Dear Editor,

Please find enclosed comments to the Author

The submitted manuscript «Quartz under stress: Raman calibration and applications to geobarometry of metamorphic inclusions» refers to an experimental calibration of the three major Raman peaks of quartz with hydrostatic pressure and uniaxial differential stress. The authors show that the position of 206 cm-1 peak depends only on hydrostatic pressure P, and its pressure dependence with a peak fitting procedure can be used for more adequate Raman barometry. Korsakov et al (ABC 2010) suggested that behavior of the inclusions under uniaxial stress is necessary for the understanding and elastic modeling of different inclusion – host-mineral pairs. Previously, similar studies were performed only at low temperatures of about 4 K (Tekippe et al., 1973), while in this study, the author performed a room temperature calibration of the most intense quartz Raman bands. I believe that the data of experimental studies presented in this paper should be arranged in the form of tables, similar to those given in the work of Schmidt & Ziemann (2000). The table in the appendix is the basis of this work, and requires comments for the reader. Firstly, repetition of stress values (column one) - what do they mean? Are these measurements at different points on the sample? Were they obtained within the one experimental run or different ones? Secondly, polarization is indicated only for "failed" experiments, while it is not indicated in successful experiments. Relatively high stress values in the table are indicated only for "failed" experiments, while similar values are shown in Figure 1 without any comments.

This work is important for recovery of the metamorphic history of different metamorphic terrains, because quartz inclusions in garnet are very promising pair of the inclusion-host mineral because they allow us to estimate PT conditions for nominally “mute” rocks for classical geothermobarometry.

The content of the submitted work is suitable for the EGUsphere, after some minor revision.

See also annotated pdf-file.

Best regards

Andrey

Review of Reynard and Zhong: “Quartz under stress: Raman calibration and applications to geobarometry of metamorphic inclusions”

Dear Editor,

I have read through this manuscript in detail. It presents a new experimental calibration of the three major Raman peaks of quartz with hydrostatic pressure and uniaxial differential stress. I believe this is a valuable contribute to the discussion on the variations of Raman shifts of quartz under an applied stress and strain. In this respect the experiments reported in this manuscript bring a useful contribute to the development of a methodology to assess the stress states of inclusions in their host minerals for mechanical thermobarometry applications. The possibility to use the differential stress of several inclusions in the same host to obtain independent constraints on the temperature of entrapment, even if suggested already in previous literature, is appealing. For this reason, a robust method to quantify the differential stress of inclusions with Raman spectroscopy would be extremely important in the field of petrology. However, I have some concerns about this manuscript which should be addressed by the authors. I believe that this work is suitable for publication in Solid Earth, provided that the following comments are addressed.

I introduce my general comments here, and further details are presented in the specific comments below.

General comments

The calibrations presented in this manuscript are based on the results from Raman experiments of quartz under hydrostatic pressure and uniaxial stresses with different orientations. In one of these experiments, the authors observe a separation of the doubly degenerate (E) mode (near 128cm^-1) when the uniaxial stress is applied along the a-axis of the quartz unit-cell. This behavior is identified by the authors as the LO-TO splitting of  the E mode, and they conclude that their results are directly applicable to quartz crystals with trigonal symmetry. However, their interpretation does not agree with the existing Raman theory and the requirements of the symmetry analysis, as shown also by previous experiments and clearly summarized in its formal aspects by Tekippe et al. (1973).  Depending on the orientation of the stress with respect to the unstrained trigonal unit-cell, this configuration leads to a reduction of symmetry from trigonal to monoclinic or triclinic. Therefore, the splitting observed in the experiments of Reynard and Zhong is not the LO-TO splitting of the E mode, but rather the splitting of the E mode into totally symmetric (A) and antisymmetric (B) non-degenerate modes (monoclinic symmetry), or into a pair of A modes (triclinic symmetry). Indeed, E modes in monoclinic and triclinic crystals are not allowed by symmetry. This is a crucial point, since the authors refer to the previous literature (Tekippe et al., 1973; Murri et al., 2022) to support the argument that their experiments apply directly to trigonal quartz inclusions without symmetry breaking, while those works conclude the opposite. Since it is possible that quartz inclusions in synthetic and natural samples have symmetry lower than trigonal because of their stress state, the results of calibrations with symmetry breakings are still useful and should be considered for the characterization of the stress states of inclusions in rocks.  For this reason, I recommend that the discussion is revised in order to make it consistent with the widely known physical theory, and to discuss the implications of the symmetry breaking. I elaborate further on this point in the specific comments below.

Moreover, as a potential user of the calibrations proposed in this manuscript, I was confused to realize that two different calibrations are proposed to estimate the same quantity (i.e. the differential stress in an inclusion), but often the values obtained from them do not agree. The disagreement arises from an apparent anti-correlation of the two proposed calibrations, the reasons for which are unfortunately not discussed in the manuscript. The averaging of the results of the two calibrations over many inclusions is proposed as a procedure to obtain the estimate of the residual differential stress of the sample, but even after this averaging the results often do not agree within uncertainties. I believe that, in order to improve the reception of the proposed approach by the scientific community, it would be important to expand the discussion on the reason why several averaging steps of the results of two calibrations that appear anti-correlated make this a robust method to estimate the residual differential stress.  I elaborate more on this point in the specific comments below.

Specific comments

• Lines 52-53. In Fig. 1 the Ne (and not He) and Hg peaks are marked with different wavenumbers to what reported in the text.

• Lines 73-76. Since the details of the experiments under uniaxial stress affect the resulting calibration, I suggest that the authors add here more details. I suggest that they describe here the dimensions of the sample and the procedure they used to orient the crystals. Reynard and Zhong mention that they oriented the sample optically and refer to Tekippe et al. (1973), who however oriented their crystal with X-rays. Determining the precise orientation of the crystal is fundamental for the correct estimate of the effect of stress, also in the light of the symmetry breaking discussed in my comment above. A slight deviation in the orientation (i.e. a stress not exactly oriented along the a-axis) can lead to a symmetry reduction to triclinic rather than monoclinic. The authors should give more details on the procedure they used and how the estimated accuracy of 3° can be achieved with optical observations. If possible, it would also be useful to add a figure that shows the experimental setup.  

• Lines 80-87. I suggest that here a few more details are given regarding the elastic properties they used to calculate the strains of the quartz inclusions. They mention the EoS, but it is not clear if they used axial EoS (e.g. Angel et al., 2021) or some extrapolation of the elastic tensors to high pressure and temperature. They should also mention the source of the elastic properties of almandine that were used in the calculation, and if they are assumed to be constant with P and T or not.

• Line 116. The authors should precisely report the orientation of the applied stress with respect to the quartz crystal. Because of the symmetry of quartz, the a-b crystallographic plane is not elastically isotropic (Nye, 1985). Assuming that the Cartesian x-axis is aligned to the a-axis of the unit-cell, and the Cartesian z to c, a uniaxial stress applied along x or along a direction orthogonal to it, would reduce the symmetry to monoclinic. On the other hand, if the non-zero component of the uniaxial stress is applied in any other direction of the Cartesian x-y plane, the symmetry would be reduced to triclinic rather than monoclinic. Therefore, it is not enough to state that the stress is applied normal to the crystallographic c-axis, and the authors should state explicitly if the a-axis is parallel to the global Cartesian x and if they oriented the stress exactly along the a-axis.

• Line 117. Before discussing the evolution of Raman shift with the applied stress, I believe it would be worthwhile to discuss if any barreling effect does take place in the sample due to the friction with the compression cell, and if the authors assessed the homogeneity of the stress in the sample. The potential inhomogeneity of stress in the sample would require a correction to determine the exact value of stress at the point of the Raman measurements, given the stress applied to the crystal rod.

• Lines 126-132: as introduced in the general comments above, I have serious concerns regarding the interpretation of the splitting of the doubly degenerate (E) mode (near 128cm^-1) under uniaxial stress applied along the a-axis as a LO-TO splitting. The symmetry of a crystal under uniaxial compression is determined by the symmetry elements common to both the unstrained crystal and the strain state. The reduction of the symmetry of the crystal point-group as a result of an applied external field is known in the literature as the morphic effect (Anastassakis, 1980; Gregora, 2013). Assuming that the orientation of the stress in this experiment is exactly along the a-axis (which in turn is parallel to the Cartesian x) of the unstrained trigonal unit-cell of quartz, this configuration leads to a reduction of symmetry from trigonal to monoclinic (see table II of Tekippe et al., 1973). Therefore, in this configuration the E mode, belonging to the parent trigonal symmetry, splits into a totally symmetric (A) and antisymmetric (B) non-degenerate mode in the new stress-induced monoclinic symmetry, as required by the theory and already shown in previous experiments (Fig. 5, table II and discussion at page 813 in Tekippe et al., 1973). This should not be confused with the LO-TO splitting of the E mode, which occurs in non-centrosymmetric crystals (even unstressed) because of the long-range polarization fields (electro-optic effect; Gregora, 2013) and it is typically unresolved for the 128cm^-1 line (Briggs & Ramdas, 1977). A similar behavior was also confirmed by the first principle calculations of Murri et al. (2022) for a stress configuration which leads to a symmetry reduction from trigonal to triclinic. They showed that each E mode of an unstressed trigonal quartz, splits into two A modes because of the applied strain/stress that induces a symmetry breaking, and both of the A modes in turn exhibit a LO-TO splitting. Therefore, the separation of the 128cm^-1 peak observed by Reynard and Zhong with a uniaxial stress parallel to the a-b plane of quartz is actually the evolution of the E mode into an A and B modes (if the uniaxial stress is applied along the a-axis or orthogonal to it, leading to a monoclinic symmetry) or into two A modes (if the uniaxial stress is applied along any other direction in the a-b plane and the final symmetry is triclinic). In order to correctly interpret which of the situations takes place in these experiments (i.e. symmetry reduction to monoclinic or triclinic), Reynard and Zhong should clearly state the orientation of the Cartesian axes with respect to the crystallographic axes of the quartz sample, and the orientation of the stress in the Cartesian reference system (see also my previous comment). Moreover, the authors use the DFT calculations of Murri et al. (2022) to support that the results of this study are applicable to quartz inclusions with trigonal symmetry (lines 130-131). However, the conclusions of Murri et al. (2022) say the opposite. They state that when the splitting between two A(LO-TO) modes in the stress-induced triclinic symmetry (originated from one E(TO-LO) mode in the parent trigonal symmetry) becomes detectable, the use of the inclusion is not recommended for elastic thermobarometry due to the symmetry breaking. Therefore Reynard and Zhong should correct the wrong identification of this behavior as a LO-TO splitting of the E mode throughout this manuscript, in table 1 and in the figures. They should also not use the results from first principle calculations to support that the effect of symmetry reduction in their experiments is small and that their results are directly applicable to trigonal crystals. Since it is possible that quartz inclusions in synthetic and natural samples have symmetry less than trigonal because of their stress state, the results of calibrations with symmetry breakings still provide useful information for the characterization of the stress states of inclusions, and in my opinion the discussion in the manuscript should head towards this direction.

• Lines 135-142. Since the authors compare their experimental results at hydrostatic conditions with the previous literature, they should also compare them with the hydrostatic results of Morana et al. (2020).

• Line 172. This sentence seems to say that DFT calculations cannot be used as a basis to calculate the LO-TO splitting. Actually DFT calculations can be used to calculate the LO and TO components and therefore their splitting (see for example Murri et al., 2019). However, as discussed in previous comments, the experiments under uniaxial stress in the a-b plane presented by Reynard and Zhong lead to a symmetry reduction to monoclinic (or triclinic) which is different to the DFT results reported in Murri et al. (2019) where no symmetry breaking occurred and the trigonal symmetry was preserved in all of the simulations. This might potentially contribute to part of the discrepancy between the results presented here and the Grueneisen tensor of Murri et al., (2019).

• Sections 6.1 and 6.2. I approached these sections as a possible user of these calibrations, and I am a bit confused by the trends shown in the reported results. In this manuscript two different calibrations (sigma128 and sigma 464) are proposed to estimate the same quantity, the value of differential stress in one inclusion. One should expect that these calibrations give the same (or similar) results when applied to the same inclusion. In other words, the stress determined in this way should fall on the 1:1 line in Fig. 5C and 6B. However, one can see that the stress of inclusions belonging to the same dataset always align along a line that forms a high angle to the 1:1 line. Therefore, often, the two calibrations give very different values of differential stress for one inclusion, which may have even opposite sign (see Fig. 5C and 6B). The fact that the inclusions in all samples show this anti-correlation between the values obtained from the sigma128 and sigma464 calibrations, points to the fact that this is a feature arising from the calibration and not from the specific features of a sample, because clearly inclusions cannot have simultaneously two different states of stress. The authors propose arbitrarily that inclusions are “valid” if the values of (sigma3-sigma1) from the two calibrations differ by less than 1 GPa (lines 222-223). The reason for choosing such a large threshold value is not discussed in the manuscript, but this choice means that the proposed methodology considers acceptable that one inclusion is simultaneously under a (sigma3-sigma1) = -0.49 GPa and (sigma3-sigma1) = +0.49 GPa. In this respect, the statement that the results of the two calibrations are self-consistent (lines 251-261) is very misleading (see also my specific comment below, with some statistics on the given results). Such results may be confusing for a user. Clearly an inclusion cannot be simultaneously under two different stress states, and therefore this method does not determine the differential stress of one inclusion (except in rare cases). In my opinion, the reason for the anti-correlation between the values obtained from the sigma128 and sigma464 calibrations should be explained, because it is not intuitive and it is not clear by which physical behavior it is originated. Moreover, when many inclusions in one sample are measured, the results of the sigma128 and sigma464 calibrations averaged on all the inclusions in the sample give somewhat similar results, but they often do not agree within mutual uncertainties (see the datasets of Cisneros et al., 2020 and Gonzalez et al., 2019 in the supplementary table of Reynard and Zhong). The authors therefore suggest that the averaged results of the two calibrations should be averaged again to give the final correct value. By reading the manuscript it is not clear to me the reason why several averaging steps of the results of two calibrations that appear anti-correlated should make this a robust method to estimate the value of differential stress.  I had the (maybe wrong) impression that the motivation is just the fact that the final averaged value is somewhat similar to the expectations of the elastic model for some of the analyzed samples. Therefore, if the authors have more physical insights that support the robustness of this procedure I suggest that they discuss them in order to avoid possible confusion for the reader.

• Lines 229-230. According to Bonazzi et al., (2019) they applied the Grueneisen tensor components of Murri et al. (2019) to calculate the strains from Raman shifts, and then they used the room-pressure elastic tensor of Wang et al. (2015) to calculate the stresses from strains, without further corrections. I am not sure why the authors say that the relationship between strain and stress is not provided in Bonazzi et al., (2019), and to which “correction” they refer. This sentence should be explained in more details or removed.

• Lines 235-236. Apparently the dataset Alm-1 (synthesis at 3GPa, 775°) of Bonazzi et al. (2019) is completely discarded, since it cannot be explained by the proposed calibrations. The authors state that those measurements were affected by “systematic uncertainties in the Raman peak positions”. However, Reynard and Zhong neglect the fact that Bonazzi et al. (2019) were able to successfully back-calculate the initial entrapment conditions of the synthesis by applying the Grueneisen tensor of Murri et al. (2019) together with the measured shifts of the 128cm^-1, 464cm^-1 and 206cm^-1 For this experiment, the method of Bonazzi et al. (2019) leads even to a higher precision on the estimate of the residual pressure, as can be observed comparing the scatters of the dataset synthetized at 3GPa, 775°C in Fig. 5a of Reynard and Zhong and Fig.4a of Bonazzi et al. (2019). This would rule out the presence of systematic uncertainties in the measurements performed by Bonazzi et al. (2018). Moreover, Bonazzi et al. (2019) report that the dataset Alm-2, which gives results more consistent with the calibration of Reynard and Zhong, was analyzed with the same procedure and instrument as Alm-1. Again, the impression is that the dataset Alm-1 is discarded because of the anticorrelation of the proposed sigma128 and sigma464 calibrations, which leads to incompatible values of differential stress obtained from the two calibrations. This could perhaps be caused by the complex stress states of those inclusions that cannot be modeled with the current calibration. However, I find misleading that the problem is reduced to   “systematic uncertainties in the Raman peak positions” of Bonazzi et al. (2018) simply because those inclusions cannot be explained with the current calibration.

• Line 251: I find not accurate the statement that the results of the two calibrations are self-consistent. Most of the inclusions in Fig. 5c and 6b fall along a line that forms a high angle to the 1:1 line. This implies that the two calibrations give different results for the same inclusion. By just considering the dataset from Syros, for 16 inclusions out of 21 the two calibrations predict a differential stress of opposite sign. In the samples from Papua Nuova Guinea, this happens for more than 40 inclusions out of 92. This rate is very high also for the inclusions in the synthetic datasets of Bonazzi et al. (2019). In my opinion the authors should have in mind the future users of such calibration for whom such discrepancies may be confusing, and explain the reason of the anticorrelation between the two calibrations which leads to this inconsistencies. 

• Lines 254-256. I suggest that this statement is explained in more detail. If they assume that the differential stress in natural inclusions is relaxed by inelastic processes, then they should expect to measure a differential stress in natural inclusions that is less than what expected from their purely elastic model. But the entire manuscript revolves around using the measured residual pressure and the residual differential stress to estimate the entrapment conditions with an elastic model, neglecting the inelastic relaxation. And at lines 262-264 they say that the measured differential stress agrees with the predictions of elastic models, which apparently rules out any inelastic relaxation.

• Lines 259-261. I believe that the statement that the high rejection rate of Gonzalez et al. (2019) is due to the discrepancies of the Grueneisen tensor is misleading. The rejection rate is determined by a different choice of criterion and threshold in the present work and in Gonzalez et al. (2019). Since the Gruneisen tensor does not have the problem of giving two different stress states for the same inclusion, the criterion in Gonzalez et al. (2019) was based on the absolute value of the differential strain of the inclusions. Gonzalez et al. (2019) applied a restrictive threshold of 1e-3 on differential strain to obtain a less dispersed distribution. However, even not applying any limiting threshold on the data of Gonzalez et al. (2019) the distributions of residual pressures of all 92 inclusions of Gonzalez et al. (2019) (see their supplementary materials) and of Reynard and Zhong (see their supplementary table, pressure obtained with the P206 calibration) are very similar, and in particular have the same standard error of 0.01 GPa. The only difference is a shift of the entire distribution of Gonzalez et al. (2019) to slightly higher pressures because of the use of different elastic properties for quartz. This shows that the high number of rejected inclusions in Gonzalez et al. (2019) is not due to problems with the Grueneisen tensor, but rather to the choice of a restrictive threshold to obtain higher accuracy on the average pressure.

• Table 1. As discussed above, the experiments under uniaxial stress in the x-y plane produce a symmetry breaking, and the two set of shift observed for the 128 cm-1 peak must not be labeled as TO-LO (Shapiro & Axe, 1972). Moreover, the note that “the TO-LO splitting was not modeled” in the calculations of Murri et al. (2019) is not correct as explained in previous comments. The LO-TO components for the 128 cm-1 peak were determined by Murri et al. (2019), but since their splitting is negligible, the Grueneisen tensor was calculated only for the TO component. Therefore, the discrepancy between the and  for the Raman modes determined in this work and those of Murri et al. (2019) may be partly due to the symmetry breaking induced during the experiments presented here. 

• Fig. 5, lines 423-424. The statement concerning the anti-correlated uncertainties is not clear. I suggest that the reason for this anticorrelation is explained in more details here or in the text (see also above comments).

• Fig 1: in order to represent without ambiguity the orientation adopted in the measurements, I recommend adding the corresponding Porto's notation (Gregora, 2013; Scott & Porto, 1967) defined as following:

A(BC)D

With:

A = direction of the incident radiation (wave-vector)

B = polarization of incident radiation

C = polarization of scattered radiation

D = direction of the scattered radiation (i.e. wave-vector)

where the direction and polarization of the incident and scattered radiation are defined with respect to the crystallographic axes of quartz.

Technical corrections

• Equation (12) at line 196. I suspect that the last sigma in the right side of the equation is a left over and should be removed.
• Fig 3c: the label of the y axis is missing
• 6a. I suggest to add a legend to identify the large and small symbols

Literature cited

Anastassakis, E. M. (1980). CHAPTER 3—Morphic Effects in Lattice Dynamics. In G. K. Horton & A. A. Maradudin (Eds.), Dynamical Properties of Solids (Vol. 4, pp. 157–375). North-Holland. https://doi.org/10.1016/B978-0-444-85315-8.50007-4

Angel, R. J., Murri, M., Mihailova, B., & Alvaro, M. (2019). Stress , strain and Raman shifts. Zeitschrift Für Kristallographie-Crystalline Materials., 234(2), 129–140. https://doi.org/10.1515/zkri-2018-2112

Angel, R., Mazzucchelli, M., Gonzalez-Platas, J., & Alvaro, M. (2021). A self-consistent approach to describe unit-cell-parameter and volume variations with pressure and temperature. Journal of Applied Crystallography, 54(6), 1621–1630. https://doi.org/10.1107/S1600576721009092

Briggs, R. J., & Ramdas, A. K. (1977). Piezospectroscopy of the Raman spectrum of α-quartz. Physical Review B, 16(8), 3815.

Gonzalez, J. P., Thomas, J. B., Baldwin, S. L., & Alvaro, M. (2019). Quartz-in-garnet and Ti-in-quartz thermobarometry: Methodology and first application to a quartzofeldspathic gneiss from eastern Papua New Guinea. Journal of Metamorphic Geology, 37(9), 1193–1208. https://doi.org/10.1111/jmg.12508

Gregora, I. (2013). Raman scattering. In International Tables for Crystallography (pp. 334–348). John Wiley & Sons, Ltd. https://doi.org/10.1107/97809553602060000913

Murri, M., Alvaro, M., Angel, R. J., Prencipe, M., & Mihailova, B. D. (2019). The effects of non-hydrostatic stress on the structure and properties of alpha-quartz. Physics and Chemistry of Minerals, 46(5), 487–499. https://doi.org/10.1007/s00269-018-01018-6

Murri, M., Gonzalez, J. P., Mazzucchelli, M. L., Prencipe, M., Mihailova, B. D., Angel, R. J., & Alvaro, M. (2022). The role of symmetry-breaking strains on quartz inclusions in anisotropic hosts: Implications for Raman elastic geobarometry. Lithos. https://doi.org/in press

Nye, J. F. (1985). Physical properties of crystals: Their representation by tensors and matrices. Oxford University Press.

Scott, J. F., & Porto, S. P. S. (1967). Longitudinal and Transverse Optical Lattice Vibrations in Quartz. Physical Review, 161(3), 903–910. https://doi.org/10.1103/PhysRev.161.903

Shapiro, S. M., & Axe, J. D. (1972). Raman Scattering from Polar Phonons. Physical Review B, 6(6), 2420–2427. https://doi.org/10.1103/PhysRevB.6.2420

Tekippe, V. J., Ramdas, A. K., & Rodriguez, S. (1973). Piezospectroscopic Study of the Raman Spectrum of $\ensuremath{\alpha}$-Quartz. Physical Review B, 8(2), 706–717. https://doi.org/10.1103/PhysRevB.8.706

Wang, J., Mao, Z., Jiang, F., & Duffy, T. S. (2015). Elasticity of single-crystal quartz to 10 GPa. Physics and Chemistry of Minerals, 42(3), 203–212. https://doi.org/10.1007/s00269-014-0711-z