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INTERNAL FRICTION ASSOCIATED WITH
DOMAIN WALLS AND FERROELASTIC PHASE
TRANSITION IN LNPP
Sun Wenyuan, Shen Huimin, Wang Yening, Lu Baosheng
To cite this version:
JOURNAL DE PHYSIQUE
C o l l o q u e C10, s u p p l 6 m e n t a u n 0 1 2 , Tome 46, dbcembre 1 9 8 5 p a g e C10-609
INTERNAL FRICTION ASSOCIATED WITH DOMAIN WALLS AND FERROELASTIC PEIBSE TRANSITION IN LNPP
SUN WENYUAN, SHEN HUIMIN, WANG YENING AND LU BAOSHENG+
I n s t i t u t e
o f
S o l i d S t a t e P h y s i c s , D e p a r t m e n t o f P h y s i c s , N a n j i n g U n i v e r s i t y , N a n j i n g , C h i n a' I n s t i t u t e
of
C r y s t a l M a t e r i a l , Shandong U n i v e r s i t y , C h i n aAbstract - ?tYo i n t e r n a l f r i c t i o n peaks (50
-
100kHz) have been masured i n LNPP near its t r a n s i t i o n temperature. The peak a t Tc=14l0C is associated with t h e f e r r o e l a s t i c t r a n s i t i o n where t h e e l a s t i c constant C55 vanishes and t h e peak a t a lower temperature is a t t r i b u t e d t o t h e motion of d m i n walls. The variation of domain walls and its r e l a t i o n t o Q-1 were obtained by i n s i t u nleasuremnts. The mechanisnsof t h e peaks are discussed.I - INTRODUCTION
Like martensitic phase t r a n s i t i o n , f e r r c e l a s t i c t r a n s i t i o n is a l s o associated with shear s t r a i n s t h a t can be re-oriented by applied stress. Several experimental r e s u l t s /1,2/ show that t h e i n t e r n a l f r i c t i o n i n t h e f i r s t order f e r r c e l a s t i c phase t r a n s i t i o n is a l s o similar t o t h a t of martensitic t r a n s i t i o n . The idea t h a t t h e i n t e r n a l f r i c t i o n under isothermal condition i s due t o the stress-induced motion of coherent boundaries /3,4,5,6/ has been widely accepted.But s o f a r , t h e r e is no report on t h e correlation, especially on t h e quantitative correlation between Q-1
and boundaries, nor t h e investigation on t h e i n t e r n a l f r i c t i o n associated with second o@er f e r r o e l a s t i c t r a n s i t i o n
In La,-xNdxPrO,+ (LNPP), t h e r e is a phase change from mm t o 2/m s p t r y a t 140f2OC. According t o Aizu /7/, it is a pure f e r r c e l a s t i c t r a n s i t i o n with te,, as t h e order p a r m t e r s /8/. Wre d e t a i l e d studies /9,10,11,12/ show that t h e c h a r a c t e r i s t i c s of
LNPP are of second order. There are two tirpes of domains i n t h e f e r r o i c phase of
LNPP c r y s t a l : a- and b-domains with t h e i r walls perpendicular t o c and a a x i s respectively. Generally, only domains of a-type that t r a v e r s e a l l the c r y s t a l are
present
/ l o / ,
s o t h e domain configuration is much s-ler. This, togather with t h e f a c t t h a t coherence is higher i n f e r r c e l a s t i c substances than in martensite, makes possible the quantitative investigation of t h e correlation between i n t e r n a l f r i c t i o n and domain walls, t h a t w i l l be helpful f o r t h e c l a r i f i c a t i o n of mechanisms of i n t e r n a l f r i c t i o n i n martensitic t r a n s i t i o n as well as i n high damping.C10-610 JOURNAL DE PHYSIQUE
I1
-
EXPERIMENTAL PROCEDUREParx three-component-resonator method was used t o drive and detect the longitudinal vibration along the c axis of samples that had been cut from single crystals t o f i t the frequency of 50, 86 and 100W respectively. Q-1 measurements m e c a n t e d out i n a special self-made furnace i n which domains can be observed i n s i t u with a polarization microscope during heating and cooling. C55 w a s measured with pulse-echo
-overlap method. A l l measurements were carried out on La,, PrO,,samples.
I11
-
RESULTS AND ANALYSISExperimental results show that domains increase proportionally t o (Tc-T)-1 (Fig. 1).
On heating, domins increase with t-rature and internal f r i c t i o n increases $imultaneously, which leads t o the ascription of the internal f r i c t i o n peak P2 t o newly appeared domains. When domins begin t o increase rapidly and become nearly periodically distributed i n the crystal (40-80 walls per nm), the internal f r i c t i o n reaches a peak (P2) value with a minimum of the resonant frequency f r , an?i then decreases as domains continue t o increase with temperature. The nunker of domains becorres larger and larger as temperature approaches Tc, and goes beyond the resolu- tion of the microscope. Domains f i n a l l y disappear a t Tc. A very narrow internal f r i c t i o n peak (PI), as w e l l a s very rapid changes of resonant frequency can be masured a t Tc, corresponding t o the minimum of C55 (Fig. 2 ) . Because the width of Pi is only about 0.l0C, it is very d i f f i c u l t t o make an accurate measurement of the peak height. Ch cooling, there
is
a 2-3°C hysteresis f o r P2 but no hysteresis f o r P i within the experimental accuracy (also see Fig. 2 ) . Results are the same i n other samples. It is essential that there is no anomaly in C55 except f o r the rapid mode softening a t Tc (Fig. 2a), which suggests that P2 is not associated with the ferro- e l a s t i c phase transition. In order t o study the mechanism of P2, a small s t r e s s was applied on sample 1 on heating. Consequently, a large n&r of domains w a s "frozen" a t room temperature in most portion of the crystal. As a r e s u l t , P2 almost dis- appeared, and the corresponding minimum of fr t o t a l l y disappeared while a broad internal f r i c t i o n peak P3 was measured a t about 60°C (Fig. 3 ) . After ren-oving the"frozen" domains with a shear s t r e s s , P2 and fr b e m the sam!
as before whereas P3 was essentially eliminated (see curve b Fig. 3). 16 Cbviously, PI remains unchanged as
can be seen i n the three curves i n Fig. 3.
In addition, the measurerent mde a t 3fr on s q l e 1 and a t different heating r a t e on sample 2 ( 86kI-k )
@40'
L o -
b o o -
I
q:
w 6 0i
1::
show no significant change e i t h e r i n peak height or i n peak tempera- ture. (h the basis of these f a c t s ,
.
-;
' it is reasonable t o consider t h a t..
P2 is a s t a t i c hysteresis loss due t o newly appeared domains, and P jis due t o the "frozen" domains, the mechanism of which i s n o t y e t studied. It should be noted that though P2 is attributed t o the motion of %main w a l l s , it is quite different from martensitic transition, because the peak does not correspond .tQ
'c
minirmrm the minirmnn of the s o f t of f r is due t o therrode.
modulusTIbk
,
,
.
.
-
defect.
The reason why the internal Fig. 1 NLnnber of domain -walls per mn f r i c t i o n reaches
a
peak valuevs. teno?erature. mgnif ication instead of varying mnotonously of the microscope is 40X. with the n&r of damins m y be
constant C55 ( a ) , Q-1 and Fig. 4 Lateral motion of domains a and t h e resonant f r e q e n c y f r of b due t o t h e foimation of Ctomin sample 1 ( b ) with t e w r a t u r e . c.
i n t e r p r e t e d i n terms of t h e i n t e r a c t i o n between domain walls. DDmains are more
mobile when t h e distance between t w o walls is l a r g e enough t h a t t h e i n t e r a c t i o n between them is negligible, howver, when t h e distance becomes smaller s o that the s t r a i n f i e l d induced by t h e walls p a r t l y overlap, t h e m b i l i t y of t h e walls is then reduced by t h e interaction. That accounts f o r t h e decrease of Q-1. It has been observed i n LNPP t h a t domains move l a t e r a l l y as a r e s u l t of t h e squeeze by t h e fonration of new domains as i l l u s t r a t e d i n Fig. 4, a t a r e l a t i v e l y l a r g e r domain density. T k phenornsnon has not been o b s v d a t smaller domain density. The reduc- t i o n of domain wall mobility due t o i n t e r a c t i o n ;xis a l s o been observed in someother f e r r o e l e c t r i c substances /13, 14/.
N - DISCUSSION
(210-612 JOURNAL DE
PHYSIQUE
understood by considering t h e surface energy of t h e f e r r o i c phase. According t o /11/, t h e presence of f e r r o e l a s t i c domains causes d e f o m t i o n of c r y s t a l surfaces, t h a t leads t o t h e increase of surface energy, a process somwhat s i m i l a r t o t h e cases of f e r r o e l e c t r i c i t y /15/ and ferromgnetism /16/. The increment of t h e e l a s t i c surface energy is given by /17/:
E=(K/N)
7
(1)where K is a constant, N is the number of domain walls per u n i t v o l m and is t h e order paremeter which is equal t o
2
e13for t h e present case. Taking i n t o account t h e surface and wall energy, t h e t o t a l tree energy should be witten as:w h e r e 0 is t h e energy of a s i n g l e wall which can be calculated with th c m n l y used m t h o d /15/. Since t h e a s s m p t i o n t h a t t h e c o e f f i c i e n t before
7
should beproportional t o (T-Tc) is s t i l l v a l i d , it should a l s o should be t r u e t h a t (a/2+K/N)= al(T-Tc), t h a t gives N=A/(Tc-T) with A>O. Pbre d e t a i l e d calculation is underway. 2) The appearance of PI a t Tc is i n c o n f l i c t with the f a c t t h a t i n second order t r a n s i t i o n , t h e i n t e r n a l f r i c t i o n can be n-easured only i n MHz range. The possible explanation is t h a t C55 changes s o r a p i d l y (it can hardly be followed a t Tc) t h a t it can be t r e a t e d as a sudden change. According,to Eshelby /18/, an energy l o s s is incurred by t h e sudden change of elastic c o n s t a n t ( s ) :
E=(1/2) (Cijh- C.. ) el
.
e dvS
ljkm 11 ]an ( 3 )where Cijh
,
eh and C i j h , el.
are the elastic constants and s t r a i n s before and 1 3a f t e r t h e sudden change respectively. Actually, a small discontinuity with 0.2"C is
not r u l e d out y e t /12/. REFERENCES
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University, z(1963) 1-10.
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Weber, H. P., Tofield, B. C. and Liao, P. F., Phys. Rev. =(1975)1152. /11/ Budin, J. P., M i l a t o s - M o s , A., Nguyen Duc Chinh and IR ROUX, G. J . Appl.Phys. 46(1975)2867.
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