Abstract

The power efficiency of luminescence excited by solar radiation in luminescent solar collectors is calculated for a glass sheet doped with Cr3+. The achievable chemical potential for an optically thick absorber irradiated by diluted blackbody radiation as a function of Cr3+ concentration, sheet thickness, sunlight dilution, and luminescence quantum yield leads directly to overall conversion efficiency of solar power to luminescence power.

© 1983 Optical Society of America

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References

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  1. A. Goetzberger, W. Greubel, Appl. Phys. 14, 123 (1977).
    [CrossRef]
  2. R. Reisfeld, C. K. Jorgensen, Struc. Bonding (Berlin) 49, 1 (1982).
    [CrossRef]
  3. P. S. Friedman, Opt. Eng. 20, 887 (1981).
  4. J. S. Batchelder, A. H. Zewail, T. Cole, Appl. Opt. 20, 3733 (1981).
    [CrossRef] [PubMed]
  5. R. G. Hutter, PINY, private communication and work to be published.Statistical treatments such as R. W. Olson, R. F. Loring, M. D. Fayer, Appl. Opt. 20, 2934 (1981) tend also to fall in the distributed category.
    [CrossRef] [PubMed]
  6. E. Yablonovitch, J. Opt. Soc. Am. 70, 1362 (1980).
    [CrossRef]
  7. R. T. Ross, J. Chem. Phys. 46, 4590 (1967).
    [CrossRef]
  8. D. E. McCumber, Phys. Rev. 136A, 954 (1964).
    [CrossRef]
  9. W. B. Fowler, D. L. Dexter, Phys. Rev. 128, 2154 (1962).
    [CrossRef]
  10. Equation (8) assumes that the up transitions are determined only by the solar flux and, therefore, neglects effects of self-absorption. This approximation overestimates the efficiency but preserves the lumped character of the treatment. Following Ref. 6, self-absorption can be introduced in treating the propagation problem.
  11. R. T. Ross, Photochem. Photobiol. 21, 401 (1975).
    [CrossRef]
  12. L. O. Bjorn, Photosynthetica 10, 121 (1976).
  13. L. J. Andrews, A. Lempicki, B. C. McCollum, J. Chem. Phys. 74, 5526 (1981).
    [CrossRef]
  14. B. I. Stepanov, Dokl. Akad Nauk SSSR 112, 839 (1957) [Sov. Phys. Dokl. 2, 81 (1957)].
  15. I. Ketskemety, J. Dombi, R. Horvai, Ann. Phys. (Leipzig) 463, 8, 342 (1961).
    [CrossRef]

1982 (1)

R. Reisfeld, C. K. Jorgensen, Struc. Bonding (Berlin) 49, 1 (1982).
[CrossRef]

1981 (3)

P. S. Friedman, Opt. Eng. 20, 887 (1981).

J. S. Batchelder, A. H. Zewail, T. Cole, Appl. Opt. 20, 3733 (1981).
[CrossRef] [PubMed]

L. J. Andrews, A. Lempicki, B. C. McCollum, J. Chem. Phys. 74, 5526 (1981).
[CrossRef]

1980 (1)

1977 (1)

A. Goetzberger, W. Greubel, Appl. Phys. 14, 123 (1977).
[CrossRef]

1976 (1)

L. O. Bjorn, Photosynthetica 10, 121 (1976).

1975 (1)

R. T. Ross, Photochem. Photobiol. 21, 401 (1975).
[CrossRef]

1967 (1)

R. T. Ross, J. Chem. Phys. 46, 4590 (1967).
[CrossRef]

1964 (1)

D. E. McCumber, Phys. Rev. 136A, 954 (1964).
[CrossRef]

1962 (1)

W. B. Fowler, D. L. Dexter, Phys. Rev. 128, 2154 (1962).
[CrossRef]

1961 (1)

I. Ketskemety, J. Dombi, R. Horvai, Ann. Phys. (Leipzig) 463, 8, 342 (1961).
[CrossRef]

1957 (1)

B. I. Stepanov, Dokl. Akad Nauk SSSR 112, 839 (1957) [Sov. Phys. Dokl. 2, 81 (1957)].

Andrews, L. J.

L. J. Andrews, A. Lempicki, B. C. McCollum, J. Chem. Phys. 74, 5526 (1981).
[CrossRef]

Batchelder, J. S.

Bjorn, L. O.

L. O. Bjorn, Photosynthetica 10, 121 (1976).

Cole, T.

Dexter, D. L.

W. B. Fowler, D. L. Dexter, Phys. Rev. 128, 2154 (1962).
[CrossRef]

Dombi, J.

I. Ketskemety, J. Dombi, R. Horvai, Ann. Phys. (Leipzig) 463, 8, 342 (1961).
[CrossRef]

Fowler, W. B.

W. B. Fowler, D. L. Dexter, Phys. Rev. 128, 2154 (1962).
[CrossRef]

Friedman, P. S.

P. S. Friedman, Opt. Eng. 20, 887 (1981).

Goetzberger, A.

A. Goetzberger, W. Greubel, Appl. Phys. 14, 123 (1977).
[CrossRef]

Greubel, W.

A. Goetzberger, W. Greubel, Appl. Phys. 14, 123 (1977).
[CrossRef]

Horvai, R.

I. Ketskemety, J. Dombi, R. Horvai, Ann. Phys. (Leipzig) 463, 8, 342 (1961).
[CrossRef]

Hutter, R. G.

R. G. Hutter, PINY, private communication and work to be published.Statistical treatments such as R. W. Olson, R. F. Loring, M. D. Fayer, Appl. Opt. 20, 2934 (1981) tend also to fall in the distributed category.
[CrossRef] [PubMed]

Jorgensen, C. K.

R. Reisfeld, C. K. Jorgensen, Struc. Bonding (Berlin) 49, 1 (1982).
[CrossRef]

Ketskemety, I.

I. Ketskemety, J. Dombi, R. Horvai, Ann. Phys. (Leipzig) 463, 8, 342 (1961).
[CrossRef]

Lempicki, A.

L. J. Andrews, A. Lempicki, B. C. McCollum, J. Chem. Phys. 74, 5526 (1981).
[CrossRef]

McCollum, B. C.

L. J. Andrews, A. Lempicki, B. C. McCollum, J. Chem. Phys. 74, 5526 (1981).
[CrossRef]

McCumber, D. E.

D. E. McCumber, Phys. Rev. 136A, 954 (1964).
[CrossRef]

Reisfeld, R.

R. Reisfeld, C. K. Jorgensen, Struc. Bonding (Berlin) 49, 1 (1982).
[CrossRef]

Ross, R. T.

R. T. Ross, Photochem. Photobiol. 21, 401 (1975).
[CrossRef]

R. T. Ross, J. Chem. Phys. 46, 4590 (1967).
[CrossRef]

Stepanov, B. I.

B. I. Stepanov, Dokl. Akad Nauk SSSR 112, 839 (1957) [Sov. Phys. Dokl. 2, 81 (1957)].

Yablonovitch, E.

Zewail, A. H.

Ann. Phys. (Leipzig) 463 (1)

I. Ketskemety, J. Dombi, R. Horvai, Ann. Phys. (Leipzig) 463, 8, 342 (1961).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. (1)

A. Goetzberger, W. Greubel, Appl. Phys. 14, 123 (1977).
[CrossRef]

Dokl. Akad Nauk SSSR (1)

B. I. Stepanov, Dokl. Akad Nauk SSSR 112, 839 (1957) [Sov. Phys. Dokl. 2, 81 (1957)].

J. Chem. Phys. (2)

L. J. Andrews, A. Lempicki, B. C. McCollum, J. Chem. Phys. 74, 5526 (1981).
[CrossRef]

R. T. Ross, J. Chem. Phys. 46, 4590 (1967).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

P. S. Friedman, Opt. Eng. 20, 887 (1981).

Photochem. Photobiol. (1)

R. T. Ross, Photochem. Photobiol. 21, 401 (1975).
[CrossRef]

Photosynthetica (1)

L. O. Bjorn, Photosynthetica 10, 121 (1976).

Phys. Rev. (2)

D. E. McCumber, Phys. Rev. 136A, 954 (1964).
[CrossRef]

W. B. Fowler, D. L. Dexter, Phys. Rev. 128, 2154 (1962).
[CrossRef]

Struc. Bonding (Berlin) (1)

R. Reisfeld, C. K. Jorgensen, Struc. Bonding (Berlin) 49, 1 (1982).
[CrossRef]

Other (2)

R. G. Hutter, PINY, private communication and work to be published.Statistical treatments such as R. W. Olson, R. F. Loring, M. D. Fayer, Appl. Opt. 20, 2934 (1981) tend also to fall in the distributed category.
[CrossRef] [PubMed]

Equation (8) assumes that the up transitions are determined only by the solar flux and, therefore, neglects effects of self-absorption. This approximation overestimates the efficiency but preserves the lumped character of the treatment. Following Ref. 6, self-absorption can be introduced in treating the propagation problem.

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Figures (6)

Fig. 1
Fig. 1

Absorption spectrum of Cr3+ in silicate glass (N = 2.8 × 1019 cm−3).

Fig. 2
Fig. 2

Relative quantum yield as a function of concentration N.

Fig. 3
Fig. 3

Effective chemical potential vs Cr concentration. Parameter is thickness of plate in centimeters: ϕ = 1; f = 5.8 × 10−6.

Fig. 4
Fig. 4

Efficiency η as a function of concentration. Parameter is plate thickness in centimeters: ϕ = 1; f = 5.8 × 10−6.

Fig. 5
Fig. 5

Effective chemical potential as a function of quantum yield at f = 5.8 × 10−6. Curves are for different optical thicknesses of the plate as defined by the following values of N and L:

1N = 1.4 × 1019 cm−3;L = 0.14 cm
24.2 × 1019 cm−3;0.42 cm
37.0 × 1019 cm−3;0.70 cm
49.8 × 1019 cm−3;0.90 cm
514 × 1019 cm−3;1.40 cm.
Fig. 6
Fig. 6

Efficiency vs quantum yield at f = 5.8 × 10−6. Curves are for different optical thicknesses of the collector as defined by the following values of N and L.

1N = 1.4 × 1019 cm−3;
24.2 × 1019 cm−3;0.42 cm
37.0 × 1019 cm−3;0.70 cm
49.8 × 1019 cm−3;0.98 cm
514 × 1019 cm−3;1.40 cm.

Equations (19)

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R = R = R r + R n r .
k l , u ( ν ) = P ( T ) σ ( ν ) ,
P ( T ) = 2 ν 2 c 2 [ exp ( h ν / k T ) 1 ] 1
k l , u ( ν ) N l 0 = k u , l ( ν ) N u 0 ,
k u , l ( ν ) = exp ( μ 0 / k T ) P ( T ) σ ( ν ) ,
exp ( μ 0 / k T ) = N l 0 N u 0 .
R r = N u k u , l ( ν ) d ν = N u exp ( μ 0 / k T ) P ( T ) σ ( ν ) d ν
R = f L 0 { 1 exp [ σ ( ν ) N l L ] } P ( T s ) d ν ,
ϕ = R r / R ,
ϕ f L 0 { 1 exp [ σ ( ν ) N l L ] } P ( T s ) d ν = N u exp ( μ 0 / k T ) 0 P ( T ) σ ( ν ) d ν .
exp ( μ * / k T ) = N u N l .
μ eff = μ 0 μ * = k T ln N l 0 N u 0 · N u N l .
N u = N exp ( μ * / k T ) 1 + exp ( μ * / k T ) .
N l N , exp ( μ * / k T ) 1 , σ ( ν ) N l σ ( ν ) N = α ( ν ) ,
μ eff = μ 0 μ * = k T ln ϕ f L 0 { 1 exp [ α ( ν ) L ] } P ( T s ) d ν 0 α ( ν ) P ( T ) d ν .
μ eff = k T ln ϕ f 0 α ( ν ) P ( T s ) d ν 0 α ( ν ) P ( T ) d ν .
μ eff = μ max + k T ln ϕ ,
η = μ eff ϕ R input flux = μ eff ϕ 0 { 1 exp [ α ( ν ) L ] } P ( T s ) d ν 0 h ν P ( T s ) d ν .
F α ( ν ) ν 2 exp ( h ν / k T ) .

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