Table of Contents
ISRN Materials Science
Volume 2012, Article ID 975897, 13 pages
http://dx.doi.org/10.5402/2012/975897
Research Article

LDA and GGA Investigations of Some Ground-State Properties and the Compton Profile of Copper with the All-Electron MAPW Method

Arnold Sommerfeld Center, University of Munich, Theresienstraße. 37 IV, 80333 Munich, Germany

Received 26 September 2011; Accepted 13 October 2011

Academic Editors: S. B. Dugdale and J. E. Lowther

Copyright © 2012 Helmut Bross. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Bross, “Verallgemeinerung der MAPW-Methode für ein beliebiges Potential,” Helvetica Physica Acta, vol. 41, p. 717, 1968. View at Google Scholar
  2. H. Bross, G. Bohn, G. Meister, W. Schubö, and H. Stöhr, “New version of the modified augmented-plane-wave method,” Physical Review B, vol. 2, no. 8, pp. 3098–3103, 1970. View at Publisher · View at Google Scholar · View at Scopus
  3. S. H. Vosko, L. Wilk, and M. Nusair, “Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis,” Canadian Journal of Physics, vol. 58, no. 8, pp. 1200–1211, 1980. View at Publisher · View at Google Scholar
  4. J. P. Perdew, J. A. Chevary, S. H. Vosko et al., “Atoms, molecules, solids, and surfaces: applications of the generalized gradient approximation for exchange and correlation,” Physical Review B, vol. 46, no. 11, pp. 6671–6687, 1992. View at Publisher · View at Google Scholar · View at Scopus
  5. J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Physical Review Letters, vol. 77, no. 18, pp. 3865–3868, 1996. View at Google Scholar · View at Scopus
  6. H. Bross, “Band structure calculation of the momentum density and Compton profile of copper,” Journal of Physics F, vol. 12, no. 10, pp. 2249–2266, 1982. View at Publisher · View at Google Scholar · View at Scopus
  7. Y. Sakurai, S. Kaprzyk, A. Bansil et al., “High-resolution Compton scattering study of Cu: experiment and theory,” Journal of Physics and Chemistry of Solids, vol. 60, no. 7, pp. 905–910, 1999. View at Publisher · View at Google Scholar · View at Scopus
  8. J. C. Slater, “Wave functions in a periodic potential,” Physical Review, vol. 51, no. 10, pp. 846–851, 1937. View at Publisher · View at Google Scholar · View at Scopus
  9. H Bross, “Electronic structure of the cubic compounds ReGa3 (Re = Er, Tm, Yb, and Lu),” Advances in Condensed Matter Physics, vol. 2011, Article ID 867074, 14 pages, 2011. View at Publisher · View at Google Scholar
  10. H. Bross, “Investigation of some ground state properties of lithium with the all electron MAPW method,” Physica Status Solidi B, vol. 229, no. 3, pp. 1359–1370, 2002. View at Publisher · View at Google Scholar · View at Scopus
  11. H. Bross, “LDA and GGA investigations of some ground state properties of aluminium with the all electron MAPW method,” European Physical Journal B, vol. 37, no. 3, pp. 405–411, 2004. View at Publisher · View at Google Scholar · View at Scopus
  12. H. Bross, “The local density approximation limit of the momentum density and the Compton profiles of Al,” Journal of Physics Condensed Matter, vol. 16, no. 41, pp. 7363–7378, 2004. View at Publisher · View at Google Scholar · View at Scopus
  13. H. Bross, “Electronic structure of Li with emphasis on the momentum density and the Compton profile,” Physical Review B, vol. 72, no. 11, Article ID 115109, 14 pages, 2005. View at Publisher · View at Google Scholar
  14. A. Bansil, “Special directions in the brillouin zone,” Solid State Communications, vol. 16, no. 7, pp. 885–889, 1975. View at Google Scholar · View at Scopus
  15. W. R. Fehlner and S. H. Vosko, “Product representation for cubic harmonics and special directions for the determination of the fermi surface and related properties,” Canadian Journal of Physics, vol. 54, no. 21, pp. 2159–2169, 1976. View at Google Scholar · View at Scopus
  16. W. R. Fehlner, S. B. Nickerson, and S. H. Vosko, “Cubic harmonic expansions using gauss integration formulas,” Solid State Communications, vol. 19, no. 1, pp. 83–86, 1976. View at Google Scholar · View at Scopus
  17. R. Prasad and A. Bansil, “Special directions for Brillouin-zone integration: application to density-of-states calculations,” Physical Review B, vol. 21, no. 2, pp. 496–503, 1980. View at Publisher · View at Google Scholar · View at Scopus
  18. H. Bross, “Special directions for surface integrals in cubic lattices with application to the evaluation of the Compton profile of copper,” Physica Status Solidi B, vol. 243, no. 3, pp. 653–665, 2006. View at Publisher · View at Google Scholar · View at Scopus
  19. L. Lam and P. M. Platzman, “Momentum density and Compton profile of the inhomogeneous interacting electronic system. I. Formalism,” Physical Review B, vol. 9, no. 12, pp. 5122–5127, 1974. View at Publisher · View at Google Scholar · View at Scopus
  20. A. Baldereschi, “Mean-value point in the Brillouin zone,” Physical Review B, vol. 7, no. 12, pp. 5212–5215, 1973. View at Publisher · View at Google Scholar · View at Scopus
  21. D. J. Chadi and M. L. Cohen, “Special points in the brillouin zone,” Physical Review B, vol. 8, no. 12, pp. 5747–5753, 1973. View at Publisher · View at Google Scholar · View at Scopus
  22. H. J. Monkhorst and J. D. Pack, “Special points for Brillouin-zone integrations,” Physical Review B, vol. 13, no. 12, pp. 5188–5192, 1976. View at Publisher · View at Google Scholar
  23. H. Bross, “Pseudopotential theory of the dielectric function of Al-the volume plasmon dispersion,” Journal of Physics F, vol. 8, no. 12, pp. 2631–2649, 1978. View at Publisher · View at Google Scholar · View at Scopus
  24. J. P. Perdew, “Density-functional approximation for the correlation energy of the inhomogeneous electron gas,” Physical Review B, vol. 33, no. 12, pp. 8822–8824, 1986. View at Publisher · View at Google Scholar
  25. J. P. Perdew, “Density-functional approximation for the correlation energy of the inhomogeneous electron gas,” Physical Review B, vol. 34, no. 10, p. 7406, 1986. View at Publisher · View at Google Scholar · View at Scopus
  26. F. D. Murnaghan, “The compressibility of media under extreme pressures,” Proceedings of the National Academy of Sciences of the United State, vol. 30, no. 9, pp. 244–247, 1944. View at Google Scholar
  27. U. Himmler, H. Peisl, A. Sepp, and W. Waidelich, “Ein Verdampfungskyrostat für Präzisions-Röntgenstreuuntersuchungen zwischn 4°K und 350°K,” Zeitschrift für Angewandte Physik, vol. 28, p. 104, 1969. View at Google Scholar
  28. S. Ajit, K.-H. Bhalla, H. L. Hellwege et al., Landolt-Börnstein, vol. 6, Springer, Berlin, Germany, 1971.
  29. W. C. Overton and J. Gaffney, “Temperature variation of the elastic constants of cubic elements. I. copper,” Physical Review, vol. 98, no. 4, pp. 969–977, 1955. View at Publisher · View at Google Scholar · View at Scopus
  30. A. Seeger and O. Buck, “Die experimentalle Ermittelung der elastischen konstanten hoherer Ordnung,” Zeitschrift Naturforschung A, vol. 15, pp. 1056–1067, 1960. View at Google Scholar
  31. V. L. Moruzzi, J. F. Janak, and A. R. Williams, Calculated Electronic Properties of Metals, Pergamon Press, New York, NY, USA, 1978.
  32. S. Kurth, J. P. Perdew, and P. Blaha, “Molecular and solid-state tests of density functional approximations: LSD, GGAs, and Meta-GGAs,” International Journal of Quantum Chemistry, vol. 75, no. 4-5, pp. 889–909, 1999. View at Google Scholar · View at Scopus
  33. S. Ajit, K.-H. Bhalla, H. L. Hellwege et al., Landolt-Börnstein, vol. 13c, Springer, Berlin, Germany, 1984.
  34. P. T. Coleridge and I. M. Templeton, “High precision de Haas-van Alphen measurements in the noble metals,” Journal of Physics F, vol. 2, no. 4, pp. 643–656, 1972. View at Publisher · View at Google Scholar · View at Scopus
  35. I. M. Templeton, “The effect of hydrostatic pressure on the fermi surfaces of copper, silver, and gold. II. High precision studies,” Canadian Journal of Physics, vol. 52, no. 17, pp. 1628–1634, 1974. View at Publisher · View at Google Scholar
  36. J. Laverock, T. D. Haynes, M. A. Alam, and S. B. Dugdale, “Experimental determination of the state-dependent enhancement of the electron-positron momentum density in solids,” Physical Review B, vol. 82, no. 12, Article ID 125127, 2010. View at Publisher · View at Google Scholar
  37. Y. Kubo, Y. Sakurai, and N. Shiotani, “Effects of self-interaction correction on momentum density in copper,” Journal of Physics Condensed Matter, vol. 11, no. 7, pp. 1683–1695, 1999. View at Google Scholar · View at Scopus
  38. M. R. Halse, “The fermi surfaces of the noble metals,” Philosophical Transactions of the Royal Society A, vol. 265, no. 1167, pp. 507–532, 1969. View at Publisher · View at Google Scholar
  39. S. Ajit, K.-H. Bhalla, H. L. Hellwege et al., Landolt-Börnstein, vol. 13c, Springer, Berlin, Germany, 1984.
  40. P. T. Coleridge and I. M. Templeton, “Fermi-surface radii in copper, silver, and gold,” Physical Review B, vol. 25, no. 12, pp. 7818–7819, 1982. View at Publisher · View at Google Scholar · View at Scopus
  41. J. R. Schneider, N. K. Hansen, and H. Kretschmer, “A charge density study of copper by γ-ray diffractometry on imperfect single crystals,” Acta Crystallographica A, vol. 37, pp. 711–722, 1981. View at Publisher · View at Google Scholar
  42. R. J. Temkin, V. E. Henrich, and P. M. Raccah, “Experimental charge density of copper,” Physical Review B, vol. 6, no. 10, pp. 3572–3581, 1972. View at Publisher · View at Google Scholar · View at Scopus
  43. P. Eisenberger and W. A. Reed, “Relationship of the relativistic Compton cross section to the electron's velocity distribution,” Physical Review B, vol. 9, no. 8, pp. 3237–3241, 1974. View at Publisher · View at Google Scholar · View at Scopus
  44. H. Roth-Seefrid and H. Bross, “Asymptotic behaviour of the Fourier coefficients of MAPW wave functions,” Zeitschrift für Physik B, vol. 26, no. 2, pp. 125–131, 1977. View at Publisher · View at Google Scholar · View at Scopus
  45. F. Biggs, L. B. Mendelsohn, and J. B. Mann, “Hartree fock Compton profiles for the elements,” Atomic Data and Nuclear Data Tables, vol. 16, no. 3, pp. 201–309, 1975. View at Google Scholar · View at Scopus
  46. B. Farid, V. Heine, G. E. Engel, and I. J. Robertson, “Extremal properties of the Harris-Foulkes functional and an improved screening calculation for the electron gas,” Physical Review B, vol. 48, no. 16, pp. 11602–11621, 1993. View at Publisher · View at Google Scholar · View at Scopus
  47. G. Ortiz and P. Ballone, “Correlation energy, structure factor, radial distribution function, and momentum distribution of the spin-polarized uniform electron gas,” Physical Review B, vol. 50, no. 3, pp. 1391–1405, 1994. View at Publisher · View at Google Scholar · View at Scopus
  48. P. Papanicolaou, N. C. Bacalis, and D. A. Papaconstantopoulus, Handbook of Calculated Electron Momentum Distributions, Compton Profiles, and Xray Form Factors of Elemental Solids, CRC Press, Boca Raton, Fla, USA, 1991.
  49. G. Gilat and L. J. Raubenheimer, “Accurate numerical method for calculating frequency-distribution functions in solids,” Physical Review, vol. 144, no. 2, pp. 390–395, 1966. View at Publisher · View at Google Scholar · View at Scopus
  50. L. J. Raubenheimer and G. Gilat, “Accurate numerical method of calculating frequency distribution functions in solids. II. Extension to hcp crystals,” Physical Review, vol. 157, no. 3, pp. 586–599, 1967. View at Publisher · View at Google Scholar · View at Scopus
  51. P. E. Mijnarends, “Determination of anisotropic momentum distributions in positron annihilation,” Physical Review, vol. 160, no. 3, pp. 512–519, 1967. View at Publisher · View at Google Scholar · View at Scopus
  52. G. E. W. Bauer and J. R. Schneider, “Electron correlation effect in the momentum density of copper metal,” Physical Review B, vol. 31, no. 2, pp. 681–692, 1985. View at Publisher · View at Google Scholar · View at Scopus
  53. D. Bagayoko, D. G. Laurent, S. P. Singhal, and J. Callaway, “Band structure, optical properties, and compton profile of copper,” Physics Letters A, vol. 76, no. 2, pp. 187–190, 1980. View at Google Scholar · View at Scopus
  54. U. von Barth and L. Hedin, “A local exchange-correlation potential for the spin polarized case. I,” Journal of Physics C, vol. 5, no. 13, pp. 1629–1642, 1972. View at Publisher · View at Google Scholar · View at Scopus
  55. H. Bross, “On the efficiency of different schemes for the evaluation of the density of states and related properties in solids,” Physica Status Solidi B, vol. 179, no. 2, pp. 429–439, 1993. View at Publisher · View at Google Scholar
  56. N. Hamada and S. Ohnishi, “Self-interaction correction to the local-density approximation in the calculation of the energy band gaps of semiconductors based on the full-potential linearized augmented-plane-wave method,” Physical Review B, vol. 34, no. 12, pp. 9042–9044, 1986. View at Publisher · View at Google Scholar · View at Scopus