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| 15 Jan 2025
High-pressure behaviour and elastic constants of 1M and 2M1 polytypes of phlogopite KMg3Si3AlO10(OH)2
Abstract. In the present work, the elastic properties of both 1M and 2M1 phlogopite polytypes, KMg3Si3AlO10(OH)2 (monoclinic crystal system) were investigated from PV equation of state fitting and by analysis of the fourth-rank elastic tensor. The analysis was performed within the Density Functional Theory framework, using all-electron Gaussian-type orbitals basis sets and the B3LYP functional corrected a posteriori to include long-range interactions (B3LYP-D*). In general, the elastic properties of the two polytypes were strongly anisotropic, with the axial moduli ratio M(a) : M(b) : M(c) being close to 4 : 4 : 1. The volume-integrated third-order Birch-Murnaghan equation of state fitting parameters at 0 K were K0 = 57.9(2) GPa, K’ = 8.29(7) and V0 = 489.82(3) Å3 for phlogopite-1M, which were very close to those of the 2M1 polytype, i.e., K0 = 58.3(1) GPa, K’ = 8.71(8) and V0 = 978.96(9) Å3. The monoclinic elastic tensors obtained for the two polytypes of phlogopite, which have never been experimentally reported for both minerals so far, were in line with the PV behaviour of the mineral, providing further data related to the directional dependence of the elastic properties and seismic wave propagation. The elastic properties from both PV hydrostatic compression and from the elastic moduli tensor were discussed against the available experimental and theoretical data in the scientific literature, extending the knowledge on this important trioctahedral phyllosilicate.
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RC1: 'Comment on egusphere-2024-3429', Anonymous Referee #1, 29 May 2025
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Review of manuscript “High-pressure behaviour and elastic constants of 1M and 2M1 polytypes of phlogopite KMg3Si3AlO10(OH)2” after Ulian et al. https://doi.org/10.5194/egusphere-2024-3429
Overall considerations:
The manuscript from Ulian et al. describes a Density Functional Theory (DFT) based computational study on the high-pressure structural evolution and the elastic properties of 1M and 2M1 polytypes of KMg3Si3AlO10(OH)2 phlogopite. More specifically, the calculations report the static equation of state parameters (K0, K’ and V0) and the full elastic tensor for both polytypes, from which polycrystalline average properties (Kvoigt, Kreuss, µvoigt, µreuss, E, υ) and seismic anisotropy are derived. The novel aspect of this work relies on the adoption of a posteriori correction of the hybrid B3LYP functional to include the dispersion effects on the elastic properties of both polytypes.
The data obtained from the theoretical calculations are overall of good quality and valuable to the mineralogical community. Although the effort and success in predicting elastic properties (11 independent elastic constants) of monoclinic compounds are remarkable, the general presentation of the manuscript needs to be improved and parts of the text rephrased to carefully explain and discuss the methodology and new findings, to make it easier to understand to non-expert readers.
In addition, the manuscript in this current form lacks a comprehensive framework describing the relevance of phlogopite in geological sciences and in particular why it is important to have a firm knowledge of both polytypes elastic properties. This is now barely described in the introduction - where the authors only state “it is also important to know the elastic properties of this mineral to understand and explain geophysical observations in subduction zones”. Proper citations necessary to provide context on how the results obtained could help understand geophysical observations (not detailed in the text) are also lacking. Some possible technological applications of phlogopite are mentioned in the introduction section, but besides a few citations, no more details are provided. This impacts directly the conclusions of the manuscript, which is only a short sum up of the main results obtained, without adding any sort of implications concerning Earth Sciences nor Material Sciences. Both the introduction and the conclusion of the manuscript therefore need to be considerably implemented by adding further context and implications.
While this manuscript represents the first attempt to calculate the elastic properties of 2M1 polytype, the full elastic tensor of phlogopite 1M was already provided by Chheda et al. (2014) (Chheda, T. D., Mookherjee, M., Mainprice, D., dos Santos, A. M., Molaison, J. J., Chantel, J., Manthilake, G., and Bassett, W. A.: Structure and elasticity of phlogopite under compression: Geophysical implications, Physics of the Earth and Planetary Interiors, 233, 1-12, 10.1016/j.pepi.2014.05.004, 2014). Importantly, despite adopting a more sophisticated computational method with respect to Chheda et al. (2014), from the current manuscript it is not clear what the improvement and the advancement with respect to the previous study are. In particular, the study by Chheda et al. (2014) reports the high-pressure evolution of the elastic constants and seismic anisotropy, describing the geophysical implications relevant to subducting zone settings, which are not presented in this manuscript, making it hard to judge the novelty of this work.
In conclusion, at the current stage, I believe the manuscript is unsuitable for publication in a broad-impact journal such as Solid Earth.
Specific comments:
1.Introduction
Line 44: when writing that the knowledge of phlogopite elastic properties could “explain geophysical observations in subduction zones” some context and citations should be provided. Which seismological/geophysical observations are attributed to phlogopite?
Line 52: here you should provide more details on why it is important to include long-range interactions in the physical treatment of phlogopite. This would particularly benefit the non-expert readers.
Line 55: even if a complete knowledge of the elastic behaviour of both 1M and 2M1 polytypes is given, how can this improve the interpretation of geophysical observations in subduction zones? The stability of polytypes cannot be predicted by thermodynamics, since the presence of either 1M or 2M1 is not a matter of free energy differences, but rather kinetics. So even if some geophysical observations are attributed to phlogopite, it is extremely difficult to point out which polytype is the main responsible or, if both polytypes are present simultaneously, to try to understand the relative amounts.
2.Computational methods
Line 67-68: the paper of Grimme (2006), which is extremely important as it contains the theoretical details of the treatment of dispersion contributions, is not present in the References section.
Line 68: the parameters that define the dispersion contribution to the total energy are not only functional-dependent, but also compound-dependent, so care should be taken when using the parameters adopted by other authors on different compounds with respect to the one investigated in this study. Since Civalleri et al. (2008) worked on “NH3, acetylene, CO2, urea, urotropine, propane, benzene, naphthalene, formamide, formic acid, 1,4-dichloro-benzene, 1,4-dicianobenzene, succinic anhydride and boric acid”, can the parameters adopted for such compounds be directly employed for phlogopite as well? Civalleri et al. (2008) used the parameters reported in Table 1 of Grimme (2006), therefore one straightforward way to remove any doubt about the parameters employed for the calculations on phlogopite would be to add a table in the supplementary material with the C6 parameter of K, Mg, Si, Al, O and H, the scaling factor s6 adopted for the B3LYP functional, and the van der Waals radii of the various atoms. Moreover, the B3LYP-D* correction employed by Civalleri et al. (2008) consists of an empirical rescaling of the scaling factor of the B3LYP functional and of “the van der Waals radii of heavy atoms and hydrogen”. As reported by Civalleri et al. (2008): “Proposed scaling factors were determined from a manual procedure by progressively increasing the atomic van der Waals radii and trying to find the best agreement between computed and experimental data”. This means that the parametrization they performed is compound-specific and calibrated over experimental results on mostly organic compounds that do not contain K, Mg, Si or Al. Again, I suggest you provide more details on the parameters that were employed for your correction either in the supplementary material or directly in the computational methods section.
Line 72: For O basis set, I think it is better to cite this work: “L. Valenzano, F.J. Torres, K. Doll, F. Pascale, C.M. Zicovich-Wilson, R. Dovesi, "Ab Initio study of the vibrational spectrum and related properties of crystalline compounds; the case of CaCO3 calcite", Z. Phys. Chem. 220, 893-912 (2006). DOI 10.1524/zpch.2006.220.7.893”, as it is the first study in which the different contraction exponents and coefficients for O were tested and that led to the 8-411d11G set.
3.Results and discussion
Lines 87-99: this section should go in the methods paragraph.
Lines 120-121: it is necessary to specify how many, and what volume states were considered, as this not only can affect the E-V fitting but also prevents the reproducibility of the calculations.
Line 130 equation 1: the term (Ƞ2-1)3 should be a factor, not an exponent. Also, it would be better to specify the natural variable of energy: E(V).
Line 132: the term “dilaton” can be avoided as it’s rarely used and can be confusing.
Lines 133-134: “The pressure values at each unit cell volume (reported in Table 2)…” Table 2 does not report any pressure value, nor unit cell volumes other than the equilibrium one. Are you referring to Table S2?
Line 136 equation 3: As already commented for equation 1, the natural variable of pressure should be specified: P(V).
Line 137: “Table 3” could be a typo, probably you were referring to Table 2 instead?
Lines 139-140, with reference to Figure 2: “In general, there is a fine agreement between the relative variation of the cited structural properties obtained from the present theoretical simulations and the experimental ones from X-ray diffraction”. Please be more specific and define the differences between experiments and calculations, and between these calculations and the previous calculations from Chheda et al. (2014). You need to explain the deviation of computed volumes with respect to experiments at high pressures in Figure 2 (panels A, B and D)? Also, add Chheda et al. (2014) results to Figure 2 and provide the fit of P-V data.
Line 141: (comment on Table 2) I think that a valuable comparison that should have been provided to support the importance of dispersion correction in evaluating EoS parameters would have been a calculation of static EoS at B3LYP level with no dispersion correction, to see how different the K0 (DFT) and K0 (DFT/D*) actually are and how impactful dispersion effects are on compressibility. This comparison has been done in a previous paper by the authors (Ulian et al., 2021).
Line 141: (comment on Table 2) The theoretical bulk moduli of 1M and 2M1 polytypes provided by this work are almost identical, so how different is their compressional behaviour?
Line 151: Please rephrase “Similar figures were calculated..”
Line 193: I believe it is not necessary to specify here which keyword allows to perform calculation of the elastic tensor in CRYSTAL.
Line 198: “whose values were reported”. Maybe “are reported” is better?
Line 200: “the present simulations were in good agreement with the experimental results” by looking at Table 4, the presented results are rather different from the references provided… Again, please discuss the differences. Also, it would be useful to have a figure displaying the Cij evolution with pressure. See for example Chheda et al. (2014)
Lines 210-211: in the text the authors mention that there is a systematic overestimation due to 1) absence of thermal effects in the calculations and 2) presence of Pulay forces…. I have some concerns about this: thermal effects may explain the overestimation with respect to experimental values, however the Cij reported in this study differ also from those of Chheda et al. (2014). Even if the overestimation with respect to plane waves calculations is to be attributed to the use of GTOs, PAW results are still in slightly better agreement with experiments. A routine is currently implemented in CRYSTAL that allows to remove eventual BSSE via a geometrical counterpoise method. Could that improve your results and mitigate the effect of the basis set? As reported in a previous comment in the equation of state section, it would have been nice to see a comparison between a B3LYP-D* corrected and B3LYP non-corrected simulation. Also, if an overestimation is “systematic” an estimate of such overestimation should be reported to quantify the expected mismatch.
Line 245: where are equations (14) from?
Lines 277 – 280: A table with a comparison between the numerical values of VP and VS predicted in this work and those obtained by Chheda et al. (2014) (and maybe also Alexandrov et al., 1974) would make it easier and more straightforward to compare the presented results and the literature data.
Figures/Tables captions
Table 1: report error bars in the experimental data
Figure 2: “Evolution of (a) unit cell volume V/V0…” should be “Evolution of normalized (a) volume (V/V0), and lattice cell parameters (b) (a/a0)…”
Table 4: there is an inconsistency between how the components of the elastic tensor are labelled: Cαβ in equations 4 and 5 whereas Cij in Table 4. Be consistent with the terminology.
Supplementary materials
Table S1: if these are the volume states used for the E – V fitting, why is the equilibrium volume not included in the table? Usually when you perform EoS calculations with CRYSTAL the equilibrium volume is always included by default regardless of how many and which E – V points you consider. Same thing for Table S2 on the 2M1 polytype. In this second case, I guess that the data at P = 0 GPa are those reported in Table 1 of the manuscript, but for the sake of clarity and completeness I would leave them also in the tables provided in the supplementary section, and report in the computational methods section of the manuscript at least the P – V conditions you considered for your static EoS.
Citation: https://doi.org/10.5194/egusphere-2024-3429-RC1
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