Metal Hydrides pp 215-242 | Cite as

Electronic Structure of Metal Hydrides

  • D. A. Papaconstantopoulos
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 76)


Theoretical studies of the electronic structure of metal hydrides will be discussed from the point of view of ordinary band theory and from the view of disordered materials theories such as the coherent potential approximation. The presentation will cover an introduction to the methodology followed in such calculations and analysis of the results obtained. A comparison will be made between the band structure of the host metal and that of the corresponding hydride. Trends as a function of changing the element of the metal site, and as a function of hydrogen content will be examined.


Metal Hydride Band Structure Calculation Coherent Potential Approximation Scatter Phase Shift Crystal Potential 
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  1. 1.
    A.C. Switendick, Electronic Band Structures of Metal Hydrides, Solid State Commun. 8, 1463 (1970); Metal Hydrides-Structure and Band Structure, Int. J. Quantum Chem. 5, 459 (1971).Google Scholar
  2. 2.
    A.C. Switendick, Electronic Energy Bands of Metal Hydrides- Palladium and Nickel Hydride, Ber. Bunsenges, Physik. Chemie 76, 535 (1972).Google Scholar
  3. 3.
    D.E. Eastman, J.K. Cashion, and A.C. Switendick, Photoemission Studies of Energy Levels in the Palladium-Hydrogen System, Phys. Rev. Lett. 27, 35 (1971).CrossRefGoogle Scholar
  4. 4.
    A.C. Switendick, “Hydrogen in Metals–A New Theoretical Model”, in Hydrogen Energy, Part B, ed. T.N. Veziroglou ( Plenum Press, NY, 1975 ) pp 1029–1042.Google Scholar
  5. 5.
    A.C. Switendick, Influence of the Electronic Structure on the Titanium Vanadium-Hydrogen Phase Diagram, J. Less-Common Metals 49, 283 (1976).CrossRefGoogle Scholar
  6. 6.
    A.C. Switendick, “The Change in Electronic Properties on Hydrogen Alloying and Hydride Formation”, in Topics in Applied Physics, Vol. 28: Hydrogen in Metals I: Basic Properties, G. Alefeld and J. V81kl eds. ( Springer Verlag, Berlin 1978 ) pp 101–129.Google Scholar
  7. 7.
    A.C. Switendick, Bandstructure Calculations for Metal Hydrogen Systems, Zeitschrift Physik. Chemie, Vol. 117, pp 89–112 (1979).Google Scholar
  8. 8.
    D.A. Papaconstantopoulos and B.M. Klein, Superconductivity in the Palladium-Hydrogen System, Phys. Rev. Lett. 35, 110 (1975); B.M. Klein and D.A. Papaconstantopoulos, Calculation of the Electron-Phonon Interaction and Superconductivity in the Palladium-Hydrogen System, in Proceedings of 14th Intern. Conf. on Low Temperature Physics, eds. M. Krusius and M. Vuorio (North Holland, Amsterdam, 1975) Vol. 2, pp 399–402.Google Scholar
  9. 9.
    B.M. Klein, D.A. Papaconstantopoulos, and L.L. Boyer, Calculations of the Superconducting Properties of Compounds: Refractory Carbides, PdH and V3Si, in Proceedings of the 2nd Rochester-Conf. on Superconductivity in d-and f-Band Metals ed. D.H. Douglass (Plenum Press, NY, 1976 ) pp 339–359.CrossRefGoogle Scholar
  10. 10.
    B.M. Klein, E.N. Economou, and D.A. Papaconstantopoulos, On the Inverse Isotope Effect and the x-Depencence of the Superconducting Transition Temperature in PdHx and PdDx, Phys. Rev. Lett. 39, 574 (1977).CrossRefGoogle Scholar
  11. 11.
    D.A. Papaconstantopoulos, B.M. Klein, E.N. Economou, and L.L. Boyer, Band Structure and Superconductivity of PdDx and PdHx, Phys. Rev. B17, 141 (1978).CrossRefGoogle Scholar
  12. 12.
    D.A. Papaconstantopoulos, B.M. Klein, J.S. Faulkner, and L.L. Boyer, Coherent-Potential-Approximation Calculations for PdHx, Phys. Rev. B18, 2784 (1978).CrossRefGoogle Scholar
  13. 13.
    D.A. Papaconstantopoulos, E.N. Economou, B.M. Klein, and L.L. Boyer, Superconductivity in Palladium-Based Hydrides, J. Physique 6, C 435 (1978).Google Scholar
  14. 14.
    D.A. Papaconstantopoulos, E.N. Economou, B.M. ‘Klein, and L.L. Boyer, Electronic Structure and Superconductivity in Pd-Ag-H and Pd-Rh-H Alloys, Phys. Rev. B20, 177 (1979).CrossRefGoogle Scholar
  15. 15.
    D.A. Papaconstantopoulos, Platinum Hydride: A Possible High Temperature Superconductor, J. Less-Common Metals 73, 305 (1980).CrossRefGoogle Scholar
  16. 16.
    J.C. Slater, Wave Functions in a Periodic Potential, Phys. Rev. 51, 846 (1937).CrossRefGoogle Scholar
  17. 17.
    L.F. Mattheiss, J.H. Wood, and A.C. Switendick, A Procedure for Calculating Electronic Energy Bands Using Symmetrized Augmented Plane Waves, in Methods in Computational Physics, Vol. 8, pp 63–147 (1968).Google Scholar
  18. 18.
    T. Loucks, “Augmented Plane Wave Method”, Benjamin, NY (1967).Google Scholar
  19. 19.
    J.0. Dimmock, The Calculation of Electronic Energy Bands by the APW Method, Solid State Phys. 26, 103 (1971).CrossRefGoogle Scholar
  20. 20.
    L.F. Mattheiss, Band Structure and Fermi Surface for Rhenium, Phys. Rev. 151, 450 (1966).CrossRefGoogle Scholar
  21. 21.
    D.D. Koelling and B.N. Harmon, A Technique for Relativistic Spin-Polarized Calculations, J. Phys. C10, 3107 (1977).Google Scholar
  22. 22.
    D.A. Liberman, D.T. Cromer and J.T. Waber, Relativistic Self-Consistent Field Program for Atoms and Ions, Comput. Phys. Commun. 2, 107 (1971).CrossRefGoogle Scholar
  23. 23.
    P.O. LBwdin, Quantum Theory of Cohesive Properties of Solids, Advan. Phys. 5, 1 (1956).Google Scholar
  24. 24.
    In what has come to be known as the Mattheiss prescription (L.F. Mattheiss, Phys. Rev. 133, A1399 (1964)) a different procedure is followed. The difference is the fact that Eq. (6) is also used in order to calculate V (r) as a super-position of atomic potentials V (r) insctead of solving Poisson’s equation.Google Scholar
  25. 25.
    S. Asano and J. Yamashita, On the Self-Consistent Potential of the Band Calculation, J. Phys. Soc. Japan, 30, 667 (1971); for a computer code see D.A. Papaconstantopoulos and W.R. Slaughter, Calculation of Crystal Potentials, Comput. Phys. Commun. 7, 207 (1974); 13, 225 (1977).Google Scholar
  26. 26.
    The MT sphere radius is usually taken equal to half the nearest neighbor distance for monatomic materials. For compounds we have chosen the radii by imposing the condition that the starting crystal potentials are equal at the point of contact of the MT spheres.Google Scholar
  27. 27.
    J.C. Slater, Statistical Exchange-Correlation in the Self-Consistent Field, in Advances in Quantum Chemistry, Vol. 6, pp 1–92, Academic Press (NY) 1972.Google Scholar
  28. 28.
    K. Schwarz, Optimization of the Statistical Exchange Parameter a for the Free Atoms H to Nb, Phys. Rev. B5, 2466 (1972); Optimized Statistical Exchange Parameter a for Atoms with Higher Z, Theor. Chim. Acta 34, 225 (1974).Google Scholar
  29. 29.
    L. Hedin and B.I. Lundqvist, Explicit Local Exchange-Correlation Potentials, J. Phys. C4, 2064 (1971).Google Scholar
  30. 30.
    In our calculations we have used the expression: a (r) = F o old(r)+(1-F)Qnew(r) where F = 0.75.Google Scholar
  31. 31.
    F.M. Mueller, J.W. Garland, M.H. Cohen, and K.H. Bennemann, Quadratic Integration: Theory and Application to the Electronic Structure of Platinum, Ann. Phys. (NY) 67, 19 (1971).CrossRefGoogle Scholar
  32. 32.
    G. Lehmann and M. Taut, On the Numerical Calculation of the Density of States and Related Properties, Phys. Status Solidi (b)54, 469 (1972); O. Jepsen, and O.K. Anderson, The Electronic Structure of hcp Ytterbium, Solid State Commun. 9, 1763 (1971).Google Scholar
  33. 33.
    J.C. Slater and G.F. Koster, Simplified LCAO Method for the Periodic Potential Problem, Phys.Rev. 94, 1498 (1954).CrossRefGoogle Scholar
  34. 34.
    L.L. Boyer, Symmetrized Fourier Method for Interpolating Band Structure Results, Phys. Rev. B19,_2824 (1979).Google Scholar
  35. 35.
    B.M. Klein, L.L.Boyer, D.A. Papaconstantopoulos, and L.F. Mattheiss, Self-Consistent Augmented-Plane-Wave Electronic-Structure Calculations for the A15 Compounds V X and Nb X, X = Al, Ga, Si, Ge, and Sn, Phys. Rev. B18, 6411 (1978).CrossRefGoogle Scholar
  36. 36.
    P. Soven, Coherent-Potential Model of Substitutional Disordered Alloys, Phys. Rev. 156, 809 (1967).CrossRefGoogle Scholar
  37. 37.
    J.S. Faulkner, Electronic States of Substoichiometric Compounds and Application to Palladium Hydride, Phys. Rev. B13, 2391 (1976).CrossRefGoogle Scholar
  38. 38.
    J. Zbasnik, and M. Mahnig, The Electronic Structure of Beta-Phase Palladium Hydride, Z. Phys. B23, 15 (1976).Google Scholar
  39. 39.
    M. Gupta and A.J. Freeman, Electronic Structure and Proton Spin-Lattice Relaxation in PdH, Phys. Rev. B17, 3029 (1978).CrossRefGoogle Scholar
  40. 40.
    M. Gupta and J.P. Burger, Experimental and Theoretical Investigation of the Coupling of Electrons with Acoustical and Optical Phonons in Metal Hydrides Relationships with Superconductivity, this volume.Google Scholar
  41. 41.
    C.D. Gelatt, Jr., H. Ehrenreich, and J. Weiss, Transition Metal Hydrides: Electronic Structure and the Heats of Formation, Phys. Rev. B17, 1940 (1978).Google Scholar
  42. 42.
    A.R. Williams, J. Kubier, and C.D. Gelatt, Jr., Cohesive Prôperties of Metallic Compounds: Augmented-Spherical-Wave Calculations, Phys. Rev. B19, 6094 (1979).CrossRefGoogle Scholar
  43. 43.
    N.I. Kulikov, Band Structure and Electronic Properties of Transition Metal Hydrides, Phys. Status Solidi (b)91, 753 (1979).Google Scholar
  44. 44.
    G.M. Stocks, R.W. Williams, and J.S. Faulkner, Electronic States in Ag-Pd Alloys, J. Phys. F3, 168 (1973); A.J. Pindor, W.M. Temmerman, B.L. Gyorffy, and G.M. Stocks, On the Electronic Structure of AgcPd1-c Alloys, J. Phys. F (1980) to be published.Google Scholar
  45. 45.
    D.J. Peterman, B.N. Harmon, J. Marchiando, and J.H. Weaver, Electronic Structure of Metal Hydrides II: Band Theory of ScH2 and YH2, Phys. Rev. B19, 4867 (1979).CrossRefGoogle Scholar
  46. 46.
    E.N. Economou, Superconductivity in Palladium-Based Hydrides, this volume.Google Scholar
  47. 47.
    D.S. MacLachlan, R. Mailfert, B. Souffaché, and J.P. Burger, Electrical Resistivity and Superconductivity in PdH, in Proc. of 14th Intern. Conf. on Low Temperature Physics, eds. M. Krusius and M. Vuorio (North Holland, Krusius and M. 1975 ) Vol. 2 pp 40–43.Google Scholar
  48. 48.
    C.A. Mackliet, D.J. Gillespie, and A.I. Schindler, Specific Heat, Electrical Resistance, and Other Properties of Superconducting Pd-H Alloys, J. Phys. Chem. Solids 37, 379 (1976).CrossRefGoogle Scholar
  49. 49.
    W.J. Venema, R. Griessen, R.S. Sorbello, N.L.M. Bakker, and P.E.M. Mijnarends, Effect of Zero-Point-Motion on the Electronic Structure of Pd-H(D), Proc. of Physics of Transition Metals Conf., Leeds (1980).Google Scholar
  50. 50.
    A. Bansil, R. Prasad, S. Bessendorf, L. Schwartz, W.J. Venema, R. Feenstra, F. Blom, and R. Griessen, Electronic States and Fermi Surface Properties of a-Phase PdHx, Solid State Commun. 32, 1115 (1979).CrossRefGoogle Scholar
  51. 51.
    B.M. Klein and D.A. Papaconstantopoulos, On Calculating the Electron-Phonon Mass Enhancement A for Compounds, J. Phys. F6, 1135 (1976).CrossRefGoogle Scholar
  52. 52.
    This formula (Eq. 23) is approximate because of the ommission of the cross term but it is particularly accurate when the mass difference MMet-MH is large as in the present case.Google Scholar
  53. 53.
    W.L. McMillan, Transition Temperature of Strong-Coupled Superconductors, Phys. Rev. 167, 331 (1968).CrossRefGoogle Scholar
  54. 54.
    J.M. Rowe, J.J. Rush, H.G. Smith, M. Mostoller, and H.E. Flotow, Lattice Dynamics of a Single Crystal of PhD0.63, Phys. Rev. Lett. 33, 1297 (1974).CrossRefGoogle Scholar
  55. 55.
    G.D. Gaspari and B.F. Gyorffy, Electron-Phonon Interaction d-Resonances and Superconductivity in Transition Metals, Phys. Rev. Lett. 28, 801 (1972).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • D. A. Papaconstantopoulos
    • 1
  1. 1.Naval Research LaboratoryUSA

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