Anisotropic glass freezing in rubidium/ammonium dihydrogen phosphate mixed crystal and its deuterated analogue

Article abstract of DOI:10.1088/0953-8984/9/21/007

Anisotropic glass freezing has been studied via dielectric measurements in the dipole glass systems of rubidium/ammonium dihydrogen phosophate RADP(x) and its perdeuterated analogue D-RADP(x), where x denotes the ammonium concentrations. The glass freezing temperatures for a-cut and c-cut crystals are measured, and found to reveal very small anisotropy in the protonated sample of RADP(0.43) but a considerable anisotropy (～7.2 K) at low frequency in the deuterated sample of D-RAPD(0.40). A higher glass freezing temperature was observed along the c-axis as compared with the a-axis freezing temperature for D-RADP(0.40) crystal. This conforms with the prediction of the cluster model theory for RADP(x < 0.5). An Arrhenius plot of the logarithmic relaxation frequency versus the reciprocal temperature for D-RADP(0.40) gave the deuteron activation energies ΔE_a ? 11.5 kJ mol^-1 along the a-axis and ΔE_c ? 13.5 kJ mol^-1 along the c-axis.

Full text of DOI:10.1088/0953-8984/9/21/007

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Anisotropic glass freezing in rubidium/ammonium dihydrogen phosphate mixed crystal and its
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1997 J. Phys.: Condens. Matter 9 4403
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J. Phys.: Condens. Matter 9 (1997) 4403–4410. Printed in the UK
PII: S0953-8984(97)79113-6
Anisotropic glass freezing in rubidium/ammonium
dihydrogen phosphate mixed crystal and its deuterated
analogue
J H Ko†, B G Kim†, J J Kim†‡§, H Fujimori‡ and S Miyajima‡
† Physics Department and Centre for Molecular Science, Korea Advanced Institute of Science
and Technology, Taejon 305-701, Korea
‡ Institute for Molecular Science, Myodaiji, Okazaki 444, Japan
Received 31 October 1996, in final form 14 February 1997
Abstract. Anisotropic glass freezing has been studied via dielectric measurements in the dipole
glass systems of rubidium/ammonium dihydrogen phosphate RADP(x) and its perdeuterated
analogue D-RADP(x), where x denotes the ammonium concentration. The glass freezing
temperatures for a-cut and c-cut crystals are measured, and found to reveal very small anisotropy
in the protonated sample of RADP(0.43) but a considerable anisotropy (∼7.2 K) at low frequency
in the deuterated sample of D-RADP(0.40). A higher glass freezing temperature was observed
along the c-axis as compared with the a-axis freezing temperature for D-RADP(0.40) crystal.
This conforms with the prediction of the cluster model theory for RADP(x < 0.5). An
Arrhenius plot of the logarithmic relaxation frequency versus the reciprocal temperature for
D-RADP(0.40) gave the deuteron activation energies 1Ea ' 11.5 kJ mol−1 along the a-axis
and 1Ec ' 13.5 kJ mol−1 along the c-axis.
1. Introduction
Ferroelectric rubidium dihydrogen phosphate (RDP) and antiferroelectric ammonium
dihydrogen phosphate (ADP) form a randomly mixed single crystal, Rb1−x(NH4)xH2PO4
(RADP(x)) over the whole range of x from x = 0 to x = 1. A dipole glass
phase was identified for this system by Courtens [1], and considerable efforts have
been devoted to the study of its interesting properties [2–9]. Since dipole glass is
formed by frustration and the competing interactions caused by random mixing of
the competing interaction units, glass phase formation is common to most of the
mixed crystals between ferroelectric alkali hydrogen phosphate or arsenate (often called
KDP-type ferroelectrics) and the antiferroelectric ammonium counterparts: deuterated
rubidium/ammonium dihydrogen phosphate (D-RADP(x)) [10–15], potassium/ammonium
dihydrogen phosphate (KADP(x)) [16–20], rubidium/ammonium dihydrogen arsenate
(RADA(x)) [21–23], potassium/ammonium dihydrogen arsenate (KADA(x)) [24], and
caesium/ammonium dihydrogen arsenate (CADA(x)) [25], in addition to the prototype
RADP(x). In each of the mixtures, x and 1 − x denote the mole fractions of ammonium
and alkali ions, respectively. Alkali(1−x)/ammonium(x) and phosphate(1−y)/arsenate(y)
multiple mixing [26, 27] was also studied to examine the dual frustration effects of the
randomly competing multiple-Ising-model system.
§ Author to whom any correspondence should be addressed.
c
0953-8984/97/214403+08$19.50 ꢀ 1997 IOP Publishing Ltd
4403

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J H Ko et al
Figure 1. The temperature dependence of the complex dielectric constant, ꢀ(ν, T ) = ꢀ0 − iꢀ00,
for the a-cut specimen of RADP(0.43) at several frequencies. The peak positions of the
dielectric loss (ꢀ00) curves correspond to the glass freezing temperatures (Tg), which depend
on the observation frequency ν.
A number of important features have been revealed for the dipole glass phase: Vogel–
Fulcher scaling laws of classical glasses, for example, were found to also hold good for the
dipole glass systems [6–7, 10–13]. There are, however, still many problems to be studied
to achieve a better understanding of this interesting phenomenon of glass freezing: for
example, (i) possible anisotropy in the dielectric susceptibility, which was predicted by the
cluster model theory [28–30]; (ii) the nature of the ferroelectric or antiferroelectric phase
coexistence with the glass phase; (iii) the roles of the NH4 and PO4 ionic dynamics during
the glass freezing; and (iv) the effect of deuteration on the glass freezing dynamics. In the
present paper we report dielectric studies on single crystals of RADP(x) and D-RADP(x),
and present new results on the dielectric anisotropy observed in the glass freezing of the
dipole glass systems, and a significant isotope effect on the anisotropy.
Matsushita and Matsubara [28–30] developed a cluster model theory of dipole glass by
incorporating short-range ice-rule correlation for proton configurations (pseudospins), and
a Gaussian random distribution for the interaction bonds, and explained the experimental
phase diagram successfully, though they neglected dipolar long-range interactions between
pseudospin dipoles, and the pseudospin–lattice interactions. An interesting prediction was
given on the anisotropy of the dielectric susceptibility tensor χ [30]. The two components,
χz along the c-axis and χx along the a-axis, were shown to have different relationships with
the three order parameters of the glass transition. In particular, for RADP(x) crystals with
x < 0.5, a sharp cusp anomaly was predicted for χz at the glass transition temperature (Tg),
while a rounded peak appears for χx at a temperature below Tg. For the mixed crystals

Anisotropic glass freezing
4405
Figure 2. The temperature dependence of the complex dielectric constants for the a-cut ( ) and
◦
c-cut (
•
) crystals of RADP(0.43) observed at (a) 3.105 MHz and (b) 12.96 kHz. The anisotropy
in Tg is observed to be less than 1 K for both high (a) and low (b) frequencies.
with x > 0.5, it was predicted that only χx exhibits a sharp cusp at Tg, while χz exhibits a
rounded peak at the same temperature Tg.
Tunnelling models [31–33] of dipole glass, incorporating dipolar interactions between
pseudospins and also the transverse field of tunnelling with random distribution of competing
interaction constants, also predict a sharp cusp anomaly of χ at the glass transition
temperature Tg. The theories predict a lowering of Tg with increasing tunnelling frequency.
The tunnelling frequencies can be increased at high pressure or decreased by deuteration,
and corresponding changes of Tg are expected [8, 15]. Anisotropic changes in Tg would
also be possible in this model if the tunnelling frequencies become anisotropic as a result
of the application of uniaxial high pressure.
Experimentally, the predicted sharp cusps were not observed in RADP(x) [4–11] or D-
RADP (x) [11–13] mixed crystals. It was shown later [33, 34] that Gaussian random fields
caused by randomly substituted ammonium ions give a rounded peak instead of the sharp
cusp, in conformity with the experimental observations. As to the anisotropic dielectric
anomaly which corresponds to the anisotropic glass freezing in RADP(x) and D-RADP(x),
confusion exists, since a number of research groups reported the absence of anisotropy
[9–12], while Stankowski et al reported an anisotropic glass transition in D-RADP(x) [35].
It is thus necessary to reexamine the behaviours of dielectric anomalies associated with
the glass freezing, and the isotope effects, by using high-precision dielectric data on single
crystals.
2. Experimental details
To obtain deuterated mixed crystal, D-RADP(x), the constituent deuterated crystals of D-
RDP and D-ADP were prepared by the following chemistry:
Rb2CO3 + 2D3PO4 → 2RbD2PO4 + CO2 + D2O

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J H Ko et al
Figure 3. The temperature dependence of the complex dielectric constant for D-RADP(0.40)
crystal at 16.45 kHz (
◦
), 286.81 kHz (
•), and 5.00 MHz (5).
and
ND4OD + D3PO4 → ND4D2PO4 + D2O.
D-RDP and D-ADP were then mixed in appropriate molar ratios to make saturated solutions
in deuterated water. Crystal growth was completed inside a closed vessel to avoid
contamination by water vapour in the atmosphere. Specific gravity measurements and
proton NMR were used to determine the mole fraction x of ammonium and the percentage
of deuteration respectively. Our D-RADP(x) crystal used in the present work was found
to have 91% deuteration. The ammonium concentrations were x = 0.43 for RADP and
x = 0.40 for D-RADP.
The dielectric constants of the samples were measured by use of an impedance analyser
(HP4192A) in the frequency range from 5 kHz to 5 MHz, and by a lock-in amplifier system
employing a function generator and a standard capacitor in the low-frequency region from
1.35 Hz to 5 kHz. Temperature control was achieved by use of a closed-cycle helium
refrigerator (Displex) and a personal-computer- (PC-) interfaced temperature controller
(Lake Shore-330) with silicon diode temperature sensors. The sample was cooled at a
rate of 0.5 to 0.25 K min−1 from above the glass freezing temperature to 10 K.
3. Results and discussion
Figures 1 and 2 show the experimental results for complex dielectric constants, ꢀ(ν, T ) =
ꢀ0 − iꢀ00, for RADP(0.43) mixed crystal. The real part of the dielectric constant ꢀ0 starts to
deviate from the Curie–Weiss behaviour at the onset temperature of freezing, and then falls
rapidly at the low-temperature end of the plateau curve. The temperature of the most rapid

Anisotropic glass freezing
4407
Figure 4. The anisotropy in the dielectric constants of D-RADP(0.40). The complex dielectric
constants are shown for the a-cut (
(a) 3.105 MHz and (b) 12.96 kHz.
◦
) and c-cut ( ) samples. The observation frequencies are
•
falling of ꢀ0 corresponds to the maximum peak of the imaginary part ꢀ00, and is defined as
the glass freezing temperature Tg [2]. Tg is clearly dependent on the observation frequency
ν, and has already fallen below the lowest attainable temperature (10 K) of our apparatus
at a frequency of 16.45 kHz for RADP(0.43). In figure 2 we have compared two dielectric
constant curves for a-cut and c-cut crystal samples of RADP(0.43) measured at 3.105 MHz
(a) and 12.96 kHz (b). We can hardly see any significant difference between the values of
Tg for a-cut and c-cut samples of RADP(0.43), in agreement with previous work [9–12].
The possible difference in Tg is estimated to be about 1 K in this frequency range.
In figure 3, temperature and frequency dependences of the complex dielectric constants
are shown for a deuterated mixed crystal, D-RADP(0.40). Figure 3 shows the dielectric
constant results for a-cut sample of D-RADP(0.40) measured at three different frequencies
above 16.45 kHz for comparison with figure 1 for the protonated RADP(0.43) sample. The
isotope shift of Tg on deuteration can be as large as 55 K in the MHz frequency region,
and frequency dependence of Tg could be observed more clearly in this region of higher
temperature. In figure 4 we have compared the two sets of dielectric constant data for a-cut
and c-cut samples of D-RADP(0.40) measured at 3.105 MHz (a) and 12.96 kHz (b). In
contrast to the case of RADP(0.43) shown in figure 2, Tg is clearly seen to be dependent
on the crystal axis of measurement, and is higher when it is measured along the c-axis than
along the a-axis. The difference in Tg is 4.4 K when measured at 3.105 MHz, and 6.4 K at
12.96 kHz. Figure 5 shows the results for dielectric constants measured at ν = 1.35 Hz for
the two crystal axes of D-RADP(0.40). The anisotropy in Tg can be as large as 7.2 K at
this low frequency. We have thus revealed that larger anisotropy in Tg is observed at lower
frequencies of measurement, and this observation is in conformity with the reported value
of 4 K at 9.3 GHz [35].
The origin of the anisotropy in the cluster model theory may be traced to the difference

4408
J H Ko et al
Figure 5. The temperature dependence of the low-frequency (ν = 1.35 Hz) dielectric constant
for D-RADP(0.40) crystal, showing very different glass freezing temperatures for the directions
along the a- and c-axes of the crystal.
between two effective order parameters [30]:
Qz = lim hPz(0)Pz(t)i/µ2
t→∞
and
Qx = lim hPx(0)Px(t)i/µ2
t→∞
where P (t) stands for a local polarization at time t, and µ stands for the dipole moment
of random dipoles. Possible differences between Qz and Qx at a given concentration
of mixing may originate from the more frequent local cluster formations of ferroelectric-
(1Pz-) type Slater units for x < 0.5 or antiferroelectric- (1Px-) type Slater units for x > 0.5.
Spatial correlation of the random local clusters (1P) will not increase, due to frustration,
and will not realize the ferroelectric or antiferroelectric long-range order until the freezing
temperature is reached. However, the dynamic autocorrelation, Qz or Qx, depending on
whether x < 0.5 or x > 0.5 respectively, will take a nonzero finite value at the freezing
temperature, so the corresponding χz or χx will show a cusp change at this temperature.
The minority Slater units—that is, antiferroelectric-type units for x < 0.5 or ferroelectric-
type units for x > 0.5—will also enter the freezing relaxation at lower temperatures than
Tg with more random—that is, single-particle—characteristics of freezing. Our observation
of a higher value of Tg in the ꢀc(T ) measurement than in the ꢀa(T ) measurement is in
conformity with the theoretical prediction of the cluster model for RADP(x < 0.5) mixed
crystal [30].
In figure 6 we have depicted the frequency dependence of the glass freezing temperature
Tg as an Arrhenius plot of the logarithmic relaxation frequency versus the reciprocal

Anisotropic glass freezing
4409
Figure 6. Arrhenius plots of the dependence of Tg on the frequency for the a-axis (
◦
) and the
c-axis ( ) in D-RADP(0.40) crystal.
•
temperature for D-RADP(0.40). This picture of the glass freezing as a relaxation rather
than an equilibrium transition should give the corresponding anisotropy in the activation
energy barrier. The slopes of the two lines give the corresponding activation energy barriers
1E for the deuteron relaxations along the a-axis (◦) and c-axis (•) respectively. We have
obtained 1Ea ' 11.5 kJ mol−1 along the a-axis and 1Ec ' 13.5 kJ mol−1 along the c-axis.
4. Conclusion
The glass freezing temperatures of dipole glass as determined from the dielectric loss peaks
are dependent not only on the frequency of a probing field but also on the crystal axis of the
dielectric measurement. The crystal axis dependence of the glass freezing temperature—that
is, anisotropy in the glass freezing—was observed to be substantial for the deuterated dipole
glass D-RADP(0.40), whereas it was very slight for the proton dipole glass RADP(0.43).
It remains a puzzle why a large anisotropy in Tg is observed for deuterated D-
RADP(0.40), while the anisotropy is negligibly small for protonated RADP(0.43), although
it may be speculated that the short-range anisotropy of the crystal is more susceptible
to deuterons in localized single-particle potentials than protons in delocalized extended
potentials of 3D correlation, due to more significant zero-point vibration and quantum
tunnelling effects.
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J H Ko et al
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