Abstract
A procedure for pseudopotential calculations of the elastic constants of BCC alkali metals is developed using radial and tangential force constants obtained from the dependence of the pairwise interatomic potential on distance. The equations for calculating elastic constants are derived using the Delaunay algorithm based on elements of a dynamic matrix defined by radial and tangential force constants and a subsequent long-wavelength approximation whose results are compared with the elements of a dynamic matrix expressed within a similar approximation in the Born-Begbie model through elastic constants c 11, c 12, and c 44. The calculations for elastic constants of alkali metals performed using the proposed procedure agree satisfactorily with the experimental data.
Similar content being viewed by others
References
Harrison, W.A., Pseudopotentials in the Theory of Metals, New York: Benjamin, 1966.
Heine, V., Cohen, M.L., and Weaire, D., The Theory of Pseudopotential, Moscow: Mir, 1973.
Animalu, A., Intermediate Quantum Theory of Crystalline Solids, Prentice Hall, 1978.
Shyu, W.M. and Gaspari, G.D., Phys. Rev., 1968, vol. 170, pp. 687–693.
Ashcroft, N.W., Phys. Lett., 1966, vol. 23, pp. 48–50; Ashcroft, N.W. and Langreth, D.C., Phys. Rev., 1967, vol. 155, pp. 682–685.
Squires, G.L., Arkiv Phys., 1963, vol. 25, pp. 21–32.
Shyam, R., Upadhyaya, S.C., and Upadhyaya, J.C., Phys. Status. Solidi B, 1990, vol. 161, pp. 565–574.
Upadhyaya, S.C., Upadhyaya, J.C., and Shyam, R., Phys. Rev. B, 1991, vol. 44, pp. 122–129.
Animalu, A.O.E. and Heine, V., Phil. Mag., 1965, vol. 12, pp. 1259–1270; Animalu, A.O.E., Phys. Rev. B, 1973, vol. 8, pp. 3542–3554.
Silonov, V.M., Rodin, S.Yu., and Enkhtor, L., Vestn. Mosk. Gos. Univ. Ser. 3. Fiz., Astron., 2000, no. 3, pp. 28–30.
Silonov, V.M., Enkhtor, L., Shilagardi, G., and Galbadrakh, R., The way to calculate some parameters of nickel and its alloys by means of modeling potential, Preprint, Faculty of Physics, Lomonosov Moscow State Univ., 2004, no. 1.
de Launay, J., Solid State Phys., 1956, vol. 2, pp. 219–295.
Habbard, J., Proc. R. Soc. London, Ser. A, 1957, vol. 240, pp. 539–560; 1958, vol. 243, p. 336–352.
Sham, L.J., Proc. R. Soc. London, Ser. A, 1965, vol. 283, pp. 33–39.
Krivoglaz, M.A., Difraktsiya rentgenovskikh luchei i neitronov v neideal’nykh kristallakh (X-Rays and Neutrons Diffraction in Non-Ideal Crystals), Kiev: Naukova dumka, 1983.
Nash, H.C. and Smith, C.S., J. Phys. Chem. Solids, 1959, vol. 9, pp. 113–118.
Huntington, H.B., Solid State Phys., 1958, vol. 7, pp. 213–285.
Bender, O., Ann. d. Phys., 1939, vol. 34, pp. 359–376.
Marquart, W.R. and Trivisonno, J., J. Phys. Chem. Solids, 1965, vol. 26, pp. 273–278.
Gutman, E.J. and Trivisonno, J., J. Phys. Chem. Solids, 1967, vol. 28, pp. 805–809.
Kollarits, F.J. and Trivisonno, J., J. Phys. Chem. Solids, 1968, vol. 29, pp. 2133–2139.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © L. Enkhtor, V.M. Silonov, 2014, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2014, Vol. 78, No. 11, pp. 1432–1437.
About this article
Cite this article
Enkhtor, L., Silonov, V.M. Procedure for pseudopotential calculations of alkali metal elastic constants. Bull. Russ. Acad. Sci. Phys. 78, 1163–1168 (2014). https://doi.org/10.3103/S1062873814110070
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1062873814110070