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https://doi.org/10.5194/ejm-35-461-2023
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https://doi.org/10.5194/ejm-35-461-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
11 Jul 2023
Research article |
| 11 Jul 2023
| 11 Jul 2023
Elasticity of mixtures and implications for piezobarometry of mixed-phase inclusions
IGG CNR, Via Giovanni Gradenigo 6, 35131 Padua, Italy
Mattia L. Mazzucchelli
Mainz Institute of Multiscale Modelling and Institute of Geosciences,
Johannes-Gutenberg University of Mainz, J.-J.-Becher-Weg 21, 55128 Mainz,
Germany
Kira A. Musiyachenko
Department of Earth and Environmental Sciences, University of Pavia,
Via A. Ferrata, 1, 27100 Pavia, Italy
current address: Department of Earth, Ocean and Atmospheric Sciences,
University of British Columbia, 2020–2207 Main Mall, Vancouver, V6T 1Z4 BC, Canada
Fabrizio Nestola
Department of Geosciences, University of Padua, Via Giovanni
Gradenigo 6, 35131 Padua, Italy
Matteo Alvaro
Department of Earth and Environmental Sciences, University of Pavia,
Via A. Ferrata, 1, 27100 Pavia, Italy
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Cited articles
Adams, H. G., Cohen, L. H., and Rosenfeld, J. L.: Solid inclusion
piezothermometry I: comparison dilatometry, Am. Mineral., 60,
574–583, 1975.
Alifirova, T., Daneu, N., Kohn, K., Griffiths, T., Rečnik, A., and
Habler, G.: Atomic scale structure of garnet-rutile interfaces in
host-inclusion systems, 23rd General Meeting of the International
Mineralogical Association, Lyon, France, 2022.
Angel, R. J., Mosenfelder, J. L., and Shaw, C. S. J.: Anomalous compression
and equation of state of coesite, Phys. Earth Planet.
In., 124, 71–79, 2001.
Angel, R. J. and Jackson, J. M.: Elasticity and equation of state of
orthoenstatite, MgSiO3, Am. Mineral., 87, 558–561, 2002.
Angel, R. J., Gonzalez-Platas, J., and Alvaro, M.: EosFit7c and a Fortran
module (library) for equation of state calculations, Z.
Kristallogr., 229, 405–419, 2014a.
Angel, R. J., Mazzucchelli, M. L., Alvaro, M., Nimis, P., and Nestola, F.:
Geobarometry from host-inclusion systems: the role of elastic relaxation,
Am. Mineral., 99, 2146–2149, 2014b.
Angel, R. J., Alvaro, M., Nestola, F., and Mazzucchelli, M. L.: Diamond
thermoelastic properties and implications for determining the pressure of
formation of diamond-inclusion systems, Russ. Geol. Geophys., 56,
211–220, https://doi.org/10.1016/j.rgg.2015.01.014, 2015a.
Angel, R. J., Nimis, P., Mazzucchelli, M. L., Alvaro, M., and Nestola, F.:
How large are departures from lithostatic pressure? Constraints from
host-inclusion elasticity, J. Metamorph. Geol., 33, 801–803,
2015b.
Angel, R. J., Alvaro, M., Miletich, R., and Nestola, F.: A simple and
generalised P-T-V EoS for continuous phase transitions, implemented in
EosFit and applied to quartz, Contrib. Mineral. Petr.,
172, 29, https://doi.org/10.1007/s00410-017-1349-x, 2017a.
Angel, R. J., Mazzucchelli, M. L., Alvaro, M., and Nestola, F.: EosFit-Pinc:
A simple GUI for host-inclusion elastic thermobarometry, Am.
Mineral., 102, 1957–1960, https://doi.org/10.2138/am-2017-6190, 2017b.
Angel, R. J., Alvaro, M., and Nestola, F.: 40 years of mineral elasticity: a
critical review and a new parameterisation of equations of state for mantle
olivines and diamond inclusions, Phys. Chem. Miner., 45,
95–113, 2018.
Angel, R. J., Miozzi, F., and Alvaro, M.: Limits to the validity of
thermal-pressure equations of state, Minerals, 9, 562, https://doi.org/10.3390/min9090562,
2019a.
Angel, R. J., Murri, M., Mihailova, B., and Alvaro, M.: Stress, strain and
Raman shifts, Z. Kristallogr., 234, 129–140,
https://doi.org/10.1515/zkri-2018-2112, 2019b.
Angel, R. J., Alvaro, M., Schmid-Beurmann, P., and Kroll, H.: Commentary on
“Constraints on the Equations of State of stiff anisotropic minerals:
rutile, and the implications for rutile elastic barometry”, Mineral.
Mag., 84, 339–347, https://doi.org/10.1180/mgm.2020.14, 2020.
Angel, R. J., Alvaro, M., and Nestola, F.: Crystallographic methods for
non-destructive characterization of mineral inclusions in diamonds, in:
Natural Diamonds: Their Mineralogy, Geochemistry and Genesis, edited by:
Pearson, G. and Smit, K., Reviews in Mineralogy and Geochemistry,
Mineralogical Society of America, Washington DC, 257–306,
https://doi.org/10.2138/rmg.2022.88.05, 2022a.
Angel, R. J., Gilio, M., Mazzucchelli, M. L., and Alvaro, M.: Garnet EoS: a
critical review and synthesis, Contrib. Mineral. Petr.,
177, 54, https://doi.org/10.1007/s00410-022-01918-5, 2022b.
Anzolini, C., Angel, R. J., Merlini, M., Derzsi, M., Tokár, K., Milani,
S., Krebs, M. Y., Brenker, F. E., Nestola, F., and Harris, J. W.: Depth of
formation of CaSiO3-walstromite included in super-deep diamonds,
Lithos, 265, 138–147, 10.1016/j.lithos.2016.09.025, 2016.
Anzolini, C., Prencipe, M., Alvaro, M., Romano, C., Vona, A., Lorenzon, S.,
Smith, E. M., Brenker, F. E., and Nestola, F.: Depth of formation of
super-deep diamonds: Raman barometry of CaSiO3-walstromite inclusions,
Am. Mineral., 103, 69–74, https://doi.org/10.2138/am-2018-6184, 2018.
Anzolini, C., Nestola, F., Mazzucchelli, M. L., Alvaro, M., Nimis, P.,
Gianese, A., Morganti, S., Marone, F., Campione, M., Hutchison, M. T., and
Harris, J. W.: Depth of diamond formation obtained from single periclase
inclusions, Geology, 47, 219–222, https://doi.org/10.1130/G45605.1, 2019.
Arlt, T. and Angel, R. J.: Pressure buffering in a diamond anvil cell,
Mineral. Mag., 64, 241–245, 2000.
Bonazzi, M., Tumiati, S., Thomas, J., Angel, R. J., and Alvaro, M.:
Assessment of the reliability of elastic geobarometry with quartz
inclusions, Lithos, 350–351, 105201, https://doi.org/10.1016/j.lithos.2019.105201, 2019.
Campomenosi, N., Scambelluri, M., Angel, R. J., Hermann, J., Mazzucchelli,
M. L., Mihailova, B., Piccoli, F., and Alvaro, M.: Using the elastic
properties of zircon-garnet host-inclusion pairs for thermobarometry of the
ultrahigh-pressure Dora-Maira whiteschists: problems and perspectives,
Contrib. Mineral. Petr., 176, 36,
https://doi.org/10.1007/s00410-021-01793-6, 2021.
Campomenosi, N., Angel, R. J., Alvaro, M., and Mihailova, B.: Resetting of
zircon inclusions in garnet: implications for elastic thermobarometry,
Geology, 51, 23–27, https://doi.org/10.1130/G50431.1, 2023.
Cesare, B., Acosta-Vigil, A., Bartoli, O., and Ferrero, S.: What can we
learn from melt inclusions in migmatites and granulites?, Lithos, 239,
186–216, https://doi.org/10.1016/j.lithos.2015.09.028, 2015.
Chopin, C.: Coesite and pure pyrope in high-grade blueschists of the Western
Alps: a first record and some consequences, Contrib. Mineral.
Petr., 86, 107–118, 1984.
Cisneros, M. and Befus, K. S.: Applications and limitations of elastic
thermobarometry: insights from elastic modeling of inclusion-host pairs and
example case studies, Geochem. Geophy. Geosy., 21,
e2020GC009231, https://doi.org/10.1029/2020GC009231, 2020.
Ehlers, A. M., Zaffiro, G., Angel, R. J., Boffa-Ballaran, T., Carpenter, M.
A., Alvaro, M., and Ross, N. L.: Thermoelastic properties of zircon:
implications for geothermobarometry, Am. Mineral., 107, 74–81,
https://doi.org/10.2138/am-2021-7731, 2022.
Ferrero, S. and Angel, R. J.: Micropetrology: are inclusions grains of
truth?, J. Petrol., 59, 1671–1700, https://doi.org/10.1093/petrology/egy075, 2018.
Frezzotti, M. L., Selverstone, J., Sharp, Z. D., and Compagnoni, R.:
Carbonate dissolution during subduction revealed by diamond-bearing rocks
from the Alps, Nat. Geosci., 4, 703–706, 2011.
Gilio, M., Angel, R. J., and Alvaro, M.: Elastic geobarometry: how to work
with residual inclusion strains and pressures, Am. Mineral., 106,
1530–1533, https://doi.org/10.2138/am-2021-7928, 2021a.
Gilio, M., Campomenosi, N., Musiyachenko, K. A., Angel, R. J., Cesare, B., and Alvaro, M.: Elastic geobarometry of quartz inclusions in garnet at high temperature, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1508, https://doi.org/10.5194/egusphere-egu21-1508, 2021b.
Gillet, P., Ingrin, J., and Chopin, C.: Coesite in subducted continental
crust: P-T history deduced from an elastic model, Earth Planet.
Sc. Lett., 70, 426–436, 1984.
Gonzalez, J. P., Thomas, J. B., Baldwin, S. L., and Alvaro, M.:
Quartz-in-garnet and Ti-in-quartz thermobarometry: Methodology and first
application to a quartzofeldspathic gneiss from eastern Papua New Guinea,
J. Metamorph. Geol., 37, 1193–1208, https://doi.org/10.1111/jmg.12508, 2019.
Gonzalez, J. P., Mazzucchelli, M. L., Angel, R. J., and Alvaro, M.: Elastic
geobarometry for anisotropic inclusions in anisotropic host minerals:
quartz-in-zircon, J. Geophys. Res.-Sol. Ea., 126,
e2021JB022080, https://doi.org/10.1029/2021JB022080, 2021.
Gonzalez, J. P., Thomas, J. B., Mazzucchelli, M. L., Angel, R. J., and Alvaro, M.:
Experimental evaluation of anisotropic elastic thermobarometry applied to
stiff mineral inclusions in soft hosts: First evaluation of zircon
inclusions in quartz, Goldschmidt, 10–15 July 2022, Hawai'i, 2022.
Gonzalez-Platas, J., Alvaro, M., Nestola, F., and Angel, R. J.:
EosFit7-GUI: A new GUI tool for equation of state calculations, analyses,
and teaching, J. Appl. Crystallogr., 49, 1377–1382,
https://doi.org/10.1107/S1600576716008050, 2016.
Hill, R.: Elastic properties of reinforced solids: some theoretical
principles, J. Mech. Phys. Solids, 11, 357–372,
1963.
Holland, T. J. B. and Powell, R.: An improved and extended internally
consistent thermodynamic dataset for phases of petrological interest,
involving a new equation of state for solids, J. Metamorph.
Geol., 29, 333–383, https://doi.org/10.1111/j.1525-1314.2010.00923.x, 2011.
Izraeli, E., Harris, J., and Navon, O.: Raman barometry of diamond
formation, Earth Planet. Sc. Lett., 173, 351–360, 1999.
Jakubová, P., Kotková, J., Wirth, R., Škoda, R., and Haifler,
J.: Morphology and Raman spectral parameters of Bohemian microdiamonds:
implications to elastic geothermobarometry, J. Geosci., 67,
253–271, https://doi.org/10.3190/jgeosci.356, 2022.
Kohn, M. J.: “Thermoba-Raman-try”: Calibration of spectroscopic barometers
and thermometers for mineral inclusions, Earth Planet. Sc.
Lett., 388, 187–196, 2014.
Korsakov, A. V., Kohn, M. J., and Perraki, M.: Applications of Raman
Spectroscopy in Metamorphic Petrology and Tectonics, Elements, 16, 105–110,
https://doi.org/10.2138/gselements.16.2.105, 2020.
Kosminska, K., Spear, F. S., Majka, J., Faehnrich, K., Manecki, M.,
Piepjohn, K., and Dallmann, W. K.: Deciphering late Devonian-early
Carboniferous P-T-t path of mylonitized garnet-mica schists from Prins Karls
Forland, Svalbard, J. Metamorph. Geol., 38, 471–493,
https://doi.org/10.1111/jmg.12529, 2020.
Kotková, J., Fedortchouk, Y., Wirth, R., and Whitehouse, M. J.:
Metamorphic microdiamond formation is controlled by water activity, phase
transitions and temperature, Sci. Rep., 11, 7694,
https://doi.org/10.1038/s41598-021-87272-1, 2021.
Kulik, E., Murzin, V., Kawaguchi, S., Nishiyama, N., and Katsura, T.:
Thermal expansion of coesite determined by synchrotron powder X-ray
diffraction, Phys. Chem. Miner., 45, 873–881,
https://doi.org/10.1007/s00269-018-0969-7, 2018.
Mazzucchelli, M. L., Burnley, P., Angel, R. J., Morganti, S., Domeneghetti,
M. C., Nestola, F., and Alvaro, M.: Elastic geothermobarometry: corrections
for the geometry of the host-inclusion system, Geology, 46, 231–234, 2018.
Mazzucchelli, M. L., Reali, A., Morganti, S., Angel, R. J., and Alvaro, M.:
Elastic geobarometry for anisotropic inclusions in cubic hosts, Lithos,
350–351, 105218, https://doi.org/10.1016/j.lithos.2019.105218, 2019.
Mazzucchelli, M. L., Angel, R. J., and Alvaro, M.: EntraPT: an online
application for elastic geothermobarometry, Am. Mineral., 106,
829–836, https://doi.org/10.2138/am-2021-7693CCBYNCND, 2021.
Milani, S., Nestola, F., Alvaro, M., Pasqual, D., Mazzucchelli, M. L.,
Domeneghetti, M. C., and Geiger, C.: Diamond–garnet geobarometry: The role
of garnet compressibility and expansivity, Lithos, 227, 140–147, 2015.
Morganti, S., Mazzucchelli, M., Alvaro, M., and Reali, A.: A numerical
application of the Eshelby theory for geobarometry of non-ideal
host-inclusion systems, Meccanica, 55, 751–764, 2020.
Murri, M., Gonzalez, J. P., Mazzucchelli, M. L., Prencipe, M., Mihailova,
B., Angel, R. J., and Alvaro, M.: The role of symmetry-breaking strains on
quartz inclusions in anisotropic hosts: implications for Raman elastic
geobarometry, Lithos, 422–423, 106716, https://doi.org/10.1016/j.lithos.2022.106716, 2022.
Musiyachenko, K. A., Murri, M., Prencipe, M., Angel, R. J., and Alvaro, M.:
A new Grüneisen tensor for rutile and its application to host-inclusion
systems, Am. Mineral., 106, 1586, https://doi.org/10.2138/am-2021-7618, 2021.
Myhill, R.: The elastic solid solution model for minerals at high pressures
and temperatures, Contrib. Mineral. Petr., 173, 12,
https://doi.org/10.1007/s00410-017-1436-z, 2018.
Nestola, F., Nimis, P., Ziberna, L., Longo, M., Marzoli, A., Harris, J. W.,
Manghnani, M. H., and Fedortchouk, Y.: First crystal-structure determination
of olivine in diamond: composition and implications for provenance in the
Earth's mantle, Earth Planet. Sc. Lett., 305, 249–255,
https://doi.org/10.1016/j.epsl.2011.03.007, 2011.
Nestola, F., Prencipe, M., Nimis, P., Sgreva, N., Peritt, S. H., Chinn, I.
L., and Zaffirio, G.: Toward a robust elastic geobarometry of kyanite
inclusions in eclogitic diamonds, J. Geophys. Res.-Sol.
Ea., 123, 6411–6423, https://doi.org/10.1029/2018JB016012, 2018.
Ni, P., Zhang, Y., and Guan, Y.: Volatile loss during homogenization of
lunar melt inclusions, Earth Planet. Sc. Lett., 478, 214–224,
https://doi.org/10.1016/j.epsl.2017.09.010, 2017.
Nimis, P., Alvaro, M., Nestola, F., Angel, R. J., Marquardt, K., Rustioni,
G., Harris, J. W., and Marone, F.: First evidence of hydrous silicic fluid
films around solid inclusions in gem-quality diamonds, Lithos, 260, 384–389,
https://doi.org/10.1016/j.lithos.2016.05.019, 2016.
Nimis, P., Angel, R. J., Alvaro, M., Nestola, F., Harris, J. W., Casati, N.,
and Marone, F.: Crystallographic orientations of magnesiochromite inclusions
in diamonds: what do they tell us?, Contrib. Mineral.
Petr., 174, 29, https://doi.org/10.1007/s00410-019-1559-5, 2019.
Perraki, M., Proyer, A., Mposkos, E., Kaindl, R., and Hoinkes, G.: Raman
micro-spectroscopy on diamond, graphite and other carbon polymorphs from the
ultrahigh-pressure metamorphic Kimi Complex of the Rhodope Metamorphic
Province, NE Greece, Earth Planet. Sc. Lett., 241, 672–685,
https://doi.org/10.1016/j.epsl.2005.11.014, 2006.
Perrillat, J. P., Daniel, I., Lardeaux, J. M., and Cardon, H.: Kinetics of
the quartz-coesite transition: application to the exhumation of
ultrahigh-pressure rocks, J. Petrol., 44, 773–788, 2003.
Pitzer, K. S. and Sterner, S. M.: Equations of state valid continuously from
zero to extreme pressures for H2O and CO2, J. Chem.
Phys., 101, 3111–3116, https://doi.org/10.1063/1.467624, 1994.
Pollard, D. D. and Fletcher, R. C.: Fundamentals of Structural Geology,
Cambridge University Press, Cambridge, UK, ISBN 978-0521839273, 2006.
Rodriguez-Carvajal, J. and Gonzalez-Platas, J.: Crystallographic Fortran 90
Modules Library (CrysFML): a simple toolbox for crystallographic computing
programs, IUCr Computing Commission Newsletter, 1, 50–58, 2003 (code available at: http://www.ill.eu/sites/fullprof/php/programs24b7.html?pagina=Crysfml, last access: 20 June 2023).
Roedder, E. and Bodnar, R. J.: Geologic pressure determinations from fluid
inclusion studies, Annu. Rev. Earth Planet. Sc., 8,
263–301, 1980.
Rosenfeld, J. L. and Chase, A. B.: Pressure and temperature of
crystallization from elastic effects around solid inclusion minerals?,
Am. J. Sci., 259, 519–541, 1961.
Schmalholz, S. M., Moulas, E., Plümper, O., Myasnikov, A. V., and
Podladchikov, Y. Y.: 2D hydro-mechanical-chemical modeling of (de)hydration
reactions in deforming heterogeneous rock: the periclase-brucite model
reaction, Geochem. Geophy. Geosy., 21, e2020GC009351,
https://doi.org/10.1029/2020GC009351, 2020.
Sobolev, N. V., Fursenko, B. A., Goryainov, S. V., Shu, J. F., Hemley, R.
J., Mao, H. K., and Boyd, F. R.: Fossilized high pressure from the Earth's
deep interior: The coesite-in-diamond barometer, P. Natl.
Acad. Sci. USA, 97, 11875–11879, 2000.
Stixrude, L. and Lithgow-Bertelloni, C.: Thermal expansivity, heat capacity
and bulk modulus of the mantle, Geophys. J. Int., 228,
1119–1149, https://doi.org/10.1093/gji/ggab394, 2022.
Ye, K., Liou, J. B., Cong, B. L., and Maruyama, S.: Overpressures induced by
coesite-quartz transition in zircon, Am. Mineral., 86, 1151–1155,
2001.
Zhang, Y.: Mechanical and phase equilibria in inclusion–host systems, Earth
Planet. Sc. Lett., 157, 209–222, https://doi.org/10.1016/S0012-821X(98)00036-3,
1998.
Zhang, Z. and Duan, Z.: Prediction of the PVT properties of water over wide
range of temperatures and pressures from molecular dynamics simulation,
Phys. Earth Planet. In., 149, 335–354, 2005.
Zhong, X., Moulas, E., and Tajčmanová, L.: Tiny timekeepers
witnessing high-rate exhumation processes, Sci. Rep., 8, 2234,
https://doi.org/10.1038/s41598-018-20291-7, 2018.
Zhong, X., Dabrowski, M., and Jamtveit, B.: Analytical solution for residual stress and strain preserved in anisotropic inclusion entrapped in an isotropic host, Solid Earth, 12, 817–833, https://doi.org/10.5194/se-12-817-2021, 2021.
Short summary
We have developed the thermodynamic theory of the properties of inclusions consisting of more than one phase, including inclusions containing solids plus a fluid. We present a software utility that enables for the first time the entrapment conditions of multiphase inclusions to be determined from the measurement of their internal pressure when that is measured in a laboratory.
We have developed the thermodynamic theory of the properties of inclusions consisting of more...
