INTERNAL FRICTION AND ACOUSTIC EMISSION DUE TO CHARGE DENSITY WAVES

HAL Id: jpa-00225354

https://hal.archives-ouvertes.fr/jpa-00225354

Submitted on 1 Jan 1985

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

INTERNAL FRICTION AND ACOUSTIC EMISSION

DUE TO CHARGE DENSITY WAVES

M. Doyama

To cite this version:

M. Doyama.

INTERNAL FRICTION AND ACOUSTIC EMISSION DUE TO CHARGE

JOURNAL DE PHYSIQUE

Colloque C10, suppl6ment au n012, Tome 46, dgcembre 1985

page

(210-669

INTERNAL FRICTION AND ACOUSTIC EMISSION DUE TO CHARGE DENSITY WAVES

M.

DOYAMA

Department o f Metallurgy and Materials Science, Faculty of

Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku,

Tokyo 113, Japan

A b s t r a c t

-

Much a t t e n t i o n has been p a i d t o t h e charge d e n s i t y waves

which a r e observed i n low-densional conductors. The e l a s t i c

behavior i n connection w i t h t h e f o r m a t i o n o f charge d e n s i t y waves i s reviewed. The change i n i n t e r n a l f r i c t i o n due t o the f o r m a t i o n o f

charge d e n s i t y wawes i s discussed. R e s u l t s on a few experiments on

the a c o u s t i c emission due t o the f o r m a t i o n of charge d e n s i t y waves

a r e presented.

I

-

INTRODUCTION

Low dimensional m a t e r i a l s have received c o n s i d e r a b l e a t t e n t i o n i n r e c e n t years because o f t h e i r c h a r a c t e r i s t i c p r o p e r t i e s based on t h e low dimension- a l i t y . The n a t u r a l m a t e r i a l s which have layered s t r u c t u r e s such as mica o r g r a p h i t e have been known f o r many years.

Recently some m a t e r i a l s a r e a r t i f i c i a l l y synthesized,for example TTF.TCNQ

( T e t r a t h i a f u l v a l e n c e - T e t r a c y a n o q u i n o d i m e t h a n e as one dimensional s t r u c t u r e polymers, one dimensional s t r u c t u r e t r a n s i t i o n metal t r i c h a l c o g e n i d e s , two d i - mensional s t r u c t u r e t r a n s i t i o n metal dichalcogenides and g r a p h i t e i n t e r c a l a - t i o n . Some o f t h e g r e a t i n t e r e s t s a r e concerned w i t h t h e P e i e r l s t r a n s i t i o n ,

charge d e n s i t y waves and super conductors based on t h e F r o h l i c h mechanism.

Consider a one-dimensional metal conductor. L e t t h e l e n g t h o f a u n i t

c e l l be a. The r e l a t i o n between t h e k i n e t i c energy o f conduction e l e c t r o n s E and the wave number k i s g i v e n by F i g . l ( a ) . When the l a t t i c e i s d i s t o r t e d

w i t h a p e r i o d o f D which i s l a r g e r than a, then energy gap can be c r e a t e d as

shown i n F i g . 1 ( b ) .

I f t h e conduction e l e c t r o n system i s s t a b i l i z e d by t h i s l a t t i c e d i s t o r - tion,and t h e s t a b i l i z e d energy i s l a r g e r than t h e energy o f l a t t i c e d i s t o r t i o n , then t h i s process spontaneously occurs. The n e t energy g a i n may be t h e l a r g e s t when the p e r i o d o f l a t t i c e d i s t r o t i o n D s a t i s f i e s t h e c o n d i t i o n kF =

_+

mn/ D,

where k, i s t h e Fermi wave number,m i s an i n t e g e r . I f t h i s energy gap i s form-

Fig. 1 . Energy gap i n a

one-dimensional l a t t i c e (a) With p e r i o d i c poten- (b) W i t h p e r i o d i c poten- t i a l and p e r i o d i c s t r a i n

C10-670 JOURNAL

DE

PHYSIQUE

ed a t t h e Fermi energy,the conductor becomes an i n s u l a t o r . T h i s i s t h e P e i e r l s

t r a n s i t i o n . At h i g h e r temperatures, t h i s energy gap w i l l disappear because o f

t h e d i s t u r b a n c e due t o the thermal energy o f l a t t i c e v i b r a t i o n s . The r e l a t i o n

k T = 1.14 EB exp ( - 1/ A) (1)

has been given, where h = v 2 D(EF)/(2Nw

'1.

(2)

k i s t h e Boltzmann constant, EB i s $bout t h e energg o f t h e band w i d t h , v t h e

p e r t u r b a t i o n p o t e n t i a l , w frequency o f t h e l a t t i c e , N t h e t o t a l numb& o f u n i t c e l l s , D ( E ~ ) t h e densiqy o f s t a t e s a t Fermi energy. The band gap E(T) i s

w r i t t e n as AE(T) = ( A D ( E ~ ) / z ) I n (1.14 E ~ / ( ~ T ) ) (3)

f o r one dimensional metals. A i s a constant r e p r e s e n t i n g a m a t r i x element.

F i g u r e 2(a) shows t h e l a t t i c e d i s t o r t i o n , F i g s . 2 (b) and (c) show t h e s t a b l e and u n s t a b l e e l e c t r o n d i s t r i b u t i o n p r o b a b i l i t i e s , which correspond t o Q and Q'

s t a t e s i n F i g . l ( b ) , r e s p e c t i v e l y . T h i s e l e c t r o n wave o f conduction and r a r e -

f a c t i o n is c a l l e d charge d e n s i t y wave (cDW). When t h e wave l e n g t h o f charge

d e n s i t y wave becomes a simple m u l t i p l e o f l a t t i c e p e r i o d i c i t y , t h e CDW i s c a l l - ed commensurate CDW (CCDW) ,when i t i s n o t a simple m u l t i p l e , t h e CDW i s c a l l e d inommensurate CDW (ICDW). The e l a s t i c s t r a i n i s lower f o r t h e commensurate CDW

than ICDW. Therefore I C D W o f t e n changes t o CCDW a t a lower temperature. The

t r a n s i t i o n from ICDW t o CCDW i s c a l l e d t h e l o c k - i n o f CDW. The speed o f e l e c - t r o n s a t Fermi l e v e l i s u s u a l l y q u i t e f a s t , much f a s t e r than t h e v e l o c i t y o f

l a t t i c e waves. The group v e l o c i t y o f e l e c t r o n s , however, i s zero. The e l e c -

t r o n system i s s t a b i l i z e d by t h e l a t t i c e d i s t o r t i o n o f s p e c i a l wave l e n g t h . For t h e l a t t i c e v i b r a t i o n o f t h i s wave l e n g t h , t h e d i s t o r t i o n becomes e a s i e r . The e l a s t i c constant becomes lower o r t h e l a t t i c e becomes s o f t e r f o r t h i s v i - b r a t i o n o f t h i s wave l e n g t h . T h i s e f f e c t i s d i s t i n c t , p a r t i c u l a r l y f o r one d i -

mensional conductors as shown i n F i g . 3. T h i s i s c a l l e d g i a n t Kohn anomaly.

The e l a s t i c c o n s t a n t changes a t t h e CDW t r a n s i t i o n temperature. T h i s

e f f e c t has been measured i n many low dimensional m a t e r i a l s . I n some m a t e r i a l s ,

p r e t r a n s f o r m a t i o n changes, even above t h e t r a n s i t i o n temperature have been

observed, such as t h e changes i n t h e l a t t i c e constant o r l a t t i c e s o f t e n i n g . At a b s o l u t e z e r o K e l v i n , CDW has a d e f i n i t e a m p l i t u d e and phase. At a f i n i t e temperature t h e amplitude and phase o f CDW have f l u c t u a t i o n s . These a r e c a l l e d a m p l i t u d e mode and phase mode, r e s p e c t i v e l y . The phase mode i s c a l l e d a

phason. The d i s p e r s i o n r e l a t i o n o f t h e modes ( q-w ) a r e shown i n F i g .

4.

The o r d e r parameter o f CDW can be w r i t t e n as $ = A exp ( i @ )

( 4 )

where A i s t h e a m p l i t u d e and

6

i s t h e phase. Above T1(CDW t r a n s i t i o n temper-

a t u r e ) $ = 0.

To s a t i s f y eq

(41,

t h e r e a r e two p o s s i b i l i t i e s . 1 ) t h e amp1 i t u d e A becomes z e r o

o r 2) t h e phase @ becomes random.

T r a n s i t i o n metals (M: T i , Z r , H f ; V, Nb, Ta; Mo, W) and chalcogens form

MX2 and MX3 compounds. MX2's a r e t h e layered dichalcogenides which e x h i b i t two- dimensional a n i s o t r o p i c p r o p e r t i e s and associated e l e c t r o n i c i n s t a b i l i t i e s . E l e c t r o n - d i f f r a c t i o n s t u d i e s revealed t h e e x i s t e n c e o f super l a t t i c e s t r u c t u r e s

which a r e a t t r i b u t e d t o t h e f o r m a t i o n o f charge-density waves. The metal

c o o r d i n a t i o n w i t h i n a l a y e r may be o c t a h e d r a l o r t r i g o n a l p r i s m a t i c , and t h e I F i g .

3.

D i s p e r s i o n r e l a t i o n o f .phonons i n TTF.TCNQ and observed g i a n t Kohn anomaly. Fig.2. Two standing wave s t a t e s caused

by p e r i o d i c l a t t i c e s t r a i n s (a) L a t t i c e l o n g i t u d i n a l waves, (b) E l e c t r o n d i s t r i -

₂

b u t i o n o f s t a b l e s t a n d i n g waves, ( c ) ~ l e c -

₂

t r o n d i s t r i b u t i o n o f u n s t a b l e s t a n d i n g P. O0

'm

k h 2 6~

waves.

l a y e r s a r e stacked i n v a r i o u s ways, p o l y t y p e s ( l H , 2H, 4Hb,

....

) . The b a s i c s t r u c t u r e o f l a y e r e d t r a n s i t i o n metal dichalcogenides i s t h a t t h e hexagonal

t r a n s i t i o n metal l a t t i c e i s sandwiched by two l a y e r s o f hexagonal chalcogens.

T h i s b a s i c s t r u c t u r e i s m u l t i p l y e d by s t a c k i n g . There a r e two b a s i c s t r u c t u r e s , o c t a h e d r a l and t r i g o n a l p r i s m types ( ~ i g .

5 ) .

1T t y p e c o n s i s t s o f o c t a h e d r a l b a s i c s t r u c t u r e s , o n l y . 2H and 3R t r i g o n a l prisms o n l y . I n 4 H ( b ) 6 ~ , o c t a h e d r a l and t r i g o n a l p r i s m a r e mixed. T r a n s i t i o n t r i - c h a l c o g e n i d s form whiskers and e x h i b i t one-dimensional a n i s o t r o p i c p r o p e r t i e s . The e l e c t r i c a l c o n d u c t i v i t y i s much h i g h e r i n t h e d i r e c t i o n of t h e a x i s o f whiskers b u t much lower i n t h e p e r p e n d i c u l a r d i r e c t i o n s t o t h e a x i s o f whiskers. The c r y s t a l s t r u c t u r e o f CDW phases have been s t u d i e d by e l e c t r o n d i f f r a c t i o n and e l e c t r o n microscopy. The i n t e r r e l a t i o n o f t h e e l a s t i c modulus, thermal expansion c o e f f i c i e n t s , and spe-

c i f i c heat has been c a l c u l a t e d /I/.

Sato e t a1 /2/ measured t h e momentum d i s t r i b u t i o n o f e l e c t r o n s i n IT-TaS2 and 2H-TaSe2 f o r t h e two c r y s t a l d i r e c t i o n s as a f u n c t i o n o f temperature by

t h e Doppler broadening technique o f p o s i t r o n a n n i h i l a t i o n . I n IT-TaS2, an

observed change a t 220K i s a s c r i b e d t o t h e l a t t i c e expansion a l o n g t h e c - a x i s ,

and t h e o t h e r change a t 350K t o t h e vanishing o f a p a r t o f t h e Fermi surface,

b o t h a r e caused by t h e commensuration o f CDW ( F i g . 6 ) . Below lOOK an e f f e c t o f

Anderson l o c a l i z a t i o n was observed. I n 2H-TaSe2 a c l e a r change was observed

below 122K which i s ascribed t o t h e onset o f CDW ( F i g .

7 ) .

F i g

F i g

lampl i t u d e modes phase modes

I

.

4. C o l l e c t i;e modes o f CDW.

Van d e r Wall ;-gap

-. .-

t l g .

>.

C r y s t a l s t r u c t u r e o f MX, " o c t a h e d r a l t r igonal

-

a , ' . 1 1 - 7 a s 2 cl 3 .*a.

-

I . . \

....

-. ow L0.2

-

'Y w ‘0.0 I- W ZT

2

39.6

2

19.d: I V) 34.8. 38.6. I . a

,.*..'

-

.

#

--

.

_+- W -CCOW-' ICON* -Nor m a -l

..:

.d. W L1.L . . , , : : : :

.

.-

.

,'

..:.:

.-,.

L."'

:.I

'

39.1 - C N a - c m .I*ECD"-.+,CDI- . :

..,1 :

!

; -a cu ul

.

,....

-CCOW+ .ICOWI +---Nor m a I-

"....' 38.7

&

'

*.

.

*-... 120 160 200

.

*.*,...

_{TEMPERATURE (K)}

- c m -*cwa +-(W-- Fig.7. Temperature dependence o f t h e Doppler

100 200 300 400 broadening S-parameter a l o n g the conducting

TEMPERATURE (K) d i r e c t i o n ( c ) ; upper curve, and along t h e

-6.

Temperature dependence of the p e r p e n d i c u l a r d i r e c t i o n ( c / / ) ;lower curve, i n

(210-672 JOURNAL

DE

PHYSIQUE

TEMPERATURE (K) F i g . 10. Temperature dependence o f t h e modulus and i n t e r n a l f r i c t i o n i n 2H- TaSe2

/ 6 / .

410 17.9 1za 121 TEMPERATURE (K)

Fig.11. Modulus and i n t e r n a l f r i c t i o n near t h e incommensurate t r a n s i t i o n i n 2H-TaSe2 /6/. F i g . 9. Low temperature - - I anomaly i n p l a t e and Young's mod- u l u s v e l o c -

- -

i t i e s f o r TTF.TCNQ /5/. 6 o v

-

--3 a. > \ LL > - - 4 -4 TEMPERATURE (K)

I I

-

CHANGES IN ELASTIC CONSTANTS DUE TO CDW TRANSITIONS

The e l a s t i c c o n s t a n t s change a t t h e CDW t r a n s i t i o n temperatures.

TTF-TCN : Barmatz e t a1 /3/ observed an anomaly o f Young's modulus i n TTF-TCNQ

a t abouP3SK. l s h i g u r o e t a1

/4/

measured t h e change i n Young's modulus along

t h e b - a x i s i n TTF-TCNQ as shown i n F i g .

8.

They observed an anomaly a t 53.5K

corresponding t o t h e anomaly i n t h e e l e c t r i c a l c o n d u c t i v i t y . T h i s anomaly i s r e l a t e d t o t h e metal-non metal t r a n s i t i o n . The sound v e l o c i t i e s as a f u n c t i o n o f temperature have been measured as shown i n F i g . 9 /5/.

2H-TaSe2: The temperature dependence o f t h e modulus i n 2H-TaSe2 i s shown i n

F i g s . l O , l l , l 2 /6/. A small e l a s t i c anomaly o c c u r s a t t h e incommensurate t r a n s i - t i o n near 121K, w h i l e a much l a r g e r anomaly t a k e s p l a c e a t t h e commensurate t r a n s i t i o n near 90K. A small h y s t e r e s i s has been found a t 121K t r a n s i t i o n , t h i s

i n d i c a t e s t h a t t h i s t r a n s i t i o n i s a second o r d e r t r a n s i t i o n . U n u s u a l f e a t u r e o f t h e modulus behavior a t t h e I C D W t r a n s i t i o n i n TaSeZ i s t h e shape o f i t s tem-

p e r a t u r e dependence. The temperature dependence i s expected t o be t h e same as

t h e s p e c i f i c heat anomaly near t h e t r a n s i t i o n temperature. F i g u r e 12 shows a

l a r g e e l a s t i c h y s t e r e s i s ( sSK) which c l e a r l y demonstrates t h e f i r s t - o r d e r c h a r a c t e r o f 2H-TaSe2 90K t r a n s i t i o n . F i g u r e 12 shows t h a t t h e d i f f e r n e c e i n t h e temperature o f t h e modulus minimum a t each frequency i n d i c a t e s t h a t e l a s - t i c h y s t e r e s i s a t t h i s t r a n s i t i o n i s frequency dependent. E l a s t i c anomalies

a r e a l s o observed a t 122K (TO) and 90K (Td)

/7/.

2H-NbSe2:Barmatz e t a1/6/ measured t h e change i n t h e e l a s t i c constant i n NbSe2.

F i g u r e 13 shows t h e temperature dependence o f t h e reed modulus i n 2H-NbSe2.

5 , I I

,

8 , 1 2 5 . . I

.*..

I '**.

.

OAL SAMPLE

-

=

----

% \ \ 0- .**...

..

\ i

"\

\.

-

:

--,

4r \

----

-1

:

Z -

''?\

VBC SAMPLE 23 \ \

A

a:

6b

go B 1.5 1 4 a 3 5 0 4 0 5 0 6 0 7 0 TEMPERATURE ( K )

T(KI 'TELPERI- (KI

-

Fig.14. R e l a t i v e change i n Young's Fig.15. I n t e r n a l f r i c t i o n f o r TTF.TCNQ as

modulus v e r u s t e m p e r a t u r e f o r ZrTe5/1 3/. a f u n c t i o n o f t e m p e r a t u r e /3/.

TCYPCRA1UI)C (It)

Fig.12. Continuous h e a t i n g and c o o l i n g Fig.13. Modulus and i n t e r n a l f r i c -

c u r v e s o f t h e e l a s t i c p r o p e r t i e s n e a r t i o n near t h e incommensurate t r a n -

t h e commensurate t r a n s i t i o n i n 2H-TaSe2/6/. s i t i o n i n 2H-NbSe2/6/.

The modulus reaches a minimum a t t h e incommensurate CDW t r a n s i t i o n a t 2 9 . 8 ~ . The h y s t e r e s i s was f a i r l y l a r g e , about 5K; t h i s i n d i c a t e s t h a t t h i s t r a n s i t i o n i s t h e f i r s t o r d e r . S k o l n i c k e t a1/8/ measured t h e apparent v e l o c i t y o f t r a n s - v e r s e sound p r o p a g a t i n g p e r p e n d i c u l a r l y t o t h e l a y e r p l a n e s i n NbSeZ. They found a n anomaly a t t h e r e g i o n around t h e incommensurate CDW phase t r a n s i t i o n .

TaS3:

B r i l l

/9/

measured t h e change i n t h e modulus i n TaSe3 n e a r t h e c h a r g e

d e n s i t y wave t r a n s i t i o n a t 222K. The modulus has a l a r g e d i p ( 2%) a t t h e

t r a n s i t i o n . The t r a n s i t i o n was t h e second o r d e r u n l i k e NbSe3.0rthorhombic TaS3

(0-TaS3) undergoes a c h a r g e d e n s i t y wave t r a n s i t i o n a t 220K. A number o f un-

u s u a l t r a n s p o r t p r o p e r t i e s , most p r o m i n e n t l y non-Ohmic c o n d u c t i v i t y

/ l o / ,

when t h e e l e c t r i c f i e l d i n t h e sample exceedsa t h r e s h o l d f i e l d ET, w h i c h i s sample

and t e m p e r a t u r e dependent. A v a r i e t y o f p h y s i c a l models had success i n de-

s c r i b i n g t h e s e phonomena i n terms o f CDW m o t i o n . The CDW i s p i n n e d t o t h e l a t -

t i c e d e f e c t s f o r f i e l d s E ET and becomes depinned f o r E ET. B r i l l and Roark

/11/ measured t h e modulus under e l e c t r i c f i e l d . They found t h e decrease i n t h e modulus. T h i s suggests t h e d e p i n n i n g o f CDW.

NbSeL: B r i l l and Ong /12/ measured Young's modulus o f NbSe3. An anomaly i n

Young's modulus was observed a t T1 ( 1 4 2 ~ ) b u t n o t a t T2 ( 5 8 ~ ) . These t r a n -

s i t i o n s a r e second o r d e r because no h y s t e r e s i s was observed. A t a second-order

phase t r a n s i t i o n , t h e change i n Young's modulus E i (measured a l o n g t h e i t h

d i r e c t i o n ) i s r e l a t e d o t h e s p e c i f i c h e a t anomaly, Acp

₅

( ~ T C / ~ U ~ I ~ = (AE/Ei ) ( T c / Acp), where i i s t h e u n i a x i a l s t r e s s i n t h e i t h d i r e c t i o n and Tc i s t h e t r a n s i t i o n t e m p e r a t u r e .

ZrTe5: B r i l l and Sambongi/l3/ measured t h e change i n Young's modulus i n ZrTe5

as a f u n c t i o n o f t e m p e r a t u r e ( ~ i ~ . 1 4 ) . A s h a r p decrease i n modulus has been

C10-674 JOURNAL

DE

PHYSIQUE

observed at 84K. They did not observe any

anomaly near 140K where charge or spin 0 I I I I

_I

densit" waves are formed. AEIE

.

-2ApIp

I

1 1 1

-

INTERNAL FRICTION DUE TO CDW TRANS IT IONS.

CDW transitions.

The internal friction exhibits a peak at

TTF-TCNO: Barmatz et a1/3/ measured inter- '42 nal friction as a function of temerature.

They found a peak near 54K corresbonding -56

-

to the metal non-metal transition(Fig. 15). (a) I I I

\q

I

TaSe2: The internal friction in TaSe2 has I I I I

-

_{been measured by Barmatz et a1 /6/. At the}

_---

-

: 1st them1 cycling : 2nd r h e d Cyc1lng

commensurate chagge-densi ty-wave transit ion _,"

-

near 90K in TaSe2,the internal friction ex-

hibit extremum, whjch is an order of magni- 6 -

tude larger than the anomalies at the in-

L-

commensurate transit ion. At a1

1

the charge- O density-wavetransitions, the internal fric-

tion maximum occurs at a lower temoerature 2

-

-

than the modulus minimum. At the transi- ( b ) t I I

I

tion temperature the internal friction as- C 170 190 210 230 250 270

sociated with the transformation is finite

TEMPERATURE

( K)

and has a tail extending into the high tern-

Fig.16.1nternal

f r i c t i o n

and correspond- perature phase (Figs. 10,11, and 12). For a

_{i n g}

changes of the resonant period

i n

single relaxation process,the internal fric-

tion is represented by

Q-1

[ U,TI = A[TI [UT / (

1

(5)

where is the characteristic relaxation time for the process. The first over- tone internal-friction maximum is appoximately twice as far below TO as the fundamental internal friction maximum. In the loss at the transition the fundamental internal friction maximum is approximately four times larger than the first order maximum. The experimental results that for the lCDW transition in TaSe2, the acoustic loss is larger at the lower frequency is puzzling and nontrivial. Barmatz et a1 /6/ thought that such low relaxation frequencies are more characteristic of atomic loss mechanism such as diffusion point defects, dislocations,or macroscopic loss mechanism such as domain wall motion. Simpson et a1 /7/also obs ;ved attenuation peak at 90K and 121K.

1T-TaS2: Suzuki et a1 /14/ measured the internal friction in 1T-TaS2 as a function of temperature. On cooling, a wide damping peak at about 188K was observed, whereas on heating, a loss sharp maximum at about 220K appeared in the temperature ranges corresponding to the anomalies in modulus (Fig. 16). Comparing this with the heat capacity measurements, they suggested that the

960 Hz (Crystal 2) 4.0 I X 3.5 %

d

v (vdts) TEMPERATURE (K)

Fig.17. internal friction as a Fig.l8.(a) Relative change in modulus and (b) function of temperature near the change in

Q-1

vs voltage at several tempera-

Temp. (

K )

?20

Tc

( T a

Se,),

I

I I

12

5 -

I I 2 r 2 6 0

270

200

290

Temp.

( K

Fig.19. A c o u s t i c emission t o t a l F i g . 20. A c o u s t i c emission t o t a l counts

counts d u r i n g h e a t i n g i n IT-TaS2 d u r i n g h e a t i n g and c o o l i n g i n (TaSe4)21

/16/. /16/.

main peak i n h e a t i n g i s preceded by a p r e t r a n s i t i o n peak, w h i l e t h e main

damping peak can be i n t e r p r e t e d as the r e s u l t s o f i n t e r n a l s t r e s s induced by

t h e change o f t h e c r y s t a l symmetry.

TiSe2: A t t e n u a t i o n peak a t CDW t r a n s i t i o n has been observed / I S / .

-

TaS3: B r i l l

/

9/ measured i n t e r n a l f r i c t i o n i n TaS3 near t h e charge d e n s i t y

-

_{wave t r a n s i t i o n (222K) ( ~ i ~ . 17). B r i l l found t h a t t h e i n t e r a n l f r i c t i o n i s}

sample dependent and some samples showed no anomaly a t CDW t r a n s i t i o n . He

suggested t h a t t h e i n t e r n a l f r i c t i o n i n t h i s sample i s due t o t h e presence o f

domain, perhaps pinned by i m p u r i t i e s . B r i l l and R o a r k / l l / measured t h e i n t e r -

n a l f r i c t i o n as a f u n c t i o n o f a p p l i e d e l e c t r i c f i e l d ( F i g . 18) T h i s a l s o i n d i - c a t e s t h e CDW w a l l s a r e depinned under a t h r e s h o l d e l e c t r i c f i e l d .

I V

-

ACOUSTIC EMISSION DURING CDW TRANSITIONS

A c o u s t i c emission may be expected when t h e t r a n s i e n t e l a s t i c waves a r e gener- a t e d i n a r a p i d , u s u a l l y l o c a l i z e d , s t r e s s ( o r s t r a i n ) r e l a x a t i o n s accompanying, f o r example, t h e propagation o f d i s l o c a t i o n s o r t h e growth o f c r a c k s . Dhtake e t a1 /16/ performed t h e experiments d e t e c t i n g a c o u s t i c emission due t o charge

d e n s i t y waves i n IT-TaS2 and (TaSe4121. F i g u r e 19 and 20 show t h e t o t a l event

counts o f a c o u s t i c emissions i n IT-TaS2 and ( ~ a S e 4 ) Z l , r e s p e c t i v e l y , as a f u n c - t i o n o f temperature. The a c o u s t i c emission was d e t e c t e d o n l y a t t h e CDW t r a n - s i t i o n temprature on h e a t i n g i n IT-TaS2. I n one d i m e n s i o n a l ( ~ a S e 4 ) 2 1 , a c o u s t i c

emission was detected above t h e CDW t r a n s i t i o n temperature b o t h c o o l i n g and

heating. They suggested t h a t t h e a c o u s t i c emission was caused by t h e motion

o f CDW domains by t h e analogy o f t h e case o f t h e m a r t e n s i t i c t r a n s f o r m a t i o n .

V

-

CDW DOMAIN WALLS

CDW domains can be c r e a t e d a t any l a t t i c e s i t e s . These domains can be grown.

At f i n i t e temperatures, domain s i z e i s a l s o f i n i t e ( ~ i g . 2 2 ( a ) ) . I f t h i s i s

F o u r i e r transformed, t h e p e r i o d has f i n i t e w i d t h . When domains i n phase(Fig.

22(a)) h i t t o g e t h e r , no domain w a l l i s formed ( ~ i ~ . 2 2 ( c ) ) , b u t when domains i n a n t i - p h a s e ( ~ i ~ . 2 2 ( b ) ) h i t , t h e CDW domain w a l l s a r e formed ( ~ I G . 2 2 ( d ) ) . T h i s

i s j u s t l i k e a n t i - p h a s e domain boundaries i n t h e o r d e r - d i s a r d e r a l l o y s . These w a l l s can move back and f o r t h under a l t e r n a t i n g s t r e s s absorbing energy. T h i s may be t h e reason why t h e i n t e r n a l f r i c t i o n shows a peak a t CDW t r a n s i t i o n .

Two dimensional domains have been discussed /17/. The n u c l e a t i o n process has

been a l s o discussed /18/.

VI

-

Summary: Change i n e l a s t i c constants, i n t e r n a l f r i c t i o n peak and a c o u s t i c

emission have been observed a t o r near t h e CDW t r a n s i t i o n temperature. The

i n t e r n a l f r i c t i o n peak

and

a c o u s t i c emission near t h e CDW t r a n s i t i o n temper- a t u r e a r e probab.ly due t o t h e motion o f CDW domain w a l l s .

ACKN0WLEDGEMENT:The a u t h o r expresses h i s g r a t i t u d e t o P r o f s . Granato and Wert f o r g i v i n g him t h e o p p o r t u n i t y o f r e p o r t i n g t h i s paper a t t h e Conference. He

a l s o thank t o P r o f . R. Yamamoto, Messeurs A. Suzuki and K. Ohtake f o r t h e i r

JOURNAL

DE PHYSIQUE

IN PHASE ANTI-PHASE NO CDW DOMAIN WALLS CDW ANT I -PHASE DOMA IN WALLS

F i g . 22. (a) Two CDW domains i n phase, (b) Two CDW domains i n a n t i-phase ( c ) Two CDW domains i n phase j o i n l a v i n g no CDW domain w a l l s , (d) Two CDW domains i n a n t i - p h a s e j o i n l e a v i n g a CDW domain w a l l .

REFERENCES

/1/ T e s t a r d i , L . ~ . , P h y s . ~ e ~ . 8 1 2 ( I 9 7 5 ) 3 8 4 9 .

/2/Sato,E.,Ohtake,K.,Yamamoto,R., Doyama, M. and Endo,K.,Proc. The 7 t h I n t e r - n a t i o n a l Conference on P o s i t r o n A n n i h i l a t i o n , 1985.

/3/ B a r m a t z , M . , T e s t a r d i , L . R . , G a r i t o . A. F., and Heeger, A.J.,Solid S t a t e Comm 1 5 ( 1 9 7 4 j 1299.

/4/lshiguro,T., Kagoshima, S. and Anzai

,

H. ,J. Soc. Japan 42(1977) 365.

/5/ Tiedie,T..Haering. R. R.,Jericho, M. H., Roger,W. A. and Simpson, A.,

SOI

i d

S t a t e ~omm-23 (1977) 713.

/6/

Barmatz,M.,Testardi, L. R.,and D i Salvo,F.J.,Phys. Rev. B 12 (1975) 4367.

/7/

Simpson,A.M.,Jericho,M.H.,DiSalvo,F.J.,Solid

S t a t e Comm.44(1982) 1543.

/8/ S k o l n i c k , M.S.,Roth, S.and Alms,H.,J.Phys.C 10(1977) 2523.

/9/ Brill,J.W.,Sol i d S t a t e Comm. 41 (1982) 925.

/ l o /

Zettl,A.,Gruner and Thompson, A. H.,Phys. Rev.6 26 (1982) 5760.

/11/ B r i l l , J.W. and Roark,W., Phys. Rev.Lett. 53(1984) 846.

/12/ B r i l l ,J.W.and Ong,N.P. ,Sol i d S t a t e Com.25 (1978) 1075.

/13/ B r i l I, J.W. and Sarnbong i ,T., J .Phys. Soc. Japan 53(1984) 20.

/14/ Suzuki ,A. ,Yamamoto,R. ,Doyama,M. ,Mizubayashi H . a n d Okuda,S. ,This Conference.

/ I S /

Caille,A.,Lepine,Y.,Tericho,M.H.,and Sirnpson,A.M.,Phys.Rev.~28(1983)5454.

/16/

Ohtake,K.,Sato,E.,Suzuki,

Y.,Yamamoto, R.,Doyama, M.,Endo, K.,Wakayama,S.,

and Kishi,T.,This Conference.

/17/ Nakanishi,K., and Shiba,H., J. Phys. Soc. Japan 53 (1984) 1103.