Experimental Determination of the Standard Gibbs Energy of Formation of Fe_3–xV_xO₄ at 1473 K

Round 1

Reviewer 1 Report

The paper presents an approach for determining the standard Gibbs energy (G_F) of the Fe_3-xV_xO₄ formation. The approach consists in determining the chemical potentials of Fe and V in the compound under the constant partial pressure of oxygen and then calculating G_F. The authors suggest an expression for the Gibbs energy of solution A_xB_1-x (Eq. 22) to be parameterized and used for calculating the G_F (Eq. 23).

I believe the presented study is very important and useful and can be accepted for publication in Metals after the revision recommended below.

1)     I recommend moving most of the equations to Appendix leaving in the main text only a few key equations.

2)     It would be useful if the authors comment on why liquid cupper has been chosen for determining the chemical potential of Fe.

3)     Check Eq. 22: the last term is incomplete.

I appreciate the authors’ intension to approximate G_F with simple expression for Gibbs energy of an ideal solution of Fe₃O₄ and FeV₂O₄ stochiometric compounds. This, however, is justified if there is no other intermediate stoichiometric compound clusters, i.e. Fe₂O₃, V₂O₃, V₂O₅, etc. (actually there are many stoichiometric compounds – see Critical evaluation and thermodynamic modeling of the Fe–V–O (FeO–Fe₂O₃–VO–V₂O₃–VO₂–V₂O₅) system, Calphad, Volume 67, December 2019, 101682). I recommend the authors to comment on this point.

I suggest modifying the style of describing the equation derivations, which should be made more readable.

Author Response

Responses to comments of Review 1

• I recommend moving most of the equations to Appendix leaving in the main text only a few key equations.

Authors’ reply: Thank for the suggestion. We will consider this suggestion, and discuss with the editor about the arrangement of the equations to find a suitable way.

• It would be useful if the authors comment on why liquid cupper has been chosen for determining the chemical potential of Fe.

Authors’ reply: This is a very constructive suggestion. We will add the explanation in the revised manuscript. Here, we make a brief interpretation. Firstly, during the present investigated oxygen partial pressure range (2.39×10^-12~3.83×10^-11 atm), the liquid cooper is stable and cannot be oxidized. Secondly, the Henry constant of Fe in liquid cooper  (24.1) is far greater than unity, which can ensure the concentration of Fe in liquid cooper is very small, so the formed Cu-Fe solution can be treated as a dilute solution.

• Check Eq. 22: the last term is incomplete.

Authors’ reply: Sorry for our carelessness. We will complete it in the revised manuscript.

• I appreciate the authors’ intension to approximate GF with simple expression for Gibbs energy of an ideal solution of Fe₃O₄and FeV₂O₄ stochiometric compounds. This, however, is justified if there is no other intermediate stoichiometric compound clusters, i.e. Fe2O3, V2O3, V2O5, etc. (actually there are many stoichiometric compounds – see Critical evaluation and thermodynamic modeling of the Fe–V–O (FeO–Fe2O3–VO–V2O3–VO2–V2O5) system, Calphad, Volume 67, December 2019, 101682). I recommend the authors to comment on this point.

Authors’ reply: This is a very interesting and important question. Our opinions are as follows: 1) the spinel solid solution phase Fe_3-xV_xO₄ is a stable oxide with complex lattice structure. It is stable in a very large oxygen partial pressure range. For example, it is stable in the oxygen partial pressure range from 10^-14 to 10^-7 atm at 1473 K. So, if a Gibbs energy model covering all its stable range is established, all the structural elements such as Fe³⁺, Fe²⁺, V³⁺ and Va need to be considered, which means a very complex model and a number of model parameters. For instance, in the reference (Calphad, Volume 67, December 2019, 101682), the two sublattice spinel solution model within the framework of the compound energy formalism (CEF) was used to describe the Gibbs energy of spinel solution, and more than ten model parameters are needed. 2) The complex model is suitable to be implanted into the database of software, but not convenient and easy for common use. 3) The simple expression proposed in the present study is easy and convenient for common use, but may limited by the applicable oxygen partial pressure range. So, in the revised manuscript, we will indicate the applicable oxygen partial pressure range of the proposed simple expression.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and questions for the authors’ attention:

(1)    There are lot of grammatical errors in the manuscript and errors in vocabulary, like the phrase ‘direct spinel’ which should be ‘normal spinel’. Please, consult a native English speaker when preparing the final version of the manuscript. Correct also the numerous typos in the text.

(2)    The Introduction Ch should be expanded to present the state-of-the art of our knowledge on the thermodynamics of the Fe-V-O system and its spinel solution phase. There are at least two recent assessments not mentioned or evaluated in the manuscript, namely: 

(2019). Critical evaluation and thermodynamic modeling of the Fe–V–O (FeO–Fe₂O₃–VO–V₂O₃–VO₂–V₂O₅) system. Calphad, 67, 101682, 

(2021). Addition of V₂O₅ and V₂O₃ to the CaO–FeO–Fe₂O₃–MgO–SiO₂ database for vanadium distribution and viscosity calculations. Calphad, 74, 102284.

A number of experimental papers have also been neglected in this manuscript, including e.g.,

(2020). Phase relations in the “FeO–V₂O₃” system at 1473 K and the magnetic properties of spinel phase Fe_3-xV_xO₄. Ceramics International, 46(5), 6160-6167,

(2018). Phase equilibria and thermodynamic evaluation of the Fe-VO system in air. Calphad, 63, 12-23, 

(1987). Alloy/oxide equilibria in Fe—V—O and Fe—Nb—O systems. Steel Research, 58(2), 71-76.

(3)    On row 85 you call the modification of the spinel composition and its vanadium concentration ‘doping’. It is not correct as vanadium is a species and component of the wide solution phase of spinel structure. Please, correct.

(4)    On row 114, you have question mark as symbol of a reference. Please, use the correct number.

(5)    Please, include a detailed description of the equilibration apparatus in the Experimental Ch. It must also provide data about the experimental uncertainties and calibrations made as well as the purities of the chemicals used and their suppliers.

(6)    Please, correct the typo on row 151 and elsewhere.

(7)    You adopted the activity coefficient of iron in molten copper (obviously referred to molten, pure iron, even if not mentioned) from a relatively old compilation. How does the value compare with the more recent assessments of the Cu-Fe system available in the literature?

(8)    You show the reference pressure (of oxygen) in Table 2 but do not give its unit. Please, upgrade.

(9)    On row 264 you use the phrase ‘changing trend’. How does that differ from ‘trend’?

(10) On rows 267-268 you seem to suspect the presence of spinel solid solution between the end members of this study, and its extension up to magnetite (Fe₃O₄). What is the fact behind such a doubt?

(11) The (temperature dependent) parameter of the regular solution term in Eq. (22) is missing.

(12) On row 287, you refer to ‘calculation quality’ of the model. What does that phrase mean?

(13) On row 289, your reference to Fig. 4 is wrong and must be corrected.

(14) In Conclusions Ch, row 293, you claim that there is ‘lack of primary thermodynamic data’ of the Fe-V-O spinel phase may be true but how does your experimental data fit with the assessed values of the available thermodynamic modellings? That vey detail may be of interest when evaluation the reliability of present databases.

Comments for author File: Comments.pdf

See the above detailed comments.

Author Response

Responses to comments of Review 2

• There are lot of grammatical errors in the manuscript and errors in vocabulary, like the phrase ‘direct spinel’ which should be ‘normal spinel’. Please, consult a native English speaker when preparing the final version of the manuscript. Correct also the numerous typos in the text.

Authors’ reply: Thank for the careful review. We will check the grammatical errors carefully, and correct the mistakes in the revised manuscript.

• The Introduction Ch should be expanded to present the state-of-the art of our knowledge on the thermodynamics of the Fe-V-O system and its spinel solution phase.

Authors’ reply: Thank for the very comprehensive review. We will refresh the introduction Ch, correct the grammatical errors carefully, and add the related and recommended references.

• On row 85 you call the modification of the spinel composition and its vanadium concentration ‘doping’. It is not correct as vanadium is a species and component of the wide solution phase of spinel structure. Please, correct.

Authors’ reply: Thank for the suggestion. We will correct it, and replace the “doping” by “substituting”.

• On row 114, you have question mark as symbol of a reference. Please, use the correct number.

Authors’ reply: Sorry for our carelessness. We will add the correct reference number.

• Please, include a detailed description of the equilibration apparatus in the Experimental Ch. It must also provide data about the experimental uncertainties and calibrations made as well as the purities of the chemicals used and their suppliers.

Authors’ reply: Thank for the suggestion. We will add a description of experimental apparatus and the details of experiments. About the uncertainty of the experimental, we will add the details of the measurement method in the revised manuscript.

• Please, correct the typo on row 151 and elsewhere.

Authors’ reply: Sorry for our careless mistakes. We will check the manuscript carefully, and correct all the mistakes.

• You adopted the activity coefficient of iron in molten copper (obviously referred to molten, pure iron, even if not mentioned) from a relatively old compilation. How does the value compare with the more recent assessments of the Cu-Fe system available in the literature?

Authors’ reply: The activity coefficient of iron in molten copper (24.1) adopted in our study is referred to pure solid iron. We will add the reference state in the revised manuscript. This value of the activity coefficient is cited from a relatively old compilation of Elliott J.F., but this compilation was accepted extensively in metallurgical field, so it was adopted in the present study.

• You show the reference pressure (of oxygen) in Table 2 but do not give its unit. Please, upgrade.

Authors’ reply: Sorry for our carelessness. We will added it in the revised manuscript.

• On row 264 you use the phrase ‘changing trend’. How does that differ from ‘trend’?

Authors’ reply: No special meaning of “changing trend”, we will modify the express to avoid the ambiguity.

• On rows 267-268 you seem to suspect the presence of spinel solid solution between the end members of this study, and its extension up to magnetite (Fe3O4). What is the fact behind such a doubt?

Authors’ reply: Sorry for our misunderstanding expression. We agree the spinel solution phase is formed by the end members of Fe3O4 and FeV2O4. We will rephrase this part in the revised manuscript.

• The (temperature dependent) parameter of the regular solution term in Eq. (22) is missing.

Authors’ reply: Sorry for our carelessness. We will complete it in the revised manuscript.

• On row 287, you refer to ‘calculation quality’ of the model. What does that phrase mean?

Authors’ reply: We will change it to the “estimating effect”.

• On row 289, your reference to Fig. 4 is wrong and must be corrected.

Authors’ reply: Sorry for our carelessness. We will correct it in the revised manuscript.

• In Conclusions Ch, row 293, you claim that there is ‘lack of primary thermodynamic data’ of the Fe-V-O spinel phase may be true but how does your experimental data fit with the assessed values of the available thermodynamic modellings? That vey detail may be of interest when evaluation the reliability of present databases.

Authors’ reply: This is a very interesting and important suggestion, it deserve to be carried out in the future work. To compare the experimental data with the assessed values of the available thermodynamic models, it is needed firstly to evaluate or measure the contents of Fe³⁺, Fe²⁺, V³⁺ and Va(vacancy) in the lattice of Fe_3-xV_xO₄ under the experimental conditions. Because the spinel solid solution phase Fe_3-xV_xO₄ is a stable oxide with complex lattice structure in a very large oxygen partial pressure range, to establish the Gibbs energy model covering its stable range, all the structural elements such as Fe³⁺, Fe²⁺, V³⁺ and Va(vacancy), as well as the interactions between them, are considered and included in the model. For instance, in the reference (Calphad, Volume 67, December 2019, 101682), the two sub-lattice spinel solution model within the framework of the compound energy formalism (CEF) was used to describe the Gibbs energy of spinel solution. Therefore, we will consider the comparing work in the future work.

 

 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments for the attention of the authors:

(1)    The author and journal names of references #23, #28, and #29 are recommended to be corrected.

(2)    The journal full name of JOM in reference #25 must be double checked.  

Author Response

Responses to comments of Review 2

(1) The author and journal names of references #23, #28, and #29 are recommended to be corrected.

 

(2) The journal full name of JOM in reference #25 must be double checked.  

Authors’ reply: Thank for the careful review. We have corrected the above mistakes in the revised manuscript.