Phonon density of states in iron at high pressures and high temperatures

Shen, Guoyin; Sturhahn, W.; Alph, E. E.; Zhao, Jiyong; Tollenner, T. S.; Prakapenka, Vitali B.; Meng, Yue; Mao, Ho‐kwang

doi:10.1007/s00269-004-0403-l

Cited by 45 publications

(19 citation statements)

References 30 publications

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“…On the other hand, for pure 57 Fe, nuclear resonant inelastic x-ray scattering (NRIXS) measurements of the phonon DOS at elevated pressure and temperature show only a small difference for the bcc α-phase and the hcp ǫ-phase [122,123]. Curiously, another NRIXS study has shown a large difference between the phonon DOS of the hcp ǫ-phase and the fcc γ-phase [124], contrary to the trend for other metals. The phonon DOS of γ-Fe was softer than the DOS for ǫ-Fe, giving the fcc γ-phase the larger vibrational entropy and lower sound velocities.…”

Section: Polymorphismmentioning

confidence: 84%

Vibrational thermodynamics of materials

Fultz¹

2010

Progress in Materials Science

570

428

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Abstract. The literature on vibrational thermodynamics of materials is reviewed. The emphasis is on metals and alloys, especially on the progress over the last decade in understanding differences in the vibrational entropy of different alloy phases and phase transformations. Some results on carbides, nitrides, oxides, hydrides and lithium-storage materials are also covered.Principles of harmonic phonons in alloys are organized into thermodynamic models for unmixing and ordering transformations on an Ising lattice, and extended for non-harmonic potentials. Owing to the high accuracy required for the phonon frequencies, quantitative predictions of vibrational entropy with analytical models prove elusive. Accurate tools for such calculations or measurements were challenging for many years, but are more accessible today. Ab-initio methods for calculating phonons in solids are summarized. The experimental techniques of calorimetry, inelastic neutron scattering, and inelastic x-ray scattering are explained with enough detail to show the issues of using these methods for investigations of vibrational thermodynamics. The explanations extend to methods of data analysis that affect the accuracy of thermodynamic information.It is sometimes possible to identify the structural and chemical origins of the differences in vibrational entropy of materials, and the number of these assessments is growing. There has been considerable progress in our understanding of the vibrational entropy of mixing in solid solutions, compound formation from pure elements, chemical unmixing of alloys, order-disorder transformations, and martensitic transformations. Systematic trends are available for some of these phase transformations, although more examples are needed, and many results are less reliable at high temperatures. Nanostructures in materials can alter sufficiently the vibrational dynamics to affect thermodynamic stability. Internal stresses in polycrystals of anisotropic materials also contribute to the heat capacity. Lanthanides and actinides show a complex interplay of vibrational, electronic, and magnetic entropy, even at low temperatures.A "quasiharmonic model" is often used to extend the systematics of harmonic phonons to high temperatures by accounting for the effects of thermal expansion against a bulk modulus. Non-harmonic effects beyond the quasiharmonic approximation originate from the interactions of thermally-excited phonons with other phonons, or with the interactions of phonons with electronic excitations. In the classical high temperature limit, the adiabatic electron-phonon coupling can have a surprisingly large effect in metals when temperature causes significant changes in the electron density near the Fermi level. There are useful similarities in how temperature, pressure, and composition alter the conduction electron screening and the interatomic force constants. Phononphonon "anharmonic" interactions arise from those non-harmonic parts of the interatomic potential that cannot be accounted for by the quasiharmonic ...

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Section: Polymorphismmentioning

confidence: 84%

Vibrational thermodynamics of materials

Fultz¹

2010

Progress in Materials Science

570

428

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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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“…The NRIXS technique has been extended to HP and obtained the DOS of ε-Fe up to over 1 Mbar [63,154] and as a function of pressure and temperature with resistively heating and laser-heating techniques [137,297,298]. The measurement of Debye sound velocity [299,300] distinguishes compression and shear wave velocities as well as their temperature and pressure dependence.…”

Section: Hp Nuclear Resonant Inelastic X-ray Scatteringmentioning

confidence: 99%

“…Since the first x-ray results of the phonon DOS of Fe at ambient pressure [295,296], the phonon DOS of hcp-Fe has been extended to high pressures up to 42 GPa [154], 153 GPa [63], 171 GPa [299,517], and recently to 136 GPa using a quasi-hydrostatic medium [518]. High temperatures have been added in the phonon DOS determination for Fe at HP [297,298]. Fig.…”

Section: Phonon Density Of Statesmentioning

confidence: 99%

High-pressure studies with x-rays using diamond anvil cells

2016

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Pressure profoundly alters all states of matter. The symbiotic development of ultrahighpressure diamond anvil cells, to compress samples to sustainable multi-megabar pressures; and synchrotron x-ray techniques, to probe materials' properties in situ, has enabled the exploration of rich high-pressure (HP) science. In this article, we first introduce the essential concept of diamond anvil cell technology, together with recent developments and its integration with other extreme environments. We then provide an overview of the latest developments in HP synchrotron techniques, their applications, and current problems, followed by a discussion of HP scientific studies using x-rays in the key multidisciplinary fields. These HP studies include: HP x-ray emission spectroscopy, which provides information on the filled electronic states of HP samples; HP x-ray Raman spectroscopy, which probes the HP chemical bonding changes of light elements; HP electronic inelastic x-ray scattering spectroscopy, which accesses high energy electronic phenomena, including electronic band structure, Fermi surface, excitons, plasmons, and their dispersions; HP resonant inelastic x-ray scattering spectroscopy, which probes shallow core excitations, multiplet structures, and spin-resolved electronic structure; HP nuclear resonant x-ray spectroscopy, which provides phonon densities of state and time-resolved Mössbauer information; HP x-ray imaging, which provides information on hierarchical structures, dynamic processes, and internal strains; HP x-ray diffraction, which determines the fundamental structures and densities of single-crystal, polycrystalline, nanocrystalline, and non-crystalline materials; and HP radial x-ray diffraction, which yields deviatoric, elastic and rheological information. Integrating these tools with hydrostatic or uniaxial pressure media, laser and resistive heating, and cryogenic cooling, has enabled investigations of the structural, vibrational, electronic, and magnetic properties of materials over a wide range of pressure-temperature conditions.

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Phonon density of states in iron at high pressures and high temperatures

Cited by 45 publications

References 30 publications

Vibrational thermodynamics of materials

Vibrational thermodynamics of materials

Geophysical applications of nuclear resonant spectroscopy

High-pressure studies with x-rays using diamond anvil cells

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