Vibrational density of states of silicon nanoparticles

Meyer, Ralf; Comtesse, Denis

doi:10.1103/physrevb.83.014301

Cited by 49 publications

(50 citation statements)

References 32 publications

(55 reference statements)

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“…It was found that, as the Si particles become smaller, the density of vibrational states increases at low frequencies, and modes are transferred from the high-frequency end to the intermediate range and transverse optical modes peak are shifted to higher frequencies. 2 In metallic glasses, vibrational characteristics have also been used for explaining mechanical properties. For example, recent MD simulations of a Cu 64 Zr 36 metallic glass showed that the strongest participation in the modes with lowest vibrational frequency and, hence, weakest spring constants (i.e., soft modes) originate predominantly from meagrely populated polyhedra.…”

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Softening of phonon spectra in metallic glasses

et al. 2016

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The vibrational spectra of a series of MgZnCa amorphous alloys were computed using density functional theory and implementing the small displacement method. The atomic structures of the alloys were obtained by ab initio molecular dynamics simulations. The vibrational thermodynamic properties were calculated as a function of temperature and, in particular, the specific heat at low temperature was approximated by temperature cubed based on the Debye model. We computed the contribution of Mg vibrations to the specific heat and investigated the softening of Mg phonon spectra, where the maximum allowed vibrational frequency is lowered and highly collective diffusion processes are promoted. The statistical correlation between the reported critical casting thickness of the alloys and softening of Mg phonons was obtained. Similar calculations were performed for two distinctively different amorphous ZrTiCuAl alloys with large and small reported critical casting thickness, respectively. The findings were consistent with those of the MgZnCa alloys. INTRODUCTIONThere has been increasing attention devoted to the effect of vibrational thermodynamics on the formation of different alloy phases and their associated phase transformations due to the improved accessibility of instruments capable of measuring and calculating the phonon frequencies. 1 Various thermodynamic properties such as specific heat and vibrational entropy can be derived through the vibrational density of states (VDOSs). The VDOS obtained by molecular dynamics (MD) simulations has provided useful insight into how phonon spectra are affected by both the size and surface properties of silicon nanoparticles; this is of major significance in the design of nanodevices with better heat transport properties. It was found that, as the Si particles become smaller, the density of vibrational states increases at low frequencies, and modes are transferred from the high-frequency end to the intermediate range and transverse optical modes peak are shifted to higher frequencies. 2 In metallic glasses, vibrational characteristics have also been used for explaining mechanical properties. For example, recent MD simulations of a Cu 64 Zr 36 metallic glass showed that the strongest participation in the modes with lowest vibrational frequency and, hence, weakest spring constants (i.e., soft modes) originate predominantly from meagrely populated polyhedra. These soft spots provide fertile sites for accommodating shear transformations. 3 The softening of long wavelength acoustic phonons in PdSiCu, ZrTiCuNiBe, CeAlNiCu and ZrNbCuNiBe amorphous alloys relative to their crystalline phases have been observed experimentally using ultrasound measurements. [4][5][6] Such observations are consistent with the low-temperature measurements of their specific heat, whereby an increase in temperature causes a steeper increase in specific heat in the amorphous alloys compared with their crystalline counterparts.Specific heat is believed to be a fundamental property of materials and, in particular,...

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Softening of phonon spectra in metallic glasses

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“…We point out that since our results 2 were published, we have independently confirmed the qualitative change of transport properties in our system near the mode-coupling crossover by analysing the temperature evolution of dynamical finite size effects 4 On the basis of their angle-resolved photoemission studies, the group from Tokyo arrived at the conclusion that the metallic state is twodimensional, anisotropic and disperses strongly in a direction perpendicular to the Au-induced nanowires 5,6 . In contrast, the group from Würzburg performed angle-resolved photoemission and scanning tunnelling microscopy (STM) experiments, and concluded that the metallic state is strictly onedimensional and originates from the Auinduced nanowires 2,7,8 . This controversy regarding the dimensionality and dispersion direction of the metallic state can only be resolved by measuring the spatially resolved local density of states (LDOS).…”

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Origin of the Au/Ge(001) metallic state

2012

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correspondenceKob et al. reply -In their Correspondence, Flenner and Szamel 1 compare the temperature dependence of an alternative dynamic length scale, ξ 4 , with that of ξ dyn , which we studied 2 . Using computer simulations of the same system, they conclude that these two length scales have a different temperature dependence. In particular, ξ 4 does not follow the striking non-monotonic temperature dependence we reported for ξ dyn . Although both types of measurements aim at quantifying the spatial extent of dynamic correlations in supercooled liquids, the two procedures differ on essential points, which we now discuss.Whereas we measured up to the distance at which the value of the relaxation time is affected by the presence of an amorphous wall 2 , Flenner and Szamel quantify instead the spatial extent of spontaneous dynamic fluctuations at low wavevectors for a fixed timescale (the bulk relaxation time). These two measurements need not be directly related, although they seem to coincide at moderate temperatures ( Fig. 1a of ref. 1). Although four-point functions as measured by Flenner and Szamel have played a pivotal role in previous analysis of dynamic heterogeneity, theoretical work has also revealed a number of shortcomings. Most notably, four-point functions display a strong dependence on the statistical ensemble chosen to perform measurements. As a result, they receive distinct contributions from density and energy fluctuations and show, even in idealized cases, complex scaling properties 3 , which complicates the direct extraction of a correlation length. A second difficulty lies in the fact that these various contributions have different temperature dependences, with a crossover taking place very close to the modecoupling temperature where the subtle effects we reported 2 occur. We remark that this corresponds to the temperature scale where ξ 4 and ξ dyn start to differ. These known weaknesses of four-point functions had in fact motivated our study of an alternative correlation length scale that is free of such ambiguities.Given these important differences, it is not clear how a non-monotonic temperature evolution of dynamic correlations will manifest itself in the numerical data of Flenner and Szamel. Although the authors argue that the evolution of ξ 4 with the relaxation time shows a crossover (Fig.1c in ref. 1), we point out that the presented data does not clearly show such a change in behaviour. Another possibility, not explored by Flenner and Szamel, could be that the functional form of the four-point correlation function S 4 (q,t) as investigated by these authors changes with temperature, in agreement with the idea that the geometry of the relaxing entities changes with temperature, as we argued 2 . As the reported effect is small (Fig. 2b in ref. 2), one would presumably need a relative accuracy of S 4 (q,t) of better than 1% at low wavevectors. The data shown by Flenner and Szamel demonstrate that at present this remains technically difficult.Finally, the crossover we report also coincides...

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“…Thus, it is very plausible that atom-atom interaction effects are responsible for the softening of the TO phonon at the X point. Using molecular dynamics calculations it was recently shown by Meyer and Comtesse, that the observed redshift in the VDOS regardless from the symmetry point can be explained by the increasing number of surface atoms [15].…”

Section: Vibrational Propertiesmentioning

confidence: 99%

Optical Properties of Silicon Nanoparticles

Meier

Lorke

2012

Nanoparticles From the Gasphase

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This chapter reviews recent results on optical spectroscopy on silicon nanoparticles. The quantum confinement effect causing a spectral shift of the photoluminescence together with an intensity enhancement is discussed. The small spatial dimensions lead not only to a change of the electronic states, but affect also the vibronic spectrum as is seen in results on first-and second-order Raman scattering. Using time-resolved spectroscopy, the excitonic fine structure of silicon nanoparticles is investigated and a crossover of bright and dark exciton states is found. The analysis of the recombination dynamics allows to determine the size-dependence of the oscillator strength, which is in the order of 10 −5 and increases with decreasing particle size. Finally, we demonstrate an electroluminescence device based on silicon particles using impact ionization. IntroductionDue to the fact that most physical, chemical, and mechanical properties of nanostructured materials are determined by their structure, especially by geometry and size, many applications have been developed based on fundamental research in this field. The reasons for the novel effects in such nanomaterials are manifold, ranging from surface effects, e.g., in nanoparticle based gas sensors, to quantum confinement effects in sufficiently small structures. Among the inorganic materials used

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Vibrational density of states of silicon nanoparticles

Cited by 49 publications

References 32 publications

Softening of phonon spectra in metallic glasses

Softening of phonon spectra in metallic glasses

Origin of the Au/Ge(001) metallic state

Optical Properties of Silicon Nanoparticles

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