Abstract

The optical constants of molybdenum, tantalum, tungsten, and rhenium have been measured at wavelengths from 537 through 5770 Å by the reflectance vs angle of incidence method. The spectra for the two parts of the complex dielectric constant exhibit structural similarities among the four metals, consisting of three broad, partially overlapping absorption bands situated in the approximate photon-energy regions between 13 and 26 eV, between 7 and 15 eV, and below 10 eV. The latter band generally has one or more narrower absorption resonances superimposed on it. The observed structure bears a resemblance to the level separations calculated by Mattheiss for tungsten and rhenium, but correlation with specific transitions has not been pursued in detail. The <i>f</i>-sum rule applied to the imaginary part of the dielectric constant yields appropriate values of 5 and 7 electrons/atom for tantalum and rhenium. For molybdenum and tungsten the corresponding values are near 8, rather than the anticipated 6, electrons/atom.

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  1. L. J. LeBlanc, J. S. Farrell, and D. W. Juenker, J. Opt. Soc. Am. 54, 956 (1964).
  2. S. Roberts, Phys. Rev. 114, 104 (1959).
  3. A. P. Lenham, J. Opt. Soc. Am. 57, 473 (1967).
  4. D. W. Juenker, J. Opt. Soc. Am. 55, 295 (1965).
  5. L. F. Mattheiss, Phys. Rev. 139, A1893 (1965); L. F. Mattheiss and R. E. Watson, Phys. Rev. Letters 13, 527 (1964).
  6. L. F. Mattheiss, Phys. Rev. 151, 450 (1966).
  7. T. L. Loucks, Phys. Rev. 139, A1181 (1965).
  8. T. L. Loucks, Phys. Rev. 139, A1333 (1965).
  9. T. L. Loucks, Phys. Rev. 143, 506 (1966).
  10. P. L. Hartman, J. Opt. Soc. Am. 51, 113 (1961).
  11. J. P. Waldron and D. W. Juenker, J. Opt. Soc. Am. 54, 204 (1964).
  12. A single such exception occurred in molybdenum, two each in tantalum and tungsten, and five in rhenium. The somewhat poorer surface finish of the rhenium samples was probably responsible for its excessive data scatter, although a slight anisotropy of the optical properties of its hcp lattice is a possible source of the discrepancies.
  13. W. R. Hunter, J. Opt. Soc. Am. 55, 1197 (1965).
  14. A lorentzian function might have been preferable; cf. N. Swanson, J. Opt. Soc. Am. 54, 1130 (1964).
  15. See, for example, F. Stern, in Solid State Physics (Academic Press Inc., New York, 1963), Vol. 15, p. 300.
  16. M. F. Manning and M. I. Chodorow, Phys. Rev. 56, 787 (1939).
  17. L. Marton, L. B. Leder, and H. Mendlowitz, in Advances in Electronics and Electron Physics, L. Marton, Ed. (Academic Press Inc., New York, 1955), Vol. 7.
  18. L. J. Haworth, Phys. Rev. 48, 88 (1935); 50, 216 (1936).
  19. V. W. Kleinn, Optik 11, 226 (1954).
  20. J. O. Dimmock, A. J. Freeman, and R. E. Watson, in Proc. Int. Colloq. on Optical Properties and Electronics Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland Publishing Co., Amsterdam, 1966), p. 237.

Chodorow, M. I.

M. F. Manning and M. I. Chodorow, Phys. Rev. 56, 787 (1939).

Dimmock, J. O.

J. O. Dimmock, A. J. Freeman, and R. E. Watson, in Proc. Int. Colloq. on Optical Properties and Electronics Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland Publishing Co., Amsterdam, 1966), p. 237.

Farrell, J. S.

L. J. LeBlanc, J. S. Farrell, and D. W. Juenker, J. Opt. Soc. Am. 54, 956 (1964).

Freeman, A. J.

J. O. Dimmock, A. J. Freeman, and R. E. Watson, in Proc. Int. Colloq. on Optical Properties and Electronics Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland Publishing Co., Amsterdam, 1966), p. 237.

Hartman, P. L.

P. L. Hartman, J. Opt. Soc. Am. 51, 113 (1961).

Haworth, L. J.

L. J. Haworth, Phys. Rev. 48, 88 (1935); 50, 216 (1936).

Hunter, W. R.

W. R. Hunter, J. Opt. Soc. Am. 55, 1197 (1965).

Juenker, D. W.

J. P. Waldron and D. W. Juenker, J. Opt. Soc. Am. 54, 204 (1964).

L. J. LeBlanc, J. S. Farrell, and D. W. Juenker, J. Opt. Soc. Am. 54, 956 (1964).

D. W. Juenker, J. Opt. Soc. Am. 55, 295 (1965).

Kleinn, V. W.

V. W. Kleinn, Optik 11, 226 (1954).

LeBlanc, L. J.

L. J. LeBlanc, J. S. Farrell, and D. W. Juenker, J. Opt. Soc. Am. 54, 956 (1964).

Leder, L. B.

L. Marton, L. B. Leder, and H. Mendlowitz, in Advances in Electronics and Electron Physics, L. Marton, Ed. (Academic Press Inc., New York, 1955), Vol. 7.

Lenham, A. P.

A. P. Lenham, J. Opt. Soc. Am. 57, 473 (1967).

Loucks, T. L.

T. L. Loucks, Phys. Rev. 139, A1181 (1965).

T. L. Loucks, Phys. Rev. 139, A1333 (1965).

T. L. Loucks, Phys. Rev. 143, 506 (1966).

Manning, M. F.

M. F. Manning and M. I. Chodorow, Phys. Rev. 56, 787 (1939).

Marton, L.

L. Marton, L. B. Leder, and H. Mendlowitz, in Advances in Electronics and Electron Physics, L. Marton, Ed. (Academic Press Inc., New York, 1955), Vol. 7.

Mattheiss, L. F.

L. F. Mattheiss, Phys. Rev. 139, A1893 (1965); L. F. Mattheiss and R. E. Watson, Phys. Rev. Letters 13, 527 (1964).

L. F. Mattheiss, Phys. Rev. 151, 450 (1966).

Mendlowitz, H.

L. Marton, L. B. Leder, and H. Mendlowitz, in Advances in Electronics and Electron Physics, L. Marton, Ed. (Academic Press Inc., New York, 1955), Vol. 7.

Roberts, S.

S. Roberts, Phys. Rev. 114, 104 (1959).

Stern, F.

See, for example, F. Stern, in Solid State Physics (Academic Press Inc., New York, 1963), Vol. 15, p. 300.

Swanson, N.

A lorentzian function might have been preferable; cf. N. Swanson, J. Opt. Soc. Am. 54, 1130 (1964).

Waldron, J. P.

J. P. Waldron and D. W. Juenker, J. Opt. Soc. Am. 54, 204 (1964).

Watson, R. E.

J. O. Dimmock, A. J. Freeman, and R. E. Watson, in Proc. Int. Colloq. on Optical Properties and Electronics Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland Publishing Co., Amsterdam, 1966), p. 237.

Other (20)

L. J. LeBlanc, J. S. Farrell, and D. W. Juenker, J. Opt. Soc. Am. 54, 956 (1964).

S. Roberts, Phys. Rev. 114, 104 (1959).

A. P. Lenham, J. Opt. Soc. Am. 57, 473 (1967).

D. W. Juenker, J. Opt. Soc. Am. 55, 295 (1965).

L. F. Mattheiss, Phys. Rev. 139, A1893 (1965); L. F. Mattheiss and R. E. Watson, Phys. Rev. Letters 13, 527 (1964).

L. F. Mattheiss, Phys. Rev. 151, 450 (1966).

T. L. Loucks, Phys. Rev. 139, A1181 (1965).

T. L. Loucks, Phys. Rev. 139, A1333 (1965).

T. L. Loucks, Phys. Rev. 143, 506 (1966).

P. L. Hartman, J. Opt. Soc. Am. 51, 113 (1961).

J. P. Waldron and D. W. Juenker, J. Opt. Soc. Am. 54, 204 (1964).

A single such exception occurred in molybdenum, two each in tantalum and tungsten, and five in rhenium. The somewhat poorer surface finish of the rhenium samples was probably responsible for its excessive data scatter, although a slight anisotropy of the optical properties of its hcp lattice is a possible source of the discrepancies.

W. R. Hunter, J. Opt. Soc. Am. 55, 1197 (1965).

A lorentzian function might have been preferable; cf. N. Swanson, J. Opt. Soc. Am. 54, 1130 (1964).

See, for example, F. Stern, in Solid State Physics (Academic Press Inc., New York, 1963), Vol. 15, p. 300.

M. F. Manning and M. I. Chodorow, Phys. Rev. 56, 787 (1939).

L. Marton, L. B. Leder, and H. Mendlowitz, in Advances in Electronics and Electron Physics, L. Marton, Ed. (Academic Press Inc., New York, 1955), Vol. 7.

L. J. Haworth, Phys. Rev. 48, 88 (1935); 50, 216 (1936).

V. W. Kleinn, Optik 11, 226 (1954).

J. O. Dimmock, A. J. Freeman, and R. E. Watson, in Proc. Int. Colloq. on Optical Properties and Electronics Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland Publishing Co., Amsterdam, 1966), p. 237.

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