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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Jogi S.: J. Phys. F4 (1974) 313.
Hemkar M. P., Prakash J., Chandra S.: Acta Phys. Pol. A44 (1973) 3.
Bose G., Gupta H. C., Tripathi B. B.: J. Phys. F2 (1972) 426.
Kushwaha S. S.: Nuovo Cimento B20 (1974) 83.
Shukla M. M., Salzberg J. B.: J. Phys. F3 (1973) 199.
Jani A. R., Gohel V. B.: Phys. Lett. A55 (1976) 350.
Fielek B. L.: J. Phys. F5 (1975) 17.
de Launay J.: Solid State Phys.2 (1956) 219.
Bhatia A. B.: Phys. Rev.97 (1955) 363.
Sharma P. K., Joshi S. K.: J. Chem. Phys.39 (1963) 2933.
Krebs K.: Phys. Rev. A138 (1965) 143.
Upadhyaya J. C., Sharma S. S., Kulshrestha O. P.: Phys. Rev. B12 (1975) 2236.
Cheveau L.: Phys. Rev.169 (1968) 496.
Gohel V. B., Jani A. R.: J. Phys. F29 (1976) 31.
Gohel V. B., Jani A. R.: Pramāna9 (1977) 593.
Sharma P. K., Pal S., Gupta R. P.: Rev. Roum. Phys.14 (1969) 247.
Manesh P., Dayal B.: Phys. Rev.143 (1966) 443.
Lahteenkorve E. E.: Ann. Acad. Sci. Fennical A321 (1955) 15.
Brovman E. G., Kagan Y.: Dynamical Properties of Solids. Vol. 1. North-Holland, 1974.
Sarkar S. K., Das S. K., Roy D., Sengupta S.: Phys. Status Solidi (b)83 (1977) 615.
Nakagawa Y., Woods A. D. B.: Lattice Dynamics. Pergamon Press, 1965, p. 39.
Sharma P. K., Semwal B. S., Mehrotra K. N.: Z. Naturforsch. A36 (1971) 747.
Singh V.P., Kharoo H.L., Prakash J., Pathak L.P.: Acta Phys. Acad. Sci. Hung.29 (1975) 37.
Gohel V. B., Jani A. R.: Indian J. Phys.50 (1976) 609.
Brescansin L. M., Padial N. T., Shukla M. M.: Nuovo Cimento B34 (1976) 103.
Pal S., Gupta R. P.: J. Phys. Soc. Japan21 (1966) 2268.
Bajpai R. P., Neelakandan K.: Nuovo Cimento B7 (1972) 177.
Wakabayashi N.: Solid State Commun.23 (1977) 737.
Sinha S. K., Harmon B. N.: Phys. Rev. Lett.35 (1975) 1515.
Allen P. B.: Phys. Rev. B16 (1977) 5139.
Author information
Authors and Affiliations
Additional information
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.
Rights and permissions
About this article
Cite this article
Jani, A.R., Gohel, V.B. Phonon dispersion curves for niobium. Czech J Phys 34, 1334–1338 (1984). https://doi.org/10.1007/BF01590418
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01590418