A thermodynamic theory of the Gr�neisen ratio at extreme conditions: MgO as an example

Anderson, Orson L.; Oda, Hitoshi; Chopelas, A.; Isaak, Donald G.

doi:10.1007/bf00202974

Cited by 50 publications

(30 citation statements)

References 48 publications

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“…The equation works well for transition metals such as bcc Ta 65 and metal oxides such as MgO. 73 As shown in Fig. 7(b), although δ T of hcp Fe shows a strong decrease during compression, it does not drop as rapidly as power order at high pressures, similar to what has been observed in bcc Fe.…”

supporting

confidence: 62%

First-principles thermal equation of state and thermoelasticity of hcp Fe at high pressures

Sha

Cohen

2010

Phys. Rev. B

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We investigate the equation of state and elastic properties of hcp iron at high pressures and high temperatures using first principles linear response linear-muffin-tin-orbital method in the generalized-gradient approximation. We calculate the Helmholtz free energy as a function of volume, temperature, and volume-conserving strains, including the electronic excitation contributions from band structures and lattice vibrational contributions from quasi-harmonic lattice dynamics. We perform detailed investigations IntroductionIron is one of the most abundant elements in the Earth, and is fundamental to our world. The study of iron at high pressures and high temperatures is of great geophysical interest, since both the Earth's liquid outer core and solid inner core are composed mostly of this element. Although the crystal structure of iron at the extremely high temperature (4000 to 8000 K) and high pressure (330 to 360 GPa) conditions found in the inner core is still under intensive debate, 1-10 the hexagonal-close-packed phase (ε-Fe) is commonly believed to have a wide stability field extending from deep mantle to core conditions, and serves as a starting point for understanding the nature of the inner core. 11 Significant experimental and theoretical efforts have been recently devoted to investigate various properties of hcp iron at high pressures and high temperatures. New high-pressure diamond-anvil-cell techniques have been developed or significantly improved, which makes it possible to reach higher pressures and provide more valuable information on material properties in these extreme states. First-principles based theoretical techniques have been improved in reliability and accuracy, and have been widely used to predicate the high pressure-temperature behavior and provide fundamental understandings to the experiment.Despite intensive investigations, numerous fundamental problems remain unresolved, and many of the current results are mutually inconsistent. 11 The melting line at very high pressures has been one of the most difficult and controversial problems. 12-19Other major problems include possible subsolidus phase transitions 2,4,5,11,20 and the magnetic structure of the dense hexagonal iron. In section II we detail the theoretical methods to perform the first-principles calculations and obtain the thermal properties and elastic moduli. We present the results and related discussions about the thermal equation of state in section III, and about the thermoelasticity in section IV. We conclude with a brief summary in Section V. II. Theoretical methodsThe Helmholtz free energy F for many metals has three major contributionswith V as the volume, T as the temperature, and δ as the strain. E static is the zerotemperature energy of a static lattice, F el is the thermal free energy arising from electronic excitations, and F ph is the lattice vibrational energy contribution. We obtain both E static and F el from first-principles calculations directly, assuming that the eigenvalues for given lattice and nuclear pos...

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supporting

confidence: 62%

First-principles thermal equation of state and thermoelasticity of hcp Fe at high pressures

Sha

Cohen

2010

Phys. Rev. B

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“…For bcc Ta, the average δ T shows δ T (η)=4.56×η 1.29 for temperature 0-6000K 44 , and δ T (η)=4.56×η 1.29 has been reported for MgO at 1000K 51 . However, bcc Fe shows different behavior.…”

Section: Lattice Dynamicsmentioning

confidence: 88%

“…At all temperatures, δ T shows a strong decrease with pressure. For many materials, the parameter δ T can be fitted to a form as a function of volume 51 :…”

Section: Lattice Dynamicsmentioning

confidence: 99%

Lattice dynamics and thermodynamics of bcc iron under pressure: First-principles linear response study

Sha

Cohen

2006

Phys. Rev. B

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We compute the lattice-dynamical and thermal equation of state properties of ferromagnetic bcc iron using the first principles linear response linear-muffin-tin-orbital method in the generalizedgradient approximation. The calculated phonon dispersion and phonon density of states, both at ambient and high pressures, show good agreement with inelastic neutron scattering data. We find the free energy as a function of volume and temperature, including both electronic excitations and phonon contributions, and we have derived various thermodynamic properties at high pressure and temperature. The thermal equation of state at ambient temperature agrees well with diamond-anvil-cell measurements. We have performed detailed investigations on the behavior of various thermal equation of state parameters, such as the bulk modulus K, the thermal expansivity α, the Anderson-Grüneisen parameter δ T , the Grüneisen ratio γ, and the heat capacity C V as function of temperature and pressure. A detailed comparison has been made with available experimental measurements, as well as results from similar theoretical studies on nonmagnetic bcc Tantalum. PACS number(s): 05.70. Ce, 64.30.+t, 71.20.Be 1

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“…The computation begins with the Suzuki et al [1979) [Birch, 1952): where f = ~[p(P,T)/p(P 0 ,TJ)] 2 / 3 -1 is the finite strain. Then the elastic parameters of the adiabatically compressed material can be calculated as follows [Sammis et al, 1970;Davies and Dziewonski, 1975]:…”

Section: Adiabatic Model For Chemically Homogeneous Lower Mantlementioning

confidence: 99%

Geodynamically consistent seismic velocity predictions at the base of the mantle

Sidorin¹,

Gurnis²

1998

The Core‐Mantle Boundary Region

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A model of thermoelastic properties for a chemically homogeneous adiabatic lower mantle is calculated. Constraints provided by this model are used in convection models to study dynamics of a chemically distinct layer at the bottom of the mantle. We find that the layer must be at least 2% denser than the overlying mantle to survive for a geologically significant period of time. Realistic decrease with depth of the thermal expansivity increases layer stability but is unable to prevent it from entrainment. Seismic velocities are computed for an assumed composition by applying the thermal and compositional perturbations obtained in convection simulations to the adiabatic values. The predicted velocity jump at the top of the chemical layer is closer to the CMB in the cold regions than in the hot. The elevation of the discontinuity above CMB in the cold regions decreases with increasing thermal expansivity and increases with increasing density contrast, while in the hot regions we find that the opposite is true. If the density contrast is small, the layer may vanish under downwellings. However, whenever the layer is present in the downwelling regions, it also exists under the upwellings. For a 4% density contrast and realistic values of expansivity, we find that the layer must be more than 400 km thick on average to be consistent with the seismically observed depth of the discontinuity. A simple chemical layer cannot be used to interpret the D" discontinuity: the required change in composition is large and must be complex, since enrichment in any single mineral probably cannot provide the required impedance contrast. A simple chemical layer cannot explain the spatial intermittance of the discontinuity.

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A thermodynamic theory of the Gr�neisen ratio at extreme conditions: MgO as an example

Cited by 50 publications

References 48 publications

First-principles thermal equation of state and thermoelasticity of hcp Fe at high pressures

First-principles thermal equation of state and thermoelasticity of hcp Fe at high pressures

Lattice dynamics and thermodynamics of bcc iron under pressure: First-principles linear response study

Geodynamically consistent seismic velocity predictions at the base of the mantle

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