Vibrational modes in nanocrystalline iron under high pressure

Papandrew, Alexander B.; Yue, A. F.; Fultz, B.; Halevy, I.; Sturhahn, W.; Toellner, T. S.; Ercan, E.; Mao, Ho‐kwang

doi:10.1103/physrevb.69.144301

Cited by 58 publications

(13 citation statements)

References 22 publications

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“…This remains true as the nanocrystalline material is subjected to pressure, as shown for bcc Fe in Fig. 28 [276]. At pressures of 0.2 and 9.5 GPa both bulk and nanocrystalline samples were bcc, but both had transformed to hcp Fe at the highest pressure of 25-27 GPa.…”

Section: Low-energy Vibrations Of Nanostructuresmentioning

confidence: 73%

“…For nanocrystals, it is generally found that phonon spectral weight is transferred to lower energies, causing an increase in the vibrational entropy as large as 0.2 k B /atom for nanocrystalline materials measured to date [273,275,276,277,285]. Nevertheless, it appears that the entropy of vibrations and configurations is only about half of what is required to give thermodynamic stabilization to a nanocrystalline microstructure at reasonable finite temperatures.…”

Section: Low-energy Vibrations Of Nanostructuresmentioning

confidence: 96%

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Vibrational thermodynamics of materials

Fultz¹

2010

Progress in Materials Science

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558

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: Low-energy Vibrations Of Nanostructuresmentioning

confidence: 73%

Section: Low-energy Vibrations Of Nanostructuresmentioning

confidence: 96%

Vibrational thermodynamics of materials

Fultz¹

2010

Progress in Materials Science

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558

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 vibrational properties of nanoscrystalline materials (nanocomposites) have been studied extensively experimentally by inelastic neutron scattering and nuclear resonant inelastic X-ray scattering (NRIXS) 9,[32][33][34][35][36][37][38][39][40][41][42] , as well as theoretically 7,8,10,13,[43][44][45][46][47] .…”

Section: Introductionmentioning

confidence: 99%

Size-dependent evolution of the atomic vibrational density of states and thermodynamic properties of isolated Fe nanoparticles

et al. 2012

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We have gained insight into the internal degree of atomic disorder in isolated sizeselected Fe nanoparticles (NPs) (~2 -6 nm in size) supported on SiO 2 /Si(111) and Al 2 O 3 (0001) from precise measurements of the low-energy (low-E) part of the phonon density of states [PDOS, g(E)] via 57 Fe nuclear resonant inelastic X-ray scattering (NRIXS), combined with transmission electron microscopy (TEM) measurements. An intriguing size-dependent trend was observed, namely, an increase of the low-E excess density of phonon states (as compared to the PDOS of bulk bcc Fe) with increasing NP size. This is unexpected, since usually the enhancement of the density of low-E phonon modes is attributed to low-coordinated atoms at the NP surface, whose relative content increases with decreasing NP size due to the increase in the surface-to-volume ratio. OurNPs are covered by a Ti coating layer, which essentially restores the local neighbourhood of surface Fe surface atoms towards bulk-like coordination, reducing the surface effect.Our data can be qualitatively explained by the existence of low-coordinated Fe atoms 2 located at grain boundaries or other defects with structural disorder in the interior of the large NPs (~3 -6 nm), while our small NPs (~2 nm) are single-grain and, therefore, characterized by a higher degree of structural order. This conclusion is corroborated by the observation of Debye behaviour at low energy [g(E) ~ E n with n ~ 2] for the small NPs, but non-Debye behaviour (with n ~ 1.4) for the large NPs. The PDOS was used to determine thermodynamic properties of the Fe NPs. Finally, our results demonstrate that, in combination with TEM, NRIXS is a suitable technique to investigate atomic disorder/defects in NPs. We anticipate that our findings are universal for similar NPs with bcc structure.Keywords: Fe, nanoparticle, nuclear resonant inelastic x-ray scattering, atomic force microscopy, transmission electron microscopy, x-ray photoelectron spectroscopy, phonon density of states.

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Vibrational modes in nanocrystalline iron under high pressure

Cited by 58 publications

References 22 publications

Vibrational thermodynamics of materials

Vibrational thermodynamics of materials

Geophysical applications of nuclear resonant spectroscopy

Size-dependent evolution of the atomic vibrational density of states and thermodynamic properties of isolated Fe nanoparticles

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