Towards an Extended Concept of Tolerance Factors for Postspinel Phases

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Even if I’m a mineralogist working on spinels, the topic of this paper is out of my field of interest as I’m not involved in high-pressure studies. This means that I think that some more words are needed to understand the scope of this work. I can see that at least one reference is given about possible applications but, in my opinion, something more is needed to attract possible readers.

Apart from this, I found nothing to comment on the text, but I’d like to point out that the quality of figures is poor. Symbols are very small and considering that it is possible to print the paper in colour I discourage the use of black and white figure (Fig. 1 for example) . So, please, enlarge the symbols and make the figures more attractive.

Author Response

Even if I’m a mineralogist working on spinels, the topic of this paper is out of my field of interest as I’m not involved in high-pressure studies.

Response: It is quite appreciated that you reviewed the paper despite that it is less interesting for you!

 

This means that I think that some more words are needed to understand the scope of this work. I can see that at least one reference is given about possible applications but, in my opinion, something more is needed to attract possible readers.

 

Response: I agree. Some further statements and references are added to the introduction. Please note that for the high-pressure community – geoscience and physics/chemistry – those postspinel phases are quite important and it is understood that not every paper can address every community or even a broad audience within one community without losing focus.

Apart from this, I found nothing to comment on the text, but I’d like to point out that the quality of figures is poor. Symbols are very small and considering that it is possible to print the paper in colour I discourage the use of black and white figure (Fig. 1 for example) . So, please, enlarge the symbols and make the figures more attractive.

Response: Thank you! The size of symbols have been changed and a more consistent choice of symbols has been used. Colour is used where more than two sets of data are plotted.

Reviewer 2 Report

Comments and Suggestions for Authors

 

Considerations on the stability of spinel- and post-spinel-structured AB₂O₄ compounds (i.e., CaFe₂O₄-, CaTi₂O₄-, and CaMn₂O₄-type) are commonly based on the ratio of atomic radii and tolerance factors at room pressure and temperature. This strategy may not be accurate when applied to high-pressure phases as the compression behavior of ionic radii at high pressure varies from ion to ion and depends on the coordination number. The author proposes an alternative approach based on pressure-dependent crystal radii determined from the literature in their previous publication (Tschauner, O., 2023, Solids 4, 235-253) to assess the relative stability of spinel phases, post-spinel phases, and their decomposition oxides. Molar volumes of several spinel- and post-spinel-structured compounds from the literature, both at room and high pressure, are compared to the crystal radii calculated from the relations proposed by Tschauner (2023). Trends in the molar vs ionic (i.e., calculated from crystal radii) volumes and ratios of ionic volumes vs total atomic number (i.e., total number of electrons) are then used to discuss the relative stability of spinel-type vs post-spinel-type phases of selected compounds.

Overall, I think this approach can be of interest to the readers of Minerals. However, in its current state, this article feels too qualitative to be of help to the high-pressure community. Some of the key aspects of the author's analysis would also benefit from a more comprehensive analysis of literature data.

Some general comments

Linear relationships are calculated between ionic and molar volume of spinel- and post-spinel-structured compounds based on data shown in Figure 1. However, no distinction is made between different post-spinel structure type, which may follow slightly different trends. Over-representation of one of these structure type could also bias the data inversion procedure. Polyhedral distortion, not necessarily due to Jahn-Teller effect, could also play a role but is not mentioned in the paper. Moreover, only one or two data points per compound and structure type are typically calculated despite the numerous pressure-volume data sets that have been published in the last several decades. I would argue the more data are used to constrain the trends in Figure 1, the better. A more comprehensive analysis would also help identify possible deviation from the proposed linear relationship as a function of pressure.

There also seems to be a tendency to over-interpret data, especially in Figure 3. The distribution of ionic volume ratios (V_ion^X/V_ion^PS) vs the total atomic number is essentially constant, except for Cd²⁺-bearing compounds. Nonetheless, the author claims that two minima exist in the distribution without exploring possible causes for this behavior. Note, for instance, that Cd²⁺ was not considered in the analysis of Tschauner (2023), therefore its high-pressure crystal radius is likely uncertain. If these the two Cd²⁺-bearing compounds are excluded from the analysis at 55 GPa, the trends are essentially flat and, therefore, no correlation between ionic volume ratios and total atomic number becomes apparent.

I would have also liked to see a more detailed treatment of solid solutions, which are especially interesting and relevant to high-pressure mineralogy and petrology. The author assumed mixing properties at cation sites to be ideal, treating solid solutions as mechanical mixtures of two or more components (see lines 74-75). However, it is well known that mixing in minerals is often non ideal. As an example, non-ideal mixing is what allows FeAl₂O₄ to exist as a component in CaFe₂O₄-type (CF-type) (Na,Mg,Fe²⁺)(Al,Si,Fe³⁺)₂O₄ CF-type phases [Ishii et al., 2023, Am Min 108(1), 217-221], although a post-spinel polymorph of FeAl₂O₄ has never been reported by experiments. A similar example is Mg₂SiO₄ existing only as a component in CF-type MgAl₂O₄ [Kojitani et al., 2007, Am Min 92(7), 1112-1118]. Can such experimental observations be explained by the model proposed by the author?

Some more line-to-line comments

Line 26. Please explain more in detail what chemical pressure is for those who might not be familiar with this term.

Line 33. Structures types -> Structure types

Lines 74-75. To avoid confusion, it would be helpful to add the coordination number to the cation notation.
Also, (B_0.85A_0.05)₂ -> (B_0.95A_0.05)₂.

Figure 1. Please add linear regressions and confidence bands to the Figure.
It would be helpful to differentiate between different post-spinel structure types. Using different colors and/or symbols might help.

Lines 88-90. This needs to be demonstrated. An easy way to do this would be to add more datapoints for a given compound in the spinel and post-spinel structure to explore the effect of pressure on the V_mol vs V_ion relations.

Line 103-104. Why is the author so sure that the observed scatter of data points is not due to data quality? Please explain and, if necessary, cite the appropriate literature.

Table 1. More data are needed if the author wants their analysis to be quantitative. For instance, after a quick search I found:
Chromite: Kyono et al. (2012) Phys Chem Minerals 39, 131-141
Magnetite (single-crystal structure refinements at high pressure): Gatta et al. (2007) Phys Chem Mienrals 34, 627-635; Glazyrin et al. (2012) Am Min 97(1), 128-133; Siersch et al. (2023) Am Min 108(7), 1322-1329.
Spinel (including effect of inversion): Nestola et al. (2007) Am Min 92(11-12), 1838-1843.
I would also recommend to compare the crystal radii determined from the structure refinements presented in these studies to those modeled by the author in their previous publication (Tschauner, 2023)

Also Table 1. I wonder why CT-type FeCr₂O₄ [Ishii et al. (2014) Am Min 99(8-9), 1788-1797] was not included.

Lines 126-128. Please, check formatting. This is hardly understandable.

Line 137. Z(B) -> 2Z(B)

Line 143-144. Either these aspects are stated here, or I do not see the point of making such a statement. Please remove.

Line 146. For clarity, please consider rephrasing.
The range of ratios V_ion^Sp/V_ion^PS of between 0.89 and 0.99 is not -> The range of ratios V_ion^Sp/V_ion^PS, between 0.89 and 0.99, is not

Lines 150-152. This sentence breaks the flow. Consider explaining the meaning of a V_ion^Sp/V_ion^PS <1 first and then discussing the specific case of Mg₂SiO₄.

Line 152. For clarity, please consider rephrasing.
Represents a labile state -> is uncertain.

Lines 162-166. This is too much information for a single sentence. Consider splitting it into two.

Line 162. “Precise” has a specific meaning in science. Please consider using “specifically” instead.
…and bond coordination crystal ionic radii… -> …and bond coordination, crystal ionic radii…
Also, are these crystal radii or ionic radii? Please use consistent terminology.

Lines 167-168: Is the enhanced kinetic energy of electrons not due to an increase in electron density and, thus, higher inter-electronic Coulomb repulsion? Please elaborate more and add references if appropriate.

Lines 168-173. Again, this is too much information for a single sentence. Consider splitting it into two.

Line 173. this is ordering -> this ordering

Lines 177-179. Please specify that this is only valid at that given pressure.

Lines 188-190. Can this not be related to polyhedral distortion and/or differences in the crystal radii of A and B cations?

Line 211. our -> this

Figure 3 and lines 244-246. Why only CT-type? It would be interesting to compare V_ion^CF/V_ion^CT of compounds for which both polymorphs have been reported, e.g., MgAl₂O₄.

Line 256. CT- to the CT-field -> CT- to the CF-field (?)

Lines 284-285. Statements such as this one should be supported by a statistical analysis of the presented data. If the author wants to keep such a statement, they should provide a correlation coefficient.

 

Author Response

Comment: Considerations on the stability of spinel- and post-spinel-structured AB₂O₄ compounds (i.e., CaFe₂O₄-, CaTi₂O₄-, and CaMn₂O₄-type) are commonly based on the ratio of atomic radii and tolerance factors at room pressure and temperature. This strategy may not be accurate when applied to high-pressure phases as the compression behavior of ionic radii at high pressure varies from ion to ion and depends on the coordination number. The author proposes an alternative approach based on pressure-dependent crystal radii determined from the literature in their previous publication (Tschauner, O., 2023, Solids 4, 235-253) to assess the relative stability of spinel phases, post-spinel phases, and their decomposition oxides. Molar volumes of several spinel- and post-spinel-structured compounds from the literature, both at room and high pressure, are compared to the crystal radii calculated from the relations proposed by Tschauner (2023). Trends in the molar vs ionic (i.e., calculated from crystal radii) volumes and ratios of ionic volumes vs total atomic number (i.e., total number of electrons) are then used to discuss the relative stability of spinel-type vs post-spinel-type phases of selected compounds.

Overall, I think this approach can be of interest to the readers of Minerals. However, in its current state, this article feels too qualitative to be of help to the high-pressure community. Some of the key aspects of the author's analysis would also benefit from a more comprehensive analysis of literature data.

 

Response: Thank you for the thorough reading of the manuscript and the helpful comments. We enlarged the set of examined data and added to the discussion.

 

Some general comments

Linear relationships are calculated between ionic and molar volume of spinel- and post-spinel-structured compounds based on data shown in Figure 1. However, no distinction is made between different post-spinel structure type, which may follow slightly different trends. Over-representation of one of these structure type could also bias the data inversion procedure.

Response: Very true! In the revision all three types of postspinels are distinguished and plotted separately. There are differences that are statistically significant as far as available data allow to assess. It is noted that several sets of data have not been considered : a) data where authors have reported mixed spin or charge-transfer evolving with pressure. In this case, the change of crystal radii would have to be modeled accordingly – this is easy to do and instructive but then the data are no longer independent from the approach that is discussed here. B) Data that are probably affected by the preferred zone sampling issue, which is a huge issue for CF,CT, and CM type phases. In the revised Method section the issue is briefly discussed and the strategy of data selection is explained.

 

Comment: Polyhedral distortion, not necessarily due to Jahn-Teller effect, could also play a role but is not mentioned in the paper.

Response: This is true! Now CM-type phases are discussed and shown separately from CT and CF.

 

Comment: Moreover, only one or two data points per compound and structure type are typically calculated despite the numerous pressure-volume data sets that have been published in the last several decades. I would argue the more data are used to constrain the trends in Figure 1, the better. A more comprehensive analysis would also help identify possible deviation from the proposed linear relationship as a function of pressure.

Response: Thank you, this is a good point. Data from several compression studies are now implemented and the data are shown in the revised figures 1 – 4, separately for spinels, CT,CM, and CF-type phases.

 

Comment: There also seems to be a tendency to over-interpret data, especially in Figure 3. The distribution of ionic volume ratios (V_ion^X/V_ion^PS) vs the total atomic number is essentially constant, except for Cd²⁺-bearing compounds. Nonetheless, the author claims that two minima exist in the distribution without exploring possible causes for this behavior. Note, for instance, that Cd²⁺ was not considered in the analysis of Tschauner (2023), therefore its high-pressure crystal radius is likely uncertain. If these the two Cd²⁺-bearing compounds are excluded from the analysis at 55 GPa, the trends are essentially flat and, therefore, no correlation between ionic volume ratios and total atomic number becomes apparent.

Response: I fully agree. A rather flat relation between the ionic volume rations and total atomic number is not expected for that pressure. There is really an issue that no sufficient data are available for several cations. There is an approximate formula for the pressure-dependencies but it does not hold for all ions. I removed the plot of ionic volume ratios (V_ion^X/V_ion^PS) vs the total atomic number at high pressure and also removed all non-ambient pressure values from Figure 3 (now Figure 8).

The discussion of pressure-effects has been augmented by using pressure-dependent electronegativities and by discussing the compound-specific variations of the molar-ionic volume relations.

It would be beneficial to examine pressure-dependent crystal radii for more elements, e,g, for Cd compression data for phases with no or little shift of fractional atomic coordinates such as monteponite, otavite etc. should be easy to collect – but this has to be left to researchers in countries that support basic science.

 

 

Comment: I would have also liked to see a more detailed treatment of solid solutions, which are especially interesting and relevant to high-pressure mineralogy and petrology. The author assumed mixing properties at cation sites to be ideal, treating solid solutions as mechanical mixtures of two or more components (see lines 74-75). However, it is well known that mixing in minerals is often non ideal. As an example, non-ideal mixing is what allows FeAl₂O₄ to exist as a component in CaFe₂O₄-type (CF-type) (Na,Mg,Fe²⁺)(Al,Si,Fe³⁺)₂O₄ CF-type phases [Ishii et al., 2023, Am Min 108(1), 217-221], although a post-spinel polymorph of FeAl₂O₄ has never been reported by experiments.

Response: To first order mixed ionic volumes correspond to ideal solid solutions, but this is not entirely true if one considers the variation of the A and V’ parameter in the linear relation between molar and ionic volume: V_mol = A V_ion – V’. For instance, for a solid solution MgAl2O4 spinel – magnesiochromite the parameters A and V’ are different and so is the mixing volume, as far as I know. The same holds for inversion, mixed spin – or partial valence changes that may occur in mixed crystals: in this case the ionic volumes of the solid solution would not necessarily be linear interpolations between the endmembers. I have not implemented a discussion of ambient pressure mixing volumes here – this is a quite relevant topic but it deserved a separate paper in my opinion.

Hercynite: This is an interesting case. I apologize that I could not add it here since the revision is already quite overdue. The question is, whether there is an intrinsic reason for the absence of a postspinel phase or rather that in experiments Fe is oxidized. This may be a call for a shock-compression experiment.

 

Comment: A similar example is Mg₂SiO₄ existing only as a component in CF-type MgAl₂O₄ [Kojitani et al., 2007, Am Min 92(7), 1112-1118]. Can such experimental observations be explained by the model proposed by the author?

 

Response: This is also an interesting point. In fact, there is a CT-type Mg2SiO4 that forms upon compression of forsterite at 300 K (‘forsterite-III’, Finkelstein et al, reference is added to paper) – the structure exhibits monoclinic distortion but it clearly is of the CT-type.

A discussion of this phase relative to ringwoodite, forsterite, and bdm + per is added to the revision. This discussion is based on the molar-ionic volume relations and pressure-dependent electronegativities from Rahm et al.

The original concept of just comparing ionic radii ratios with the total nuclear charge number could not be extended to the pressure of forsterite-III formation – or any high pressure – simply for lack of data. All reference data would have to be taken at the same pressure -  the figure is maintained for 1bar volumes and radii. All high-pressure data are removed. You are right that they should not be compared to 1bar data directly.

Comment:  Some more line-to-line comments

Line 26. Please explain more in detail what chemical pressure is for those who might not be familiar with this term.

 

Response: Thank you – I added some more explanation to the introduction but also to the Results and Discussion section.

Line 33. Structures types -> Structure types

Response: Thank you – corrected!

Lines 74-75. To avoid confusion, it would be helpful to add the coordination number to the cation notation.
Also, (B_0.85A_0.05)₂ -> (B_0.95A_0.05)₂.

 

Response: Agree – the coordinations are added as superscripts.

Figure 1. Please add linear regressions and confidence bands to the Figure.
It would be helpful to differentiate between different post-spinel structure types. Using different colors and/or symbols might help.

 

Response: The fitted equations and confidence bands are added – all structure types are now plotted separately for clarification.

Lines 88-90. This needs to be demonstrated. An easy way to do this would be to add more datapoints for a given compound in the spinel and post-spinel structure to explore the effect of pressure on the V_mol vs V_ion relations.

 

Response: Several sets of compression data are now added. The discussion section has been thoroughly revised for clarification and a new section that uses pressure-dependent electronegativities has been added.

Line 103-104. Why is the author so sure that the observed scatter of data points is not due to data quality? Please explain and, if necessary, cite the appropriate literature.

Response: This is quite an issue, indeed. In the revised Method section the criteria for data selection are now outlined. Further, the issue of the preferred zone sampling for postspinel phases is indicated. Since the comments and responses will be public I should not comment on individual data sets that were not considered – in short, the issue is not poor work but limitations of technique or samples that affect some sets of data (for cubic spinel this can be tested because the O x-parameter is directly related to the cell parameter but for postspinels one would have to look at bond distances, but these are implicitly used in the P-dependent crystal radii already).

Generally, instead of selecting data by the criteria that are outlines in the revised Method section, one may employ a purely statistical approach that uses all data – however, for high pressure studies the statistics is not sufficient.

 

Comment:

Table 1. More data are needed if the author wants their analysis to be quantitative. For instance, after a quick search I found:
Chromite: Kyono et al. (2012) Phys Chem Minerals 39, 131-141
Magnetite (single-crystal structure refinements at high pressure): Gatta et al. (2007) Phys Chem Mienrals 34, 627-635; Glazyrin et al. (2012) Am Min 97(1), 128-133; Siersch et al. (2023) Am Min 108(7), 1322-1329.
Spinel (including effect of inversion): Nestola et al. (2007) Am Min 92(11-12), 1838-1843.

 

Response: I agree! Data from Kyono et al (2021) and Nestola et al. (2007, 2014), further Merlini et al (2010) and Yamanaka et al. (2008) are added. Spinels which exhibit mixed spin states and/or charge transfer are not considered here because this would require adjustments of the crystal radii and make those data at best a consistency check.

 

Comment: I would also recommend to compare the crystal radii determined from the structure refinements presented in these studies to those modeled by the author in their previous publication (Tschauner, 2023)

Response: For instance for Kyono et al. 9.5 GPa, the calculated Cr[6]-O[4] distance is 1.963 Å versus 1.972 Å based on the reported O coordinates and cell parameters.

Fig 2 (! Not Fig 1!) in the revised version shows that none of the examined spinels deviates from the general trend. Hence, within the context here, the data are consistent with the radii.

 

An exhaustive evaluation requires assessment of radii of ferrous tetrahedrally coordinated Fe from the same spinels that would then serve as non-independent test: Unfortunately, there are only data for spinels. It would be important to have at least one independent set of data to cross-check the radii.

Note that at pressures btw 0 and 2-5 GPa there is always some non-linearity of P-dependent radii. The limit is material specific but above 2-5 GPa the radii are generally linear functions of P. at low pressure directional variations of bond overlap is generally more prominent and cannot be corrected universally, this was already noticed by Vincent Gibbs.

Since the O-x parameter can be checked by the unit cell dimensions in cubic spinels I shall try to find time to examine all those data on ferrous spinels and try to extract P-dependent crystal radii for ferrous Fe in tetrahedral and for ferric Fe in octahedral coordination – but this takes more than one or two weeks.

 

Comment: Also Table 1. I wonder why CT-type FeCr₂O₄ [Ishii et al. (2014) Am Min 99(8-9), 1788-1797] was not included.

 

Response: It is now included!

 

Lines 126-128. Please, check formatting. This is hardly understandable.

Response: This has been changed – thank you!

Line 137. Z(B) -> 2Z(B)

Reponse: Changed – thank you!

 

Line 143-144. Either these aspects are stated here, or I do not see the point of making such a statement. Please remove.

Response: Removed!

 

Line 146. For clarity, please consider rephrasing.
The range of ratios V_ion^Sp/V_ion^PS of between 0.89 and 0.99 is not -> The range of ratios V_ion^Sp/V_ion^PS, between 0.89 and 0.99, is not

Lines 150-152. This sentence breaks the flow. Consider explaining the meaning of a V_ion^Sp/V_ion^PS <1 first and then discussing the specific case of Mg₂SiO₄.

 

Response: This entire section has been removed.

Line 152. For clarity, please consider rephrasing.
Represents a labile state -> is uncertain.

 

Response: This entire section has been removed.

 

Lines 162-166. This is too much information for a single sentence. Consider splitting it into two.

Response: This entire section has been removed.

 

Line 162. “Precise” has a specific meaning in science. Please consider using “specifically” instead.
…and bond coordination crystal ionic radii… -> …and bond coordination, crystal ionic radii…
Also, are these crystal radii or ionic radii? Please use consistent terminology.

 

Response: This entire section has been removed.

In the entire paper radii means crystal radii.

Lines 167-168: Is the enhanced kinetic energy of electrons not due to an increase in electron density and, thus, higher inter-electronic Coulomb repulsion? Please elaborate more and add references if appropriate.

Response: It is the exchange interaction that causes the increase of E_kin of electron to increase with power 5/3 with density whereas the Coulomb energy = integral over the Coulomb potential increases linearly with density - see for instance Hund’s paper on compression of matter or Landau-Lifshitz volume V (statistical physics). In any case, this section is removed, it is not needed here.

Lines 168-173. Again, this is too much information for a single sentence. Consider splitting it into two.

Response: This entire section has been removed.

 

Line 173. this is ordering -> this ordering

Response: This entire section has been removed.

 

Lines 177-179. Please specify that this is only valid at that given pressure.

Response: This entire section has been removed.

 

Lines 188-190. Can this not be related to polyhedral distortion and/or differences in the crystal radii of A and B cations?

Response: This entire section has been removed.

 

Line 211. our -> this

Response: This entire section has been removed.

 

Figure 3 and lines 244-246. Why only CT-type? It would be interesting to compare V_ion^CF/V_ion^CT of compounds for which both polymorphs have been reported, e.g., MgAl₂O₄.

Response: Yes! The revised figure (now: 8) shows both types separately. Chenmingite (CT) and xieite (CF) are both shown.

Line 256. CT- to the CT-field -> CT- to the CF-field (?)

Response: This entire section has been removed.

 

Lines 284-285. Statements such as this one should be supported by a statistical analysis of the presented data. If the author wants to keep such a statement, they should provide a correlation coefficient.

Response: This entire section has been removed (and you are very right!)

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The author has addressed all the points I raised, expanded the data set used to derive the relations between crystal radii and molar properties, and included an implication section where their new method is applied to a few phases of mineralogical and petrological interest, i.e. MgAl₂O₄ and Mg₂SiO₄ compounds.

Overall, the manuscript is in much better shape and I only have a few minor suggestions that might help improve the readability of the paper.

Line 127: Perhaps it is worth defining A and V' here rather than in the Discussion section.

Line 151: What does the author mean by dependency? Perhaps correlation would be more appropriate?

Line 190-193: I would suggest removing the parentheses.

Line 320-321: Consider rephrasing: A = 1.57 and V' = 16.5 (Table 2).

Line 393: Remove comma between "both" and "oxide-spinels".

Author Response

Comment: The author has addressed all the points I raised, expanded the data set used to derive the relations between crystal radii and molar properties, and included an implication section where their new method is applied to a few phases of mineralogical and petrological interest, i.e. MgAl₂O₄ and Mg₂SiO₄ compounds.

Overall, the manuscript is in much better shape and I only have a few minor suggestions that might help improve the readability of the paper.

 

Response: Thank you again for the very helpful comments on the initial submission and for the thorough reading and comments on the revision!

 

Comment: Line 127: Perhaps it is worth defining A and V' here rather than in the Discussion section.

 

Response: This is certainly better – the definition of these two parameters has been moved to ‘Results’ pages 3 and 4 lines 103-118.

 

Comment: Line 151: What does the author mean by dependency? Perhaps correlation would be more appropriate?

Response: I agree, the section has been reformulated as follows:’ Thus, correlation (2) provides a measure of structure-type specific values of A and V’, while these parameters vary for the various compounds with spinel structure. This is shown here for ambient pressure volume and for compression data of spinel- and postspinel-type phases (filled symbols) in comparison to other oxide compounds (hollow symbols, data from [15]). Figure 2 shows that the correlation between A and (V’ / Vmol)3/2 for spinels and postspinels follows the general trend of oxides [15].

’

I follow your suggestion and use the term ‘correlation’: On one side A’ is substituted through V’ via relation (3) (in the revision), which makes it a ‘relation’, on the other hand the functional relation has not yet been derived, which makes it an empirical correlation.

 

 

Comment: Line 190-193: I would suggest removing the parentheses.

Response: Yes, this is better – thank you!

 

 

Comment: Line 320-321: Consider rephrasing: A = 1.57 and V' = 16.5 (Table 2).

 

Response: Thank you! Rephrased as ‘With A and V’ = 1.57 and 16.5 (Table 2) for the spinel-type phase the sequence…’

 

Comment: Line 393: Remove comma between "both" and "oxide-spinels".

 

Response: Done – thank you!