Abstract

The principal complex refractive indices for gypsum have been derived in the infrared region of the spectrum. These values were obtained by dispersion analysis of the reflection spectra for Eb and the a-c (monoclinic) plane. Two sets of complex indices are obtained for the latter plane, taking account of axis wander. The oscillator parameters are presented here, together with formulas for calculating the optical constants at any desired infrared frequency. In addition the usefulness of such optical constants for modeling the infrared properties of powders is demonstrated for gypsum and spodumene.

© 1983 Optical Society of America

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References

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  1. J. R. Aronson, A. G. Emslie, E. M. Smith, P. F. Strong, in Proceedings, Tenth Lunar Planet Science Conference (1979), pp. 1787–1795.
  2. J. R. Aronson, A. G. Emslie, J. Geophys. Res. 80, 4925 (1975).
    [CrossRef]
  3. J. R. Aronson, A. G. Emslie, “Applications of Infrared Spectroscopy and Radiative Transfer to Earth Sciences,” in Infrared and Raman Spectroscopy of Lunar and Terrestrial Minerals, C. Karr, Ed. (Academic, New York, 1975), pp. 143–164.
  4. M. F. Belousov, V. F. Pavinich, Opt. Spektrosk. 45, 920 (1978)[Opt. Spectrosc. 45, 771 (1978)].
  5. V. F. Pavinich, M. V. Belousov, Opt. Spektrosk. 45, 1114 (1978)[Opt. Spectrosc. 45, 881 (1978)].
  6. J. R. Aronson, P. F. Strong, Appl. Opt. 14, 2914 (1975).
    [CrossRef] [PubMed]
  7. A. G. Emslie, J. R. Aronson, J. Opt. Soc. Am. 73, 916 (1983).
    [CrossRef]
  8. L. Bragg, G. F. Claringbull, W. H. Taylor, Crystal Structures of Minerals (Cornell U.P., Ithaca, N.Y., 1964), p. 141.
  9. S. Newcomb, Am. J. Math. 8, 343 (1886).
    [CrossRef]
  10. M. R. Querry, R. Strecker, in Proceedings, Aerosol and Obscuration Conference Edgewood, Md. (1982);M. R. Querry, U. Missouri,Kansas City; private communication.
  11. A. N. Lazarev, N. O. Zulumyan, V. F. Pavinich, B. Piriou, A. P. Mirgorodskiy, Kolebaniya Okisnykh Reshetok (Nauka Press, Lengingrad, 1980).
  12. J. R. Aronson, A. G. Emslie, Appl. Opt. 12, 2573 (1973).
    [CrossRef] [PubMed]

1983 (1)

1982 (1)

M. R. Querry, R. Strecker, in Proceedings, Aerosol and Obscuration Conference Edgewood, Md. (1982);M. R. Querry, U. Missouri,Kansas City; private communication.

1979 (1)

J. R. Aronson, A. G. Emslie, E. M. Smith, P. F. Strong, in Proceedings, Tenth Lunar Planet Science Conference (1979), pp. 1787–1795.

1978 (2)

M. F. Belousov, V. F. Pavinich, Opt. Spektrosk. 45, 920 (1978)[Opt. Spectrosc. 45, 771 (1978)].

V. F. Pavinich, M. V. Belousov, Opt. Spektrosk. 45, 1114 (1978)[Opt. Spectrosc. 45, 881 (1978)].

1975 (2)

J. R. Aronson, P. F. Strong, Appl. Opt. 14, 2914 (1975).
[CrossRef] [PubMed]

J. R. Aronson, A. G. Emslie, J. Geophys. Res. 80, 4925 (1975).
[CrossRef]

1973 (1)

1886 (1)

S. Newcomb, Am. J. Math. 8, 343 (1886).
[CrossRef]

Aronson, J. R.

A. G. Emslie, J. R. Aronson, J. Opt. Soc. Am. 73, 916 (1983).
[CrossRef]

J. R. Aronson, A. G. Emslie, E. M. Smith, P. F. Strong, in Proceedings, Tenth Lunar Planet Science Conference (1979), pp. 1787–1795.

J. R. Aronson, A. G. Emslie, J. Geophys. Res. 80, 4925 (1975).
[CrossRef]

J. R. Aronson, P. F. Strong, Appl. Opt. 14, 2914 (1975).
[CrossRef] [PubMed]

J. R. Aronson, A. G. Emslie, Appl. Opt. 12, 2573 (1973).
[CrossRef] [PubMed]

J. R. Aronson, A. G. Emslie, “Applications of Infrared Spectroscopy and Radiative Transfer to Earth Sciences,” in Infrared and Raman Spectroscopy of Lunar and Terrestrial Minerals, C. Karr, Ed. (Academic, New York, 1975), pp. 143–164.

Belousov, M. F.

M. F. Belousov, V. F. Pavinich, Opt. Spektrosk. 45, 920 (1978)[Opt. Spectrosc. 45, 771 (1978)].

Belousov, M. V.

V. F. Pavinich, M. V. Belousov, Opt. Spektrosk. 45, 1114 (1978)[Opt. Spectrosc. 45, 881 (1978)].

Bragg, L.

L. Bragg, G. F. Claringbull, W. H. Taylor, Crystal Structures of Minerals (Cornell U.P., Ithaca, N.Y., 1964), p. 141.

Claringbull, G. F.

L. Bragg, G. F. Claringbull, W. H. Taylor, Crystal Structures of Minerals (Cornell U.P., Ithaca, N.Y., 1964), p. 141.

Emslie, A. G.

A. G. Emslie, J. R. Aronson, J. Opt. Soc. Am. 73, 916 (1983).
[CrossRef]

J. R. Aronson, A. G. Emslie, E. M. Smith, P. F. Strong, in Proceedings, Tenth Lunar Planet Science Conference (1979), pp. 1787–1795.

J. R. Aronson, A. G. Emslie, J. Geophys. Res. 80, 4925 (1975).
[CrossRef]

J. R. Aronson, A. G. Emslie, Appl. Opt. 12, 2573 (1973).
[CrossRef] [PubMed]

J. R. Aronson, A. G. Emslie, “Applications of Infrared Spectroscopy and Radiative Transfer to Earth Sciences,” in Infrared and Raman Spectroscopy of Lunar and Terrestrial Minerals, C. Karr, Ed. (Academic, New York, 1975), pp. 143–164.

Lazarev, A. N.

A. N. Lazarev, N. O. Zulumyan, V. F. Pavinich, B. Piriou, A. P. Mirgorodskiy, Kolebaniya Okisnykh Reshetok (Nauka Press, Lengingrad, 1980).

Mirgorodskiy, A. P.

A. N. Lazarev, N. O. Zulumyan, V. F. Pavinich, B. Piriou, A. P. Mirgorodskiy, Kolebaniya Okisnykh Reshetok (Nauka Press, Lengingrad, 1980).

Newcomb, S.

S. Newcomb, Am. J. Math. 8, 343 (1886).
[CrossRef]

Pavinich, V. F.

M. F. Belousov, V. F. Pavinich, Opt. Spektrosk. 45, 920 (1978)[Opt. Spectrosc. 45, 771 (1978)].

V. F. Pavinich, M. V. Belousov, Opt. Spektrosk. 45, 1114 (1978)[Opt. Spectrosc. 45, 881 (1978)].

A. N. Lazarev, N. O. Zulumyan, V. F. Pavinich, B. Piriou, A. P. Mirgorodskiy, Kolebaniya Okisnykh Reshetok (Nauka Press, Lengingrad, 1980).

Piriou, B.

A. N. Lazarev, N. O. Zulumyan, V. F. Pavinich, B. Piriou, A. P. Mirgorodskiy, Kolebaniya Okisnykh Reshetok (Nauka Press, Lengingrad, 1980).

Querry, M. R.

M. R. Querry, R. Strecker, in Proceedings, Aerosol and Obscuration Conference Edgewood, Md. (1982);M. R. Querry, U. Missouri,Kansas City; private communication.

Smith, E. M.

J. R. Aronson, A. G. Emslie, E. M. Smith, P. F. Strong, in Proceedings, Tenth Lunar Planet Science Conference (1979), pp. 1787–1795.

Strecker, R.

M. R. Querry, R. Strecker, in Proceedings, Aerosol and Obscuration Conference Edgewood, Md. (1982);M. R. Querry, U. Missouri,Kansas City; private communication.

Strong, P. F.

J. R. Aronson, A. G. Emslie, E. M. Smith, P. F. Strong, in Proceedings, Tenth Lunar Planet Science Conference (1979), pp. 1787–1795.

J. R. Aronson, P. F. Strong, Appl. Opt. 14, 2914 (1975).
[CrossRef] [PubMed]

Taylor, W. H.

L. Bragg, G. F. Claringbull, W. H. Taylor, Crystal Structures of Minerals (Cornell U.P., Ithaca, N.Y., 1964), p. 141.

Zulumyan, N. O.

A. N. Lazarev, N. O. Zulumyan, V. F. Pavinich, B. Piriou, A. P. Mirgorodskiy, Kolebaniya Okisnykh Reshetok (Nauka Press, Lengingrad, 1980).

Am. J. Math. (1)

S. Newcomb, Am. J. Math. 8, 343 (1886).
[CrossRef]

Appl. Opt. (2)

J. Geophys. Res. (1)

J. R. Aronson, A. G. Emslie, J. Geophys. Res. 80, 4925 (1975).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Spektrosk. (2)

M. F. Belousov, V. F. Pavinich, Opt. Spektrosk. 45, 920 (1978)[Opt. Spectrosc. 45, 771 (1978)].

V. F. Pavinich, M. V. Belousov, Opt. Spektrosk. 45, 1114 (1978)[Opt. Spectrosc. 45, 881 (1978)].

Proceedings, Aerosol and Obscuration Conference Edgewood, Md. (1)

M. R. Querry, R. Strecker, in Proceedings, Aerosol and Obscuration Conference Edgewood, Md. (1982);M. R. Querry, U. Missouri,Kansas City; private communication.

Proceedings, Tenth Lunar Planet Science Conference (1)

J. R. Aronson, A. G. Emslie, E. M. Smith, P. F. Strong, in Proceedings, Tenth Lunar Planet Science Conference (1979), pp. 1787–1795.

Other (3)

A. N. Lazarev, N. O. Zulumyan, V. F. Pavinich, B. Piriou, A. P. Mirgorodskiy, Kolebaniya Okisnykh Reshetok (Nauka Press, Lengingrad, 1980).

L. Bragg, G. F. Claringbull, W. H. Taylor, Crystal Structures of Minerals (Cornell U.P., Ithaca, N.Y., 1964), p. 141.

J. R. Aronson, A. G. Emslie, “Applications of Infrared Spectroscopy and Radiative Transfer to Earth Sciences,” in Infrared and Raman Spectroscopy of Lunar and Terrestrial Minerals, C. Karr, Ed. (Academic, New York, 1975), pp. 143–164.

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Figures (6)

Fig. 1
Fig. 1

Normal incidence reflectance attachment diagram.

Fig. 2
Fig. 2

Reflectance spectrum of gypsum (Eb) fitted with six Lorentz lines.

Fig. 3
Fig. 3

Reflectance spectra of gypsum (monoclinic plane) fitted with seven Lorentz lines.

Fig. 4
Fig. 4

Spectral absorption index obtained for the monoclinic plane of gypsum.

Fig. 5
Fig. 5

Emittance spectrum of gypsum powder.

Fig. 6
Fig. 6

Emittance spectrum of spodumene powder.

Tables (2)

Tables Icon

Table I Lorentz Line Parameters for Gypsum, Eb Range of Validity is 400 cm−1 < ν < 3800 c−1

Tables Icon

Table II Lorentz Line Parameters for Gypsum, Monoclinic Plane (a-c) Range of Validity is 400 cm−1 < ν < 3600 cm−1

Equations (51)

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ɛ = ( ɛ xx ɛ xz ɛ xz ɛ zz ) = ɛ + k = 1 N ( u xxk u xzk u xzk u zzk ) L k ,
u xxk = cos 2 ( θ k ϕ ) , u xzk = cos 2 ( θ k ϕ ) sin ( θ k ϕ ) , u zzk = sin 2 ( θ k ϕ ) ,
L k = S k 1 + i γ k ( ν ν k ) ( ν ν k ) 2 ,
ɛ = ( ɛ xx ɛ xz ɛ xz ɛ zz ) , the high frequency dielectric tensor ,
R ( ν , P ) = | r xx | 2 + | r xz | 2 ,
r xx = υ ( 1 s ) ɛ xx + ɛ zz υ ( 1 + s ) + 2 s + ɛ xx + ɛ zz ,
r xz = 2 ɛ xz υ ( 1 + s ) + 2 s + ɛ xx + ɛ zz ,
υ = ( ɛ xx + ɛ zz + 2 s ) 1 / 2 ,
s = ( ɛ xx ɛ zz ɛ xz 2 ) 1 / 2 .
E = j [ R ( ν j , P ) R j ] 2 .
p 01 = ɛ xx , p 02 = ɛ xz , p 03 = ɛ zz , p 1 k = S k , p 2 k = γ k / ν k , p 3 k = 1 / ν k 2 , p 4 k = θ k ,
E p l k = 0 ,
j [ R ( ν j , P ) R j ] R ( ν j , P ) p l k = 0 .
R ( ν , p ) p l k = 2 Re ( r xx * r xx p l k ) + 2 Re ( r xz * r xz p l k ) ,
r xx p l k = r xx ɛ xx ɛ xx p l k + r xx ɛ xz ɛ xz p l k + r xx ɛ zz ɛ zz p l k ,
r xz p l k = r xz ɛ xx ɛ xx p l k + r xz ɛ xz ɛ xz p l k + r xz ɛ zz ɛ zz p l k .
F = υ ( 1 + s ) + 2 s + ɛ xx + ɛ zz
r xx ɛ α β = 1 F [ υ ɛ α β ( 1 s ) υ s ɛ α β + C α β r xx F ɛ α β ] ,
C xx = 1 , C xz = 0 , C zz = 1 ,
r xz ɛ α β = 1 F ( C α β r xz F ɛ α β ) ,
C xx = 0 , C xz = 2 , C zz = 0 ,
F ɛ α β = υ ɛ α β ( 1 + s ) + ( υ + 2 ) s ɛ α β + C α β ,
C xx = 1 , C xz = 0 , C zz = 1 ,
υ ɛ α β = 1 2 υ ( c α β + 2 s ɛ α β ) ,
s ɛ xx = ɛ zz 2 s , s ɛ xz = ɛ xz s , s ɛ zz = ɛ xx 2 s ,
ɛ xx p 01 = ɛ xx p 02 = ɛ zz p 03 = 1 .
ɛ α β p 0 k = 0 .
L k = p 1 k 1 + i p 2 k ν p 3 k ν 2 ,
D k = 1 + i p 2 k ν p 3 k ν 2 .
ɛ α β p 1 k = u α β k D k ,
ɛ α β p 2 k = i ν L k D k u α β k ,
ɛ α β p 3 k = ν 2 L k D k u α β k ,
ɛ xx p 4 k = 2 L k u xzk , ɛ xz p 4 k = L k ( u xxk u zzk ) , ɛ zz p 4 k = 2 L k u xzk . }
j R ( ν j , P ) p l k R ( ν j , P ) p λ κ .
δ P δ P T = ( UU T ) 1 σ 2 ,
σ 2 = E M 4 N 3 ,
( δ ɛ xx ) 2 = δ p 01 2 , ( δ ɛ xz ) 2 = δ p 02 2 ,
( δ ɛ zz ) 2 = δ p 03 2 , δ S k 2 = δ p 1 k 2 ,
δ γ k 2 = δ p 2 k 2 p 2 k p 3 k 3 / 2 δ p 2 k δ p 3 k + ¼ p 3 k 3 δ p 3 k 2 ,
δ ν k 2 = ¼ p 3 k 3 δ p 3 k 2 ,
δ θ k 2 = δ p 4 k 2 .
m 2 = ɛ = ɛ + k = 1 N S k 1 + i γ k ( ν ν k ) ( ν ν k ) 2 = ɛ + k = 1 N L k ,
m = n ik .
m 1 , 2 2 = ɛ xx + ɛ zz 2 ± [ ( ɛ xx ɛ zz ) 2 4 + ɛ xz 2 ] 1 / 2 .
ɛ xx = 2.2819
σ ( ɛ xx ) = 0.0130 ɛ xz = 0.0086
ɛ zz = 2.4545 σ ( ɛ zz ) = 0.0073
σ ( ɛ zz ) = 0.0429
ɛ = ( cos ϕ sin ϕ sin ϕ cos ϕ ) ( ɛ xx ɛ xz ɛ xz ɛ zz ) ( cos ϕ sin ϕ sin ϕ cos ϕ )
ɛ α β p 0 k = 0
ɛ xx p 01 = cos 2 ϕ , ɛ xz p 01 = sin ϕ cos ϕ , ɛ zz p 01 = sin 2 ϕ , ɛ xx p 02 = 2 cos ϕ sin ϕ , ɛ xz p 02 = cos 2 ϕ sin 2 ϕ , ɛ zz p 02 = 2 sin ϕ cos ϕ , ɛ xx p 03 = sin 2 ϕ , ɛ xz p 03 = sin ϕ cos ϕ , ɛ zz p 03 = cos 2 ϕ .

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