Density of Phonon States in Iron at High Pressure

Lübbers, R.; Grünsteudel, H.; Chumakov, A. I.; Wortmann, G.

doi:10.1126/science.287.5456.1250

Cited by 123 publications

(46 citation statements)

References 32 publications

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“…NRIXS signals originate from particular resonant nuclei only, and this complete isotope selec tivity is truly unique among techniques for the study of lattice vibrations. For example, materials surrounding the sample that do not contain resonant nuclei produce no unwanted background, and this feature now permits experiments under extreme pressuretemperature conditions that were impossible before (Lubbers et al, 2000a;Mao et al, 2001Mao et al, , 2004bStruzhkin et al, 2001;Lin et al, 2003Lin et al, , 2004aLin et al, , 2004bLin et al, , 2005bShen et al, 2004;Papandrew et al, 2004;Kobayashi et al, 2004;Zhao et al, 2004). Details on the scattering mechanisms and methodology for NRJXS and SMS have been published elsewhere Sturhahn, 2004).…”

Section: Experimental Methodsmentioning

confidence: 99%

Geophysical applications of nuclear resonant spectroscopy

Sturhahn¹,

Jackson²

2007

Advances in High-Pressure Mineralogy

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We summarize recent developments of nuclear resonant spectroscopy methods, such as nuclear resonant inelastic X-ray scattering and synchrotron Mossbauer spec troscopy, and their uses for the geophysical sciences. The inelastic method provides specific vibrational information, for example, the phonon density of states, and, in combination with compression data, it permits the determination of sound velocities and Gruneisen parameters under high pressure and high temperature. The Moss bauer method provides hyperfine interactions between the resonant nucleus and elec tronic environment, such as isomer shifts, quadrupole splittings, and magnetic fields, which provide important information on valence, spin state, and magnetic ordering.Both methods use a nuclear resonant isotope as a probe and can be applied under high pressure and high temperature. The physical mechanism of nuclear resonant scattering and the specifics in applications to Earth materials are presented with ref erence to several high-pressure studies on iron-bearing compounds.

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Section: Experimental Methodsmentioning

confidence: 99%

Geophysical applications of nuclear resonant spectroscopy

Sturhahn¹,

Jackson²

2007

Advances in High-Pressure Mineralogy

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“…Many different techniques have been used to determine the Grüneisen ratio of hcp Fe, including nuclear resonant inelastic x-ray scattering, 51 Raman, 54 x-ray diffraction, 61,74 shock wave, 75 and thermodynamic analysis. 76,77 At a given pressure, our calculated γ first increases with temperature, and then drops rapidly at high temperatures (T >1500 K), as shown in Fig.…”

Section: Thermal Equation Of Statementioning

confidence: 99%

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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“…During the past decade, tremendous experimental [1][2][3][4][5][6][7] and theoretical [8][9][10][11][12][13][14] efforts have been devoted to investigate various properties of iron, especially for those at high pressure and temperature conditions. Body-center-cubic (bcc) is the ground state structure for iron at ambient conditions.…”

Section: Introductionmentioning

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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Density of Phonon States in Iron at High Pressure

Cited by 123 publications

References 32 publications

Geophysical applications of nuclear resonant spectroscopy

Geophysical applications of nuclear resonant spectroscopy

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

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