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.