Frequency Dependence and Anisotropy of
the Glass Transition Tg of
Rb0.52(ND4)0.48D2PO4
Authors: J. Stankowski, Z. Trybula, & V. Hugo
Schmidt
This is an Accepted Manuscript of an article published in Ferroelectrics on March 1, 1988,
available online: http://www.tandfonline.com/10.1080/00150198808229467.
Stankowski, J., Z. Trybula, and V. H. Schmidt. “Frequency Dependence and Anisotropy of the
Glass Transition Tg of Rb0.52(ND4)0.48D2PO4.” Ferroelectrics 79, no. 1 (March 1, 1988): 351–
354. doi: 10.1080/00150198808229467
Made available through Montana State University’s ScholarWorks
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6 1988 Gordon and Breach Science Publishers S.A.
Ferroelecrrics. 1988, Vol. 79, pp. 351-354
Reprints available directly from the publisher
Photocopying permitted by license only
Rinted in the United States of America
FREQUENCY DEPENDENCE AND ANISOTROPY OF THE GLASS TRANSITION
OF Rb0.52(N04)0.48 D2 PO4
9
J.STANKOWSK1, Z.TRYBUtA,
I n s t i t u t e o f Molecular Physics,Polish Academy o f Sciences,
Poznari, POLAND
V.H.SCHMIDT
Department o f Physics, Montana State U n i v e r s i t y Bozeman,
Montana, U.S.A.
Abstract
The frequency dependence o f the glass t r a n s i t i o n
temperature T
has been c a l c u l e d from the Vogel-Fulcher law
9
2
10
u s i n g d i e l e c t r i c data obtained i n t h e 10 Hz t o 1 0 Hz region.
The best f i t was obtained with I n f o = 29 and To= 38 K. The
anisotropy o f T
ved
.
9
p r e d i c t e d r e c e n t l y by theory has been obser-
EXPERIMENTAL RESULTS AND DISCUSION
Studies of the frequency-dependent d i e l e c t r i c p r o p e r t i e s o f
D2PO
Rb0.52(N04)0.48
1
Schmidt and others
9
a t low frequency were done by Samara and
. In this
paper we r e p o r t t h e r e a l e ' and
imaginary r " d i e 1 e c t r i c permi t t i v i t y i n the X-band microwave r e g i o n
f o r temperatures from 5 K t o 180 K. T y p i c a l rounded cusp dependence
for r'(T)
and narrow rounded maximum f o r
€"(TI
were observed.Tre-
of t h e glass " t r a n s i t i o n " ,
9
T =86 K f o r f=9.3 GHz when the microwave e l e c t r i c f i e l d i s p a r a l l e l
9
t o the c-axis o f the Rbo~52(ND4)o~48D2P04
mixed c r y s t a l (FIGURE 1).
a t i n g t h i s maximum as the temperature T
According t o c l u s t e r models o f p r o t o n glass4
, short
range i n t e -
r a c t i o n s form p a r t l y ordered c l u s t e r s imbedded i n t h e f r u s t r a t e d
proton system. The c l u s t e r s have a mean r e l a x a t i o n t i m e r s t r o n g l y
r e l a t e d t o t h e i r volume and temperature, and
z decreases
rapidly
with i n c r e a s i n g temperature. According t o another viewpoint, t o be
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J . STANKOWSKI er al.
646/(352]
explained i n d e t a i l elsewhere
5 , the 2' d i s t r i b u t i o n i s governed by
e f f e c t i v e d i f f u s i o n o f HP04 and H3P04 d e f e c t s . I n e i t h e r case, t h e
II
9
"33
7
0
too
200
T (lo
FIGURE 1 Temoerature deoendences o f the r e a l E : x and imaginary
part's o f d i e l e c k c p e r m i t t i v i t y o f 72g'deuterated
RADP.
6
mean 1
' : i s given by the Vogel-Fulcher l a w :
r-l=foexp(-E/k(T-To)),
(1)
where f o and To are s c a l i n g parameters and E i s an a c t i v a t i o n energy. The frequency f o is t h e 0-0
...0
deuteron intrabond t r a n s f e r
attempt frequency, and To should be t r e a t e d as the temperature be2
low which t h e 0-0.. .O deuteron system i s "frozen". Courtens proposed that Eq.(l) should be modified t o the form:
Z -l=foexp(-E/k(T-To)@ )
.
(2)
where
A t t h e temperature g i v i n g maximum g ' ' we can say t h a t Z-'=f,
f i s t h e measurement frequency and T=T
formula :
( l n f o - l n f )-l=
k(TS-Tol4 /E
Q- *
Then Eq.(2) gives t h e
.
(3)
Figure 2 shows the p l o t - o f Eq.(2) f o r a t - 2 , l n f o = 2 9 and To=38 K,
using our experimental p o i n t and low frequency measurements'*
€;3
. The
for
good agreement shows t h a t t h e Eq.(2) form o f t h e Vogel-
Fulcher l a w describes t h e p r o t o n glass system i n our c r y s t a l . The
values o f l n f o and To are p r a c t i c a l l y the same as found by C o u r t e d ,
lnfo=28.5 and To=30 K f o r Rbo.38(ND4)o.6202P04
. I n terms
of physi-
c a l parameters,these r e s u l t s i l l u s t r a t e t h e r a p i d slowing down o f
dynamic processes w i t h decreasing temperature, and depending on the
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FREQUENCY DEPENDENCE AND ANISOTROPY
[353]/647
model adopted, the increase in cluster size4 or the increase in
5
defect diffusion path length between creatio and annihilation
.
0.20
FIGURE 2
1
A plot of (lnfo-lnf)
1
-1V S . ( T ~ ~ ~ -2T ~for
) lnfo=29
To=38 K and 4 =2.
7
4
Matsushita and Matsubara (MM) using a cluster theory predicted
anisotropy of T - different values of T for susceptibility along
9
9
the c and a axes. They introduced two order parameters,qx and q,
which give the temperatures T
and Tg33. Figure 3 shows that for
gll
maxima occur at different temperatures
Rbo.52(ND4)o.4802P04
the
for microwave electric field parallel to the a and c axes. Our data
show T =82 K and T =86 K, in accord with MM theory which gives
gll
933
Tg33> Tgll for concentration x < 0.5. Further experiments are
planned.
CONCLUSION
These experiments show that
obeys the Vogel-Fulcher law
ness (72 % deuteration ) as
In addition, the anisotropy
Matsubara was observed.
’
dielectric behavior for proton glasses
also when these is isotropic randomwell as cation randomness (48 % NO4).
of T predicted by Matsushita and
9
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J. STANKOWSKI er al.
648/[354]
0
1
50
I
100
T (K)
1
i
200
150
FIGURE 3 Temperature dependences of the imaginary part of
electric permittivity in arbitrary units f o r two orientations
and o
of microwave electric field: L
y3
;I1 .
REFERENCES
1. G.A.Samara and V.H.Schmidt,Phys.Rev.B 34 ,2035 (1986).
2. E.Courtens, Phvs.Rev.6 33 ,2975 (1986).
3. V.H.Schmidt,S.Waplak,S.Hutton and P.Schnackenberg, Phys.Rev.630,
2795 (1984).
4. E.Matsushita and T.Matsubara, J.Phys.Soc. Japan ,54, 1161 (1985).
5. V.H.Schmidt , Proc. 6-th Eur.Mtg. on Ferroelec., t o appear in
Ferroelectrics.
6. L Lundgren , P .Svedlindh , 0.Beckman, Phys Rev.826, 3990 (1982).
7. E.Matsushita and T.Matsubara, J.Phys.Soc. Japan , 55,666 (1986).
.
.