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Submitted on 1 Jan 1978
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DIRECT EXPERIMENTAL OBSERVATION OF
SPECTRAL DIFFUSION IN VITREOUS SILICA AT
LOW TEMPERATURES
W. Arnold, C. Martinon, S. Hunklinger
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-961
DIRECT EXPERIMENTAL OBSERVATION OF SPECTRAL DIFFUSION IN V I T R E O U S SILICA AT LOW TEMPERATURES
W. Arnold, C. Martinon and S. Hunklinger
Max-Planek-Institut fur Festkorperforsehung, 7 Stuttgart, West Germany
Résumé.- Nous présentons des expériences de "hole burning" acoustique dans de la silice vitreuse à 0.5 K. Une forte dépendance en temps est observée et est interprétée en termes de diffusion spectrale.
Abstract.- We have carried out acoustic "hole burning" experiments in vitreous silica at 0.5 K. A strong time dependence was observed and is interpreted in terms of spectral dif-fusion.
The anomalous thermal /!/ and acoustic HI properties of glasses at low temperatures can be explained by the existence of two-level systems (2LS). These states are assumed to arise from the configurational disorder present in the network of amorphous materials. In a more specific model /3/ the 2LS are ascribed to particles (of still un-known nature, but probably groups of atoms) moving in double well potentials. Transitions from one well to the other are possible even at the lowest
temperatures via tunneling. The parameters characterizing such double well potentials exhibit -within certain limits - a random distribution of their values caused by the randomness of the amor-phous network. The result is a broad, approximately constant density of states of the energy splitting of these 2LS.
The dynamic properties of glasses at low temperatures are governed by the strong coupling between the 2LS and elastic strains /3/. Measure-ments of the phonon mean free path by ultrasonic
techniques have demonstrated that the resonant absorption and emission of phonons is the dominant interaction. This process not only explains the low thermal conductivity but also the temperature variation of the sound velocity and above all the power dependence of the ultrasonic absorption / 2 , 4/ : Below a critical intensity I the population of the two states is not influenced and therefore the acoustic absorption is found to be power-inde-pendent. With increasing intensity, however, both levels become more and more equally populated leading to a decrease of the acoustic attenuation, i.e. saturation occurs. For example Ic=10~^W/cm2
in vitreous silica at 750 MHz and T = 0-5 K. The 2LS not only couple to external strains, but also to each other via internal strains/5-6/ : a 2LS located at site i feels the strain field of a 2LS at site j . Because of the broad energy distri-bution of the 2LS and their random spatial arrange-ment, an interaction between 2LS of equal energy splitting is very improbable. The coupling discussed here mainly occurs between 2LS of different energy. Driven by thermal agitation transitions between the two states of a 2LS take place continuously. This transitions modulate the local strain field surroun-ding a 2LS and lead to a temporal fluctuation of the energy splitting of neighbouring 2LS. This interac-tion gives rise to a considerable broadening of the resonance line observed in ultrasonic "hole burning" experiments/6/.
Here we report on the temporal aspect of the interaction, which has not been experimentally studied so far. Since the level splitting E of a 2LS is a time dependent quantity interesting effects occur when the characteristic times of the energy fluctuations become comparable with the time of observation / 7 / . The fluctuation of the energy of a given 2LS depends on the relaxation time of its neighbouring 2LS.
At T = 0.5 K this relaxation time is of the order of microseconds. Ultrasonic experiments pro-bing the energy splitting on this time scale should therefore reveal time dependent effects.
In this paper we report on the first direct experimental study of this problem : Two acoustic pulses P, and P„ of variable duration (between 0.3 and 1.2us) and of different power I (Ii»I >I2)
were g e n e r a t e d i n a sample of v i t r e o u s s i l i c a ( S u p r a s i l I ) . Both p u l s e s t r a v e l t o g e t h e r t h r o u g h t h e sample. We measured t h e change of t h e r e s o n a n t a t t e n u a t i o n of t h e weak t e s t p u l s e P2 a s a function o f t h e f r e q u e n c y of t h e s t r o n g s a t u r a t i n g p u l s e P 1 . The time dependence of t h e e f f e c t was s t u d i e d by v a r y i n g t h e w i d t h of t h e u l t r a s o n i c p u l s e s a p p l i e d i n t h e experiment. S i m i l a r t o e x p e r i m e n t s c a r r i e d o u t pre- v i o u s l y , a broad minimum i n t h e a t t e n u a t i o n of t h e p r o b i n g p u l s e o c c u r s a t f r e q u e n c i e s c l o s e t o t h e f r e q u e n c y of t h e s a t u r a t i n g p u l s e ( s e e F i g u r e 1 ) . The w i d t h of t h e l i n e i s much l a r g e r t h a n expected from t h e f r e q u e n c y u n c e r t a i n t y of t h e u l t r a s o n i c p u l s e s o r t h e f i n i t e l i f e t i m e s of t h e 2LS. VITREOUS SILICA a6650 700 750 600 6 9 900 F i g . 1 : V a r i a t i o n of t h e r e s o n a n t a b s o r p t i o n of t h e weak p r o b i n g p u l s e P a s f u n c t i o n o f t h e s a t u - r a t i n g p u l s e P I f o r two 8 i f f e r e n t p u l s e d u r a t i o n s T ~ . Furthermore, t h e l i n e w i d t h depends on t h e d u r a i ~ i o n of t h e a p p l i e d p u l s e : w i t h i n c r e a s i n g T P t h e l i n e becomes w i d e r . T h i s r e s u l t i s shown more q u a n t i t a t i v e l y i n f i g u r e 2 where t h e l i n e w i d t h i s p l o t t e d as a f u n c t i o n of t h e p u l s e d u r a t i a n T P ' THEORY
-
0 05 1 15 PULSE WIDTH I w s l F i g . 2 : Observed l i n e w i d t h i n v i t r e o u s s i l i c a a t 0.42 K a s a f u n c t i o n of t h e p u l s e d u r a t i o n T P' Dashed l i n e r e p r e s e n t s t h e t h e o r e t i c a l p r e d i c t i o n of 171. T h i s e x p e r i m e n t a l r e s u l t c a n b e d e s c r i b e di n terms of s p e c t r a l d i f f u s i o n 171. The energy r a - d i a t e d i n t o t h e ensemble of 2LS w i t h a n energy s p l i t t i n g c l o s e t o t h e energy of t h e u l t r a s o n i c phonons i s a b l e t o d i f f u s e t o t h e wings of t h e l i n e d u r i n g t h e p r o b i n g time r The maximum l i n e -
P'
w i d t h i s g i v e n by t h e e n e r g y of i n t e r a c t i o n b e t - ween t h e 2LS :
AE = hAvm = P2/r3j
where p i s t h e a v e r a g e e l a s t i c d i p o l e moment asso- c i a t e d w i t h t h e 2LS and r i j i s t h e d i s t a n c e between t h e 2LS l o c a t e d a t s i t e i and j , r e s p e c t i v e l y . A d e t a i l e d a n a l y s i s o f t h e t i m e e v o l u a t i o n of t h e l i n e h a s been c a r r i e d o u t by Black and H a l p e r i n 171 and l e a d s t o t h e e x p r e s s i o n : Av ( t ) = Av,f(t) The f u n c t i o n f ( t ) d e s c r i b e s , how t h e h o l e b u r n t i n t o t h e p o p u l a t i o n of t h e 2LS d e v e l o p s w i t h t i m e t . It depends m a i n l y o n t h e d i s t r i b u t i o n of t h e b a r r i e r h e i g h t s of t h e double w e l l p o t e n t i a l s mentioned above. I n f i g u r e 2 t h e dashed l i n e r e - p r e s e n t s a n u m e r i c a l c a l c u l a t i o n I 7 1 which i s i n good q u a n t i t a t i v e agreement w i t h o u r r e s u l t s . A d i s t r i b u t i o n i n which t h e h i g h e r b a r r i e r s a r e more pronounced would even l e a d t o b e t t e r agreement.
I n summary we have demonstrated f o r t h e f i r s t time t h a t t h e l i n e w i d t h observed i n a c o u s t i c "hole burning" experiments i s time dependent i n g l a s s e s . The e x p e r i m e n t a l r e s u l t s g i v e new i n f o r - m a t i o n on t h e dynamic b e h a v i o u r of t h e low-energy e x c i t a t i o n s p r e s e n t i n g l a s s e s and a r e i n good agreement w i t h t h e o r e t i c a l c a l c u l a t i o n s . R e f e r e n c e s
111
S e e f o r e x a m p l e : S t e p h e n s , R.B., Phys. R e v . E 3 (1976) 852./ 2 / See f o r example : Hunklinger, S., and Arnold, W . , i n P h y s i c a l A c o u s t i c s , Mason, W.P.and T h u r s t o n , R.N. ( e d s . ) , (Academic P r e s s , New York) 1976, Vol. 12, p.155.
131 Anderson, P.W., H a l p e r i n , B . I . , and Varma,C.M., P h i l . Mag.
5
(1972) 1 ; P h i l l i p s , W.A., J . Low Temp. Phys. l ( 1 9 7 2 ) 351.1 4 1 Golding, B., Graebner, J.E., and S c h u t z , R . J .
Phys. Rev. (1976) 1660.
151 J o f f r i n , J. and L e v e l u t , A . , J . Physique
2fi
' (1975) 831.1 6 1 Arnold, W. and Hunklinger, S., S o l i d S t a t e Commun. ( 1975) 883.
