewhere [30], and only a brief summary is given below. The MQM takes the short-range ordering (SRO) of second-nearestneighbor (SNN) pair exchange reactions of cation species into account. For example, for the binary AOx-BOy solution, the reactions between SNN cations can be considered: (A-A) þ (B–B) ¼ 2(A-B): ΔgAB

3. Critical evaluation and optimization of experimental data A great number of the experimental data within the Fe–V–O system are available in the oxygen partial pressure from air to metallic satu­ ration, and they were critically evaluated for the optimization. The experimental data can be divided into three groups: (i) thermodynamic and structural properties of the spinel phase, (ii) phase equilibrium data at subsolidus temperature, and (iii) phase equilibrium data involving slag (molten oxides) phase.

(7)

3.1. Fe3O4–FeV2O4 spinel solution

where A and B are cation species in the solution, and (A-B) represents a SNN pair containing oxygen as common anion species. ΔgAB corre­ sponding to the molar Gibbs energy of exchange reaction is a model parameter of the solution, which can be expanded as an empirical function of composition and temperature. The Gibbs energy of the binary solution is then given by: �n � � AB Gm ¼ nA gοA þ nB gοB TΔSconfig þ (8) ΔgAB 2

3.1.1. Cation distribution of FeV2O4 The cationic distribution between tetrahedral and octahedral sub­ lattices is a unique characteristic of spinel, and can influence the physico-chemical properties of spinel phase. The cation distribution data of spinel solution can define the configurational entropy of the spinel solution, and therefore they are important experimental data to determine the present spinel model parameter. FeV2O4 has normal spinel structure where V3þ preferentially oc­ cupies octahedral sites at low temperature. There have been several experimental studies on the site occupation of Fe2þ in FeV2O4 spinel. Gupta and Mathur [31] prepared powder samples under reducing at­ mosphere (H2/CO2 ¼ 3) at 1473 K (1200� C) for 8 h, and annealed them at 1173 K (900� C) for 2.5 h. Then, the samples were cooled slowly in the furnace until 298 K (25� C). The cation distribution in slow-cooled samples were analyzed for the degree of inversion (the mole fraction of V3þ in tetrahedral site). The analyses by X-Ray Diffraction (XRD) and €ssbauer spectroscopy showed 8% and 10% � 3% of the degree of Mo inversion, respectively. Nakamura and Fuwa [10] prepared powder specimen of FeV2O4 under reducing oxygen atmosphere (CO2/H2 ¼ 0.7) at 1473 K (1200� C) for 12 h, then used M€ ossbauer spectroscopy method at the temperature range from 18 K to 600 K ( 255� C–327� C) and found approximately 6% of iron ion on the octahedral site (that is, 12% V3þ in tetrahedral site), which is consistent with the results of Gupta and Mathur [31]. Later, Nakamura et al. [32] prepared single crystal FeV2O4 sample at 1473 K (1200� C) for 24 h, and then reported 85% � 1% of Fe2þ stayed at tetrahedral sites and 15% at octahedral sites. That is, the degree of inversion is 15%, which is slightly higher than previous data. Unfortunately, no in-situ cation distribution measurement was carried out for the FeV2O4. In addition, as no proper quenching process of sample was carried out in all the previous studies, the available results are difficult to use to properly define the cation distribution with temperature. It is widely accepted [33–36] that the cation distribution cannot reach an equilibrium state if the sample temperature is below so-called frozen temperature due to the slow kinetics. Jung et al. [33] considered this frozen temperature to be around 973 K (700� C) for MgAl2O4. No quenching method were applied in all available experimental studies on the FeV2O4 spinel, but all samples were slowly cooled. Therefore, we could assume that cation distributions in all the previous studies were most probably frozen at about 973 K (700� C) during the slow cooling process. Although strong affinity of V3þ for octahedral sites can be under­ stood from the crystal field theory [27,28], it is hard to find out the variation of cation distribution with temperature. In order to resolve this lack of data, the cation distribution of FeV2O4 was estimated from those of MnAl2O4 and MgAl2O4. According to the crystal field theory in Fig. 2, the site preference energy for Fe2þ-V3þ pair (Fe2þ in tetrahedral is 16 kJ, and V3þ in octahedral is 55 kJ, so the difference is 71 kJ) is between the site preference energy of Mn2þ-Al3þ pair (45 kJ 36 kJ ¼ 81 kJ) 36 kJ ¼ 56 kJ). The spinel solutions and Mg2þ-Al3þ pair (20 kJ MgAl2O4 and MnAl2O4 were previously optimized by Jung et al. [33] and Chatterjee and Jung [34], respectively, considering their existing cation distribution data. Fig. 3 shows the calculated cation distribution of FeV2O4 spinel along

where ni and goi are the number of moles and molar Gibbs energies of the component i, respectively, and nAB and XAB represent the number of moles and fraction of (A–B) bonds at equilibrium, respectively. ΔSconfig is the configurational entropy of mixing of random distribution of bonds over pseudo ‘bond sites’ in the Ising approximation and is a function of nAB. ΔgAB is the model parameter, which is expressed as a function of bond fraction, XAB: X X 0j j i ΔgAB ¼ ΔgοAB þ gi0 gAB X BB (9) AB X AA þ i�1

i�1

This ΔgAB parameter can be determined to reproduce the thermo­ dynamic properties of liquid phase and phase equilibria involving liquid phase. For the present liquid oxide phase in the Fe–V–O system, FeO, FeO1.5, VO, VO1.5, VO2, and VO2.5 are the components in the liquid solution. Totally 15 possible pair exchange reactions like Eq. (7) can be consid­ ered. Since the FeO–FeO1.5 and VO–VO1.5–VO2–VO2.5 were critically evaluated and optimized previously by Decterov et al. [18] and Kang [19], respectively, only the binary sub-systems of FeOx–VOy were opti­ mized in the present study. In order to calculate the Gibbs energies of ternary and higher order liquid solution, a geometric interpolation technique was used. That is, the Gibbs energy of ternary solution can be predicted from binary so­ lution parameters using a certain geometric interpolation method; symmetric Kohler interpolation technique or asymmetric Toops inter­ polation technique is commonly used. The details of the geometric interpolation technique are available elsewhere [29]. In the present study, VO2 and VO2.5 were considered as acidic components and all others were considered as basic components for the interpolation tech­ nique. When two basic components and one acidic component construct ternary solution, the Gibbs energy was interpolated using Toop method considering acidic component as asymmetric component. For the ternary subsystem with two acidic components and one basic compo­ nent was treated similarly. When all three components were basic components, the symmetric Kohler technique was used. No ternary excess parameters were necessary in the present study. 2.4. Metallic and gas phases In order to calculate the phase equilibria under metallic saturation condition, a thermodynamic database for the metallic Fe–V system is required. In this study, the FactSage FSStel database [21] was employed for all the Gibbs energies of metallic phases (FCC, BCC, and liquid) in the Fe–V metallic system. The Gibbs energies of all gas species were taken from the FACTPS database [21]. 4

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proposed (Fe2þ)T [Fe3þxV3þ2-x] OO4 (0 � x � 0.66) and (Fe2þ)T €ssbauer [Fe2þV4þ] OO4 (x ¼ 1). Banerjee et al. [39] studied the Mo spectrum of Fe2VO4 and reported the identical results to Rossiter [38]. Varskoi et al. [40] prepared spinel samples at 1373 K (1100� C) in ni­ trogen atmosphere, then conducted XRD measurements for the sample slowly cooled to room temperature. They proposed Fe2þ and Fe3þ at both tetrahedral and octahedral sites over the entire spinel composition range. Bernier and Poix [41] proposed the cation distribution of Fe2VO4 as (Fe3þ)T [Fe2þV3þ] OO4 on the basis of XRD lattice constant and the magnetic moment. Wakihara et al. [42] synthesized the FeV2O4–Fe3O4 spinel solution at 1500 K (1227� C), and carried out the same analysis as Bernier and Poix [41]. They proposed the cation distribution of (Fe3þ)T [Fe2þFe3þxV3þ1-x]OO4 (0 � x � 1) for the Fe3O4–Fe2VO4 region, and (Fe3þyFe2þ1-y)T [Fe3þyV3þ2-y]OO4 (0 � y � 1) for the Fe2VO4–FeV2O4 region. Abe et al. [43] reported (Fe2þ)T [Fe3þxV3þ2-x] OO4 (0 � x � 0.35) and (Fe3þ)T [Fe2þFe3þx-1V3þ2-x] OO4 (1 � x � 2) structures using €ssbauer spectrum analysis. Lee and Schroeer [44] conducted the Mo similar experiment in the temperature range of 80 K–500 K ( 193� C–227� C), and reported the existence of Fe2þ and Fe3þ at both tetrahedral and octahedral sites over the entire spinel composition range, except for FeV2O4. Riedel et al. [45,46] investigated the structure €ssbauer analysis of FeV2O4–Fe3O4 spinel solutions using Mo (-196� C–327� C) and proposed the existence of Fe2þ, Fe3þ and V3þ at both tetrahedral and octahedral sites over the entire FeV2O4–Fe3O4 re­ gion. Nohair et al. [47,48] and Gillot and Nohair [49] investigated the cation distribution for the samples from 423 K to 923 K (150� C–650� C) using thermogravimetry and infrared spectroscopy method, and pro­ posed V2þ and V3þ only occupied octahedral sites while Fe2þ and Fe3þ occupied both tetrahedral and octahedral sites. Varskoi et al. [40] pointed out that the replacement of V3þ in octahedral sites by Fe3þ ions are hard to detected by the XRD lattice parameter method because the size of V3þ cation is similar to that of Fe3þ. The cation distribution for the FeV2O4–Fe3O4 at 1673 K (1400� C) was calculated by Petric and Jacob [50]. They used the equations of octahedral site preference en­ ergies for two competing ions together with the relevant mass and site balance equations, and presented both sites were occupied by Fe2þ, Fe3þ, and V3þ. In summary, the experimental cation distribution data for the FeV2O4–Fe3O4 spinel solution are less agreement with each other. In the present study, the sublattice structure of general spinel solu­ tion is formulated as (Fe2þ, Fe3þ, V3þ)T [Fe2þ, Fe3þ,V3þ, Va] O 2 O4 in order to describe the spinel solution from FeV2O4 to Fe3O4. At least this basic structure is general enough to explain all previous reported data. As discussed above, there are no reliable experimental cation distribu­ tion data from samples quenched above the frozen temperature (about 700� C). Considering the cation distribution data for FeV2O4 in Fig. 3 and Fe3O4 in the previous assessment by Decterov et al. [18], the cation distribution data of the FeV2O4–Fe3O4 spinel solution were calculated at 1673 K (1400� C) in Fig. 4, and compared with the data by Petric and Jacob [50]. Please note that Fe3O4 has an inverse spinel structure where Fe3þ preferentially occupy tetrahedral sites. According to the present prediction, the amount of V3þ and Fe2þ in tetrahedral sites and V3þ in octahedral sites decrease with increasing Fe3O4 content in spinel solu­ tion, while the Fe3þ and Fe2þ in octahedral sites increase. That is, in general, the amount of Fe3þ in tetrahedral and octahedral sites decreases gradually from Fe3O4 to FeV2O4 composition. The present results agree well with the data by Petric and Jacob [50] except for Fe3O4 rich region. The present description is based on the optimization by Decterov et al. [24] who reproduced a lot of available experimental cation distribution data for Fe3O4 including the results of Wu and Mason [51]. Therefore, we believe that the present results in Fig. 4 are predicted accurately.

Fig. 2. Site preference energy of cations in spinel solution according to the crystal field theory [27,28].

with all available experimental data. The present model predicted that the FeV2O4 spinel has normal spinel structure at low temperature, but it become gradually disordered with increasing temperature. The data points at the end of the arrows represent the cation distributions at the frozen temperature. The present modeling result is in good agreement with the experimental data considering the frozen temperature. The cation distribution of FeV2O4 spinel is predicted between those of MnAl2O4 spinel [34] and MgAl2O4 spinel [33], considering the site preference energy from the crystal field theory [27,28]. 3.1.2. Cation distribution of FeV2O4–Fe3O4 spinel solution Several cation distribution structures were proposed for the FeV2O4–Fe3O4 spinel solution. Rogers et al. [37] investigated the structural properties of the spinel solution systematically and proposed the cation distributions of (Fe2þ)T[Fe2þxV4þxV3þ2-2x]OO4 (0 � x � 1) mixed with a small amount of (Fe3þ)T [Fe2þV3þ] OO4. Rossiter [38] used €ssbauer spectrometry for the sample at room temperature and Mo

3.1.3. Gibbs energy of FeV2O4 A number of investigations were carried out to determine the stan­ dard Gibbs energy of formation of FeV2O4. The first Gibbs energy measurement was performed by Chipman and Dastur [52] by equili­ bration of FeV2O4 with liquid Fe–V solution under controlled H2–H2O

Fig. 3. Calculated cation distribution in FeV2O4 (solid line), MgAl2O4 [33] (dashed line) and MnAl2O4 [34] (dotted line) spinel with temperature. 5

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Fig. 4. Calculated cation distributions in Fe3O4–FeV2O4 spinel solution at 1673 K (1400� C) in the present study. Moles of cations on tetrahedral and octahedral sites per mole of the spinel solution.

Fig. 5. Calculated Gibbs energy of formation for FeV2O4 from Fe, solid V2O3, and O2 in the present study in comparison to the literature data [52–63].

oxygen partial pressures were determined by emf technique. Schmahl and Dillenburg [56] determined composition of spinel phase equili­ brated with Fe (or FeO wüstite phase) under controlled CO–CO2 gas mixtures at 1173 K (900� C) and reported the activity of Fe3O4. Figs. 6–8 show the thermodynamic properties of the FeV2O4–Fe3O4 spinel solution calculated from the present study in comparison to the experimental data. The most original data of experimental studies are the variation of oxygen partial pressures for the phase equilibria of ‘3Fe (s) þ 2O2(g) ¼ Fe3O4 (in spinel solution)’ with change in spinel composition. When spinel is enriched with Fe3O4, the equilibration is changed to ‘3FeO(wüstite) þ ½O2(g) ¼ Fe3O4 (in spinel solution)’. The experimental data by Katsura et al. [64] and Marhabi et al. [65,66] at 1123 K–1500 K (850� C–1223� C) are well reproduced in the present study, as shown in Fig. 6. The activity of Fe3O4 in the FeV2O4–Fe3O4 spinel solution can be easily derived from the same equilibrium exper­ iments. The activity data of Petric and Jacob [50] were measured using Pt–Fe alloy. All the experimental activity data [50,56,64–66] are well reproduced in the present study as shown in Fig. 7. It should be noted that the activity data of FeV2O4 were derived from those of Fe3O4 using the Gibbs-Duhem relationship. So there could be a certain error accu­ mulated in the derivation. Petric and Jacob [50] presented the calcu­ lated Gibbs energy of mixing data for the FeV2O4–Fe3O4 spinel solution

gas atmosphere at 1873 K (1600� C). The similar experiments were performed by Karasev et al. [53] in the temperature range from 1808 K to 1973 K (1535� C–1700� C) and by Narita [54] at 1873–1973 K (1600� C–1700� C). Narita [54] obtained a negative temperature dependence term for the formation Gibbs energy, which is less possible. Kunnmann et al. [55], and Schmahl and Dillenburg [56] equilibrated liquid Fe and V2O3 to form FeV2O4 under the controlled oxygen partial pressures using CO–CO2 gas mixtures at 1073–1380 K (800� C–1103� C), and at 1173 K (900� C), respectively. Similarly, Kojima et al. [57] equilibrated the FeV2O4 and V2O3 with liquid Fe containing oxygen. Wakihara and Katsura [58] determined the equilibrium oxygen partial pressure for three phase assemblage of Fe þ FeV2O4þV2O3 at 1500 K (1227� C) using a thermo-gravimetric (TG) method with H2–CO2 gas mixture. The oxygen partial pressures for the same three phase equi­ libria at 1073–1973 K (800–1700� C) were determined by Kontopolous [59], Kay and Kontopolous [60], Apte [61], Jacob and Alcock [62], and Kumar and Jacob [63] using solid electrolytic cells. All available data for the FeV2O4 were analyzed and the experi­ mental results were reexamined to obtain the reaction Gibbs energy for ‘Fe þ ½O2(g) þ V2O3 ¼ FeV2O4’. As can be seen in Fig. 5, there are certain discrepancies between the experimental data. The reliability of experimental data was evaluated based on the experimental techniques and the fact of whether the existence of the final products like FeV2O4 was confirmed or not. The emf data obtained by Jacob et al. [62,63], and Apte [61], and the gas equilibration data by Chipman and Dastur [52] and Kojima et al. [57] are in good agreement with each other, and they were used to determine the Gibbs energy of FeV2O4 in the present study. The gas equilibration data by Kunnmann et al. [55] are systematically higher than the result of the emf data obtained by Jacob et al. [62,63]. 3.1.4. Activity in FeV2O4–Fe3O4 spinel solution Katsura et al. [64] measured the oxygen partial pressures for the ‘FeV2O4–Fe3O4 spinel phase þ Fe (or FeO wüstite phase)’ assemblage at 1500 K (1227� C) by emf technique. Petric and Jacob [50] equilibrated the Pt–Fe metal and spinel solution at 1673 K (1400� C) under controlled oxygen partial pressure by CO–CO2 gas mixture, and derived the activity of Fe3O4 in the spinel solution from the measured activity of Fe in Pt and controlled oxygen partial pressure. Marhabi et al. [65,66] equilibrated spinel-wüstite phase under CO–CO2 gas and spinel-iron phase under H2–H2O gas, and the equilibrated compositions of spinel solution at 1123, 1273 and 1373 K (900, 1000 and 1100� C) were analyzed and

Fig. 6. Oxygen partial pressures for the Fe3O4–FeV2O4 spinel solutions in equilibrium with metallic Fe–V or wüstite at various temperatures. 6

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Fig. 7. Calculated activities of FeV2O4 and Fe3O4 in spinel solution at various temperatures in comparison to the experimental data [50,56,64–66].

Fig. 8. Calculated Gibbs energy of mixing of spinel solution at 1673 K (1400� C) in comparison to the experimental data by Petric and Jacob [50].

at 1673 K (1400� C) from their activity data, as shown in Fig. 8. The Gibbs energy of mixing of the spinel solution calculated from the present thermodynamic model are also compared in Fig. 8. In general, all the thermodynamic data in literature are well reproduced within the experimental error range.

Fig. 9. Calculated phase diagrams of (a) the Fe–Fe2O3–V2O3 system and (b) FeO–Fe2O3–V2O3 system at 1500 K (1227� C) along with experimental data [58, 64]. Oxygen isobar values are given in ‘–log(P(O2), atm)’.

distribution in FeV2O4 spinel, all the Gibbs energies of end-members GAG, GAA, GGG and GGA for (Fe2þ,V3þ)T [Fe2þ,V3þ]O 2 O4 spinel should be defined. Because GAA was determined in the previous optimization of Fe3O4 [18], GGG and GGA should be further defined in this study. For the determination of these two end-members, Gibbs energy relationships ΔAG:AG and IAG were used. The reciprocal Gibbs energy relationship ΔAG: AG was set to be zero, and inverse parameter IAG was used to reproduce cation distribution of FeV2O4 spinel in Fig. 3. Then, ΔEA:EG and ΔAE:GE parameters determining GEG and GGE were optimized to reproduce the structural data and thermodynamic properties of the FeV2O4–Fe3O4 spinel solution in Fig. 4, and 6-8. The Gibbs energy of the end-member GV is related to the vacancy in FeV2O4 spinel, which was determined to reproduce the non-stoichiometry of the spinel based on the phase dia­ gram data.

3.1.5. Thermodynamic modeling of the FeV2O4–Fe3O4 spinel solution As mentioned in section 2, there are twelves end-member Gibbs energies should be determined to describe the spinel solution using the present thermodynamic model. Among them, six end-members were already determined in the previous system of Fe3O4 [18]. The remaining six end-member Gibbs energies were determined in the present study to reproduce all the structural data and thermodynamic properties data present in section 3.1.1 to 3.1.4 and also phase diagram data discussed in section 3.2. The Gibbs energy of (Fe2þ)T [V3þ] O 2 O4 end-member, GAG, can be mainly determined by the Gibbs energy of formation data of FeV2O4 in Fig. 5. The Neumann-Kopp rule was firstly applied to create the Gibbs energy FeV2O4 from FeO and V2O3. Then, the ΔH0298 K and S0298 K were modified to reproduce the Gibbs energy data of FeV2O4. Of course, actual FeV2O4 spinel is not completely normal spinel but has cation distribution shown in Fig. 3, the Gibbs energy of formation in Fig. 5 is calculated using spinel solution model considering real FeV2O4 spinel solution with cation distribution. In order to reproduce such cation

3.2. Phase diagram in the Fe–V–O system Mathewson et al. [67] first determined the phase relations at high temperature (�1350� C) using XRD phase determination for the 7

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quenching and thermogravimetric methods. The phases of quenched samples were identified by XRD, and the oxygen partial pressure was measured by a solid electrolytic cell. Similar experiments were per­ formed by Katsura et al. [64] to establish precise phase equilibria extended to the Fe–Fe2O3–V2O3 system at 1500 K (1227� C). Fig. 9 show the phase diagrams of the Fe–Fe2O3–V2O3 system and FeO–Fe2O3–V2O3 system. Complete solid solutions of Fe3O4–FeV2O4 spinel and Fe2O3–V2O3 corundum phase exist in this system. Equilib­ rium oxygen partial pressures for ‘spinel þ corundum’ and ‘spinel þ wüstite’, and ‘spinel þ Fe’ as well as the phase boundary of all solid solution phases determined by Wakihara and Katsura [58] and Katsura et al. [64] are well reproduced in the present study. The phase boundary and the oxygen partial pressure change in the wüstite solution phase are calculated in Figs. 10 and 11. The solubility of V2O3 in wüstite phase was determined by many researchers. Wakihara and Katsura [58] first measured 5.6 mol% V2O3 solubility at 1500 K (1227� C) (see Fig. 9), and re-measured it as 6.7 mol% at 1500 K (1227� C) in their later study [64]. Vorob’ev [70] measured the XRD lattice parameters of wüstite and the electrical resistivity of quenched samples, and reported maximum (1.9–2.0) mol% of V2O3 dissolved in wüstite phase saturated with metallic iron at 1273 K (1000� C). Tan­ nieres et al. [71] found the limit composition of dissolved V2O3 was 1 mol% at 1173 K (900� C) but the detailed experimental method was not mentioned. Dyachuk et al. [72] determined the wüstite phase with the maximum vanadium concentration, which was in equilibrium with the spinel Fe3O4–FeV2O4 solution and metallic iron, by XRD phase identi­ fication of quenched samples at 1273 K (1000� C). The oxygen partial pressure change in wüstite was also measured by emf measurements. Lykasov et al. [73] performed the similar measurements with chemical analysis (CA) to obtain the homogeneity range of wüstite solution at temperatures of 1073, 1173, and 1273 K (800, 900, and 1000� C). They found that the solubility of V2O3 in wüstite increased with increasing temperature. As can be seen in Figs. 10 and 11, the homogeneity range (solubility limit of V2O3 and Fe2O3) of wüstite solution is well repro­ duced at various temperature, and the oxygen partial pressure change within wüstite solution (see Fig. 10 (a)) is also well reproduced. In order to reproduce these experimental data, the end-member Gibbs energy of VO1.5 was determined by G(VO1.5) ¼ 0.5G� (V2O3, solid) þ 48517.6 J/mol, and binary q00 and ternary q010 FeO; VO1:5 FeO; FeO1:5 ; VO1:5 interaction parameters were employed. Cox et al. [74] and Shirane et al. [75] reported the Fe2O3–V2O3 corundum solid solution had a miscibility gap between 80 mol% and 90 mol% V2O3 at 1273 K (1000� C), based on the XRD lattice parameters of quenched samples. Schmahl and Dillenburg [56] also reported a narrow immiscible region in the corundum solution between 78 mol% and 93 mol% V2O3 at 1173 K (900� C). Fotiev et al. [76,77] carried out the similar experiments as Cox et al. [74] and found the formation of the intermediate compounds instead of a miscibility gap at the composition between 80 mol% and 85 mol% V2O3 and at 973–1173 K (700–900� C). Sorescu et al. [78] reported no miscibility gap in the Fe2O3–V2O3 solid solution at room temperature after ball-milling of powder mixtures of Fe2O3 and V2O3. In the present study, we tried to reproduce the misci­ bility gap reported by Cox et al. [74], Shirane et al. [75] and Schmahl and Dillenburg [56] in the V2O3 rich region. But it was very difficult to reproduce the phase diagram results at about 1500 K (1227� C) with a miscibility gap at about 1173 K (900� C). For example, in order to reproduce the phase equilibria (tie-lines) between spinel and corundum solution, slightly negative interaction parameters are necessary. There­ fore, it is doubtable to have a miscibility gap in the V2O3 rich region. For example, the miscibility gaps in the similar binary corundum solutions such as Al2O3–Fe2O3, Al2O3–Cr2O3, and Al2O3–V2O3 are more sym­ metric shape. Unfortunately, the formation of compound as suggested by Fotiev et al. [76,77] has not be confirmed by others yet. It is worthwhile to do the experiments to reexamine the possibility of the formation of compound at V2O3 rich region of the Fe2O3–V2O3 binary

Fig. 10. Calculated phase diagram involving wüstite phase at 1273 K (1000� C). Oxygen isobar values are given in ‘–log(P(O2), atm)’.

Fig. 11. Calculated inhomogeneity range of wüstite solution at various tem­ peratures along with experimental data [73].

quenched powder samples, and presented the first schematic phase di­ agram of the Fe–V–O system including spinel FeV2O4. Mikhailov and Lushnikova [68] and Lushnikova et al. [69] also presented the schematic phase diagram of this system by same method at 1373 K (1100� C). Wakihara and Katsura [58] determined the phase relations of FeO–Fe2O3–V2O3 system at 1500 K (1227� C) by combination of the 8

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Fig. 12 shows the optimized phase diagram of the Fe2O3(VO2)2–V2O5 system at 873 K (600� C). Burdese [79,80] first investigated the Fe2O3–V2O3–V2O5 system using quenching method at 873 K (600� C) followed by XRD, and found two new compounds, FeVO4 and FeV2O6. These two compounds were also found by Jager [81] who used the same method from 973 K to 1173 K (700� C–900� C). Galy et al. [82] rein­ vestigated the system using quenching technique at 973 K (700� C) and found so-called ‘bronze phases’ (FexV2O5 solid solution); one phase at x ¼ 0–0.02 and the other at x ¼ 0.33–0.38. Unfortunately, no thermo­ dynamic properties of these phases were measured experimentally. The FexV2O5 (0 � x � 0.02) solid solution phase could be understood as V2O5 solid solution with substitution of V5þ with Fe3þ, as suggested by Burzo et al. [83,84]. However, the change in solubility limit of this solid so­ lution with temperature is still unknown. As the solubility limit of this phase is less significant, therefore, this phase was considered as a stoi­ chiometric V2O5 phase in the present study. Based on the similar consideration, the other FexV2O5 (0.33 � x � 0.38) was treated as a stoichiometric compound FeV6O15 in this optimization . Volkov [85] studied the phase diagram of the Fe2O3–V2O4–V2O5 system at 873 K (600� C) by XRD phase determination. He also deter­ mined the equilibrium oxygen partial pressure for the three phase as­ semblages using the emf technique. He reported various iron vanadate phases including FeVO4, Fe2V4O13, FeV2O6, FexV1-xO2, and FexV2O5. The oxygen partial pressures for various three phase region measured by Volkov [85] are listed in Table 2 and compared with the present cal­ culations. It should be noted that Volkov [85] stated that some parts of the phase diagram, namely regions 1, 3, 5, and 8 in Fig. 12, could most probably be in non-equilibrium state, and the oxygen partial pressures in

Fig. 12. Calculated phase diagram of the Fe2O3–V2O4–V2O5 system at 873 K (600� C).

system in air. In the present study, the Fe2O3–V2O3 corundum solid solution was treated as a complete solid solution. Two excess Gibbs energy model parameters were introduced to reproduce the tie-lines between spinel solution and corundum solid solution in Fig. 9.

Fig. 13. Calculated FeO–V2O3 phase diagrams at reducing condition along with experimental data [81,92,93]. (a) 10 2.99 � 10 9 atm, and (d) 2.31 � 10 8 atm. 9

11

atm, (b) 3.02 � 10

10

atm, (c)

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Fig. 14 shows the phase diagram of the Fe2O3–V2O5 system in air. Cirilli et al. [94] first studied this system in air by thermal analysis (TA) method. They found one intermediate compound FeVO4 with 1113 � 10 K (840 � 10� C) melting temperature, and the eutectic reac­ tion at 10 mol % Fe2O3 and 908 � 10 K (635 � 10� C). It should be noted that the data given in the literature by Burdese [79,80] are exactly the same as the data given in Cirilli et al. [94]. Otsubo and Utsumi [95] found that both FeVO4 and Fe2V4O13 melt in air peritectically at 1163 K and 988 K (890� C 715� C), separately, and eutectic reaction L → V2O5 þ Fe2V4O13 occurred at 0–2 mol% Fe2O3 and 948 K (675� C). Kerby and Wilson [96] determined the peritectic melting point of FeVO4 at 1143 K (870� C) and the eutectic reaction at 20 mol% Fe2O3 and 918 K (645� C). However, the phase diagram data by Kerby and Wilson [96] seem to be less reliable because of the formation of a liquid miscibility gap and no Fe2V4O13 compound formation. Fotiev et al. [97] performed phase diagram experiments and reported the peritectic melting points of Fe2V4O13 at 1143 � 4 K (870 � 4� C) and FeVO4 at 965 � 4 K (692 � 4� C), and the eutectic point at 2.5 mol% Fe2O3 and 931 � 4 K (658 � 4� C). Walczak et al. [98] identified two compounds Fe2V4O13 and FeVO4 with melting points at 938 � 5 K (665 � 5� C) and 1123 � 5 K (850 � 5� C), respectively, and a eutectic point at around 5 mol% Fe2O3 and 888 � 5 K (615 � 5� C). The solubility limit of Fe2O3 in V2O5 was measured roughly 3 mol% by DTA, which was not taken into account due to less reliable experimental technique. The most recent experi­ mental study was carried out by Malan et al. [17] who determined liq­ uidus and solidus composition using quenching experiments, followed by scanning electron microscope (SEM) and EPMA for phase composi­ tion analysis. All experimental data except the results by Kerby and Wilson [96] and Walczak et al. [98] are well reproduced in the present study within the experimental scatters, as shown in Fig. 14. It should be noted that the solubility in V2O3 in Fe2O3 corundum solid solution measured by Malan et al. [17] was part of the complete Fe2O3–V2O3 corundum solution (see Fig. 9). In the present study, this phase diagram was also taken into account for the optimization of the Gibbs energies of the FeVO4 and Fe2V4O13 compounds. The phase diagrams of Fe–V–O system at 1273 K, 1500 K, and 1673 K (1000� C, 1223� C, and 1400� C) depending on oxygen partial pressure are plotted in Fig. 15. Vorobev and Chufarov [99] determined the phase boundary of spinel solution against wüstite and Fe at 1273 K (1000� C) depending on oxygen partial pressures. All other experimental data [17, 58,64–66,72,73,92,93] presented in Figs. 9–11, 13, and 14 are also plotted together in Fig. 15 to present the accuracy of the calculated phase diagrams. According to the diagram, the spinel phase and corundum phase exist in a wide range of oxygen partial pressures. With increasing V oxide content in the spinel and corundum solutions, the stability of the solid solutions extends toward lower oxygen partial pressure region. The optimization of the model parameters of MQM for liquid solu­ tion is difficult because of multivalent V and Fe oxide components in liquid state. As mentioned earlier, there are six constituent oxides in the liquid of the present system; FeO, FeO1.5, VO, VO1.5, VO2, VO2.5. The available experimental data related to liquid solution in the system are only limited to the phase diagram data in air by Malan et al. [17] (see Fig. 14) and at PO 2 ¼ 10 8–10 10 atm by Coetsee and Pistorius [92,93] (see Fig. 13). Therefore, in the present study, the following equality relationships were assumed depending on valence of Fe (FeO and FeO1.5) to reproduce the liquidus of the Fe–V–O system:

Fig. 14. Calculated Fe2O3–V2O5 phase diagram at air (PO2 ¼ 0.21 atm) along with experimental data [17,79,80,94–98].

these regions might not reflect the real situation. As can be seen in Table 2, the calculated equilibrium oxygen partial pressures are well fitted to the experimentally measured data by Volkov [85] except the regions 1, 3, 5, and 8. The solubility of Fe oxide in VO2 solid was first studied by Kosuge and Kachi [86] by means of XRD and Differential Scanning Calorimetry (DSC) analysis. They reported inhomogeneity range of the solid to be FexV1-xO2 with x ¼ 0–0.25. In this study, the FexV1-xO2 solid solution is considered as a simple random mixing solution of VO2 dissolving a hy­ pothetical component ‘FeVO4’ (strictly speaking, (FeV)0.5O2 was considered in the modeling). The heat capacity of stoichiometric FeVO4 compound was deter­ mined by Borukhovich et al. [87] by calorimetric measurements in temperature range from 60 K to 300 K ( 213� C–27� C). However, due to the large experimental errors induced from quartz capsule in their ex­ periments, their data were not taken into account in this study. Enthalpy of formation of FeVO4 was reported to be 1181 � 7 kJ/mol by Kesler et al. [90] using calorimetric measurements and the optimized value in the present study is 1187.99 kJ/mol. The Gibbs energies of the FeVO4, Fe2V4O13, and FeV6O15 compounds were optimized to reproduce the three-phase assemblage in Fig. 12 and corresponding oxygen partial pressures. In the optimization, the Cp of the intermediate compounds were estimated using the Neumann-Kopp rule based on the Cp of solid Fe2O3, V2O4 and V2O5. The estimated Cp of FeVO4 and Fe2V4O13 are good agreement with the Cp data by Cheshnitskii et al. [88,89] using the DSC and drop calorimetry techniques between 298 and 873 K (25 and 600� C). The optimized thermodynamic properties of all stable ternary Fe–V–O compounds in this study are summarized in Table 1. The phase diagrams of the FeO–V2O3 system at reducing condition are presented in Fig. 13. Koerber and Oelsen [91] first presented a schematic diagram of the FeO–V2O3 system but no experiment data were presented. Jager et al. [81] investigated this system under reducing condition (with gas mixture of 60–65 vol% N2 þ 15–20 vol% H2 þ 20 vol % H2O which is corresponding to logPO2 ¼ 10.941 to 11.191) at 1523 K (1250� C) using quenching method and XRD for phase identifi­ cation, and found wüstite, spinel, and corundum phase. Coetsee and Pistorius [92,93] performed the phase diagram experiments at 1673–1873 K (1400–1600� C) under controlled CO–CO2 gas mixtures (PO2 ¼ 3.02 � 10 10, 2.99 � 10 9, and 2.31 � 10 8 atm at 1400� C, 1500� C, and 1600� C, respectively) and identified slag, spinel and corundum phase in this system using XRD, electron microprobe analysis (EPMA), and optical microscopy. In particular, they determined the phase boundary composition of slag, spinel and corundum phases. As can be seen in Fig. 13, the phase diagrams of the FeO–V2O3 system at reducing condition are well reproduced in the present study.

Δg FeO,VO ¼ Δg FeO,VO1.5 ¼ Δg FeO,VO2 ¼ Δg FeO,VO2.5

(11)

Δg FeO1.5,VO ¼ Δg FeO1.5,VO1.5 ¼ Δg FeO1.5,VO2 ¼ Δg FeO1.5,VO2.5 (12) In general, the liquidus in air (Fig. 14) was mainly controlled by Δg FeO1.5,VO2.5 and the liquidus in reducing conditions (Fig. 13) by Δg FeO,VO1.5. Therefore, by assuming above equality relationships, all bi­ nary MQM pair exchange reactions were set up first. Unfortunately, in the optimization, it was necessary to assign slight different value for the 10

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4. Summary In the present study, a comprehensive critical evaluation and opti­ mization of all available phase equilibrium and thermodynamic prop­ erties data of the entire Fe–V–O ternary system were performed for the first time. Certain discrepancies in cation distribution data and ther­ modynamic data of the spinel solution in literatures were resolved. By using a set of self-consistent model parameters, a wide variety of reliable data in the ternary system can be reproduced within the experimental error limits. The optimized thermodynamic model parameters can be used with the Gibbs energy minimization software such as FactSage to calculate any phase diagrams and thermodynamic properties of the Fe–V–O system depending on temperatures, compositions and oxygen partial pressures. Data availability All data generated or used during the study appear in the submitted article. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements Financial support from Hyundai Steel, JFE Steel, Nippon Steel Corp., Nucor Steel, POSCO, RHI, RioTinto Iron and Titanium, Tata Steel Europe, and Voestalpine Stahl are gratefully acknowledged. This work was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF2015R1A5A1037627). Weitong Du acknowledges financial support by the Chinese Scholarship Council (CSC, No.201706050139). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.calphad.2019.101682. References [1] I.L. Júnior, J.-M.M. Millet, M. Aouine, M. do Carmo Rangel, The role of vanadium on the properties of iron based catalysts for the water gas shift reaction, Appl. Catal. Gen. 283 (2005) 91–98, https://doi.org/10.1016/j.apcata.2004.12.038. [2] A. Heydari, M. Sheykhan, M. Sadeghi, I. Radfar, Nanorods of FeVO4 : An efficient heterogeneous catalyst for chemoselective oxidation of benzylic alcohols, Inorg. Nano-Metal Chem. 47 (2017) 248–255, https://doi.org/10.1080/ 15533174.2016.1186035. [3] J. Deng, J. Jiang, Y. Zhang, X. Lin, C. Du, Y. Xiong, FeVO4 as a highly active heterogeneous Fenton-like catalyst towards the degradation of Orange II, Appl. Catal. B Environ. 84 (2008) 468–473, https://doi.org/10.1016/j. apcatb.2008.04.029. [4] W.T. Du, Y. Wang, X.P. Liang, System Assessment of carbon dioxide used as gas oxidant and coolant in vanadium-extraction converter, JOM (J. Occup. Med.) 69 (2017) 1785–1789, https://doi.org/10.1007/s11837-017-2463-y. [5] S.E. Chamberlin, I.H. Nayyar, T.C. Kaspar, P.V. Sushko, S.A. Chambers, Electronic structure and optical properties of α-(Fe1-xVx)2O3 solid-solution thin films, Appl. Phys. Lett. 106 (2015), 041905, https://doi.org/10.1063/1.4906597. [6] A.H. Pohl, A.A. Guda, V.V. Shapovalov, R. Witte, B. Das, F. Scheiba, J. Rothe, A. V. Soldatov, M. Fichtner, Oxidation state and local structure of a high-capacity LiF/ Fe(V2O5) conversion cathode for Li-ion batteries, Acta Mater. 68 (2014) 179–188, https://doi.org/10.1016/j.actamat.2014.01.016. [7] T. Katsufuji, T. Suzuki, H. Takei, M. Shingu, K. Kato, K. Osaka, M. Takata, H. Sagayama, T.H. Arima, Structural and magnetic properties of spinel FeV2O4 with two ions having orbital degrees of freedom, J. Phys. Soc. Japan. 77 (2008) 1–4, https://doi.org/10.1143/JPSJ.77.053708. [8] J.S. Kang, J. Hwang, D.H. Kim, E. Lee, W.C. Kim, C.S. Kim, S. Kwon, S. Lee, J. Y. Kim, T. Ueno, M. Sawada, B. Kim, B.H. Kim, B.I. Min, Valence states and spin structure of spinel FeV2O4 with different orbital degrees of freedom, Phys. Rev. B Condens. Matter Mater. Phys. 85 (2012) 1–5, https://doi.org/10.1103/ PhysRevB.85.165136.

Fig. 15. Phase evolution of the Fe–V system depending on oxygen partial pressure. (a) 1273 K (1000� C), (b) 1500 K (1223� C), and (c) 1673 K (1400� C).

Δg FeO,VO1.5 (¼ Δg FeO,VO) and Δg FeO,VO2.5 (¼ Δg FeO,VO2) to reproduce the liquidus better. Of course, the optimized liquid parame­ ters for the FeO–FeO1.5 liquid [18] and VO-VO1.5-VO2-VO2.5 liquid [19] in the previous studies were taken into account without any modifica­ tion. It should be also noted that the present MQM parameters were already expanded successfully toward the higher order liquid solution containing SiO2 and CaO.

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