Brillouin scattering near the ferroelectric
phase transition in TSCC
Authors: T. Hikita, P. Schnackenberg, & V. Hugo Schmidt
This is an Accepted Manuscript of an article published in Ferroelectrics in 1985, available online:
http://www.tandfonline.com/10.1080/00150198508221390.
T. Hikita, P. Schnackenberg, and V.H. Schmidt, “Brillouin scattering near the ferroelectric
phase transition in TSCC,” Ferroelectrics 63, 107-114 (1985).
http://dx.doi.org/10.1080/00150198508221390
Made available through Montana State University’s ScholarWorks
scholarworks.montana.edu
0 1985 Gordon and Breach, Science Publishers, Inc.
and OPA Ltd. Printed in the United States of America
Ferroehetnes, 1985, Vol. 63, pp. 107-1 14
0015-0193/85/6301 -0107/$15 .OO/O
BRILLOUIN SCATTERING NEAR THE FERROELECTRIC PHASE
TRANSITION I N TSCC
TOMOYUKI HIKITA*, PAUL SCHNACKENBERG AND V. HUGO SCHMIDT
Physics Department, Montana S t a t e University,
Bozeman, Montana 59717 U.S.A.
Abstract B r i l l o u i n s p e c t r a from l o n g i t u d i n a l phonons in f e r r o electric t r i s - s a r c o s i n e calcium c h l o r i d e (TSCC) propagating
along IlOOJ, lOl0’) and [OOll have been measured as f u n c t i o n s of
temperature. Large anomalies were found i n t h e B r i l l o u i n s h i f t
and l i n e w i d t h in t h e I 100) and [ 001) phonons. These anomalies
are i n t e r p r e t e d as a r i s i n g from t h e l i n e a r coupling of t h e
p o l a r i z a t i o n and phonons. From t h e t h e temperature where t h e
l i n e w i d t h is maximum, t h e r e l a x a t i o n time f t h e p o l a r i z a t i o n
sec, where
f l u c t u a t i o n s is estimated t o be 7=3.lxl0-lq/(Tc-T)
T, is t h e f e r r o e l e c t r i c t r a n s i t i o n temperature. W e a l s o
observed anomalies i n B r i l l o u i n s h i f t and l i n e w i d t h of t h e [ O l O ]
phonons which propagate along t h e f e r r o e l e c t r i c a x i s . These
anomalies are i n t e r p r e t e d as roming from e l e c t r o s t r i c t i v e couThe energy r e l a x a t i o r time m s estimated t o be rE’2.5
xl0plinfb/(T-Tc)
sec in t h e pardelectr2-c (PE) phase and
.O
x10- 9 /(T-Tc) sec i n t h e f e r r o e l e c t r i c (FE) phase, by comparing
our B r i l l o u i n r e s u l t s w i t h t h o s e f t h e u l t r a s o n i c measurements.
INTRODUCTION
Tris-sarcosine calcium c h l o r i d e (TSCC) i s a u n i a x i a l f e r r o e l e c t r i c ,
w i t h a Curie temperature near 130 K.l
A t room temperature i t has
orthorhombic symmetry c h a r a c t e r i z e d by space group D2i6-Pnma with
f o u r formula u n i t s per u n i t c e l l . 2 I n t h e FE phase t h i s c r y s t a l
9
remains orthorhombic with spase group C2v-Pna21.
There a r e d i s p u t e s concerning whether t h e FE t r a n s i t i o n of t h i s
c r y s t a l i s order-disorder o r d i s p l a c i v e . S o f t modes have been found
3-5
S c o t t ’ s group c l a i m s that
i n TSCC both i n t h e PE and FE phases.
t h i s c r y s t a l is a textbook example of a d i s p l a c i v e t y p e f e r r o e l e c t r i c
from t h e i r a n a l y s i s of t h e r e s u l t s
107
of m i l l i m e t e r wavelength spec-
T. HIKITA, P. SCHNACKENBERG AND V. H. SCHMIDT
108
t r o ~ c o p y .They
~
could s a t i s f a c t o r i l y e x p l a i n t h e t e m p e r a t u r e
dependence of t h e d i e l e c t r i c c o n s t a n t i n t h e above frequency r e g i o n
by a simple o s c i l l a t o r model. However, Chen and Schaack r e c e n t l y
showed t h a t t h e i r Raman and i n f r a r e d s p e c t r a can b e much b e t t e r
e x p l a i n e d by t h e pseudospin-phonon c o u p l i n g t h e o r y . 6 y
They concluded
t h a t TSCC and p a r t i a l l y brominated TSCC (5.e. TSCC1-xBx) undergo
phase t r a n s i t i o n s which are mostly of t h e o r d e r - d i s o r d e r type. 6 9 7
Furthermore, Schmidt showed that t h e pressure-temperature
diagram’
phase
of TSCC can be i n t e r p r e t e d by a c l u s t e r model,’ which
i n d i c a t e s t h a t t h i s phase t r a n s i t i o n i s p a r t l y of t h e o r d e r - d i s o r d e r
type. S i n c e B r i l l o u i n s c a t t e r i n g measures t h e v e l o c i t y and attenu a t i o n o f a c o u s t i c phonons i n t h e GHz r e g i o n , i t s u s e i n TSCC h e l p s
t o understand t h e dynamical behavior i n t h i s frequency r e g i o n .
EXPERIMENTAL
S i n g l e c r y s t a l s of TSCC w e r e grown from a n aqueous s o l u t i o n of p u r e
sarcsine and r e a g e n t g r a d e CaC12. S i n c e t h i s c r y s t a l has f e r r o e l a s t i c
domains a t room temperature, s i n g l e domain p o r t i o n s were c a r e f u l l y
examined w i t h a p o l a r i z i n g microscope. E x c e p t i o n a l l y c l e a r p a r t s
were chosen from t h e s e c r y s t a l s and two samples which have t h e form
3
of a r e c t a n g u l a r p a r a l l e l e p i p e d 3 x 3 ~ 2mm were prepared. One sample
was c u t so t h a t t h e - l o n g i t u d i n a l phonons q I1 [lo01 and q 11 [OlOl
could be measured by r i g h t a n g l e s c a t t e r i n g and t h e o t h e r w a s c u t
so that l o n g i t u d i n a l phonons q I\
LO011 and q I] [0101could b e measured.
The two samples w e r e p o l i s h e d and t h e n masked t o g e t h e r by a blackened coper f o i l w i t h p i n h o l e s f o r t h e i n c i d e n t and t h e s c a t t e r e d l i g h t
beams. The masked sample p a i r was p l a c e d i n a h i g h p r e s s u r e o p t i c a l
c e l l d e s c r i b e d previously.”
The c e l l w a s f i l l e d w i t h i s o p e n t a n e
f o r index matching. The o p t i c a l c e l l t e m p e r a t u r e could be c o n t r o l l e d
w i t h i n 3 mK during t h e measurement.
A L e x e l Model 95-2 argon laser o p e r a t i n g i n a s i n g l e mode a t a
wavelength of 514.5 nm and a power level of 200 t o 300 mW was used
as a l i g h t source. The s c a t t e r e d l i g h t was c o l l e c t e d i n a c o n e of
109
BRILMUIN SCATTERING OF TSCC
1' and analyzed by a p i e z o e l e c t r i c a l l y scanned Burleigh Model 140
Fabry-Perot i n t e r f e r o m e t e r . F i n e s s e o p t i m i z a t i o n and d r i f t c o n t r o l
were achieved by a home-made c o n t r o l system using an AIM-65 microcomputer
.
RESULTS AND DISCUSSION
F i g u r e s 1-3 show t h e temperature dependence of t h e B r l l o u i n s h i f t
and l i n e w i d t h f o r l o n g i t u d i n a l phonons propagating along [ 1001 ,
[ O l O l and [ O O l I . The temperature dependence of t h e B r i l l o u i n s h i f t
and t h e decay r a t e of t h e [lo01 phonons i s q u i t e similar t o that of
t h e [ O O I ] phonons though t h e anomlies a r e smaller f o r t h e l a t t e r
c a s e . I n t h e above t w o cases, t h e p o l a r i z a t i o n and t h e s t r a i n couple
For t h e s e two phonon propagations, t h e
12-14
the attenuation
i n t h e FE phase a r e given by
b i l i n e a r l y i n t h e FE phase."
v e l o c i t y v and
v
2
2
2 2
9 2 -2
= v,- [(V,-Vo)/(l+W-Tot
..'--.
)I,
TSCC
q // Do01
'.i
Figure 1
Temperature dependence of B r i l l o u i n s h i f t
linewidth
(0)
along t h e
(0)
and
(FWHM) of l o n g i t u d i n a l phonons i n TSCC propagating
[loo]
d i r e c t i o n . The s c a t t e r i n g geometry is xSy(zz)-xSy.
T. HIKITA, P. SCHNACKENBERG AND V.H. SCHMIDT
110
c1 = [(v,-vo)/2v,l[
2 2
3
w2 Tot-l/(l+w 2 Tot
2 -2 11
where t is t h e reduced temperature (Tc-T)/T,,
.
(3)
To is t h e i n d i v i d u a l
for t h e r e l a x a i o n
d i p o l e r e l a x a t i o n time i n t h e e x p r e s s i o n ==Tot-'
t i m e T. From Eq. (2) we n o t i c e that t h e phase t r a n s i t i o n is marked by
a q u i c k d r o p i n t h e v e l o c i t y w i t h d e c r e a s i n g temperature. However,
e x p e r i m e n t a l l y t h e [lo03 and [ O O l ] phonon v e l o c i t i e s do n o t e x h i b i t
.
t, 20.6
I
.:
z
W
e
TSCC
q//[OIO]
-......*.*.-.
##
20.2
I
- 200
5
0 5 .
D
TEMPERATURE (K)
Figure 2
z
100 ;
Temperature dependence of B r i l l o u i n s h i f t
(0)
and
l i n e w i d t h (0) (FWHM) of l o n g i t u d i n a l phonons i n TSCC propagating
along t h e [ O l O ] d i r e c t i o n . The s c a t t e r i n g geometry i s x+y(zz)x-y.
-I"
P
... . ..
+-
&I.*
4
21.6-
t 21.48
L
- -. - . .. .. .
1 " " I " " I " " ~ J " '
*.
*a.
*
*
i
TSCC
q//[ooll
21.2-
- 400
TEMPERATURE (K)
F i g u r e 3 Temperature dependence of B r i l l o u i n s h i f t
(0)
and
l i n e w i d t h (0)(FWHM) of l o n g i t u d i n a l phonons i n TSCC propagating
a l o n g t h e [OOll d i r e c t i o n . The s c a t t e r i n g geometry i s x+y(xx)y-z.
BRILLOUIN SCATTERING OF TSCC
111
such s h a r p d r o p s a t Tc, b u t r a t h e r slow rounding. These anomlies are
a t t r i b u t e d t o t h e q u a d r a t i c coupling of t h e p o l a r i z a t i o n and t h e
s t r a i n or i n o t h e r words, e l e c t r o s t r i c t i v e coupling. 11y15Such con-
t r i b u t i o n s t o t h e anomalies of t h e v e l o c i t y and t h e a t t e n u a t i o n are
s c h e m a t i c a l l y i l l u s t r a t e d i n Fig. 4. As we see from Fig.4,
t h e tem-
p e r a t u r e Tm a t which t h e a t t e n u a t i o n c o e f f i c i e n t is maximum does n o t
equal Tc,but occurs somewhat below Tc. From Eqs. (2) and (3) w e
obtain the relation
(Tc-T,)/Tc=~~o. By t h i s r e l a t i o n w e can calcu-
l a t e t h e elementary r e l a x a t i o n time. Though t h e c l e a r i n d i c a t i o n of
TC i s b l u r r e d by t h e a d d i t i o n a l small anomaly from t h e e l e c t r o s t r i c t i v e c o n t r i b u t i o n s , w e can u s e t h e s t e e p e s t dropping p o i n t of t h e
v e l o c i t y a s Tc. From t h e v e l o c i t y and a t t e n u a t i o n f o r t h e above two
cases, we o b t a i n t h e following r e s u l t s : For t h e q11[1001 phonons,-ro=
2.4x10-l~ sec, and f o r t h e 911
-14
[ 0013 phonons ,~ ~ = 2 . 3 x l O sec
.
These two r e s u l t s a g r e e s w e l l . w e
w i l l u s e t h e i r average, ~ , = 2 . 4 x
1 0 - l ~sec.
We next consider t h e temp e r a t u r e dependence of t h e B r i l l o u i n s h i f t and t h e phonon decay
rate f o r t h e l o n g i t u d i n a l phonons
p a r a l l e l t o t h e spontaneous pol a r i z a i o n . I n t h i s case, p o l a r i z a t i o n f l u c t u a t i o n s do n o t c o u p l e
b i l i n e a r l y t o t h e s t r a i n , because
Figure 4
Anomalies i n t h e
of t h e appearance of t h e depolar-
v e l o c i t y and t h e a t t e n u a t i o n
ization f i e l d i n the longitudinal
caused by p i e z o e l e c t r i c cou-
p o l a r i z a i o n wave. 15’l6 Therefore,
p l i n g and e l e c t r o s t r i c t i v e
t h e anomalies i n t h e v e l o c i t y and
coupling f o r l o n g i t u d i n a l
a t t e n u a t i o n of t h e s e phonons
phonons propergating per-
should b e expained by q u a d r a t i c
pendicular t o t h e p o l a r i z a -
coupling of t h e p o l a r i z a t i o n t o
tion axis.
t h e strain in both PE and FE
T. HIKITA, P. SCHNACKENBERGAND V. H. SCHMIDT
112
phases.
We now compare t h e v e l o c i t y and a t t e n u a t i o n of t h e a c o u s t i c
waves in t h e GHz and MHz regions. Ultrasonic v e l o c i t y and attenuat i o n measurements have been performed on t h i s c r y s t a l by Sorge and
Straube.17 Their r e s u l t s are reproduced in Figs. 5 and 6, together
with our B r i l l o u i n r e s u l t s which are converted t o t h e v e l o c i t y and
a t t e n u a t i o n scale.
We u s e t h e v e l o c i t i e s obtained by B r i l l o u i n s c a t t e r i n g and
and vo, r e s p e c t i v e l y . W e assume t h e
E -1
s i m p l e s t form f o r t h e r e l a x a t i o n time t o be7E=To t
, where7: i s
u l t r a s o n i c measurements f o r v,
t h e elementary r e l a x a t i o n time. The E designates that t h e s e relaxat i o n times a r e r e l a t e d t o energy r a t h e r than p o l a r i z a t i o n f l u c t u p u t t i n g i n t o Eq. (3) t h e values of t h e a t t e n u a t i o n
a t i o n s . By
c o e f f i c i e n t of t h e u l t r a s o n i c measurements a t , t h e temperature T-Tc=
=0.9K and -1.3 K (2.7 db/cm and 11.1 db/cm, r e s p e c t i v e l y ) , we
E
-12
obtain t h e following values of t h e r e l a x a t i o n time: ~ r ~ = 1 . 9 x l O
E
-12
sec f o r T)T, andTo=7.7x10
sec for TCT,.
Chen and S ~ h a a c k obtaied
~’~
T , = ~ . ~ x I O sec
- ~ ~from t h e i r analy-
sis of t h e pseudospin-phonon coupling of Raman and i n f r a r e d s p e c t r a .
This value i s one order of magnitude l a r g e r than ours. Deguchi e t
showed that t h e r e l a x a t i o n time i n TSCC i s expressed byTe3.8
c,)
sec from t h e i r d i e l e c t r i c d i s p e r s i o n measurements. I f
w e use t h e values
+
r e l a t i o n C /C-=2,
+
C =30 t o 50 K f o r t h e Curie constant 19’20 and t h e
-14
we obtain t h e valuesT,=4.4 t o 8 . 5 ~ 1 0
sec f o r
t h e elementary r e l a x a t i o n time which i s in r e l a t i v e l y good agreement
with our values. Though we can obtain an order-parameter r e l a x a t i o n
time from
t h e B r i l l o u i n s c a t t e r i n g experiment, t h i s does n o t
n e c e s s a r i l y mean t h a t TSCC undergoes an order-disorder phase trans i t i o n s . It is a l s o p o s s i b l e t o adopt t h e i n t e r p r e t a t i o n t h a t s o f t
mode frequency wedecreases and t h e damping constant Y diverges a s Tc
i s approached. I n such an extremely damped case, t h e system has t h e
same c o r r e l a t i o n function a s t h a t of t h e r e l a x a t i o n a l mode where
2
t h e e f f e c t i v e r e l a x a t i o n time i s given by Y / w o . Recently, Sugo et
a1.21
performed an p r e c i s e Raman measurements i n t h e f e r r o e l e c t r i c
BRILLOUIN SCATTERING OF TSCC
113
TEMPERATURE (K)
Figure 5
Temperature dependence of sound v e l o c i t y i n TSCC for
Brillouin (BS) a t 16 GHz and for ultrasonic (US) measurements
a t 20 MHz. The v e l o c i t y s c a l e f o r the Brillouin scattering was
adjusted t o that of the ultrasonic measurements.
TSCC
I .o
q//C0103
1
i
TEMPERATURE (K)
Figure 6
Temperature dependence of the attenuation in TSCC f o r
Brillouin scattering (BS) a t 16 GHz and for ultrasonic (US)
measurements a t 20 MHz.
T. HIKITA, P. SCHNACKENBERG AND V. H.SCHMIDT
114
phase of TSCC up to Tc.
They showed that w o 2 / 7 is nearly propor-
tional to Tc-T near Tc (within about 10 K) and 7=5.9xlO-"
Tc-0.05 K.
ture.
eec at
Our result gives T = 6 . 3 ~ 1 0 - ~sec
~ at the same tempera-
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