Abstract

The thermal-emission spectra of small MgO cubes (about 0.1 μm) were measured in the frequency region of their surface phonon modes. From the partial derivative of emissivity with respect to particle density, the emissivity of an MgO coagulation has been determined as a function of frequency. With an assumption of spherical coagulation, it is concluded that the dielectric function of small MgO particles and its temperature dependence are nearly the same as those of a bulk crystal.

© 1981 Optical Society of America

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References

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  1. R. Fuchs and K. L. Kliewer, “Optical modes of vibration in an ionic crystal sphere,” J. Opt. Soc. Am. 58, 319–330 (1968).
    [Crossref]
  2. R. Ruppin and R. Englman, “Optical lattice vibrations in finite ionic crystals: II,” J. Phys. C 1, 630–643 (1968).
    [Crossref]
  3. R. Fuchs, “Theory of the optical properties of ionic crystal cubes,” Phys. Rev. B 11, 1732–1740 (1975).
    [Crossref]
  4. L. Genzel and T. P. Martin, “Infrared absorption in small ionic crystals,” Phys. Status Solidi B 51, 91–99 (1972).
    [Crossref]
  5. R. Kälin and F. Kneubühl, “Size effects on the spectral thermal emissivity of alkali halides,” Infrared Phys. 16, 491–508 (1976).
    [Crossref]
  6. I. J. Dayawansa and C. F. Bohren, “The effects of substrate and aggregation in infrared extinction spectra of MgO particles,” Phys. Status Solidi B 86, K27–30 (1978).
    [Crossref]
  7. T. P. Martin and H. Shaber, “Infrared absorption of aggregated and isolated microcrystals,” Phys. Status Solidi B 81, K41–45 (1977).
    [Crossref]
  8. J. R. Jasperse and et al., “Temperature dependence of infrared dispersion in ionic crystals LiF and MgO,” Phys. Rev. 146, 526–542 (1966).
    [Crossref]
  9. L. H. Skolnik, “A review of techniques for measuring small optical losses in infrared transmitting materials,” in Optical Properties of Highly Transparent Solids, S. S. Mitra and R. Bendow, eds. (Plenum, New York, 1975), pp. 405–433.
    [Crossref]
  10. P. Kubelka, “New contributions to the optics of intensely light-scattering materials,” J. Opt. Soc. Am. 38, 448–457 (1948); J. Opt. Soc. Am. 44, 330–335 (1954).
    [Crossref] [PubMed]
  11. H. O. McMahon, “Thermal radiation from partially transparent reflecting bodies,” J. Opt. Soc. Am. 40, 376–380 (1950).
    [Crossref]
  12. The factor 2 appears because the definition of blackbody emissive power is the energy radiated within a solid angle of 2π sr, whereas the definition of volume emissive power is the energy radiated for 4π sr.

1978 (1)

I. J. Dayawansa and C. F. Bohren, “The effects of substrate and aggregation in infrared extinction spectra of MgO particles,” Phys. Status Solidi B 86, K27–30 (1978).
[Crossref]

1977 (1)

T. P. Martin and H. Shaber, “Infrared absorption of aggregated and isolated microcrystals,” Phys. Status Solidi B 81, K41–45 (1977).
[Crossref]

1976 (1)

R. Kälin and F. Kneubühl, “Size effects on the spectral thermal emissivity of alkali halides,” Infrared Phys. 16, 491–508 (1976).
[Crossref]

1975 (1)

R. Fuchs, “Theory of the optical properties of ionic crystal cubes,” Phys. Rev. B 11, 1732–1740 (1975).
[Crossref]

1972 (1)

L. Genzel and T. P. Martin, “Infrared absorption in small ionic crystals,” Phys. Status Solidi B 51, 91–99 (1972).
[Crossref]

1968 (2)

R. Ruppin and R. Englman, “Optical lattice vibrations in finite ionic crystals: II,” J. Phys. C 1, 630–643 (1968).
[Crossref]

R. Fuchs and K. L. Kliewer, “Optical modes of vibration in an ionic crystal sphere,” J. Opt. Soc. Am. 58, 319–330 (1968).
[Crossref]

1966 (1)

J. R. Jasperse and et al., “Temperature dependence of infrared dispersion in ionic crystals LiF and MgO,” Phys. Rev. 146, 526–542 (1966).
[Crossref]

1950 (1)

1948 (1)

Bohren, C. F.

I. J. Dayawansa and C. F. Bohren, “The effects of substrate and aggregation in infrared extinction spectra of MgO particles,” Phys. Status Solidi B 86, K27–30 (1978).
[Crossref]

Dayawansa, I. J.

I. J. Dayawansa and C. F. Bohren, “The effects of substrate and aggregation in infrared extinction spectra of MgO particles,” Phys. Status Solidi B 86, K27–30 (1978).
[Crossref]

Englman, R.

R. Ruppin and R. Englman, “Optical lattice vibrations in finite ionic crystals: II,” J. Phys. C 1, 630–643 (1968).
[Crossref]

Fuchs, R.

R. Fuchs, “Theory of the optical properties of ionic crystal cubes,” Phys. Rev. B 11, 1732–1740 (1975).
[Crossref]

R. Fuchs and K. L. Kliewer, “Optical modes of vibration in an ionic crystal sphere,” J. Opt. Soc. Am. 58, 319–330 (1968).
[Crossref]

Genzel, L.

L. Genzel and T. P. Martin, “Infrared absorption in small ionic crystals,” Phys. Status Solidi B 51, 91–99 (1972).
[Crossref]

Jasperse, J. R.

J. R. Jasperse and et al., “Temperature dependence of infrared dispersion in ionic crystals LiF and MgO,” Phys. Rev. 146, 526–542 (1966).
[Crossref]

Kälin, R.

R. Kälin and F. Kneubühl, “Size effects on the spectral thermal emissivity of alkali halides,” Infrared Phys. 16, 491–508 (1976).
[Crossref]

Kliewer, K. L.

Kneubühl, F.

R. Kälin and F. Kneubühl, “Size effects on the spectral thermal emissivity of alkali halides,” Infrared Phys. 16, 491–508 (1976).
[Crossref]

Kubelka, P.

Martin, T. P.

T. P. Martin and H. Shaber, “Infrared absorption of aggregated and isolated microcrystals,” Phys. Status Solidi B 81, K41–45 (1977).
[Crossref]

L. Genzel and T. P. Martin, “Infrared absorption in small ionic crystals,” Phys. Status Solidi B 51, 91–99 (1972).
[Crossref]

McMahon, H. O.

Ruppin, R.

R. Ruppin and R. Englman, “Optical lattice vibrations in finite ionic crystals: II,” J. Phys. C 1, 630–643 (1968).
[Crossref]

Shaber, H.

T. P. Martin and H. Shaber, “Infrared absorption of aggregated and isolated microcrystals,” Phys. Status Solidi B 81, K41–45 (1977).
[Crossref]

Skolnik, L. H.

L. H. Skolnik, “A review of techniques for measuring small optical losses in infrared transmitting materials,” in Optical Properties of Highly Transparent Solids, S. S. Mitra and R. Bendow, eds. (Plenum, New York, 1975), pp. 405–433.
[Crossref]

Infrared Phys. (1)

R. Kälin and F. Kneubühl, “Size effects on the spectral thermal emissivity of alkali halides,” Infrared Phys. 16, 491–508 (1976).
[Crossref]

J. Opt. Soc. Am. (3)

J. Phys. C (1)

R. Ruppin and R. Englman, “Optical lattice vibrations in finite ionic crystals: II,” J. Phys. C 1, 630–643 (1968).
[Crossref]

Phys. Rev. (1)

J. R. Jasperse and et al., “Temperature dependence of infrared dispersion in ionic crystals LiF and MgO,” Phys. Rev. 146, 526–542 (1966).
[Crossref]

Phys. Rev. B (1)

R. Fuchs, “Theory of the optical properties of ionic crystal cubes,” Phys. Rev. B 11, 1732–1740 (1975).
[Crossref]

Phys. Status Solidi B (3)

L. Genzel and T. P. Martin, “Infrared absorption in small ionic crystals,” Phys. Status Solidi B 51, 91–99 (1972).
[Crossref]

I. J. Dayawansa and C. F. Bohren, “The effects of substrate and aggregation in infrared extinction spectra of MgO particles,” Phys. Status Solidi B 86, K27–30 (1978).
[Crossref]

T. P. Martin and H. Shaber, “Infrared absorption of aggregated and isolated microcrystals,” Phys. Status Solidi B 81, K41–45 (1977).
[Crossref]

Other (2)

L. H. Skolnik, “A review of techniques for measuring small optical losses in infrared transmitting materials,” in Optical Properties of Highly Transparent Solids, S. S. Mitra and R. Bendow, eds. (Plenum, New York, 1975), pp. 405–433.
[Crossref]

The factor 2 appears because the definition of blackbody emissive power is the energy radiated within a solid angle of 2π sr, whereas the definition of volume emissive power is the energy radiated for 4π sr.

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Figures (7)

Fig. 1
Fig. 1

Size distribution of MgO particles. The average dimension is indicated by the arrow.

Fig. 2
Fig. 2

Observed spectra of MgO particles in three different powder densities at 873 K.

Fig. 3
Fig. 3

Geometry illustrating the two-parameter model and the boundary conditions.

Fig. 4
Fig. 4

Observed emissivity and particle-density relations for different frequencies at 873 K.

Fig. 5
Fig. 5

Observed spectrum (filled circles), calculated spectrum of a small MgO cube (filled triangles), and calculated spectrum of spherically aggregated MgO particles (open circles) at 873 K.

Fig. 6
Fig. 6

Geometry illustrating the calculation of thermal radiation from a sphere.

Fig. 7
Fig. 7

Observed (filled circles) and calculated (open circles) spectra at 573 K.

Equations (6)

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d i T = ( S + β ) i T d x - S i R d x , d i R = - ( S + β ) i R d x + S i T d x ,
i T ( x = 0 ) = I 0 , i R ( x = l ) = 0 ,
T ( l ) = q / [ P sinh ( q S l ) + q cosh ( q S l ) ] , R ( l ) = sinh ( q S l ) / [ P sinh ( q S l ) + q cosh ( q S l ) ] ,
E ( l ) = q [ cosh ( q S l ) - 1 ] + ( P - 1 ) sinh ( q S l ) P sinh ( q S l ) + q cosh ( q S l ) .
I = j cos θ exp ( - β r ) / ( 4 π r 2 ) d v d s .
I = j b 2 π R 2 { 1 + 2 [ 2 n A R exp ( - 2 n A R ) + exp ( - 2 n A R ) - 1 ] / ( 2 n A R ) 2 } .