Abstract

The attenuated total reflectance spectroscopy method of determining the complex refractive indices of materials which occur only as small particles was applied at a 10.6-μm wavelength to numerous pressed powder samples. Fresnel relations were used to obtain best fit values for the complex refractive indices of the samples. Good fits were obtained only when the particles were small compared to the wavelength. For such samples, several effective medium theories were used to predict values of bulk material refractive indices from those of samples with different volume packing fractions. Only the Bruggeman theory produced consistent results.

© 1989 Optical Society of America

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References

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  1. S. G. Jennings, J. B. Gillespie, “Mie Theory Sensitivity Studies—Part II,” ASL-TR-0003, Mar.1978, U.S. Army Atmospheric Sciences Laboratory, White Sands Missile Range, NM.
  2. J. B. Gillespie, S. G. Jennings, J. D. Lindberg, “Use of an Average Complex Refractive Index in Atmospheric Propagation Calculations,” Appl. Opt. 17, 989–991 (1978).
    [CrossRef] [PubMed]
  3. S. A. Schleusner, J. D. Lindberg, K. O. White, “Differential Spectrophone Measurements of the Absorption of Laser Energy by Atmospheric Dust,” Appl. Opt. 15, 2564–2565 (1975).
    [CrossRef]
  4. A. P. Waggoner, M. B. Baker, R. J. Charlson, “Optical Absorption by Atmospheric Aerosols,” Appl. Opt. 12, 896 (1973).
    [CrossRef] [PubMed]
  5. J. D. Lindberg, L. S. Laude, “Measurement of the Absorption Coefficient of Atmospheric Dust,” Appl. Opt. 13, 1923–1927 (1974).
    [CrossRef] [PubMed]
  6. F. E. Voltz, “Infrared Refractive Index of Atmospheric Aerosol Substances,” Appl. Opt. 11, 755–759 (1972).
    [CrossRef]
  7. M. Querry, “Optical Constants of Natural Minerals and Other Materials in the 350–50,000 CM-1 Spectral Region,” Final Report, Aug.1983, U.S. Army Research Office contract DAAG-29-79-C0131.
  8. W. C. McCrone, J. G. Delly, The Particle Atlas (Ann Arbor Science Publishers, Inc. Ann Arbor, MI, 1973).
  9. H. E. Gerber, E. E. Hindman, Light Absorption by Aerosol Particles (Spectrum Press, Hampton, VA, 1982).
  10. O. B. Toon, J. B. Pollack, B. N. Khare, “The Optical Constants of Several Atmospheric Aerosol Species: Ammonium Sulfate, Aluminum Oxide, and Sodium Chloride,” J. Geophys. Res. 81, 5733 (1976).
    [CrossRef]
  11. N. J. Harrick, N. J. Riederman, “Infrared Spectra of Powders by Internal Reflection Spectroscopy,” Spectrochim Acta 21, 2135 (1965).
    [CrossRef]
  12. V. Zolotarev, “Spectra of Frustrated Multiple Internal Reflection of Powders and Fibers,” Opt. Spectrosc. USSR 37, 295 (1974).
  13. J. Fahrenfort, W. M. Visser, “On the Determination of Optical Constants in the Infrared by Attenuated Total Reflection,” Spectrochim Acta 18, 1103 (1962).
  14. J. Fahrenfort, “Attenuated Total Reflection: A New Principle for the Production of Useful Infrared Reflection Spectra of Organic Compounds,” J. Spectrochim Acta 17, 698 (1961).
    [CrossRef]
  15. N. J. Harrick, Internal Reflection Spectroscopy (Interscience, New York, 1967).
  16. R. W. Cohen, G. D. Cody, M. D. Coutts, B. Abeles, “Optical Properties of Granular Silver and Gold Films,” Phys. Rev. B 8, 2689 (1973).
    [CrossRef]
  17. W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison–Wesley, Reading, MA, 1962).
  18. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).
  19. W. Heller, “Remarks on Refractive Index Mixture Rules,” J. Phys. Chem. 69, 113 (1965).
    [CrossRef]
  20. L. K. H. Van Beek, “Dielectric Behaviour of Hetrogeneous Systems,” Prog. Dielectr. 7, 69 (1967).
  21. D. A. G. Bruggemann, “Calculation of the Various Physical Constants of Hetrogeneous Substances. 1: Dielectric Constants and Conductives of Mixtures of Isotropic Substances,” Ann. Phys. Leipzig 24, 636 (1935).
  22. R. Landauer, “Title,” in Electrical Transport and Optical Properties of Inhomogeneous Media, J. C. Garland, D. B. Tinner, Eds. (American Institute of Physics, New York, 1978), pp. 2–43.
  23. C. Lichtenecker, “Die Dielektrizitatskonstante Naturlicher und Kunstlicher Mischkorper,” Phys. Z. 27, 115 (1926).
  24. C. J. F. Bottcher, Theory of Electric Polarization (Elsevier, New York, 1952).
  25. C. F. Bohren, “Applicability of Effective-Medium Theories to Problems of Scattering and Absorption by Nonhomogeneous Atmospheric Particles,” J. Atmos. Sci. 43, 468–475 (1986).
    [CrossRef]
  26. J. B. Gillespie, “On the Determination of the Complex Refractive Index of Powdered Materials in the 9 to 11 m Spectral Region Utilizing An Attenuated Total Reflectance Technique,” Ph.D. Dissertation, New Mexico State U. (1982).

1986 (1)

C. F. Bohren, “Applicability of Effective-Medium Theories to Problems of Scattering and Absorption by Nonhomogeneous Atmospheric Particles,” J. Atmos. Sci. 43, 468–475 (1986).
[CrossRef]

1978 (1)

1976 (1)

O. B. Toon, J. B. Pollack, B. N. Khare, “The Optical Constants of Several Atmospheric Aerosol Species: Ammonium Sulfate, Aluminum Oxide, and Sodium Chloride,” J. Geophys. Res. 81, 5733 (1976).
[CrossRef]

1975 (1)

S. A. Schleusner, J. D. Lindberg, K. O. White, “Differential Spectrophone Measurements of the Absorption of Laser Energy by Atmospheric Dust,” Appl. Opt. 15, 2564–2565 (1975).
[CrossRef]

1974 (2)

J. D. Lindberg, L. S. Laude, “Measurement of the Absorption Coefficient of Atmospheric Dust,” Appl. Opt. 13, 1923–1927 (1974).
[CrossRef] [PubMed]

V. Zolotarev, “Spectra of Frustrated Multiple Internal Reflection of Powders and Fibers,” Opt. Spectrosc. USSR 37, 295 (1974).

1973 (2)

R. W. Cohen, G. D. Cody, M. D. Coutts, B. Abeles, “Optical Properties of Granular Silver and Gold Films,” Phys. Rev. B 8, 2689 (1973).
[CrossRef]

A. P. Waggoner, M. B. Baker, R. J. Charlson, “Optical Absorption by Atmospheric Aerosols,” Appl. Opt. 12, 896 (1973).
[CrossRef] [PubMed]

1972 (1)

1967 (1)

L. K. H. Van Beek, “Dielectric Behaviour of Hetrogeneous Systems,” Prog. Dielectr. 7, 69 (1967).

1965 (2)

W. Heller, “Remarks on Refractive Index Mixture Rules,” J. Phys. Chem. 69, 113 (1965).
[CrossRef]

N. J. Harrick, N. J. Riederman, “Infrared Spectra of Powders by Internal Reflection Spectroscopy,” Spectrochim Acta 21, 2135 (1965).
[CrossRef]

1962 (1)

J. Fahrenfort, W. M. Visser, “On the Determination of Optical Constants in the Infrared by Attenuated Total Reflection,” Spectrochim Acta 18, 1103 (1962).

1961 (1)

J. Fahrenfort, “Attenuated Total Reflection: A New Principle for the Production of Useful Infrared Reflection Spectra of Organic Compounds,” J. Spectrochim Acta 17, 698 (1961).
[CrossRef]

1935 (1)

D. A. G. Bruggemann, “Calculation of the Various Physical Constants of Hetrogeneous Substances. 1: Dielectric Constants and Conductives of Mixtures of Isotropic Substances,” Ann. Phys. Leipzig 24, 636 (1935).

1926 (1)

C. Lichtenecker, “Die Dielektrizitatskonstante Naturlicher und Kunstlicher Mischkorper,” Phys. Z. 27, 115 (1926).

Abeles, B.

R. W. Cohen, G. D. Cody, M. D. Coutts, B. Abeles, “Optical Properties of Granular Silver and Gold Films,” Phys. Rev. B 8, 2689 (1973).
[CrossRef]

Baker, M. B.

Bohren, C. F.

C. F. Bohren, “Applicability of Effective-Medium Theories to Problems of Scattering and Absorption by Nonhomogeneous Atmospheric Particles,” J. Atmos. Sci. 43, 468–475 (1986).
[CrossRef]

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).

Bottcher, C. J. F.

C. J. F. Bottcher, Theory of Electric Polarization (Elsevier, New York, 1952).

Bruggemann, D. A. G.

D. A. G. Bruggemann, “Calculation of the Various Physical Constants of Hetrogeneous Substances. 1: Dielectric Constants and Conductives of Mixtures of Isotropic Substances,” Ann. Phys. Leipzig 24, 636 (1935).

Charlson, R. J.

Cody, G. D.

R. W. Cohen, G. D. Cody, M. D. Coutts, B. Abeles, “Optical Properties of Granular Silver and Gold Films,” Phys. Rev. B 8, 2689 (1973).
[CrossRef]

Cohen, R. W.

R. W. Cohen, G. D. Cody, M. D. Coutts, B. Abeles, “Optical Properties of Granular Silver and Gold Films,” Phys. Rev. B 8, 2689 (1973).
[CrossRef]

Coutts, M. D.

R. W. Cohen, G. D. Cody, M. D. Coutts, B. Abeles, “Optical Properties of Granular Silver and Gold Films,” Phys. Rev. B 8, 2689 (1973).
[CrossRef]

Delly, J. G.

W. C. McCrone, J. G. Delly, The Particle Atlas (Ann Arbor Science Publishers, Inc. Ann Arbor, MI, 1973).

Fahrenfort, J.

J. Fahrenfort, W. M. Visser, “On the Determination of Optical Constants in the Infrared by Attenuated Total Reflection,” Spectrochim Acta 18, 1103 (1962).

J. Fahrenfort, “Attenuated Total Reflection: A New Principle for the Production of Useful Infrared Reflection Spectra of Organic Compounds,” J. Spectrochim Acta 17, 698 (1961).
[CrossRef]

Gerber, H. E.

H. E. Gerber, E. E. Hindman, Light Absorption by Aerosol Particles (Spectrum Press, Hampton, VA, 1982).

Gillespie, J. B.

J. B. Gillespie, S. G. Jennings, J. D. Lindberg, “Use of an Average Complex Refractive Index in Atmospheric Propagation Calculations,” Appl. Opt. 17, 989–991 (1978).
[CrossRef] [PubMed]

J. B. Gillespie, “On the Determination of the Complex Refractive Index of Powdered Materials in the 9 to 11 m Spectral Region Utilizing An Attenuated Total Reflectance Technique,” Ph.D. Dissertation, New Mexico State U. (1982).

S. G. Jennings, J. B. Gillespie, “Mie Theory Sensitivity Studies—Part II,” ASL-TR-0003, Mar.1978, U.S. Army Atmospheric Sciences Laboratory, White Sands Missile Range, NM.

Harrick, N. J.

N. J. Harrick, N. J. Riederman, “Infrared Spectra of Powders by Internal Reflection Spectroscopy,” Spectrochim Acta 21, 2135 (1965).
[CrossRef]

N. J. Harrick, Internal Reflection Spectroscopy (Interscience, New York, 1967).

Heller, W.

W. Heller, “Remarks on Refractive Index Mixture Rules,” J. Phys. Chem. 69, 113 (1965).
[CrossRef]

Hindman, E. E.

H. E. Gerber, E. E. Hindman, Light Absorption by Aerosol Particles (Spectrum Press, Hampton, VA, 1982).

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).

Jennings, S. G.

J. B. Gillespie, S. G. Jennings, J. D. Lindberg, “Use of an Average Complex Refractive Index in Atmospheric Propagation Calculations,” Appl. Opt. 17, 989–991 (1978).
[CrossRef] [PubMed]

S. G. Jennings, J. B. Gillespie, “Mie Theory Sensitivity Studies—Part II,” ASL-TR-0003, Mar.1978, U.S. Army Atmospheric Sciences Laboratory, White Sands Missile Range, NM.

Khare, B. N.

O. B. Toon, J. B. Pollack, B. N. Khare, “The Optical Constants of Several Atmospheric Aerosol Species: Ammonium Sulfate, Aluminum Oxide, and Sodium Chloride,” J. Geophys. Res. 81, 5733 (1976).
[CrossRef]

Landauer, R.

R. Landauer, “Title,” in Electrical Transport and Optical Properties of Inhomogeneous Media, J. C. Garland, D. B. Tinner, Eds. (American Institute of Physics, New York, 1978), pp. 2–43.

Laude, L. S.

Lichtenecker, C.

C. Lichtenecker, “Die Dielektrizitatskonstante Naturlicher und Kunstlicher Mischkorper,” Phys. Z. 27, 115 (1926).

Lindberg, J. D.

McCrone, W. C.

W. C. McCrone, J. G. Delly, The Particle Atlas (Ann Arbor Science Publishers, Inc. Ann Arbor, MI, 1973).

Panofsky, W. K. H.

W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison–Wesley, Reading, MA, 1962).

Phillips, M.

W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison–Wesley, Reading, MA, 1962).

Pollack, J. B.

O. B. Toon, J. B. Pollack, B. N. Khare, “The Optical Constants of Several Atmospheric Aerosol Species: Ammonium Sulfate, Aluminum Oxide, and Sodium Chloride,” J. Geophys. Res. 81, 5733 (1976).
[CrossRef]

Querry, M.

M. Querry, “Optical Constants of Natural Minerals and Other Materials in the 350–50,000 CM-1 Spectral Region,” Final Report, Aug.1983, U.S. Army Research Office contract DAAG-29-79-C0131.

Riederman, N. J.

N. J. Harrick, N. J. Riederman, “Infrared Spectra of Powders by Internal Reflection Spectroscopy,” Spectrochim Acta 21, 2135 (1965).
[CrossRef]

Schleusner, S. A.

S. A. Schleusner, J. D. Lindberg, K. O. White, “Differential Spectrophone Measurements of the Absorption of Laser Energy by Atmospheric Dust,” Appl. Opt. 15, 2564–2565 (1975).
[CrossRef]

Toon, O. B.

O. B. Toon, J. B. Pollack, B. N. Khare, “The Optical Constants of Several Atmospheric Aerosol Species: Ammonium Sulfate, Aluminum Oxide, and Sodium Chloride,” J. Geophys. Res. 81, 5733 (1976).
[CrossRef]

Van Beek, L. K. H.

L. K. H. Van Beek, “Dielectric Behaviour of Hetrogeneous Systems,” Prog. Dielectr. 7, 69 (1967).

Visser, W. M.

J. Fahrenfort, W. M. Visser, “On the Determination of Optical Constants in the Infrared by Attenuated Total Reflection,” Spectrochim Acta 18, 1103 (1962).

Voltz, F. E.

Waggoner, A. P.

White, K. O.

S. A. Schleusner, J. D. Lindberg, K. O. White, “Differential Spectrophone Measurements of the Absorption of Laser Energy by Atmospheric Dust,” Appl. Opt. 15, 2564–2565 (1975).
[CrossRef]

Zolotarev, V.

V. Zolotarev, “Spectra of Frustrated Multiple Internal Reflection of Powders and Fibers,” Opt. Spectrosc. USSR 37, 295 (1974).

Ann. Phys. Leipzig (1)

D. A. G. Bruggemann, “Calculation of the Various Physical Constants of Hetrogeneous Substances. 1: Dielectric Constants and Conductives of Mixtures of Isotropic Substances,” Ann. Phys. Leipzig 24, 636 (1935).

Appl. Opt. (5)

J. Atmos. Sci. (1)

C. F. Bohren, “Applicability of Effective-Medium Theories to Problems of Scattering and Absorption by Nonhomogeneous Atmospheric Particles,” J. Atmos. Sci. 43, 468–475 (1986).
[CrossRef]

J. Geophys. Res. (1)

O. B. Toon, J. B. Pollack, B. N. Khare, “The Optical Constants of Several Atmospheric Aerosol Species: Ammonium Sulfate, Aluminum Oxide, and Sodium Chloride,” J. Geophys. Res. 81, 5733 (1976).
[CrossRef]

J. Phys. Chem. (1)

W. Heller, “Remarks on Refractive Index Mixture Rules,” J. Phys. Chem. 69, 113 (1965).
[CrossRef]

J. Spectrochim Acta (1)

J. Fahrenfort, “Attenuated Total Reflection: A New Principle for the Production of Useful Infrared Reflection Spectra of Organic Compounds,” J. Spectrochim Acta 17, 698 (1961).
[CrossRef]

Opt. Spectrosc. USSR (1)

V. Zolotarev, “Spectra of Frustrated Multiple Internal Reflection of Powders and Fibers,” Opt. Spectrosc. USSR 37, 295 (1974).

Phys. Rev. B (1)

R. W. Cohen, G. D. Cody, M. D. Coutts, B. Abeles, “Optical Properties of Granular Silver and Gold Films,” Phys. Rev. B 8, 2689 (1973).
[CrossRef]

Phys. Z. (1)

C. Lichtenecker, “Die Dielektrizitatskonstante Naturlicher und Kunstlicher Mischkorper,” Phys. Z. 27, 115 (1926).

Prog. Dielectr. (1)

L. K. H. Van Beek, “Dielectric Behaviour of Hetrogeneous Systems,” Prog. Dielectr. 7, 69 (1967).

Spectrochim Acta (2)

J. Fahrenfort, W. M. Visser, “On the Determination of Optical Constants in the Infrared by Attenuated Total Reflection,” Spectrochim Acta 18, 1103 (1962).

N. J. Harrick, N. J. Riederman, “Infrared Spectra of Powders by Internal Reflection Spectroscopy,” Spectrochim Acta 21, 2135 (1965).
[CrossRef]

Other (10)

M. Querry, “Optical Constants of Natural Minerals and Other Materials in the 350–50,000 CM-1 Spectral Region,” Final Report, Aug.1983, U.S. Army Research Office contract DAAG-29-79-C0131.

W. C. McCrone, J. G. Delly, The Particle Atlas (Ann Arbor Science Publishers, Inc. Ann Arbor, MI, 1973).

H. E. Gerber, E. E. Hindman, Light Absorption by Aerosol Particles (Spectrum Press, Hampton, VA, 1982).

N. J. Harrick, Internal Reflection Spectroscopy (Interscience, New York, 1967).

W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison–Wesley, Reading, MA, 1962).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).

C. J. F. Bottcher, Theory of Electric Polarization (Elsevier, New York, 1952).

R. Landauer, “Title,” in Electrical Transport and Optical Properties of Inhomogeneous Media, J. C. Garland, D. B. Tinner, Eds. (American Institute of Physics, New York, 1978), pp. 2–43.

J. B. Gillespie, “On the Determination of the Complex Refractive Index of Powdered Materials in the 9 to 11 m Spectral Region Utilizing An Attenuated Total Reflectance Technique,” Ph.D. Dissertation, New Mexico State U. (1982).

S. G. Jennings, J. B. Gillespie, “Mie Theory Sensitivity Studies—Part II,” ASL-TR-0003, Mar.1978, U.S. Army Atmospheric Sciences Laboratory, White Sands Missile Range, NM.

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Figures (13)

Fig. 1
Fig. 1

Geometry of the experiment.

Fig. 2
Fig. 2

Effective medium refractive indices (n,k) vs volume fraction predicted by several mixing rules for a material complex refractive index of m = 3.76–1.66i mixed with air. The upper group of curves is for n, the lower for k.

Fig. 3
Fig. 3

Bruggemann, Biot-Arago, the Lorentz-Lorenz mixing rules fit to experimentally determined effective medium refractive indices for carbon black pressed powder samples. Only the Bruggemann model satisfactorily fits the data and produces a result consistent with other measured carbon values.

Fig. 4
Fig. 4

Experimental ATR reflectivity data for micronized quartz particles with an average size of 1.5 μM pressed to a volume packing fraction of 0.472. No unique Fresnel reflectivity curve could be fit through the data points. A curve for an effective medium average value of m = 1.45–0.097i is shown for comparison.

Fig. 5
Fig. 5

Experimental ATR reflectivity data for micronized calcite particles with average size of 1.5 μM pressed to a volume packing fraction of 0.594. No unique Fresnel reflectivity curve could be fit through the data points. A curve for an effective medium average value of m = 1.31–0.04i is shown for comparison.

Fig. 6
Fig. 6

Experimental ATR reflectivity data for soda lime glass spheres 1–3 μM in diameter pressed to a volume packing fraction of 0.534. No unique Fresnel reflectivity could be fit through the data points. A curve for an effective medium average value of m = 1.33– 0.14i is shown for comparison.

Fig. 7
Fig. 7

Experimental ATR reflectivity data for soda lime glass spheres 2-6 μM in diameter pressed to a volume packing fraction of 0.621. No unique Fresnel reflectivity could be fit through the data points. A curve for an effective medium average value of m = 1.17– 0.20s is shown for comparison.

Fig. 8
Fig. 8

Experimental ATR reflectivity data for soda lime glass spheres 10–15 μM in diameter pressed to a volume packing fraction of 0.801. No unique Fresnel reflectivity could be fit through the data points. A curve for an effective medium average value of m = 0.91–0.33i is shown for comparison.

Fig. 9
Fig. 9

Experimental ATR reflectivity data for carbon black, particle size 0.0106 μM in diameter, pressed to a volume packing fraction of 0.590. A Fresnel reflectivity curve with an effective medium index m = 2.6–1.01i fits all the data.

Fig. 10
Fig. 10

Experimental ATR reflectivity data for lamp black pressed to a volume packing fraction of 0.417. A Fresnel reflectivity curve with an effective medium index m = 1.844–0.638 fits all the data.

Fig. 11
Fig. 11

Experimental ATR reflectivity data for Mogul-L (carbon black) pressed to a volume packing fraction of 0.447. A Fresnel reflectivity curve with an effective medium index m = 1.815–0.480i fits all the data.

Fig. 12
Fig. 12

Experimental ATR reflectivity data for kaolin clay (particle size, 0.1–0.4 μM) pressed to a volume packing fraction of 0.387. A Fresnel reflectivity curve with an effective medium index m = 1.22– 0.245i fits all the data.

Fig. 13
Fig. 13

Experimental ATR reflectivity data for Dixon microfyne graphite pressed to a volume packing fraction of 0.615. A Fresnel reflectivity curve with an effective medium index m = 1.27–0.855i fits all the data. However, no effective medium theory could be fit to the Fresnel data.

Equations (7)

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R s = a 2 + b 2 + cos 2 θ 2 a cos 2 θ a 2 + b 2 + cos 2 θ + 2 a cos 2 θ
a 2 + b 2 = [ ( n 2 k 2 sin 2 θ ) 2 + 4 n 2 k 2 ] 1 / 2 , a 2 b 2 = ( n 2 k 2 sin 2 θ ) .
Biot - Arago m = i ϕ i ,
Newton m 2 = i ϕ i m i 2 ,
Maxwell Garnett m 2 1 m 2 + 2 = i ϕ i m i 2 1 m i 2 + 2 ,
Bruggemann 0 = i ϕ i m i 2 m 2 m i 2 + 2 m 2 ,
Generalized 16 m 2 m 0 2 L m 2 + ( 1 L ) m 0 2 = i ϕ i m i 2 m 0 2 L i m i 2 + ( 1 L i ) m 0 2 .

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