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Cited by 41Geological and Geochemical AnalysisMetallurgical Processes and ThermodynamicsMineralogy and Gemology Studies

Iterative thermodynamic modelling—Part 1: A theoretical scoring technique and a computer program (Bingo‐Antidote)

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Duesterhoeft, Erik, Lanari, Pierre·2020·Journal of Metamorphic Geology
DOI 10.1111/jmg.12538
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Abstract

Abstract This paper introduces the software solution Bingo‐Antidote for thermodynamic calculations at equilibrium based on iterative thermodynamic models. It describes a hybrid strategy combining the strength of Gibbs energy minimization (GEM) and inverse thermobarometry models based on the comparison between the modelled and observed mineral assemblage, modes and compositions. The overall technique relies on quantitative compositional maps acquired by electron probe micro‐analyser for obtaining a mutually consistent set of observed data such as bulk rock and mineral compositions. Thus it offers the opportunity to investigate metamorphic rocks on a microscale. The scoring part Bingo integrates three statistical model quality factors for the assemblage, for the mineral modes, for the mineral compositions combined in a global evaluation criterion that quantifies how the model reproduces the observations for the investigated volume. The input parameters of GEM affecting the model quality such as pressure, temperature and eventually some components of the bulk composition (e.g. the molar amount of hydrogen, carbon or oxygen) or activity variables of fluids and gases (e.g. , , f(O2)) can be optimized by inversion in Antidote using several mapping stages followed by a direct search optimization. Examples of iterative models based on compositional maps processed with Bingo‐Antidote demonstrate the utility of the program. In contrast to the qualitative interpretation of phase diagrams, the inversion maximizes the benefits of GEM and permits the derivation of statistically ‘optimal’ pressure–temperature conditions for well‐equilibrated samples. In addition, Bingo‐Antidote opens new avenues for petrological investigations such as the generation of chemical potential landscape maps.

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Research works printed but not linked: 51

  1. Anovitz, L., & Essene, E. (1990). Thermobarometry and pres- sure-temperature paths in the Grenville Province of Ontario. Journal of Petrology, 31, 197-241. https://doi.org/10.1093/petro logy/31.1.197 · DOI · Paper page
  2. Berman, R. G. (1988). Internally-consistent thermodynamic data for minerals in the system Na 2 O-K 2 O-CaO-MgO-FeO-Fe 2 O 3 -Al 2 O 3 - SiO 2 -TiO 2 -H 2 O-CO 2 . Journal of Petrology, 29(2), 445-552. https:// doi.org/10.1093/petro logy/29.2.445 · DOI
  3. Berman, R. G., Aranovich, L. Y., Rancourt, D. G., & Mercier, P. H. J. (2007). Reversed phase equilibrium constraints on the stability of Mg-Fe-Al biotite. American Mineralogist, 92(1), 139-150. https:// doi.org/10.2138/am.2007.2051 · DOI
  4. Brown, T. H., & Skinner, B. J. (1974). Theoretical prediction of equi- librium phase assemblages in multicomponent systems. American Journal of Science, 274(9), 961-986. https://doi.org/10.2475/ ajs.274.9.961 · DOI
  5. Carlson, W. D., Pattison, D. R. M., & Caddick, M. J. (2015). Beyond the equilibrium paradigm: How consideration of kinetics enhances metamorphic interpretation. American Mineralogist, 100(8-9), 1659-1667. https://doi.org/10.2138/am-2015-5097 · DOI
  6. Clarke, G. L., Daczko, N. R., & Nockolds, C. (2001). A method for applying matrix corrections to X-ray intensity maps using the Bence-Albee algorithm and Matlab. Journal of Metamorphic Geology, 19(6), 635-644. https://doi. org/10.1046/j.0263-4929.2001.00336.x · DOI
  7. Connolly, J. A. D. (1990). Multivariable phase diagrams: An algo- rithm based on generalized thermodynamics. American Journal of Science, 290, 666-718. https://doi.org/10.2475/ajs.290.6.666 · DOI
  8. Connolly, J. A. D. (2005). Computation of phase equilibria by linear programming: A tool for geodynamic modeling and its appli- cation to subduction zone decarbonation. Earth and Planetary Science Letters, 236(1-2), 524-541. https://doi.org/10.1016/j. epsl.2005.04.033 · DOI
  9. Connolly, J. A. D. (2005). Computation of phase equilibria by linear programming: A tool for geodynamic modeling and its appli- cation to subduction zone decarbonation. Earth and Planetary Science Letters, 236(1-2), 524-541. https://doi.org/10.1016/j. epsl.2005.04.033 · DOI
  10. Connolly, J. A. D. (2009). The geodynamic equation of state: What and how. Geochemistry, Geophysics, Geosystems, 10(10), 1-19. https:// doi.org/10.1029/2009G C002540 · DOI
  11. Connolly, J. A. D., & Kerrick, D. M. (1987). An algorithm and computer program for calculating composition phase dia- grams. CALPHAD, 11(1), 1-55. https://doi.org/10.1016/0364- 5916(87)90018 -6 · DOI
  12. De Andrade, V., Vidal, O., Lewin, E., O'Brien, P., & Agard, P. (2006). Quantification of electron microprobe compositional maps of rock thin sections: An optimized method and examples. Journal of Metamorphic Geology, 24(7), 655-668. https://doi. org/10.1111/j.1525-1314.2006.00660.x · DOI
  13. de Capitani, C., & Brown, T. H. (1987). The computation of chemi- cal equilibrium in complex systems containing non-ideal solutions. Geochimica et Cosmochimica Acta, 51(10), 2639-2652. https://doi. org/10.1016/0016-7037(87)90145 -1 · DOI
  14. de Capitani, C., & Petrakakis, K. (2010). The computation of equi- librium assemblage diagrams with Theriak/Domino software. American Mineralogist, 95(7), 1006-1016. https://doi.org/10.2138/ am.2010.3354 · DOI
  15. Duesterhoeft, E. (2016). A volume equation of state that extends ther- modynamic datasets, using the Bridgman power series, to very high pressures (20 GPa). American Journal of Science, 316(6), 578-589. https://doi.org/10.2475/06.2016. · DOI
  16. Duesterhoeft, E. (2017). BED92.v1 -Theriak-Domino database. ResearchGate. http://doi.org/10.13140 /RG.2.2.10285.69609. · DOI
  17. Duesterhoeft, E., & de Capitani, C. (2013). Theriak_D: An add-on to implement equilibrium computations in geodynamic models. Geochemistry, Geophysics, Geosystems, 14(11), 4962-4967. https:// doi.org/10.1002/ggge.20286 · DOI
  18. Duesterhoeft, E., Raase, P., & Gremler, P. (2017). A new occur- rence of extremely rare Ferro-Chloro-Pargasite in Tudor, Ontario. International Journal of Earth Sciences, 106(8), 2815-2816. https:// doi.org/10.1007/s0053 1-017-1492-7 · DOI · Paper page
  19. Dunn, S. R., Markley, M. J., Kotikian, M., Achenbach, K., Montanye, B., & Peck, W. H. (2019). Geothermometry of the Western Half of the Central Metasedimentary Belt, Grenville Province, Ontario, and its Implications. American Mineralogist, 104, 791-809. https://doi. org/10.2138/am-2019-6757 · DOI · Paper page
  20. Forshaw, J. B., Waters, D. J., Pattison, D. R. M., Palin, R. M., & Gopon, P. (2019). A comparison of observed and thermodynamically pre- dicted phase equilibria and mineral compositions in mafic granu- lites. Journal of Metamorphic Geology, 37(2), 153-179. https://doi. org/10.1111/jmg.12454 · DOI
  21. Freund, J., & Ingalls, R. (1989). Inverted isothermal equations of state and determination of B0, B'0 and B''0. Journal of Physics and Chemistry of Solids, 50(3), 263-268. https://doi.org/10.1016/0022- 3697(89)90486 -1 · DOI
  22. Green, E. C. R., White, R. W., Diener, J. F. A., Powell, R., Holland, T. J. B., & Palin, R. M. (2016). Activity-composition relations for the calculation of partial melting equilibria in metabasic rocks. Journal of Metamorphic Geology, 34(9), 845-869. https://doi.org/10.1111/ jmg.12211 · DOI
  23. Guevara, V. E., & Caddick, M. J. (2016). Shooting at a moving target: Phase equilibria modelling of high-temperature metamorphism. Journal of Metamorphic Geology, 34(3), 209-235. https://doi. org/10.1111/jmg.12179 · DOI
  24. Hanmer, S. (1988). Ductile thrusting at mid-crustal level, southwest- ern Grenville Province. Canadian Journal of Earth Sciences, 25, 1049-1059. https://doi.org/10.1139/e88-102 · DOI · Paper page
  25. Henry, D. J., Guidotti, C. V., & Thomson, J. A. (2005). The Ti- saturation surface for low-to-medium pressure metapelitic biotites: Implications for geothermometry and Ti-substitution mechanisms. American Mineralogist, 90(2-3), 316-328. https://doi.org/10.2138/ am.2005.1498 · DOI
  26. Holland, T. J. B., & Powell, R. (1998). An internally consistent thermodynamic data set for phases of petrological interest. Journal of Metamorphic Geology, 16(3), 309-343. https://doi. org/10.1111/j.1525-1314.1998.00140.x · DOI · Paper page
  27. Holland, T. J. B., & Powell, R. (2011). An improved and extended internally consistent thermodynamic dataset for phases of pe- trological interest, involving a new equation of state for solids. Journal of Metamorphic Geology, 29(3), 333-383. https://doi. org/10.1111/j.1525-1314.2010.00923.x · DOI
  28. Kohn, M. J., & Spear, F. (2000). Retrograde net transfer reaction in- surance for pressure-temperature estimates. Geology, 28(12), 1127- 1130. https://doi.org/10.1130/0091-7613(2000)28<1127:RNTRI F>2.0.CO;2 · DOI
  29. Lanari, P., & Duesterhoeft, E. (2019). Modeling metamorphic rocks using equilibrium thermodynamics and internally consistent da- tabases: Past achievements, problems and perspectives. Journal of Petrology, 60(1), 19-56. https://doi.org/10.1093/petro logy/ egy105 · DOI
  30. Lanari, P., & Engi, M. (2017). Local bulk composition effects on metamorphic mineral assemblages. Reviews in Mineralogy and Geochemistry, 83, 55-102. https://doi.org/10.2138/ rmg.2017.83.3 · DOI
  31. Lanari, P., Giuntoli, F., Loury, C., Burn, M., & Engi, M. (2017). An inverse modeling approach to obtain P-T conditions of metamor- phic stages involving garnet growth and resorption. European Journal of Mineralogy, 29, 181-199. https://doi.org/10.1127/ ejm/2016/0029-2597 · DOI
  32. Lanari, P., Vho, A., Bovay, T., Airaghi, L., & Centrella, S. (2019). Quantitative compositional mapping of mineral phases by elec- tron probe micro-analyser. Geological Society Special Publication, 478(1), 39-63. https://doi.org/10.1144/SP478. · DOI
  33. Lanari, P., Vidal, O., De Andrade, V., Dubacq, B., Lewin, E., Grosch, E. G., & Schwartz, S. (2014). XMapTools: A MATLAB®-based program for electron microprobe X-ray image processing and geo- thermobarometry. Computers & Geosciences, 62, 227-240. https:// doi.org/10.1016/j.cageo.2013.08.010 · DOI
  34. Lanari, P., Wagner, T., & Vidal, O. (2014). A thermodynamic model for di-trioctahedral chlorite from experimental and natural data in the system MgO-FeO-Al2O3-SiO2-H2O: applications to P-T sections and geothermometry. Contributions to Mineralogy and Petrology, 167-968, https://doi.org/10.1007/s0041 0-014-0968-8 · DOI
  35. Markley, M. J., Dunn, S. R., Jercinovic, M. J., Peck, W. H., & Williams, M. L. (2018). Monazite U-Th-Pb geochronology of the Central Metasedimentary Belt Boundary Zone (CMBbz), Grenville Province, Ontario Canada. Canadian Journal of Earth Sciences, 55(9), 1063-1078. https://doi.org/10.1139/cjes-2018-0039 · DOI · Paper page
  36. McEachern, S. J., & van Breemen, O. (1993). Age of deformation within the Central Metasedimentary Belt boundary thrust zone, southwest Grenville Orogen: Constraints on the collision of the Mid- Proterozoic Elzevir terrane. Canadian Journal of Earth Sciences, 30, 1155-1165. https://doi.org/10.1139/e93-098 · DOI · Paper page
  37. Nelder, J. A., & Mead, R. (1965). A simplex method for function minimization. The Computer Journal, 7(4), 308-313. https://doi. org/10.1093/comjn l/7.4.308 · DOI · Paper page
  38. Palin, R. M., Weller, O. M., Waters, D. J., & Dyck, B. (2016). Quantifying geological uncertainty in metamorphic phase equilibria modelling: A Monte Carlo assessment and implications for tectonic interpretations. Geoscience Frontiers, 7(4), 591-607. https://doi. org/10.1016/j.gsf.2015.08.005 · DOI · Paper page
  39. Pattison, D. R. M., & Spear, F. S. (2018). Kinetic control of stauro- lite-Al 2 SiO 5 mineral assemblages: Implications for Barrovian and Buchan metamorphism. Journal of Metamorphic Geology, 36(6), 667-690. https://doi.org/10.1111/jmg.12302 · DOI
  40. Pattison, D. R. M., & Tinkham, D. K. (2009). Interplay between equilibrium and kinetics in prograde metamorphism of pelites: An example from the Nelson aureole, British Columbia. Journal of Metamorphic Geology, 27(4), 249-279. https://doi. org/10.1111/j.1525-1314.2009.00816.x · DOI
  41. Powell, R., Holland, T., & Worley, B. (1998). Calculating phase diagrams involving solid solutions via non-lin- ear equations, with examples using THERMOCALC. Journal of Metamorphic Geology, 16, 577-588. https://doi. org/10.1111/j.1525-1314.1998.00157.x · DOI
  42. Santos, C. A., Moraes, R., & Szabó, G. A. J. (2019). A com- parison between phase diagram modelling of metamafic rocks and experimental and independent thermobarometric data. Lithos, 340-341, 108-123. https://doi.org/10.1016/j. lithos.2019.04.024 · DOI
  43. Shrestha, S., Larson, K. P., Duesterhoeft, E., Soret, M., & Cottle, J. M. (2019). Thermodynamic modelling of phosphate minerals and its implications for the development of P-T-t histories: A case study in garnet -monazite bearing metapelites. Lithos, 334-335, 141-160. https://doi.org/10.1016/j.lithos.2019.03.021 · DOI
  44. Spear, F. S., Pattison, D. R. M., & Cheney, J. T. (2016). The meta- morphosis of metamorphic petrology. Geological Society of America Special Paper, 523(02), 31-74. https://doi. org/10.1130/2016.2523(02 · DOI
  45. Spear, F. S., & Pyle, J. M. (2010). Theoretical modeling of monazite growth in a low-Ca metapelite. Chemical Geology, 273(1-2), 111- 119. https://doi.org/10.1016/j.chemg eo.2010.02.016 · DOI
  46. Stüwe, K. (1997). Effective bulk composition changes due to cooling: A model predicting complexities in retrograde reaction textures. Contributions to Mineralogy and Petrology, 129(1), 43-52. https:// doi.org/10.1007/s0041 00050322 · DOI
  47. Tajčmanová, L., Konopásek, J., & Schulmann, K. (2006). Thermal evolution of the orogenic lower crust during exhumation within a thickened Moldanubian root of the Variscan belt of Central Europe. Journal of Metamorphic Geology, 24(2), 119-134. https://doi. org/10.1111/j.1525-1314.2006.00629.x · DOI
  48. Waters, D. J., & Lovegrove, D. P. (2002). Assessing the extent of dis- equilibrium and overstepping of prograde metamorphic reactions in metapelites from the Bushveld Complex aureole, South Africa. Journal of Metamorphic Geology, 20(1), 135-149. https://doi. org/10.1046/j.0263-4929.2001.00350.x · DOI · Paper page
  49. White, R. W., Powell, R., & Holland, T. J. B. (2007). Progress relat- ing to calculation of partial melting equilibria for metapelites. Journal of Metamorphic Geology, 25(5), 511-527. https://doi. org/10.1111/j.1525-1314.2007.00711.x · DOI
  50. White, R. W., Powell, R., Holland, T. J. B., Johnson, T. E. & Green, E. C. R. (2014). New mineral activity-composition relations for thermodynamic calculations in metapelitic systems. Journal of Metamorphic Geology, 32(3), 261-286. https://doi.org/10.1111/ jmg.12071 · DOI
  51. Yakymchuk, C. (2017). Applying phase equilibria modelling to meta- morphic and geological processes: Recent developments and future potential. Geoscience Canada, 44(1), 27. https://doi.org/10.12789 / geoca nj.2017.44.114 · DOI

Cited by

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Authors
Duesterhoeft, E., & Lanari, P.
Affiliations
  • Christian-Albrechts-Universität zu Kiel (DE)
  • University of Bern (CH)
Corresponding author
Duesterhoeft, Erik
ORCID
Venue
Journal of Metamorphic Geology
Publisher
Wiley
Published
2020-06
Volume
38
Issue
5
Pages
527-551
ISSN
  • 0263-4929 (ISSN-L)
  • 1525-1314
DOI
10.1111/jmg.12538
OpenAlex
W3034761246
Cited by
41
References
2
Citations by year
2026: 7 · 2025: 8 · 2024: 4 · 2023: 8 · 2022: 6 · 2021: 5 · 2020: 3
FWCI
3.37
Type
journal article
Language
en
Open access
Licence
Locations
  • Journal of Metamorphic Geology (publishedVersion, cc-by-nc-nd)
  • BORIS (University Library Bern) (submittedVersion, cc-by-nc-nd)
  • Geo-Leo e-docs (Deutsche Initiative für Netzwerkinformation) (submittedVersion, cc-by-nc-nd)
  • FID-GEO SUB
Funders
Deutsche Forschungsgemeinschaft (DU1603/1‐1)
Topics
  • Physical Sciences › Earth and Planetary Sciences › Geophysics › Geological and Geochemical Analysis
  • Physical Sciences › Engineering › Mechanical Engineering › Metallurgical Processes and Thermodynamics
  • Physical Sciences › Earth and Planetary Sciences › Geochemistry and Petrology › Mineralogy and Gemology Studies
Keywords
Gibbs free energy minimization, mineral assemblages, mineral composition, electron probe microanalysis, pressure-temperature conditions, metamorphic rock

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