High pressure equations of state with applications to the lower mantle and core

Stacey, Frank D.; Davis, Paul M.

doi:10.1016/j.pepi.2004.02.003

Cited by 228 publications

(240 citation statements)

References 69 publications

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“…Jackson [1998] concluded that third-order Eulerian finite strain isotherms and isentropes are adequate for the range of strains encountered in the lower mantle and further showed that hot finite strain isentropes are consistent with the Mie-Grüneisen-Debye description of thermal pressure and a cold isothermal third-order compression. If we then fix a reference temperature and composition for the lower mantle using a 1D seismic reference model and choose the right mineral physics data, it is straightforward to obtain the sensitivities analytically or numerically [Karato, 1993;Stacey and Davis, 2004].…”

Section: Sensitivities Of Wave Speeds To Temperature and Compositionmentioning

confidence: 99%

Towards a quantitative interpretation of global seismic tomography

Trampert

Hilst

2005

Geophysical Monograph Series

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We review the success of seismic tomography in delineating spatial variations in the propagation speed of seismic waves on length scales from several hundreds to many thousands of kilometers. In most interpretations these wave speed variations are thought to reflect variations in temperature. Careful consideration of shear wave, bulk sound, and, most recently, density variations is, however, producing increasingly compelling evidence for chemical heterogeneity (that is, spatial variations in bulk major element composition) having a first-order effect on the lateral variations in mass density and elasticity of the mantle. This has profound consequences for our understanding of mantle dynamics and the thermochemical evolution of our planet. We argue that the quantitative integration of constraints from seismology, mineral physics, and geodynamics, which underlies the inference of thermochemical parameters, requires careful uncertainty analyses and should move away from emphasizing visually pleasing images and single, nonunique solutions.

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Section: Sensitivities Of Wave Speeds To Temperature and Compositionmentioning

confidence: 99%

Towards a quantitative interpretation of global seismic tomography

Trampert

Hilst

2005

Geophysical Monograph Series

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“…Figure 7 shows the experimental data in K ′ -space (Stacey and Davis 2004), where it becomes clear that K ′ increasingly diverges from the MgSiO 3 trend Murakami et al 2007), and from the K ′ of the lower mantle. Extrapolation from the experimental MgSiO 3 and (MgSi) 0.9 (FeAl) 0.1 O 3 data requires increasing non-ideality with pressure to avoid negative values of K ′ for the FeAlO 3 endmember (see Eq.…”

Section: The Bridgmanite Solid Solutionmentioning

confidence: 99%

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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“…This observation is crucial, but often forgotten, when combining seismic tomography and mineral physics data to estimate the thermo-chemical structure of the mantle. Equation-of-state modeling (e.g., Karato & Karki, 2001;Trampert et al, 2001;Stacey & Davis, 2004;Stixrude & Lithgow-Bertelloni, 2005;2011) of mineral physics data allows us to infer sensitivities (partial derivatives) of velocity variations to temperature and chemical variations. To make the conversion, amplitude and position of the seismic anomalies has to be known with great precision.…”

Section: Isotropic Velocity Tomographymentioning

confidence: 99%