B. B. Tripathi

Noncentral forces in the study of lattice dynamics of metals

A comparative study of angular force models proposed by Clark et al (1964) and deLauney (1956) including the electron-ion interaction on the lines of Behari and Tripathi (1970) as applied to the cubic metals has been made. The forces are considered up to second neighbours only. Analytically it is found that the two models are equivalent for bcc structures but they give different results for fcc metals. The phonon dispersion curves for three transition metals (V,Nb,Ta) have been computed and the numerical results from both the models are found to be exactly coincident and also in good agreement with the experimental data.

Phonon dispersion relations of graphite and first stage alkali metal-graphite intercalation compounds

Abstract The phonon dispersion relations of graphite and first stage alkali metal-graphite intercalation compounds (KC 8 ) have been calculated using an angular force model approach. Initially, for graphite, the investigations were made by considering the interactions up to two neighbours in the plane and one neighbour between the planes. We present the first calculation of the phonon dispersion relations of graphite where the recent experimental measurement A 2u out of plane mode at 868 cm −1 is satisfactorily explained as output data, whereas earlier workers have presented the phonon spectrum considering this mode as input data. We have extended the analysis to the evaluation of the phonon spectrum and elastic constants of first stage potassium-graphite intercalation compounds. Good agreement has been observed between theory and the available experimental results. An inference is drawn that the angular forces play a vital role in explaining the acoustic modes of the phonon spectra.

Angular forces in the lattice dynamics of diamond crystal lattices

Abstract The lattice dynamics of the diamond lattice has been investigated using a model in which the interatomic forces include, in addition to central forces, the angular forces of the type employed by de Launay and Clark, Gazis and Wallis. The 2 models have been applied to silicon and germanium to investigate the phonon dispersion curves in the three symmetry directions of the Brillioun zone. The results are found to be qualitatively in good agreement with experiments.

Long wavelength optical lattice vibrations in mixed chalcogenide spinels Zn1−xCdxCr2S4 and CdCr2 (S1−xSex)4

Abstract The composition dependence of the long wavelength optical lattice vibrations of mixed spinels Zn1−xCdxCr2S4 and CdCr2 (S1−xSex)4 was studied using the de Launay-type angular force constant model. One-mode type behaviour is predicted for all the vibrational modes in mixed Zn1−xCdxCr2S4 and CdCr2 (S1−xSex)4 spinel systems. Good agreement between the theoretical and the experimental values was obtained.

Lattice dynamics of gold: A pseudopotential approach

Abstract The phonon dispersion of gold is calculated by means of a transition metal model potential. Comparison of the results with the experimental ones shows a fair agreement.

Lattice dynamics of lithium using a pseudopotential approach

The phonon dispersion in the three symmetry directions, the binding energy, the compressibility and the elastic constants of crystalline lithium and the electrical resistivity of the liquid metal are reported using the pseudopotential approach. Two unknown parameters of the pseudopotential were adjusted to fit the observed vibration frequencies at the zone boundary in the [100] and the [110] direction. An exponential term has been introduced in the repulsive part of the model pseudopotential of Harrison to obtain a rapid convergence. Further, because of this exponential term, the attractive and the repulsive parts of the pseudopotential cancel each other at high wave numbers, as demanded by the theory. Also the repulsive part vanishes rapidly outside the core region as pointed out by Sham and Ziman. The phonon frequencies are in very good agreement with the experiment. In particular, this form of the model pseudopotential reproduces the crossing of the longitudinal and the transverse branches along the [100] direction. The agreement between theory and experiment in the case of binding energy, the compressibility and the elastic constants is also very good. The real test of the proposed model comes from the successful interpretation of the electrical resistivity of the liquid metal.

Crystal dynamics of light weight alkali metals

The lattice dynamics of lithium, sodium and potassium have been studied on a modified de Launay type angular force interaction, where an account is also taken of the presence of conduction electrons, on the lines of the Sharma and Joshi model. A calculation of the phonon dispersion relations, the Debye temperature and the Debye-Waller factor gives very good agreement with the experimental results.

Phonon dispersion relations in iron-based FCC alloys

The phonon dispersion relations for the FCC cubic alloys Fe0.7Ni0.3, Fe0.5Ni0.5, Fe0.25Ni0.75 and Fe0.72Ni0.28 have been investigated using an angular force model. The theoretical results are found to be in good agreement with the experiment. An inference is drawn that in these alloys there is no disorder or clustering effect.

Study of interaction forces and phonons in some spinels and mixed systems

Abstract A detailed study of zone centre phonons in mixed spinel structure compounds is presented, using an angular force constant model considering interatomic interactions up to third neighbours only. For the first time the dynamical matrix for spinel structure compounds AB 2 X 4 of the order of 42 × 42 has been solved analytically at the zone centre. Using these analytical expressions and the measured zone centre frequencies, the evaluation of the force constants has been carried out first in the case of CdCr 2 S 4 , CdCr 2 Se 4 and ZnCr 2 S 4 . It has been found that the second neighbour interatomic interaction between B-X atoms is more significant than the first neighbour interaction between A-X atoms in these normal spinels. The physical aspects for the same are discussed. The computed phonon frequencies of CdCr 2 S 4 , CdCr 2 Se 4 and ZnCr 2 S 4 at the zone centre agree well with the Raman and the infrared measurements. Finally, the analysis is carried out to study the zone centre phonons in mixed crystals of these spinels.

Lattice dynamics of PbxCd1-xF2 mixed superionic crystals

Abstract A modified rigid ion model has been used to investigate the one-mode behaviour in the PbxCd1-xF2 mixed crystals. It has been found that the said correlation between ionic transport properties and the flourine-cation interaction coefficient for PbxCd1-xF2 crystals is not reasonable. The agreement obtained for the zone centre frequencies with the experiment is satisfactory for all composition range.