Publications

@article{gilio_pressure-induced_2025,

title = {The pressure-induced stiffening of quartz and its effect on the strain-stress relationship. Implications for elastic geobarometry},

author = {Mattia Gilio and Ross J. Angel and Mattia L. Mazzucchelli and Matteo Alvaro},

url = {https://www.sciencedirect.com/science/article/pii/S0024493725002695},

doi = {10.1016/j.lithos.2025.108210},

issn = {0024-4937},

year  = {2025},

date = {2025-11-01},

urldate = {2025-11-01},

journal = {Lithos},

volume = {514-515},

pages = {108210},

abstract = {Elastic geobarometry allows us to estimate the pressure and temperature conditions of the entrapment of a mineral within a host from the residual pressure of the inclusion. The residual pressure is often calculated as the mean normal stress by applying the elastic tensor (Cij) measured at ambient pressure (1 bar) to the measured inclusion strains. While neglecting the pressure dependence of the Cij is a reasonable assumption for stiffer minerals such as olivine and zircon, this method may induce significant errors in the calculation of inclusion pressures and hence entrapment conditions of softer minerals like quartz trapped in stiff hosts such as garnets. Here we describe a method to calculate stress from the measured strains of quartz inclusions by considering the progressive stiffening of the elastic tensor of quartz with pressure, and discuss its implications for elastic geobarometry. Additionally, we extend this method to the stiffer olivine and zircon to emphasise its broader utility to ultra-high-pressure and temperature rocks and inclusions in diamonds. The changes in inclusion pressures for these latter two minerals are, however, not as significant as those in quartz, and it can be assumed that the elastic tensor remains invariant with pressure for most geological cases. A MATLAB code is provided with a comprehensive guide to calculate the inclusion pressures accounting for the change in the elastic tensor with pressure for quartz, olivine, and zircon. This code will be implemented within future updates of the online platform for elastic geothermobarometry EntraPT (https://www.mineralogylab.com/software/entrapt).},

keywords = {Elastic thermobarometry, Elasticity, QuiG, Raman thermobarometry},

pubstate = {published},

tppubtype = {article}

}

@article{gonzalez_elastic_2025,

title = {Elastic thermobarometry of natural and experimental quartz inclusions in garnet (QuiG) under tension},

author = {Joseph P. Gonzalez and Mattia L. Mazzucchelli and Jay B. Thomas and Ross J. Angel and Robert S. Darling and Khi X. Atchinson and Mattia Gilio and Matteo Alvaro},

url = {https://doi.org/10.1007/s00410-025-02252-2},

doi = {10.1007/s00410-025-02252-2},

issn = {1432-0967},

year  = {2025},

date = {2025-09-01},

urldate = {2025-09-01},

journal = {Contributions to Mineralogy and Petrology},

volume = {180},

number = {10},

pages = {70},

abstract = {Elastic thermobarometry has been rarely applied to quartz inclusions entrapped in garnet (QuiG) in granulite and igneous terranes, in part, because there is uncertainty about the reliability of the thermobarometric results arising from the quartz inclusions being subject to tensile strain and stress when examined at room conditions. Here, we present QuiG results from high-temperature metapelites from the Adirondacks, NY, USA and piston-cylinder experiments that give insight into the deformation behavior of quartz inclusions under tension. Measured remnant pressures (Pinc) of experimental and natural samples calculated using the quartz phonon mode Grüneisen tensor are too tensile with respect to the expected Pinc values based on experimental and petrologic constraints. We show that these discrepancies are not related to non-elastic deformation nor inaccuracies in the quartz equation of state. Evaluation of previous density functional theory (DFT) results shows that the structural response of quartz is non-linear with increasing tensile strain. Therefore, because the available quartz phonon mode Grüneisen tensor was determined with a linear fit optimized for compressive strains, obtained tensile strains using this tensor are too large in magnitude. Pinc values obtained using the hydrostatic calibrations of the 128 and 464 cm−1 peaks have better agreement with the expected values and return entrapment conditions that are consistent with petrologically constrained or known experimental pressures. Pinc values obtained through hydrostatic calibrations must nonetheless be treated with caution because the behavior of Raman phonon modes under tension has not been calibrated experimentally.},

keywords = {Elastic thermobarometry, Elasticity, Garnet, Quartz, QuiG, Raman thermobarometry},

pubstate = {published},

tppubtype = {article}

}

@article{eberhard_coupling_2025,

title = {Coupling antigorite deformation and dehydration in high-pressure experiments},

author = {Lisa Eberhard and Mattia Luca Mazzucchelli and Stefan Markus Schmalholz and Holger Stünitz and Ahmed Addad and Patrick Cordier and Oliver Plümper},

url = {https://doi.org/10.1007/s00410-025-02255-z},

doi = {10.1007/s00410-025-02255-z},

issn = {1432-0967},

year  = {2025},

date = {2025-08-01},

urldate = {2025-08-01},

journal = {Contributions to Mineralogy and Petrology},

volume = {180},

number = {9},

pages = {64},

abstract = {The dehydration of antigorite is an important reaction in subduction zones with implications on both geochemical and geophysical processes. In this experimental study we focus on the onset of antigorite dehydration and investigate various chemical and physical parameters as possible drivers for the fluid release. We performed hydrostatic and co-axial Griggs experiments on antigorite serpentinites with variable chemical composition and microstructures at high-pressure and high-temperature conditions across the antigorite dehydration (1.5 GPa, 620–670 °C). For these conditions, our thermodynamic models predict the formation of olivine from magnetite decomposition and partial dehydration of antigorite. Detailed analyses of the run products reveal limited magnetite decomposition. Antigorite dehydration is restricted to samples that have been deformed. Nano-sized olivine and orthopyroxene formed locally in oblique dehydration bands and exhibit neither a clear crystallographic preferred orientation nor a topotactic relation with precursor antigorite. We argue that limited local dehydration in our experiments is related to strain and variations in reaction kinetics. Systematic investigation excludes mineralogical and chemical heterogeneities, and temperature gradients as reaction driving potentials. The structural relation of the dehydration bands suggests deformation-related dehydration, which is supported by numerical simulations that couple reaction kinetics with mechanical work rate and self-consistently predict dehydration bands. In this scenario, strain concentration due to applied axial stress locally increases the internal energy of antigorite to reach the activation energy of the dehydration reaction, enabling dehydration. This study highlights the importance of coupled mechanical and chemical processes and provides a mechanistic framework for deformation-induced dehydration of antigorite.},

keywords = {Continuum modeling, mineral-fluid interaction, THMC},

pubstate = {published},

tppubtype = {article}

}

@article{angel_uncertainties_2025,

title = {Uncertainties of recalculated bond lengths, angles and polyhedral volumes as implemented in the textitCrystal Palace program for parametric crystal structure analysis},

author = {Ross J. Angel and Mattia L. Mazzucchelli and Lisa Baratelli and Catherine F. Schweinle and Tonci Balić-Žunić and Javier Gonzalez-Platas and Matteo Alvaro},

url = {https://journals.iucr.org/paper?S2053273325002682},

doi = {10.1107/S2053273325002682},

issn = {2053-2733},

year  = {2025},

date = {2025-05-01},

urldate = {2025-05-01},

journal = {Acta Crystallographica Section A Foundations and Advances},

volume = {81},

number = {3},

pages = {202–210},

abstract = {Crystal Palace 

 is a new Windows program for Parametric Analysis of Least-squares and Atomic Coordination with Estimated standard uncertainties (e.s.u.'s). The primary purpose of the program is to organize the refined structures from parametric structural studies (as a function of pressure or temperature or a series of compositions) for analysis of the structural trends, and the production of tables for publication without the risks associated with manual editing. The program reads structural information from one or more crystallographic information format (cif) files. It organizes the data by finding the structurally equivalent atoms in each structure and therefore can correctly organize structural information even if atom names or site occupancies are different, or the atom lists in the cif files are ordered differently. A major shortcoming of cif files as currently used is that they do not contain the full variance–covariance matrix from the structure refinement, but only the uncertainties of the individual positional parameters. Without the covariance of positional parameters, the e.s.u.'s of bond lengths and angles cannot be determined. 

 Crystal Palace 

 uses symmetry to estimate the major contributions to the covariance of atomic coordinates and thus realistic uncertainties of bond lengths, angles and polyhedral volumes. 

 Crystal Palace 

 also calculates various polyhedral distortion parameters and rigid-body corrections to bond lengths.},

keywords = {Crystallography, Single-crystal X-ray diffraction, software development},

pubstate = {published},

tppubtype = {article}

}

@article{gonzalez_first_2024,

title = {First evaluation of stiff-in-soft host–inclusion systems: experimental synthesis of zircon inclusions in quartz crystals},

author = {Joseph P. Gonzalez and Jay B. Thomas and Mattia L. Mazzucchelli and Ross J. Angel and Matteo Alvaro},

url = {https://link.springer.com/10.1007/s00410-023-02081-1},

doi = {10.1007/s00410-023-02081-1},

issn = {0010-7999, 1432-0967},

year  = {2024},

date = {2024-02-01},

urldate = {2024-02-01},

journal = {Contributions to Mineralogy and Petrology},

volume = {179},

number = {2},

pages = {13},

abstract = {Quartz crystals with zircon inclusions were synthesized using a piston-cylinder apparatus to experimentally evaluate the use of inclusions in “soft” host minerals for elastic thermobarometry. Synthesized zircon inclusion strains and, therefore, pressures (Pinc) were measured using Raman spectroscopy and then compared with the expected inclusion strains and pressures calculated from elastic models. Measured inclusion strains and inclusion pressures are systematically more tensile than the expected values and, thus, re-calculated entrapment pressures are overestimated. These discrepancies are not caused by analytical biases or assumptions in the elastic models and strain calculations. Analysis shows that inclusion strain discrepancies progressively decrease with decreasing experimental temperature in the α-quartz field. This behavior is consistent with inelastic deformation of the host–inclusion pairs induced by the development of large differential stresses during experimental cooling. Therefore, inclusion strains are more reliable for inclusions trapped at lower temperature conditions in the α-quartz field where there is less inelastic deformation of the host–inclusion systems. On the other hand, entrapment isomekes of zircon inclusions entrapped in the β-quartz stability field plot along the α–β quartz phase boundary, suggesting that the inclusion strains were mechanically reset at the phase boundary during experimental cooling and decompression. Therefore, inclusions contained in soft host minerals can be used for elastic thermobarometry and inclusions contained in β-quartz may provide constraints on the P–T at which the host–inclusion system crossed the phase boundary during exhumation.},

keywords = {Elastic thermobarometry, Elasticity, Experiments, high-pressure, high-temperature, Quartz, Raman thermobarometry, Zircon},

pubstate = {published},

tppubtype = {article}

}

@article{mazzucchelli_fluid-mineral_2024,

title = {Fluid-mineral Equilibrium Under Nonhydrostatic Stress: Insight From Molecular Dynamics},

author = {Mattia L. Mazzucchelli and Evangelos Moulas and Boris J. P. Kaus and Thomas Speck},

url = {https://ajsonline.org/article/92881-fluid-mineral-equilibrium-under-nonhydrostatic-stress-insight-from-molecular-dynamics},

doi = {10.2475/001c.92881},

issn = {1945-452X, 0002-9599},

year  = {2024},

date = {2024-02-01},

urldate = {2024-02-01},

journal = {American Journal of Science},

volume = {324},

abstract = {The interpretation of phase equilibria and reactions in geological materials is based on standard thermodynamics that assumes hydrostatic and homogeneous stress conditions. However, rocks and minerals in the lithosphere can support stress gradients and nonhydrostatic stresses. Currently, there is still not an accepted macroscopic thermodynamic theory to include the effect of nonhydrostatic stress on mineral reactions, and the use of several thermodynamic potentials in stressed geological system remains under debate. In experiments under nonhydrostatic stress, it is often difficult to resolve the direct effect of differential stress on phase equilibria because pressure gradients may be developed. Such gradients can affect the metamorphic equilibria at the local scale. Here, we investigate the direct effect of a homogeneous, nonhydrostatic stress field on the solid-fluid equilibrium using molecular dynamics simulations at non-zero pressure and elevated temperature conditions. Our results show that, for simple single-component systems at constant temperature, the equilibrium fluid pressure of a stressed system is always larger than the value of fluid pressure at hydrostatic stress conditions. The displacement of the equilibrium value of the fluid pressure is about an order of magnitude smaller compared to the level of differential stress in the solid crystal. Thus, phase equilibria can be accurately predicted by taking the fluid pressure as a proxy of the equilibration pressure. On the contrary, the mean stress of the solid can deviate substantially from the pressure of the fluid in stressed systems at thermodynamic equilibrium. This has implications on the use of thermodynamic pressure in geodynamic models since the fluid pressure is a more accurate proxy for predicting the location of metamorphic reactions, while the equilibrium density of the solid has to be determined from its mean stress.},

keywords = {mineral-fluid interaction, molecular dynamics, thermodynamics},

pubstate = {published},

tppubtype = {article}

}

@article{angel_elasticity_2023,

title = {Elasticity of mixtures and implications for piezobarometry of mixed-phase inclusions},

author = {Ross J. Angel and Mattia L. Mazzucchelli and Kira A. Musiyachenko and Fabrizio Nestola and Matteo Alvaro},

url = {https://ejm.copernicus.org/articles/35/461/2023/},

doi = {10.5194/ejm-35-461-2023},

issn = {0935-1221},

year  = {2023},

date = {2023-07-01},

urldate = {2023-07-01},

journal = {European Journal of Mineralogy},

volume = {35},

number = {4},

pages = {461–478},

abstract = {Elastic thermobarometry (or piezobarometry) is the process of determining the P (pressure) and T (temperature) of entrapment of inclusions from their pressure, stress or strain measured when their host mineral is at room conditions. The methods and software used for piezobarometry are currently restricted to inclusions consisting of single phases. In this contribution we describe the theory of the elasticity of mixtures of different phases and combine it with the existing isotropic analysis of the elastic interactions between single-phase inclusions and their hosts to calculate the inclusion pressures of mixed-phase inclusions. The analysis shows that the reliability of calculated entrapment conditions for mixed-phase inclusions, including those containing fluid plus minerals, depends in a complex way upon the contrasts between the elastic properties of the host and the phases in the inclusion. The methods to calculate the entrapment conditions of mixed-phase inclusions have been incorporated into the EosFit7c program (version 7.6) that is available as freeware from http://www.rossangel.net.},

note = {Publisher: Copernicus GmbH},

keywords = {Elastic thermobarometry, Elasticity},

pubstate = {published},

tppubtype = {article}

}

@article{kohn_elastic_2023,

title = {Elastic Thermobarometry},

author = {Matthew J. Kohn and Mattia L. Mazzucchelli and Matteo Alvaro},

url = {https://doi.org/10.1146/annurev-earth-031621-112720},

doi = {10.1146/annurev-earth-031621-112720},

year  = {2023},

date = {2023-01-01},

urldate = {2023-01-01},

journal = {Annual Review of Earth and Planetary Sciences},

volume = {51},

number = {1},

abstract = {Upon exhumation and cooling, contrasting compressibilities and thermal expansivities induce differential strains (volume mismatches) between a host crystal and its inclusions. These strains can be quantified in situ using Raman spectroscopy or X-ray diffraction. Knowing equations of state and elastic properties of minerals, elastic thermobarometry inverts measured strains to calculate the pressure-temperature conditions under which the stress state was uniform in the host and inclusion. These are commonly interpreted to represent the conditions of inclusion entrapment. Modeling and experiments quantify corrections for inclusion shape, proximity to surfaces, and (most importantly) crystal-axis anisotropy, and they permit accurate application of the more common elastic thermobarometers. New research is exploring the conditions of crystal growth, reaction overstepping, and the magnitudes of differential stresses, as well as inelastic resetting of inclusion and host strain, and potential new thermobarometers for lower-symmetry minerals. ▪A physics-based method is revolutionizing calculations of metamorphic pressures and temperatures. ▪Inclusion shape, crystal anisotropy, and proximity to boundaries affect calculations but can be corrected for. ▪New results are leading petrologists to reconsider pressure-temperature conditions, differential stresses, and thermodynamic equilibrium. Expected final online publication date for the Annual Review of Earth and Planetary Sciences, Volume 51 is May 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.},

note = {_eprint: https://doi.org/10.1146/annurev-earth-031621-112720},

keywords = {Elastic thermobarometry, Elasticity, Raman thermobarometry},

pubstate = {published},

tppubtype = {article}

}

@article{murri_role_2022,

title = {The role of symmetry-breaking strains on quartz inclusions in anisotropic hosts: Implications for Raman elastic geobarometry},

author = {M. Murri and J. P. Gonzalez and M. L. Mazzucchelli and M. Prencipe and B. Mihailova and R. J. Angel and M. Alvaro},

url = {https://www.sciencedirect.com/science/article/pii/S0024493722001256},

doi = {10.1016/j.lithos.2022.106716},

issn = {0024-4937},

year  = {2022},

date = {2022-08-01},

urldate = {2022-08-01},

journal = {Lithos},

volume = {422-423},

pages = {106716},

abstract = {Raman elastic geobarometry for mineral host-inclusion systems is used to determine the strains acting on an inclusion still entrapped in its host by measuring its Raman wavenumber shifts which are interpreted through the phonon-mode Grüneisen tensors of the inclusion phase. The calculated inclusion strains can then be used in an elastic model to calculate the pressure and temperature conditions of entrapment. This method is applied frequently to host inclusion systems where the host is almost elastically isotropic (e.g. garnet) and the inclusion is elastically anisotropic (e.g. quartz and zircon). In this case, when the entrapment occurs under hydrostatic conditions the host will impose isotropic strains on the inclusion which in turn will develop non-hydrostatic stress. In this scenario the symmetry of the inclusion mineral is preserved and the strains in the inclusion can be measured via Raman spectroscopy using the phonon-mode Grüneisen tensor approach. However, a more complex situation arises when the host-inclusion system is fully anisotropic, such as when a quartz inclusion is entrapped within a zircon host, because the symmetry of the inclusion can be broken due to the external anisotropic strain field imposed on the inclusion by the host, which in turn will modify the phonon modes. We therefore calculated the strain states of quartz inclusions entrapped in zircon hosts in multiple orientations and at various geologically relevant pressure and temperature conditions. We then performed ab initio Hartree-Fock/Density Functional Theory (HF/DFT) simulations on α-quartz in these strain states. These HF/DFT simulations show that the changes in the positions of the Raman modes produced by strains that are expected for symmetry broken quartz inclusions in zircon are generally similar to those that would be seen if the quartz inclusions remained truly trigonal in symmetry. Therefore, the use of the trigonal phonon-mode Grüneisen tensor to determine the inclusion strains does not lead to geologically significant errors in calculated quartz inclusion entrapment pressures in zircon.},

keywords = {ab-initio, Crystallography, Density Functional Theory, DFT, Elastic anisotropy, Elastic thermobarometry, Raman spectroscopy, Raman thermobarometry},

pubstate = {published},

tppubtype = {article}

}

@article{angel_garnet_2022,

title = {Garnet EoS: a critical review and synthesis},

author = {Ross J. Angel and Mattia Gilio and Mattia Mazzucchelli and Matteo Alvaro},

url = {https://doi.org/10.1007/s00410-022-01918-5},

doi = {10.1007/s00410-022-01918-5},

issn = {1432-0967},

year  = {2022},

date = {2022-05-01},

urldate = {2022-05-01},

journal = {Contributions to Mineralogy and Petrology},

volume = {177},

number = {5},

pages = {54},

abstract = {All available volume and elasticity data for the garnet end-members grossular, pyrope, almandine and spessartine have been re-evaluated for both internal consistency and for consistency with experimentally measured heat capacities. The consistent data were then used to determine the parameters of third-order Birch–Murnaghan EoS to describe the isothermal compression at 298 K and a Mie–Grüneisen–Debye thermal-pressure EoS to describe the PVT behaviour. In a full Mie–Grüneisen–Debye EoS, the variation of the thermal Grüneisen parameter with volume is defined as $$textbackslashgamma = textbackslashgamma _0textbackslashleft(textbackslashfracVV_0textbackslashright)textasciicircumq$$. For grossular and pyrope garnets, there is sufficient data to refine q which has a value of q = 0.8(2) for both garnets. For other garnets, the data do not constrain the value of q and we therefore refined a q-compromise version of the Mie–Grüneisen–Debye EoS in which both γ/V and the Debye temperature θ D are held constant at all P and T, leading to $$textbackslashleft( textbackslashraise0.7extextbackslashhbox$textbackslashpartial C_textbackslashtextV $ textbackslash!textbackslashmathordtextbackslashleft/ textbackslashvphantom textbackslashpartial C_textbackslashtextV  textbackslashpartial Ptextbackslashright.textbackslashkern-textbackslashnulldelimiterspace textbackslash!textbackslashlower0.7extextbackslashhbox$textbackslashpartial P$ textbackslashright)_textbackslashtextT = 0$$, parallel isochors and constant isothermal bulk modulus along an isochor. Final refined parameters for the q-compromise Mie–Grüneisen–Debye EoS are: PyropeAlmandineSpessartineGrossularV0 (cm3/mol)a113.13115.25117.92125.35K0T (GPa)169.3 (3)174.6 (4)177.57 (6)167.0 (2)$$Ktextasciicircumtextbackslashprime_0textbackslashtextT$$4.55 (5)5.41 (13)4.6 (3)5.07 (8)θ D0771 (28)862 (22)860 (35)750 (13)γ01.185 (12)1.16 (fixed)1.18 (3)1.156 (6)for pyrope and grossular, the two versions of the Mie–Grüneisen–Debye EoS predict indistinguishable properties over the metamorphic pressure and temperature range, and the same properties as the EoS based on experimental heat capacities. The biggest change from previously published EoS is for almandine for which the new EoS predicts geologically reasonable entrapment conditions for zircon inclusions in almandine-rich garnets.},

keywords = {Crystallography, Elastic thermobarometry, Elasticity, Garnet, Single-crystal X-ray diffraction, thermodynamics},

pubstate = {published},

tppubtype = {article}

}

@article{angel_self-consistent_2021,

title = {A self-consistent approach to describe unit-cell-parameter and volume variations with pressure and temperature},

author = {R. Angel and M. Mazzucchelli and J. Gonzalez-Platas and M. Alvaro},

doi = {10.1107/S1600576721009092},

issn = {1600-5767},

year  = {2021},

date = {2021-12-01},

urldate = {2021-12-01},

journal = {Journal of Applied Crystallography},

volume = {54},

number = {6},

pages = {1621--1630},

abstract = {A method is presented for the self-consistent description of the variations of unit-cell parameters of crystals with pressure and temperature.},

keywords = {Crystallography, Elastic anisotropy, Elastic thermobarometry, Elasticity, thermodynamics},

pubstate = {published},

tppubtype = {article}

}

@article{mazzucchelli_entrapt_2021,

title = {EntraPT: An online platform for elastic geothermobarometry},

author = {Mattia Luca Mazzucchelli and Ross John Angel and Matteo Alvaro},

url = {https://doi.org/10.2138/am-2021-7693CCBYNCND},

doi = {10.2138/am-2021-7693CCBYNCND},

issn = {0003-004X},

year  = {2021},

date = {2021-05-01},

urldate = {2021-05-01},

journal = {American Mineralogist},

volume = {106},

number = {5},

pages = {830--837},

abstract = {EntraPT is a web-based application for elastic geobarometry freely accessible at the “Fiorenzo Mazzi” experimental mineralogy lab website (http://www.mineralogylab.com/software/). It provides an easy-to-use tool to calculate the entrapment conditions of inclusions, with error propagation, from the residual strain measured in mineral inclusions. EntraPT establishes a method and a workflow to import and analyze the measured residual strains, correctly calculates the mean stress in the inclusions, computes the entrapment isomekes with uncertainty estimation, and visualizes all the results in relevant graphs. It enables the user to avoid the many possible errors that can arise from manual handling of the data and from the numerous steps required in geobarometry calculations. All of the data, parameters, and settings are stored in a consistent format and can be exported as project files and spreadsheets, and imported back to EntraPT for further analysis. This allows researchers to store and/or share their data easily, making the checking and the comparison of data and results reliable. EntraPT is an online tool that does not require any download and/or installation, and it will be updated in the future with new functionalities made available from advances in the development of elastic geobarometry.},

keywords = {Elastic thermobarometry, Elasticity, Matlab, Raman thermobarometry, software development},

pubstate = {published},

tppubtype = {article}

}

@article{campomenosi_using_2021,

title = {Using the elastic properties of zircon-garnet host-inclusion pairs for thermobarometry of the ultrahigh-pressure Dora-Maira whiteschists: problems and perspectives},

author = {Nicola Campomenosi and Marco Scambelluri and Ross J. Angel and Joerg Hermann and Mattia L. Mazzucchelli and Boriana Mihailova and Francesca Piccoli and Matteo Alvaro},

url = {https://doi.org/10.1007/s00410-021-01793-6},

doi = {10.1007/s00410-021-01793-6},

issn = {1432-0967},

year  = {2021},

date = {2021-04-01},

urldate = {2021-04-01},

journal = {Contributions to Mineralogy and Petrology},

volume = {176},

number = {5},

pages = {36},

abstract = {The ultrahigh-pressure (UHP) whiteschists of the Brossasco-Isasca unit (Dora-Maira Massif, Western Alps) provide a natural laboratory in which to compare results from classical pressure (P)–temperature (T) determinations through thermodynamic modelling with the emerging field of elastic thermobarometry. Phase equilibria and chemical composition of three garnet megablasts coupled with Zr-in-rutile thermometry of inclusions constrain garnet growth within a narrow P–T range at 3–3.5 GPa and 675–720 °C. On the other hand, the zircon-in-garnet host-inclusion system combined with Zr-in-rutile thermometry would suggest inclusion entrapment conditions below 1.5 GPa and 650 °C that are inconsistent with the thermodynamic modelling and the occurrence of coesite as inclusion in the garnet rims. The observed distribution of inclusion pressures cannot be explained by either zircon metamictization, or by the presence of fluids in the inclusions. Comparison of the measured inclusion strains with numerical simulations shows that post-entrapment plastic relaxation of garnet from metamorphic peak conditions down to 0.5 GPa and 600–650 °C, on the retrograde path, best explains the measured inclusion pressures and their disagreement with the results of phase equilibria modelling. This study suggests that the zircon-garnet couple is more reliable at relatively low temperatures (textless 600 °C), where entrapment conditions are well preserved but chemical equilibration might be sluggish. On the other hand, thermodynamic modelling appears to be better suited for higher temperatures where rock-scale equilibrium can be achieved more easily but the local plasticity of the host-inclusion system might prevent the preservation of the signal of peak metamorphic conditions in the stress state of inclusions. Currently, we cannot define a precise threshold temperature for resetting of inclusion pressures. However, the application of both chemical and elastic thermobarometry allows a more detailed interpretation of metamorphic P–T paths.},

keywords = {Elastic thermobarometry, Garnet, metamorphic rocks, petrology, Raman spectroscopy, Raman thermobarometry, Zircon},

pubstate = {published},

tppubtype = {article}

}

@article{gonzalez_elastic_2021,

title = {Elastic Geobarometry for Anisotropic Inclusions in Anisotropic Host Minerals: Quartz-in-Zircon},

author = {Joseph P. Gonzalez and Mattia L. Mazzucchelli and Ross J. Angel and Matteo Alvaro},

url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2021JB022080},

doi = {10.1029/2021JB022080},

issn = {2169-9356},

year  = {2021},

date = {2021-01-01},

urldate = {2021-01-01},

journal = {Journal of Geophysical Research: Solid Earth},

volume = {126},

number = {6},

pages = {e2021JB022080},

abstract = {Current models for elastic geobarometry have been developed with the assumption that the host and/or inclusion minerals are elastically isotropic. This assumption has limited applications of elastic thermobarometry to mineral inclusions contained in cubic quasi-isotropic host minerals (e.g., garnet). Here, we report a new elastic model that takes into account the anisotropic elastic properties and relative crystallographic orientation (RCO) of a host-inclusion system where both minerals are noncubic. This anisotropic elastic model can be used for host-inclusion elastic thermobarometric calculations provided that the RCO and elastic properties of both the host and inclusion are known. We then used this anisotropic elastic model to numerically evaluate the effects of elastic anisotropy and RCO on the strains and stresses developed in a quartz inclusion entrapped in a zircon host after exhumation from known entrapment P-T conditions to room P-T conditions. We conclude that the anisotropic quartz-in-zircon elastic model is suitable for elastic thermobarometry and may be widely applicable to crustal rocks. Our results demonstrate that isotropic elastic models cannot be used to determine the entire strain state of an elastically anisotropic inclusion contained in an elastically anisotropic host mineral, and therefore may lead to errors on estimated remnant inclusion pressures.},

keywords = {Elastic anisotropy, Elastic thermobarometry, FEM, Finite element method, Quartz, Zircon},

pubstate = {published},

tppubtype = {article}

}

@article{angel_eosfit-pinc_2020,

title = {“EosFit-Pinc: A simple GUI for host-inclusion elastic thermobarometry”—Reply to Zhong et al.},

author = {Ross J. Angel and Mattia L. Mazzucchelli and Matteo Alvaro and Fabrizio Nestola},

url = {https://doi.org/10.2138/am-2020-7616CCBY},

doi = {10.2138/am-2020-7616CCBY},

issn = {0003-004X},

year  = {2020},

date = {2020-10-01},

urldate = {2021-01-04},

journal = {American Mineralogist},

volume = {105},

number = {10},

pages = {1587--1588},

abstract = {We provide a further algebraic proof that the lines of entrapment conditions for inclusions calculated with the formula of Guiraud and Powell (2006) are not thermodynamic isomekes and therefore do not represent exactly lines of possible entrapment conditions.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Campomenosi2020,

title = {Using polarized Raman spectroscopy to study the stress gradient in mineral systems with anomalous birefringence},

author = {N. Campomenosi and Mattia Luca Mazzucchelli and B. D. Mihailova and Ross John Angel and Matteo Alvaro},

url = {https://doi.org/10.1007/s00410-019-1651-x},

doi = {10.1007/s00410-019-1651-x},

issn = {14320967},

year  = {2020},

date = {2020-02-01},

urldate = {2020-02-01},

journal = {Contributions to Mineralogy and Petrology},

volume = {175},

number = {2},

pages = {1--16},

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 A1g 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.},

keywords = {Crystallography, Elastic anisotropy, Elasticity, Raman spectroscopy, Stress},

pubstate = {published},

tppubtype = {article}

}

@article{Morganti2020,

title = {A numerical application of the Eshelby theory for geobarometry of non-ideal host-inclusion systems},

author = {S. Morganti and Mattia Luca Mazzucchelli and M. Alvaro and A. Reali},

url = {http://link.springer.com/10.1007/s11012-020-01135-z},

doi = {10.1007/s11012-020-01135-z},

issn = {0025-6455},

year  = {2020},

date = {2020-02-01},

urldate = {2020-02-01},

journal = {Meccanica},

pages = {1--14},

abstract = {In the complex geodynamic processes occurring at convergent plate margins, rocks can be subducted at depth into the Earth experiencing metamorphism. A mineral inhomogeneity entrapped into another mineral, after exhumation to the Earth surface, will exhibit stress and strain fields different from those of the host because of the different thermoelastic properties. In the present paper, we propose a finite-element-based approach to determine the Eshelby and the relaxations tensors for any morphology of the inhomogeneity and for any crystallographic symmetry of the host. The proposed procedure can be directly applied in the framework of elastic geobarometry to estimate, on the basis of the Eshelby theory, the entrapment conditions (pressure and temperature) from the residual strain field measured in the inhomogeneity. This aspect represents a step forward to currently available models for geobarometry allowing the investigation of complex morphologies of the inhomogeneity in systems with general material anisotropy. We validate the proposed approach versus Eshelby analytical solutions available for spherical and ellipsoidal inclusions and we show the application to a real geological case of high pressure metamorphic rocks.},

keywords = {Elastic anisotropy, Elastic thermobarometry, Elasticity, FEM, Finite element method, Mechanics},

pubstate = {published},

tppubtype = {article}

}

@article{Alvaro2020,

title = {Fossil subduction recorded by quartz from the coesite stability field},

author = {M. Alvaro and M. L. Mazzucchelli and Ross John Angel and M. Murri and N. Campomenosi and M. Scambelluri and F. Nestola and A. Korsakov and A. A. Tomilenko and F. Marone and M. Morana},

url = {https://doi.org/10.1130/G46617.1},

doi = {10.1130/G46617.1},

issn = {19432682},

year  = {2020},

date = {2020-01-01},

urldate = {2020-01-01},

journal = {Geology},

volume = {48},

number = {1},

pages = {24--28},

abstract = {Metamorphic rocks are the records of plate tectonic processes whose reconstruction relies on correct estimates of the pressures and temperatures (P-T) experienced by these rocks through time. Unlike chemical geothermobarometry, elastic geobarometry does not rely on chemical equilibrium between minerals, so it has the potential to provide information on overstepping of reaction boundaries and to identify other examples of non-equilibrium behavior in rocks. Here we introduce a method that exploits the anisotropy in elastic properties of minerals to determine the unique P and T of entrapment from a single inclusion in a mineral host. We apply it to preserved quartz inclusions in garnet from eclogite xenoliths hosted in Yakutian kimberlites (Russia). Our results demonstrate that quartz trapped in garnet can be preserved when the rock reaches the stability field of coesite (the high-pressure and hightemperature polymorph of quartz) at 3 GPa and 850 °C. This supports a metamorphic origin for these xenoliths and sheds light on the mechanisms of craton accretion from a subducted crustal protolith. Furthermore, we show that interpreting P and T conditions reached by a rock from the simple phase identification of key inclusion minerals can be misleading.},

keywords = {Deviatoric stress, Elastic anisotropy, Elastic thermobarometry, petrology, Raman thermobarometry, Single-crystal X-ray diffraction},

pubstate = {published},

tppubtype = {article}

}

@article{Nestola2019,

title = {Diamond-inclusion system recording old deep lithosphere conditions at Udachnaya (Siberia)},

author = {Fabrizio Nestola and Gabriele Zaffiro and Mattia Luca Mazzucchelli and Paolo Nimis and Giovanni B. Andreozzi and Benedetta Periotto and Francesco Princivalle and Davide Lenaz and Luciano Secco and Leonardo Pasqualetto and Alla M. Logvinova and Nikolay V. Sobolev and Alessandra Lorenzetti and Jeffrey W. Harris},

url = {https://doi.org/10.1038/s41598-019-48778-x},

doi = {10.1038/s41598-019-48778-x},

issn = {2045-2322},

year  = {2019},

date = {2019-12-01},

urldate = {2019-12-01},

journal = {Scientific Reports},

volume = {9},

number = {1},

keywords = {Diamond, Elastic thermobarometry, equations of state, petrology, Single-crystal X-ray diffraction},

pubstate = {published},

tppubtype = {article}

}

@article{Mazzucchelli2019,

title = {Elastic geobarometry for anisotropic inclusions in cubic hosts},

author = {Mattia Luca Mazzucchelli and A. Reali and S. Morganti and Ross John Angel and Alvaro M},

url = {https://doi.org/10.1016/j.lithos.2019.105218},

doi = {10.1016/j.lithos.2019.105218},

issn = {00244937},

year  = {2019},

date = {2019-10-01},

urldate = {2019-10-01},

journal = {Lithos},

pages = {105218},

keywords = {Deviatoric stress, Elastic anisotropy, Elastic thermobarometry, FEM, Finite element method},

pubstate = {published},

tppubtype = {article}

}

@article{Anzolini2019,

title = {Depth of diamond formation obtained from single periclase inclusions},

author = {Chiara Anzolini and Fabrizio Nestola and Mattia Luca Mazzucchelli and Matteo Alvaro and Paolo Nimis and Andrea Gianese and Simone Morganti and Federica Marone and Marcello Campione and Mark T. Hutchison and Jeffrey W. Harris},

url = {https://pubs.geoscienceworld.org/gsa/geology/article/47/3/219/568391/Depth-of-diamond-formation-obtained-from-single},

doi = {10.1130/G45605.1},

issn = {0091-7613},

year  = {2019},

date = {2019-03-01},

urldate = {2019-03-01},

journal = {Geology},

volume = {47},

number = {3},

pages = {219--222},

keywords = {Diamond, Elastic thermobarometry, FEM, Finite element method, petrology, Single-crystal X-ray diffraction},

pubstate = {published},

tppubtype = {article}

}

@article{Campomenosi2018,

title = {How geometry and anisotropy affect residual strain in host-inclusion systems: Coupling experimental and numerical approaches},

author = {Nicola Campomenosi and Mattia Luca Mazzucchelli and Boriana Mihailova and Marco Scambelluri and Ross John Angel and Fabrizio Nestola and Alessandro Reali and Matteo Alvaro},

url = {https://pubs.geoscienceworld.org/msa/ammin/article/103/12/2032/567206/How-geometry-and-anisotropy-affect-residual-strain},

doi = {10.2138/am-2018-6700CCBY},

issn = {0003-004X},

year  = {2018},

date = {2018-12-01},

urldate = {2018-12-01},

journal = {American Mineralogist},

volume = {103},

number = {12},

pages = {2032--2035},

keywords = {Elastic anisotropy, Elastic thermobarometry, Elasticity, Experiments, Raman spectroscopy},

pubstate = {published},

tppubtype = {article}

}

@article{murri_raman_2018,

title = {Raman elastic geobarometry for anisotropic mineral inclusions},

author = {Mara Murri and Mattia Luca Mazzucchelli and Nicola Campomenosi and Andrey V. Korsakov and Mauro Prencipe and Boriana D. Mihailova and Marco Scambelluri and Ross John Angel and Matteo Alvaro},

url = {https://doi.org/10.2138/am-2018-6625CCBY},

doi = {10.2138/am-2018-6625CCBY},

issn = {0003004X},

year  = {2018},

date = {2018-11-01},

urldate = {2018-11-01},

journal = {American Mineralogist},

volume = {103},

number = {11},

pages = {1869--1872},

keywords = {ab-initio, Density Functional Theory, Deviatoric stress, DFT, Elastic anisotropy, Elastic thermobarometry, metamorphic rocks, Raman spectroscopy, Raman thermobarometry},

pubstate = {published},

tppubtype = {article}

}

@article{Mazzucchelli2018,

title = {Elastic geothermobarometry: Corrections for the geometry of the host-inclusion system},

author = {Mattia Luca Mazzucchelli and P. Burnley and Ross John Angel and S. Morganti and M. C. C Domeneghetti and F. Nestola and M. Alvaro},

url = {https://pubs.geoscienceworld.org/gsa/geology/article/46/3/231/526077/Elastic-geothermobarometry-Corrections-for-the},

doi = {10.1130/G39807.1},

issn = {0091-7613},

year  = {2018},

date = {2018-03-01},

urldate = {2018-03-01},

journal = {Geology},

volume = {46},

number = {3},

pages = {231--234},

keywords = {Elastic thermobarometry, Elasticity, FEM, Finite element method},

pubstate = {published},

tppubtype = {article}

}

@article{angel2017eosfit,

title = {EosFit-Pinc: A simple GUI for host-inclusion elastic thermobarometry},

author = {Ross John Angel and Mattia Luca Mazzucchelli and Matteo Alvaro and Fabrizio Nestola},

url = {https://doi.org/10.2138/am-2017-6190},

doi = {10.2138/am-2017-6190},

year  = {2017},

date = {2017-01-01},

urldate = {2017-01-01},

journal = {American Mineralogist},

volume = {102},

number = {9},

pages = {1957--1960},

abstract = {Elastic geothermobarometry is a method of determining metamorphic conditions from the excess pressures exhibited by mineral inclusions trapped inside host minerals. An exact solution to the problem of combining non-linear Equations of State (EoS) with the elastic relaxation problem for elastically isotropic spherical host-inclusion systems without any approximations of linear elasticity is presented. The solution is encoded into a Windows GUI program EosFit-Pinc. The program performs host-inclusion calculations for spherical inclusions in elastically isotropic systems with full P-V-T EoS for both phases, with a wide variety of EoS types. The EoS values of any minerals can be loaded into the program for calculations. EosFit-Pinc calculates the isomeke of possible entrapment conditions from the pressure of an inclusion measured when the host is at any external pressure and temperature (including room conditions), and it can calculate final inclusion pressures from known entrapment conditions. It also calculates isomekes and isochors of the two phases.},

keywords = {Elastic thermobarometry, Elasticity, equations of state, Fortran, Raman thermobarometry, software development},

pubstate = {published},

tppubtype = {article}

}

@article{Milani2017,

title = {Thermo-elastic behavior of grossular garnet at high pressures and temperatures},

author = {S. Milani and Ross John Angel and L. Scandolo and M. L. Mazzucchelli and T. B. Ballaran and S. Klemme and M. C. Domeneghetti and R. Miletich and K. S. Scheidl and M. Derzsi and K. Tokár and M. Prencipe and M. Alvaro and F. Nestola},

url = {https://doi.org/10.2138/am-2017-5855},

doi = {10.2138/am-2017-5855},

issn = {19453027},

year  = {2017},

date = {2017-01-01},

urldate = {2017-01-01},

journal = {American Mineralogist},

volume = {102},

number = {4},

pages = {851--859},

abstract = {© 2017 by Walter de Gruyter Berlin/Boston 2017. The thermo-elastic behavior of synthetic single crystals of grossular garnet (Ca 3 Al 2 Si 3 O 12 ) has been studied in situ as a function of pressure and temperature separately. The same data collection protocol has been adopted to collect both the pressure-volume (P-V) and temperature-volume (T-V) data sets to make the measurements consistent with one another. The consistency between the two data sets allows simultaneous fitting to a single pressure-volume-temperature Equation of State (EoS), which was performed with a new fitting utility implemented in the latest version of the program EoSFit7c. The new utility performs fully weighted simultaneous fits of the P-V-T and P-K-T data using a thermal pressure EoS combined with any P-V EoS. Simultaneous refinement of our P-V-T data combined with that of K T as a function of T allowed us to produce a single P-V-T-K T equation of state with the following coefficients: V 0 =1664.46(5)Å 3 K TO =166.57(17)GPa and K′=4.96(7)α (300K,1bar) =2.09(2)×10 -5 K -1 with a refined Einstein temperature (θ E ) of 512 K for a Holland-Powell-type thermal pressure model and a Tait third-order EoS. Additionally, thermodynamic properties of grossular have been calculated for the first time from crystal Helmholtz and Gibbs energies, including the contribution from phonons, using density functional theory within the framework of the quasi-harmonic approximation.},

keywords = {ab-initio, Density Functional Theory, DFT, Elastic thermobarometry, equations of state, high-pressure, high-temperature, thermal expansion, thermodynamics},

pubstate = {published},

tppubtype = {article}

}

@article{Milani2015,

title = {Diamond–garnet geobarometry: The role of garnet compressibility and expansivity},

author = {Sula Milani and Fabrizio Nestola and Matteo Alvaro and Daria Pasqual and Mattia Luca Mazzucchelli and M C Domeneghetti and C A Geiger},

url = {http://www.sciencedirect.com/science/article/pii/S0024493715001097},

doi = {10.1016/j.lithos.2015.03.017},

year  = {2015},

date = {2015-01-01},

urldate = {2015-01-01},

journal = {Lithos},

volume = {227},

number = {0},

pages = {140--147},

keywords = {Crystallography, Diamond, Elastic thermobarometry, equations of state, Experiments, Garnet, petrology, Raman thermobarometry, Single-crystal X-ray diffraction, thermal expansion, thermodynamics},

pubstate = {published},

tppubtype = {article}

}

@article{Scandolo2015ab,

title = {Thermal expansion behaviour of orthopyroxenes: the role of the Fe-Mn substitution},

author = {L. Scandolo and Mattia Luca Mazzucchelli and M. Alvaro and Fabrizio Nestola and F. Pandolfo and M. C. C Domeneghetti},

url = {https://doi.org/10.1180/minmag.2015.079.1.07},

doi = {10.1180/minmag.2015.079.1.07},

issn = {14718022},

year  = {2015},

date = {2015-01-01},

urldate = {2015-01-01},

journal = {Mineralogical Magazine},

volume = {79},

number = {1},

pages = {71--87},

keywords = {Crystallography, Elasticity, equations of state, Single-crystal X-ray diffraction, thermal expansion, thermodynamics},

pubstate = {published},

tppubtype = {article}

}

@article{Angel2015JMGb,

title = {How large are departures from lithostatic pressure? Constraints from host–inclusion elasticity},

author = {Ross John Angel and P Nimis and Mattia Luca Mazzucchelli and M Alvaro and Fabrizio Nestola},

url = {http://dx.doi.org/10.1111/jmg.12138},

doi = {10.1111/jmg.12138},

year  = {2015},

date = {2015-01-01},

urldate = {2015-01-01},

journal = {Journal of Metamorphic Geology},

volume = {33},

number = {8},

pages = {801--813},

keywords = {Diamond, Elastic thermobarometry, Elasticity, equations of state, metamorphic rocks, petrology},

pubstate = {published},

tppubtype = {article}

}

@article{Angel2015diamond,

title = {Diamond thermoelastic properties and implications for determining the pressure of formation of diamond–inclusion systems},

author = {Ross John Angel and Matteo Alvaro and Fabrizio Nestola and Mattia Luca Mazzucchelli},

doi = {10.1016/j.rgg.2015.01.014},

year  = {2015},

date = {2015-01-01},

urldate = {2015-01-01},

journal = {Russian Geology and Geophysics},

volume = {56},

number = {1-2},

pages = {211--220},

keywords = {Diamond, Elastic thermobarometry, Elasticity, equations of state, petrology, thermodynamics},

pubstate = {published},

tppubtype = {article}

}

@article{Alvaro2015,

title = {A new micro-furnace for in situ high-temperature single-crystal X-ray diffraction measurements},

author = {M. Alvaro and Ross John Angel and C. Marciano and S. Milani and L. Scandolo and Mattia Luca Mazzucchelli and G. Zaffiro and G. Rustioni and M. Briccola and M. C. Domeneghetti and F. Nestola},

url = {http://scripts.iucr.org/cgi-bin/paper?S1600576715011371},

doi = {10.1107/s1600576715011371},

issn = {1600-5767},

year  = {2015},

date = {2015-01-01},

urldate = {2015-01-01},

journal = {Journal of Applied Crystallography},

volume = {48},

number = {4},

pages = {1192--1200},

abstract = {A new micro-furnace equipped with an H-shaped resistance heater has been developed to conduct in situ single-crystal X-ray diffraction experiments at high temperature. The compact design of the furnace does not restrict access to reciprocal space out to 2θ = 60°. Therefore, unit-cell parameters and intensity data can be determined to a resolution of 0.71 Å with Mo radiation. The combined use of mineral phases with well characterized lattice expansion ( e.g. pure Si and SiO 2 quartz) and a small-diameter (0.025 mm) K-type thermocouple allowed accurate temperature calibration from room temperature to about 1273 K and consequent evaluation of thermal gradients and stability. The new furnace design allows temperatures up to about 1273 K to be reached with a thermal stability better than ±5 K even at the highest temperatures. Measurements of the lattice thermal expansion of pure silicon (Si), pure synthetic grossular garnet (Ca 3 Al 2 Si 3 O 12 ) and quartz (SiO 2 ) are presented to demonstrate the performance of the device. Its main advantages and limitations and important considerations for using it to perform high-temperature diffraction measurements are discussed.},

keywords = {Crystallography, Experiments, Single-crystal X-ray diffraction, thermal expansion},

pubstate = {published},

tppubtype = {article}

}

@article{Angel2014relaxation,

title = {Geobarometry from host-inclusion systems: The role of elastic relaxation},

author = {Ross John Angel and Mattia Luca Mazzucchelli and Matteo Alvaro and Paolo Nimis and Fabrizio Nestola},

url = {https://doi.org/10.2138/am-2014-5047},

doi = {10.2138/am-2014-5047},

issn = {19453027},

year  = {2014},

date = {2014-01-01},

urldate = {2014-01-01},

journal = {American Mineralogist},

volume = {99},

number = {10},

pages = {2146--2149},

abstract = {© 2014 by Walter de Gruyter Berlin/Boston. Minerals trapped as inclusions within other host minerals can develop residual stresses on exhumation as a result of the differences between the thermo-elastic properties of the host and inclusion phases. The determination of possible entrapment pressures and temperatures from this residual stress requires the mutual elastic relaxation of the host and inclusion to be determined. Previous estimates of this relaxation have relied on the assumption of linear elasticity theory. We present a new formulation of the problem that avoids this assumption. We show that for soft inclusions such as quartz in relatively stiff host materials such as garnet, the previous analysis yields entrapment pressures in error by the order of 0.1 GPa. The error is larger for hosts that have smaller shear moduli than garnet.},

keywords = {Elastic thermobarometry, Elasticity, equations of state, Raman thermobarometry},

pubstate = {published},

tppubtype = {article}

}