Abstract
The dependence of the static binding energy of a crystal on the crystal structure as calculated in the initial quasi-classical approximation is shown to allow the equilibrium lattice parameter to be found analytically. The application of this method to boron nitride modifications leads to lattice parameters that coincide with experimental values to within several percent. This method gives lattice parameters of 2.66, 3.49, and 2.44 Å for the BN hexagonal layer and the cubic c-BN and “ideal” wurtzite-like w-BN crystals, respectively. The corresponding binding energies are estimated to be 23.2, 14.1, and 13.6 eV/mol, respectively.
Similar content being viewed by others
References
L. S. Chkhartishvili, Quasi-Classical Theory of the Ground State of Matter (Technical University, Tbilisi, Georgia, 2004) [in Russian].
L. Chkhartishvili, Mat. Zametki 69(3), 421 (2001).
L. Chkhartishvili, Mat. Zametki 77(1), 273 (2005).
L. S. Chkhartishvili, Tr. Gruz. Tekh. Univ. 3(427), 13 (1999).
L. Chkhartishvili, D. Lezhava, O. Tsagareĭshvili, and D. Gulua, Tr. Akad. Minist. Vnutr. Del Gruz. 1, 295 (1999).
L. Chkhartishvili, D. Lezhava, and O. Tsagareĭshvili, J. Solid State Chem. 154(1), 148 (2000).
L. Chkhartishvili and D. Lezhava, Tr. Gruz. Tekh. Univ. 6(439), 87 (1999).
L. Chkhartishvili, in Proceedings of the First International Boron Symposium, Dumlupinar University, Kütahya, Turkey, 2002 (Dumlupinar University, 2002), p. 139.
L. Chkhartishvili, J. Solid State Chem. 177(2), 395 (2004).
L. S. Chkhartishvili, Fiz. Tverd. Tela (St. Petersburg) 46(11), 2056 (2004) [Phys. Solid State 46 (11), 2126 (2004)].
L. S. Chkhartishvili, in Proceedings of the Second International Boron Symposium, Osmangazi University, Eskişehir, Turkey, 2004 (Osmangazi University, 2004), p. 255.
L. S. Chkhartishvili, Tr. Gruz. Tekh. Univ. 3(411), 45 (1996).
K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure, Vol. 4: Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979; Mir, Moscow, 1984).
A. Gaydon, Dissociation Energies and Spectra of Diatomic Molecules (Chapman and Hall, London, 1947; Inostrannaya Literatura, Moscow, 1949).
J. L. Masse and M. Bärlocher, Helv. Chim. Acta 47(1), 314 (1964).
Yu. G. Khaĭt and V. I. Baranovskiĭ, Zh. Strukt. Khim. 21(1), 153 (1980).
Ch. M. Marian, M. Gastreich, and J. D. Gale, Phys. Rev. B: Condens. Matter 62(5), 3117 (2000).
V. V. Pokropivny, V. V. Skorokhod, G. S. Oleinik, A. V. Kurdiumov, T. S. Bartnitskaya, A. V. Pokropivny, A. G. Sisonyuk, and D. M. Sheichenko, J. Solid State Chem. 154(1), 214 (2000).
Yu. B. Kuz’ma and N. F. Chaban, Binary and Ternary Boron-Containing Systems: A Reference Book (Metallurgiya, Moscow, 1990) [in Russian].
Selected Values of Chemical Thermodynamic Properties (Series I), Ed. by D. D. Wagmann, W. H. Evans, V. B. Parker, J. Halow, S. M. Bairly, and R. H. Shumn (US Department of Commerce: National Bureau of Standards, Washington, 1968).
D. L. Strout, J. Phys. Chem. A 104(15), 3364 (2000).
A. Zunger, J. Phys. C: Solid State Phys. 7, 76 (1974).
A. Zunger, J. Phys. C: Solid State Phys. 7, 96 (1974).
K. Albe, Phys. Rev. B: Condens. Matter 55, 6203 (1997).
N. P. Bezheran, S. A. Bozhko, N. N. Belyavina, and V. Ya. Markin, Sverkhtverd. Mater. 4, 15 (1999).
B. F. Ormont, Izv. Akad. Nauk SSSR, Neorg. Mater. 4(4), 611 (1968).
W. A. Harrison, Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond, Vol. 1 (Freeman, San Francisco, 1980; Mir, Moscow, 1983).
A. Blacha, H. Presting, and M. Cardona, Phys. Status Solidi B 126(1), 11 (1984).
C. Prasad and J. D. Dubey, Phys. Status Solidi B 125, 629 (1984).
K. T. Park, K. Terakura, and N. Hamada, J. Phys. C: Solid State Phys. 20, 1241 (1987).
P. E. van Camp, V. E. van Doren, and J.T. Devreese, Phys. Status Solidi B 146(2), 573 (1988).
P. E. van Camp, V. E. van Doren, and J. T. Devreese, Solid State Commun. 71(12), 1055 (1989).
E. Knitte, R. M. Wentzcovich, R. Janloz, and M. L. Cohen, Nature (London) 337(1), 349 (1989).
M. V. Ganduglia Pirovano and G. Stollhoff, Phys. Rev. B: Condens. Matter 44-I(8), 3526 (1991).
Y.-N. Xu and W. Y. Ching, Phys. Rev. B: Condens. Matter 44-I, 7784 (1991).
N. E. Christensen and I. Gorczya, Phys. Rev. B: Condens. Matter 50-I, 4397 (1994).
D. Vogel, P. Krüger, and J. Pollman, Phys. Rev. B: Condens. Matter 55-I, 12 836 (1997).
A. Malatesta, S. Fahy, and G. B. Bachelet, Phys. Rev. B: Condens. Matter 56-I, 12 201 (1997).
K. Karch and F. Bechstedt, Phys. Rev. B: Condens. Matter 56-II, 7404 (1997).
Encyclopedia of Chemistry, Ed. by I. L. Knunyants (Sovetskaya Éntsiklopediya, Moscow, 1988), Vol. 1 [in Russian].
Y.-N. Xu and W. Y. Ching, Phys. Rev. B: Condens. Matter 48-I, 4335 (1993).
K. Albe, Forschungszent. Rossendorf [Ber.] FZR 228, 1 (1998).
Author information
Authors and Affiliations
Additional information
Original Russian Text © L.S. Chkhartishvili, 2006, published in Fizika Tverdogo Tela, 2006, Vol. 48, No. 5, pp. 606–612.
Rights and permissions
About this article
Cite this article
Chkhartishvili, L.S. Analytical optimization of the lattice parameter using the binding energy calculated in the quasi-classical approximation. Phys. Solid State 48, 846–853 (2006). https://doi.org/10.1134/S1063783406050064
Received:
Issue Date:
DOI: https://doi.org/10.1134/S1063783406050064