The ferroelectric and proton glass 
coexistence region in 
K0.77(NH4)0.23H2AsO4 detected by 
complex permittivity measurements
Authors: Z. Trybuta, S. Los, C. S. Tu and V. Hugo 
Schmidt
This is an author-created, un-copyedited version of an article published in Journal of Physics 
Condensed Matter. IOP Publishing Ltd is not responsible for any errors or omissions in this 
version of the manuscript or any version derived from it. 
The Version of Record is available online at http://dx.doi.org/10.1088/0953-8984/7/5/017.
Z. Trybula, S. Los, C.-S. Tu, and V.H. Schmidt, “The ferroelectric and proton glass 
coexistence region in K0.77(NH4)0.23H2AsO4 detected by complex permittivity 
measurements,” Journal of Physics Condensed Matter 7, 947-956 (1995).
Made available through Montana State University’s ScholarWorks 
scholarworks.montana.edu 
I. Phys.: Condens. Matter 7 (1995) 941-956. Printed in the UK 
The ferroelectric and proton glass coexistence region in 
K o J ~ ( N H ~ ) ~ . ~ ~ H ~ A s O ~  detected by complex permittivity 
measurements 
Zbigniew Tryhulat, Szymon to i t ,  C S Tu$ and V Hugo Schmidt$ 
t Institute of Molecular Physics, Polish Academy of Sciences. Pomari. Poland 
3 Physics Department. Montana State University, Bozeman, MT 59711. USA 
Received 23 September 1994, in final form 10 November 1994 
Abstract This paper reports results of the studies on complex permittivity E* = E' - id' 
in a mixed Ko.~,(N&h,z3HzAsO* crystal. Measurements along the crystallographic a axis 
have c l w l y  indicated the coexistence of the ferroelectric state and proton glass state in this 
c r y a l .  The temperature dependence of E:, shows a maximum at T, = 61 K, indicating a 
ferroelectric transition, while the dispersion of E; and e: below T = 40 K satisfies the Vogel- 
Fulcher equation with the parameters To = 8.3 K, Ec = 183.5 K and vE = 1.65 x 10" Hz, 
which proves the presence of the proton glass state. Analysis of the shape of the temperature 
dependence of dielectric losses E:(", T )  observed in the measurements along the ferroelectric c 
axis revealed the presence of another process of relaxation apart from that related to the freezing 
of ferroelectric domain wall motion known for KDP type crystals. The two relaxation processes 
m also described by the Vogel-Fulcher equation with the parameten To1 = 34 K, E,I = 7.7 K 
and vel = 6.8 x IOs Hz for one of them and for the other Tm = 20.5 K, E,z = 13.4 K and 
uCz = 5.6 x IO6 Hz. Our results prove the coexistence of the ferroelectric and proton glass states 
in the K O , ~ ( N & ) O ~ ~ H Z A S O ~  crystal, and the occurrence of different kinds of cluster of local 
ordering (proton glass and relaxor clusters) and ferroelectric domains, 
1. Introduction 
The proton glass state was discovered by Courtens [ l ]  in 1982 in mixed Rbt-,(N&),HzP04 
(RADP) crystals, composed of ferroelectric RbHZP04 (RDP) and antifemoelectric NH4H2Po4 
(ADP). The presence of this state, characterized by the disappearance of long-range order 
and the existence of short-range order within clusters [2j, has also been shown for the 
isomorphous arsenate crystal Rhl-x(NH4),H~As04 (RADA) by Trybufa et al [3-61 and 
confirmed by other authors [7,Sj. The presence of this state was also reported for the 
deuterated forms DRADP [9,10] and DRADA [ l l ,  121. Recently much attention has been paid 
to investigation of the coexistence of the glass and ordered states [6,12j, which is expected 
to contribute to explaining the phenomena leading to the formation of the proton glass state. 
This work has been undertaken to study the region of coexistence of the ferroelectric 
state and proton glass state in a & . ~ ~ ( N H ~ ) ~ . Z ~ H Z A S O ~  ( M - 2 3 )  crystal. 
2. Experimental method 
The crystal studied in this work was grown from an aqueous solution of KHzAs04, (KDA) 
and N H ~ H ~ A s O ~  (ADA) in a 77/23 ratio, by the slow evaporation method. From this 
0953-8984/95/050947+10$19SO @ 1995 IOP Publishing Ltd 941 
948 Z Trybuta et a1 
monocrystal of &.~~(NH.+)o.uHzAsO~. the samples to be studied were cut out along the 
crystallographic a axis and along the ferroelechic c axis of the crystal. The size of the 
sample cut out along the a axis was 2.57 x 8.52 x 1.05 mm, whereas the size of that cut 
along the c axis was 2.56 x 2.81 x 0.6 mm. The polished surfaces of the samples were 
coated with graphite electrodes. The measurements of the complex permittivity E* = E‘-~E” 
were performed between 3.4 K and 300 K in the Leybold He flow cryostat, with frequency 
varied from 200 Hz to 100 kHz using a RLC 1689M General Radio bridge and a 6425 
Wayne Kerr analyser. The temperature of the studied samples was measured by a Lake 
Shore Cryotronic DT-500 Si diode thermometer. 
3. Results 
The temperature dependence of the real part of the permittivity E: measured along the a 
axis is shown in figure 1. At ambient temperature the value of E: was about 66. With 
decreasing temperature of the sample E: monotonically increased. Figure l(a) presents the 
temperature dependence of E: in the range from 3.4 K to 120 K. At Tc = 61 K the real 
part of the permittivity reaches a clear maximum E: = 152.7, indicating a phase transition 
to the ferroelectric phase. For temperatures below 40 K, a dispersion of E: characteristic 
of the proton glass state was observed for five different frequencies (figure l(b)). Figure 2 
presents the temperature dependence of E: measured along the ferroelectric c axis. At 300 K 
E: = 20 and with decreasing temperature of the sample, as is the case of measurements 
along the a axis, E: values increase following the Curie-Weiss law: 
(E: - EL)-’ = c-l(T - Tcw) (1) 
where C is the Curie-Weiss constant and Tcw is the Curie-Weiss temperature. The values 
of these parameters were found to be C = 2185.4 K and Tw = 58.9 K. Deviation from 
the CurieWeiss law was observed at 67 K, whereas below 61 K dispersion of E: began 
(figure 2(b)). The temperature dependence of the inverse of the real part of the permittivity, 
described by (l), is shown in figure 3: In figures 2(a) and 3 the Curie-Weiss dependence 
is marked with a solid line. 
The temperature dependence of the imaginary part of the permittivity measured along 
the a axis, shown in figure 4 for a few frequencies, revealed below 40 K a dispersion 
characteristic for proton glass. These dependences were approximated by a Gaussian shape, 
according to the equation 
&:(U, T) = A(u)exp(-[T - ~ ~ ( u ) ~ ~ / 2 4 * ]  (2) 
where T,(v) is the temperature at which E:’ reaches a maximum value for a given frequency, 
and 2 4  is the width of the Gaussian curve. From the Tg values obtained in this way for all 
frequencies of the measuring electric field we could determine the Vogel-Fulcher dependence 
for this relaxation process: 
v = u,exp(-E,/(T, - TO)) (3) 
where To is the Vogel-Fulcher temperature at which the system is completely frozen, Ec 
is the activation energy needed for reorientation of electric dipoles in a cluster, and v, 
is the cut-off frequency. The best fit was obtained for the following values of these 
parameters: To = 8.3 K Ec = 183.5 K v, = 1.65 x 10” Hz. The Vogel-Fulcher 
Complex permittivity of Ko.n(NH4)o.z~ Hz AsO, 949 
8 0 -  
60 
'a 
40 
20 
,"o 100 A 
~ 
A A: 
0 
A 0  
A0 
A 
AC2 
- 
- a 
- 
c A 0  
I 
! 
0 20 40 60 80 100 120 
0 '  
120 - 
90 
60 
- 
41 
- 
on 
5 10 15 20 25 30 35 40 
0 '  " " " ' I .  ' ' I .  I '  
0 
T(K) 
Figure 1. The temperature dependence of &: for K,,.~~(NHa)n,uH~As04: (a) E:,(T) in the 
temperature range from 3.4 K to 120 K (b) the dispersion of 6;.  
dependence for the measurements along the a axis is shown in figure 5. The character of 
the temperature dependence of E:( measured along the ferroelectric c axis is much more 
complex. Figure 6 presents the dependences for a few frequencies. Assuming a Gaussian 
950 Z Trybuta et a1 
500 
400 
300 
c'c 
200 
100 
0 
0 0.4lcHz 
* 2.0lcHz 
0 1o.olcHz 
v 40.0 kHz 
Figure 2. The temperature dependence of E: for the measurements dong the ferroeleclric c 
axis for & ~ . ~ ( N H & ~ ~ H ~ A s O ~ :  (a) E:(T) for an electric field frequency of I kHz; (b) lhe 
dispersion of E: in the tempemlure range from 10 K 10 61 K. 
shape of the temperature dependence of E: and the existence of two relaxation mechanisms 
the experimental curve was approximated by the following equation (the solid lines in 
Complex permittivify of Ko.n(NH4 )0.23 HzAsOa 95 I 
. .  
0.045 
7 h 0.030 
8 
0- 
-w 
-lo 
I 
o 0.015 
W 
0.000 
40 60 80 100 120 140 160 180 
Figure 3. The Curie-Weiss dependence in KII,~~(NH~)II.~H~A~O~ for the measurements dong 
the ferroelecuic e axis. 
I 
n 
sltai 2 00 
10 
I 
20 30 40 
T ( K )  
F i y r e  4. The temperature dependence of E% in KII.~,(NH~)I~~~HzAsO~ for a few frequencies 
of electric measuring field. 
952 2 Trybuta et  a1 
- 
lo4 
v , ( m  : 
io3 
- 
I I 
Figure 5. 
I41.77(NHa)o.zsHzAsO4. 
The Vogel-Fulcher dependence for the relaxation region along the CL axis of 
30 
25 
20 
15 
E”, 
10 
5 
O L  
0 
0 10.0 !a2 
v 40.0 ktIz 
Figure 6. The temperature dependences of e: along the ferroelectric c axis for a few frequencies 
of the electric measuring field in Ko,7,(NFb)o.~HzAsO+ 
25 
20 
15 
Ellc 
10 
5 
0 1m 
fit 
fit 
- fit 
------ 
.......... 
0 
0 10 20 30 40 50 60 70 80 
Figure 7. The fit of lhe experimental course of E:(T) for 1 kHz by (4). The sum of the comes  
marked by the broken and dotted lines gives the solid line course. The existence of two regions 
of relaxation is c l w l y  visible. 
figure 6): 
s"(T) = A[exp[-(T - T,1)~/2A~ll  +B[exp[-(T - T , I I ) ~ / ~ A ~ ] I  (4) 
where A and E are the amplitudes of the Gaussian curves, 2A1 and 2An are their widths, 
and T,l and T,II are the temperatures at which 8; reaches a maximum. Figure 7 presents 
the c o m e  of the temperature dependence of E; for a frequency of 1 H z .  The solid 
line represents the fit according to (4) while the dotted and the broken lines illustrate a 
decomposition of $(T) into two Gaussian curves. For each of the studied frequencies we 
obtained a similar course of E:(T). The character of these courses indicates the existence 
of two different relaxation mechanisms, each  described by a Vogel-Fulcher dependence. 
The relaxation occurring at higher temperatures (the dotted line in figure 7) is related to the 
freezing of the motion of ferroelectric domain walls and the best fit to (3) was obtained for 
the parameters Tol = 34 K, Ecl = 7.7 K and u,l = 6.8 x IO5 Hz (figure 8). The other 
relaxation process (the broken line in figure 7) is also described by (3) but for'different 
parameters: To2 = 20.5 K E,z = 13.4 K; U& = 5.6 x IO6 Hz (figure 9). 
4. Discussion and conclusion 
The results of temperature measurements of complex permittivity E' = E' - is" in a mixed 
&.n(N€b)o.~H~As04 crystal along the a and the ferroelecttic c axes prove the coexistence 
of the ferroelectric and the proton glass states in this crystal. This phenomenon has been 
also observed in RADA mixed crystals [6,7]. In RADA [6] the coexistence on the ferroelectric 
954 2 Trybuia et a1 
15 20 25 30 35 40 45 
100/(T-To) (K-’) 
Figure 8. The Vogel-Fulcher dependence for the relaxation region marked by the dotted line in 
figure 7 for the mmurements along the e axis of ~ I .~~(NH~)~I .UH~ASO~.  
side of the phase diagram ends for ammonium concentration x Z 0.15, while for the studied 
KADA crystal the coexistence is clearly detected for x = 0.23. This suggests that the range 
of the glass state Occurrence in KADA is narrower than for RADA. 
The temperature dependences of the imaginary part of permittivity E“ measured along 
the a and c axes are different. Analysis of the measurement along the a axis proved 
the presence of proton glass. The temperature dependence of E;(T) was approximated by 
a Gaussian curve, which permitted determination of the parameters of the Vogel-Fulcher 
equation: TO = 8.3 K E, = 183.5 K uc = 1.65 x 101’ Hz. A comparison of these 
parameters with those obtained by Trybda et al 1131 for KADA with x = 0.4 (To = 5.4 K 
Ec = 409 K v, = 2.5 x IOl3 Hz) shows that in  KADA with x = 0.23 the clusters are greater 
than for KADA with x = 0.4, as expected, because KADA-23 has coexistence of ferroelectric 
and proton glass phases while KADA-40 only exhibits the proton glass phase. 
Analysis of the temperature course of dielectric loss E;(U,  T )  observed in measurements 
along the ferroelectric c axis revealed the presence of another process of relaxation different 
from that related to the freezing of ferroelectric domains. The two processes of relaxation 
are described by the Vogel-Fulcher equation but with different parameters: TO] = 34 K; 
E,] = 7.7 K U,, = 6.8 x IO5 Hz and To2 = 20.5 K E a  = 13.4 K uc2 = 45.6 x lo6 Hz. As 
these parameters are significantly different from those obtained from the measurements along 
the a axis, we have concluded that there are three different relaxation regions corresponding 
to clusters of different size: from the smallest ones (proton glass with parameters TO = 8.3 K, 
E, = 183.5 K, U, = 1.65 x 10” Hz) through ‘relaxor’ for the parameters To2 = 20.5 K, 
E,z = 13.4 K, ucz = 5.6 x 106 Hz to ferroelectric domains (To1 = 34 K E,] = 7.7 K 
us] = 6.8 x IO5 Hz). The larger the cluster the lower the frequency of dipole reorientation in 
Complex permittivity of K0.77(NH~Jo.23 H ~ A s O ~  955 
i o 5 :  I I I 
io4 - 
.,(a) 
io3 - 
I I 
Fignre 9. The Vogel-Fulcher dependence for the relaxation region marked by the broken line 
in figure 7 for the meast"ents dong the c axis of KU.~~(NH~)(,.~~HIASO~. 
the cluster, the lower the activation energy of the process and the higher the Vogel-Fulcher 
temperature TO at which the dipoles are completely frozen in the cluster. A similar effect 
of the occurrence of two different relaxation mechanisms has been recently observed in 
deuterated DRADA. x = 0.39,0.46 [12,14] in the region of coexistence of the antiferroelectric 
and proton glass states. 
In conclusion we can say that OUT measurements of complex permittivity E* = &'-id' in 
a mixed & . ~ ~ ( N H ~ ) o . ~ ~ H ~ A s O , ,  crystal along the a and c axes prove the coexistence of the 
ferroelectric and the proton glass state in the crystal, and the occurrence of different kinds 
of cluster of local ordering (proton glass and relaxor clusters) and ferroelecaic domains. 
Acknowledgments 
The authors wish to thank Professor J Stankowski for valuable discussions, and the 
authorities of the gas denitrification plant 'KRIO' in Odolan6w. which hosts the laboratory 
of the Institute of Molecular Physics, Polish Academy of Sciences, for providing the liquid 
He used in the studies whose results are reported in this work. 
References 
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[2] Counens E 1987 Ferroelectrics 72 229 
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