Special Issue "Mineral Physics—In Memory of Orson Anderson"

A special issue of Minerals (ISSN 2075-163X). This special issue belongs to the section "Crystallography and Physical Chemistry of Minerals".

Deadline for manuscript submissions: closed (15 October 2019).

Special Issue Editor

Prof. Dr. Robert Cooper Liebermann
E-Mail Website
Guest Editor
Department of Geosciences and Mineral Physics Institute, Stony Brook University, Stony Brook, NY 11794-2100, USA
Interests: elasticity of minerals at high pressure and temperature; ultrasonic interferometry; multi-anvil, high-pressure apparatus; synchrotron X-radiation

Special Issue Information

Dear Colleagues,

This Special Issue is dedicated to Professor Orson L. Anderson on the occasion of his 95th birthday. This Special Issue is planned to include a representative group of experimental and theoretical papers in the field of mineral physics (and also rock physics).

Mineral physics is the study of mineralogical problems through the application of condensed matter physics. In reality, mineral physicists use not only physics, but also solid-state chemistry; they study not only minerals, but all materials related to natural minerals (e.g., structural analogs, but also glasses, melts and fluids).

We welcome contributions from all practitioners of this scientific discipline.

Please confirm your interest in submitting a paper directly to the Guest Editor.

Prof. Dr. Robert Cooper Liebermann
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Minerals is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (16 papers)

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Editorial

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Open AccessEditorial
My Career as a Mineral Physicist at Stony Brook: 1976–2019
Minerals 2019, 9(12), 761; https://doi.org/10.3390/min9120761 - 07 Dec 2019
Abstract
In 1976, I took up a faculty position in the Department of Geosciences of Stony Brook University. Over the next half century, in collaboration with graduate students from the U.S., China and Russia and postdoctoral colleagues from Australia, France and Japan, we pursued [...] Read more.
In 1976, I took up a faculty position in the Department of Geosciences of Stony Brook University. Over the next half century, in collaboration with graduate students from the U.S., China and Russia and postdoctoral colleagues from Australia, France and Japan, we pursued studies of the elastic properties of minerals (and their structural analogues) at high pressures and temperatures. In the 1980s, together with Donald Weidner, we established the Stony Brook High Pressure Laboratory and the Mineral Physics Institute. In 1991, in collaboration with Alexandra Navrotsky at Princeton University and Charles Prewitt at the Geophysical Laboratory, we founded the NSF Science and Technology Center for High Pressure Research. Full article
(This article belongs to the Special Issue Mineral Physics—In Memory of Orson Anderson)
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Research

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Open AccessArticle
Evaluating the Role of Iron-Rich (Mg,Fe)O in Ultralow Velocity Zones
Minerals 2019, 9(12), 762; https://doi.org/10.3390/min9120762 - 08 Dec 2019
Abstract
The composition of ultralow velocity zones (ULVZs) remains an open question, despite advances in both seismology and experimental work. We investigate the hypothesis of iron-rich (Mg,Fe)O (magnesiowüstite) as a cause of ULVZ seismic signatures. We report new quasi-hydrostatic X-ray diffraction measurements to constrain [...] Read more.
The composition of ultralow velocity zones (ULVZs) remains an open question, despite advances in both seismology and experimental work. We investigate the hypothesis of iron-rich (Mg,Fe)O (magnesiowüstite) as a cause of ULVZ seismic signatures. We report new quasi-hydrostatic X-ray diffraction measurements to constrain the equation of state of (Mg0.06Fe0.94)O with fit parameters V0 = 9.860 ± 0.007 Å3, K0T = 155.3 ± 2.2 GPa, K0T = 3.79 ± 0.11, as well as synchrotron Mössbauer spectroscopy measurements to characterize the high-pressure magnetic and spin state of magnesiowüstite. We combine these results with information from previous studies to calculate the elastic behavior at core–mantle boundary conditions of magnesiowüstite, as well as coexisting bridgmanite and calcium silicate perovskite. Forward models of aggregate elastic properties are computed, and from these, we construct an inverse model to determine the proportions of magnesiowüstite that best reproduce ULVZ observations within estimated mutual uncertainties. We find that the presence of magnesiowüstite can explain ULVZ observations exhibiting 1:2 VP:VS reduction ratios relative to the Preliminary Reference Earth Model (PREM), as well as certain 1:3 VP:VS reductions within estimated uncertainty bounds. Our work quantifies the viability of compositionally distinct ULVZs containing magnesiowüstite and contributes to developing a framework for a methodical approach to evaluating ULVZ hypotheses. Full article
(This article belongs to the Special Issue Mineral Physics—In Memory of Orson Anderson)
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Open AccessArticle
A Simple Derivation of the Birch–Murnaghan Equations of State (EOSs) and Comparison with EOSs Derived from Other Definitions of Finite Strain
Minerals 2019, 9(12), 745; https://doi.org/10.3390/min9120745 - 30 Nov 2019
Abstract
Eulerian finite strain of an elastically isotropic body is defined using the expansion of squared length and the post-compression state as reference. The key to deriving second-, third- and fourth-order Birch–Murnaghan equations-of-state (EOSs) is not requiring a differential to describe the dimensions of [...] Read more.
Eulerian finite strain of an elastically isotropic body is defined using the expansion of squared length and the post-compression state as reference. The key to deriving second-, third- and fourth-order Birch–Murnaghan equations-of-state (EOSs) is not requiring a differential to describe the dimensions of a body owing to isotropic, uniform, and finite change in length and, therefore, volume. Truncation of higher orders of finite strain to express the Helmholtz free energy is not equal to ignoring higher-order pressure derivatives of the bulk modulus as zero. To better understand the Eulerian scheme, finite strain is defined by taking the pre-compressed state as the reference and EOSs are derived in both the Lagrangian and Eulerian schemes. In the Lagrangian scheme, pressure increases less significantly upon compression than the Eulerian scheme. Different Eulerian strains are defined by expansion of linear and cubed length and the first- and third-power Eulerian EOSs are derived in these schemes. Fitting analysis of pressure-scale-free data using these equations indicates that the Lagrangian scheme is inappropriate to describe P-V-T relations of MgO, whereas three Eulerian EOSs including the Birch–Murnaghan EOS have equivalent significance. Full article
(This article belongs to the Special Issue Mineral Physics—In Memory of Orson Anderson)
Open AccessArticle
Thermal Equation of State of Fe3C to 327 GPa and Carbon in the Core
Minerals 2019, 9(12), 744; https://doi.org/10.3390/min9120744 - 30 Nov 2019
Abstract
The density and sound velocity structure of the Earth’s interior is modeled on seismological observations and is known as the preliminary reference Earth model (PREM). The density of the core is lower than that of pure Fe, which suggests that the Earth’s core [...] Read more.
The density and sound velocity structure of the Earth’s interior is modeled on seismological observations and is known as the preliminary reference Earth model (PREM). The density of the core is lower than that of pure Fe, which suggests that the Earth’s core contains light elements. Carbon is one plausible light element that may exist in the core. We determined the equation of state (EOS) of Fe3C based on in situ high-pressure and high-temperature X-ray diffraction experiments using a diamond anvil cell. We obtained the PV data of Fe3C up to 327 GPa at 300 K and 70–180 GPa up to around 2300 K. The EOS of nonmagnetic (NM) Fe3C was expressed by two models using two different pressure scales and the third-order Birch–Murnaghan EOS at 300 K with the Mie–Grüneisen–Debye EOS under high-temperature conditions. The EOS can be expressed with parameters of V0 = 148.8(±1.0) Å3, K0 = 311.1(±17.1) GPa, K0 = 3.40(±0.1), γ0 = 1.06(±0.42), and q = 1.92(±1.73), with a fixed value of θ0 = 314 K using the KBr pressure scale (Model 1), and V0 = 147.3(±1.0) Å3, K0 = 323.0(±16.6) GPa, K0 = 3.43(±0.09), γ0 = 1.37(±0.33), and q = 0.98(±1.01), with a fixed value of θ0 = 314 K using the MgO pressure scale (Model 2). The density of Fe3C under inner core conditions (assuming P = 329 GPa and T = 5000 K) calculated from the EOS is compatible with the PREM inner core. Full article
(This article belongs to the Special Issue Mineral Physics—In Memory of Orson Anderson)
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Open AccessArticle
Viscoelastic Behaviour from Complementary Forced-Oscillation and Microcreep Tests
Minerals 2019, 9(12), 721; https://doi.org/10.3390/min9120721 - 21 Nov 2019
Abstract
There is an important complementarity between experimental methods for the study of high-temperature viscoelasticity in the time and frequency domains that has not always been fully exploited. Here, we show that the parallel processing of forced-oscillation data and microcreep records, involving the consistent [...] Read more.
There is an important complementarity between experimental methods for the study of high-temperature viscoelasticity in the time and frequency domains that has not always been fully exploited. Here, we show that the parallel processing of forced-oscillation data and microcreep records, involving the consistent use of either Andrade or extended Burgers creep function models, yields a robust composite modulus-dissipation dataset spanning a broader range of periods than either technique alone. In fitting this dataset, the alternative Andrade and extended Burgers models differ in their partitioning of strain between the anelastic and viscous contributions. The extended Burgers model is preferred because it involves a finite range of anelastic relaxation times and, accordingly, a well-defined anelastic relaxation strength. The new strategy offers the prospect of better constraining the transition between transient and steady-state creep or, equivalently, between anelastic and viscous behaviour. Full article
(This article belongs to the Special Issue Mineral Physics—In Memory of Orson Anderson)
Open AccessArticle
Effect of Carbon on the Volume of Solid Iron at High Pressure: Implications for Carbon Substitution in Iron Structures and Carbon Content in the Earth’s Inner Core
Minerals 2019, 9(12), 720; https://doi.org/10.3390/min9120720 - 20 Nov 2019
Abstract
: Understanding the effect of carbon on the density of hcp (hexagonal-close-packed) Fe-C alloys is essential for modeling the carbon content in the Earth's inner core. Previous studies have focused on the equations of state of iron carbides that may not be applicable [...] Read more.
: Understanding the effect of carbon on the density of hcp (hexagonal-close-packed) Fe-C alloys is essential for modeling the carbon content in the Earth's inner core. Previous studies have focused on the equations of state of iron carbides that may not be applicable to the solid inner core that may incorporate carbon as dissolved carbon in metallic iron. Carbon substitution in hcp-Fe and its effect on the density have never been experimentally studied. We investigated the compression behavior of Fe-C alloys with 0.31 and 1.37 wt % carbon, along with pure iron as a reference, by in-situ X-ray diffraction measurements up to 135 GPa for pure Fe, and 87 GPa for Fe-0.31C and 109 GPa for Fe-1.37C. The results show that the incorporation of carbon in hcp-Fe leads to the expansion of the lattice, contrary to the known effect in body-centered cubic (bcc)-Fe, suggesting a change in the substitution mechanism or local environment. The data on axial compressibility suggest that increasing carbon content could enhance seismic anisotropy in the Earth’s inner core. The new thermoelastic parameters allow us to develop a thermoelastic model to estimate the carbon content in the inner core when carbon is incorporated as dissolved carbon hcp-Fe. The required carbon contents to explain the density deficit of Earth’s inner core are 1.30 and 0.43 wt % at inner core boundary temperatures of 5000 K and 7000 K, respectively. Full article
(This article belongs to the Special Issue Mineral Physics—In Memory of Orson Anderson)
Open AccessArticle
A Paris-Edinburgh Cell for High-Pressure and High-Temperature Structure Studies on Silicate Liquids Using Monochromatic Synchrotron Radiation
Minerals 2019, 9(11), 715; https://doi.org/10.3390/min9110715 - 19 Nov 2019
Abstract
A Paris-Edinburgh press combined with a multi-channel collimator assembly has been commissioned at the GeoSoilEnviro Center for Advanced Radiation Sources (GSECARS) beamline for monochromatic X-ray scattering, with an emphasis on studying low-Z liquids, especially silicate liquids at high pressure. The Paris-Edinburgh press is [...] Read more.
A Paris-Edinburgh press combined with a multi-channel collimator assembly has been commissioned at the GeoSoilEnviro Center for Advanced Radiation Sources (GSECARS) beamline for monochromatic X-ray scattering, with an emphasis on studying low-Z liquids, especially silicate liquids at high pressure. The Paris-Edinburgh press is mounted on a general-purpose diffractometer, with a pixel array detector mounted on the detector arm. The incident monochromatic undulator beam with energies up to 60 keV is focused both horizontally and vertically to a beam size about 30 × 30 µm. With this setup, background scattering from the surrounding pressure media is completely removed at 2θ angles above 10° for samples larger than 1.05 mm in diameter. Thirty minutes is typically sufficient to collect robust X-ray scattering signals from a 1.6 mm diameter amorphous silicate sample. Cell assemblies for the standard Paris-Edinburgh anvils have been developed and pressures and temperatures up to 7 GPa and 2300 K, respectively, have been maintained steadily over hours. We have also developed a cupped-toroidal Drickamer anvil to further increase pressure and temperature capabilities. The cupped-toroidal Drickamer anvil combines features of a modified Drickamer anvil and the traditional Paris-Edinburgh anvil. Pressures up to 12 GPa have been generated at temperatures up to 2100 K. Full article
(This article belongs to the Special Issue Mineral Physics—In Memory of Orson Anderson)
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Open AccessArticle
Cracked, Porous Rocks and Fluids: Moon and Earth Paradox
Minerals 2019, 9(11), 693; https://doi.org/10.3390/min9110693 - 09 Nov 2019
Abstract
Elastic wave velocities are key parameters in geosciences. In seismology at a large scale, or in seismic exploration at a more local and shallower scale, they were the main source of information for a long time. At the time of the Apollo mission, [...] Read more.
Elastic wave velocities are key parameters in geosciences. In seismology at a large scale, or in seismic exploration at a more local and shallower scale, they were the main source of information for a long time. At the time of the Apollo mission, Anderson explained the unexpected result of very low velocities in Moon surface rocks by an intense cracking resulting from meteoritic impacts. Yet, it was also known that the Q factor was high. This could appear as a paradox. In the shallow layers of the Earth, rocks are porous. These shallow layers are of major importance in the Earth since they contain fluids. This is why velocities are higher and Q values lower in the Earth’s shallow layers than in the Moon’s shallow layers. Cracks have a determining effect on elastic properties because they are very compliant. Fluids also play a key role. Combining poroelasticity and effective elasticity, two independent theories much developed since the time of the Apollo mission, makes it possible to revisit the contrasting results observed in the Moon case and in the Earth case. Experimental results obtained on cracked synthetic glass show that dry cracks result in a strong decrease in velocity. On the other hand, saturated porous limestones exhibit a strong frequency-dependent attenuation when thermally cracked. The presence of fluid is the key factor. Full article
(This article belongs to the Special Issue Mineral Physics—In Memory of Orson Anderson)
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Open AccessArticle
Hydrogen Effect on the Sound Velocities of Upper Mantle Omphacite
Minerals 2019, 9(11), 690; https://doi.org/10.3390/min9110690 - 08 Nov 2019
Abstract
Clinopyroxene (Cpx) is commonly believed to be the best structural water (hydrogen) carrier among all major upper mantle nominally anhydrous minerals (NAMs). In this study, we have measured the single-crystal elastic properties of a Cpx, a natural omphacite with ~710 ppm water at [...] Read more.
Clinopyroxene (Cpx) is commonly believed to be the best structural water (hydrogen) carrier among all major upper mantle nominally anhydrous minerals (NAMs). In this study, we have measured the single-crystal elastic properties of a Cpx, a natural omphacite with ~710 ppm water at ambient pressure (P) and temperature (T) conditions. Utilizing the single-crystal X-ray diffraction (XRD) and electron microprobe data, the unit cell parameters and density were determined as a = 9.603(9) Å, b = 8.774(3) Å, c = 5.250(2) Å, β = 106.76(5)o, V = 255.1(4) Å3, and ρ = 3.340(6) g/cm3. We performed Brillouin spectroscopy experiments on four single crystals along a total of 52 different crystallographic directions. The best-fit single-crystal elastic moduli (Cijs), bulk and shear moduli were determined as: C11 = 245(1) GPa, C22 = 210(2) GPa, C33 = 249.6(9) GPa, C44 = 75.7(9) GPa, C55 = 71.2(5) GPa, C66 = 76(1) GPa, C12 = 85(2) GPa, C13 = 70(1) GPa, C23 = 66(2) GPa, C15 = 8.0(6) GPa, C25 = 6(1) GPa, C35 = 34.7(6) GPa, and C46 = 8.7(7) GPa, KS0 = 125(3) GPa, and G0 = 75(2) GPa, respectively. Compared with the anticipated elastic properties of an anhydrous omphacite with the same chemical composition, our results indicate that the incorporation of ~710 ppm structural water has no resolvable effect on the aggregate elastic properties of omphacite, although small differences (up to ~9 GPa) were observed in C13, C25, C44, and C66. Full article
(This article belongs to the Special Issue Mineral Physics—In Memory of Orson Anderson)
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Open AccessArticle
Equations of State of Simple Solids (Including Pb, NaCl and LiF) Compressed in Helium or Neon in the Mbar Range
Minerals 2019, 9(11), 684; https://doi.org/10.3390/min9110684 - 05 Nov 2019
Abstract
The equations of state measured under ambient temperature in the Mbar range are reviewed, focusing on experiments using diamond anvils cells with a quasi-hydrostatic pressure transmitting medium (helium or neon) and coupled with X-ray diffraction. Equations of state (EoS) parameters are listed with [...] Read more.
The equations of state measured under ambient temperature in the Mbar range are reviewed, focusing on experiments using diamond anvils cells with a quasi-hydrostatic pressure transmitting medium (helium or neon) and coupled with X-ray diffraction. Equations of state (EoS) parameters are listed with an unified pressure metrology for all data. This metrology is based on the efforts made in the 2000s to update the ruby luminescence pressure scale, after the collection of original data. To complete this database, unpublished P-V data for lead (Pb), sodium chloride (NaCl) and lithium fluoride (LiF) are also provided with the same metrology. Systematic effects of the pressure metrology on the EoS parameters are discussed. Full article
(This article belongs to the Special Issue Mineral Physics—In Memory of Orson Anderson)
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Open AccessArticle
Validation of Digital Rock Physics Algorithms
Minerals 2019, 9(11), 669; https://doi.org/10.3390/min9110669 - 31 Oct 2019
Abstract
With a detailed microscopic image of a rock sample, one can determine the corresponding 3-D grain geometry, forming a basis to calculate the elastic properties numerically. The issues which arise in such a calculation include those associated with image resolution, the registration of [...] Read more.
With a detailed microscopic image of a rock sample, one can determine the corresponding 3-D grain geometry, forming a basis to calculate the elastic properties numerically. The issues which arise in such a calculation include those associated with image resolution, the registration of the digital numerical grid with the digital image, and grain anisotropy. Further, there is a need to validate the numerical calculation via experiment or theory. Because of the geometrical complexity of the rock, the best theoretical test employs the Hashin–Shtrikman result that, for an aggregate of two isotropic components with equal shear moduli, the bulk modulus is uniquely determined, independent of the micro-geometry. Similarly, for an aggregate of two isotropic components with a certain combination of elastic moduli defined herein, the Hashin–Shtrikman formulae give a unique result for the shear modulus, independent of the micro-geometry. For a porous, saturated rock, the solid incompressibility may be calculated via an “unjacketed” test, independent of the micro-geometry. Any numerical algorithm proposed for digital rock physics computation should be validated by successfully confirming these theoretical predictions. Using these tests, we validate a previously published staggered-grid finite difference damped time-stepping algorithm to calculate the static properties of digital rock models. Full article
(This article belongs to the Special Issue Mineral Physics—In Memory of Orson Anderson)
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Open AccessArticle
Equations of State for the Deep Earth: Some Fundamental Considerations
Minerals 2019, 9(10), 636; https://doi.org/10.3390/min9100636 - 17 Oct 2019
Abstract
None of the 40+ equations that have been proposed to describe material properties at the pressures of the Earth’s core and mantle have escaped serious criticism. In this paper, some basic algebraic and thermodynamic constraints are reviewed, with the conclusion that the next [...] Read more.
None of the 40+ equations that have been proposed to describe material properties at the pressures of the Earth’s core and mantle have escaped serious criticism. In this paper, some basic algebraic and thermodynamic constraints are reviewed, with the conclusion that the next step should be a re-examination of the relationship between the dependence of the bulk modulus, K, on pressure, P, that is K d K / d P , and the normalized (dimensionless) pressure, P / K . A linear relationship between 1 / K and P / K terminating at the infinite pressure asymptote, at which these quantities become equal, has been used for analysing properties at extreme pressure, but may be inadequate for calculations requiring precise derivatives of an equation of state. A new analysis indicates that d ( 1 / K ) / d ( P / K ) increases with compression (or P / K ), but there are, at present, no reliable equations representing this. Relationships between higher derivatives of K and the thermodynamic Grüneisen parameter offer the prospect of a resolution of the problem and hence a new generation of fundamentally-based equations of state. Although an earlier conclusion that a completely general ‘universal’ equation is not possible, in principle, is confirmed in this study, the fundamental relationships present strong constraints for the forms of other proposed equations. Full article
(This article belongs to the Special Issue Mineral Physics—In Memory of Orson Anderson)
Open AccessArticle
High-Pressure and High-Temperature Phase Transitions in Fe2TiO4 and Mg2TiO4 with Implications for Titanomagnetite Inclusions in Superdeep Diamonds
Minerals 2019, 9(10), 614; https://doi.org/10.3390/min9100614 - 06 Oct 2019
Abstract
Phase transitions of Mg2TiO4 and Fe2TiO4 were examined up to 28 GPa and 1600 °C using a multianvil apparatus. The quenched samples were examined by powder X-ray diffraction. With increasing pressure at high temperature, spinel-type Mg2 [...] Read more.
Phase transitions of Mg2TiO4 and Fe2TiO4 were examined up to 28 GPa and 1600 °C using a multianvil apparatus. The quenched samples were examined by powder X-ray diffraction. With increasing pressure at high temperature, spinel-type Mg2TiO4 decomposes into MgO and ilmenite-type MgTiO3 which further transforms to perovskite-type MgTiO3. At ~21 GPa, the assemblage of MgTiO3 perovskite + MgO changes to 2MgO + TiO2 with baddeleyite (or orthorhombic I)-type structure. Fe2TiO4 undergoes transitions similar to Mg2TiO4 with pressure: spinel-type Fe2TiO4 dissociates into FeO and ilmenite-type FeTiO3 which transforms to perovskite-type FeTiO3. Both of MgTiO3 and FeTiO3 perovskites change to LiNbO3-type phases on release of pressure. In Fe2TiO4, however, perovskite-type FeTiO3 and FeO combine into calcium titanate-type Fe2TiO4 at ~15 GPa. The formation of calcium titanate-type Fe2TiO4 at high pressure may be explained by effects of crystal field stabilization and high spin–low spin transition in Fe2+ in the octahedral sites of calcium titanate-type Fe2TiO4. It is inferred from the determined phase relations that some of Fe2TiO4-rich titanomagnetite inclusions in diamonds recently found in São Luiz, Juina, Brazil, may be originally calcium titanate-type Fe2TiO4 at pressure above ~15 GPa in the transition zone or lower mantle and transformed to spinel-type in the upper mantle conditions. Full article
(This article belongs to the Special Issue Mineral Physics—In Memory of Orson Anderson)
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Open AccessArticle
Limits to the Validity of Thermal-Pressure Equations of State
Minerals 2019, 9(9), 562; https://doi.org/10.3390/min9090562 - 17 Sep 2019
Abstract
Thermal-pressure Equations of State (EoS) such as the Mie-Grüneisen-Debye (MGD) model depend on several assumptions, including the quasi-harmonic approximation (QHA) and a simplified phonon density of states. We show how the QHA is violated by materials exhibiting anisotropic thermal pressure. We also show [...] Read more.
Thermal-pressure Equations of State (EoS) such as the Mie-Grüneisen-Debye (MGD) model depend on several assumptions, including the quasi-harmonic approximation (QHA) and a simplified phonon density of states. We show how the QHA is violated by materials exhibiting anisotropic thermal pressure. We also show that at pressures lower than those of the isochor of the reference volume, the static pressure may become sufficiently negative to make the compressional part of the EoS invalid. This limit is sensitive to the combined effects of the EoS parameters K’0, q and the Grüneisen parameter γ0. Large values of q, which correspond to a rapid decrease in phonon mode frequencies with increasing volume, can also lead to the bulk modulus becoming zero at high pressures and temperatures that are not particularly extreme for planetary geotherms. The MGD EoS therefore has an extremely limited P and T regime over which it is both valid and has physically-meaningful properties. Outside of this range, additional terms should be included in the thermal pressure that represents the physical properties of the solid. Or, alternatively, ‘isothermal’ EoS in which the temperature variation of the elastic properties is explicitly modeled without reference to a physical model can be used. Full article
(This article belongs to the Special Issue Mineral Physics—In Memory of Orson Anderson)
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Open AccessArticle
Phase Relations in MAFSH System up to 21 GPa: Implications for Water Cycles in Martian Interior
Minerals 2019, 9(9), 559; https://doi.org/10.3390/min9090559 - 16 Sep 2019
Abstract
To elucidate the water cycles in iron-rich Mars, we investigated the phase relation of a water-undersaturated (2 wt.%) analog of Martian mantle in simplified MgO-Al2O3-FeO-SiO2-H2O (MAFSH) system between 15 and 21 GPa at 900–1500 °C [...] Read more.
To elucidate the water cycles in iron-rich Mars, we investigated the phase relation of a water-undersaturated (2 wt.%) analog of Martian mantle in simplified MgO-Al2O3-FeO-SiO2-H2O (MAFSH) system between 15 and 21 GPa at 900–1500 °C using a multi-anvil apparatus. Results showed that phase E coexisting with wadsleyite or ringwoodite was at least stable at 15–16.5 GPa and below 1050 °C. Phase D coexisted with ringwoodite at pressures higher than 16.5 GPa and temperatures below 1100 °C. The transition pressure of the loop at the wadsleyite-ringwoodite boundary shifted towards lower pressure in an iron-rich system compared with a hydrous pyrolite model of the Earth. Some evidence indicates that water once existed on the Martian surface on ancient Mars. The water present in the hydrous crust might have been brought into the deep interior by the convecting mantle. Therefore, water might have been transported to the deep Martian interior by hydrous minerals, such as phase E and phase D, in cold subduction plates. Moreover, it might have been stored in wadsleyite or ringwoodite after those hydrous materials decomposed when the plates equilibrated thermally with the surrounding Martian mantle. Full article
(This article belongs to the Special Issue Mineral Physics—In Memory of Orson Anderson)
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Review

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Open AccessReview
The Orson Anderson Era of Mineral Physics at Lamont in the 1960s
Minerals 2019, 9(6), 342; https://doi.org/10.3390/min9060342 - 04 Jun 2019
Abstract
From 1964 to the early 1970s, Orson Anderson led a research program at the Lamont Geological Observatory in the newly-emerging field of “mineral physics”. In collaboration with colleagues Edward Schreiber and Naohiro Soga, Orson exploited the techniques of physical acoustics to study the [...] Read more.
From 1964 to the early 1970s, Orson Anderson led a research program at the Lamont Geological Observatory in the newly-emerging field of “mineral physics”. In collaboration with colleagues Edward Schreiber and Naohiro Soga, Orson exploited the techniques of physical acoustics to study the behavior of the sound velocities of minerals at elevated pressures and temperatures. This research program also included semi-empirical studies of the relationships between the bulk modulus and the molar volume of solids, the use of lattice dynamics to calculate the elastic moduli of cubic structures as a function of pressure to predict instabilities, and theoretical investigations of the Lagrangian and Eulerian formulations of finite strain equations of state. Full article
(This article belongs to the Special Issue Mineral Physics—In Memory of Orson Anderson)
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