Correlation between core-level shift and bulk modulus in transition-metal carbides and nitrides

Physical Review B - Condensed Matter and Materials Physics

Volumn 64, Issue 23, 2001, Pages

  Šimůnek, Antonín ^a   Vackář, Jiří ^a  

^a INSTITUTE OF PHYSICS   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

CARBON; METAL COMPLEX; NIOBIUM; NITROGEN; TITANIUM DERIVATIVE; VANADIUM DERIVATIVE; ZIRCONIUM DERIVATIVE;

ARTICLE; CALCULATION; CRYSTAL; CRYSTALLIZATION; ELECTRONICS; ENERGY; MODEL;

EID: 0035894140     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.64.235115     Document Type: Article

References (21)

1. K. Schwarz, Crit. Rev. Solid State Mater. Sci.13, 211 (1987).
2. R. Ahuja, O. Eriksson, J M. Wills, and B. Johansson, Phys. Rev. B53, 3072 (1996).
3. W. Wolf, R. Podloucky, T. Antretter, and F D. Fischer, Philos. Mag. B79, 839 (1999).
4. J C. Grossmann, A. Mizel, M. Côté, M L. Cohen, and S G. Louie, Phys. Rev. B60, 6343 (1999).
5. M. Marlo and V. Milman, Phys. Rev. B62, 2899 (2000).
6. C. Stampfl, W. Mannstadt, R. Asahi, and A J. Freeman, Phys. Rev. B63, 155106 (2001).
7. P. Hohenberg and W. Kohn, Phys. Rev.136, B864 (1964).
8. J. Ihm, A. Zunger, and M L. Cohen, J. Phys. C12, 4409 (1979).
9. W. Kohn and L J. Sham, Phys. Rev.140, A1133 (1965).
10. J. Vackář, M. Hyt’ha, and A. Šimůnek, Phys. Rev. B58, 12 712 (1998).
11. We use the Ceperley-Alder exchange-correlation functional parametrized by Perdew and Zunger (Refs. 1820). The cutoff energies of 55–70 Ry were required to ensure convergence in the total energy to less than 0.01 eV. The convergence is achieved with a range of 10–28 k points in the irreducible part of the Brillouin zone, depending on a compound. The lattice constant, bulk modulus, and its volume derivative were obtained by calculating the total energy for different values of the unit-cell volume and by fitting the calculated data to the Murnaghan equation of state (Ref. 21).
12. In the case of tails of semicore states exceeding the sphere boundary, the condition of asymptotic electrical neutrality is satisfied.
13. The radius (formula presented) is large enough that the boundary of the atomic sphere is in a region where the valence charge density of a crystal is correct, not pseudized.
14. The external charge density forming the boundary conditions for the inner valence wave functions is self-consistent in a solid, i.e., there is no force affecting a valence charge at the sphere boundary if the sphere is in the crystal environment.
15. It should be noted that, as a result of the potential shift, the value of the valence-electron electrostatic potential (formula presented) at the boundary of the atomic sphere is the same for all the atomic spheres. This is in accordance with the intuitive requirement of zero voltage differences among surfaces of all atomic spheres modeling atoms in the solid.
16. R C. Fang and L. Ley, Phys. Rev. B40, 3818 (1989).
17. L. Hedin and B I. Lundqvist, J. Phys. C4, 2064 (1971).
18. D M. Ceperley and B J. Alder, Phys. Rev. Lett.45, 566 (1980).
19. J. Vackář and A. Šimůnek, Solid State Commun.81, 837 (1992).
20. J P. Perdew and A. Zunger, Phys. Rev. B23, 5048 (1981).
21. F D. Murnaghan, Proc. Natl. Acad. Sci. U.S.A.30, 244 (1944).