Phonon spectra of Zn and Cd using a model pseudopotential approach

Recently Animalu has developed a model potential approach to study the electronic properties of transition metals. We have applied the transition metal model potential (TMMP) of Animalu in the local approximation to derive the phonon dispersion curves of Zn and Cd alongΓA,ΓM andΓKM symmetry directions. Our results differ widely from the experimental data. Further we have added the non-local contribution to the dynamical matrix following the scheme of Eschrig and Wonn and found the resuits comparable to the measured ones.     

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 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 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 small-polaron conductivity problem: A solvable model

The stochastic properties of harmonically coupled oscillators studied by Ford, Kac and Mazur are used to investigate the role of the phonon dispersion in the phonon-assisted small-polaron hopping. It is shown that a particular choice of the vibrational frequency spectrum allows one to express the effect of a weak phonon dispersion as an effective damping of independent local oscillators. Therefore, this particular choice makes it possible to employ literally the theory developed in a previous paper. The dependence on the phonon-dispersion width of the small polaron hopping conductivity determined in this way is illustrated by numerical calculations.     

Lattice dynamics of lithium: A pseudopotential approach

The phonon dispersion of lithium is reported using the model potential approach. One unknown parameter of the pseudopotential was adjusted to fit the observed vibration frequency at the zone boundary in the [110] direction. The agreement between theory and experiment is fair, in particular, reproducing the crossing of the longitudinal and the transverse branches along the [100] direction.     

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 in quasiperiodic semiconductor superlattices

The phonon spectra of unstrained and strained quasiperiodic semiconductor superlattices (QSSL) have been calculated using one-dimensional linear chain model. We consider two types of quasiperiodic systems, namely cantor triadic bar (CTB) and Fibonacci sequences (FS), constituting of AlAs, GaAs and GaSb of which the latter two have a lattice mismatch of about 7%. The calculations have been made using transfer matrix method and also with and without the inclusion of strain. We present the results on phonon spectra of two component CTB and two as well as three component FS semiconductor superlattices (SSL), thickness and order dependence on LO mode of GaAs, effect of strain on LO frequency of GaAs. The calculated results show that the strain generated due to lattice mismatch reduces significantly the magnitudes of the confined optical phonon frequency of GaAs.     

Phonon dispersion in scandium and yttrium

Phonon dispersion relations for Sc and Y are calculated along [0001] and [01$\text{1}$0] symmetry directions using Animalu transition metal model potential.     

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 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.