Does non-hydrostatic stress influence the equilibrium of metamorphic reactions?

Hobbs, B. E.; Ord, Alison

doi:10.1016/j.earscirev.2016.08.013

Cited by 30 publications

(41 citation statements)

References 158 publications

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“…It should also be possible to design ab initio simulations to test the full anisotropic elastic model. Such work would provide a better understanding of the variation of shear modulus within solid solutions, and more generally the effect of deviatoric stresses on the thermodynamics and elasticity of natural rocks (Hobbs and Ord 2016). (Thomson et al 1996;Brodholt 2000;Caracas and Cohen 2005;Panero et al 2006).…”

Section: Discussionmentioning

confidence: 99%

“…The models developed are typically still parameterised in terms of the Gibbs free energy, but the parameterizations include a consideration of the elastic energy required to match the volumes of the endmember lattices at 1 bar (e.g., Ferreira et al 1988;Ganguly et al 1996;Urusov 2000). In this study, I show that this technique is equivalent to reformulating nonideality as a function of the Helmholtz free energy, which has long been recognised as a natural potential to use for solid-solid reactions (e.g., Landau 1937;Dove 1997;Hobbs and Ord 2016).…”

Section: Introductionmentioning

confidence: 99%

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The elastic solid solution model for minerals at high pressures and temperatures

Myhill

2018

Contrib Mineral Petrol

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Non-ideality in mineral solid solutions affects their elastic and thermodynamic properties, their thermobaric stability, and the equilibrium phase relations in multiphase assemblages. At a given composition and state of order, non-ideality in minerals is typically modelled via excesses in Gibbs free energy which are either constant or linear with respect to pressure and temperature. This approach has been extremely successful when modelling near-ideal solutions. However, when the lattice parameters of the solution endmembers differ significantly, extrapolations of thermodynamic properties to high pressures using these models may result in significant errors. In this paper, I investigate the effect of parameterising solution models in terms of the Helmholtz free energy, treating volume (or lattice parameters) rather than pressure as an independent variable. This approach has been previously applied to models of order-disorder, but the implications for the thermodynamics and elasticity of solid solutions have not been fully explored. Solid solution models based on the Helmholtz free energy are intuitive at a microscopic level, as they automatically include the energetic contribution from elastic deformation of the endmember lattices. A chemical contribution must also be included in such models, which arises from atomic exchange within the solution. Derivations are provided for the thermodynamic properties of n-endmember solutions. Examples of the use of the elastic model are presented for the alkali halides, pyroxene, garnet, and bridgmanite solid solutions. Elastic theory provides insights into the microscopic origins of non-ideality in a range of solutions, and can make accurate predictions of excess enthalpies, entropies, and volumes as a function of volume and temperature. In solutions where experimental data are sparse or contradictory, the Helmholtz free energy approach can be used to assess the magnitude of excess properties and their variation as a function of pressure and temperature. The formulation is expected to be useful for geochemical and geophysical studies of the Earth and other planetary bodies.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The elastic solid solution model for minerals at high pressures and temperatures

Myhill

2018

Contrib Mineral Petrol

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“…The quantity

\overset{P}{true}

is known as the mean stress; the mechanical pressure which, by convention, is always positive, is the magnitude of

\overset{P}{true}

. Notice that the mean stress is simply defined by a piece of algebra; it is an invariant of the stress tensor but is not a thermodynamic state variable and its use as a thermodynamic state variable can lead to large errors in some circumstances (Hobbs & Ord, ; Sekerka & Cahn, ).…”

Section: Some Thermodynamicsmentioning

confidence: 99%

“…The outcome of these statements is that for any crystalline structure to be at equilibrium, which means that the structure is stable in the sense that any small departure from equilibrium will return the structure to its stable form, any departure from equilibrium, will result in one or more of the following adjustments in order to minimize the elastic energy density (see Hobbs & Ord, for discussion and references): If it is possible, as in solid solution series, the material will change its chemical composition so that elastic strains generated by the change in chemistry reduce the local elastic stored energy. Such chemically induced elastic strains are sometimes called eigen‐strains (Mishin, ). If it is possible, as in many mineral systems, the material will change its state of order/disorder so that elastic strains generated by the change in order reduce the local elastic stored energy. If it is possible, as in many mineral systems that develop symplectites, some form of exsolution or compositional patterning develops so that elastic strains generated by the new arrangement of mineral phases reduce the local elastic stored energy. In minerals such as quartz, and also in minerals capable of solid solution, geometrically necessary dislocations, expressed as lattice curvature or subgrains, are introduced to minimize the misfit strains. …”

Section: Some Thermodynamicsmentioning

confidence: 99%

Pressure and equilibrium in deforming rocks

Hobbs

Ord

2017

Journal Metamorphic Geology

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It is widely proposed that tectonic pressure (the difference between the mean stress and the pressure arising from a lithostatic load) is large, and has a significant influence on mineral phase equilibria in deforming metamorphic rocks. The implication/assertion is that the mean stress is equivalent to the thermodynamic pressure which characterizes mineral phase equilibria and is a measure of how the energy changes as the volume changes. We distinguish two useful thermodynamic pressures. The first is an equilibrium thermodynamic pressure, characteristic of non‐dissipative systems and related directly to equilibrium values of the chemical potentials that define stable, equilibrium phase assemblages. The second is a non‐equilibrium thermodynamic pressure characteristic of dissipative systems with zero net entropy production and related to non‐equilibrium chemical potentials that define stable non‐equilibrium phase assemblages. In many dissipative metamorphic systems discussed in the literature, the concepts of thermodynamic pressure and chemical potential are not usefully defined because the system is not at equilibrium and/or no volume change is involved in the deformation. The conclusion of this note is that the influence of tectonic pressure on phase equilibria is minor. The role of tectonic pressure is an important issue but is only relevant to phase equilibrium when an equilibrium thermodynamic pressure can be defined; in such cases, the influence of tectonic pressure is small compared to many proposals in the literature. Except for elastic deformations, the mean stress is not useful in discussing mineral phase equilibrium.

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“…The dynamics of hydrothermal ore systems is then fundamentally linked to these episodic slip events in faults and shear zones, which have been qualitatively compared to non-equilibrium open chemical reactors (Hobbs & Ord, 2016). A quantitative description of the complex Thermo-Hydro-Mechanical-Chemical couplings taking place in these environments have been formulated as a multi-physics oscillator occurring in shear zones under constant stress boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Episodic mineralising fluid injection through chemical shear zones

Poulet

Alevizos²,

Veveakis³

et al. 2018

ASEG Extended Abstracts

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SUMMARYThe nature of the geological mechanisms allowing mineralising fluids to flow from depth and form localized mineral deposits is uncertain and a matter of debate. Traditional assumptions of fluids travelling through highly permeable faults raise interesting questions about the existence of highly permeable faults at depths below the brittle-ductile transition, for example. A recent model of multiphysics oscillation can explain the behaviour of impermeable shear zones in such environments, under specific conditions where temperature sensitive endothermal reactions trigger in-situ release of fluids that lubricate the fault and lead to their reactivation. The response of such systems can be of various nature, including slow creep, one-off reactivation events, or episodic reactivation events during which the permeability increases by several orders of magnitudes and allows fluids from depth to flow upwards. In this contribution, we review briefly the previous studies on this chemo-mechanical oscillator and place the findings in the context of mineral exploration. We extend the parameter sensitivity analysis to the main two dimensionless parameters controlling the chemical reactions, the Arrhenius and Damköhler numbers, to understand how they affect the location of episodic slip instabilities in the global parameter space. We show that lower values of the Damköhler number reduce the range of Gruntfest values in which the oscillator operates and we propose some fitting relationships between the main parameters in various interesting areas of the parameter space.

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Does non-hydrostatic stress influence the equilibrium of metamorphic reactions?

Cited by 30 publications

References 158 publications

The elastic solid solution model for minerals at high pressures and temperatures

The elastic solid solution model for minerals at high pressures and temperatures

Pressure and equilibrium in deforming rocks

Episodic mineralising fluid injection through chemical shear zones

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