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Dynamics and thermodynamics of magma mixing: Insights from a simple exploratory model

  • Frank J. Spera EMAIL logo , Jason S. Schmidt , Wendy A. Bohrson and Guy A. Brown
Published/Copyright: March 4, 2016
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American Mineralogist
From the journal American Mineralogist Volume 101 Issue 3

Abstract

The mixing of magmas of distinct temperature, bulk composition, mineralogy, and physical properties plays a central role in explaining the diversity of magma types on Earth and in explaining the growth of continental and oceanic crust. Magma mixing is also of practical importance. For example, the mixing of distinct magmas has been cited as an important process in creation of economically important horizons in layered intrusions as well as a triggering mechanism for initiation of volcanic eruptions. The motivation for better quantifying the dynamics and thermodynamics of magma mixing and its attendant plutonic and volcanic products is clear. The degree of magma mixing, which spans a continuum from mingling to complete hybridization, depends upon initial and boundary conditions, magma properties, driving forces, and time available for mixing. Magma mingling produces a heterogeneous mixture of discrete clumps of the end-member magmas, whereas complete hybridization involves the thermodynamic equilibration of two distinct magmas to form a third. Qualitatively, mixing occurs via reduction in the size of compositional heterogeneities (i.e., clumps) through stretching and folding by viscous flow, followed by homogenization, once shear has reduced the size of compositional anomalies to diffusive length scales. Quantification of this process relies on two statistical measures: the linear scale of segregation (Λ) defined as the spatial integral of the compositional correlation function related to the size-distribution of the segregated clumps within the mixture, and the intensity of segregation (I) a measure that quantifies how much the composition at each location differs from the average. The mixing dynamics of a layered system are analyzed in terms of the parameters governing mixing (Rayleigh, Lewis, and buoyancy numbers and viscosity ratio) to estimate how the timescale for magma hybridization, τH, compares to solidification, recharge, diffusive, and assimilation timescales. This analysis illustrates that hybridization times can be shorter than or comparable to thermal, solidification, and replenishment timescales; thus, formation of hybridized or nearly hybridized magmas is one anticipated outcome of mixing. The machinery of thermodynamics can be used to compute the hybrid magma state. An exploratory model for the thermochemistry of hybridization is developed based on binary eutectic phase relations and thermodynamics. Eight thermodynamic parameters define the phase diagram and associated energetics, and six parameters (initial temperatures, compositions, mass ratio of mixing magmas, and an enthalpy parameter) are necessary and sufficient to determine the state of hybrid magma uniquely. While relevant combinations of 14 thermodynamic and mixing parameters might suggest that the number of mixing outcomes (i.e., products) is too high to systematize, Monte Carlo simulations using the exploratory model document how millions of arbitrary initial states evolve into five possible final (mixed) states. Such an analysis implies that a magma mixing taxonomy that defines possible mixed product states can be developed and tied to petrologic indicators of mixing. Additional insights gained from this exploratory model that are supported by independent results from a multicomponent, multiphase thermodynamic model of magma mixing (Magma Chamber Simulator) include: (1) the proclivity of invariant point hybrid states, which may explain some instances of compositionally monotonous melts associated with mixed magma eruptions; (2) a surprising thermal effect such that the temperature of hybridized magma can be significantly less than the initial temperature of either of the mixing magmas. This type of magma mixing may result in crystal resorption, thus invalidating an assumption that resorption textures in crystals are typically the result of a magma heating event; (3) illustration of the differing effects of stoped block temperature and composition on hybrid magma temperature and phase state; and (4) illustration of a cessation of crystallization effect that may pertain to the MORB pyroxene “paradox.” Differences between adiabatic or R-hybridization and diabatic or RFC-hybridization are also explored. The model can be used to elucidate the thermodynamic principles underlying magma mixing in the hybridization limit. These principles are of general applicability and carry over to more compositionally complicated systems.

Keywords: Magma mixing; hybridization; thermodynamics; recharge

Special collection papers can be found online at http://www.minsocam.org/MSA/AmMin/special-collections.html.

Acknowledgments

We thank R. Wiebe, K. Putrika, and C. Miller for useful comments on earlier versions of this work. Support from the National Science Foundation grants EAR-0810127 and EAR-1427737 is gratefully acknowledged.

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  1. Manuscript handled by Calvin Miller.

Received: 2015-1-15
Accepted: 2015-10-27
Published Online: 2016-3-4
Published in Print: 2016-3-1

© 2016 by Walter de Gruyter Berlin/Boston

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  1. Editorial
  2. The most-cited journal in mineralogy and petrology (and what scientists can learn from baseball)
  3. Fluids in the Crust
  4. Fluids in the crust during regional metamorphism: Forty years in the Waterville limestone
  5. Research Article
  6. Remanent magnetization, magnetic coupling, and interface ionic configurations of intergrown rhombohedral and cubic Fe-Ti oxides: A short survey
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  13. Special Collection: Advances in Ultrahigh-Pressure Metamorphism
  14. Multi-stage barite crystallization in partially melted UHP eclogite from the Sulu belt, China
  15. Spinels Renaissance: The Past, Present, and Future of those Ubiquitous Minerals and Materials
  16. Crystal chemistry of spinels in the system MgAl2O4-MgV2O4-Mg2VO4
  17. Spinels Renaissance: The Past, Present, and Future of those Ubiquitous Minerals and Materials
  18. Magnetite spherules in pyroclastic iron ore at El Laco, Chile
  19. Special Collection: Apatite: A Common Mineral, Uncommonly Versatile
  20. Evidence for dissolution-reprecipitation of apatite and preferential LREE mobility in carbonatite-derived late-stage hydrothermal processes
  21. Special Collection: Apatite: A Common Mineral, Uncommonly Versatile
  22. Compositional variation of apatite from rift-related alkaline igneous rocks of the Gardar Province, South Greenland
  23. Special Collection: Perspectives on Origins and Evolution of Crustal Magmas
  24. Dynamics and thermodynamics of magma mixing: Insights from a simple exploratory model
  25. Special Collection: From Magmas to Ore Deposits
  26. Geochemistry, petrologic evolution, and ore deposits of the Miocene Bodie Hills Volcanic Field, California and Nevada
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  28. Recognizing sulfate and phosphate complexes chemisorbed onto nanophase weathering products on Mars using in-situ and remote observations
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  30. Crystallographic orientation relationships in host–inclusion systems: New insights from large EBSD data sets
  31. Research Article
  32. In-situ infrared spectroscopic studies of hydroxyl in amphiboles at high pressure
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  35. Research Article
  36. Equation of state of the high-pressure Fe3O4 phase and a new structural transition at 70 GPa
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  38. Reflectance spectroscopy of chromium-bearing spinel with application to recent orbital data from the Moon
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  40. Temperature dependences of the hyperfine parameters of Fe2+ in FeTiO3 as determined by 57Fe-Mössbauer spectroscopy
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  43. Research Article
  44. New Mineral Names
https://doi.org/10.2138/am-2016-5305
Keywords for this article
Magma mixing; hybridization; thermodynamics; recharge

Articles in the same Issue

  1. Editorial
  2. The most-cited journal in mineralogy and petrology (and what scientists can learn from baseball)
  3. Fluids in the Crust
  4. Fluids in the crust during regional metamorphism: Forty years in the Waterville limestone
  5. Research Article
  6. Remanent magnetization, magnetic coupling, and interface ionic configurations of intergrown rhombohedral and cubic Fe-Ti oxides: A short survey
  7. Research Article
  8. Are covalent bonds really directed?
  9. Dana Medal Paper
  10. Constraints on the early delivery and fractionation of Earth’s major volatiles from C/H, C/N, and C/S ratios
  11. Crossroads in Earth and Planetary Materials
  12. Octahedral chemistry of 2:1 clay minerals and hydroxyl band position in the near-infrared: Application to Mars
  13. Special Collection: Advances in Ultrahigh-Pressure Metamorphism
  14. Multi-stage barite crystallization in partially melted UHP eclogite from the Sulu belt, China
  15. Spinels Renaissance: The Past, Present, and Future of those Ubiquitous Minerals and Materials
  16. Crystal chemistry of spinels in the system MgAl2O4-MgV2O4-Mg2VO4
  17. Spinels Renaissance: The Past, Present, and Future of those Ubiquitous Minerals and Materials
  18. Magnetite spherules in pyroclastic iron ore at El Laco, Chile
  19. Special Collection: Apatite: A Common Mineral, Uncommonly Versatile
  20. Evidence for dissolution-reprecipitation of apatite and preferential LREE mobility in carbonatite-derived late-stage hydrothermal processes
  21. Special Collection: Apatite: A Common Mineral, Uncommonly Versatile
  22. Compositional variation of apatite from rift-related alkaline igneous rocks of the Gardar Province, South Greenland
  23. Special Collection: Perspectives on Origins and Evolution of Crustal Magmas
  24. Dynamics and thermodynamics of magma mixing: Insights from a simple exploratory model
  25. Special Collection: From Magmas to Ore Deposits
  26. Geochemistry, petrologic evolution, and ore deposits of the Miocene Bodie Hills Volcanic Field, California and Nevada
  27. Research Article
  28. Recognizing sulfate and phosphate complexes chemisorbed onto nanophase weathering products on Mars using in-situ and remote observations
  29. Research Article
  30. Crystallographic orientation relationships in host–inclusion systems: New insights from large EBSD data sets
  31. Research Article
  32. In-situ infrared spectroscopic studies of hydroxyl in amphiboles at high pressure
  33. Research Article
  34. Confined water in tunnel nanopores of sepiolite: Insights from molecular simulations
  35. Research Article
  36. Equation of state of the high-pressure Fe3O4 phase and a new structural transition at 70 GPa
  37. Research Article
  38. Reflectance spectroscopy of chromium-bearing spinel with application to recent orbital data from the Moon
  39. Research Article
  40. Temperature dependences of the hyperfine parameters of Fe2+ in FeTiO3 as determined by 57Fe-Mössbauer spectroscopy
  41. Letter
  42. Accurate predictions of iron redox state in silicate glasses: A multivariate approach using X-ray absorption spectroscopy
  43. Research Article
  44. New Mineral Names
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