Phonon dispersion in graphite

We measured the dispersion of the graphite optical phonons in the in-plane Brillouin zone by inelastic x-ray scattering. The longitudinal and transverse optical branches cross along the Gamma-K as well as the Gamma-M direction. The dispersion of the optical phonons was, in general, stronger than expected from the literature. At the K point the transverse optical mode has a minimum and is only approximately 70 cm(-1) higher in frequency than the longitudinal mode. We show that first-principles calculations describe very well the vibrational properties of graphene once the long-range character of the dynamical matrix is taken into account.     

Phonon dispersion in NiO

The phonon dispersion relations in NiO have been measured using coherent inelastic neutron diffraction. Good fits to the data were obtained using various shell models. The room temperature phonon density of states was calculated and used to determine the temperature dependence of the lattice specific heat and the Debye temperature.     

Phonon dispersion in graphene

Taking into account the constraints imposed by the lattice symmetry, we calculate the phonon dispersion for graphene with interactions between the first and second nearest neighbors. We show that only five force constants give a very good fitting to the elastic constants and phonon frequencies observed in graphite. The text was submitted by the author in English.     

Phonon dispersion in Xe

The predictions of the Mie-Lennard-Jones potentials for phonon dispersion in solid Xe at 10°K and at 77°K are compared with the results of recent measurements. The dynamics of the crystal are described by the first order self-consistent phonon theory for the imaginary part of the one phonon Green's function. The fit obtained is quite poor though we point out that no conclusion can be drawn about the size of three-body forces. We conclude that improved potentials are needed to account for the experimental data.     

Phonon dispersion of graphene revisited

The phonon dispersion of graphene is derived by using a simple mass spring model and considering up to the first, second, third, and fourth nearest-neighbor interactions. The results obtained from different nearest-neighbor interactions are compared and it is shown that the k ² dependence for the out-of-plane transverse acoustic mode obtained in other sophisticated methods as well as experiment occurs only after including the fourth nearest-neighbor interaction.     

Phonon dispersion of carbon nanotubes

We present the phonon dispersion relations of single-wall carbon nanotubes calculated within a force-constants approach. By using the full symmetry group of the tubes, we are able to calculate the dispersion relations for any chirality starting from one single carbon atom. We find an overbending in the highest optical branch between 6 and 12 cm⁻¹ independent of the tube diameter. The order of the high-energy modes at the Γ-point differs from the results derived from simple zone folding. The splitting between the two Raman active optical modes with A₁ symmetry at the Γ-point of chiral tubes is ≈4 cm⁻¹ for typical diameters; it increases with decreasing tube diameter.     

Phonon dispersion curves for niobium

Conclusion The experimentally measured phonon dispersion relation for niobium is very complex. This complexity may be due to the incomplete electronicd shells which make an important contribution to very large cohesive energy, and its likely effect on the phonon frequencies. Also the anomalies in the dispersion curves may be due to the departure of the Fermi surface from sphericity. In the present study none of the above effects is included explicitly and so theory fails to achieve exact agreement with the experimental data. Finally, we would like to put a concluding remark that an appropriate microscopic treatment given tod electron could explain the phonon dispersion curves of transition metal like niobium.One of the authors (ARJ) would like to express his appreciation to Professor M. K. Agarwal (Head of the Department) for his support and encouragement to carry out this work. Thanks are also due to Sardar Patel University for providing computer facilities.     

Phonon dispersion relations in copper

Phonon frequencies for copper have been obtained by extending the work of Yuenand Varshni to include the electron-ion interaction term of de Launay's model. The results thus obtained show a better agreement with the experimental data.     

Phonon dispersion curves of GaAsAlAs superlattices

The phonon properties of (GaAs)_m(AlAs)_n superlattices are studied with an eleven-parameter rigid-ion model. Short-range interactions up to the second neighbours are included, and the long-range Coulomb interaction is calculated exactly. Modes propagating both normal (k_// = 0) oblique (k_// ≡ 0) to the interfaces are studied. Anisotropy of zone center optical phonons is examined. The theoretical results are compared with the existing experimental data with favorable agreement.     

Phonon dispersion relations of tetrahedrally-bonded crystals

The lattice dynamics of the tetrahedrally-bonded compounds is formulated from first principle by using a model of binding force proposed by us, which mainly includes covalent interactions in the perturbational treatment based on the pseudopotential formalism and also partly on ionic interactions. Numerical calculations are performed for GaP and ZnS. In spite of our introducing no adjustable parameter except the optical phonon-frequency splitting in the long-wavelength limit, the resulting phonon dispersion curves are qualitatively in good agreement with the observed data. We show that ionic contributions are important for the optical phonon frequencies of these compounds.     

Phonon dispersion of ice under pressure

We report measurements of the phonon dispersion of ice Ih under hydrostatic pressure up to 0.5 GPa, at 140 K, using inelastic neutron scattering. They reveal a pronounced softening of various low-energy modes, in particular, those of the transverse acoustic phonon branch in the [100] direction and polarization in the hexagonal plane. We demonstrate with the aid of a lattice dynamical model that these anomalous features in the phonon dispersion are at the origin of the negative thermal expansion (NTE) coefficient in ice below 60 K. Moreover, extrapolation to higher pressures shows that the mode frequencies responsible for the NTE approach zero at approximately 2.5 GPa, which explains the known pressure-induced amorphization (PIA) in ice. These results give the first clear experimental evidence that PIA in ice is due to a lattice instability, i.e., mechanical melting.     

Phonon dispersion relation of liquid metals

The phonon dispersion curves of some liquid metals, viz. Na (Z = 1), Mg (Z = 2), Al (Z = 3) and Pb (Z = 4), have been computed using our model potential. The charged hard sphere (CHS) reference system is applied to describe the structural information. Our model potential along with CHS reference system is capable of explaining the phonon dispersion relation for monovalent, divalent, trivalent and tetravalent liquid metals.