Variationally induced breathing equations of state of pyrope, grossular, and majorite garnets

Downs, James W.; Bukowinski, M. S. T.

doi:10.1029/97gl01762

Cited by 7 publications

(6 citation statements)

References 36 publications

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“…Since the bonding in high pressure silicate phases is primarily ionic, VIB should perform well in determining the structures and equations of state of such minerals. However, experience shows that VIB tends to overestimate the bulk moduli and underestimates the Si‐O bond lengths in silicates [ Downs and Bukowinski , 1997; Bukowinski and Downs , 2000]. It is possible to significantly improve VIB's treatment of Si‐O interactions by simply reducing the ionicities of Si and O [ Bukowinski and Downs , 2000], consistent with Pauling's claim that the Si‐O bond is as much as 50% covalent [ Pauling , 1980].…”

Section: Techniquementioning

confidence: 84%

On the structure and compressibility of CaSiO₃ perovskite

Akber-Knutson

2002

Geophysical Research Letters

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[1] The equation of state and structure of CaSiO 3 perovskite are determined at high pressures using the density-functional-based Variationally Induced Breathing (VIB) method, modified with a small, parameterized covalent correction to the short-range Si-O interaction. Our thermally corrected room temperature equation of state parameters (V 0 = 45.90 ± 0.02 Å , K 0 = 228 ± 2 GPa, K 0 = 4.3 ± 0.1) are in very good agreement with near-hydrostatic compression data as well as recent calculations based on first-principles methods. We examined the tetragonal, orthorhombic, and triclinic structures, and compared their stabilities relative to the cubic structure at lower mantle pressures. We found that the orthorhombic perovskite structure of CaSiO 3 is the thermodynamically stable phase at all mantle pressures. The structural and energy differences between the orthorhombic and cubic lattices under static conditions are small, and increase only slightly with pressure. Consequently, the cubic structure may be thermodynamically stable at lower mantle temperatures.

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Section: Techniquementioning

confidence: 84%

On the structure and compressibility of CaSiO₃ perovskite

Akber-Knutson

2002

Geophysical Research Letters

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“…Ilmenite: Horiuchi et al (1982), Reynard et al (1996), Chopelas (1999); Karki and Wentzcovitch (2002). Majorite: Angel et al (1989), Gerald Pacalo and Weidner (1997); Downs and Bukowinski (1997), Yu et al to be published (2010) correlation functionals for structural properties. Complete analysis of these thermodynamic properties at high pressures and temperatures can be found in Karki et al (2000a).…”

Section: Mgomentioning

confidence: 99%

Thermodynamic Properties and Phase Relations in Mantle Minerals Investigated by First Principles Quasiharmonic Theory

Wentzcovitch

Wu³

2010

Reviews in Mineralogy and Geochemistry

123

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“…Here we present a first‐principles quasi‐harmonic calculation of the high P ‐ T thermodynamic properties of majorite which are absent from previous calculations [ Downs and Bukowinski , 1997; Li et al , 2007; Vinograd et al , 2006]. We use empirical‐potential‐based Monte Carlo calculations to address the order‐disorder transition in MgSiO 3 majorite.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic properties of MgSiO₃majorite and phase transitions near 660 km depth in MgSiO₃and Mg₂SiO₄: A first principles study

Yu¹,

Wentzcovitch²,

Vinograd³

et al. 2011

J. Geophys. Res.

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[1] Thermodynamic properties of MgSiO 3 tetragonal majorite have been calculated at high pressures and temperatures within the quasi-harmonic approximation based on density functional theory using the local density approximation (LDA) and the generalized gradient approximation (GGA). The LDA results compare exceptionally well with measured thermodynamic properties. A classical Monte Carlo simulation based on results from a cluster expansion method demonstrates that disorder between magnesium and silicon in the octahedral sites in MgSiO 3 majorite does not occur below 3600 K at transition zone pressures. The ensuing calculations on phase boundaries of MgSiO 3 between majorite, perovskite, and ilmenite show that a much better agreement with experiment can be obtained by using GGA rather than LDA, for LDA underestimates the transition pressures by as much as 11 GPa. The Clapeyron slopes predicted by GGA and LDA are close to each other: 0.9-1.7 MPa/K for majorite-perovskite transition, 6.9-7.9 MPa/K for majorite-ilmenite transition, and −7-−3 MPa/K for ilmenite-perovskite transition. The triple point predicted by GGA is located at 21.8 ± 1 GPa and 1840 ± 200 K which is ∼400 K lower in temperature than most experimental estimates. This result suggests that ilmenite is restricted to lower temperatures and that the majorite to ilmenite transition may occur in cold subducting slabs in the transition zone. Our calculation also reveals that wadsleyite decomposes to an assemblage of majorite plus periclase above 2280 K with a large negative Clapeyron slope (−22-−12 MPa/K) and that ringwoodite decomposes to ilmenite plus periclase below 1400 K (1.2 MPa/K). These two decomposition transitions may influence hot plumes and cold slabs near 660 km depth, respectively. Further calculations show that discontinuities in density, bulk modulus, and bulk sound velocity associated with the majorite to perovskite transition in MgSiO 3 are much larger than those from the postspinel transition in Mg 2 SiO 4 at conditions close to 660 km depth. This suggests that the large density discontinuity at 660 km depth as proposed by PREM (9.3%) might be accounted by a piclogite compositional model or marginally accounted by a pyrolite compositional model with, for example, 50 vol % ringwoodite, 45 vol % majorite, and 5 vol % other phases (such as calcium perovskite) at the bottom of the transition zone, provided that the density contrast between majorite and perovskite will not be greatly altered by the presence of other elements such as Fe, Al, Ca, and H. On the other hand, the smaller density discontinuity at 660 km depth as derived from impedance studies (4-6%) disfavors sharp contributions to seismic discontinuities from the majorite to perovskite transition.

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Variationally induced breathing equations of state of pyrope, grossular, and majorite garnets

Cited by 7 publications

References 36 publications

On the structure and compressibility of CaSiO₃ perovskite

On the structure and compressibility of CaSiO₃ perovskite

Thermodynamic Properties and Phase Relations in Mantle Minerals Investigated by First Principles Quasiharmonic Theory

Thermodynamic properties of MgSiO₃majorite and phase transitions near 660 km depth in MgSiO₃and Mg₂SiO₄: A first principles study

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Variationally induced breathing equations of state of pyrope, grossular, and majorite garnets

Cited by 7 publications

References 36 publications

On the structure and compressibility of CaSiO3 perovskite

On the structure and compressibility of CaSiO3 perovskite

Thermodynamic Properties and Phase Relations in Mantle Minerals Investigated by First Principles Quasiharmonic Theory

Thermodynamic properties of MgSiO3majorite and phase transitions near 660 km depth in MgSiO3and Mg2SiO4: A first principles study

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Product

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On the structure and compressibility of CaSiO₃ perovskite

On the structure and compressibility of CaSiO₃ perovskite

Thermodynamic properties of MgSiO₃majorite and phase transitions near 660 km depth in MgSiO₃and Mg₂SiO₄: A first principles study