Abstract

Emissivity modeling of metals has been developed to elucidate behavior during the growth of oxide film, and the modeling results have been compared with experimental results. To express emissivities, pseudo-optical constants of a bare metal and of an oxide film obtained by an ellipsometer are substituted into the model equations. Emissivity behavior during the growth of an oxide film upon the surface of a specimen is shown in terms of spectral, directional, and polarized characteristics, and it coincides with the experimental results, both quantitatively and qualitatively. The modeling is simple and provides useful guidance for the development of emissivity-compensated radiation thermometry.

© 2003 Optical Society of America

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References

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  1. W. M. Brandenberg, O. W. Clausen, “The directional spectral emittance of surface between 200° and 600°,” in Symposium on Thermal Radiation of Solids, NASA document SP-55 (NASA, Washington, D.C., 1965), pp. 313–320.
  2. D. J. Price, “The emissivity of hot metals in the infra-red,” Proc. Phys. Soc. London Sec. A 59, 118–131 (1947).
    [CrossRef]
  3. W. J. Parker, G. C. Abbott, “Total emittance of metals,” in Symposium on Thermal Radiation of Solids, NASA document SP-55 (NASA, Washington, D.C., 1965), pp. 11–28.
  4. A. J. Sievers, “Thermal radiation from metal surfaces,” J. Opt. Soc. Am. 68, 1505–1516 (1978).
    [CrossRef]
  5. P. Drude, “Bestimmung der Optischen Constanten der Metalle,” Ann. Phys. 64, 159–167 (1898).
    [CrossRef]
  6. E. Aschkinass, “Die Warmestrallung der Metalle,” Ann. Phys. (Leipzig) 17, 960–976 (1905).
    [CrossRef]
  7. E. Hagen, H. Rubens, “Emissionvermogen und Electrische Leitfahigkeit der Metallefierunger,” Verh. Dtsch. Phys. Ges. 6, 128–136 (1904).
  8. R. Gardon, “The emissivity of transparent materials,” J. Am. Ceram. Soc. 39, 278–287 (1956).
    [CrossRef]
  9. P. Kubelka, “New contributions to the optics of intensely light-scattering material,” J. Opt. Soc. Am. 38, 448–457 (1948).
    [CrossRef] [PubMed]
  10. R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 3rd ed. (Hemisphere, Washington, D.C., 1992), Chaps. 4 and 5.
  11. D. P. DeWitt, J. C. Richmond, “Thermal radiative properties of materials,” in Theory and Practice of Radiation Thermometry, D. P. DeWitt, G. C. Nutter, eds. (Wiley, New York, (1988), pp. 91–187.
    [CrossRef]
  12. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999), pp. 735–758.
    [CrossRef]
  13. T. Iuchi, S. Wada, “Simultaneous measurement system of emissivity and temperature for glossy metals near room temperature,” Temperature (to be published).
  14. T. Furukawa, T. Iuchi, “Experimental apparatus for radiometric emissivity measurements of metals,” Rev. Sci. Instrum. 71, 2843–2847 (2000).
    [CrossRef]
  15. T. Furukawa, T. Iuchi, “A measurement system of radiances using optical fibers for the analysis of emissivity properties,” presented at the 39th Annual Conference of the Society of Instruments and Control Engineers, Iizuka, Japan, 26–28 July 2000.
  16. T. Tiwald, “Measurement report” (J. A. Woollam Company, Inc., Lincoln, Neb., August1999); personal communication.
  17. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1986).
  18. D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 16, 3513–3534 (1979).
  19. G. Neuer, F. Güntert, “In situ ! measurements of layer thickness during oxidation of titanium,” Thermochim. Acta 133, 299–304 (1988).
    [CrossRef]
  20. T. Iuchi, T. Furukawa, “Emissivity-compensated radiation thermometry,” in Proceedings of the 16th Imeko World Congress, M. N. Durakbasa, A. Ffjehi-Sadat, P. H. Osanna, eds. (Austrian Society for Measurement and Automation, Vienna, 2000), Vol. VI, pp. 365–369.
  21. T. Iuchi, T. Tsurukawaya, A. Tazoe, “Emissivity compensated radiation thermometry using directional radiances,” Trans. Soc. Instrum. Control Engin. E-1, 305–311 (2001).

2001 (1)

T. Iuchi, T. Tsurukawaya, A. Tazoe, “Emissivity compensated radiation thermometry using directional radiances,” Trans. Soc. Instrum. Control Engin. E-1, 305–311 (2001).

2000 (1)

T. Furukawa, T. Iuchi, “Experimental apparatus for radiometric emissivity measurements of metals,” Rev. Sci. Instrum. 71, 2843–2847 (2000).
[CrossRef]

1988 (1)

G. Neuer, F. Güntert, “In situ ! measurements of layer thickness during oxidation of titanium,” Thermochim. Acta 133, 299–304 (1988).
[CrossRef]

1979 (1)

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 16, 3513–3534 (1979).

1978 (1)

1956 (1)

R. Gardon, “The emissivity of transparent materials,” J. Am. Ceram. Soc. 39, 278–287 (1956).
[CrossRef]

1948 (1)

1947 (1)

D. J. Price, “The emissivity of hot metals in the infra-red,” Proc. Phys. Soc. London Sec. A 59, 118–131 (1947).
[CrossRef]

1905 (1)

E. Aschkinass, “Die Warmestrallung der Metalle,” Ann. Phys. (Leipzig) 17, 960–976 (1905).
[CrossRef]

1904 (1)

E. Hagen, H. Rubens, “Emissionvermogen und Electrische Leitfahigkeit der Metallefierunger,” Verh. Dtsch. Phys. Ges. 6, 128–136 (1904).

1898 (1)

P. Drude, “Bestimmung der Optischen Constanten der Metalle,” Ann. Phys. 64, 159–167 (1898).
[CrossRef]

Abbott, G. C.

W. J. Parker, G. C. Abbott, “Total emittance of metals,” in Symposium on Thermal Radiation of Solids, NASA document SP-55 (NASA, Washington, D.C., 1965), pp. 11–28.

Aschkinass, E.

E. Aschkinass, “Die Warmestrallung der Metalle,” Ann. Phys. (Leipzig) 17, 960–976 (1905).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 16, 3513–3534 (1979).

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1986).

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1986).

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999), pp. 735–758.
[CrossRef]

Brandenberg, W. M.

W. M. Brandenberg, O. W. Clausen, “The directional spectral emittance of surface between 200° and 600°,” in Symposium on Thermal Radiation of Solids, NASA document SP-55 (NASA, Washington, D.C., 1965), pp. 313–320.

Clausen, O. W.

W. M. Brandenberg, O. W. Clausen, “The directional spectral emittance of surface between 200° and 600°,” in Symposium on Thermal Radiation of Solids, NASA document SP-55 (NASA, Washington, D.C., 1965), pp. 313–320.

DeWitt, D. P.

D. P. DeWitt, J. C. Richmond, “Thermal radiative properties of materials,” in Theory and Practice of Radiation Thermometry, D. P. DeWitt, G. C. Nutter, eds. (Wiley, New York, (1988), pp. 91–187.
[CrossRef]

Drude, P.

P. Drude, “Bestimmung der Optischen Constanten der Metalle,” Ann. Phys. 64, 159–167 (1898).
[CrossRef]

Furukawa, T.

T. Furukawa, T. Iuchi, “Experimental apparatus for radiometric emissivity measurements of metals,” Rev. Sci. Instrum. 71, 2843–2847 (2000).
[CrossRef]

T. Furukawa, T. Iuchi, “A measurement system of radiances using optical fibers for the analysis of emissivity properties,” presented at the 39th Annual Conference of the Society of Instruments and Control Engineers, Iizuka, Japan, 26–28 July 2000.

T. Iuchi, T. Furukawa, “Emissivity-compensated radiation thermometry,” in Proceedings of the 16th Imeko World Congress, M. N. Durakbasa, A. Ffjehi-Sadat, P. H. Osanna, eds. (Austrian Society for Measurement and Automation, Vienna, 2000), Vol. VI, pp. 365–369.

Gardon, R.

R. Gardon, “The emissivity of transparent materials,” J. Am. Ceram. Soc. 39, 278–287 (1956).
[CrossRef]

Güntert, F.

G. Neuer, F. Güntert, “In situ ! measurements of layer thickness during oxidation of titanium,” Thermochim. Acta 133, 299–304 (1988).
[CrossRef]

Hagen, E.

E. Hagen, H. Rubens, “Emissionvermogen und Electrische Leitfahigkeit der Metallefierunger,” Verh. Dtsch. Phys. Ges. 6, 128–136 (1904).

Hottier, F.

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 16, 3513–3534 (1979).

Howell, J. R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 3rd ed. (Hemisphere, Washington, D.C., 1992), Chaps. 4 and 5.

Iuchi, T.

T. Iuchi, T. Tsurukawaya, A. Tazoe, “Emissivity compensated radiation thermometry using directional radiances,” Trans. Soc. Instrum. Control Engin. E-1, 305–311 (2001).

T. Furukawa, T. Iuchi, “Experimental apparatus for radiometric emissivity measurements of metals,” Rev. Sci. Instrum. 71, 2843–2847 (2000).
[CrossRef]

T. Furukawa, T. Iuchi, “A measurement system of radiances using optical fibers for the analysis of emissivity properties,” presented at the 39th Annual Conference of the Society of Instruments and Control Engineers, Iizuka, Japan, 26–28 July 2000.

T. Iuchi, S. Wada, “Simultaneous measurement system of emissivity and temperature for glossy metals near room temperature,” Temperature (to be published).

T. Iuchi, T. Furukawa, “Emissivity-compensated radiation thermometry,” in Proceedings of the 16th Imeko World Congress, M. N. Durakbasa, A. Ffjehi-Sadat, P. H. Osanna, eds. (Austrian Society for Measurement and Automation, Vienna, 2000), Vol. VI, pp. 365–369.

Kubelka, P.

Neuer, G.

G. Neuer, F. Güntert, “In situ ! measurements of layer thickness during oxidation of titanium,” Thermochim. Acta 133, 299–304 (1988).
[CrossRef]

Parker, W. J.

W. J. Parker, G. C. Abbott, “Total emittance of metals,” in Symposium on Thermal Radiation of Solids, NASA document SP-55 (NASA, Washington, D.C., 1965), pp. 11–28.

Price, D. J.

D. J. Price, “The emissivity of hot metals in the infra-red,” Proc. Phys. Soc. London Sec. A 59, 118–131 (1947).
[CrossRef]

Richmond, J. C.

D. P. DeWitt, J. C. Richmond, “Thermal radiative properties of materials,” in Theory and Practice of Radiation Thermometry, D. P. DeWitt, G. C. Nutter, eds. (Wiley, New York, (1988), pp. 91–187.
[CrossRef]

Rubens, H.

E. Hagen, H. Rubens, “Emissionvermogen und Electrische Leitfahigkeit der Metallefierunger,” Verh. Dtsch. Phys. Ges. 6, 128–136 (1904).

Siegel, R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 3rd ed. (Hemisphere, Washington, D.C., 1992), Chaps. 4 and 5.

Sievers, A. J.

Tazoe, A.

T. Iuchi, T. Tsurukawaya, A. Tazoe, “Emissivity compensated radiation thermometry using directional radiances,” Trans. Soc. Instrum. Control Engin. E-1, 305–311 (2001).

Theeten, J. B.

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 16, 3513–3534 (1979).

Tiwald, T.

T. Tiwald, “Measurement report” (J. A. Woollam Company, Inc., Lincoln, Neb., August1999); personal communication.

Tsurukawaya, T.

T. Iuchi, T. Tsurukawaya, A. Tazoe, “Emissivity compensated radiation thermometry using directional radiances,” Trans. Soc. Instrum. Control Engin. E-1, 305–311 (2001).

Wada, S.

T. Iuchi, S. Wada, “Simultaneous measurement system of emissivity and temperature for glossy metals near room temperature,” Temperature (to be published).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999), pp. 735–758.
[CrossRef]

Ann. Phys. (1)

P. Drude, “Bestimmung der Optischen Constanten der Metalle,” Ann. Phys. 64, 159–167 (1898).
[CrossRef]

Ann. Phys. (Leipzig) (1)

E. Aschkinass, “Die Warmestrallung der Metalle,” Ann. Phys. (Leipzig) 17, 960–976 (1905).
[CrossRef]

J. Am. Ceram. Soc. (1)

R. Gardon, “The emissivity of transparent materials,” J. Am. Ceram. Soc. 39, 278–287 (1956).
[CrossRef]

J. Opt. Soc. Am. (2)

Phys. Rev. B (1)

D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 16, 3513–3534 (1979).

Proc. Phys. Soc. London Sec. A (1)

D. J. Price, “The emissivity of hot metals in the infra-red,” Proc. Phys. Soc. London Sec. A 59, 118–131 (1947).
[CrossRef]

Rev. Sci. Instrum. (1)

T. Furukawa, T. Iuchi, “Experimental apparatus for radiometric emissivity measurements of metals,” Rev. Sci. Instrum. 71, 2843–2847 (2000).
[CrossRef]

Thermochim. Acta (1)

G. Neuer, F. Güntert, “In situ ! measurements of layer thickness during oxidation of titanium,” Thermochim. Acta 133, 299–304 (1988).
[CrossRef]

Trans. Soc. Instrum. Control Engin. (1)

T. Iuchi, T. Tsurukawaya, A. Tazoe, “Emissivity compensated radiation thermometry using directional radiances,” Trans. Soc. Instrum. Control Engin. E-1, 305–311 (2001).

Verh. Dtsch. Phys. Ges. (1)

E. Hagen, H. Rubens, “Emissionvermogen und Electrische Leitfahigkeit der Metallefierunger,” Verh. Dtsch. Phys. Ges. 6, 128–136 (1904).

Other (10)

T. Iuchi, T. Furukawa, “Emissivity-compensated radiation thermometry,” in Proceedings of the 16th Imeko World Congress, M. N. Durakbasa, A. Ffjehi-Sadat, P. H. Osanna, eds. (Austrian Society for Measurement and Automation, Vienna, 2000), Vol. VI, pp. 365–369.

T. Furukawa, T. Iuchi, “A measurement system of radiances using optical fibers for the analysis of emissivity properties,” presented at the 39th Annual Conference of the Society of Instruments and Control Engineers, Iizuka, Japan, 26–28 July 2000.

T. Tiwald, “Measurement report” (J. A. Woollam Company, Inc., Lincoln, Neb., August1999); personal communication.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1986).

W. J. Parker, G. C. Abbott, “Total emittance of metals,” in Symposium on Thermal Radiation of Solids, NASA document SP-55 (NASA, Washington, D.C., 1965), pp. 11–28.

W. M. Brandenberg, O. W. Clausen, “The directional spectral emittance of surface between 200° and 600°,” in Symposium on Thermal Radiation of Solids, NASA document SP-55 (NASA, Washington, D.C., 1965), pp. 313–320.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 3rd ed. (Hemisphere, Washington, D.C., 1992), Chaps. 4 and 5.

D. P. DeWitt, J. C. Richmond, “Thermal radiative properties of materials,” in Theory and Practice of Radiation Thermometry, D. P. DeWitt, G. C. Nutter, eds. (Wiley, New York, (1988), pp. 91–187.
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999), pp. 735–758.
[CrossRef]

T. Iuchi, S. Wada, “Simultaneous measurement system of emissivity and temperature for glossy metals near room temperature,” Temperature (to be published).

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Figures (16)

Fig. 1
Fig. 1

Reflection model of metal with an oxide film on its surface.

Fig. 2
Fig. 2

Apparatus for measuring emissivity near room temperature.

Fig. 3
Fig. 3

Experimental apparatus for rapid measurement of directionally polarized radiances at high temperature where two fiber-type radiometers, each equipped with an InGaAs sensor, are set, permitting measurement of p- and s-polarized emissivities. (a) Connecting components and (b) schematic of the apparatus.

Fig. 4
Fig. 4

Apparatus for measuring emissivity under atmosphere-controlled conditions.14

Fig. 5
Fig. 5

Apparatus for measuring spectrally polarized radiance by use of optical fibers in air.15 Eight spectral, polarized directional emissivities can be simultaneously measured by use of polarizing beam-splitter cubes.

Fig. 6
Fig. 6

Comparison of simulation (solid curves) and experimental (symbols) results for directionally polarized emissivities.

Fig. 7
Fig. 7

Variations in a pseudo-optical constant as functions of oxide film thickness h for index of refraction n 2 (real part) and extinction coefficient k 2 (imaginary part).

Fig. 8
Fig. 8

Simulation results of polarized emissivities at λ = 1.5 µm for increasing oxide film thickness h. The simulation is based on the data in Table 1. (a) s-polarized emissivity and (b) p-polarized emissivity (specimen, cold-rolled steel, Ra = 0.08 µm).

Fig. 9
Fig. 9

Experimental results for spectral directionally polarized emissivities of cold-rolled steel at λ = 1.5 µm, heated to 773 K and maintained at 623 K to prevent further growth of the oxide film, by use of the apparatus of Fig. 3. Oxide film thickness, ∼h = 40 nm.

Fig. 10
Fig. 10

Experimental results for spectral directionally polarized emissivities at 4.7 µm of cold-rolled steel (Ra = 0.08 µm) measured at room temperature by use of the apparatus of Fig. 2.

Fig. 11
Fig. 11

Simulation results for emissivity changes at λ = 1.5 µm during growth of an oxide film. The simulation is based on the data of sample 6 in Table 1 (specimen, cold-rolled steel, Ra = 0.08 µm).

Fig. 12
Fig. 12

Experimental results for emissivity variations during growth of an oxide film upon cold-rolled steel (Ra = 0.08 µm) by use of the apparatus of Fig. 4. The specimen is heated to 823 K in vacuum and then oxidized rapidly by injection of a small amount of air into the vacuum chamber. The emissivity behavior resembles the simulation results shown in Fig. 11.

Fig. 13
Fig. 13

Simulation results for directional emissivities of cold-rolled steel with increasing thickness of oxide film at four values of angle θ1.

Fig. 14
Fig. 14

Experimental results for emissivity variations of cold-rolled steel at four values of angle θ1, and λ = 1.5 µm with the elapse of time when the specimen is heated to 723 K by use of the apparatus of Fig. 5.

Fig. 15
Fig. 15

Simulation results for spectral emissivity behavior of cold-rolled steel at an angle θ1 = 60° for varying thicknesses h of oxide film.

Fig. 16
Fig. 16

Experimental results for spectral emissivity behavior of cold-rolled steel at angle θ1 = 60° with the elapse of time when the specimen is heated to 873 K by use of the apparatus of Fig. 5.

Tables (1)

Tables Icon

Table 1 Pseudo-optical Constants ñ3 and ñ2 of As-Grown Cold-Rolled Steel and an Oxide Film at λ = 1.5 µm and Thickness h of the Oxide Film Measured by an Ellipsometer

Equations (19)

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

ρs=|r12s+r23s exp-iδ/1+r12sr23s exp-iδ|2,
ρp=|r12p+r23p exp-iδ/1+r12pr23p exp-iδ|2,
δ=2π/λ2ñ2h cos θ2,
r12s=n1 cos θ1-ñ2 cos θ2/n1 cos θ1+ñ2 cos θ2,
r23s=ñ2 cos θ2-ñ3 cos θ3/ñ2 cos θ2+ñ3 cos θ3,
r12p=ñ2 cos θ1-n1 cos θ2/ñ2 cos θ1+n1 cos θ2,
r23p=ñ3 cos θ2-ñ2 cos θ3/ñ3 cos θ2+ñ2 cos θ3,
n1 sin θ1=ñ2 sin θ2=ñ3 sin θ3.
εsθ1=1-ρsθ1.
εpθ1=1-ρpθ1.
εθ1=εsθ1+εpθ1/2.
Ep,1=kpεpθLλ,bT1+ρpθLλ,bTb+N=εpθEp,λ,bT1+ρpθEp,λ,bTb+N,
Ep,λ,bT1=kpLλ,bT1, Ep,λ,bTb=kpLλ,bTb,
Ep,2=εpθEp,λ,bT2+ρpθEp,λ,bTb+N.
εpθ=Ep,1-Ep,2Ep,λ,bT1-Ep,λ,bT2.
εsθ=Es,1-Es,2Es,λ,bT1-Es,λ,bT2,
εθ=E1-E2Eλ,bT1-Eλ,bT2,
εpθ=EpkpLλ,bT=EpEp,λ,bT,
εsθ=EsksLλ,bT=EsEs,λ,bT,

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