MODELLING OF PHASE TRANSITIONS IN CALCIUM–STRONTIUM SUPERSTRUCTURES AT LOW PRESSURES

V.V. Pozhivatenko

Èlektron. model. 2017, 39(1):113-125
https://doi.org/10.15407/emodel.39.01.113

ABSTRACT

First-principal calculations of structural phase transitions essentially underestimate the values of pressure of phase transitions in alkaline-earth metals. Using fitting parameters which are estimated in calculations for calcium and strontium the author has conducted numerical calculations of parameters of phase transitions in superstructures Ca1-xSrx consistent with face-centered cubic—body-centered cubic (FCC — BCC) transition at low pressure, modeled by the supercells containing up to sixteen atoms. Dependence of thermodynamic properties of Ca1-xSrx on concentration of strontium and parameter of smearing has been studied.

KEYWORDS

structural phase transitions, density functional theory, smearing technique for the states about Fermi level.

REFERENCES

1. Winzenick, M. and Holzapfel, W.B. (1996), “Structural study on the high-pressure phase strontium III”, Physical Review B, Vol. 53, no. 5, pp. 2151-2154.
https://doi.org/10.1103/PhysRevB.53.2151
2. Wang, G.M., Papaconstantopoulos, D.A. and Blaisten-Barojas, E. (2003), “Pressure induced transitions in calcium: a tight-binding approach”, J. Phys. Chem. Solids, Vol. 64, no. 2, pp. 185-192.
https://doi.org/10.1016/S0022-3697(02)00199-3
3. Errea, I. et al. (2008), “Fermi surface nesting and phonon instabilities in simple cubic calcium”, // High Pressure Research, Vol. 28, no. 4, pp. 443-448.
https://doi.org/10.1080/08957950802497331
4. Arapan, S., Mao, H.-k. and Ahuja, R. (2008), “Prediction of incommensurate crystal structure in Ca at high pressure”, P. Natl. Acad. Sci. USA, Vol. 105, no. 52, pp. 20627-20630.
https://doi.org/10.1073/pnas.0810813105
5. Gao, G. et al. (2008), “Electronic structures, lattice dynamics, and electron-phonon coupling of simple cubic Ca under pressure”, Solid State Comm., Vol. 146, no. 3-4, pp. 181-185.
https://doi.org/10.1016/j.ssc.2008.01.026
6. Qiu, S.I. and Marcus, P.M. (2009), “Phases of Ca from first principles”, J. Phys.: Condens.Matter, Vol. 21, no. 43, pp. 435403-1 – 435403-8.
https://doi.org/10.1088/0953-8984/21/43/435403
7. Ishikawa, T. et al. (2010), “Review of high pressure phases of calcium by first-principles calculations”, J. Phys.: Conf. Ser., Vol. 215, pp. 012105-1-012105-6.
https://doi.org/10.1088/1742-6596/215/1/012105
8. Oganov, A.R. et al. (2010), “Exotic behavior and crystal structures of calcium under pressure”, P. Natl. Acad. Sci. USA, Vol. 107, no. 17, pp. 7646-7651.
https://doi.org/10.1073/pnas.0910335107
9. Mao, W.L. et al. (2010), “Distortions and stabilization of simple-cubic calcium at high pressure and low temperature”, P. Natl. Acad. Sci. USA, Vol. 107, no. 22, pp. 9965-9968.
https://doi.org/10.1073/pnas.1005279107
10. Liu, Zh.-L. et al. (2011), “Phase transition and thermodynamic properties of Sr under high pressure”, Physica B, Vol. 406, no. 23, pp. 4518-4522.
https://doi.org/10.1016/j.physb.2011.09.028
11. Alcock, C.B. and Itkin, V.P. (1986), “The Ca-Sr (Calcium-Strontium) System”, J. of Phase Equilibria, Vol. 7, no. 5, pp. 455-457.
https://doi.org/10.1007/BF02867809
12. Aljarrah, M. and Medraj, M. (2008), “Thermodynamic modeling of the Mg-Ca, Mg-Sr, Ca-Sr and Mg-Ca-Sr systems using the modified quasi-chemical model”, Calphad, Vol. 32, no. 2, pp. 240-251.
https://doi.org/10.1016/j.calphad.2007.09.001
13. Okamoto, H. (2010), “Ca-Sr (Calcium-Strontium)”, J. of Phase Equilibria and Diffusion, Vol. 31, no. 5, p. 491.
https://doi.org/10.1007/s11669-010-9757-x
14. Maksimov, E.G., Magnitskaya, M.V. and Fortov, V.E. (2005), “Non-simple behavior of simple metals at high pressure”, Uspekhi fizicheskikh nauk, Vol. 175, no. 8, pp. 793-813.
https://doi.org/10.3367/UFNr.0175.200508a.0793
15. Degtyareva, V.F. (2006), “Simple metals at high pressures: the Fermi sphere – Brillouin zone interaction model”, Uspekhi fizicheskikh nauk, Vol. 176, no. 4, pp. 383-402.
https://doi.org/10.3367/UFNr.0176.200604c.0383
16. Hohenberg, P. and Kohn, W. (1964), “Inhomogeneous electron gas”, Physical Review, Vol. 136, no. 3, pp. B864-B871.
17. Weinert, M. and Davenport, J.V. (1992), “Fractional occupations and density-functional energies and forces”, Physical Review B, Vol. 45, no. 23, pp. 13709-13712.
https://doi.org/10.1103/PhysRevB.45.13709
18. Springborg, M., Albers, R.C. and Schmidt, K. (1998), “Fractional occupancies and temperature in electronic-structure calculations”, Physical Review B, Vol. 57, no. 3, pp. 1427- 1435.
https://doi.org/10.1103/PhysRevB.57.1427
19. Methfessel, M. and Paxton, A.T. (1989), “High-precision sampling for Brillouin-zone integration in metals”, Physical Review B, Vol. 40, no. 6, pp. 3616-3621.
https://doi.org/10.1103/PhysRevB.40.3616
20. Pozhivatenko, V.V. (2013), “Calculation of thermodynamic potentials with the inclusion of fractional occupation numbers and investigation of FCC – BCC structural phase transitions in alkaline-earth metals”, Fizika tvyordogo tela, Vol. 55, no. 10, pp. 1879-1886.
https://doi.org/10.1134/S1063783413100260
21. Perdew, J.P., Burke, K. and Ernzerhof, M. (1996), “Generalized gradient approximation made simple”, Phys. Rev. Lett., Vol. 77, no. 18, pp. 3865-3868.
https://doi.org/10.1103/PhysRevLett.77.3865
22. Vanderbilt, D. (1990), “Soft self-consistent pseudopotentials in a generalized eigenvalue formalism”, Physical Review B, Vol. 41, no. 11, pp. 7892-7895.
https://doi.org/10.1103/PhysRevB.41.7892
23. Giannozzi, P. et al. (2009), “QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials”, J. Phys.: Condens. Matter, Vol. 21, no. 39, pp. 395502-1-395502-19.
https://doi.org/10.1088/0953-8984/21/39/395502
24. Marzari, N., Vanderbilt, D., De Vita, A. and Payne, M.C. (1999), “Thermal contraction and disordering of the Al(100) surface”, Phys. Rev. Lett., Vol. 82, no. 16, pp. 3296-3299.
https://doi.org/10.1103/PhysRevLett.82.3296
25. Murnaghan, F.D. (1944), “The compressibility of media under extreme pressures”, P. Natl. Acad. Sci. USA, Vol. 30, no. 9, pp. 244-247.
https://doi.org/10.1073/pnas.30.9.244
26. Birch, F. (1947), “Finite elastic strain of cubic crystals”, Physical Review, Vol. 71, no. 11, pp. 809-824.
https://doi.org/10.1103/PhysRev.71.809
27. Birch, F. (1978), “Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high pressures and 300°K”, J. Geophys. Res., Vol. 83, no. B3, pp. 1257-1268.
https://doi.org/10.1029/JB083iB03p01257
28. Monkhorst, H.J. and Pack, J.D. (1976), “Special points for Brillouin-zone integrations”, Physical Review B, Vol. 13, no. 12, pp. 5188-5192.
https://doi.org/10.1103/PhysRevB.13.5188

Full text: PDF (in Russian)