Abstract
A dynamic matrix of rare-gas crystals is constructed within the model of deformable and polarizable atoms based on the nonempirical short-range repulsion potential taking into account the three-body interaction and deformation of electron shells of dipole-type atoms within the pair and three-body approximations. Ab initio calculations of the phonon energy for compressed rare-gas crystals are performed at two and ten mean-value points of the Chadi–Kohen method in a wide pressure range. It is shown that the contribution of three-body forces to the phonon frequencies due to overlap of electron shells of neighboring atoms is small as compared to the pair interaction even at a high pressure and most pronounced for Xe. The contributions of the deformation of electron shells within the pair and three-body approximations differ for different mean-value points and increase with an increase in pressure. The zero-point energies calculated by the Chadi–Kohen method for crystals of the Ne–Xe series are compared with the known experimental data at p = 0 and calculation results obtained by other researchers.
Similar content being viewed by others
REFERENCES
T. Kihara and S. Koba, J. Phys. Soc. Jpn. 7, 348 (1952).
M. Born, Proc. Cambridge Philos. Soc. 40, 262 (1944).
J. A. Prins, J. M. Dumore, and L. T. Tjoan, Physica (Amsterdam) 18, 307 (1952).
G. L. Pollack, Rev. Mod. Phys. 36, 748 (1964).
B. W. van deWaal, Phys. Rev. Lett. 67, 3263 (1991).
J. A. Venables, in Rare Gas Solids, Ed. by M. L. Klein and J. A. Venables (Academic, London, 1976).
E. Kim and M. Nicol, Phys. Rev. Lett. 96, 035504 (2006).
I. Kwon, L. A. Collins, J. D. Kress, and N. Troullier, Phys. Rev. B 52, 15165 (1995).
J. K. Dewhurst, R. Ahuja, S. Li, and B. Johansson, Phys. Rev. Lett. 88, 075504 (2002).
M. G. Medvedev, I. S. Bushmarinov, J. Sun, J. P. Perdew, and K. A. Lyssenko, Science (Washington, DC, U. S.) 355, 49 (2017).
H. Larsen, J. Olsen, C. Hattig, P. Jorgensen, O. Christiansen, and J. Gauss, J. Chem. Phys. 111, 1917 (1999).
N. Gaston and P. Schwerdtfeger, Phys. Rev. B 74, 024105 (2006).
F. O. Kannemann and A. D. Becke, J. Chem. Theory Comput. 5, 719 (2009).
P. Schwerdtfeger and A. Hermann, Phys. Rev. B 80, 064106 (2009).
P. Schwerdtfeger, K. G. Steenbergen, and E. Pahl, Phys. Rev. B 95, 214116 (2017).
K. Rosciszewski, B. Paulus, P. Fulde, and H. Stoll, Phys. Rev. B 62, 5482 (2000).
K. Rosciszewski, B. Paulus, P. Fulde, and H. Stoll, Phys. Rev. B 60, 7905 (1999).
K. Rosciszewski and B. Paulus, Phys. Rev. B 66, 092102 (2002).
L. Trombach, R. S. Hoy, D. J. Wales, and P. Schwerdtfeger, Phys. Rev. E 97, 043309 (2018).
L. Trombach and P. Schwerdtfeger, Phys. Rev. E 98, 033311 (2018).
E. P. Troitskaya, Ie. Ie. Gorbenko, and E. A. Pilipenko, J. Low Temp. Phys. 42, 411 (2016).
E. P. Troitskaya, V. V. Chabanenko, Ie. Ie. Gorbenko, and E. A. Pilipenko, Phys. Solid State 57, 119 (2015).
D. J. Chadi and M. L. Cohen, Phys. Rev. B 8, 5747 (1973).
E. A. Pilipenko, E. P. Troitskaya, and Ie. Ie. Gorbenko, Fiz. Tekh. Vys. Davl. 29 (1), 64 (2019).
E. P. Troitskaya, V. V. Chabanenko, Ie. Ie. Gorbenko, and N. V. Kuzovoi, Fiz. Tekh. Vys. Davl. 17 (3), 14 (2007).
E. P. Troitskaya, E. A. Pilipenko, and Ie. Ie. Gorbenko, Phys. Solid State 61, 30 (2019).
A. Baldereschi, Phys. Rev. B 7, 5212 (1973).
J. Eckert, W. B. Daniels, and J. D. Axe, Phys. Rev. B 14, 3649 (1976).
R. H. Beaumont, H. Chihara, and J. A. Morrison, Proc. Phys. Soc. 78, 1462 (1961).
B. Farid and R. Godby, Phys. Rev. B 43, 14248 (1991).
American Institute of Physics Handbook, and Ed. D. E. Gray, 3rd ed. (McGraw-Hill, New York, 1965).
E. V. Zarochentsev, K. B. Tolpygo, and E. P. Troitskaya, Sov. J. Low Temp. Phys. 5, 626 (1979).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare that they have no conflicts of interest.
Additional information
Translated by A. Sin’kov
Rights and permissions
About this article
Cite this article
Troitskaya, E.P., Pilipenko, E.A. & Gorbenko, I.I. Energy of Phonons and Zero-Point Vibrations in Compressed Rare-Gas Crystals. Phys. Solid State 61, 1846–1853 (2019). https://doi.org/10.1134/S1063783419100366
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063783419100366