Abstract

The emission band of Sr2Si5N8:Eu2+ phosphors consists of two peaks originating from two different crystallographic sites for Eu2+ activators in the Sr2Si5N8 structure. The two-peak emission behavior is closely related to the energy transfer between activators at those sites. A rate-equation model involving the crystallographic information of the host was used to quantify the time-resolved photoluminescence spectra and to systematically analyze the energy transfer behavior.

© 2009 Optical Society of America

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  1. R.-J. Xie, N. Hirosaki, N. Kimura, K. Sakuma, and M. Mitomo, Appl. Phys. Lett. 90, 191101 (2007).
    [CrossRef]
  2. R.-J. Xie, N. Hirosaki, T. Suehiro, F.-F. Xu, and M. Mitomo, Chem. Mater. 18, 5578 (2006).
    [CrossRef]
  3. M. Zeuner, F. Hintze, and W. Schnick, Chem. Mater. 21, 336 (2009).
    [CrossRef]
  4. H.-L. Li, R.-J. Xie, N. Hirosaki, and Y. Yajim, J. Electrochem. Soc. 155, J378 (2008).
    [CrossRef]
  5. Y. Q. Li, G. de With, and H. T. Hintzen, J. Lumin. 116, 107 (2006).
    [CrossRef]
  6. Y. Q. Li, J. E. J. van Steen, J. W. H. van Krevel, G. Botty, A. C. A. Delsing, F. J. DiSalvo, G. de With, and H. T. Hintzen, J. Alloys Compd. 417, 273 (2006).
    [CrossRef]
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    [CrossRef]
  8. X. Q. Piao, T. Horikawa, H. Hanzawa, and K. Machida, Chem. Lett. 35, 334 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. S. O. Vásquez, J. Chem. Phys. 104, 7652 (1996).
    [CrossRef]
  17. S. O. Vásquez, J. Chem. Phys. 106, 8664 (1997).
    [CrossRef]
  18. S. O. Vásquez, Phys. Rev. B 60, 8575 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  21. C. Kulshreshtha, N. Shin, and K.-S. Sohn, Electrochem. Solid-State Lett. 12, J55 (2009).
    [CrossRef]
  22. W. E. Boyce and R. C. Diprima, Elementary Differential Equations and Boundary Value Problems (Wiley, 1986).
  23. D. Ahn, N. Shin, K. D. Park, and K.-S. Sohn, J. Electrochem. Soc. 156, J242 (2009).
    [CrossRef]

2009

M. Zeuner, F. Hintze, and W. Schnick, Chem. Mater. 21, 336 (2009).
[CrossRef]

K.-S. Sohn, S. Lee, R.-J. Xie, and N. Hirosaki, Appl. Phys. Lett. 95, 121903 (2009).
[CrossRef]

C. Kulshreshtha, N. Shin, and K.-S. Sohn, Electrochem. Solid-State Lett. 12, J55 (2009).
[CrossRef]

D. Ahn, N. Shin, K. D. Park, and K.-S. Sohn, J. Electrochem. Soc. 156, J242 (2009).
[CrossRef]

2008

H.-L. Li, R.-J. Xie, N. Hirosaki, and Y. Yajim, J. Electrochem. Soc. 155, J378 (2008).
[CrossRef]

C. J. Duan, W. M. Otten, A. C. A. Delsing, and H. T. Hintzen, J. Solid State Chem. 181, 751 (2008).
[CrossRef]

X. Teng, W. Zhuang, Y. Hu, and X. Huang, J. Rare Earths 26, 652 (2008).
[CrossRef]

2007

R.-J. Xie, N. Hirosaki, N. Kimura, K. Sakuma, and M. Mitomo, Appl. Phys. Lett. 90, 191101 (2007).
[CrossRef]

2006

R.-J. Xie, N. Hirosaki, T. Suehiro, F.-F. Xu, and M. Mitomo, Chem. Mater. 18, 5578 (2006).
[CrossRef]

Y. Q. Li, G. de With, and H. T. Hintzen, J. Lumin. 116, 107 (2006).
[CrossRef]

Y. Q. Li, J. E. J. van Steen, J. W. H. van Krevel, G. Botty, A. C. A. Delsing, F. J. DiSalvo, G. de With, and H. T. Hintzen, J. Alloys Compd. 417, 273 (2006).
[CrossRef]

X. Q. Piao, T. Horikawa, H. Hanzawa, and K. Machida, Chem. Lett. 35, 334 (2006).
[CrossRef]

2001

S. O. Vásquez, Phys. Rev. B 64, 125103 (2001).
[CrossRef]

2000

H. Ebendorff-Heidepriem and D. Ehrt, Opt. Mater. 15, 7 (2000).
[CrossRef]

H. A. Höppe, H. Lutz, P. Morys, W. Schnick, and A. Seilmeier, J. Phys. Chem. Solids 61, 2001 (2000).
[CrossRef]

1999

S. O. Vásquez, Phys. Rev. B 60, 8575 (1999).
[CrossRef]

1998

S. O. Vásquez, J. Chem. Phys. 108, 723 (1998).
[CrossRef]

1997

S. O. Vásquez, J. Chem. Phys. 106, 8664 (1997).
[CrossRef]

1996

S. O. Vásquez, J. Chem. Phys. 104, 7652 (1996).
[CrossRef]

1972

R. Reisfeld, E. Greenberg, R. Velapoldi, and B. Barnett, J. Chem. Phys. 56, 1698 (1972).
[CrossRef]

Ahn, D.

D. Ahn, N. Shin, K. D. Park, and K.-S. Sohn, J. Electrochem. Soc. 156, J242 (2009).
[CrossRef]

Barnett, B.

R. Reisfeld, E. Greenberg, R. Velapoldi, and B. Barnett, J. Chem. Phys. 56, 1698 (1972).
[CrossRef]

Botty, G.

Y. Q. Li, J. E. J. van Steen, J. W. H. van Krevel, G. Botty, A. C. A. Delsing, F. J. DiSalvo, G. de With, and H. T. Hintzen, J. Alloys Compd. 417, 273 (2006).
[CrossRef]

Boyce, W. E.

W. E. Boyce and R. C. Diprima, Elementary Differential Equations and Boundary Value Problems (Wiley, 1986).

de With, G.

Y. Q. Li, J. E. J. van Steen, J. W. H. van Krevel, G. Botty, A. C. A. Delsing, F. J. DiSalvo, G. de With, and H. T. Hintzen, J. Alloys Compd. 417, 273 (2006).
[CrossRef]

Y. Q. Li, G. de With, and H. T. Hintzen, J. Lumin. 116, 107 (2006).
[CrossRef]

Delsing, A. C. A.

C. J. Duan, W. M. Otten, A. C. A. Delsing, and H. T. Hintzen, J. Solid State Chem. 181, 751 (2008).
[CrossRef]

Y. Q. Li, J. E. J. van Steen, J. W. H. van Krevel, G. Botty, A. C. A. Delsing, F. J. DiSalvo, G. de With, and H. T. Hintzen, J. Alloys Compd. 417, 273 (2006).
[CrossRef]

Di Bartolo, B.

B. Di Bartolo, in Energy Transfer Processes in Condensed Matter, B.Di Bartolo and A.Karipidou, eds. (Plenum, 1984), p. 103.
[CrossRef]

Diprima, R. C.

W. E. Boyce and R. C. Diprima, Elementary Differential Equations and Boundary Value Problems (Wiley, 1986).

DiSalvo, F. J.

Y. Q. Li, J. E. J. van Steen, J. W. H. van Krevel, G. Botty, A. C. A. Delsing, F. J. DiSalvo, G. de With, and H. T. Hintzen, J. Alloys Compd. 417, 273 (2006).
[CrossRef]

Duan, C. J.

C. J. Duan, W. M. Otten, A. C. A. Delsing, and H. T. Hintzen, J. Solid State Chem. 181, 751 (2008).
[CrossRef]

Ebendorff-Heidepriem, H.

H. Ebendorff-Heidepriem and D. Ehrt, Opt. Mater. 15, 7 (2000).
[CrossRef]

Ehrt, D.

H. Ebendorff-Heidepriem and D. Ehrt, Opt. Mater. 15, 7 (2000).
[CrossRef]

Greenberg, E.

R. Reisfeld, E. Greenberg, R. Velapoldi, and B. Barnett, J. Chem. Phys. 56, 1698 (1972).
[CrossRef]

Hanzawa, H.

X. Q. Piao, T. Horikawa, H. Hanzawa, and K. Machida, Chem. Lett. 35, 334 (2006).
[CrossRef]

Hintze, F.

M. Zeuner, F. Hintze, and W. Schnick, Chem. Mater. 21, 336 (2009).
[CrossRef]

Hintzen, H. T.

C. J. Duan, W. M. Otten, A. C. A. Delsing, and H. T. Hintzen, J. Solid State Chem. 181, 751 (2008).
[CrossRef]

Y. Q. Li, G. de With, and H. T. Hintzen, J. Lumin. 116, 107 (2006).
[CrossRef]

Y. Q. Li, J. E. J. van Steen, J. W. H. van Krevel, G. Botty, A. C. A. Delsing, F. J. DiSalvo, G. de With, and H. T. Hintzen, J. Alloys Compd. 417, 273 (2006).
[CrossRef]

Hirosaki, N.

K.-S. Sohn, S. Lee, R.-J. Xie, and N. Hirosaki, Appl. Phys. Lett. 95, 121903 (2009).
[CrossRef]

H.-L. Li, R.-J. Xie, N. Hirosaki, and Y. Yajim, J. Electrochem. Soc. 155, J378 (2008).
[CrossRef]

R.-J. Xie, N. Hirosaki, N. Kimura, K. Sakuma, and M. Mitomo, Appl. Phys. Lett. 90, 191101 (2007).
[CrossRef]

R.-J. Xie, N. Hirosaki, T. Suehiro, F.-F. Xu, and M. Mitomo, Chem. Mater. 18, 5578 (2006).
[CrossRef]

Höppe, H. A.

H. A. Höppe, H. Lutz, P. Morys, W. Schnick, and A. Seilmeier, J. Phys. Chem. Solids 61, 2001 (2000).
[CrossRef]

Horikawa, T.

X. Q. Piao, T. Horikawa, H. Hanzawa, and K. Machida, Chem. Lett. 35, 334 (2006).
[CrossRef]

Hu, Y.

X. Teng, W. Zhuang, Y. Hu, and X. Huang, J. Rare Earths 26, 652 (2008).
[CrossRef]

Huang, X.

X. Teng, W. Zhuang, Y. Hu, and X. Huang, J. Rare Earths 26, 652 (2008).
[CrossRef]

Kimura, N.

R.-J. Xie, N. Hirosaki, N. Kimura, K. Sakuma, and M. Mitomo, Appl. Phys. Lett. 90, 191101 (2007).
[CrossRef]

Kulshreshtha, C.

C. Kulshreshtha, N. Shin, and K.-S. Sohn, Electrochem. Solid-State Lett. 12, J55 (2009).
[CrossRef]

Lee, S.

K.-S. Sohn, S. Lee, R.-J. Xie, and N. Hirosaki, Appl. Phys. Lett. 95, 121903 (2009).
[CrossRef]

Li, H.-L.

H.-L. Li, R.-J. Xie, N. Hirosaki, and Y. Yajim, J. Electrochem. Soc. 155, J378 (2008).
[CrossRef]

Li, Y. Q.

Y. Q. Li, J. E. J. van Steen, J. W. H. van Krevel, G. Botty, A. C. A. Delsing, F. J. DiSalvo, G. de With, and H. T. Hintzen, J. Alloys Compd. 417, 273 (2006).
[CrossRef]

Y. Q. Li, G. de With, and H. T. Hintzen, J. Lumin. 116, 107 (2006).
[CrossRef]

Loudon, R.

R. Loudon, The Quantum Theory of Light (Oxford U. Press, 1973).

Lutz, H.

H. A. Höppe, H. Lutz, P. Morys, W. Schnick, and A. Seilmeier, J. Phys. Chem. Solids 61, 2001 (2000).
[CrossRef]

Machida, K.

X. Q. Piao, T. Horikawa, H. Hanzawa, and K. Machida, Chem. Lett. 35, 334 (2006).
[CrossRef]

Mitomo, M.

R.-J. Xie, N. Hirosaki, N. Kimura, K. Sakuma, and M. Mitomo, Appl. Phys. Lett. 90, 191101 (2007).
[CrossRef]

R.-J. Xie, N. Hirosaki, T. Suehiro, F.-F. Xu, and M. Mitomo, Chem. Mater. 18, 5578 (2006).
[CrossRef]

Morys, P.

H. A. Höppe, H. Lutz, P. Morys, W. Schnick, and A. Seilmeier, J. Phys. Chem. Solids 61, 2001 (2000).
[CrossRef]

Otten, W. M.

C. J. Duan, W. M. Otten, A. C. A. Delsing, and H. T. Hintzen, J. Solid State Chem. 181, 751 (2008).
[CrossRef]

Park, K. D.

D. Ahn, N. Shin, K. D. Park, and K.-S. Sohn, J. Electrochem. Soc. 156, J242 (2009).
[CrossRef]

Piao, X. Q.

X. Q. Piao, T. Horikawa, H. Hanzawa, and K. Machida, Chem. Lett. 35, 334 (2006).
[CrossRef]

Reisfeld, R.

R. Reisfeld, E. Greenberg, R. Velapoldi, and B. Barnett, J. Chem. Phys. 56, 1698 (1972).
[CrossRef]

Sakuma, K.

R.-J. Xie, N. Hirosaki, N. Kimura, K. Sakuma, and M. Mitomo, Appl. Phys. Lett. 90, 191101 (2007).
[CrossRef]

Schnick, W.

M. Zeuner, F. Hintze, and W. Schnick, Chem. Mater. 21, 336 (2009).
[CrossRef]

H. A. Höppe, H. Lutz, P. Morys, W. Schnick, and A. Seilmeier, J. Phys. Chem. Solids 61, 2001 (2000).
[CrossRef]

Seilmeier, A.

H. A. Höppe, H. Lutz, P. Morys, W. Schnick, and A. Seilmeier, J. Phys. Chem. Solids 61, 2001 (2000).
[CrossRef]

Shin, N.

C. Kulshreshtha, N. Shin, and K.-S. Sohn, Electrochem. Solid-State Lett. 12, J55 (2009).
[CrossRef]

D. Ahn, N. Shin, K. D. Park, and K.-S. Sohn, J. Electrochem. Soc. 156, J242 (2009).
[CrossRef]

Sohn, K.-S.

D. Ahn, N. Shin, K. D. Park, and K.-S. Sohn, J. Electrochem. Soc. 156, J242 (2009).
[CrossRef]

K.-S. Sohn, S. Lee, R.-J. Xie, and N. Hirosaki, Appl. Phys. Lett. 95, 121903 (2009).
[CrossRef]

C. Kulshreshtha, N. Shin, and K.-S. Sohn, Electrochem. Solid-State Lett. 12, J55 (2009).
[CrossRef]

Suehiro, T.

R.-J. Xie, N. Hirosaki, T. Suehiro, F.-F. Xu, and M. Mitomo, Chem. Mater. 18, 5578 (2006).
[CrossRef]

Teng, X.

X. Teng, W. Zhuang, Y. Hu, and X. Huang, J. Rare Earths 26, 652 (2008).
[CrossRef]

van Krevel, J. W. H.

Y. Q. Li, J. E. J. van Steen, J. W. H. van Krevel, G. Botty, A. C. A. Delsing, F. J. DiSalvo, G. de With, and H. T. Hintzen, J. Alloys Compd. 417, 273 (2006).
[CrossRef]

van Steen, J. E. J.

Y. Q. Li, J. E. J. van Steen, J. W. H. van Krevel, G. Botty, A. C. A. Delsing, F. J. DiSalvo, G. de With, and H. T. Hintzen, J. Alloys Compd. 417, 273 (2006).
[CrossRef]

Vásquez, S. O.

S. O. Vásquez, Phys. Rev. B 64, 125103 (2001).
[CrossRef]

S. O. Vásquez, Phys. Rev. B 60, 8575 (1999).
[CrossRef]

S. O. Vásquez, J. Chem. Phys. 108, 723 (1998).
[CrossRef]

S. O. Vásquez, J. Chem. Phys. 106, 8664 (1997).
[CrossRef]

S. O. Vásquez, J. Chem. Phys. 104, 7652 (1996).
[CrossRef]

Velapoldi, R.

R. Reisfeld, E. Greenberg, R. Velapoldi, and B. Barnett, J. Chem. Phys. 56, 1698 (1972).
[CrossRef]

Xie, R.-J.

K.-S. Sohn, S. Lee, R.-J. Xie, and N. Hirosaki, Appl. Phys. Lett. 95, 121903 (2009).
[CrossRef]

H.-L. Li, R.-J. Xie, N. Hirosaki, and Y. Yajim, J. Electrochem. Soc. 155, J378 (2008).
[CrossRef]

R.-J. Xie, N. Hirosaki, N. Kimura, K. Sakuma, and M. Mitomo, Appl. Phys. Lett. 90, 191101 (2007).
[CrossRef]

R.-J. Xie, N. Hirosaki, T. Suehiro, F.-F. Xu, and M. Mitomo, Chem. Mater. 18, 5578 (2006).
[CrossRef]

Xu, F.-F.

R.-J. Xie, N. Hirosaki, T. Suehiro, F.-F. Xu, and M. Mitomo, Chem. Mater. 18, 5578 (2006).
[CrossRef]

Yajim, Y.

H.-L. Li, R.-J. Xie, N. Hirosaki, and Y. Yajim, J. Electrochem. Soc. 155, J378 (2008).
[CrossRef]

Zeuner, M.

M. Zeuner, F. Hintze, and W. Schnick, Chem. Mater. 21, 336 (2009).
[CrossRef]

Zhuang, W.

X. Teng, W. Zhuang, Y. Hu, and X. Huang, J. Rare Earths 26, 652 (2008).
[CrossRef]

Appl. Phys. Lett.

R.-J. Xie, N. Hirosaki, N. Kimura, K. Sakuma, and M. Mitomo, Appl. Phys. Lett. 90, 191101 (2007).
[CrossRef]

K.-S. Sohn, S. Lee, R.-J. Xie, and N. Hirosaki, Appl. Phys. Lett. 95, 121903 (2009).
[CrossRef]

Chem. Lett.

X. Q. Piao, T. Horikawa, H. Hanzawa, and K. Machida, Chem. Lett. 35, 334 (2006).
[CrossRef]

Chem. Mater.

R.-J. Xie, N. Hirosaki, T. Suehiro, F.-F. Xu, and M. Mitomo, Chem. Mater. 18, 5578 (2006).
[CrossRef]

M. Zeuner, F. Hintze, and W. Schnick, Chem. Mater. 21, 336 (2009).
[CrossRef]

Electrochem. Solid-State Lett.

C. Kulshreshtha, N. Shin, and K.-S. Sohn, Electrochem. Solid-State Lett. 12, J55 (2009).
[CrossRef]

J. Alloys Compd.

Y. Q. Li, J. E. J. van Steen, J. W. H. van Krevel, G. Botty, A. C. A. Delsing, F. J. DiSalvo, G. de With, and H. T. Hintzen, J. Alloys Compd. 417, 273 (2006).
[CrossRef]

J. Chem. Phys.

S. O. Vásquez, J. Chem. Phys. 108, 723 (1998).
[CrossRef]

R. Reisfeld, E. Greenberg, R. Velapoldi, and B. Barnett, J. Chem. Phys. 56, 1698 (1972).
[CrossRef]

S. O. Vásquez, J. Chem. Phys. 104, 7652 (1996).
[CrossRef]

S. O. Vásquez, J. Chem. Phys. 106, 8664 (1997).
[CrossRef]

J. Electrochem. Soc.

H.-L. Li, R.-J. Xie, N. Hirosaki, and Y. Yajim, J. Electrochem. Soc. 155, J378 (2008).
[CrossRef]

D. Ahn, N. Shin, K. D. Park, and K.-S. Sohn, J. Electrochem. Soc. 156, J242 (2009).
[CrossRef]

J. Lumin.

Y. Q. Li, G. de With, and H. T. Hintzen, J. Lumin. 116, 107 (2006).
[CrossRef]

J. Phys. Chem. Solids

H. A. Höppe, H. Lutz, P. Morys, W. Schnick, and A. Seilmeier, J. Phys. Chem. Solids 61, 2001 (2000).
[CrossRef]

J. Rare Earths

X. Teng, W. Zhuang, Y. Hu, and X. Huang, J. Rare Earths 26, 652 (2008).
[CrossRef]

J. Solid State Chem.

C. J. Duan, W. M. Otten, A. C. A. Delsing, and H. T. Hintzen, J. Solid State Chem. 181, 751 (2008).
[CrossRef]

Opt. Mater.

H. Ebendorff-Heidepriem and D. Ehrt, Opt. Mater. 15, 7 (2000).
[CrossRef]

Phys. Rev. B

S. O. Vásquez, Phys. Rev. B 60, 8575 (1999).
[CrossRef]

S. O. Vásquez, Phys. Rev. B 64, 125103 (2001).
[CrossRef]

Other

B. Di Bartolo, in Energy Transfer Processes in Condensed Matter, B.Di Bartolo and A.Karipidou, eds. (Plenum, 1984), p. 103.
[CrossRef]

R. Loudon, The Quantum Theory of Light (Oxford U. Press, 1973).

W. E. Boyce and R. C. Diprima, Elementary Differential Equations and Boundary Value Problems (Wiley, 1986).

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Figures (3)

Fig. 1
Fig. 1

Schematics of proposed energy transfer model. R C is the critical distance for quenching to killer sites, and R O is the critical distance for inter-activator energy transfer.

Fig. 2
Fig. 2

Sr 1 Sr 1 , Sr 1 Sr 2 , and Sr 2 Sr 2 energy transfer routes depicted within the 12 Å boundaries around an arbitrary Sr1 (or Sr2) site in the Sr 2 Si 5 N 8 structure.

Fig. 3
Fig. 3

(a) Decay curve fits along with experimental data monitored at 635 and 740 nm , (b) calculated time evolution (decay curve) of ρ Sr 1 e ρ Total , ρ ¯ Sr 1 e ρ Total , ρ Sr 2 e ρ Total , and ρ ¯ Sr 2 e ρ Total for Sr 2 Si 5 N 8 : 0.02 Eu 2 + .

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

d ρ Sr 1 e d t = G ρ Sr 1 g k Sr 1 ρ Sr 1 e Ω Sr 1 Sr 2 k T ρ Sr 1 e ρ Sr 2 g Ω Sr 1 Sr 1 k T ρ Sr 1 e ρ ¯ Sr 1 g Ω Sr 1 Sr 2 k T ρ Sr 1 e ρ ¯ Sr 2 g ,
d ρ Sr 2 e d t = G ρ Sr 2 g k Sr 2 ρ Sr 2 e + Ω Sr 1 Sr 2 k T ρ Sr 1 e ρ Sr 2 g Ω Sr 2 Sr 2 k T ρ Sr 2 e ρ ¯ Sr 2 g ,
d ρ Sr 1 g d t = G ρ Sr 1 g + k Sr 1 ρ Sr 1 e + Ω Sr 1 Sr 2 k T ρ Sr 1 e ρ Sr 2 g + Ω Sr 1 Sr 1 k T ρ Sr 1 e ρ ¯ Sr 1 g + Ω Sr 1 Sr 2 k T ρ Sr 1 e ρ ¯ Sr 2 g ,
d ρ Sr 2 g d t = G ρ Sr 2 g + k Sr 2 ρ Sr 2 e Ω Sr 1 Sr 2 k T ρ Sr 1 e ρ Sr 2 g + Ω Sr 2 Sr 2 k T ρ Sr 2 e ρ ¯ Sr 2 g ,
d ρ ¯ Sr 1 e d t = G ρ ¯ Sr 1 g ( k Sr 1 + K n ) ρ ¯ Sr 1 e + Ω Sr 1 Sr 1 k T ρ Sr 1 e ρ ¯ Sr 1 g ,
d ρ ¯ Sr 2 e d t = G ρ ¯ Sr 2 g ( k Sr 2 + K n ) ρ ¯ Sr 2 e + Ω Sr 1 Sr 2 k T ρ Sr 1 e ρ ¯ Sr 2 g + Ω Sr 2 Sr 2 k T ρ Sr 2 e ρ ¯ Sr 2 g ,
d ρ ¯ Sr 1 g d t = G ρ ¯ Sr 1 g + ( k Sr 1 + K n ) ρ ¯ Sr 1 e Ω Sr 1 Sr 1 k T ρ Sr 1 e ρ ¯ Sr 1 g ,
d ρ ¯ Sr 2 g d t = G ρ ¯ Sr 2 g + ( k Sr 2 + K n ) ρ ¯ Sr 2 e Ω Sr 1 Sr 2 k T ρ Sr 1 e ρ ¯ Sr 2 g Ω Sr 2 Sr 2 k T ρ Sr 2 e ρ ¯ Sr 2 g ,
ρ Sr 1 e + ρ Sr 2 e + ρ Sr 1 g + ρ Sr 2 g + ρ ¯ Sr 1 e + ρ ¯ Sr 2 e + ρ ¯ Sr 1 g + ρ ¯ Sr 2 g = total Eu 2 + number per unit volume ( ρ Total ) .
k d d = X k T l n l max ( 1 R l g ) 6 ,
Ω Sr 1 Sr 2 = 7.5 Ω Sr 1 Sr 1 ; Ω Sr 2 Sr 2 Ω Sr 1 Sr 1 .
m ( ρ Sr 1 e + ρ ¯ Sr 1 e ) * + ( 1 m ) ( ρ Sr 2 e + ρ ¯ Sr 2 e ) * = I 635 , ( ρ Sr 2 e + ρ ¯ Sr 2 e ) * = I 740 ,
ρ Sr 1 e = 0 , ρ Sr 2 e = 0 , ρ Sr 1 g = ρ Sr 2 g = ( 1 q ) ρ Total 2 ,
ρ ¯ Sr 1 e = 0 , ρ ¯ Sr 2 e = 0 , ρ ¯ Sr 1 g = ρ ¯ Sr 2 g = q ρ Total 2 ,

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