Abstract

Reflectance of thermally oxidized, mechanically polished titanium surfaces was measured with a spectrometer at 5889–5895 A. The principal aim of the experiments was to furnish an optical means of measuring the thickness of thermal oxide layers on titanium. These measurements also provided a method for determining the optical constants of the metal and the thermal oxide. The system was found to be an absorbing base with an absorbing film. The optical constant of titanium was found to be nˆ3=2.41−3.24i and the optical constant of the thermal oxide film was nˆ2=2.40−0.17i. From these constants, the oxide growth curve at 482°C was determined. The curve is of the same type found by other workers, and indicates that the growth rate can be expressed as a combination of a simple parabolic law and a linear law.

© 1962 Optical Society of America

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References

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  1. R. J. Archer, Phys. Rev. 110, 354 (1958).
    [Crossref]
  2. Reference 1, p. 354.
  3. Reference 1, p. 355.
  4. G. Hass and A. P. Bradford, J. Opt. Soc. Am. 47, 125 (1957).
    [Crossref]
  5. O. S. Heavens. Optical Properties of Thin Solid Films (Butterworths Scientific Publications, Ltd., London, 1955), Chap. 3.
  6. A. B. Winterbottom, Trans. Faraday Soc. 42, 487 (1946).
    [Crossref]
  7. A. B. Winterbottom, J. Opt. Soc. Am. 38, 1074 (1948).
    [Crossref]
  8. A. B. Winterbottom, J. Iron Steel Inst. (London) 165, 9 (1950).
  9. Reference 8, p. 10.
  10. G. Hall, Vacuum 2, 331 (1952).
    [Crossref]
  11. A. B. Winterbottom, reference 6, p. 490.
  12. Reference 5, Chap. 5.
  13. T. C. Fry, J. Opt. Soc. Am. 16, 1 (1928).
    [Crossref]
  14. A. B. Winterbottom, reference 6, p. 488.
  15. E. A. Gulbransen and K. F. Andrew, Metals Transactions 185, 741 (1949).
  16. A. E. Jenkins, J. Inst. Metals 82, 220 (1954).
  17. W. A. Alexander and L. M. Pidgeon, Can. J. Research 28, 60 (1950).
  18. G. Hass, reference 4, p. 335.

1958 (1)

R. J. Archer, Phys. Rev. 110, 354 (1958).
[Crossref]

1957 (1)

1954 (1)

A. E. Jenkins, J. Inst. Metals 82, 220 (1954).

1952 (1)

G. Hall, Vacuum 2, 331 (1952).
[Crossref]

1950 (2)

W. A. Alexander and L. M. Pidgeon, Can. J. Research 28, 60 (1950).

A. B. Winterbottom, J. Iron Steel Inst. (London) 165, 9 (1950).

1949 (1)

E. A. Gulbransen and K. F. Andrew, Metals Transactions 185, 741 (1949).

1948 (1)

1946 (1)

A. B. Winterbottom, Trans. Faraday Soc. 42, 487 (1946).
[Crossref]

1928 (1)

Alexander, W. A.

W. A. Alexander and L. M. Pidgeon, Can. J. Research 28, 60 (1950).

Andrew, K. F.

E. A. Gulbransen and K. F. Andrew, Metals Transactions 185, 741 (1949).

Archer, R. J.

R. J. Archer, Phys. Rev. 110, 354 (1958).
[Crossref]

Bradford, A. P.

Fry, T. C.

Gulbransen, E. A.

E. A. Gulbransen and K. F. Andrew, Metals Transactions 185, 741 (1949).

Hall, G.

G. Hall, Vacuum 2, 331 (1952).
[Crossref]

Hass, G.

Heavens, O. S.

O. S. Heavens. Optical Properties of Thin Solid Films (Butterworths Scientific Publications, Ltd., London, 1955), Chap. 3.

Jenkins, A. E.

A. E. Jenkins, J. Inst. Metals 82, 220 (1954).

Pidgeon, L. M.

W. A. Alexander and L. M. Pidgeon, Can. J. Research 28, 60 (1950).

Winterbottom, A. B.

A. B. Winterbottom, J. Iron Steel Inst. (London) 165, 9 (1950).

A. B. Winterbottom, J. Opt. Soc. Am. 38, 1074 (1948).
[Crossref]

A. B. Winterbottom, Trans. Faraday Soc. 42, 487 (1946).
[Crossref]

A. B. Winterbottom, reference 6, p. 490.

A. B. Winterbottom, reference 6, p. 488.

Can. J. Research (1)

W. A. Alexander and L. M. Pidgeon, Can. J. Research 28, 60 (1950).

J. Inst. Metals (1)

A. E. Jenkins, J. Inst. Metals 82, 220 (1954).

J. Iron Steel Inst. (London) (1)

A. B. Winterbottom, J. Iron Steel Inst. (London) 165, 9 (1950).

J. Opt. Soc. Am. (3)

Metals Transactions (1)

E. A. Gulbransen and K. F. Andrew, Metals Transactions 185, 741 (1949).

Phys. Rev. (1)

R. J. Archer, Phys. Rev. 110, 354 (1958).
[Crossref]

Trans. Faraday Soc. (1)

A. B. Winterbottom, Trans. Faraday Soc. 42, 487 (1946).
[Crossref]

Vacuum (1)

G. Hall, Vacuum 2, 331 (1952).
[Crossref]

Other (8)

A. B. Winterbottom, reference 6, p. 490.

Reference 5, Chap. 5.

A. B. Winterbottom, reference 6, p. 488.

G. Hass, reference 4, p. 335.

Reference 8, p. 10.

Reference 1, p. 354.

Reference 1, p. 355.

O. S. Heavens. Optical Properties of Thin Solid Films (Butterworths Scientific Publications, Ltd., London, 1955), Chap. 3.

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Figures (4)

Fig. 1
Fig. 1

Schematic representation of polarization spectrometer.

Fig. 2
Fig. 2

Cartesian coordinate system for spectrometer readings.

Fig. 3
Fig. 3

Plot of R ˆ p / R ˆ n. Open circles–experimental tanψ vs Δ (time in minutes); closed circles–calculated with n ˆ 2=2.4−0.17i, thickness in d0.

Fig. 4
Fig. 4

Oxide thickness vs time of oxidation TiO2 on Ti (482°C).

Tables (2)

Tables Icon

Table I Spectrometer data from titanium samples with various degrees of surface roughness.

Tables Icon

Table II Spectrometer data for titanium samples oxidized at 482°C for various times (angle of incidence=70°).

Equations (10)

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n 2 - k 2 = tan 2 ϕ sin 2 ϕ ( cos 2 2 ψ - sin 2 2 ψ sin 2 Δ ) ( 1 + sin 2 ψ cos Δ ) 2 + sin 2 ϕ
2 n k = tan 2 ϕ sin 2 ϕ sin 4 ψ sin Δ ( 1 + sin 2 ψ cos Δ ) 2 ,
tan Δ = sin δ cot 2 P
tan 2 ψ = cot A cot A ,
n ˆ = 2.33 - 3.18 i .
n ˆ = 2.72 - 3.48 i
R ˆ x = ( r ˆ 12 x + r ˆ 23 x exp [ - 2 i δ ] ) ( 1 + r ˆ 12 x r ˆ 23 x exp [ - 2 i δ ˆ ] ) ,
r ˆ α β p = ( n ˆ β cos ϕ ˆ α - n ˆ α cos ϕ ˆ β ) ( n ˆ β cos ϕ ˆ α + n ˆ α cos ϕ ˆ β )
r ˆ α β n = ( n ˆ α cos ϕ ˆ α - n ˆ β cos ϕ ˆ β ) ( n ˆ α cos ϕ ˆ α + n ˆ β cos ϕ ˆ β ) ,
δ ˆ = 2 π n ˆ 2 cos ϕ ˆ 2 d / Λ 0 ,