Abstract
General analytical expressions are obtained for the dynamical matrix D(k) and the elastic constants C ik in an HCP crystal in terms of the Born-von Karman (BvK) parameters. An analytical method is proposed for constructing D(k) on the basis of data about the phonon frequencies ω i (N) at the symmetry points of the Brillouin zone and the elastic constants C ik . A number of relations between the values of ω i (N) and C ik are presented for conventional interaction models. It is shown that the standard method for determining BvK parameters by fitting them to experimental phonon spectra in HCP lattices is, as a rule, ambiguous, whereas the analytical method proposed allows one to find all the solutions of the problem. The methods developed are illustrated by the construction of dynamical matrices for Tb, Sc, Ti, and Co.
Similar content being viewed by others
References
M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Clarendon, Oxford, 1954; Inostrannaya Literatura, Moscow, 1958), Chap. 5.
E. C. Svensson, B. N. Brockhouse, and J. M. Rowe, Phys. Rev. 155, 619 (1967).
R. E. DeWames, T. Wolfram, and G. W. Lehman, Phys. Rev. [Sect. A] 138, 717 (1965).
J. C. Glyden Houmann and R. M. Nicklow, Phys. Rev. B 1, 3943 (1970).
R. M. Nicklow, N. Wakabayashi, and P. R. Vijayaraghavan, Phys. Rev. B 3, 1229 (1971).
N. Wakabayashi, S. K. Sinha, and F. H. Spedding, Phys. Rev. B 4, 2398 (1971).
R. Pynn and G. L. Squires, Proc. R. Soc. London, Ser. A 326, 347 (1972).
J. Pleschiutschnig, O. Blaschko, and W. Reichardt, Phys. Rev. B 44, 6794 (1991).
V. G. Vaks and K. Yu. Khromov, Zh. Éksp. Teor. Fiz. 133, 313 (2008).
A. G. Khachaturyan, The Theory of Phase Transformations and the Structure of Solid Solutions (Nauka, Moscow, 1974) [in Russian].
S. V. Beiden and V. G. Vaks, Phys. Lett. A 163, 209 (1992).
M. S. Blanter, E. B. Granovsky, et al., J. Alloys Compd. 335, 1 (2002); M. S. Blanter, I. S. Golovin, E. B. Granovsky, and H. R. Sinning, J. Alloys Compd. 345, 1 (2002).
V. G. Vaks and K. Yu. Khromov, Zh. Éksp. Teor. Fiz. 133, 115 (2008).
H. R. Schober and P. H. Dederichs, in Landolt-Börnstein, Vol. 13A: Metals (Springer, Berlin, 1992), p. 1.
N. Wakabayashi, R. H. Scherm, and H. G. Smith, Phys. Rev. B 25, 5122 (1982).
A. P. Roy, B. A. Dasannacharya, C. L. Thaper, and P. K. Iyengar, Phys. Rev. Lett. 30, 906 (1973).
R. Heid, L. Pitchovius, W. Reichardt, and K.-P. Bohnen, Phys. Rev. B 61, 12059 (2000).
N. J. Chesser and J. D. Axe, Phys. Rev. B 9, 4060 (1974).
Second and Higher Order Elastic Constants, Ed. by A. Every and A. McCurdy (Springer, Berlin, 1992), Landolt-Bornstein New Series, Group III, Vol. 29a, p. 105.
J. L. Warren, Rev. Mod. Phys. 46, 38 (1968).
C. Kittel, Introduction to Solid State Physics, 5th ed. (Wiley, New York, 1976; Nauka, Moscow, 1978), Table 1.4.
V. G. Vaks and K. Yu. Khromov, Phys. Rev. B 75, 212103 (2007).
G. Gilat, G. Rizzi, and G. Cubiotti, Phys. Rev. 185, 971 (1969).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.G. Vaks, K. Yu. Khromov, 2008, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2008, Vol. 133, No. 3, pp. 571–592.
Rights and permissions
About this article
Cite this article
Vaks, V.G., Khromov, K.Y. Construction of a dynamical matrix for an HCP crystal using phonon data at the symmetry points of the Brillouin zone and elastic constants. J. Exp. Theor. Phys. 106, 495–516 (2008). https://doi.org/10.1134/S1063776108030102
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776108030102