Abstract

Methods previously developed for studying the optical properties of solid metals were modified to permit their use for studying liquid Hg and liquid Ga. Reflectivities were measured at an angle of incidence of 45° at glass-metal, quartz-metal, and NaCl-metal interfaces in the wavelength range of 0.23 μ to 13 μ. In a second type of experiment the phase change accompanying reflection at normal incidence at a mica-metal interface was measured in the range 0.4 μ to 0.87 μ. In this shorter wavelength range the two measured quantities, reflectivity and phase change, were used to compute the optical constants n and k. The values thus obtained agreed to within the experimental accuracy with those calculated with the Drude free electron theory. The fact that the experimentally determined reflectivity for the complete range of 0.23 μ to 13 μ agreed closely with that predicted by the Drude theory strongly suggests that the theory applies throughout this entire wavelength range.

© 1957 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Drude, Ann. Physik 39, 530 (1890).
  2. W. Meier, Ann. Physik 31, 1017 (1910).
    [Crossref]
  3. P. Erochin, Ann. Physik 39, 213 (1912).
    [Crossref]
  4. R.W. Duncan and R. C. Duncan, Phys. Rev. 1, 294 (1913).
    [Crossref]
  5. Brian O’Brien, Phys. Rev. 27, 93 (1926).
    [Crossref]
  6. L. Tronstad and C. Feacham, Proc. Roy. Soc. (London) A145, 115 (1934).
  7. H. Lange, Z. Physik 94, 650 (1935).
    [Crossref]
  8. H. Ives and H. Briggs, J. Opt. Soc. Am. 26, 240 (1936).
  9. R. Emberson, J. Opt. Soc. Am. 26, 443 (1936).
    [Crossref]
  10. J. Nathanson, J. Opt. Soc. Am. 28, 300 (1938).
    [Crossref]
  11. E. Hagen and H. Rubens, Ann. Physik 11, 873 (1903).
    [Crossref]
  12. E. Hagen and H. Rubens, Ann. Physik 1, 352 (1900).
    [Crossref]
  13. F. Seitz, Modern Theory of Solids (McGraw-Hill Book Company, Inc., New York, 1941), Chap. 17.
  14. N. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys (Oxford University Press, New York, 1936), Chap. 3.
  15. L. G. Schulz and F. R. Tangherlini, J. Opt. Soc. Am. 44, 362 (1954).
    [Crossref]
  16. L. G. Schulz, J. Opt. Soc. Am. 44, 357 (1954).
    [Crossref]
  17. Measurements on liquid Ga by J. Nathanson, Phys. Rev. 49, 887 (1936) seem to be grossly incorrect.
  18. C. V. Kent, Phys. Rev. 14, 459 (1919).
    [Crossref]
  19. International Critical Tables (McGraw-Hill Book Company, Inc., New York, 1926).
  20. Erich Einecke, Das Gallium (Edwards Brothers, Inc., Ann Arbor, 1944).
  21. P. Bridgman, Proc. Am. Acad. Arts Sci. 56, 104 (1920).
  22. J. H. Stratton, Electromagnetic Theory (McGraw-Hill Book Company, Inc., New York, 1941), p. 520.
  23. L. G. Schulz, J. Opt. Soc. Am. 44, 540 (1954).
    [Crossref]

1954 (3)

1938 (1)

1936 (3)

Measurements on liquid Ga by J. Nathanson, Phys. Rev. 49, 887 (1936) seem to be grossly incorrect.

H. Ives and H. Briggs, J. Opt. Soc. Am. 26, 240 (1936).

R. Emberson, J. Opt. Soc. Am. 26, 443 (1936).
[Crossref]

1935 (1)

H. Lange, Z. Physik 94, 650 (1935).
[Crossref]

1934 (1)

L. Tronstad and C. Feacham, Proc. Roy. Soc. (London) A145, 115 (1934).

1926 (1)

Brian O’Brien, Phys. Rev. 27, 93 (1926).
[Crossref]

1920 (1)

P. Bridgman, Proc. Am. Acad. Arts Sci. 56, 104 (1920).

1919 (1)

C. V. Kent, Phys. Rev. 14, 459 (1919).
[Crossref]

1913 (1)

R.W. Duncan and R. C. Duncan, Phys. Rev. 1, 294 (1913).
[Crossref]

1912 (1)

P. Erochin, Ann. Physik 39, 213 (1912).
[Crossref]

1910 (1)

W. Meier, Ann. Physik 31, 1017 (1910).
[Crossref]

1903 (1)

E. Hagen and H. Rubens, Ann. Physik 11, 873 (1903).
[Crossref]

1900 (1)

E. Hagen and H. Rubens, Ann. Physik 1, 352 (1900).
[Crossref]

1890 (1)

P. Drude, Ann. Physik 39, 530 (1890).

Bridgman, P.

P. Bridgman, Proc. Am. Acad. Arts Sci. 56, 104 (1920).

Briggs, H.

H. Ives and H. Briggs, J. Opt. Soc. Am. 26, 240 (1936).

Drude, P.

P. Drude, Ann. Physik 39, 530 (1890).

Duncan, R. C.

R.W. Duncan and R. C. Duncan, Phys. Rev. 1, 294 (1913).
[Crossref]

Duncan, R.W.

R.W. Duncan and R. C. Duncan, Phys. Rev. 1, 294 (1913).
[Crossref]

Einecke, Erich

Erich Einecke, Das Gallium (Edwards Brothers, Inc., Ann Arbor, 1944).

Emberson, R.

Erochin, P.

P. Erochin, Ann. Physik 39, 213 (1912).
[Crossref]

Feacham, C.

L. Tronstad and C. Feacham, Proc. Roy. Soc. (London) A145, 115 (1934).

Hagen, E.

E. Hagen and H. Rubens, Ann. Physik 11, 873 (1903).
[Crossref]

E. Hagen and H. Rubens, Ann. Physik 1, 352 (1900).
[Crossref]

Ives, H.

H. Ives and H. Briggs, J. Opt. Soc. Am. 26, 240 (1936).

Jones, H.

N. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys (Oxford University Press, New York, 1936), Chap. 3.

Kent, C. V.

C. V. Kent, Phys. Rev. 14, 459 (1919).
[Crossref]

Lange, H.

H. Lange, Z. Physik 94, 650 (1935).
[Crossref]

Meier, W.

W. Meier, Ann. Physik 31, 1017 (1910).
[Crossref]

Mott, N. F.

N. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys (Oxford University Press, New York, 1936), Chap. 3.

Nathanson, J.

J. Nathanson, J. Opt. Soc. Am. 28, 300 (1938).
[Crossref]

Measurements on liquid Ga by J. Nathanson, Phys. Rev. 49, 887 (1936) seem to be grossly incorrect.

O’Brien, Brian

Brian O’Brien, Phys. Rev. 27, 93 (1926).
[Crossref]

Rubens, H.

E. Hagen and H. Rubens, Ann. Physik 11, 873 (1903).
[Crossref]

E. Hagen and H. Rubens, Ann. Physik 1, 352 (1900).
[Crossref]

Schulz, L. G.

Seitz, F.

F. Seitz, Modern Theory of Solids (McGraw-Hill Book Company, Inc., New York, 1941), Chap. 17.

Stratton, J. H.

J. H. Stratton, Electromagnetic Theory (McGraw-Hill Book Company, Inc., New York, 1941), p. 520.

Tangherlini, F. R.

Tronstad, L.

L. Tronstad and C. Feacham, Proc. Roy. Soc. (London) A145, 115 (1934).

Ann. Physik (5)

P. Drude, Ann. Physik 39, 530 (1890).

W. Meier, Ann. Physik 31, 1017 (1910).
[Crossref]

P. Erochin, Ann. Physik 39, 213 (1912).
[Crossref]

E. Hagen and H. Rubens, Ann. Physik 11, 873 (1903).
[Crossref]

E. Hagen and H. Rubens, Ann. Physik 1, 352 (1900).
[Crossref]

J. Opt. Soc. Am. (6)

Phys. Rev. (4)

Measurements on liquid Ga by J. Nathanson, Phys. Rev. 49, 887 (1936) seem to be grossly incorrect.

C. V. Kent, Phys. Rev. 14, 459 (1919).
[Crossref]

R.W. Duncan and R. C. Duncan, Phys. Rev. 1, 294 (1913).
[Crossref]

Brian O’Brien, Phys. Rev. 27, 93 (1926).
[Crossref]

Proc. Am. Acad. Arts Sci. (1)

P. Bridgman, Proc. Am. Acad. Arts Sci. 56, 104 (1920).

Proc. Roy. Soc. (London) (1)

L. Tronstad and C. Feacham, Proc. Roy. Soc. (London) A145, 115 (1934).

Z. Physik (1)

H. Lange, Z. Physik 94, 650 (1935).
[Crossref]

Other (5)

F. Seitz, Modern Theory of Solids (McGraw-Hill Book Company, Inc., New York, 1941), Chap. 17.

N. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys (Oxford University Press, New York, 1936), Chap. 3.

J. H. Stratton, Electromagnetic Theory (McGraw-Hill Book Company, Inc., New York, 1941), p. 520.

International Critical Tables (McGraw-Hill Book Company, Inc., New York, 1926).

Erich Einecke, Das Gallium (Edwards Brothers, Inc., Ann Arbor, 1944).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Graph showing experimental values of n and k obtained in the past.26 The curves labeled “Drude” were obtained by calculation using the Drude free-electron theory Eqs. (1)(3).

Fig. 2
Fig. 2

The reflectivity Rair at a Hg-air interface for normal incidence. These values for Rair were computed from the n and k values of Fig. 1.

Fig. 3
Fig. 3

Graph showing the values of n/λ, k/λ and Rair for Hg obtained with Eqs. (1)(3). The values of σ and N used in the computations are shown on the graph.

Fig. 4
Fig. 4

Graph showing the values of n/λ, k/λ and Rair for Ga obtained with Eqs. (1)(3). The values of σ and N used in the computations are shown on the graph.

Fig. 5
Fig. 5

General features of the reflection samples. (A) gives the arrangement for samples using glass, quartz, and NaCl prisms in the visible and infrared; (C) is the arrangement for quartz prism samples in the ultraviolet. In (B) is given the method of putting on Hg with the pre-Ag treatment which was used for prisms of glass and quartz. (D) shows the infrared polarizer which minimized beam displacement.

Fig. 6
Fig. 6

Reflectivity values for samples using glass or quartz prisms. [ R ¯ is equal to 1 2 ( R s + R p ) as defined in reference 15.] The solid lines were obtained with the Drude theory; the solid circles are experimental values. For Hg-glass samples the crosses are values from prisms which were not given the pre-Ag treatment of Fig. 5(B).

Fig. 7
Fig. 7

R ¯ values for samples using NaCl prisms; solid lines were obtained with the Drude theory; the solid circles are experimental values.

Fig. 8
Fig. 8

Experimental arrangement for pouring Ga in a vacuum. The vacuum was formed by sealing a 6″ bell jar BJ to a metal base plate BP. A hole H in the cylinder of the medical syringe MS permitted the air to be pumped off from above the liquid metal LM. A small glass funnel F directed the liquid metal from the needle N into the sample S.

Fig. 9
Fig. 9

Steps in the preparation of samples to be used for phase change measurements.

Fig. 10
Fig. 10

Representative results of phase change measurements. In (A) are shown Δψλ values for several samples for Hg relative to Al, while (B) gives similar results for Ga relative to Ag.

Tables (3)

Tables Icon

Table I Comparison of the values of σ and N given in tables of physical constants with the values obtained experimentally.

Tables Icon

Table II Comparison of values of n and k predicted by the Drude theory with values obtained experimentally. The probable errors in the experimental values of n and k are 4% and 2%, respectively.

Tables Icon

Table III Effect of variations in σ and N on n, k, R, and ψλ/2π at 0.6 μ. As the skin effect region is approached changes in N cease to have any effect on n and k whereas the percentage change in n and k for any change in σ becomes equal to one-half the percentage change in σ.

Equations (3)

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

n 2 - k 2 = 1 - 2 ( N e 2 2 π m * ) 1 ν 2 + γ 2 ,
n k = γ ν ( N e 2 2 π m * ) 1 ν 2 + γ 2
γ = ( N e 2 2 π m * ) 1 σ .