Abstract

The infrared optical constants of a few different powders of chromites, XCr2O4 (where X is Fe, Ni, Mg, Zn, or Cu), have been determined by Kramers–Kronig analysis of their infrared transmission and reflection spectra. The knowledge of these constants allows one to predict the different thin-layer infrared reflection spectra and to compare them, when it is possible, with the reflection spectra calculated with n and k obtained by the use of the classical oscillator method.

© 1996 Optical Society of America

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  1. C. A. Worrel, “Infrared optical constants for CO2 laser waveguide materials,” J. Mater. Sci. 21, 781–787 (1986).
  2. J. E. Bertie, S. L. Zhang, “Infrared intensities in liquids IX: the Kramers–Kronig transform, and its approximation by the finite Hilbert transform via fast Fourier transforms,” Can. J. Chem. 70, 520–531 (1992).
  3. J. E. Bertie, V. Behnam, R. N. Jones, “Infrared intensities in liquids II: accuracy of FT–IR transmission measure-ments,” Appl. Spectrosc. 39, 401–404 (1985).
  4. T. G. Goplen, D. G. Cameron, R. N. Jones, “The control of the error in infrared spectrophotometry. VI. The evaluation of optical constants by combined transmission and attenuated total reflection measurement,” Appl. Spectrosc. 34, 652–656 (1980).
  5. J. M. Machefert, M. LeCalvar, M. Lenglet, “FTIR study of nickel and copper alloys oxidation: theoretical approach and experiment,” Surf. Interface Anal. 17, 137–142 (1991).
  6. M. Lenglet, J. Lopitaux, L. Terrier, P. Chartier, J. F. Koenig, P. Nkeng, G. Poillerat, “Initial stages of cobalt oxidation by FTIR spectroscopy,” J. Phys. IV 3, Colloque C9, 477–483 (1993).
  7. M. Lenglet, R. Guillamet, J. Lopitaux, B. Hannoyer, “Caractérisation par spectrométrie infrarouge de reflexion spéculaire à angle variable des premières étapes de l’oxydation à haute température d’un acier inoxydable AISI 304,” Mater. Res. Bull. 25, 575–782 (1990).
  8. J. P. Hawranek, P. Neelakantan, R. P. Young, R. N. Jones, “The control of the errors spectrophotometry. III. Transmission measurements using thin cells,” Spectrochim. Acta 32, 75–84 (1976).
  9. J. P. Hawranek, P. Neelakantan, R. P. Young, R. N. Jones, “The control of the errors spectrophotometry. IV. Corrections for the dispersion distortion and the evaluation of both optical constants,” Spectrochim. Acta 32, 85–98 (1976);“The control of the errors spectrophotometry. V. Assessment of the errors in the evaluation of the optical constants by transmission measurements on thin films,” Spectrochim. Acta 32, 99–109 (1976);“Determination of the optical constants of benzene and chloroform in the ir by thin film transmission,” Spectrochim. Acta 32, 111–123 (1976).
  10. D. M. Roesseler, “Kramers–Kronig analysis of reflection data,” Br. J. Appl. Phys. 16, 1119–1123 (1965).
  11. J. Himmrich, G. Schneider, J. Zwinscher, H. D. Lutz, “Lattice vibration spectra. LXX. Evaluation of IR reflection spectra. Model calculation and experimental data,” Z. Naturforsch. 46, 1095–1102 (1991).
  12. H. D. Lutz, B. Müller, H. J. Steiner, “Lattice vibration spectra. LIX. Single crystal infrared and Raman studies of spinel type oxides,” J. Solid State Chem. 90, 54–60 (1991).
  13. B. Lefez, M. Lenglet, “Theoretical and experimental study of the infrared reflectance of multilayer oxide film on metals,” Surf. Interface Anal. 22, 456–461 (1994).

1994 (1)

B. Lefez, M. Lenglet, “Theoretical and experimental study of the infrared reflectance of multilayer oxide film on metals,” Surf. Interface Anal. 22, 456–461 (1994).

1993 (1)

M. Lenglet, J. Lopitaux, L. Terrier, P. Chartier, J. F. Koenig, P. Nkeng, G. Poillerat, “Initial stages of cobalt oxidation by FTIR spectroscopy,” J. Phys. IV 3, Colloque C9, 477–483 (1993).

1992 (1)

J. E. Bertie, S. L. Zhang, “Infrared intensities in liquids IX: the Kramers–Kronig transform, and its approximation by the finite Hilbert transform via fast Fourier transforms,” Can. J. Chem. 70, 520–531 (1992).

1991 (3)

J. M. Machefert, M. LeCalvar, M. Lenglet, “FTIR study of nickel and copper alloys oxidation: theoretical approach and experiment,” Surf. Interface Anal. 17, 137–142 (1991).

J. Himmrich, G. Schneider, J. Zwinscher, H. D. Lutz, “Lattice vibration spectra. LXX. Evaluation of IR reflection spectra. Model calculation and experimental data,” Z. Naturforsch. 46, 1095–1102 (1991).

H. D. Lutz, B. Müller, H. J. Steiner, “Lattice vibration spectra. LIX. Single crystal infrared and Raman studies of spinel type oxides,” J. Solid State Chem. 90, 54–60 (1991).

1990 (1)

M. Lenglet, R. Guillamet, J. Lopitaux, B. Hannoyer, “Caractérisation par spectrométrie infrarouge de reflexion spéculaire à angle variable des premières étapes de l’oxydation à haute température d’un acier inoxydable AISI 304,” Mater. Res. Bull. 25, 575–782 (1990).

1986 (1)

C. A. Worrel, “Infrared optical constants for CO2 laser waveguide materials,” J. Mater. Sci. 21, 781–787 (1986).

1985 (1)

1980 (1)

1976 (2)

J. P. Hawranek, P. Neelakantan, R. P. Young, R. N. Jones, “The control of the errors spectrophotometry. III. Transmission measurements using thin cells,” Spectrochim. Acta 32, 75–84 (1976).

J. P. Hawranek, P. Neelakantan, R. P. Young, R. N. Jones, “The control of the errors spectrophotometry. IV. Corrections for the dispersion distortion and the evaluation of both optical constants,” Spectrochim. Acta 32, 85–98 (1976);“The control of the errors spectrophotometry. V. Assessment of the errors in the evaluation of the optical constants by transmission measurements on thin films,” Spectrochim. Acta 32, 99–109 (1976);“Determination of the optical constants of benzene and chloroform in the ir by thin film transmission,” Spectrochim. Acta 32, 111–123 (1976).

1965 (1)

D. M. Roesseler, “Kramers–Kronig analysis of reflection data,” Br. J. Appl. Phys. 16, 1119–1123 (1965).

Behnam, V.

Bertie, J. E.

J. E. Bertie, S. L. Zhang, “Infrared intensities in liquids IX: the Kramers–Kronig transform, and its approximation by the finite Hilbert transform via fast Fourier transforms,” Can. J. Chem. 70, 520–531 (1992).

J. E. Bertie, V. Behnam, R. N. Jones, “Infrared intensities in liquids II: accuracy of FT–IR transmission measure-ments,” Appl. Spectrosc. 39, 401–404 (1985).

Cameron, D. G.

Chartier, P.

M. Lenglet, J. Lopitaux, L. Terrier, P. Chartier, J. F. Koenig, P. Nkeng, G. Poillerat, “Initial stages of cobalt oxidation by FTIR spectroscopy,” J. Phys. IV 3, Colloque C9, 477–483 (1993).

Goplen, T. G.

Guillamet, R.

M. Lenglet, R. Guillamet, J. Lopitaux, B. Hannoyer, “Caractérisation par spectrométrie infrarouge de reflexion spéculaire à angle variable des premières étapes de l’oxydation à haute température d’un acier inoxydable AISI 304,” Mater. Res. Bull. 25, 575–782 (1990).

Hannoyer, B.

M. Lenglet, R. Guillamet, J. Lopitaux, B. Hannoyer, “Caractérisation par spectrométrie infrarouge de reflexion spéculaire à angle variable des premières étapes de l’oxydation à haute température d’un acier inoxydable AISI 304,” Mater. Res. Bull. 25, 575–782 (1990).

Hawranek, J. P.

J. P. Hawranek, P. Neelakantan, R. P. Young, R. N. Jones, “The control of the errors spectrophotometry. IV. Corrections for the dispersion distortion and the evaluation of both optical constants,” Spectrochim. Acta 32, 85–98 (1976);“The control of the errors spectrophotometry. V. Assessment of the errors in the evaluation of the optical constants by transmission measurements on thin films,” Spectrochim. Acta 32, 99–109 (1976);“Determination of the optical constants of benzene and chloroform in the ir by thin film transmission,” Spectrochim. Acta 32, 111–123 (1976).

J. P. Hawranek, P. Neelakantan, R. P. Young, R. N. Jones, “The control of the errors spectrophotometry. III. Transmission measurements using thin cells,” Spectrochim. Acta 32, 75–84 (1976).

Himmrich, J.

J. Himmrich, G. Schneider, J. Zwinscher, H. D. Lutz, “Lattice vibration spectra. LXX. Evaluation of IR reflection spectra. Model calculation and experimental data,” Z. Naturforsch. 46, 1095–1102 (1991).

Jones, R. N.

J. E. Bertie, V. Behnam, R. N. Jones, “Infrared intensities in liquids II: accuracy of FT–IR transmission measure-ments,” Appl. Spectrosc. 39, 401–404 (1985).

T. G. Goplen, D. G. Cameron, R. N. Jones, “The control of the error in infrared spectrophotometry. VI. The evaluation of optical constants by combined transmission and attenuated total reflection measurement,” Appl. Spectrosc. 34, 652–656 (1980).

J. P. Hawranek, P. Neelakantan, R. P. Young, R. N. Jones, “The control of the errors spectrophotometry. III. Transmission measurements using thin cells,” Spectrochim. Acta 32, 75–84 (1976).

J. P. Hawranek, P. Neelakantan, R. P. Young, R. N. Jones, “The control of the errors spectrophotometry. IV. Corrections for the dispersion distortion and the evaluation of both optical constants,” Spectrochim. Acta 32, 85–98 (1976);“The control of the errors spectrophotometry. V. Assessment of the errors in the evaluation of the optical constants by transmission measurements on thin films,” Spectrochim. Acta 32, 99–109 (1976);“Determination of the optical constants of benzene and chloroform in the ir by thin film transmission,” Spectrochim. Acta 32, 111–123 (1976).

Koenig, J. F.

M. Lenglet, J. Lopitaux, L. Terrier, P. Chartier, J. F. Koenig, P. Nkeng, G. Poillerat, “Initial stages of cobalt oxidation by FTIR spectroscopy,” J. Phys. IV 3, Colloque C9, 477–483 (1993).

LeCalvar, M.

J. M. Machefert, M. LeCalvar, M. Lenglet, “FTIR study of nickel and copper alloys oxidation: theoretical approach and experiment,” Surf. Interface Anal. 17, 137–142 (1991).

Lefez, B.

B. Lefez, M. Lenglet, “Theoretical and experimental study of the infrared reflectance of multilayer oxide film on metals,” Surf. Interface Anal. 22, 456–461 (1994).

Lenglet, M.

B. Lefez, M. Lenglet, “Theoretical and experimental study of the infrared reflectance of multilayer oxide film on metals,” Surf. Interface Anal. 22, 456–461 (1994).

M. Lenglet, J. Lopitaux, L. Terrier, P. Chartier, J. F. Koenig, P. Nkeng, G. Poillerat, “Initial stages of cobalt oxidation by FTIR spectroscopy,” J. Phys. IV 3, Colloque C9, 477–483 (1993).

J. M. Machefert, M. LeCalvar, M. Lenglet, “FTIR study of nickel and copper alloys oxidation: theoretical approach and experiment,” Surf. Interface Anal. 17, 137–142 (1991).

M. Lenglet, R. Guillamet, J. Lopitaux, B. Hannoyer, “Caractérisation par spectrométrie infrarouge de reflexion spéculaire à angle variable des premières étapes de l’oxydation à haute température d’un acier inoxydable AISI 304,” Mater. Res. Bull. 25, 575–782 (1990).

Lopitaux, J.

M. Lenglet, J. Lopitaux, L. Terrier, P. Chartier, J. F. Koenig, P. Nkeng, G. Poillerat, “Initial stages of cobalt oxidation by FTIR spectroscopy,” J. Phys. IV 3, Colloque C9, 477–483 (1993).

M. Lenglet, R. Guillamet, J. Lopitaux, B. Hannoyer, “Caractérisation par spectrométrie infrarouge de reflexion spéculaire à angle variable des premières étapes de l’oxydation à haute température d’un acier inoxydable AISI 304,” Mater. Res. Bull. 25, 575–782 (1990).

Lutz, H. D.

J. Himmrich, G. Schneider, J. Zwinscher, H. D. Lutz, “Lattice vibration spectra. LXX. Evaluation of IR reflection spectra. Model calculation and experimental data,” Z. Naturforsch. 46, 1095–1102 (1991).

H. D. Lutz, B. Müller, H. J. Steiner, “Lattice vibration spectra. LIX. Single crystal infrared and Raman studies of spinel type oxides,” J. Solid State Chem. 90, 54–60 (1991).

Machefert, J. M.

J. M. Machefert, M. LeCalvar, M. Lenglet, “FTIR study of nickel and copper alloys oxidation: theoretical approach and experiment,” Surf. Interface Anal. 17, 137–142 (1991).

Müller, B.

H. D. Lutz, B. Müller, H. J. Steiner, “Lattice vibration spectra. LIX. Single crystal infrared and Raman studies of spinel type oxides,” J. Solid State Chem. 90, 54–60 (1991).

Neelakantan, P.

J. P. Hawranek, P. Neelakantan, R. P. Young, R. N. Jones, “The control of the errors spectrophotometry. III. Transmission measurements using thin cells,” Spectrochim. Acta 32, 75–84 (1976).

J. P. Hawranek, P. Neelakantan, R. P. Young, R. N. Jones, “The control of the errors spectrophotometry. IV. Corrections for the dispersion distortion and the evaluation of both optical constants,” Spectrochim. Acta 32, 85–98 (1976);“The control of the errors spectrophotometry. V. Assessment of the errors in the evaluation of the optical constants by transmission measurements on thin films,” Spectrochim. Acta 32, 99–109 (1976);“Determination of the optical constants of benzene and chloroform in the ir by thin film transmission,” Spectrochim. Acta 32, 111–123 (1976).

Nkeng, P.

M. Lenglet, J. Lopitaux, L. Terrier, P. Chartier, J. F. Koenig, P. Nkeng, G. Poillerat, “Initial stages of cobalt oxidation by FTIR spectroscopy,” J. Phys. IV 3, Colloque C9, 477–483 (1993).

Poillerat, G.

M. Lenglet, J. Lopitaux, L. Terrier, P. Chartier, J. F. Koenig, P. Nkeng, G. Poillerat, “Initial stages of cobalt oxidation by FTIR spectroscopy,” J. Phys. IV 3, Colloque C9, 477–483 (1993).

Roesseler, D. M.

D. M. Roesseler, “Kramers–Kronig analysis of reflection data,” Br. J. Appl. Phys. 16, 1119–1123 (1965).

Schneider, G.

J. Himmrich, G. Schneider, J. Zwinscher, H. D. Lutz, “Lattice vibration spectra. LXX. Evaluation of IR reflection spectra. Model calculation and experimental data,” Z. Naturforsch. 46, 1095–1102 (1991).

Steiner, H. J.

H. D. Lutz, B. Müller, H. J. Steiner, “Lattice vibration spectra. LIX. Single crystal infrared and Raman studies of spinel type oxides,” J. Solid State Chem. 90, 54–60 (1991).

Terrier, L.

M. Lenglet, J. Lopitaux, L. Terrier, P. Chartier, J. F. Koenig, P. Nkeng, G. Poillerat, “Initial stages of cobalt oxidation by FTIR spectroscopy,” J. Phys. IV 3, Colloque C9, 477–483 (1993).

Worrel, C. A.

C. A. Worrel, “Infrared optical constants for CO2 laser waveguide materials,” J. Mater. Sci. 21, 781–787 (1986).

Young, R. P.

J. P. Hawranek, P. Neelakantan, R. P. Young, R. N. Jones, “The control of the errors spectrophotometry. III. Transmission measurements using thin cells,” Spectrochim. Acta 32, 75–84 (1976).

J. P. Hawranek, P. Neelakantan, R. P. Young, R. N. Jones, “The control of the errors spectrophotometry. IV. Corrections for the dispersion distortion and the evaluation of both optical constants,” Spectrochim. Acta 32, 85–98 (1976);“The control of the errors spectrophotometry. V. Assessment of the errors in the evaluation of the optical constants by transmission measurements on thin films,” Spectrochim. Acta 32, 99–109 (1976);“Determination of the optical constants of benzene and chloroform in the ir by thin film transmission,” Spectrochim. Acta 32, 111–123 (1976).

Zhang, S. L.

J. E. Bertie, S. L. Zhang, “Infrared intensities in liquids IX: the Kramers–Kronig transform, and its approximation by the finite Hilbert transform via fast Fourier transforms,” Can. J. Chem. 70, 520–531 (1992).

Zwinscher, J.

J. Himmrich, G. Schneider, J. Zwinscher, H. D. Lutz, “Lattice vibration spectra. LXX. Evaluation of IR reflection spectra. Model calculation and experimental data,” Z. Naturforsch. 46, 1095–1102 (1991).

Appl. Spectrosc. (2)

Br. J. Appl. Phys. (1)

D. M. Roesseler, “Kramers–Kronig analysis of reflection data,” Br. J. Appl. Phys. 16, 1119–1123 (1965).

Can. J. Chem. (1)

J. E. Bertie, S. L. Zhang, “Infrared intensities in liquids IX: the Kramers–Kronig transform, and its approximation by the finite Hilbert transform via fast Fourier transforms,” Can. J. Chem. 70, 520–531 (1992).

J. Mater. Sci. (1)

C. A. Worrel, “Infrared optical constants for CO2 laser waveguide materials,” J. Mater. Sci. 21, 781–787 (1986).

J. Phys. IV (1)

M. Lenglet, J. Lopitaux, L. Terrier, P. Chartier, J. F. Koenig, P. Nkeng, G. Poillerat, “Initial stages of cobalt oxidation by FTIR spectroscopy,” J. Phys. IV 3, Colloque C9, 477–483 (1993).

J. Solid State Chem. (1)

H. D. Lutz, B. Müller, H. J. Steiner, “Lattice vibration spectra. LIX. Single crystal infrared and Raman studies of spinel type oxides,” J. Solid State Chem. 90, 54–60 (1991).

Mater. Res. Bull. (1)

M. Lenglet, R. Guillamet, J. Lopitaux, B. Hannoyer, “Caractérisation par spectrométrie infrarouge de reflexion spéculaire à angle variable des premières étapes de l’oxydation à haute température d’un acier inoxydable AISI 304,” Mater. Res. Bull. 25, 575–782 (1990).

Spectrochim. Acta (2)

J. P. Hawranek, P. Neelakantan, R. P. Young, R. N. Jones, “The control of the errors spectrophotometry. III. Transmission measurements using thin cells,” Spectrochim. Acta 32, 75–84 (1976).

J. P. Hawranek, P. Neelakantan, R. P. Young, R. N. Jones, “The control of the errors spectrophotometry. IV. Corrections for the dispersion distortion and the evaluation of both optical constants,” Spectrochim. Acta 32, 85–98 (1976);“The control of the errors spectrophotometry. V. Assessment of the errors in the evaluation of the optical constants by transmission measurements on thin films,” Spectrochim. Acta 32, 99–109 (1976);“Determination of the optical constants of benzene and chloroform in the ir by thin film transmission,” Spectrochim. Acta 32, 111–123 (1976).

Surf. Interface Anal. (2)

B. Lefez, M. Lenglet, “Theoretical and experimental study of the infrared reflectance of multilayer oxide film on metals,” Surf. Interface Anal. 22, 456–461 (1994).

J. M. Machefert, M. LeCalvar, M. Lenglet, “FTIR study of nickel and copper alloys oxidation: theoretical approach and experiment,” Surf. Interface Anal. 17, 137–142 (1991).

Z. Naturforsch. (1)

J. Himmrich, G. Schneider, J. Zwinscher, H. D. Lutz, “Lattice vibration spectra. LXX. Evaluation of IR reflection spectra. Model calculation and experimental data,” Z. Naturforsch. 46, 1095–1102 (1991).

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Figures (5)

Fig. 1
Fig. 1

Infrared transmission spectra of different chromites, XCr2O4.

Fig. 2
Fig. 2

Optical constants (——, n; ----, k) of CuCr2O4 calculated by Kramers–Kronig analysis from the transmission spectrum.

Fig. 3
Fig. 3

Spectra of the dielectric constants: ----, Im(∊); ——, −Im1(1/∊).

Fig. 4
Fig. 4

Specular reflectance of a thin film on a metallic substrate.

Fig. 5
Fig. 5

Calculated spectra of (a) CuCr2O4, (b) FeCr2O4, (c) MnCr2O4, (d) NiCr2O4, and (e) ZnCr2O4 for different thicknesses: 1, 0.1 μm; 2, 0.5 μm; 3, 1 μm.

Tables (1)

Tables Icon

Table 1 Positions of the Local Optical (LO) and the Transverse Optical (TO) (in Inverse Centimeters) Calculated by Kramers–Kronig Analysis (KK) and the Oscillator Method (OF)

Equations (11)

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n ( v i ) = n + 1 2 π P 0 v k ( v ) v 2 v i 2 d v ,
k ( v i ) = ( 2 / π ) v i P 0 n ( v i ) n v 2 v i 2 d v ,
k = 2.30258   log ( I 0 / I ) / ( 4 π v d ) ,
n ( v i ) = n + 1 2 π P 0 v k ( v ) v 2 v i 2 d v ,
θ ( v i ) = ( 2 / π ) v i P 0    ln   r ( v ) ln   r ( v i ) v 2 v i 2 d v .
n = 1 R 1 + R 2 R 1 / 2   cos  θ ,
k = 2 R   sin θ 1 + R 2 R 1 / 2   cos   θ .
= n 2 k 2 , = 2 n k ,
r 1 = r 12 + r 23   exp ( i δ 2 ) 1 + r 12 r 23   exp ( i δ 2 ) ,
R = r 1 r 1 * .
r 1 = r 12 + r 23   exp ( i δ 2 ) 1 + r 12 r 23   exp ( i δ 2 ) , δ 2 = 4 π r 2 d  cos θ/λ ,

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