Joseph L. Feldman

Diffusons, locons and propagons: Character of atomie yibrations in amorphous Si

Abstract Numerical studies of amorphous Si show that the lowest 4% of vibrational modes are piane wave like (‘propagons’) and the highest 3% of modes are localized (‘locons’). The rest are neither piane wave like nor localized. We cali them ‘diffusons’. Since diffusons are by far the most numerous, we try to characterize them by calculating such properties as the wave-vector and polarization (which do not seem to be useful), ‘phase auotient’ (a measure of the change of vibrational phase between first-neighbour atoms), spadal polarization memory and diffusivity. Localized states are characterized by finding decay lengths, inverse participation ratios and coordination numbers of the participating atoms.

First principles determination of the interatomic force-constant tensor of the fullerene molecule

Abstract We have determined the full force constant tensor (Hessian) of the fullerene molecule, C 60 from first principles. From our all-electron density functional code, the forces on all of the atoms are calculated for different displacements of a single atom. Using finite differences and the symmetry operations of the molecule, the full matrix is determined. Diagonalization of the dynamical matrix yields the vibrational modes, which are in excellent agreement with experiment. The range and nature of the force constant tensor will be presented.

Fullerene molecules and tubules polarizabilities, vibrational modes and nanocapillarity

Abstract Recent algorithmic and computational advances for density-functional-based investigations of clusters now allow for the calculation of a multitude of low-energy phenomena in complex clusters and molecules. Here we discuss methods for the first-principles calculation of linear and non-linear electronic polarizabilities and for vibrational modes. Results from recent calculations on the C60 molecule show that the local-density-approximation (LDA) is capable of a very accurate quantitative description of such phenomena. As an example of how the high polarizability of caged carbon compounds might be beneficially exploited for new technological applications, we review recent simulations which predicted that fullerene tubules behave as molecular straws.

Properties of Novel Thermoelectrics from First Principles Calculations

The use of first principles methods based on density functional theory to investigate novel thermoelectric materials is illustrated for several empty and filled skutterudite compounds, including CoSb 3 , COP 3 , La(Fe,Co) 4 Sb 12 and La(Fe,Co)P 12 . Band structures and their relationship to transport properties especially as regards optimization of thermoelectric properties is discussed. Phonon models constructed from calculations and existing experimental data for CoSb 3 are presented. These have been extended to the filled skutterudites, particularly LaFe 4 Sb 12 using additional first principles calculations to fix the La related parameters in the model. This model allows an interpretation of neutron scattering data as well as an understanding of the low frequency phonon modes that transport heat in these compounds.

Anisotropy effects in the linearly polarized x-ray absorption spectrum of Br2 intercalated graphite fibers and highly oriented pyrolytic graphite

Abstract Angle dependent Br K edge x-ray absorption spectra were obtained for residual compounds of Br 2 intercalated HOPG and TP4104B graphite fibers using polarized synchrotron radiation. In both materials, the bromine appears to be in the form of Br 2 molecules oriented at an angle of about 20° with respect to the graphite planes. The intramolecular distance is found to be 2.31A. Br-C EXAFS has also been observed and indicates that the Br 2 molecules lie between the graphite planes.

Tight-binding study of structure and vibrations of amorphous silicon

We present a tight-binding calculation that, for the first time, accurately describes the structural, vibrational and elastic properties of amorphous silicon. We compute the interatomic force constants and find an unphysical feature of the Stillinger-Weber empirical potential that correlates with a much noted error in the radial distribution function associated with that potential. We also find that the intrinsic first peak of the radial distribution function is asymmetric, contrary to usual assumptions made in the analysis of diffraction data. We use our results for the normal mode frequencies and polarization vectors to obtain the zero-point broadening effect on the radial distribution function, enabling us to directly compare theory and a high resolution x-ray diffraction experiment.

Influence of order-disorder on the vibron excitations of H2 and D2 in ortho-para mixed crystals

We present a detailed experimental and theoretical study of the vibrons in ortho-para mixed crystals of solid hydrogen and deuterium at ambient and high pressure. Experimental results were obtained at ambient pressure and T=6–7 K (e.g., for hydrogen samples having ortho fractions of 19–62%) using high-resolution Fabry-Perot techniques, and at high pressure and T=77 K (e.g., hydrogen 50–50% ortho-para samples) using dispersive spectrographic techniques with diamond-anvil cells. The numerical calculations are based on the James and Van Kranendonk theory, and were performed by exactly diagonalizing the Hamiltonian for a large supercell of randomly placed molecular “species” on a crystalline lattice. Overall, excellent agreement between theory and experiment is obtained. The calculations show that disorder leads to Anderson localized vibrons for many of the pressures and concentrations studied experimentally and that a substantial portion of the Raman intensity is derived from these localized vibrons. We also calculate the species characteristics of the individual Raman peaks, the results of which suggest an explanation for the previously noted disagreement between experimental high-pressure results and the predictions of the van Kranendonk theory. Specifically, our analysis indicates that the higher frequency peak is associated with anisotropic scattering arising from partial alignment of J=1 angular momenta with respect to the crystallographic axes. Finally, our calculations show that the observed doublet structure in the lower frequency Raman peak for deuterium at low para (J=1) concentrations is well represented by added (para-molecule) diagonal terms in the van Kranendonk Hamiltonian that are plausibly associated with electric quadrupole-quadrupole interactions.

Local dynamic properties

Abstract Local elastic and dynamie properties of a 4096-atom model of amorphous silicon within the Stillinger–Weber potential are discussed. In particular the recently introduced frustration parameter, mean square displacements and Einstein frequencies are calculated. It is obtained that the isotropy associated with the Einstein frequencies is considerably less than that associated with the mean square displacements. It is also seen that the distribution function for the squares of the Einstein frequencies is symmetric whereas that related to the mean square displacements is strongly skewed to high values. In addition, the Keating potential is considered in an attempt to estimate the power of Q in the linewidth of the low-frequency dynamie structure factor for models of amorphous silicon.

Molecular dynamics simulations of vibrational lifetimes in amorphous silicon

Abstract Recent theoretical and time resolved Raman studies disagree on the lifetime of high energy vibrational modes in amorphous silicon. The latter suggests that the lifetime increases with increasing frequency and is of the order of 10 ns for the highest frequency modes, while the former predicts a picosecond timescale that follows the two-phonon density of states. Here we present the results of molecular dynamics simulations which are complementary to the perturbative calculations. At different temperatures, kinetic energy is put into selected modes of vibration in 216 and 4096 atom systems with periodic boundary conditions and the Stillinger—Weber potential. The lifetime of medium and high frequency modes is found to be of the order of 1 ops at 5, 10 and 30 K, in qualitative agreement with the perturbative calculations.

Realistic model calculations based on the Kubo theory for the thermal conductivity of amorphous insulators

Abstract The thermal conductivity of models of amorphous silicon and vitreous silica are discussed. In previous work on amorphous silicon, 216-and 1000-atom models were studied within the Kubo theory and the harmonic approximation using the Stillinger-Weber potential and good agreement with the experimental high-temperature apparent saturation value was obtained. In order to test the model dependence of such results we performed calculations for models based on the Keating potential. The Keating model apparently gives much less force-constant disorder than does the Stillinger-Weber model, as evident from the N dependence and the frequency range of localized states. We also present results of calculations for vitreous silica based on the Feuston-Garofalini model that we relaxed, using their potential, to zero pressure. The results for vitreous silica are in fair agreement with experiment at temperatures above 100K which corresponds to the lowest normal-mode frequency contained within the model.