Intermediate frequency range (511 - 514 cm-1) Si phonons in Si-SiO2 nanocomposites are shown to have contribution from both core1 and surface/interface1 Si phonons, where, ratio of contribution of the two depends on the size of a Si nanocrystal. Furt
her, laser heating experiment shows that contribution of the core phonon increases due to increase in size of a nanocrystal. Wavelength dependent Raman mapping reveals that interface phonons are observable due to Resonance Raman scattering. This can well be corroborated with the absorption spectra. This understanding can be gainfully used to manipulate and characterize Si-SiO2 nanocomposite, simultaneously for photovoltaic device applications.
Si-SiO2 multilayer nanocomposite (NCp) films, grown using pulsed laser deposition with varying Si deposition time are investigated using Raman spectroscopy/mapping for studying the variation of Si phonon frequency observed in these NCps. The lower fr
equency (LF) phonons (~ 495 - 510 cm-1) and higher frequency (HF) phonons (~ 515 - 519 cm-1) observed in Raman mapping data (Fig. 1A) in all samples studied are attributed to have originated from surface (Si-SiO2 interface) and core of Si nanocrystals, respectively. The consistent picture of this understanding is developed using Raman spectroscopy monitored laser heating/annealing and cooling (LHC) experiment at the site of a desired frequency chosen with the help of Raman mapping, which brings out clear difference between core and surface (interface) phonons of Si nanocrystals. In order to further support our attribution of LF being surface (interface) phonons, Raman spectra calculations for Si41 cluster with oxygen termination are performed which shows strong Si phonon frequency at 512 cm-1 corresponding to the surface Si atoms. This can be considered analogous to the observed phonon frequencies in the range 495 - 510 cm-1 originating at the Si-SiO2 interface (extended). These results along with XPS data show that nature of interface (oxygen bonding) in turn depends on the size of nanocrystals and thus LF phonons originate at the surface of smaller Si nanocrystals. The understanding developed can be extended to explain large variation observed in Si phonon frequencies of Si-SiO2 nanocomposites reported in the literature, especially lower frequencies.
A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the spherical 2D
pendulum models as special cases. The case where the rigid body is asymmetric and the center of mass is distinct from the pivot location leads to the 3D pendulum. Full and reduced 3D pendulum models are introduced and used to study important features of the nonlinear dynamics: conserved quantities, equilibria, invariant manifolds, local dynamics near equilibria and invariant manifolds, and the presence of chaotic motions. These results demonstrate the rich and complex dynamics of the 3D pendulum.
