Vibrations of Micro-eV Energies in Nanocrystalline Microstructures

Abstract

The phonon density of states of nanocrystalline bcc Fe and nanocrystalline fcc Ni 3 Fe were measured by inelastic neutron scattering in two different ranges of energy. As has been reported previously, the nanocrystalline materials showed enhancements in their phonon density of states at energies from 2 to 15 meV, compared to control samples composed of large crystals. The present measurements were extended to energies in the micro-eV range, and showed significant, but smaller, enhancements in the number of modes in the energy range from 5 to 18 eV. These modes of micro-eV energies provide a long-wavelength limit that bounds the fraction of modes at milli-eV energies originating with the cooperative dynamics of the nanocrystalline microstructure. DOI: 10.1103/PhysRevLett.93.205501 PACS numbers: 63.22.+m, 61.46.+w, 81.07.-b The vibrational spectra of nanocrystalline materials differ from those of materials composed of larger crystals. Earlier measurements of Debye-Waller factors and Lamb-Mössbauer factors showed large mean-squared atomic displacements in nanocrystalline materials [1][2][3][4]. More recently, neutron and x-ray inelastic scattering measurements revealed that nanocrystalline materials have an increased number of vibrational modes at the highest and lowest energies of their measured spectra, compared to materials with crystals of conventional sizes [5][6][7][8][9][10][11][12]. Enhanced intensity above the high-energy cutoff of the bulk material has been attributed to phonon lifetime broadening caused by phonon interactions with grain boundaries [9][10][11] and recent measurements on iron have isolated a contribution from surface oxides [12]. The increased number of phonon modes at low energies [5][6][7][8][9][10][11] is less well understood. The phonon density of states (DOS) at low energies is up to a factor of 5 times larger than the DOS of control samples of material composed of larger crystals [10]. The number of these low-energy modes was found to increase with the inverse of the crystallite size, implying a scaling with the number of grain boundaries. Surface vibrational modes could be responsible for such behavior because grain boundaries have elastic constants differing from the crystal interiors. There are some experimental and computational reports that the low-energy phonon DOS in nanocrystalline materials scales linearly with energy, indicative of twodimensional vibrations [13,14]. Other theoretical models include the idea of a nonintegral spatial dimension of the low-energy modes [15][16][17][18].Surface modes on individual, isolated crystallites have a maximum wavelength comparable to the crystallite size, and therefore a lower bound on their energy. For a wave velocity of 2 km=s and a particle of 10 nm dimension, the characteristic energy is 1 meV. Energies of a milli-electron volt have been approximately the lower limit of the inelastic spectra measured to date. Surface modes around nanoparticles should not extend to energies much below 100 eV, however. The present experiment was d...

Vibrational thermodynamics of materials

“…In measurements of phonons in the µeV energy range [279], it was found that the enhancement in the phonon DOS around 10 µeV was only about half of what was found around 10 meV. Some enhancement of the phonon DOS is expected owing Figure 27.…”

Lattice dynamics in Sn nanoislands and cluster-assembled films

“…Phonon softening in these structures was attributed to grain boundary atoms and the decrease of the phonon lifetime was attributed to phonon scattering at the grain boundaries 7,8,11,12,15,18,21,23,24 . In some nanocrystalline structures an enhancement of high-energy modes above the cut-off energy was observed which was attributed to surface oxides 12,16 , grain boundary atoms 9,21 or to changes in the inter-atomic force constants 11,18,26 . Another type of nanostructure that was studied is isolated nanoparticles 7,8,10,17,20,22,25 for which also an enhancement of low-and high-energy phonon modes as well as a broadening of the PDOS features was observed.…”

“…The phonon density of states (PDOS) of low dimensional systems is expected to be modified due to the restriction of phonon propagation [7][8][9][10][11] . Previously, clear differences between the phonon density of states of bulk and that of nanostructures have been observed, with as most commonly observed anomalies in the phonon spectra of nanostructures: an enhancement of low-energy modes, appearance of high-energy modes above the cut-off energy of the bulk material and a broadening of the PDOS features [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] . For thin films, the broadening of features in the PDOS was attributed to phonon damping 13,19,27,28 and the enhancement of low-energy phonon modes due to the appearance of surface modes 14,19,27 .…”

“…In general it was found that for thin films the phonon behaviour is strongly influenced by the monolayer in contact with the substrate and the monolayer at the surface. Nanocrystalline structures with a high density of grain boundaries have been studied theoretically 7,9,26,29 and experimentally 8,12,15,16,18,21,23,24 for different materials. In these nanocrystalline structures, an enhancement of low-energy modes and broadening of different features of the PDOS was observed.…”

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

“…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] .…”