Chpt 06 Piezoelectric Materials

8/8/2019 Chpt 06 Piezoelectric Materials

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C h a p t e r 6P i e z o e l e c t r i c M a t e r i a l s

Ti m King I and Michele Pozzi 21School of Mechanical Engineering,

University of Leeds,Leeds LS2 9JT, UK.

2Sirindhorn International Institute of Technology,Thammasat University,Pathum Thani 12121, Thailand.

6 .1 I n t r o d u c t i o n t o P i e z o e l e c t r i c i t yThe phenomenon of piezoelectricity has been known for more than a cen-tury. In fact, in 1880 Jacques and Pierre Curie reported to the Acad6miede Sciences about a new discovery: suitable compression of a hemihedral*crystal with oblique faces leads to the development of electrical chargeson the surfaces. Such crystals were already known for the phenomenon ofpyroelectricityt : electrical charges develop on the surfaces normal to thehemihedral axis following heat ing or cooling. The Curie brothers realizedthat the underlying explanation was identical: the variation in tempera-ture causes a dimensional change, which is ultimately responsible for theelectrical charges.*A crystal is said to be hemi hedr al if it has at least one axis whose ends are dissimilar.

Fro m a sym me tr y point of view, the crysta l lacks a centre of symm etry .t The term pyroelectrici ty comes from Ancient Greek and describes the fact that

heat ( T r v p = f i r e ) produce s electricity. In the same way piezoelectricity is pressure( Tr ~ c@ ~ v = p r e s s u r e ) that induces electricity.

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142 Piezoelectric Materials

Po sitive ion (A)@ Neg at ive ion

Q Po sitive ion (B)

Fig. 6.1 In the elemen tary cell of som e crystals, the 'centres of gravity' of positive andnegative charges do not coincide: an electric dipole is created.6 .1 .1 C rys t a l lo g ra p hy o f P i ezo e l ec t r i c i t yP i e z o e l e c t r i c i t y c a n b e o b s e r v e d i n s o m e c r y s t a l s w h i c h l a c k a c e n t r e o fs y m m e t r y . I f t h e e l e m e n t a r y u n i t ( o r ' ce l l' ) o f t h e c r y s t a l l a t t i c e is s u c ht h a t t h e ' c e n t r e o f g r a v i t y ' o f i ts p o s i ti v e c h a r g e s d o e s n o t c o i n ci d e w i t ht h a t o f i ts n e g a t i v e c h a r g e s i t c r e a t e s a p e r m a n e n t 'd i p o l e '$ t h e c ell ise l e c t r i c a l l y a s y m m e t r i c a s i l l u s t r a t e d i n F i g . 6 . 1 . A m a c r o s c o p i c e l e c t r i c a lp o l a r i z a t i o n is o b s e r v e d if t h e d i po l es a r e a l ig n e d t h r o u g h o u t t h e c r y s t a l.A p p l y i n g e x t e r n a l m e c h a n i c a l s t r e s s w i l l s t r a i n t h e d i p o l e s w h i c h a l t e r s t h ep o l a r i z a t i o n s o t h a t e l e c t r ic a l c h a r g e s a p p e a r o n t h e s u r f a c e o f t h e c r y s -t a l. T h i s is t e r m e d t h e d i r e c t p i e z o e l e c t r i c e f f e c t ( F i g . 6 . 2 ( a ) ) . C o n v e r s e l y ,a p p l y i n g a n e x t e r n a l e l e c t r i c f i e l d t o t h e c r y s t a l w i l l d e f o r m t h e n a t u r a ld i p o le s in d u c i n g s t r a i n s w h i c h c h a n g e t h e d i m e n s i o n s o f t h e c r y s t al . W ec a l l t h i s t h e i n v e r s e (o r c o n v e r s e ) p i e z o e l e c t r i c e f f e c t ( F i g . 6 . 2 ( b ) ) .

P i e z o e l e c t ri c i ty i s e x h i b i t e d b y m a n y n a t u r a l l y o c c u r r i n g m a t e ri a ls :q u a r t z i s a n i m p o r t a n t e x a m p l e a n d to u r m a l i n e , l i t h iu m s u l p h a t e a n d p o t as -s i u m t a r t r a t e a r e a ls o s i g n if i ca n t . I n su c h c r y s t a l s , h o w e v e r , t h e p ie z o el ec -t r i c e f f e c t s a r e n o t a l w a y s v e r y s t r o n g .

F e r r o e l e c tr i c s a r e a n i m p o r t a n t s u b s e t o f p i e z o el e c tr ic m a t e r i a l s w h i c hh a v e p e r m a n e n t e l e c tr i c d ip o l e s in t h e i r l a t t i c e c e lls w h i c h c a n b e ' s w i t c h e d 'o r r e - o r i e n te d u n d e r c e r t a i n c i r c u m s t a n c e s . A t h i g h t e m p e r a t u r e , t h e s e$Piezoelectric behaviour can be still be exhibited in the absence of a permanent dipoleif a dipole is created by inducing a separation between the positive and negative chargecentres throu gh th e ap plication of an externa l electric field or mechanical stress. Thisis the case for quartz crystals for example.


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Introduction to Piezoelectricity 143

(a) ~ _ _ (b)I

Fig. 6.2 Ex em plification of (a) the direct piezoelectric effect and (b) the conv erse piezo-electric effect.c r y s t a l s h a v e h i g h s y m m e t r y , b u t o n t r a n s i t i o n t h r o u g h t h e i r s p e c i f i c C ur iet e m p e r a t u r e t h e y u n d e r g o a c r y s t a ll o g r a p h i c t r a n s f o r m a t i o n . T h e lo w -t e m p e r a t u r e c r y s t a l s t r u c t u r e ( f er r o el e c tr ic ) h a s a s y m m e t r y w h i c h is as u b g r o u p o f t h a t f o u n d a t h ig h t e m p e r a t u r e ( p a r a e le c t r ic ) . I t is w o r t h n o t -i n g t h a t t h e t e r m i n o l o g y is a n a l o g o u s t o , a n d d e r i v e d fr o m , t h a t u s e d tod e s c r i b e m a g n e t i c p r o p e r t i e s : - - e . g . f e r r o m a g n e t i c , p a r a m a g n e t i c , e t c .

A h i s to r i c a l ly i m p o r t a n t e x a m p l e o f f e r ro e l e ct r ic m a t e r i a l i s b a r i u m t i-t a n a t e ( B a T i O 3 ) , w h i c h s h a r e s t h e P e r o v s k i t e ( c a lc i u m t i t a n a t e ) c r y s t a ls t r u c t u r e . A t h ig h t e m p e r a t u r e i t h a s a p e r f e c tl y c e n t r o s y m m e t r i c cu b i cs t r u c t u r e : t h e o x y g e n a t o m s a re i n t e t r a h e d r a l c o o r d i n a t i o n w i t h v e r t i c e ss h a r in g ; a t t h e c e n t r e o f t h e t e t r a h e d r o n is T i ( se e F i g . 6 . 3 (a ) ). W h e n t h et e m p e r a t u r e is l o w e r ed b e lo w 1 20C ( i t s C u r i e t e m p e r a t u r e ) , t h e s y m m e -t r y is r e d u c e d t o te t r a g o n a l . W h a t h a p p e n s i s t h a t t h e u n i t c ell b e c o m e ss t r e t c h e d a l o n g o n e a x i s a n d t h e p o s i t i v e a n d n e g a t i v e a t o m s i n i t m o v ein o p p o s i t e d i r e c ti o n s t h e m o s t n o t i c e a b l e m o v e m e n t is b y t h e t i t a n i u ma t o m w h i c h a p p r o a c h e s o n e o f t h e o x y g e n a t o m s in t h e d i r e c ti o n o f s t r e tc h -i n g ( F i g . 6 .3 (b ) ) . T h i s r e l a t i v e d i s p l a c e m e n t o f i o n s o f o p p o s i t e s ig n i n d u c e sa n e l e c t r i c d i p o l e i n t h e l a t t i c e c e l l .

S e v e r al o t h e r i m p o r t a n t m a t e r i a l s u n d e r g o t h is fe r r o e le c t ri c t r a n s f o r m a -t io n . A k e y f a c t o r is t h a t a l o n g - r a n g e c o r r e l a t i o n e x i s t s a m o n g t h e e l e c t ri cd i po l es , s o t h a t m a c r o s c o p i c p o r t i o n s o f t h e c r y s t a l s ( d o m a i n s ) s h o w t h es a m e p o l a r i z a t i o n . H o w e v e r , s e v e r a l d i f fe r e n t o r i e n t a t i o n s a r e p o s s i b le fo rt h e d i p o l e s a n d n o r m a l l y a l l o r i e n t a t i o n s w i l l b e p r e s e n t i n d i f f e r e n t r e g i o n so f t h e c r y s t a l ( t h i s is a f o r m o f t w i n n i n g ) . T h e r e f o r e , w h i l s t e a c h d o m a i nis p i e z o e l e c t r i c a l l y a c t i v e b e c a u s e o f t h e i n t r in s i c p o l a r i z a t i o n , i n g e n e r a l


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1 4 4 Piezoelectric Materials

( a l (b )~ . 0

I

Fig. 6.3 Cry stal struc ture of Ba TiO 3 (a) above and (b) below its Curie tem peratu re;the cubic ce ll is stretched in one direction and becomes tetragona l.

t h e w h o l e c r y s t a l d o e s n o t d i s p l a y p i e z o e l e c t r i c e ff ec ts . T h e a p p l i c a t i o n o fa n e l e c t r i c f i e l d , d u r i n g o r a f t e r c o o l i n g , s w i t c h e s t h e d i p o l e s a n d f o r c e s ac o m m o n o r i e n t a t i o n ( th is p r o c e s s is c a ll e d po l ing) . A s a c o n s e q u e n c e , t h ec r y s t a l a s a w h o l e b e c o m e s p i e z o e l e c t r i c a l ly a c ti v e . A l t h o u g h a n i n t ri n s i cp o l a r i z a t i o n is p r e s e n t i n t h e p o l e d c r y s t a l, i t c a n n o t b e o b s e r v e d d i re c t l yin e q u i l ib r i u m c o n d i t i o n s b e c a u s e e l e ct r i c a l c h a r g e s , o r i g i n a t i n g e i t h e r f ro mt h e a i r o r f r o m t h e c r y s t a l i t s e l f , a r e p r e s e n t o n i t s s u r f a c e s o a s t o c o u n -t e r b a l a n c e t h e i n t e r n a l d ip o le . H o w e v e r , t h e a p p l i c a t i o n o f a m e c h a n i c a ls t r e s s f i e l d c a n a l t e r t h e i n t r i n s i c p o l a r i z a t i o n ; b e f o r e a n e w e q u i l i b r i u m i sr e a c h e d ( b y d i s p l a c e m e n t o r a d s o r p t i o n o f c h a r g e s ) , a n e l e c tr ic c h a r g e c a nb e o b s e r v e d o n t h e s u r f a c e t h i s is t h e d i r e c t p i e z o e l e c t r i c e ff ec t.6 . 1 . 2 T h e I n t e r a c t i o n B e t w e e n M e c h a n i c a l a n d E l e c t r ic a l

S y s t e m sT h e u n i q u e n e s s o f p i e z o e le c t r i c m a t e r i a l s l ie s i n t h e i n t i m a t e i n t e r a c t i o n b e -t w e e n t h e i r m e c h a n i c a l a n d e l e c tr ic a l b e h a v i o u r s . T h e s t r o n g c o u p l in g be -t w e e n e le c t ri c a l a n d m e c h a n i c a l s y s t e m s i m p l ie s t h a t t h e m e c h a n i c a l p ro p -e r ti e s o f p i e z o e l e c tr i c m a t e r i a l d e p e n d h e a v i l y o n t h e e l e c t ri c a l p a r a m e t e r so f t h e e x t e r n a l c i r cu i t . F o r e x a m p l e , w h e n a p i e z o e l e c t r i c m a t e r i a l is s u b -j e c t e d t o c o m p r e s s i v e s tr e ss , e l e c tr i ca l c h a r g e s a r e i n d u c e d d u e t o t h e d i r e c tM ore precise ly, the whole crysta l w ould be piezoelectrically active on ly if it had dis-played these properties before the ferroelectric transformation, but this is not usuallyof practical interest.


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Introduction to Piezoelectricity 145p i e z o e le c t ri c effe ct. L o o k i n g a t t h e p h e n o m e n o n a s t w o s e p a r a t e s t a g e s , o n ec a n s ee t h e i n d u c e d c h a r g e s a s c a u s i n g a s t r a i n i n t h e o p p o s i t e d i r e c t i o n d u et o t h e i n v e r s e p i e z o e le c t ri c e ffe ct. T h e c o m b i n e d r e s u l t is t h a t t h e m a t e r i a la p p e a r s t o b e s t i f f e r b e c a u s e t h e Y o u n g ' s m o d u l u s r e c e i v e s a p o s i t i v e c o n -t r i b u t i o n f r o m t h e e le c t ri c a l s y s t e m . O n t h e o t h e r h a n d , i f e l e c t ro d e s a r ep l a c e d o n t h e s u r f a c e a n d s h o r t - c i r c u i t e d , t h e i n d u c e d c h a r g e s w i l l n e u t r a l -i z e e a c h o t h e r a n d t h e o b s e r v e d s t i f f n e s s w i l l b e l o w e r , a n d p u r e l y m e c h a n -i ca l. As w i l l be sho w n in a f o l lowing se c t ion , t h i s c a n be e x pe r im e n ta l lyv e ri fi ed b y o b s e r v i n g a s h i ft i n t h e n a t u r a l f r e q u e n c y o f v i b r a t i o n o f a p ie z o-e l e c t r i c d e v i c e b e t w e e n o p e n - a n d s h o r t - c i r c u i t c o n d i t i o n s .

6 . 1 . 3 S o m e P i e z o e l e c t r i c M a t e r i a l sT h e C u r i e b r o t h e r s w o r k e d o n n a t u r a l c r y s t a l s s u c h a s t o u r m a l i n e , t o p a z ,q u a r t z a n d R o c h e l l e s a l t , a l t h o u g h o n l y t h e l a t t e r t w o a r e p i e z o e l e c t r i c t oa h igh l eve l. M uc h l a r ge r p i e z oe le c t r i c a c t iv i ty i s f oun d in c r ys t a l s a r t if i -c ia ll y s y n t h e s i s e d fo r t h e p u r p o s e . T h e a l r e a d y m e n t i o n e d p e r o v s k i t e fa m i l yh a v e p r o v e d to b e p a r t i c u l a r l y s u cc es sf ul : b a r i u m t i t a n a t e ( B a T i 0 3 ) , l ea dt i t a n a t e ( P b T i O 3 o r P T ) a n d p a r t i c u la r l y le ad zi rc o n a te t i ta n a t e ( P b ( Z r ,T i ) 0 3 o r P Z T ) a n d l ea d l a n t h a n u m z i rc o n a te t i ta n a t e ( P L Z T ) . S i m i la r c ry s-t a l s t r u c t u r e s a r e f o u n d i n l i t h i u m n i o b a t e ( L i N b O 3 ) a n d l i t h i u m t a n t a l a t e( L i T a 0 3 ) .

I t i s d i f f i c u l t t o g r o w s i z e a b l e c r y s t a l s o f t h e s e m a t e r i a l s a n d s o t h e ya r e u s e d i n c e r a m i c f o r m i n s t e a d . C e r a m i c s a r e a g g r e g a t i o n s o f m i c r o -c r y s t a l l i n e p a r t i c l e s ( g r a i n s ) , w i t h s i z e s v a r y i n g f r o m s e v e r a l n a n o m e t r e su p t o m i c r o n s . T h e y a r e u s u a l l y f o r m e d b y f i r i n g a c o m p a c t e d s l u r r y o f t h ef i n e l y g r o u n d c o n s t i t u e n t s . T h i s p r o c e s s i s t e r m e d s i n t e r i n g . B e c a u s e t h eg r a i n s , a n d h e n c e t h e i r d i p o l e s , a r e r a n d o m l y o r i e n t e d a p o l i n g p r o c e s s i se s s e n t i a l b e f o r e t h e s e c e r a m i c m a t e r i a l s c a n e x h i b i t p i e z o e l e c t r i c i t y .

B e c a u s e s i n t e r i n g t a k e s p l a c e a t v e r y h i g h t e m p e r a t u r e s , a s t h e c e r a m i cc o o l s t h r o u g h i t s C u r i e t e m p e r a t u r e d i p o l e s a r e f o r m e d w i t h o u t p r e f e r e n t i a lo r i e n t a t i o n w i t h i n e a c h g r a i n . T h e c e r a m i c e x h i b i t s n o n e t d i p o l e , a n dh e n c e n o p i e z o e l e c t r i c a c t i v i t y . P i e z o e l e c t r i c p r o p e r t i e s t h e r e f o r e h a v e t ob e d e v e l o p e d i n d e v i c e s m a d e f r o m f e r r o e l e c t r i c c e r a m i c s b y p o l i n g . T h i si s a c h i e v e d b y a p p l y i n g a s t r o n g e l e c t r i c f i e l d w h i c h o r i e n t s t h e d i p o l e s i ne a c h g r a i n a l o n g t h e m o s t f a v o u r a b l e d i r e c t i o n . P e r f e c t a l i g n m e n t c a n n o t b ea c h i e v e d b e c a u s e o n l y s p e c i f i c d i r e c t i o n s a r e a v a i l a b l e t o t h e d i p o l e s w i t h i nt h e g r a i n s w h o s e o r i e n t a t i o n s a r e v i r t u a l l y f i x e d d u r i n g s i n t e r i n g , b u t a


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146 Piezoelectr ic Materialsl e ve l o f p o l a r i s a t i o n o f 8 0 % o r m o r e c a n b e e f f ec t e d. P i e z o e l e c t r i c c e r a m i c sp r o d u c e d b y t h is m e t h o d h a v e b e c o m e t h e n o r m fo r a c t u a t o r a p p l i ca t i o n so n a c c o u n t o f t h e i r s t r o n g l y p i e z o e l e c tr i c p r o p e r t i e s , w h i c h c a n b e t a il o r e d ,a n d t h e f l e x i b i li t y t o r e a d i l y c r e a t e a w i d e r a n g e o f s h a p e s .S i nc e t h e d i s c o v e r y o f t h e s u p e r i o r p r o p e r t i e s o f P Z T , t a r g e t e d s t u d -ie s h a v e l e d t o t h e d e v e l o p m e n t o f a w h o l e s e r ie s o f p i e z o e l e c t r i c c e r a m i c sb a s e d o n P b ( Z r o .5 5 T i 0 . 4 5 )0 3 , w h o s e e l e m e n t s d i f fe r b y t h e a d d i t i o n o f o x -i d e s o f s e v e r a l m e t a l s ( N b , C r , L a a n d F e ) . T h i s s e r ie s c a n b e d i v i d e d i n t ot w o m a i n f a m i l i e s : s o f t P Z T ( su c h a s ' P Z T - 5 H ' ) a n d h a r d P Z T ( s u c h a s' P Z T - 8 ' ) . T h e f o r m e r a r e c h a r a c t e r i s e d b y h ig h e r p ie z o e le c t ri c a c t i v i t y a n dt h e r e f o r e h i g h e r o u t p u t d i s p l a c e m e n t s , b u t t h e y a l s o s u f f e r f r o m c o n s i d -e r a b le h y s te r e si s a n d e n e r g y d is s ip a t io n . T h i s m e a n s t h a t t h e y a r e m o r es u i t a b l e f or q u a s i - s t a t i c a c t u a t i o n a p p l i c a t i o n s . T h e la t t e r , h a r d P Z T s , gi ves m a l l e r d i s p l a c e m e n t s f o r a g i v e n e l e c t r i c f i e l d b u t a l s o v e r y s m a l l h y s t e r e -s i s a n d e n e r g y l o s s , w h i c h m a k e s t h e m m o r e a t t r a c t i v e f o r h i g h f r e q u e n c ya p p l i c a t i o n s .

P i e z o e l e c t r i c i t y i s n o t l i m i t e d t o i n o r g a n i c s . I t is a l s o p r e s e n t i n p o l y -m e r s h a v i n g a c h a i n s t r u c t u r e : e v e n t h e n a t u r a l m a t e r i a l s w o o l a n d s il ks h o w p i e z o e l e c t r i c i t y t o s o m e e x t e n t , a l t h o u g h s i g n i f i c a n t p i e z o e l e c t r i c a c -t i v i t y is o n l y f o u n d w h e n t h e m o l e c u l e h a s s t r o n g d i p o le s . T h e b e s t e x a m p l eis a g a i n a n a r t i f ic i a ll y s y n t h e s iz e d m a t e r i a l : t h e p o l y m e r p o l y v i n y l i d e n e d i -f lo ri de ( P V D F ) , w h o s e m o n o m e r i s - C F 2 - C H 2 - , is m o r e p ie z o el e ct ri c t h a nq u a r t z . A l t h o u g h i t is le ss a c t i v e t h a n t h e p e r o v s k i t e c e r a m i c s a n d c a nd e v e l o p s m a l l e r f o rc e s , i t h a s t h e a d v a n t a g e s o f b e i n g l i g h t w e i g h t a n d e a s i l ys h a p e d . I n o r d e r t o e x h i b i t s i g n i f i c a n t p i e z o e l e c t r i c a c t i v i t y , P V D F h a s t o

Pol ing d i rec tion

2- - t ~

Fig. 6.4 System of axe s com m only defined for piezoelectric ceramics.


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App l i ca t ions o f t he Direc t P iezoe lec tr i c E f f ec t 147

be extruded and drawn so as to orient the molecules and their dipoles asmuch as possible. Due to the low value of its dielectric constant, the valueof the piezoelectric constant g is higher in PVDF than in ceramics, mak-ing the polymer more suitable for sensing applications. It is preferable toceramics also as an acoustic generator in medical devices because its lowdensity and Young's modulus allow for a better acoustic coupling with thehuman body.

Some fundamental constants can be defined describing piezoelectric ma-terials which allow us to compare their behaviours. For piezoceramic actu-ator applications a vital characteristic is the coupling between the appliedelectric field and the mechanical str ain which results from it. We te rm thisd. As with most mater ials, stra ining in one direct ion causes strains in or-thogonal directions also. For piezoelectric materials it is also possible thatan electric field in one direct ion can cause shear strains. For this reasonwe need to define a set of values for d relating electric field in one directionto all the possible strains which it may cause in various directions . Todo this we first define a set of axes. By convention, for piezoceramics wealign axis 3 with the poling direction (Fig. 6.4). By using subscrip ts we cannow give names to the different d values. For example, d 3 3 is the value ofd relating electric field in the (poling) direction 3 to strain in the (same) 3direction; d31 relates electric field in the 3 direction to strain in the (orthog-onal) 1 direction. Since piezoceramic devices are almost invar iably drivenusing the same electrodes employed for poling them, electric fields appliedother th an in the 3 direct ion will not be considered here. In practice the d 3 3and d31 values are the most important from the point of view of actuatorapplications. Values of these constants are given in Table 6.1 for sele

6 .2 Appl ica t ions o f t h e D i r e c t P i e z o e l e c t r i c E f f e c tAs described in the int roduction, the direct piezoelectric effect is responsiblefor the generation of electrical charges on a piezoelectric material subjectedto mechanical stress. These charges are propor tional to the intensity of the I n t h e m o s t g e n e r a l c a s e t h e r e c o u l d t h e r e f o r e b e 1 8 i n d e p e n d e n t d v a l u e s ( ' p i e z o e l e c -

t r i c c ha r g e c o n s t a n t s ' ) . H o w e v e r, fo r p i e z o c e r a m i c m a t e r i a l s , s y m m e t r y c o n s i d e r a t i o n sd i c t a t e t h a t m a n y o f t h e m a r e z e ro a n d o t h e r s e q u i v a le n t , w h i c h g r e a t l y re d u c e s t h en u m b e r o f v a l u e s o f i n t e r e s t. F o r e x a m p l e d3 2 is e q u a l t o d31 a n d h e n c e u s u a l l y n o tq u o t e d . S u b s c r i p t s 4, 5 a n d 6 r e l a t e t o i n d u c e d m e c h a n i c a l s h e a r . C h a r g e c o n s t a n t si n v o l v i n g t h e s e s u b s c r i p t s a r e n o t g e n e r a l l y si g n i fi c a n t fo r p i e z o c e r a m i c a c t u a t o r s .


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Fig. 6.5 The direct piezoelectric effect is exp loited to m easure accelerations. In thefigure, a piezoelectric elem ent is fitted together with the signa l cond itioning electronicsin one single integ rated circuit [12].f or c e a p p l i e d , s o t h a t t h e y c a n b e u s e d t o m e a s u r e t h e f o rc e i ts e lf . T h a n k s t ot h e i r h i g h r e s o n a n t f r e q u en c y , f o rc e s en s o r s b a s e d o n p i e z o e l e c t r i c i t y h a v ev e r y s h o r t r e s p o n s e t i m e s a n d a r e p e r f e c t f o r m e a s u r i n g r a p i d l y v a r y i n gf o r c e s ( o n t h e o t h e r h a n d t h e y p e r f o r m p o o r l y i n v e r y l o w f r e q u e n c y a p p l i -c a t i o n s d u e to d r i f t c a u s e d b y t h e i n t e r n a l e l e c t r i c a l c o n d u c t i o n ) . O n e o ft h e m a i n a p p l i c a t i o n s o f s u c h s e n s in g p r o p e r t i e s is in a c c e l e r o m e t e r s w h e r ea k n o w n m a s s t r a n s l a t e s a n a c c e l e r a t i o n in t o a f or ce . T h e t e c h n o l o g y ofp i e z o e l e c t r i c a c c e l e r o m e t e r s i s s o w e l l d e v e l o p e d t h a t t h e y a r e m i n i a t u r i z e dd o w n t o i n t e g r a t e d c i r c u i t s c o n t a i n i n g t h e s e n s i n g e l e m e n t a n d t h e s i g n a lc o n d i t i o n i n g e l e c t r o n i c s ( s e e F i g . 6 . 5 ) . c t e d p i e z o e l e c t r i c m a t e r i a l s .

T h e d i r ec t p i ezo e l ec t r i c e f f ec t i s a l s o u s ed i n l e s s h ig h - t ech ap p l i ca t i o n s ,w h i c h a r e n o n e t h e l e s s w i d e s p r e a d a n d i m p o r t a n t . F o r e x a m p l e , t h e h i g h in -t e n s i t y o f t h e e l e c t ri c fie ld t h a t b u i l d s u p i n a p ie z o e l e c t r ic m a t e r i a l s u b j e c tt o s t r a i n a l l ow s h i g h v o l t a g e s to b e g e n e r a t e d ( in t h e o r d e r o f t h o u s a n d s o fv o l ts ) . T h e s e v o l t a g e s a r e e x p l o i t e d t o g e n e r a t e l o w p o w e r s p a r k s f o r f ue li g n i t i o n a p p l i c a t i o n s .

A n i m p o r t a n t a p p l i c a t i o n w h e r e t h e d i r e c t a n d c o n v e r s e p i e z o e l e c t r i ce f fe c ts a r e u s e d t o g e t h e r is i n p i e z o e l e c tr i c t r a n s f o r m e r s . T h e b a s i c id e a ,p ro p o s ed b y R o s en i n t h e 1 9 5 0s , is t o ex c i t e o n e r eg io n o f a p i ezo e l ec t r i cm a t e r i a l e l e c t r i c a ll y w i t h a d r i v i n g s in e w a v e a n d t o c o ll ec t th e t r a n s f o r m e d


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Table 6.1Acoustic Transducers 149

Piezoelectric c ha rge constants for sev eral piezoelectric m ateria ls of interest.d33 d31M ate r ia l ( 1 0 -1 2m V -1 ) ( 1 0 -1 2 m V -1 )

BaTiO 3 191 - 7 8P V D F - 3 3 2 -1 4PZ T -4 289 - 123PZ T -5 A 37 4 -1 7 1PZ T -5 H 593 -2 7 4

e l e c t r i c a l o u t p u t f r o m a n o t h e r r e g i o n w h i c h i s m e c h a n i c a l l y c o u p l e d w i t ht h e f i r s t [ 1 3 ] . T h e s e d e v i c e s h a v e h i g h e r e f f i c i e n c y i n r e s o n a n t m o d e t h a nt h e i r e l e c t r o m a g n e t i c c o u n t e r p a r t s a n d a r e w i d e l y u s e d t o p o w e r , f o r e x a m -p l e , b a c k l i g h t s f o r p o r t a b l e c o m p u t e r s .

6 .3 A c o u s t i c T r a n s d u c e r sT h e f ir s t t e c h n o l o g i c a l a p p l i c a t i o n o f p i e z o e l e c t r i c i t y w a s r e a l i z e d i n th ey e a r s a r o u n d t h e F i r s t W o r l d W a r b y P a u l L a n g e v i n , w h o b u i l t a n a c o u s t i ct r a n s d u c e r fo r n a v a l a p p l i c a t i o n : t h e fi rs t p i e z o e l e c t r ic s o n a r . T h a n k s t ot h e d i r e c t c o u p l i n g b e t w e e n e l e c t r i c a l a n d m e c h a n i c a l s y s t e m s a n d t h e h i g hr e s o n a n t f r e q u e n c y , q u a r t z c r y s t a l s s a n d w i c h e d i n s t e e l w e r e f o u n d t o b ev e r y a p p r o p r i a t e f or t h e e m i s si o n o f t h e s o n a r " c h i r p ". P i e z o e l e c t ri c s o n a r sh a v e b e e n i m p r o v e d s in c e f or b e t t e r c o u p l in g w i t h t h e w a t e r m e d i u m a n d b yi n c lu d i n g p ie z o e l e c tr i c c e r a m i c s r a t h e r t h a n q u a r t z . P i e z o e l e c tr i c m a t e r i a l s ,e s p e c i al ly P V D F , a r e o f te n u s e d fo r t h e ' t w e e t e r s ' i n m o d e r n l o u d s p e a k e rs y s t e m s a n d , a s m e n t i o n e d b e f o r e , i n a h o s t o f m e d i c a l a p p l i c a t i o n s f r o me c h o - g r a p h i c d e v i c e s t o u l t r a s o u n d s u r g e r y .

6 . 4 P i e z o e l e c t r i c A c t u a t o r s

N e w a c t u a t o r s w i t h b e t t e r p e r f o r m a n c e a re a lw a y s s o u g h t fo r m e c h a t r o n i c sd e vi ce s a n d m i c r o -e l e c t ro - m e c h a n i c a l s y s te m s . A m o n g t h e m a n y t ec h n o lo -g i e s a v a i l a b l e , p i e z o e l e c t r i c a c t u a t i o n o f f e r s h i g h s p e e d , p r e c i s i o n a n d h i g he n e r g y d e n s it i e s. D i f f e r en t p i e z o e l e c t r ic m a t e r i a l s h a v e b e e n u s e d f o r a c t u -a t i o n i n a w i d e r a n g e o f a p p l i c a t io n s , s o m e t i m e s t o e x p l o i t p a r t i c u l a r a d -


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Fig. 6.6 A selection of com m ercial piezoelectric actuators: (A-D ) mu lti-layer actuators;(E-G) bimorphs; (H) unimorph.

v a n t a g e s ; e . g . l o w c o n t a m i n a t i o n i n u l t r a - h i g h - v a c u u m e n v i r o n m e n t s , b u tm o r e o f t e n t o t a k e a d v a n t a g e o f t h e u n r i v a l l e d l e v e ls o f s p e e d a n d p r e c i-s io n a v a i l a b le f r o m p i e z o e l e c t r ic d e v ic e s . I n d e e d , p i e z o e l e c t ri c a c t u a t o r s a r es o m e t i m e s e s s e n t i a l t o a w h o l e t e c h n o l o g y i t is d if fi cu lt t o i m a g i n e a na t o m i c f o rc e m i c r o s c o p e w i t h o u t p i e z o e l e c t ri c c o n t r o l o f t h e s c a n n i n g .

P i e z o e l e c t r i c a c t u a t o r s e x p l o i t t h e i n v e r s e p i e z o e l e c t r i c e f f e c t t o t r a n s -f o r m e l e c t r i c a l e n e r g y i n t o m e c h a n i c a l w o r k . A s d e s c r i b e d p r e v i o u s l y , t h i sc o n v e r s i o n t a k e s p l a c e a t t h e c r y s t a l - l a t t i c e l e v e l a n d i s d i r e c t ( b y c o n t r a s t ,i n s o l e n o i d s a n d m a g n e t o s t r i c t i v e a c t u a t o r s t h e e l e c t r i c a l e n e r g y m u s t f i r s tb e c o n v e r t e d i n t o m a g n e t i c e n e r g y ; o r in t h e c a s e o f e l e c t r i c a l ly d r i v e n s h a p em e m o r y a l l o y s , i n t o t h e r m a l e n e r g y ) . T h i s l e a d s t o s o m e a d v a n t a g e s s u c ha s n e g l i g i b l e e l e c t r o m a g n e t i c n o i s e a n d h i g h e n e r g y d e n s i t y .

T h i s s e c t i o n d e a ls w i t h t h e a p p l i c a t i o n o f p i e z o e l e c t r i c i t y t o a c t u a -t i o n te c h n o l o g y , d e s c r i b i n g t h e m o s t i m p o r t a n t c o n f i g u r a t i o n s o f p ie z o-a c t u a t o r s .6 . 4 . 1 B i m o r p h s a nd Ot h e r B e n d i n g P i e z o - A c t u a t o r sI n it s a c t u a t i o n p r i n c ip l e , t h e p i e z o e l e c t r i c b i m o r p h is v e r y s i m i l a r to t h em o r e c o m m o n ' b i m e t a l s tr ip ' . I n b o t h c as es a b e n d i n g m o m e n t i s p r o d u c e db y t h e d i f f e r e n t ia l c o n t r a c t i o n / e x p a n s i o n o f t w o d i ff e re n t s t r i p s j o i n e d t o -


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( a ) Direction of Dolaraisation

(b )

( c )

Fig. 6.7 Piez oele ctric bim orph s: (a) series bim orph ; (b) parallel bimorph; (c) parallelbimorph with biasing voltage.

R a i n b o w a c t u a t o r s a r e c a p a b l e o f l a rg e r d is p l a c e m e n t s a n d h i g h e r fo rc est h a n u n i m o r p h / b i m o r p h b e n d e r s a n d offe r t h e a d d i t i o n a l b e n ef it t h a t t h e yc a n b e s t a c k e d to f u r t h e r i n c r e a s e t h e o u t p u t d i s p l a c e m e n t . H a e r t l i n g [1]r e p o r t s d i s p l a c e m e n t s u p to l m m a n d 1 00 N fo rc es w i t h 0 . 2 m m - t h i c k w a f e rs( see F ig . 6 .8 ) .

6 . 4 . 2 M o n o l i t h i c A c t u a t o r s

T h e u s e of s in g le c r y s t a l p i e z o e l e c tr i c d e v ic e s h a s t h e a d v a n t a g e t h a t t h ec o m p l e x i t y o f t h e e l e c t r o - m e c h a n i c a l c o u p l i n g c a n b e f u ll y e x p l o it e d . B ys u i t a b l y c u t t i n g a p i e z o e le c t ri c c r y s t a l i t is p o s s ib l e t o o b t a i n e x t e n s io n ,b e n d i n g o r t o r s i o n t h r o u g h t h e a p p l i c a t i o n o f a n e l e c tr ic fie ld . M a n y s m a l ld i s p l a c e m e n t a c t u a t o r s h a v e b e e n r e a l i z e d i n t h i s w a y , e s p e c i a l l y f o r m i c r o -p o s i t io n i n g . T o o b t a i n s o m e w h a t l a r g e r d i s p l a c e m e n t s s o li d p i e z o c e r a m i cd e v i ce s a re a ls o a t t r a c t i v e . F o r e x a m p l e , a c o m m o n d e s i g n f or s a m p l e h o l d-


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Piezoelectric Actuators 153

e r s is t h e p i e z o e l ec t ri c t u b e , w h i c h is m a d e o f c e r a m i c a n d l o n g i t u d i n a l l yd i v i d e d i n t o f o u r s e c t io n s w i t h s e p a r a t e e l e c t r o d e s o n e a c h q u a d r a n t . B ye n e r g i s in g t h e c o r r e c t c o m b i n a t i o n s o f s u c h e l e c t ro d e s , i t is p o s s i b le t o t i l ta n d t r a n s l a t e t h e s a m p l e w i t h g r e a t f l e x i b i l i t y .S ince the e lec t r i c f i e lds r equ i r ed to ach ieve s ign i f i can t d i sp lacements a r ei n t h e o r d e r o f 1 M V m - 1 , h i g h d r i v i n g v o l t a g e s a r e u s u a l l y n e c e s s a r y f ort h e s e b u l k p i e z o e l e ct r ic de v ic e s. F o r p u s h i n g a c t u a t o r a p p l i c a t i o n s t h i sl i m i t a t i o n i s n o w c o m m o n l y o v e r c o m e b y d i v i d i n g t h e a c t u a t o r i n t o t h i nlaye r s to g ive s t a c k o r m u l t i - l a y e r dev ice s (desc r ibed l a t e r ) . How eve r , inspec ia l conf igura t ions , mono l i th ic ( i . e . no t l aye red) ac tua to r s can s t i l l bev e r y a p p e a l i n g . T h i s is t h e c a s e f or t h e M o o n i e and i t s de r iva t ive , theCymbal .6.4.2.1 M o o n i e s a n d C y m b a l sT h e c o n c e p t u n d e r l y i n g t h e M o o n i e a c t u a t o r w a s f i r s t e m p l o y e d i n t h ea c o u s t i c a l t r a n s d u c e r f o r o c e a n o g r a p h i c a p p l i c a t i o n p a t e n t e d i n 1 9 9 1 b yN e w n h a m et al. a n d p r e s e n t e d l a t e r i n a p a p e r [ 2 ] . T h e b a s i c i d e a i s t oa p p l y m e t a l e n d - c a p s t o b o t h t h e f ac es o f a p ie z o e l ec t ri c d i s k ( a s s h o w n inF i g . 6 . 9 ( a ) ) s o t h a t t h e c o m p r e s s i v e f o r c e s o r t h o g o n a l t o t h e d i s c p r o d u c e ar ad ia l ex te ns io n o f the d i sc a s we l l a s com press ion . I n such a conf ig ura t ion ,the e ff ect ive d33 co ns tan t w h ich r e la te s the e lec tr i c fi eld to the s t r a in , in th i s

E x t e r n a l l o a d+ I I L V D T o r

o ~ d i a l i n d i c a t o r0

Elec trodeP L Z T + I I /

R e d u c e d l a y e r ~ EI~P l a n a r s u r fa c e

E l e c t r o d e

F i g. 6 .8 A r a i n b o w a c t u a t o r w i t h a n L V D T d i s p l a c e m e n t m e t e r [ 12].


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154 P i e z o e l e c t r i c M a t e r i a l s

c a s e b o t h o r t h o g o n a l t o t h e d i s c d i r e c t i o n , r e c e i v e s a p o s i t i v e c o n t r i b u t i o nf r o m t h e d 31 c o n s t a n t o f t h e p i e z o e le c t ri c d i s k ( w h i c h r e l a te s t o t h e s t r a i nd e v e l o p e d i n t h e p l a n e o f t h e d i s k b y t h e o r t h o g o n a l a p p l i e d e le c tr ic f ie ld ).I t c a n b e s h o w n t h a t t h e f o ll o w i ng f o r m u l a h o l d s [2]:

d~ f - K id 33 + K 2 d 3 1 , (6.1)w h e r e K 1 a n d K 2 a r e b o t h p o s i t i v e a n d d e p e n d o n th e g e o m e t r ic d i m e n s io n s( a n d m a t e r i a l c h a r a c t e r i s t ic s ) o f t h e d i s c a n d e n d - c a p s . I t is o b s e r v e d t h a tl a r ge c a v i ty d i a m e te r s l e a d to h ighe r va lue s o f d err bu t a l so to lowe r r e son a n t33~f requencies [2] .A f e w ye a r s l a t e r , t he sa m e r e se a r c he r s e xp lo i t e d th i s i de a f o r a c tu -a t i n g p u r p o s e s , w h i c h l e d t o t h e M o o n i e a c t u a t o r s k e t c h e d i n F i g . 6 . 9 ( b )( N e w n h a m et a l . [ 3 ]) . M o o n i e a c t u a t o r s a re p r e f e r ab l y m a d e o f P Z T - 5 Ad is c s w i t h b r a s s e n d - c a p s ; t h e d i m e n s i o n s o f t h e c o m p o s i t e a r e a b o u t l c mi n d i a m e t e r a n d 2 t o 7 m m i n th i c k n e s s . E f f ec t iv e d33 c o n s t a n t s c a n b e ash i g h a s 3 x 1 0 - 9 m V - 1 ( la t e r i m p r o v e d u p t o 10 x 1 0 - 9 m V - 1 ) w h i c h ise qu iva le n t t o a n a m pl i f i c a t ion r a t io o f 5 . I t is f oun d th a t i nc r e a s ing e nd-c a p t h i c k n e s s l e a d s t o a n i n c r e a s e d r e s o n a n t f r e q u e n c y , a t t h e e x p e n s e o fa r e duc e d d i sp la c e m e n t ( a nd e f f e c t ive d33) . On the o the r ha nd , a r e duc e de n d - c a p t h i c k n e s s l e a d s t o s m a l l e r o u t p u t f o r c e s , a l t h o u g h 2 0 N c a n s t i l l b ed e l iv e r e d w i t h 0 . 4 m m - t h i c k e n d - c a p s . V a r i o u s s t u d i e s h a v e b e e n c a r r i e d o u ts in c e t h e f ir st a p p e a r a n c e o f M o o n i e s t o o p t i m i s e th e i r p e r f o r m a n c e . T h em o s t i m p o r t a n t i m p r o v e m e n t r e q u ir e s c u t ti n g a g r o o v e i n t h e m e t a l ca p s,c lo se to the r e g ion whe r e the y a r e bonde d to the p i e z oe le c t r i c d i sc . S inc ea t t h a t p o i n t t h e r e is a c o n c e n t r a t i o n o f s t r e ss a n d t h e g r o v e l o c a ll y r e d u c e sthe r ig id i ty o f t he s t r u c tu r e , a l a r ge r d i sp la c e m e n t is a c h ie ve d a nd l e ss e n -e r gy i s e l a s t i c a l ly s to r e d in the e nd - c a ps [ 4 ] . Howe ve r , t he m os t s ign i f i c a n ti m p r o v e m e n t t o t h e M o o n i e a c t u a t o r c a m e f r o m i t s i n v e n t o r s a f e w y e a r sl a t e r [5] w i t h t h e C y m b a l d e s i g n ( se e F i g . 6 . 9 (c ) ). T h e m a j o r d i s a d v a n t a g e so f t h e p r e v i o u s d e s ig n w e re th e d e p e n d e n c e o f t h e o u t p u t d i s p l ac e m e n t o nt h e c o n t a c t p o s i t i o n ( t h e e n d - c a p s a r e n o t f l a t i n t h e d e f o r m e d s t a t e ) a n dc o m p l e x m a n u f a c t u r e b e c a u s e o f t h e c a v i t y t h a t h a s to b e m a c h i n e d i n t ot h e e n d - ca p s . A s h a s a l r e a d y b e e n m e n t i o n e d , o n e s u g g e s t e d e n h a n c e m e n to f t h e M o o n i e re q u i re s m a c h i n i n g a n a n n u l a r g r o o v e a b o v e t h e b o n d i n g re -g i o n (' g r o o v e d M o o n i e ') , b u t t h i s f u r t h e r in c r e a s e s p r o d u c t i o n c o m p l e x i ty .B y c o n t r a s t , t h e C y m b a l a c t u a t o r h a s p u n c h e d e n d - c a p s w h i c h a r e f l a t i nt h e m i d d l e , t h e r e f o r e s i m p l i f y i n g m a n u f a c t u r e a n d o f f e r i n g a m o r e r e l i a b l e


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( a )

( b )

Piezoelectric ceramic

l M e t a l c a p s

i i i i i i i i i i i i i i i i i i i i i i i i i i ! i i i i i N N i i

( c ) / . . . . . \/ \

l i ! i i i i ii i i i i i i i i i i i i i i i i i i ii i i i i i i i i i i i i i i i i i i i i i i i/ ~ / / / / A-..... . . . . . , 1... . . . . . /

F i g . 6 .9 M o o n i e s a n d C y m b a l s " ( a ) M o o n i e a c o u s ti c a l t r a n s d u c e r ; (b ) M o o n i e a c t u a t o r ;( c) C y m b a l a c t u a t o r [6 ].

c o n t a c t s u r fa c e . A t t h e s a m e t i m e t h e t h i c k n e s s o f t h e e n d - c a p s i s r e d u c e di n t h e b o n d i n g a r e a , w h i c h i n c r e a s e s t h e f l e x i b i l i t y a n d m i n i m i s e s m e c h a n i -c al l o s s e s - w i t h o u t t h e n e e d f or m a c h i n i n g t h e g ro o v e. S o i t is f o u n d t h a tC y m b a l a c t u a t o r s h a v e b e t t e r p e r f o r m a n c e t h a n b o t h t h e o r i g i n a l M o o n i ea n d the ' g r oo ve d M oon ie ' , w i th e f f e ct ive d33 o f 15 x 10 - 9 m V - 1 [ 5] . I n a dd i -t i o n , t h e f l at n e s s o f t h e e n d - c a p s s im p l i fi es t h e s t a c k i n g o f m a n y a c t u a t o r st o b u i l d a n a r r a y ( f o r g r e a t e r d i s p l a c e m e n t a n d / o r o u t p u t f o r c e s ) .

A n ' e x h a u s t i v e ' a p p r o a c h h a s r e c e n t l y b e e n d e v e l o p e d b y S i l v a a n dK i k u c h i t o f in d t h e b e s t t o p o l o g y f o r a c o m p o s i t e a c t u a t o r m a d e o f a p ie zo -e l e ct r ic c e r a m i c a n d s o m e i n a c t iv e m a t e r i a l t y p i c a l l y m e t a l [1 ]. I n t h i s


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156 P i e z o e l e c t r i c M a t e r i a l s

I

~i ~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~i~!~i~!~i~!~i~i!~i~1

~i i i i ~! i i i i i i i i i i ~I i i ~ i i i i i I i i i i i i i i i i i i i i i i ! i i ! i ~ i i i i I i ~ i i i ~ i ~i i i i i i i i i i i i i i i i ! i i i i i i i i i i

Fig. 6.10 A piezoelectric stack actuator is formed by assembling together several elec-troded piezoelectric elements.

m e t h o d t h e t r a d i t i o n a l i n t u i t i v e a p p r o a c h b a s e d o n " e n g i n e e r i n g c o m m o ns e n se " i s r e p l a c e d b y a s y s t e m a t i c o p t i m i s a t i o n o f a s t r u c t u r e . I n t h e f ir stp l ace , a n a r r a y o f ce ll s is c r e a t e d an d a l l ow ed t o h ave a deg ree o f f il li ng o fa d e f in e d m a t e r i a l . T h e d i s t r i b u t i o n o f m a t e r i a l is t h e n o p t i m i s e d e it h e rfo r m a x i m u m fo rc e o r d i s p la c e m e n t . T h e a l g o r i t h m d e v e l o p e d d e t e rm i n e sa u t o m a t i c a l l y w h i c h c el ls a r e t o b e v o id s a n d w h i c h m u s t b e f ille d w i t hm a t e r i a l . I n t e r e st in g l y , t h e p r o c e d u r e h a s b e e n a p p l i e d to a M o o n i e -l ik ea c t u a t o r a n d t h e r e s u l t i n g c o n f i g u r a t i o n i s v e r y s i m i l a r t o a C y m b a l .

6 . 4 . 3 S t a c k a n d M u l t i - L a y e r A c t u a t o r sA s h a s a l r e a d y b e e n b r i e f l y m e n t i o n e d , t h e n e c e s s i t y f o r h i g h d r i v i n g v o l t -a g e s h i n d e r s t h e e x t e n s i v e a p p l i c a t i o n o f l o n g e x t e n s i o n a l p i e z o e l e c t r ic a c -t u a t o r s . T h i s p r o b l e m w a s a m e l i o r a te d w i t h t h e d e v e l o p m e n t o f s t ac k ac -t u a t o r s . I n th i s c o n f i g u r a t i o n , s e v e r a l l a y e r s o f t h i n p i e z o e l e c t r ic c e r a m i c sa r e i n d i v i d u a l l y p r o v i d e d w i t h e l e c t r o d e s a n d t h e n s t a c k e d o n e u p o n t h eo t h e r a s i l l u s t r a t e d i n F i g . 6 . 1 0 . T h e r e s u l t i n g s t r u c t u r e i s a s u c c e s s i o n o fc e r a m i c - e l e c t ro d e e le m e n t s . B y c o n n e c t i n g to g e t h e r e v e r y o t h e r e le c t ro d e ,t h e p i e z o e l e c t r ic e l e m e n t s a r e e l e c t r ic a l l y c o n n e c t e d i n p a r a l l e l , w h i l s t m e -c h a n i c a l ly t h e y a r e p la c e d i n s er ie s. T h e o b v i o u s a d v a n t a g e is t h a t t h ed r i v i n g v o l ta g e d o e s n o t a c t a c r o ss th e w h o l e l e n g t h o f t h e a c t u a t o r b u to n l y a c r o s s e a c h t h i n l a y e r. I n t h i s w a y t h e r e s u l t i n g e l e c t ri c f ie ld is m u c hh i g h e r .


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Piezoelectric Actuators 157A f u r t h e r i m p r o v e m e n t c a m e w i t h t h e m u l t i -l a y e r t e ch n o l og y , i n it i a ll y

d e v e l o p e d f or c a p a c i t o r s . H e r e t h e p i e z o e l e c t ri c m a t e r i a l is l a i d d o w n int h i n l a y e r s o n w h i c h e le c t r o d e s a re d e p o s i t e d b y s c re e n p r i n t in g . T h e s ea r e t h e n s t a c k e d o n e u p o n t h e o t h e r , a n d t h e c e r a m i c a c t u a t o r f o r m e d b yf ir in g t h e a s s e m b l y . T h e s t r u c t u r e i s i l l u s t r a t e d i n F i g . 6 .1 1 , w h e r e a s ar a n g e o f r e a l d e vi c e s is s h o w n i n F i g . 6 . 6 ( A - D ) . T h i s t e c h n i q u e d e c r e a s e sp r o d u c t i o n c o s t s w h i l e i n c r e a s i n g re l i a b il i ty . A f t e r f ir in g t h e a c t u a t o r isp o l e d ( i n m u l t i - l a y e r s , a s i n s t a c k s , a d j a c e n t l a y e r s h a v e o p p o s i t e p o l i n gd i r e c t i o n s ) .

6 .4 .3 .1 Multi-Layer CharacteristicsM u l t i - la y e r a c t u a t o r s a r e t h e m o s t r o b u s t c o n f i g u r a ti o n a v a i l ab l e f or p ie z o-a c t u a t o r s . T h e y a r e u s e d a s p u s h e r s b e c a u s e i n t h i s m o d e t h e y c a n d e v e l o pv e r y h i g h f o r c e s , w h i l s t b e i n g r a t h e r f r a g i l e i n t e n s i o n , b e n d i n g o r t o r s i o n .T h e o p e r a t i n g v o l t a g e s r a n g e f r o m a b o u t 6 0 t o 1 5 0 V o r m o r e , d e p e n d i n gp r i m a r i l y o n t h e t h i c k n e s s o f t h e l a y e r s a n d s e c o n d a r i l y on t h e m a t e r i a l .R e c e n t l y , v e r y t h i n l a y e r s h a v e b e e n r e a l i z e d ( d o w n t o 3 0 p m ) . W h i l e th i sr e d u c e s t h e v o l t a g e n e c e s s a r y i t a l s o p r e j u d i c e s t h e e n e r g y d e n s i t y ( t h e r a t i oo f e l e c t r o d e t o a c t i v e m a t e r i a l i n c re a s e s) . T h e p r o d u c t i o n o f v e r y t h i n l a y e rsr e q u i r e s a s o p h i s t i c a t e d a p p r o a c h t o a v o i d p o r o s i t y ; v o i d s i n t h e s t r u c t u r ec a n r e s u l t i n c r a c k i n g o r a r c i n g b e t w e e n t h e e l e c t r o d e s .

= v , . . . . ' e l e c t r o d e

I n t e r n a l e l e c t r o d e s

Fig. 6.1 1 The multi-layer structure of piezoelectric actuators: man y sandwiches ofelectrode-ceramic-electrode are built together so tha t the va rious piezoelectric layersare electrically connected in parallel and mechanically in series.


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4~ A

= = 28 Bi5 1

i I0 0 .025 0 .05 0 .075 0 .1T i m e ( m s )

Fig. 6.12 Dyn ami c response of two piezoelectric actuators . Act uat or A is 2 3 10mm 3and Act uat or B is 5 5 18mm 3. The driving circuit has negligible induct ance but aresistance of 5gt (in series with the actuator).

the Young's modulus and the length of the actuator. Electrical parame-ters are also import ant : the capacitance of the piezoelectric actuato r is afactor in determining the time constant of the circuit (in conjunction withthe resistance of the electrodes and any external circuit resistance) and sothe time before the electrodes of the actuator reach the nominal voltage.Further, as explained in the introduction, the actual resonant frequency ofthe actuator is strongly affected by the piezoelectric effect and therefore bythe relevant constants.

Figure 6.12 shows the response to a voltage step as observed on twodifferent commercial actuators in the same experimental conditions: one is2 3mm 2 in cross-section, the other is 5 5mm2; their respective lengths are10 and 18mm. It is possible to observe the effects of the different resonantfrequencies and capacitances on the response.

Prediction of the behaviour of a piezo-actuator in a given condition ispossible through a computational model that takes into due account boththe mechanical and the electrical systems and their strong interaction. Sucha model also needs to implement a distributed mass scheme for the actuatorto be able to describe various normal modes of vibration.

It has been anticipated in the introduction that the resonant frequencyof a piezoelectric material is dependent on electrical parameters. In order


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Chpt 06 Piezoelectric Materials

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