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PHOTOACOUSTIC INVESTIGATION OF THE RELAXATION OF THE 2E STATE OF RUBY
M. Gallmeier, E. Strauss, R. Germer, W. Schubert, R. Brundage, W. Yen
To cite this version:
M. Gallmeier, E. Strauss, R. Germer, W. Schubert, R. Brundage, et al.. PHOTOACOUSTIC INVES-
TIGATION OF THE RELAXATION OF THE 2E STATE OF RUBY. Journal de Physique Colloques,
1983, 44 (C6), pp.C6-401-C6-405. �10.1051/jphyscol:1983666�. �jpa-00223225�
JOURNAL DE PHYSIQUE
Colloque C6, suppl6ment au nO1O, Tome 44, octobre 1983 page C6- 401
PHOTOACOUSTIC I N V E S T I G A T I O N OF THE RELAXATION OF THE 'E STATE OF RUBY
M. Gallmeier, E. Strauss, R. Germer, W. Schubert, R.T. ~ r u n d a ~ e * and W.M. yen*
Elniversitat Oldenburg, Fachbereich Physik, 2900 Oldenburg, F.R.G.
University o f Wisconsin, Dep. o f Physics, Madison, WI 53706, U.S.A.
Rgsurng
-
La d g p e n d a n c e e n f r g q u e n c e d u s i g n a l p h o t o a c o u s t i q u e e s t u t i l i s g e p o u r e t u d i e r l a r e l a x a t i o n n o n r a d i a t i v e d u r u b i s( ~ 1 2 0 3 : ~ r 3 + ) . Une c o r r g l a t i o n q u a n t i t a t i v e a v e c d e s d o n n B e s o p t i - q u e s i n d i q u e q u e , p o u r T
>
200 K , l e r e n d e m e n t q u a n t i q u e t o t a l d e la f l u o r e s c e n c e n ' e s t p a s d g t e r m i n 6 e x c l u s i v e m e n t p a r l a r e l a x a t i o n( 2 ~ + 4 ~ 2 )
.
A b s t r a c t
-
The m o d u l a t i o n f r e q u e n c y dependence of t h e PA r e s p o n s e h a s been u i i z e d t o s t u d y 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 o f p h o t o e x c i t e d r u b y (Ik:03:Cr3+). A q u a n t i t a t i v e c o r r e l a t i o n w i t h a p t i ~ a l d a t a i n d i c a t e s t h a t a t T2200 K the o v e r a l l fluorescence quantum e f f i c i e n c y 1s not s o l e l y governed by t h e ( ' E + ~ A ~ ) relaxation.The m o d u l a t i o n f r e q u e n c y dependence of t h e p h o t o a c o u s t i c (PA) r e s p o n s e c a n be u t i l i z e d advantageouslyto i n v e s t i g a t e the r e l a x a t i o n of longlived metastable s t a t e s i n l i q u i d s and s o l i d s . I n p a r t i c u l a r it is s u i t a b l e t o d e t e r m i n e t h e l i f e t i m e of t h e s e s t a t e s and i s t h e method of c h o i c e i n t h e c a s e of n o n f l u o r e s c e n t t r i p l e t s t a t e s of organic dyes and pigments. With t h i s technique t h e o p t i c a l r e l a x a t i o n of ruby (?+1203:cr3+) has been studied a t low temperatures 2. In t h i s work we extend t h e e x p e r i m e n t s t o t e m p e r a t u r e s up t o 500 K and c o r r e l a t e t h e r e s u l t s q u a n t i t a t i v e l y with o p t i c a l data.
The e x c i t e d 'E s t a t e of ruby h a s been s t u d i e d t h o r o u g h l y o v e r t h e y e a r s and an extensive l i t e r a t u r e e x i s t s on its p r o p e r t i e s , f o r a review see ref. 2. The methods used t o probe its p r o p e r t i e s include photoacoustic3 and low temperature photothermal s p e c t r o s c o p y 4 . The 2~ is t h e e n e r g y s t o r i n g s t a t e i n t h e ruby l a s e r and its fluorescence quantum e f f i c i e n c y QE is an e s s e n t i a l number f o r its performance. It h a s been concluded from t h e low t e m p e r a t u r e PA d a t a t h a t t h e QE of t h e 'E is n e a r u n i t y l.
Fig.1: Energy l e v e l d i a g r a m of
c r 3 +
i n a n o c t a h e d r a l c r y s t a lf i e l d . The absorption and lumines- 4 ~ 2
1
c e n c e s p e c t r a a r e d e p i c t e d
schematically
'.
octahedral fieldabsor~tion luminescence
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983666
C6-402 JOURNAL DE PHYSIQUE
cr3+
i o n s occupy o c t a h e d r a l s i t e s and have a l e v e l o r d e r i n g a s d e p i c t e d i n f i g . 1.I n t h e PA experiment the e x c i t a t i o n is i n t h e prominent ' ~ 2 t r a n s i t i o n (see f i g . 1).
Nonradiative r e l a x a t i o n is very f a s t and p p u l a t e s the 'E s t a t e s . %is l e v e l has a l i f e t i m e T of s e v e r a l m s and r e l a x e s 133th r a d i a t i v e l y and twnradiatively to the 'A ground s t a t e , t h e fluorescence known as the R-lines. The nonradiative r e l a x a t i o n of t h e 'TZ r e l e a s e s h e a t immediately a f t e r absorption while t h e heat released by the 2~
r e l a x a t i o n is delayed. In such a system the modulation frequency ( w ) dependence of t h e PA r e s p o n s e , a f t e r d e c o n v o l u t i o n o f t h e PA transducer's t r a n s f e r f u n c t i o n , is given by3,5
(1) ~ ( w ) = { [ E J ( ~ + ~ ~ T ~ ) + E ~ ] ~
+
[ ( E ~ O T ) / ( ~ + W ~ T ~ ) ~ ~ jM ( w ) is t h e a m p l i t u d e of t h e P A s i g n a l and O ( w ) is t h e phase a n g l e r e l a t i v e t o t h e s i n e wave modulated excitation. Ef is t h e "fast" heat amplitude and E s = Q E * E ( 2 ~ + 4 ~ )
is t h e "slow" heat amplitude, with QE t h e R-line fluorescence quantum efficiency.
Up t o 400 K A E ( ? T ~ + ~ E ) > > kT and t h e f l u o r e s c e n c e quantum e f f i c i e n c y QE, t h e l i f e t i m e T and the o s c i l l a t o r s t r e n g t h ~ ~ ( ' A Z + ~ E ) of t h e 2~ s t a t e a r e r e l a t e d 6 :
where T,' is t h e r a d i a t i v e decay r a t e and T,' is t h e nonradiative one.
Fig.2: PA a m p l i t u d e and phase s p e c t r a of ruby a t 300K ( l e f t ) and a t 450K ( r i g h t ) . The b a r s i n d i c a t e t h e s t a n d a r d d e v i a t i o n o f 10 measurements. The s o l i d l i n e s a r e f i t s t o e q u a t i o n s (1) and ( 2 ) . The f i t s a r e v e r y s e n s i t i v e t o t h e r a t i o Es/Ef ( s e e t e x t ) .
Y 1 D
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qvantenavraevte 80.81 und 86 luntere.m?ttlere und obere L l n i e )
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-.o u.
I I . . . .
Experimental
-
The experimental set-up c o n s i s t s of a l i g h t source (an Ar' l a s e r o r a cw dye l a s e r ) , an e l e c t r o o p t i c m o d u l a t o r , t h e PA c e l l w i t h c h a r g e a m p l i f i e r , a vector-lock-in-amplifier and a microcomputer. The ruby sample used was a 5 mm cube w i t h a l l s i d e s p o l i s h e d . Itscr3+
c o n c e n t r a t i o n was d e t e r m i n e d by o p t i c a l absorption7 to be 0 - 0 6 mol%. l h e sample was sandwiched between highly r e f l e c t i v e A 1 2 0 3 c e r a m i c d i s c s and clamped i n a s t a c k w i t h a p i e z o t r a n s d u c e r and a p i e c e of n e u t r a l d e n s i t y f i l t e r glass. The r e f l e c t i v e ceramic e f f e c t i v e l y prevents secondary PA s i g n a l s from f l u o r e s c e n c e l i g h t which o t h e r w i s e would be absorbed i n t h e transducer. The n e u t r a l d e n s i t y f i l t e r g l a s s was used t o measure the transducer's t r a n s f e r function. lhis transducer was f r e e of troublesome acoustical resonances up t o 10 kHz.Fluorescence l i f e t i m e s were measured with a standard set-up (pulsed l a s e r and box- c a r a v e r a g e r ) . The o p t i c a l measurements of t h e f l u o r e s c e n c e quantum e f f i c i e n c y ( r e l a t i v e t o t h e 300 K value) were performed using 514 nm e x c i t a t i o n , a Schott E 6 3 0 cut-off f i l t e r a d a S-20 cathode photodetector. Care was taken to absorb t h e same power a t a l l temperatures.
Results
-
The amplitude and phase s p e c t r a of t h e PA response were measured from 170 K t o 500 K. T y p i c a l s p e c t r a a r e d e p i c t e d i n f i g . 2. The transducer's t r a n s f e r function has been deconvoluted. The s o l i d l i n e s a r e numerical f i t s of equation (1) and ( 2 ) t o t h e d a t a . I f s t e p w i s e r e l a x a t i o n i n t h e e l e c t r o n i c s t a t e s is assumed, i.e. 4 ~ z + 2 ~ + 4 ~ 2 , the "fast" heat amplitude is proportional to the d i f f e r e n c e of the e x c i t a t i o n energy t o t h e 'E s t a t e s . In t h a t case the only a d j u s t a b l e parameters a r e t h e 'E l i f e t i m e s T and its fluorescence quantum e f f i c i e n c y QE. The 'E l i f e t i m e s a r e summarized i n fig. 3. Above 250 K both photoacoustic arYi fluorescence l i f e t i m e s a r e i n e x c e l l e n t agreement and confirm t h e d a t a of Nelson and sturge6. Below 250 K t h e l i f e t i m e s i n o u r sample i n c r e a s e due t o r a d i a t i o n t r a p p i n g which i s d i f f e r e n t i n both experiments.A
Fig.3: P h o t o a c o u s t i c and fluores-
cence l i f e t i m e s of t h e 'E s t a t e i n 2 r u b y . The d a t a of N e l s o n and
s t u r g e 6 w e r e o b t a i n e d w i t h o u t
r a d i a t i o n trapping. The s o l i d l i n e O i i 0 2 0 0 300 100 SO0 L ~ ~ ~ ~ ~ ~ ~ ~ ~
is calculated from equation (6). TEnPEllRTUllE I% I
Discussion
-
The s o l i d l i n e i n fig. 3 is t h e calculated temperature dependence from e q u a t i o n ( 3 ) assuming multiphonon r e l a x a t i o n 8 a s t h e main s o u r c e of t e m p e r a t u r e dependenceJOURNAL DE PHYSIQUE
with ~ 2 4 , i. e. a phonon energy of -600 cm-l, rr-l=206s-l and rm-'(0)=25 s-'.
Equ. ( 4 ) is used to determine t h e temperature dependence of rr-'. Nelson and Sturge measured u ( ~ A z + ~ E ) v e r y c a r e f u l l y . I t i n c r e a s e s 10% from 20 K t o 300 K. W e measured G ( ~ A Z + ~ E ) up t o 500 K r e l a t i v e t o its 300 K v a l u e . The i n c r e a s e is less t h a n 50%. The weak t e m p e r a t u r e dependence of rr-I h a s been i n c l u d e d i n t h e c a l c u l a t i o n of t h e s o l i d l i n e in f ig.3.
The temperature dependence of t h e QE was c a l c u l a t e d combining equations (5) and (6).
The r e s u l t is d e p i c t e d i n fig.4 (dashed l i n e ) . The s t r o n g d e c r e a s e above 300 K a g r e e s w e l l w i t h t h e o p t i c a l l y measured r e l a t i v e f l u o r e s c e n c e QE. These d a t a a r e scaled f o r a 300 K value of QE=0.8. The temperature dependence of t h e QE c a l c u l a t e d from t h e P A phase s p e c t r a is l e s s pronounced. E s p e c i a l l y above 300K t h e t h u s obtained QE values a r e i n c o n t r a d i c t i o n t o t h e o p t i c a l data.
T h i s c o n t r a d i c t i o n i n d i c a t e s t h a t t h e a s s u m p t i o n o f s t e p w i s e r e l a x a t i o n i n t h e e l e c t r o n i c states is not c o r r e c t , i. e. not a l l of t h e 4 ~ z population r e l a x e s t o t h e
?-E. Under t h e s e c i r c u m s t a n c e s t h e a m p l i t u d e o f t h e f a s t h e a t s o u r c e is n o t s i m p l y proportional t o t h e energy d i f f e r e n c e t o t h e 2~ b u t might have as w e l l c o n t r i b u t i o n s from t h e '+TZ+~AZ relaxation.
1.0
$
0'3Fig.4: T e m p e r a t u r e dependence of : 0 . 8
t h e f l u o r e s c e n c e q u a n t u m e f f i c i e n c y QE o f r u b y . The PA
v a l u e s a r e o b t a i n e d u n d e r t h e 0 . 7 a s s u m p t i o n g i v e n i n t h e t e x t . The
(1.6
o p t i c a l d e t e r m i n e d v a l u e s a r e s c a l e d f o r QE=0.8 a t 300K. The
m u l t i p h o n o n r e l a x a t i o n c u r v e 0 . 5
I n m n c l u s i o n , we have shown t h a t modulation frequency s p e c t r a a r e a r e l i a b l e method
-
t o determine l i f e t i m e s of metastable s t a t e s i n solids. The q u a n t i t a t i v e c o r r e l a t i o n with o p t i c a l d a t a i n d i c a t e s t h a t i n ruby t h e ' T ~ + ~ A Z r e l a x a t i o n can n o t k e neglected above 250K.-
-
PHOTORCOUSTIC-.-I-. nULIIPHOr(ON R E L R X R i l O l l + RELRTIUE OE
(OPTICRLLI OETERIIINED)
-
- +.\
- +'i.
'.4
So t o m . c ZOO i J~~ r . +ell c 8soo
Acknowledgements: W e t h a n k W. Keller f o r h e l p f u l d i s c u s s i o n s and D. O t t e k e n f o r s k i l l f u l t e c h n i c a l assistance. This work was supported i n p a r t by NATO Grant No DMR 76-21574.
i n c l u d e s t h e t e m p e r a t u r e iEnPERRiURE ( X I
dependence of -rr-l.
References
[l
]
R.T. Brundage, W.M. Yen, Proceedings of2nd I n t e r n . Topical Meeting On Photoacoustic Spectroscopy, The Optical Society of America, Washington IX1981 [ 2 ] W.M. Yen, P.M. S e l z e r (4.):
Laser Spectroscopy of S o l i d s , Springer Verlag, B e r l i n 1981 [3] J.C. Murphy, L.C. Aamodt
J. Appl. Phys. 4 8 ( 8 ) , 3502-9 (1977) [4] M.B. Robin, N.A. Kuebler
J. Chem. Phys. %(1), 169-76 (1977)
[5J W. Keller, W. Schubert, R. Germer, E. S t r a u s s t h i s journal, preceding paper
161 D.F. Nelson, M.D. Sturge Phys. Rev.
137,
1117 (1965) [7] D.M. Dodd, D.L. Wood, R.L. BarnsJ. Appl. Phys.
35,
1183 (1964) [ 8 j M.D. SturgePhys. Rev. B
