Approximate Calculation of Electronic Structure of Disordered Alloys—Application to Alpha Brass

P. Soven

doi:10.1103/PhysRev.151.539

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Approximate Calculation of Electronic Structure of Disordered Alloys—Application to Alpha Brass

P. Soven

Bell Telephone Laboratories, Murray Hill, New Jersey

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Phys. Rev. 151, 539 – Published 11 November, 1966

DOI: https://doi.org/10.1103/PhysRev.151.539

Abstract

We have investigated the predictions of a model of a disordered binary alloy employing the averaged atomic $t$ matrices as the effective scatterer. In order to facilitate the calculation we have introduced an energy-dependent model potential of $δ$ -function character in place of the true atomic potentials. The energy dependence of the model potentials requires us to make an approximation other than the one invoked by the use of the averaged $t$ matrix. On the other hand,the use of the model potentials allows us to do numerical calculations for a disordered alloy. Our calculations are done for $α$ -brass. We have computed the spectral density for states of various symmetries. When considered as a function of wave vector, the width of the peaks in the spectral density corresponding to $s - p$ -type states are of the order of 1% of a Brillouinzone dimension, indicating that the wave functions are very nearly Bloch functions. The peaks corresponding to $d$ -type states are considerably broader, the widths being of the order of 5% of a Brillouin-zone dimension.

References (29)

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S. F. Edwards, Phil. Mag. 6, 617 (1961) Proc. Roy. Soc. (London) A267, 518 (1962)
J. L. Beeby and S. F. Edwards, Proc. Roy. Soc. (London) A274, 395 (1962)
J. L. Beeby, Proc. Roy. Soc. (London) A279, 82 (1964)
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M. Lax, Rev. Mod. Phys. 23, 287 (1951)
E. A. Stern, Physics 1, 255 (1965) Phys. Rev. 144, 545 (1966)
C. B. Sommers, H. Amar, and K. H. Johnson, Bull. Am. Phys. Soc. 11, 73 (1966)
V. Heine and I. Abarenkov, Phil. Mag. 9, 451 (1964) I. Abarenkov and V. Heine, ibid. 12, 529 (1965)
J. C. Slater, Phys. Rev. 51, 846 (1937)
P. M. Morse, Proc. Natl. Acad. Sci. U. S. 42, 276 (1956)
J. Korringer, Physica 13, 392 (1947)
W. Kohn and N. Rostoker, Phys. Rev. 94, 1111 (1954)
P. A. Wolff, Phys. Rev. 124, 1030 (1961) A. M. Clogston, ibid. 125, 439 (1962) ibid.136, A138 (1964)
F. Herman and S. Skillman, Atomic Structure Calculations (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1965)
(a) G. A. Burdick, Phys. Rev. 129, 138 (1963) (b) B. Segall, ibid. 125, 109 (1962) private communication in [16] [16]
E. A. Owen and E. W. Roberts, Phil. Mag. 27, 294 (1939)
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J. L. Beeby, Phys. Rev. 137, A933 (1965)
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F. S. Ham and B. Segall, Phys. Rev. 124, 1786 (1961)
Omitted endnote
W. R. G. Kemp et al., Acta Met. 5, 303 (1957)
F. M. Mueller, Phys. Rev. (to be published)
J. Friedel, Advan. Phys. 3, 446 (1954) P. W. Anderson and W. F. McMillan (to be published)
J. A. Rayne, Phys. Rev. 108, 22 (1957) B. W. Veal and J. A. Rayne, ibid. 130, 2156 (1963) L. I. Isaacs and T. B. Massalski, ibid. 138, A134 (1965)
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C. N. Berglund and W. E. Spicer, Phys. Rev. 136, A1030, (1964) ibid.136, A1044 (1964)

[c1] N. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys (Dover Publications, Inc., New York, 1959)

[c2] S. F. Edwards, Phil. Mag. 6, 617 (1961) Proc. Roy. Soc. (London) A267, 518 (1962)

[c3] J. L. Beeby and S. F. Edwards, Proc. Roy. Soc. (London) A274, 395 (1962)

[c4] J. L. Beeby, Proc. Roy. Soc. (London) A279, 82 (1964)

[c5] J. L. Beeby, Phys. Rev. 135, A130 (1964)

[c6] M. Lax, Rev. Mod. Phys. 23, 287 (1951)

[c7] E. A. Stern, Physics 1, 255 (1965) Phys. Rev. 144, 545 (1966)

[c8] C. B. Sommers, H. Amar, and K. H. Johnson, Bull. Am. Phys. Soc. 11, 73 (1966)

[c9] V. Heine and I. Abarenkov, Phil. Mag. 9, 451 (1964) I. Abarenkov and V. Heine, ibid. 12, 529 (1965)

[c10] J. C. Slater, Phys. Rev. 51, 846 (1937)

[c11] P. M. Morse, Proc. Natl. Acad. Sci. U. S. 42, 276 (1956)

[c12] J. Korringer, Physica 13, 392 (1947)

[c13] W. Kohn and N. Rostoker, Phys. Rev. 94, 1111 (1954)

[c14] P. A. Wolff, Phys. Rev. 124, 1030 (1961) A. M. Clogston, ibid. 125, 439 (1962) ibid.136, A138 (1964)

[c15] F. Herman and S. Skillman, Atomic Structure Calculations (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1965)

[c16] (a) G. A. Burdick, Phys. Rev. 129, 138 (1963) (b) B. Segall, ibid. 125, 109 (1962) private communication in [16] [16]

[c17] E. A. Owen and E. W. Roberts, Phil. Mag. 27, 294 (1939)

[c18] J. C. Slater, Phys. Rev. 145, 599 (1966)

[c19] J. L. Beeby, Phys. Rev. 137, A933 (1965)

[c20] I. M. Lifshitz, Usp. Fiz. Nauk 83, 617 (1964) [English transl.: Soviet Phys.—Usp. 7, 549 (1964)]

[c21] F. S. Ham and B. Segall, Phys. Rev. 124, 1786 (1961)

[c22] Omitted endnote

[c23] W. R. G. Kemp et al., Acta Met. 5, 303 (1957)

[c24] F. M. Mueller, Phys. Rev. (to be published)

[c25] J. Friedel, Advan. Phys. 3, 446 (1954) P. W. Anderson and W. F. McMillan (to be published)

[c26] J. A. Rayne, Phys. Rev. 108, 22 (1957) B. W. Veal and J. A. Rayne, ibid. 130, 2156 (1963) L. I. Isaacs and T. B. Massalski, ibid. 138, A134 (1965)

[c27] M. A. Biondi and J. A. Rayne, Phys. Rev. 115, 1522 (1959)

[c28] H. Ehrenreich and H. R. Phillip, Phys. Rev. 128, 1622 (1962)

[c29] C. N. Berglund and W. E. Spicer, Phys. Rev. 136, A1030, (1964) ibid.136, A1044 (1964)

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Approximate Calculation of Electronic Structure of Disordered Alloys—Application to Alpha Brass

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