POSSIBLE WAYS OF RELAXATIONS FOR EXCITED STATES OF RARE EARTH IONS IN AMORPHOUS MEDIA

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POSSIBLE WAYS OF RELAXATIONS FOR EXCITED

STATES OF RARE EARTH IONS IN AMORPHOUS

MEDIA

R. Reisfeld, M. Eyal

To cite this version:

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P O S S I B L E WAYS OF R E L A X A T I O N S FOR E X C I T E D S T A T E S OF RARE EARTH I O N S I N AMORPHOUS M E D I A

R. Reisfeld and M. Eyal

Department of Inorganic and AnaZyticaZ Chemistry, The Hebrew University of JerusaZern, 91 904 JerusaZem, Israel

Abstract

-

The various mechanisms of relaxation of r a r e earths i n glasses a r e outlined. Examples a r e given f o r r a d i a t i v e t r a n s f e r as a means of increasing pumping e f f i c i e n c i e s . Nonradiative relaxation of r a r e earths in oxide and f l u o r i d e glasses follow an exponential law when two glass former phonons are subtracted. Cross-relaxations a r e calculated f o r P r ( I I I ) , Ho(II1) and Nd(II1).

The excited s t a t e of a r a r e earth ion in an amorphous matrix can relax by four main channels: 1. Radiative t r a n s f e r ; 2. Multiphonon relaxation; 3. Cross-relaxation t o another ion of the same nature; 4. Energy transfer t o an ion of different nature.

1. The r a d i a t i v e t r a n s f e r consists of absorption of the emitted l i g h t from a donor molecule or ion by t h e acceptor species. In order t h a t such transfer takes place the emission of the donor has t o coincide with the absorption of the acceptor. The r a d i a t i v e t r a n s f e r can be increased considerably by designing a proper geometry. Such t r a n s f e r may be important i n increasing pumping e f f i c i e n c i e s of glass l a s e r s

/1/ and luminescent s o l a r concentrators whereby energy emitted from organic molecu- l e s can be absorbed by ions such a s C r ( I I I ) , Mn(I1) o r Nd(II1) followed by c h a r a c t e r i s t i c emission from these ions.

2. Multiphonon relaxation in lanthanide ions i s today a well understood process contrary t o t r a n s i t i o n metal ions which s t i l l requires additional understanding. Excited electronic l e v e l s of r a r e earths (RE) i n s o l i d s decay nonradiatively by exciting l a t t i c e vibrations (phonons). When the energy gap between t h e excited level and the next e l e c t r o n i c level i s l a r g e r than the phonon energy several l a t t i - ce phonons a r e emitted in order t o bridge t h e energy gap. I t was recognized t h a t t h e most energetic vibrations a r e responsible f o r t h e non-radiative decay since such a process can conserve energy in t h e lowest order. In glasses the most ener- g e t i c vibrations a r e the stretching vibrations of the glass network polyhedra and i t was shown t h a t these d i s t i n c t vibrations a r e a c t i v e in the multiphonon process rather than the less energetic vibrations of the bond between t h e RE and i t s sur- rounding ligands. I t was demonstrated t h a t these l e s s energetic vibrations may

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C7-350 JOURNAL DE PHYSIQUE

p a r t i c i p a t e i n cases when t h e energy gap i s n o t b r i d g e d t o t a l l y by t h e h i g h energy v i b r a t i o n s . The experimental r e s u l t s reveal t h a t t h e l o g a r i t h m o f t h e multiphonon decay r a t e decreases l i n e a r l y w i t h t h e energy gap, o r t h e number o f phonons b r i d g i n g t h e gap when t h e number o f phonons i s l a r g e r than two. F i g u r e 1 presents t h e loga- r i t h m o f t h e n o n - r a d i a t i v e r e l a x a t i o n r a t e versus t h e number o f phonons o f t h e glass-forming m a t e r i a l . F i g u r e 2 presents t h e same dependence however two phonons a r e taken as t h e o r i g i n o f t h e abscissa.

I

NUMBER OF PHONONS

Fig. 1. Dependence o f rnultiphonon r e l a x a t i o n o f t h e number o f phonons i n t h e g l a s s former.

NUMBER OF PHONONS

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ses, the vibrational frequencies show in homogeneous broadening due to t h e variation of s i t e s . Table I shows t h e average frequencies of t h e network formers. The vibrations involving the network modifiers a r e lower by a f a c t o r of 2 t o 4. Considering the dependence of the multiphonon relaxation r a t e , Wp, on t h e phonon occupation number f o r a p-order multiphonon decay a t temperature T>O

where AE i s t h e energy gap between the emitting and next lower level

a = - t n ( ~ ) / f i ~ (2) and a and B are dependent on t h e host but independent of the specific electronic level of RE from which the decay occurs.

In calculating t h e o r e t i c a l l y the mu1 tiphonon relaxation Siebrand /2/ has used the Condon approximation in which the electronic matrix elements a r e separated from the vibrational ones and assuming t h a t t h e t r a n s i t i o n i s dominated by a small number of promoting modes which consume t h e energy Kw. The accepting modes provide only f o r the remaining energy difference AEo-Rwmax

.

The theoretical r e s u l t s a r i s i n g from t h i s theory a r e

WNR = Belexp[-AE

-

2hw)al

The multiphonon decay r a t e from a given level t o the next lower level decreases with t h e lowering of energy of the stretching frequencies of t h e glass former. Since a l a r g e number of phonons i s needed in f l u o r i d e glasses and more so i n chalco- genide glasses in order t o reach the same energy gap the nonradiative relaxations a r e smallest in these hosts.

A tabulation of the parameters B and a of eq. ( 1 ) together w i t h the highest phonon energy f o r a variety of glasses and c r y s t a l s i s presented in Table I . For oxide glasses a i s f a i r l y constant while B d i f f e r s by several orders of magnitude between various glasses. Recently t h i s phenomenon was elaborated by Schuurmans and Van Dijk /3/ who propose formula (3) r a t h e r than eq. (1 ). Hence one can define a re- vised Bel as

The loglo of e l e c t r o n i c f a c t o r B i s a l s o presented i n Table I where i t can be seen t h a t i t i s of the same order o? magnitude f o r a l l glasses contrary t o B which varies by several orders of magnitude f o r various glasses. See Fig. 2.

The multiphonon t r a n s i t i o n r a t e s f o r r a r e earths in a variety of glasses can be obtained from formula ( 4 ) by use of the tabulated values of Bel, a and iiw in Table I and energy differences t o the next e l e c t r o n i c level AE. The correspondence of theory with experiment has been shown f o r P r ( I I 1 ) /4/, Nd(II1) /5/, Ho(II1) /6/,

and E r ( 1 I I ) /7/.

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C7-352 JOURNAL DE PHYSIQUE

c o n s i d e r a t i o n t h e l a s t process i s much l e s s e f f i c i e n t .

TABLE I. Parameters f o r N o n r a d i a t i v e Relaxations i n Glasses

M a t r i x B s - I a cm Rw cm-l 10g,~B~, - - T e l l u r i te Phosphate Borate S i l i c a t e Germana t e ALS, GLS ZBLA

ALS 3AlZS3, 0.872LazS3, 0.1 28NdzS3

GLS 3GazS,,0.85LazS3,0.15NdzS3

ZBLA 57ZrF,, 34BaF,, 3LaF3, 4A1 F,

,

ZREF, mole % (RE = r a r e e a r t h )

3. Cross-relaxations. Special cases o f energy t r a n s f e r a r e c r o s s - r e l a x a t i o n where t h e o r i g i n a l system l o s e s t h e energy (E,-E,) b y o b t a i n i n g t h e lower s t a t e E, (which may a l s o be t h e groundstate E l ) and another system a c q u i r e s t h e energy by going t o a h i g h e r s t a t e E,. C r o s s - r e l a x a t i o n may t a k e p l a c e between t h e same l a n t h a n i d e (being a major mechanism f o r quenching a t h i g h e r c o n c e n t r a t i o n i n a g i v e n m a t e r i a l ) o r between two d i f f e r i n g elements, which happen t o have two p a i r s o f energy l e v e l s separated by t h e same amount.

The c r o s s - r e l a x a t i o n between a p a i r o f RE i o n s i s g r a p h i c a l l y presented i n Fig. 3.

The two energy gaps may be equal o r can be matched by one o r two phonons. C r o s s - r e l a x a t i o n has been measured i n a v a r i e t y o f i o n s and i t i s a dominating f a c - t o r i n n o n r a d i a t i v e r e l a x a t i o n s a t h i g h concentration. The n o n - r a d i a t i v e r e l a x a t i o n r a t e s can be obtained by a n a l y s i s o f t h e decay curves o f RE fluorescence u s i n g t h e formula o f t h e general form where t h e p o p u l a t i o n number o f s t a t e i, Ni i s propor- t i o n a l t o t h e i n t e n s i t y o f e m i t t e d l i g h t Ii.

d N . ( t ) / d t i s t h e decrease o f i n t e n s i t y a f t e r p u l s e e x c i t a t i o n , y i s t h e r e c i p r o c a l

.

of'the l i f e t i m e o f t h e e x c i t e d s t a t e i n t h e absence o f c r o s s - r e l i x a t i o n process.

CW.. i s W e p r o b a b i l i t y f o r c r o s s - r e l a x a t i o n , W.i i s t h e p r o b a b i l i t y o f i n v e r s e d prh$ess, and Wij i s t h e r a t e o f c r o s s - r e l a x a t i o a .

T h e o r e t i c a l l y t h e c r o s s - r e l a x a t i o n r a t e f o r a d i pole-dip01 e t r a n s f e r can be

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Ion A

I o n

A'

Fig. 3. Scheme f o r cross-relaxation between two ions of t h e same o r d i f f e r e n t nature.

Here R a r e the Judd-Ofelt i n t e n s i t y parameters, < J ~ ~ u ( ~ ) I ] J ' > i s t h e matrix element of the t r a n s i t i o n between the ground and excited s t a t e of the s e n s i t i z e r and a c t i v a t o r respectively ( t h e calculation of these matrix elements in the intermediate- couplfng scheme i s now a well known procedure and may be found i n references 181 and

/9/: S i s the overlap integral and R i s t h e i n t e r i o n i c distance.

The measured lifetime of luminescence i s related t o t h e t o t a l relaxation r a t e by

1

r

=

zwNR

+ IA + pCR =

f

+ pCR (7

1

0

where LA i s t h e t o t a l r a d i a t i v e r a t e , CW i s t h e nonradiative r a t e and PCR i s the r a t e of cross-relaxation between adjacenKRions.

The possible cross-relaxation channels f o r p r ( I I I ) , ~ o ( I 1 1 ) and Nd( 111) a r e outlined i n Table 11. /lo/

In order t o obtain the c r i t i c a l radii which a r e the distances a t which the probability f o r cross-relaxation i s equal t o the sum of the r a d i a t i v e and multiphonon p r o b a b i l i t i e s t h e decay curves a r e analyzed with respect t o the Inokuti-Hirayama model /I I / .

The energy t r a n s f e r between Cr(II1) and Nd(II1) /12/ and Cu(II1) and Yb(II1)

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/ I / Reisfeld, R., Chem. Phys. L e t t .

114

(1985) 306. /2/ Struck, C.W. and Fonger, W.H., J. Lumin.

10

(1975) 31.

/3/ Schuurmans, M.F.H. and Van D i j k , J.M.F., Physica 123B (1984) 131.

/4/ Eyal, M., Greenberg, E., Reisfeld, R. and Spect,,or Chem. Phys. L e t t . (1985) i n press.

/5/ Lucas, J., Chanthanasinh, M., Poulain, M., Poulain, M., Brun, P. and Weber, M.J., J. Noncryst. Solids,

7

(1978) 273.

/6/ R e i s f e l d , R., Eyal, M., Greenberg, E. and Jbrgensen, C.K., Chem. Phys. L e t t . (1985) i n press.

/7/ R e i s f e l d , R., Katz, G., Jacoboni, C., de Pape, R., Drexhage, M.G., Brown, R.N. and Jbrgensen, C.K., J. S o l i d S t a t e Chem. 4 8 (1983) 323.

/8/ R e i s f e l d , R., S t r u c t u r e and Bonding 30 ( 1 9 z ) 65.

/9/ Riseberg, L.A. and Weber, M.J., R e l a z t i o n Phenomena i n Rare E a r t h Luminescence, i n Progress i n Optics, Ed. E. Wolf, Vol. X I V , North-Holland, Amsterdam (1976). / l o / R e i s f e l d , R., N o n r a d i a t i v e R e l a x a t i o n o f Rare Earths i n F l u o r i d e Glasses, 3 r d