Abstract
The short-range many-body forces induced by the overlap of electron shells of atoms have been investigated. The nonorthogonality of atomic orbitals of the nearest neighbor atoms of a crystal leads to the appearance of terms in the potential energy, which depend on the coordinates of three, four, and more nearest neighbor atoms. An expression has been obtained for the energy of the electron subsystem of the crystal in the Hartree-Fock approximation in the basis set of atomic orbitals exactly orthogonalized at different crystal sites. The behavior of the contributions from two-particle, three-particle, and many-body interactions to the crystal energy under compression has been analyzed. The short-range three-particle potential has been calculated from first principles and proposed in the simple form. The three-particle forces obtained change the behavior of the dispersion curves for all wave vectors, in particular, thus violating the Cauchy relation. The theoretical and experimental deviations from the Cauchy relation for argon are in good agreement over a wide pressure range.
Similar content being viewed by others
References
R. J. Hemley and H.-K. Ashcroft, Phys. Today 51(8), 26 (1998).
A. L. Ruoff, C. O. Rodrigez, and N. E. Christensen, Phys. Rev. B: Condens. Matter 58, 2998 (1998).
K. Rosciszewski, B. Paulus, P. Filde, and H. Stoll, Phys. Rev. B: Condens. Matter 60(11), 7905 (1999).
P. Vinet, J. H. Rose, J. Ferrante, and L. R. Smith, J. Phys.: Condens. Matter 1, 1941 (1989).
J. Hama and K. Suito, J. Phys.: Condens. Matter 8, 67 (1996).
Yu. A. Freiman and S. M. Tretyak, Low Temp. Phys. 33(6), 545 (2007).
R. A. Aziz and M. J. Slaman, Chem. Phys. 130, 187 (1989).
P. Loubeyre, Phys. Rev. Lett. 58, 1857 (1987).
P. Loubeyre, Phys. Rev. B: Condens. Matter 37, 5432 (1988).
E. Pechenic, I. Kelson, and G. Makov, Phys. Rev. B: Condens. Matter 78, 134109 (2008).
K. B. Tolpygo and E. P. Troitskaya, Sov. Phys. Solid State 17(1), 58 (1975).
V. G. Bar’yakhtar, E. V. Zarochentsev, E. P. Troitskaya, and Yu. V. Eremeichenkova, Phys. Solid State 40(8), 1330 (1998).
K. B. Tolpygo and E. P. Troitskaya, Sov. Phys. Solid State 13(4), 939 (1971).
I. V. Abarenkov, I. M. Antonova, V. G. Bar’yakhtar, V. L. Bulatov, and E. V. Zarochentsev, Electronic Structure of Ideal and Defective Crystals (Naukova Dumka, Kiev, 1991) [in Russian].
F. Clementi and C. Roetti, At. Data Nucl. Data Table 14(3–4), 177 (1974).
E. P. Troitskaya, Val. V. Chabanenko, I. V. Zhikharev, E. E. Horbenko, and E. A. Pilipenko, Fiz. Tekh. Vys. Davlenii (Donetsk, Ukr.) 20(2), 15 (2010).
E. P. Troitskaya, Yu. V. Eremeichenkova, and A. V. Chaika, Fiz. Tekh. Vys. Davlenii (Donetsk, Ukr.) 9(3), 20 (1999).
K. B. Tolpygo and E. P. Troitskaya, Sov. Phys. Solid State 16(3), 514 (1974).
M. M. Neuman and M. Zoppi, Phys. Rev. B: Condens. Matter 62, 41 (2000).
I. F. Silvera and V. V. Goldman, J. Chem. Phys. 69, 4209 (1978).
D. Wallace, in Solid State Physics, Ed. by H. Ehrenreich, F. Seitz, and D. Turnbull (Academic, New York, 1970), Vol. 25, p. 301.
H. Shimizu, H. Imaeta, T. Kume, and S. Sasaki, Phys. Rev. B: Condens. Matter 71, 014108 (2005).
T. Tsuchiya and K. Kawamura, J. Chem. Phys. 117, 5859 (2002).
M. Grimsditch, P. Loubeyre, and A. Poian, Phys. Rev. B: Condens. Matter 33(10), 7192 (1986).
H. Shimizu, H. Tashiro, T. Kume, and S. Sasaki, Phys. Rev. Lett. 86, 4568 (2001).
T. Iitaka and T. Ebisuzaki, Phys. Rev. B: Condens. Matter 65, 012103 (2001).
M. Aoki and T. Kurokawa, J. Phys.: Condens. Matter 19, 236228 (2007).
K. B. Tolpygo and E. P. Troitskaya, Ukr. Fiz. Zh. 19(3), 428 (1974).
E. V. Zarochentsev, V. I. Orekhov, and E. P. Troitskaya, Sov. Phys. Solid State 16(8), 1468 (1974).
E. V. Zarochentsev, E. P. Troitskaya, and Val. V. Chabanenko, Phys. Solid State 46(2), 249 (2004).
E. V. Zarochentsev, V. N. Varyukhin, E. P. Troitskaya, Val. V. Chabanenko, and E. E. Horbenko, Phys. Status Solidi B 243(12), 2672 (2006).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © E.P. Troitskaya, Val.V. Chabanenko, I.V. Zhikharev, Ie. Ie. Gorbenko, 2011, published in Fizika Tverdogo Tela, 2011, Vol. 53, No. 8, pp. 1555–1563.
Rights and permissions
About this article
Cite this article
Troitskaya, E.P., Chabanenko, V.V., Zhikharev, I.V. et al. Ab initio theory of many-body interaction and cauchy relations in compressed rare-gas crystals. Phys. Solid State 53, 1634 (2011). https://doi.org/10.1134/S1063783411080300
Received:
Accepted:
Published:
DOI: https://doi.org/10.1134/S1063783411080300