Abstract
The scattering of conduction electrons on dilute point defects in aluminium was investigated, for zero temperature, by pseudopotential calculations considering the realistic form of the Al Fermi surface (FS) and band structure. The 4-OPW wavefunctions, band velocities and FS curvatures were calculated for 1,300 pointsk on 1/48 (cubic symmetry element) of the FS. The scattering potentials were obtained as follows: for the impurities Ge, Mg, Zn, and Ga tabulated pseudopotentials were used and rescreened for the electron density of Al, the vacancy was treated as a missing Al atom and the [100] dumbbell interstitial as two Al atoms with a vacancy in between (always with strain field corrections). The scattering matrixP kk′ was obtained in first order Born approximation. The linearized Boltzmann equation was solved numerically by iteration, for zero magnetic field and for a reduced set of 109 points on 1/48 FS, to yield the anisotropic transport relaxation timesτ k and lifetimesτ 0 k .
Theτ k were interpolated for the 1,300 points again and inserted into low-field FS integrals for the galvanomagnetic coefficients which depend sensitively on the details of the FS and the anisotropy ofτ k . Without any free parameter, our results agree very well with experimental data for the case of Ge, Mg, and Zn impurities, and less so for the homovalent Ga impurities and for the self-defects. The diffusion thermopower was also calculated.
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Proc. Int. Conf. on Electron Lifetimes in Metals: Phys. cond. Matter19, No. 1–4 (1975)
Animalu, A.O.E., Heine, V.: Phil. Mag.12, 1249 (1965)
Ashcroft, N.W.: Phil. Mag.8, 2055 (1963)
Anderson, J.R., Lane, S.S.: Phys. Rev. B2, 298 (1970)
Böning, K., Pfändner, K., Rosner, P., Schlüter, M.: J. Phys. F: Metal Phys.5, 1176 (1975)
Sorbello, R.S.: J. Phys. F: Metal Phys.4, 503 (1974)
Böning, K., Pfändner, K., Rosner, P., Lengeler, B., Welter, J.-M.: will be submitted to Z. Physik (companion paper)
Fukai, Y.: Phys. Rev.186, 697 (1969)
Sorbello, R.S.: Solid State Commun.12, 287 (1973)
Taylor, P.L.: A Quantum Approach to the Solid State, 1st ed.; New Jersey: Prentice Hall 1970
Taylor, P.L.: Proc. R. Soc. A275, 200 (1963)
Tsuji, M.: J. Phys. Soc. Japan13, 979 (1958)
Böning, K.: Phys. kondens. Materie11, 177 (1970)
Wilson, A.H.: The Theory of Metals, Cambridge: Cambridge University Press 1953
Jan, J.P.: Can. J. Phys.46, 1371 (1968)
Böning, K.: Thermoelectricity in Metallic Conductors, Editors Blatt, F.J., and Schroeder, P.A.; pp. 333–358, Plenum Publ. Corp. 1978
Davydov, A.S.: Quantum Mechanics, 1st ed., Oxford: Pergamon Press 1965
Harrison, W.A.: Pseudopotentials in the Theory of Metals. New York: Benjamin 1966
Sorbello, R.S.: J. Phys. F: Metal Phys.4, 1665 (1974)
Animalu, A.O.E.: Phil. Mag.11, 379 (1964)
Lindhardt, J.: Kgl. Danske Videnskab. Selskab. Mat.-Fys. Medd.28, 8 (1954)
Pfändner, K.: Ph. D. Thesis, Techn. Universität München (1977)
Martin, R.S., Reinsch, C., Wilkinson, J.H.: Numerische Mathematik11, 181 (1968)
Wegehaupt, T., Doezema, R.E.: Phys. Rev. B16, 2515 (1977)
Leung, H.K., Kus, F.W., McKay, N., Carbotte, J.P.: Phys. Rev. B16, 4358 (1977)
Bross, H.: Phys. Lett.64A, 418 (1978)
Bronstein, I., Semendjajew, K.: Taschenbuch der Mathematik, 13. ed., Zürich, Frankfurt: Harri Deutsch 1973
Pearson, W.B.: A Handbook of Lattice Spacings and Structures of Metals and Alloys. New York: Pergamon Press 1958
Blatt, F.J., Fankhauser, H.R.: National Bureau Standards, Misc. Publ.287, 109 (1966)
Schilling, W.: J. Nucl. Materials69+70, 465 (1978)
Cohen, M.L., Heine, V.: Solid State Physics24, Editors Seitz, F., Turnbull, D., Ehrenreich, H., pp. 37–248. New York: Academic Press 1970
Appapillai, M., Williams, A.R.: J. Phys. F: Metal Phys.3, 759 (1973)
Haubold, H.-G.: private communication
Ziman, J.M.: Principles of the Theory of Solids, 1st ed., Cambridge: University Press 1965
Pfändner, K., Böning, K., Brenig, W.: Solid State Commun.23, 31 (1977)
Fickett, F.R.: Cryogenics11, 349 (1971)
Sato, H., Babauchi, T., Yonemitsu, K.: appears in phys. stat. sol. (1978)
Mauer, W.: Diplomarbeit, Technische Universität München, 1976
Rosner, P., Sieber, G., Böning, K.: unpublished
Sieber, G., Wehr, G., Böning, K.: J. Phys. F: Metal Phys.7, 2503 (1977)
Kesternich, W., Ullmaier, H., Schilling, W.: J. Phys. F: Metal Phys.6, 1867 (1976)
Papastaikoudis, C., Rocoffylou, E., Tselfes, W., Chountas, K.: Z. Physik B25, 131 (1976)
Yonemitsu, K., Takano, K., Matsuda, T.: submitted to phys. stat. sol.
Ashcroft, N.W.: Phys. Lett.23, 48 (1966)
Kittel, C.: Einführung in die Festkörperphysik, 3rd ed., München: Oldenbourg 1973
Shaw, R.W. Jr.: Phys. Rev.174, 769 (1968)
Bèal-Monod, M.T., Kohn, W.: J. Phys. Chem. Solids19, 1877 (1968)
Nielsen, P.E., Taylor, P.L.: Phys. Rev. B10, 4061 (1974)
Wannier, G.H.: Phys. Rev. B5, 3836 (1972)
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Auszug aus der vom Fachbereich Physik der Techn. Universität München genehmigten Dissertation über „Berechnung von elektrischen Transporteigenschaften von Aluminium mit der Pseudopotentialmethode“ des Dipl.-Phys. Klaus Pfändner. Tag der Promotion: 29. 11. 1977
This work was supported by the German Bundesministerium für Forschung und Technologie
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Pfändner, K., Böning, K. & Brenig, W. 4 OPW calculations of electronic transport coefficients of aluminium containing point defects. Z Physik B 32, 287–300 (1979). https://doi.org/10.1007/BF01351506
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DOI: https://doi.org/10.1007/BF01351506