Abstract
A procedure to solve the coherent potential approximation (CPA) equation for energy and k-dependent self-energies is described. As illustrative example calculations for the \( {\left( {SN} \right)_x} - {\left( {\begin{array}{*{20}{c}} {SN} \\ H \end{array}} \right)_x} \) two-component mixed polymer are presented. Spikes and dips in the density of states of the mixed system are found already for 3 mol. per cent hydrogen concentration.
The resolvent method developed previously for the ab initio self-consistent field linear-combination of atomic-orbitals (SCF LCAO) treatment of a cluster of impurities embedded in a one-dimensional periodic polymer is extended for the ab initio SCF LCAO computation of the surface and chemisorption states of a three-dimensional semi-infinite crystal. The way of solving the matrix equations which are derived is outlined.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. Del Re, J. Ladik and G. Biczó, Phys. Rev. 155, 967 (1967).
For a review of this method see : A.J. Elliot, J.A. Krumhansl and P.L. Leath, Rev. Mod. Phys. 46, 465 (1974).
F. Hartino in “Quantum Theory of Polymers”, J.-M. André, J. Delhalle and J. Ladik, Eds., D. Reidel Publ. Co., Dordrecht Boston, p. 169 (1978).
M. Seel, T.C. Collins, F. Martino, D.K. Rai and J. Ladik, Phys. Rev. B (submitted).
J. Ladik and M. Seel, Phys. Rev. B13, 5338 (1976).
J. Ladik, Phys. Rev. B17, 1663 (1978).
For a review see : H.P. Geserich and L. Pintschovius, Adv. Solid State Phys. 16, 65 (1976).
H. Kamimura, A.J. Grant, F. Levy, A.D. Yoffe, C.D. Pitt, Solid State Commun. 17, 49 (1975)
D.E. Parry, J.M. Thomas, J. Phys. C3, L45 (1975)
A. Zunger, J. Chem. Phys. 63, 4854 (1975)
S. Suhai, M. Kertész, J. Phys. C9, L347 (1976)
N.T. Rajan and L.M. Falicov, Phys. Rev. B12, 1240 (1975).
C. Merkel and J. Ladik, Phys. Lett. 56A, 395 (1976)
M. Kertész, J. Koller, A. Ažman and S. Suhai, Phys. Lett. 55A, 107 (1975).
W.E. Rudge and P.M. Grant, Phys. Rev. Lett. 35, 1799 (1975)
W.Y. Ching, J.G. Harrison and C.C. Lin, Phys. Rev. B15, 5975 (1977)
I.P. Batra, S. Ciraci and W.E. Rudge, Phys. Rev. B15, 5858 (1977).
S. Suhai and J. Ladik, Solid State Commun. 22, 227 (1977).
B.L. Gyorffy and J.S. Faulkner (personal communication).
W.D. Gill, W. Bludan, R.H. Geiss, P.M. Grant, R.L. Greene, J.J. Mayerle and G.B. Street, Phys. Rev. Lett. 38, 1305 (1977).
M. Seel, “Theoretische Untersuchungen zur Aperiodizitat und zum Korrelationsproblern in Polymeren und Molekülkristallen” (Theoretical Investigations of Aperiodicity and Correlation in Polymers and Molecular Crystals) Thesis, University Erlangen Nürnberg 1978.
See for instance : W.L. McCubbin in “Quantum Theory of Polymers” p. 185 (1978).
P. Soven, Phys. Rev. 156, 809 (1967)
S. Kirkpatrick, B. Velický, H. Ehrenreich, Phys. Rev. B1, 3250 (1970).
See for instance : J. Callaway “Quantum Theory of the Solid State”, Academic Press, New York-London, p. 517 (1974).
S. Suhai (unpublished results).
J. Delhalle, Bull. Soc. Chim. Belg. 84, 135 (1975).
See for instance : G. Rickayzen, “Theory of Superconductivity” Interscience-Wiley, New York-London (1965).
P.W. Anderson, Phys. Rev. 124, 41 (1961).
T.B. Grimley, Proc. Phys. Soc. Lond. 90, 751 (1966); 92, 776 (1967)
T.B. Grimley, Ber. Bunsen Ges. 75, 1003 (1971)
H.J. Kelly, Surf. Sci. 43, 587 (1974).
A. van der Avoird, S.P. Liebmann, and J.M. Fassaert, Phys. Rev. B10, 1230 (1974).
J. Koutecký, Progr. Surf. and Membr. Sci. 11, 1 (1976).
J. Ladik, in “Electronic Structure of Polymers and Molecular Crystals”, J.-M. Andre and J. Ladik, Eds., Plenum Press, New York, p. 23 (1975).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1979 Plenum Press, New York
About this chapter
Cite this chapter
Ladik, J., Seel, M. (1979). On the Theory of Disordered Systems: CPA Calculation of (SN)x with Hydrogen Impurities and Hartree-Fock Theory of Surface States of Three-Dimensional Crystals. In: Phariseau, P., Györffy, B.L., Scheire, L. (eds) Electrons in Disordered Metals and at Metallic Surfaces. NATO Advanced Study Institutes Series, vol 42. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-3500-9_16
Download citation
DOI: https://doi.org/10.1007/978-1-4684-3500-9_16
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-3502-3
Online ISBN: 978-1-4684-3500-9
eBook Packages: Springer Book Archive