Abstract

Normal-incidence reflectivity data for β′ CuZn has been subjected to a Kramers–Kronig analysis for its optical constants in the spectral region 2 eV ≤ħω≤3 eV (4140 Å ≤λ≤6200 Å) in order to explain the nature of an observed reflectivity edge at 5000 Å. Extrapolations of the data into the infrared and ultraviolet were made. The frequency dependence of the optical constants indicates a plasma resonance at 2.52 eV (4920 Å), shifted and damped from its classically predicted value by the influence of interband transitions occurring at approximately the same energy. The spectral behavior of the optical constants in this region is not very sensitive to the exact nature of the extrapolation.

© 1964 Optical Society of America

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References

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  1. H. Lowery, H. Wilkinson, and D. L. Smare, Proc. Phys. Soc. (London) 49, 345 (1937).
    [Crossref]
  2. N. F. Mott, Proc. Phys. Soc. (London) 49, 354 (1937).
    [Crossref]
  3. J. A. Rayne, as reported in The Fermi Surface, edited by W. A. Harrison and M. B. Webb (John Wiley & Sons, Inc., New York, 1960), p. 269.
  4. L. Muldawer, Phys. Rev. 127, 1551 (1962).
    [Crossref]
  5. F. C. Jahoda, Phys. Rev. 107, 1261 (1957).
    [Crossref]
  6. H. R. Philipp and E. A. Taft, Phys. Rev. 113, 1002 (1959).
    [Crossref]
  7. B. Velicky, Czech. J. Phys. B11, 787 (1961).
    [Crossref]
  8. M. P. Givens, Solid State Phys. 6, 313 (1958).
    [Crossref]
  9. H. Goldman (private communication).
  10. H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
    [Crossref]
  11. H. R. Philipp and H. Ehrenreich, Phys. Rev. 129, 1550 (1963).
    [Crossref]
  12. L. Muldawer (unpublished data).
  13. R. J. Esposito, F. Rothwarf, and J. N. Brown, “A Computer Program for a Kramers–Kronig Transformation of the Optical Reflectivity,” Frankford Arsenal M. R. Report.
  14. M. Suffczynski, Phys. Rev. 117, 663 (1960).
    [Crossref]
  15. W. A. Harrison, Phys. Rev. 118, 1190 (1960).
    [Crossref]
  16. A. Beck, J. P. Jan, W. B. Pearson, and I. M. Templeton, Phil. Mag. 8, 351 (1963).
    [Crossref]
  17. H. Fröhlich and H. Pelzer, Proc. Phys. Soc. (London) A68, 525 (1955).
  18. P. Nozieres and D. Pines, Phys. Rev. 109, 762 (1958).
    [Crossref]
  19. P. Nozieres and D. Pines, Phys. Rev. 113, 1254 (1959).
    [Crossref]
  20. D. Bohm and D. Pines, Phys. Rev. 82, 625 (1951).
    [Crossref]
  21. In thin film specimens it is possible to excite a surface type of collective oscillation with electromagnetic radiation at the plasma frequency obliquely incident and polarized in the plane of incidence. See R. A. Ferrell and E. A. Stern, Am. J. Phys. 30, 810 (1962).
    [Crossref]
  22. E. A. Taft and H. R. Philipp, Phys. Rev. 121, 1100 (1961).
    [Crossref]

1963 (2)

H. R. Philipp and H. Ehrenreich, Phys. Rev. 129, 1550 (1963).
[Crossref]

A. Beck, J. P. Jan, W. B. Pearson, and I. M. Templeton, Phil. Mag. 8, 351 (1963).
[Crossref]

1962 (3)

In thin film specimens it is possible to excite a surface type of collective oscillation with electromagnetic radiation at the plasma frequency obliquely incident and polarized in the plane of incidence. See R. A. Ferrell and E. A. Stern, Am. J. Phys. 30, 810 (1962).
[Crossref]

L. Muldawer, Phys. Rev. 127, 1551 (1962).
[Crossref]

H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[Crossref]

1961 (2)

B. Velicky, Czech. J. Phys. B11, 787 (1961).
[Crossref]

E. A. Taft and H. R. Philipp, Phys. Rev. 121, 1100 (1961).
[Crossref]

1960 (2)

M. Suffczynski, Phys. Rev. 117, 663 (1960).
[Crossref]

W. A. Harrison, Phys. Rev. 118, 1190 (1960).
[Crossref]

1959 (2)

P. Nozieres and D. Pines, Phys. Rev. 113, 1254 (1959).
[Crossref]

H. R. Philipp and E. A. Taft, Phys. Rev. 113, 1002 (1959).
[Crossref]

1958 (2)

M. P. Givens, Solid State Phys. 6, 313 (1958).
[Crossref]

P. Nozieres and D. Pines, Phys. Rev. 109, 762 (1958).
[Crossref]

1957 (1)

F. C. Jahoda, Phys. Rev. 107, 1261 (1957).
[Crossref]

1955 (1)

H. Fröhlich and H. Pelzer, Proc. Phys. Soc. (London) A68, 525 (1955).

1951 (1)

D. Bohm and D. Pines, Phys. Rev. 82, 625 (1951).
[Crossref]

1937 (2)

H. Lowery, H. Wilkinson, and D. L. Smare, Proc. Phys. Soc. (London) 49, 345 (1937).
[Crossref]

N. F. Mott, Proc. Phys. Soc. (London) 49, 354 (1937).
[Crossref]

Beck, A.

A. Beck, J. P. Jan, W. B. Pearson, and I. M. Templeton, Phil. Mag. 8, 351 (1963).
[Crossref]

Bohm, D.

D. Bohm and D. Pines, Phys. Rev. 82, 625 (1951).
[Crossref]

Brown, J. N.

R. J. Esposito, F. Rothwarf, and J. N. Brown, “A Computer Program for a Kramers–Kronig Transformation of the Optical Reflectivity,” Frankford Arsenal M. R. Report.

Ehrenreich, H.

H. R. Philipp and H. Ehrenreich, Phys. Rev. 129, 1550 (1963).
[Crossref]

H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[Crossref]

Esposito, R. J.

R. J. Esposito, F. Rothwarf, and J. N. Brown, “A Computer Program for a Kramers–Kronig Transformation of the Optical Reflectivity,” Frankford Arsenal M. R. Report.

Ferrell, R. A.

In thin film specimens it is possible to excite a surface type of collective oscillation with electromagnetic radiation at the plasma frequency obliquely incident and polarized in the plane of incidence. See R. A. Ferrell and E. A. Stern, Am. J. Phys. 30, 810 (1962).
[Crossref]

Fröhlich, H.

H. Fröhlich and H. Pelzer, Proc. Phys. Soc. (London) A68, 525 (1955).

Givens, M. P.

M. P. Givens, Solid State Phys. 6, 313 (1958).
[Crossref]

Goldman, H.

H. Goldman (private communication).

Harrison, W. A.

W. A. Harrison, Phys. Rev. 118, 1190 (1960).
[Crossref]

Jahoda, F. C.

F. C. Jahoda, Phys. Rev. 107, 1261 (1957).
[Crossref]

Jan, J. P.

A. Beck, J. P. Jan, W. B. Pearson, and I. M. Templeton, Phil. Mag. 8, 351 (1963).
[Crossref]

Lowery, H.

H. Lowery, H. Wilkinson, and D. L. Smare, Proc. Phys. Soc. (London) 49, 345 (1937).
[Crossref]

Mott, N. F.

N. F. Mott, Proc. Phys. Soc. (London) 49, 354 (1937).
[Crossref]

Muldawer, L.

L. Muldawer, Phys. Rev. 127, 1551 (1962).
[Crossref]

L. Muldawer (unpublished data).

Nozieres, P.

P. Nozieres and D. Pines, Phys. Rev. 113, 1254 (1959).
[Crossref]

P. Nozieres and D. Pines, Phys. Rev. 109, 762 (1958).
[Crossref]

Pearson, W. B.

A. Beck, J. P. Jan, W. B. Pearson, and I. M. Templeton, Phil. Mag. 8, 351 (1963).
[Crossref]

Pelzer, H.

H. Fröhlich and H. Pelzer, Proc. Phys. Soc. (London) A68, 525 (1955).

Philipp, H. R.

H. R. Philipp and H. Ehrenreich, Phys. Rev. 129, 1550 (1963).
[Crossref]

H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[Crossref]

E. A. Taft and H. R. Philipp, Phys. Rev. 121, 1100 (1961).
[Crossref]

H. R. Philipp and E. A. Taft, Phys. Rev. 113, 1002 (1959).
[Crossref]

Pines, D.

P. Nozieres and D. Pines, Phys. Rev. 113, 1254 (1959).
[Crossref]

P. Nozieres and D. Pines, Phys. Rev. 109, 762 (1958).
[Crossref]

D. Bohm and D. Pines, Phys. Rev. 82, 625 (1951).
[Crossref]

Rayne, J. A.

J. A. Rayne, as reported in The Fermi Surface, edited by W. A. Harrison and M. B. Webb (John Wiley & Sons, Inc., New York, 1960), p. 269.

Rothwarf, F.

R. J. Esposito, F. Rothwarf, and J. N. Brown, “A Computer Program for a Kramers–Kronig Transformation of the Optical Reflectivity,” Frankford Arsenal M. R. Report.

Smare, D. L.

H. Lowery, H. Wilkinson, and D. L. Smare, Proc. Phys. Soc. (London) 49, 345 (1937).
[Crossref]

Stern, E. A.

In thin film specimens it is possible to excite a surface type of collective oscillation with electromagnetic radiation at the plasma frequency obliquely incident and polarized in the plane of incidence. See R. A. Ferrell and E. A. Stern, Am. J. Phys. 30, 810 (1962).
[Crossref]

Suffczynski, M.

M. Suffczynski, Phys. Rev. 117, 663 (1960).
[Crossref]

Taft, E. A.

E. A. Taft and H. R. Philipp, Phys. Rev. 121, 1100 (1961).
[Crossref]

H. R. Philipp and E. A. Taft, Phys. Rev. 113, 1002 (1959).
[Crossref]

Templeton, I. M.

A. Beck, J. P. Jan, W. B. Pearson, and I. M. Templeton, Phil. Mag. 8, 351 (1963).
[Crossref]

Velicky, B.

B. Velicky, Czech. J. Phys. B11, 787 (1961).
[Crossref]

Wilkinson, H.

H. Lowery, H. Wilkinson, and D. L. Smare, Proc. Phys. Soc. (London) 49, 345 (1937).
[Crossref]

Am. J. Phys. (1)

In thin film specimens it is possible to excite a surface type of collective oscillation with electromagnetic radiation at the plasma frequency obliquely incident and polarized in the plane of incidence. See R. A. Ferrell and E. A. Stern, Am. J. Phys. 30, 810 (1962).
[Crossref]

Czech. J. Phys. (1)

B. Velicky, Czech. J. Phys. B11, 787 (1961).
[Crossref]

Phil. Mag. (1)

A. Beck, J. P. Jan, W. B. Pearson, and I. M. Templeton, Phil. Mag. 8, 351 (1963).
[Crossref]

Phys. Rev. (11)

P. Nozieres and D. Pines, Phys. Rev. 109, 762 (1958).
[Crossref]

P. Nozieres and D. Pines, Phys. Rev. 113, 1254 (1959).
[Crossref]

D. Bohm and D. Pines, Phys. Rev. 82, 625 (1951).
[Crossref]

M. Suffczynski, Phys. Rev. 117, 663 (1960).
[Crossref]

W. A. Harrison, Phys. Rev. 118, 1190 (1960).
[Crossref]

L. Muldawer, Phys. Rev. 127, 1551 (1962).
[Crossref]

F. C. Jahoda, Phys. Rev. 107, 1261 (1957).
[Crossref]

H. R. Philipp and E. A. Taft, Phys. Rev. 113, 1002 (1959).
[Crossref]

H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[Crossref]

H. R. Philipp and H. Ehrenreich, Phys. Rev. 129, 1550 (1963).
[Crossref]

E. A. Taft and H. R. Philipp, Phys. Rev. 121, 1100 (1961).
[Crossref]

Proc. Phys. Soc. (London) (3)

H. Lowery, H. Wilkinson, and D. L. Smare, Proc. Phys. Soc. (London) 49, 345 (1937).
[Crossref]

N. F. Mott, Proc. Phys. Soc. (London) 49, 354 (1937).
[Crossref]

H. Fröhlich and H. Pelzer, Proc. Phys. Soc. (London) A68, 525 (1955).

Solid State Phys. (1)

M. P. Givens, Solid State Phys. 6, 313 (1958).
[Crossref]

Other (4)

H. Goldman (private communication).

J. A. Rayne, as reported in The Fermi Surface, edited by W. A. Harrison and M. B. Webb (John Wiley & Sons, Inc., New York, 1960), p. 269.

L. Muldawer (unpublished data).

R. J. Esposito, F. Rothwarf, and J. N. Brown, “A Computer Program for a Kramers–Kronig Transformation of the Optical Reflectivity,” Frankford Arsenal M. R. Report.

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Figures (4)

Fig. 1
Fig. 1

Spectral reflectivity profiles for Cu (Ehrenreich and Philipp10) and β′ CuZn (Muldawer4).

Fig. 2
Fig. 2

Spectral dependence of the absorption coefficient of β′ CuZn for a uv copper extrapolation.

Fig. 3
Fig. 3

Spectral dependence of the real part of the dielectric constant and the energy loss factor for β′ CuZn, using a uv copper extrapolation.

Fig. 4
Fig. 4

Spectral dependence of the energy loss factor for β′ CuZn, using, respectively, an exponential and constant extrapolation in the uv.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

= 1 - i 2
N = n - i k ,
ϕ ( ω 0 ) = 2 ω 0 π 0 ln r ( ω ) ω 2 - ω 0 2 d ω ,
r = ( N - 1 ) / ( N + 1 ) = r e - i ϕ .
n = 1 - r 2 1 + r 2 - 2 r cos ϕ
k = 2 r sin ϕ 1 + r 2 - 2 r cos ϕ .
1 = n 2 - k 2
2 = 2 n k .
Im ( 1 / ) = 2 / ( 1 2 + 2 2 ) ,
ω p = ( 4 π n e 2 / m ) 1 2 ,
1 = 1 b + 1 f ,