ULTRASONIC ABSORPTION IN SOME HIGHLY ATTENUATING IONIC-MOLECULAR CRYSTALS

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ULTRASONIC ABSORPTION IN SOME HIGHLY ATTENUATING IONIC-MOLECULAR CRYSTALS

F. Michard, F. Plicque

To cite this version:

F. Michard, F. Plicque. ULTRASONIC ABSORPTION IN SOME HIGHLY ATTENUATING

IONIC-MOLECULAR CRYSTALS. Journal de Physique Colloques, 1981, 42 (C5), pp.C5-683-C5-

688. �10.1051/jphyscol:19815105�. �jpa-00220973�

ULTRASONIC ABSORPTION IN SOME HIGHLY ATTENUATING IONIC-MOLECULAR CRYSTALS

F . Michard and F. P l i c q u e

Lahoratoire D y n d q u e C r i s t a l l i n e e t Ultrasons, D.R.P., Tour 2 2 , Uiziversite' Pierre e t Marie Curie, 4 , pZaco Jussieu, 75230 Paris Cedex 05, France A b s t r a c t . - U n u s u a l l y h i g h v a l u e s o f t h e u l t r a s o n i c a b s o r p t i o n observed a t f r e q u e n c i e s below 1 GHz i n some i o n i c - m o l e c u l a r c r y s t a l s t h e s t r o n t i u m , baryum and l e a d n i t r a t e s i s a consequence o f t h e e x i s t e n c e o f complex i o n s i n t h e l a t t i c e . A c o u s t o - o p t i c a l i n t e r a c t i o n performed i n t h e f r e q u e n c y range 0.1 GHz

-

1 GHz and completed by d a t a o b t a i n e d a t about 20 GHz by B r i l l o u i n s c a t t e r i n g , a l l o w e d a v e r y complete s t u d y f r o m room t e m p e r a t u r e t o 4 K o f t h e dynamics o f energy t r a n s f e r between c o u p l e d i n t e r n a l and e x t e r n a l v i b r a t i o n a l modes i n t h e s e compounds.

The b e h a v i o u r o f t h e u l t r a s o n i c a b s o r p t i o n i n some i o n i c - m o 7 e c u l a r c r y s t a l s : t h e isomorphous c u b i c c r y s t a l s Sr, Ba and P b n i t r a t e s has been s t u d i e d v e r s u s f r e q u e n c y and temperature. Fleasurements have been performed f r o m room t e m p e r a t u r e t o 4 K u s i n g an a c o u s t o o p t i c t e c h n i q u e i n t h e f r e q u e n c y range 100 MHz

-

1 GHz (11

.

The i n t e r p r e t a t i o n o f t h e u n u s u a l l y h i g h v a l u e s o f t h e u l t r a s o n i c a b s o r p t i o n i n t h e s e i o n i c - m o l e c u l a r c r y s t a l s i s based on t h e c o e x i s t e n c e o f two main damping processes : t h e c l a s s i c a l A k h i e s e r mechanism 12) which o c c u r s i n d i e l e c t r i c c r y s t a l s and a supplementary t e r m c o r r e l a t e d w i t h t h e e x i s t e n c e o f complex i o n s i n t h e s e compounds. These two c o n t r i b u t i o n s a r e r e l a x a t i o n a l b u t w i t h e x t r e m e l y d i f f e r e n t v a l u e s o f t h e c h a r a c t e r i s t i c r e l a x a t i o n t i m e s .

I n d i e l e c t r i c c r y s t a l s t h e mechanism o f t h e u l t r a s o n i c a b s o r p t i o n was f i r s t l y d e s c r i b e d b y A k h i e s e r . F o r u l t r a s o n i c f r e q u e n c i e s much l o w e r t h a n

1 / < ~ > ( < T > mean phonon l i f e t i m e ) , t h e s t r a i n produced by t h e u l t r a s o n i c wave modu- l a t e s t h e f r e q u e n c i e s o f t h e thermal phonons and t h e r e f o r e t h e i r e q u i l i b r i u m popu- l a t i o n s . The r e e s t a b l i s h m e n t o f e q u i l i b r i u m r e s u l t s i n an a b s o r p t i o n o f t h e u l t r a - s o n i c wave w h i c h depends on t h e square o f t h e frequency and does n o t depend on t h e temperature.

I n case o f i o n i c - m o l e c u l a r c r y s t a l s t h e r e e s t a b l i s h m e n t o f t h e r m a l e q u i - l i b r i u m between t h e l a t t i c e modes and t h e i n t e r n a l modes o f t h e complex i o n s a r e c h a r a c t e r i z e d by a slow exchange o f energy w h i c h corresponds t o a r e l a x a t i o n t i m e

T = 2 k >> T and o f t h e o r d e r o f 1n8 t o 16' seconde.This mechanism f i r s t l y suggested by Liebermann 131 i n case o f p u r e l y m o l e c u l a r c r y s t a l s i s v e r y s i m i l a r t o t h e r e l a x a t i o n a l a b s o r p t i o n which o c c u r s i n p o l y a t o m i c gazes o r normal l i q u i d s 141

,

151.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19815105

JOURNAL DE _PHYSIQUE

Tableau 1

v

=

700

YHz

b

(--TI dB

cm GHz

k

(MHz)

u ^(dB/cm)

-

uv

(Ne~er) 2k

v 1 ~ 4 dB

2 ( X I

Ba (NO3I2

[loo] [lioJ

0.3 0.2 (3%) (3%) 11+1 7+1 4.2 3.0 (17%) (15%)

22 15

26+l 19fl

8.5 6.2

205 240

225 16

2 1

5 3

S r

(NO3I2 [loo] [lio]

0.1 0,l (0.5%) (0.7%) 19.5+1 14+1

1.3 1.2 (1%) (1.5%)

111 8 7 113+2 67+2

2.7 2.6

630 685

200 171

7 6

5 3.5

Pb (

PJO3 2

[loo] [iiol

0.3 0.25 (0.8%) (0.8%)

40+1 30+1

4.0 2.9 (4%) (4%)

86 7 2 95+2 75+2

8.2 6.0

225 260

94 8 2

7 5.5

19 12

7

where aA i s t h e Akhieser c o n t r i b u t i o n and aR t h e supplementary r e l a x a t i o n a l term.

The Akhieser c o n t r i b u t i o n aA = bv2 i s small r e l a t i v e t o oR a t frequencies below 1

GHz

b u t becomes dominant a t 20 GHz as i t i s shown by a t t e n u a t i o n data obtained by B r i l l o u i n s c a t t e r i n g (61 i n t h i s frequency range. We have used t h e B r i l l o u i n data t o o b t a i n t h e value of b and then used Eq. (1) t o f i n d aR from t h e observed absorp- t i o n . The r e s u l t i n g uR c o n t r i b u t i o n i s then described w i t h a s i n g l e r e l a x a t i o n form:

Where v i s the u l t r a s o n i c frequency, k i s an energy exchange frequency parameter (equal t o t h e r e l a x a t i o n frequency vR) a i s a r e l a x a t i o n s t r e n g t h which depends on t h e heat c a p a c i t i e s i n v o l v e d i n t h e r e l a x a t i o n process and 'J = ak corresponds t o t h e h i g h frequency l i m i t o f aR.

P l o t s o f aR/v vs.logv/k obtained a t 'aR'V/ (~RIv),

-

t h e o r i e room temperature i n case o f Sr, Ba and

(

SdNO3I2

295K BWO&

.

Pb n i t r a t e s a r e g i v e n i n F i g . 1.

( ^PWU03h

.

The experimental data agree q u i t e we1 1 w i t h t h e t h e o r e t i c a l curve. So t h e r e - s u l t s a r e c o n s i s t e n t w i t h the hypothe- s i s o f a supplementary r e l a x a t i o n process dominated by a s i n g l e r e l a x a - t i o n time. Some p l o t s o f a vs. T a r e given i n Fig. 2 and Fig. 3, we can observe the d r a s t i c a l l y decrease o f the u l t r a s o n i c a b s o r p t i o n a as t h e tem- log v/k p e r a t u r e T decreases

-

The parameters

Z

-0.5 o 0.5 a and k c h a r a c t e r i s t i c o f t h e term aR being temperature dependant. I n F i g . 3 we observe t h e change i n the regime of F i g u r e 1

propagation of t h e u l t r a s o n i c wave from t h e Akhieser t o t h e Landau-Rumer regime a t about 50 K. The two c o n t r i b u t i o n s aA and aR t o t h e whole damping a t room temperature and t h e values o f 11 and k c h a r a c t e r i s t i c s o f the aR term a r e given i n t a b l e 1 i n case o f l o n g i t u d i n a l u l t r a s o n i c waves propagating along [100] and

[I101 f o r two d i f f e r e n t frequencies. As shown i n t a b l e 1 the Akhieser c o n t r i b u t i o n i s very s i m i l a r i n case o f Ba (N03)2 and Pb (N03)2 and g r e a t e r than f o r Sr (N03)2.

JOURNAL DE PHYSIQUE

F i g u r e 2 F i g u r e 3

T h i s p o i n t i s o b v i o u s i n F i g . 4 where e x p e r i m e n t a l and t h e o r e t i c a l v a l u e s o f l o g a vs. l o g v a r e p l o t t e d . F o r u l t r a s o n i c f r e q u e n c i e s o f t h e o r d e r o f 30 GHz t h e A k h i e s e r process dominates and t h e t h e o r e t i c a l c u r v e s o b t a i n e d i n case o f Ba (N03)2 and Pb (NO3)* a r e s i m i l a r . T h i s r e s u l t i s c o n s i s t e n t w i t h t h e f a c t t h a t t h e v i b r a - t i o n a l c o n t r i b u t i o n t o t h e t e m p e r a t u r e dependance o f t h e second o r d e r e l a s t i c c o n s t a n t s ( a C . ./aT),, i s more i m p o r t a n t i n case o f Ba (N03)2 and Pb (N03)2 t h a n f o r

1 J

S r (P103)2 171 181. F u r t h e r m o r e a n i s o t r o p y o f t h e u l t r a s o n i c damping i s e x h i b i t e d b y b o t h c o n t r i b u t i o n s .

Because o f t h e r e l a x a t i o n a l energy exchange w i t h t h e i n t e r n a l degrees o f freedom, t h e h e a t c a p a c i t y may n o t have i t s s t a t i c value. I n s t e a d , t h e r e i s an e f - f e c t i v e h e a t c a p a c i t y , w h i c h i s a complex q u a n t i t y :

where C i s t h e s t a t i c h e a t c a p a c i t y and C' t h a t p a r t o f i t w h i c h i s s l o w l y r e l a x i n g c o r r e s p o n d i n g t o t h e i n t e r n a l modes w h i c h a r e i n v o l v e d i n t h e exchange process. The e x p r e s s i o n o f aR i n terms o f h e a t c a p a c i t y i s g i v e n by ( 3 1 :

Tableau 2

l ^{a (db~crn}

⁾ w i t h t h e i n t e r n a l modes a r e e v a l u a t e d w i t h d a t a g i v e n i n Ref. 191 as a f u n c -

%(NO3) ² [loo]

l/

t i o n o f t e m p e r a t u r e i n t a b l e

2.

They 1 04!

Ba(No3)

2 a r e compared w i t h t h e t h e o r e t i c a l eva-

103

lo2.

70

.

^{Pb(N03) 2}

)' /

l u a t i o n o f C ' a s s o c i a t e d w i t h t h e l o w e s t

-

t h e o r e t i c a l

.

^/ i n t e r n a l mode u 4 (735cs1). The b e h a v i o u r

1.1

/ ,

^{o f C '} as a f u n c t i o n o f t e m p e r a t u r e i s e x p

v e r y c l o s e f r o m t h a t o f C I t h , b a c k i n g up t h e mechanism o f r e l a x a t i o n we p u t

A''

f o r w a r d .

The t e m p e r a t u r e dependance o f

/ t h e exchange f r e q u e n c y parameter k

/;

^'/ f o l l o w s an e x p o n e n t i a l l a w w i t h an a c t i -

1 9 6 ' v a t i o n energy AE c l o s e t o t h e v a l u e

I/!'

h u4 = 1.20 x loZ0 j o u l e c o r r e s p o n d i n g t o t h e energy o f t h e l o w e s t i n t e r n a l

I mode v4. T h i s suggests t h a t t h e exchange

V~MHZ)

102 103 104 of energy between t h e l a t t i c e and t h e

i n t e r n a l modes t a k e s p l a c e v i a t h e l o -

F i ~ u r e 4 west i n t e r n a l mode.

5-688 JOURNAL DE PHYSIQUE

I n o t h e r r e s p e c t s , t h e l o w e r v a l u e s o f k a r e observed i n case o f Ba(N03)2 and Pb(N03)2, t h i s p o i n t may be c o r r e l a t e d w i t h t h e weakness o f t h e i n t e r i o n i c bonds observed i n t h e s e compounds 1101 l e a d i n g t o a s l o w e r process o f energy exchange.

F u r t h e r m o r e we must p o i n t e d o u t t h e s i g n i f i a n t v a l u e o f t h e i o n i c p o l a r i z a b i l i t y encountered i n t h e s e compounds w h i c h perhaps be t a k e n i n t o account t o e x p l a i n t h e a n i s o t r o p y o f k : kOOll[ > kLllOj. Such a n i s o t r o p y i s n o t c o n t a i n e d i n L i e b e r m a n n ' s t h e o r y . To t e s t t h i s h y p o t h e s i s t h i s work must be e n l a r g e d t o o t h e r i o n i c - m o l e c u l a r c r y s t a l s ; t h e f r e q u e n c y range f r o m 0 . 1 t o 20 GHz seems t o be i d e a l f o r s t u d y i n g t h e dynamics o f energy t r a n s f e r between c o u p l e d i n t e r n a l and e x t e r n a l v i b r a t i o n a l modes i n t h e s e compounds.

Acknowledgments.

We w i s h t o thank J. CHAPELLE, J.P. MATHIEU, J.L. RIBET f o r k i n d l y p r o v i d i n g t h e c r y s t a l s and E. VERNAZZA who o r i e n t a t e d and p o l i s h e d t h e samples.

We a r e e x t r e m e l y g r a t e f u l t o A. ZAREMBOWITCH who i n i t i a t e d t h i s work, f o r many s t i m u l a t i n g d i s c u s s i o n s . We a l s o t h a n k B. PERRIN f o r many v a l u a b l e comments.

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1

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(21 A. AKHIESER J . Phys. U.S.S.R., 1, 277, ( 1 9 3 9 ) .

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89, (1976).

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1093 (1978).

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⁵⁷² - 576 (1973).

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