Generalized Anderson-Grüneisen parameters for cubic solids

Perrin, G.; Delannoy‐Coutris, M.

doi:10.1016/0022-3697(88)90111-4

Cited by 16 publications

(3 citation statements)

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“…At the inner core conditions (P ∼ 329 GPa; T ∼ 6000 K), the extrapolated density of Fe 4 P is around, ∼ 12.50 g/cm 3 . We have assumed a thermal expansion α 0 ∼ 1.27 × 10 −5 K −1 based on the thermal expansion of Ni 3 P [ Samsonov et al , 1971] and its high‐pressure extrapolation based on the relation α ( P , T ) = We have assumed the Anderson‐Grüneisen parameter, δ T ∼ 4, based on cubic solid metals [ Perrin and Delannoy‐Coutris , 1988]. We determined the maximum volume fraction of Fe 4 P in the inner core boundary pressure and temperatures using the relation where, ρ Fe ∼ 12.9 g/cm 3 , and ρ PREM ∼ 12.76 g/cm 3 [ Dziewonski and Anderson , 1981], and the volume fraction x .…”

Section: Discussionmentioning

confidence: 99%

“…We have assumed a thermal expansion a 0 ∼ 1.27 × 10 −5 K −1 based on the thermal expansion of Ni 3 P [Samsonov et al, 1971] and its high-pressure extrapolation based on the relation a(P, T) = a 0 (r 0 /r) d T . We have assumed the Anderson-Grüneisen parameter, d T ∼ 4, based on cubic solid metals [Perrin and Delannoy-Coutris, 1988]. We determined the maximum volume fraction of Fe 4 P in the inner core boundary pressure and temperatures using the relation…”

Section: Discussionmentioning

confidence: 99%

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Elasticity and anisotropy of iron-nickel phosphides at high pressures

Mookherjee

et al. 2011

Geophys. Res. Lett.

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[1] Geochemical estimates indicate that around 90% of the planet's inventory of phosphorus is likely to be sequestered in the Earth's core. Iron phosphides such as scheirbisites (Fe 3 P) are commonly found in iron meteorites. Recently, melliniite (Fe,Ni) 4 P with 12.2 wt% phosphorus has been reported in iron-meteorites. Using static electronic structure calculations, we predict that Fe 4 P is unlikely to dissociate into Fe 3 P and hcp Fe at inner core conditions. Among the different structural varieties of Fe 4 P, we find the cubic polymorph with P2 1 3 space group symmetry to be stable over a wide range of geophysically relevant pressures. We have determined the equation of state and the full elastic constant tensor of the stable (Fe,Ni) 4 P phase at pressures up to 400 GPa. Upon compression, Fe 4 P undergoes a ferromagnetic ( fm) to nonmagnetic (nm) transition at 80 GPa. In nonmagnetic (Fe,Ni) 4 P, nickel incorporation results in reduction of the P-and S-wave velocities. However, incorporation of nickel enhances the P-and S-wave anisotropy. Citation: Wu, X., M. Mookherjee, T. Gu, and S. Qin (2011), Elasticity and anisotropy of iron-nickel phosphides at high pressures, Geophys. Res. Lett., 38, L20301,

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Elasticity and anisotropy of iron-nickel phosphides at high pressures

Mookherjee

et al. 2011

Geophys. Res. Lett.

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“…[2][3]. The Grüneisen parameters and their volume dependence are very interesting [4][5][6]. The knowledge of intermolecular interactions is very important in understanding the properties of solids [7][8].…”

Section: Introductionmentioning

confidence: 99%

Low Temperature Thermal Properties of Al₂O₃

Vinu¹

2022

IOP Conf. Ser.: Mater. Sci. Eng.

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There are three Second Order Elastic Constants and six Third Order Elastic Constants for Al2O3 system. We calculate all the second and third Elastic Constants using Strain Elasticity theory. At standard temperature, the thermal properties of Al2O3 are theoretically analyzed. Grüneisen Parameters of the elastic waves at different angles of Al2O3 are evaluated using the elastic constants. The Brugger Gamma and normal-temperature Grüneisen Gamma are calculated by the method adopted by Menon and Ramji Rao. The volume expansion for Al2O3 system is positive since the normal-temperature value of Grüneisen Gamma is positive.

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