## Abstract

Polarized Raman spectroscopy was applied to garnet hosts which exhibit anomalous birefringence around inclusions of zircon and quartz to elucidate the spatial distribution of the anisotropic strain fields in the vicinity of the host-inclusion boundary. We show that there is a direct relationship between the stress-induced birefringence and the Raman scattering generated by the fully symmetric phonon modes (the *A*_{1g} modes in cubic crystals). Our experimental results coupled with selected finite element models show that the ratio between the measured Raman peak intensity collected in cross and parallel polarized scattering geometries of totally symmetric modes represents a useful tool to constrain the radial stress profile in the host around the inclusions. Further, we demonstrate how group-theoretical considerations and tensor analysis of the morphic effect (external-field-induced change of the symmetry) on the phonons and the optical properties of the host can help to derive useful information on the symmetry of the stress field. Finally, we show experimentally that, under the same amount of applied stress, this approach is more sensitive than the commonly used approach of measuring differences in phonon frequencies and provides better opportunities to map the spatial variations of strain. This approach is an alternative technique to study structural phenomena associated with anomalous birefringence in host crystals surrounding stressed inclusions and could be applied to other systems in which similar optical effects are observed.

This is a preview of subscription content, log in to check access.

## References

Alvaro M, Mazzucchelli ML, Angel RJ, Murri M, Campomenosi N, Scambelluri M, Nestola F, Korsakov A, Tomilenko AA, Marone F, Morana M (2019) Fossil subduction recorded by quartz from the coesite stability field. Geology 48(1):24–28

Anastassakis EM (1980) Morphic effects in lattice dynamics. In: Horton GK, Maradudin AA (eds) Dynamical properties of solids, vol 4. Anastassakis, North-Holland Publishing Company, Amsterdam, pp 159–375

Angel RJ, Mazzucchelli ML, Alvaro M, Nimis P, Nestola F (2014) Geobarometry from host-inclusion systems: the role of elastic relaxation. Am Mineral 99:2146–2149

Angel RJ, Nimis P, Mazzucchelli ML, Alvaro M, Nestola F (2015) How large are departures from lithostatic pressure? Constraints from host-inclusion elasticity. J Metamorph Geol 33:801–813

Angel RJ, Murri M, Mihailova BD, Alvaro M (2018) Stress, strain and Raman shifts. Z Kristallogr. https://doi.org/10.1515/zkri-2018-2112

Anzolini C, Prencipe M, Alvaro M, Romano C, Vona A, Lorenzon S, Smith EM, Brenker FE, Nestola F (2018) Depth of formation of super-deep diamonds: Raman barometry of CaSiO

_{3}-walstromite inclusions. Am Mineral 103:69–74Binvignat FAP, Malcherek T, Angel RJ, Paulmann C, Schlüter J, Mihailova B (2018) Radiation-damaged zircon under high pressures. Phys Chem Miner 45(10):981–993

Campomenosi N, Mazzucchelli ML, Mihailova BD, Scambelluri M, Angel RJ, Nestola F, Reali A, Alvaro M (2018) How geometry and anisotropy affect residual strain in host-inclusion system: coupling experimental and numerical approaches. Am Mineral 103:2032–2035

Cesare B, Nestola F, Johnson T, Mugnaioli E, Della Ventura G, Peruzzo L, Bartoli O, Viti C, Erickson T (2019) Garnet, the archetypal cubic mineral, grows tetragonal. Sci Rep 9:14672

Chopin C (1984) Coesite and pure pyrope in high-grade blueschists of the Western Alps: a first record and some consequences. Contrib Miner Petrol 86(2):107–118

Enami M, Nishiyama T, Mouri T (2007) Laser Raman microspectrometry of metamorphic quartz: a simple method for comparison of metamorphic pressures. Am Mineral 92:1303–1315

Eshelby J (1957) The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc R Soc Lond A Math Phys Eng Sci R Soc 241:376–396

Everall NJ (2016) Confocal Raman microscopy: why the depth resolution and spatial accuracy can be much worse than you think. Appl Spectrosc 54(10):1515–1520

Geisler T, Pidgeon RT, van Bronswijk W, Pleysier R (2001) Kinetics of thermal recovery and recrystallization of partially metamict zircon: a Raman spectroscopic study. Eur J Miner 13(6):1163–1176

Gregora I (2006) Raman scattering. In: Authier A (ed) International tables for crystallography, vol D-2.3. Wiley Publishers, England, pp 314–328. https://doi.org/10.1107/97809553602060000640

Hermann J (2003) Experimental evidence of diamond facies metamorphism in Dora Maira Massif. Lithos 70:163–182

Howell D (2012) Strain-induced birefringence in natural diamonds. Eur J Mineral 24:575–585

Howell D, Wood IG, Dobson DP, Jones AP, Nasdala L, Harris JW (2010) Quantifying strain birefringence halos around inclusions in diamond. Contrib Mineral Petrol 160:705–717

Izraeli E, Harris J, Navon O (1999) Raman barometry of diamond formation. Earth Planet Sci Lett 173:351–360

Kohn MJ (2014) “Thermoba-Raman-try”: calibration of spectroscopic barometers and thermometers for mineral inclusions. Earth Planet Sci Lett 388:187–196

Korsakov AV, Perraki M, Zhukov VP, De Gussem K, Vandenabeele P, Tomilenko AA (2009) Is quartz a potential indicator of ultra high pressure metamorphism? Laser Raman spectroscopy of quartz inclusions in ultrahigh-pressure garnets. Eur J Mineral 21:1313–1323

Kroumova E, Aroyo MI, Perez-Mato JM, Kirov A, Capillas C, Ivantchev S, Wondratschek H (2010) Bilbao crystallographic server: useful databases and tools for phase-transition studies. Phase Transit 76(1–2):155–170

Kuzmany H (2009) Solid-state spectroscopy. An introduction. Springer, Berlin

Mazzucchelli ML, Burnley P, Angel RJ, Domeneghetti MC, Nestola F, Alvaro M (2016) Elastic geobarometry: uncertainties arising from the shape of the inclusion. In: 12nd European mineralogical conference, Rimini, Italy, September, 2016. Book of abstracts, p 232

Mazzucchelli ML, Burnley P, Angel RJ, Morganti S, Domeneghetti MC, Nestola F, Alvaro M (2018) Elastic geothermobarometry: corrections for the geometry of the host-inclusion system. Geology 46(3):231–234

Mazzucchelli ML, Reali A, Morganti S, Angel RJ, Alvaro M (2019) Elastic geobarometry for anisotropic inclusions in cubic hosts. Lithos 350:105218

Murri M, Mazzucchelli ML, Campomenosi N, Korsakov AV, Prencipe M, Mihailova B, Scambelluri M, Angel RJ, Alvaro M (2018) Raman elastic geobarometry for anisotropic mineral inclusions. Am Mineral 103:1869–1872

Nakamoto K (2009) Infrared and Raman spectra of inorganic and coordination compounds part A: theory and applications in inorganic chemistry. Wiley, New York

Nasdala L, Wenzel M, Vavra G, Irmer G, Wenzel T, Kober B (2001) Metamictisation of natural zircon: accumulation versus thermal annealing of radioactivity-induced damage. Contrib Miner Petrol 141(2):125–144

Nasdala L, Brenker FE, Glinnemann J, Hofmeister W, Gasparik T, Harris JW, Stachel T, Reese I (2003) Spectroscopic 2D tomography: residual pressure and strain around mineral inclusions in diamonds. Eur J Mineral 15:931–935

Nasdala L, Hofmeister W, Harris JW, Glinnemann J (2005) Growth zoning and strain patterns inside diamond crystals as revealed by Raman maps. Am Mineral 90:745–748

Nye JF (1985) Physical properties of crystals. Oxford Science Publications, Oxford

Özkan H, Cartz L, Jamieson JC (1974) Elastic constants of nonmetamict zirconium silicate. J Appl Phys 45:556–562

Putnis A (1992) Introduction to mineral science. Cambridge University Press, New York, p 457

Rosenfeld JL, Chase AB (1961) Pressure and temperature of crystallization from elastic effects around solid inclusion minerals? Am J Sci 259:519–541

Shtukenberg A, Punin Y (2007) Optically anomalous crystals. Springer, Amsterdam

Sinogeikin SV, Bass JD (2002) Elasticity of pyrope and majorite-pyrope solid solutions to high temperatures. Earth Planet Sci Lett 203:549–555

Tajmanova L, Vrijmoed J, Moulas E (2014) Grain-scale pressure variations in metamorphic rocks: implications for the interpretation of petrographic observations. Lithos 216:338–351

van der Molen I, van Roermund HLM (1986) The pressure path of solid inclusions in minerals: the retention of coesite inclusions during uplift. Lithos 19:317–324

Zhang Y (1998) Mechanical and phase equilibria in inclusion–host systems. Earth Planet Sci Lett 157:209–222

Zhukov VP, Korsakov AV (2015) Evolution of host-inclusion systems: a visco-elastic model. J Metamorph Geol 33(8):815–828

Ziman JM (1960) Electrons and phonons: the theory of transport phenomena in solids. Oxford University Press, Oxford, p 469

## Acknowledgements

This work was financially supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program GRANT agreements 714936 to M. Alvaro and by the Italian Ministry of Education, University and Research (MIUR) (PRIN-2017ZE49E7). A special thanks to A. Korsakov (University of Novosibirsk) for providing us the garnet sample with quartz inclusions. The authors thank M. Prencipe (University of Torino) and M. Scambelluri (University of Genova) for helpful discussions. Campomenosi acknowledges the University of Genova for funding.

## Author information

## Additional information

### Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Communicated by Steven Reddy.

## Appendix

### Appendix

As discussed in the main text, each Raman-active phonon mode *m* in a crystal will have its own Raman polarizability tensor \(\alpha^{m}\) and the intensity of the Raman scattering peak from the mode depends on Eq. (2) which is repeated here:

Thus the intensity of the Raman scattering peak from the mode depends on the orientation of the electric-field unit vectors \(e^{i}\) and \(e^{s}\) of both the incident and scattered light. Experimentally, the directions of the electric-field vectors of the incident and scattered light are defined by the polarisers placed in the incident and scattered beam paths, so \(e^{i}\) and \(e^{s}\) (in the crystal) depend on the orientation of the crystal with respect to the polarisers in the spectrometer system. Written out in the terms of the individual components of the tensors, Eq. (13) becomes:

With \(\alpha^{m}_{kl} = \alpha^{m}_{lk}\) for first-order Raman scattering.

### Symmetry constraints on the Raman polarizability tensor for *A*
_{1g} modes

Which components of the Raman polarizability tensor are zero, and the constraints on the values of the non-zero components, are defined by the symmetry of the mode. As shown in Table 2, for the *A*_{1g} modes in cubic crystals cubic crystals with point symmetry \(m\bar{3}m\), \(\alpha^{{A_{1g} }}_{11} = \alpha^{{A_{1g} }}_{22} = \alpha^{{A_{1g} }}_{33}\), and \(\alpha^{{A_{1g} }}_{12} = \alpha^{{A_{1g} }}_{13} = \alpha^{{A_{1g} }}_{23} = 0\), the same as the constraints on the \(\varvec{B}\) tensor for optical birefringence. This is the reason why the behaviour of the intensities of *A*_{1g} modes in cubic crystals under stress follows that of the optical birefringence. And the expression for the intensity for *A*_{1g} mode in cubic crystals becomes:

This equation shows that the symmetry of the Raman polarizability tensor of the *A*_{1g} modes in cubic crystals means that the intensity is independent of the direction of propagation of light through the crystal, and depends only on the relative orientation of the two polarisers to one another. We can now choose any convenient coordinate system for these polarisers and the experiment. For this example, we choose the incident beam to be along the *z*-axis, and the polarisation direction to be along the *x*-axis. Thus \(e^{i}\) = [1 0 0]. If one makes measurements in HH polarisation, the polarisation of the scattered beam is parallel to the incident beam, so \(e^{i}\) = \(e^{s}\), and Eq. (14) for the intensity becomes:

By contrast, when the polarisations of the incident and scattered radiation are ‘crossed’, (i.e. mutually perpendicular and denoted VH), then \(e^{s}\) = [0 1 0] and the intensity given by 14 is zero. Thus, in cubic crystals, *A*_{1g} modes can be observed by polarised Raman spectroscopy with HH polarisation, but are not observed with VH polarisation.

## Rights and permissions

## About this article

### Cite this article

Campomenosi, N., Mazzucchelli, M.L., Mihailova, B.D. *et al.* Using polarized Raman spectroscopy to study the stress gradient in mineral systems with anomalous birefringence.
*Contrib Mineral Petrol* **175, **16 (2020). https://doi.org/10.1007/s00410-019-1651-x

Received:

Accepted:

Published:

### Keywords

- Polarized Raman spectroscopy
- Anomalous birefringence
- Stress
- Morphic effect
- Depolarization ratio