Coexistence of paraelectric/proton-glass and ferroelectric (antiferroelectric) orders in Rb₁₋x(NH₄)xH₂AsO₄ crystals
This paper reviews the results of dielectric studies of the proton glass state in a mixed crystal Rubidium Ammonium Dihydrogen Arsenate (RADA) The coexistence of paraelectric/proton glass and ferroelectric or antiferroelectric orders, confirmed by other studies, has been discussed in detail. The...
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| Cite this: | Coexistence of paraelectric/proton-glass and ferroelectric (antiferroelectric) orders in Rb₁₋x(NH₄)xH₂AsO₄ crystals / Z. Trybuła, J. Stankowski // Condensed Matter Physics. — 1998. — Т. 1, № 2(14). — С. 311-330. — Бібліогр.: 52 назв. — англ. |
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Trybuła, Z. Stankowski, J. 2017-06-01T15:42:48Z 2017-06-01T15:42:48Z 1998 Coexistence of paraelectric/proton-glass and ferroelectric (antiferroelectric) orders in Rb₁₋x(NH₄)xH₂AsO₄ crystals / Z. Trybuła, J. Stankowski // Condensed Matter Physics. — 1998. — Т. 1, № 2(14). — С. 311-330. — Бібліогр.: 52 назв. — англ. 1607-324X DOI:10.5488/CMP.1.2.311 PACS: 77.22.ch, 77.22.gm, 64.70.-p, 74.84.-s https://nasplib.isofts.kiev.ua/handle/123456789/118952 This paper reviews the results of dielectric studies of the proton glass state in a mixed crystal Rubidium Ammonium Dihydrogen Arsenate (RADA) The coexistence of paraelectric/proton glass and ferroelectric or antiferroelectric orders, confirmed by other studies, has been discussed in detail. The phase diagram of RADA is asymmetric. The proton glass state exists for ammonium concentration in the range of 0.1 < x < 0.5 . The phase diagram of deuterated DRADA is presented. The proton glass state region in DRADA, 0.2 < x < 0.35 is narrower than that for non-deuterated RADA. The effects of hydrostatic pressure on the dielectric properties in the proton glass state are presented. The glass temperature Tg decreases with pressure and is expected to vanish at 5 kbar. Low temperature behaviour is still an open question, since there is no experimental evidence of Tg(p) dependence below 4K for proton glass systems. Ця стаття є оглядом результатів діелектричного вивчення стану протонного скла у змішаних кристалах Rb₁₋x(NH₄)xH₂AsO₄ (RADA).Співіснування впорядкувань параелектричного/протонне скло та сегнетоелектричного чи антисегнетоелектричного, підтверджене іншими дослідженнями, детально обговорюється. Фазова діаграма RADA є асиметричною. Стан протонного скла існує для концентрації аміаку в межах 0, 1 < x < 0, 5 . Представлена фазова діаграма дейтерованого DRADA. Область стану протонного скла в DRADA (0, 2 < x < 0, 35) є вужчою, ніж у недейтерованому RADA. Представлені ефекти впливу гідростатичного тиску на діелектричні властивості кристалу в стані протонного скла. Температура склування Tg спадає з тиском і за оцінками прямує до нуля при 5 кбар. Низькотемпературна поведінка є все ще дискусійною, оскільки немає експериментально підтвердженої Tg(p) залежності нижче 4 К для систем протонного скла. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Coexistence of paraelectric/proton-glass and ferroelectric (antiferroelectric) orders in Rb₁₋x(NH₄)xH₂AsO₄ crystals Співіснування параелектричного/протонне скло та сегнетоелектричного (антисегнетоелектричного) впорядкування в кристалах Rb₁₋x(NH₄)xH₂AsO₄ Remove selected Article published earlier |
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Coexistence of paraelectric/proton-glass and ferroelectric (antiferroelectric) orders in Rb₁₋x(NH₄)xH₂AsO₄ crystals |
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Coexistence of paraelectric/proton-glass and ferroelectric (antiferroelectric) orders in Rb₁₋x(NH₄)xH₂AsO₄ crystals Trybuła, Z. Stankowski, J. |
| title_short |
Coexistence of paraelectric/proton-glass and ferroelectric (antiferroelectric) orders in Rb₁₋x(NH₄)xH₂AsO₄ crystals |
| title_full |
Coexistence of paraelectric/proton-glass and ferroelectric (antiferroelectric) orders in Rb₁₋x(NH₄)xH₂AsO₄ crystals |
| title_fullStr |
Coexistence of paraelectric/proton-glass and ferroelectric (antiferroelectric) orders in Rb₁₋x(NH₄)xH₂AsO₄ crystals |
| title_full_unstemmed |
Coexistence of paraelectric/proton-glass and ferroelectric (antiferroelectric) orders in Rb₁₋x(NH₄)xH₂AsO₄ crystals |
| title_sort |
coexistence of paraelectric/proton-glass and ferroelectric (antiferroelectric) orders in rb₁₋x(nh₄)xh₂aso₄ crystals |
| author |
Trybuła, Z. Stankowski, J. |
| author_facet |
Trybuła, Z. Stankowski, J. |
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1998 |
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Condensed Matter Physics |
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Інститут фізики конденсованих систем НАН України |
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Article |
| title_alt |
Співіснування параелектричного/протонне скло та сегнетоелектричного (антисегнетоелектричного) впорядкування в кристалах Rb₁₋x(NH₄)xH₂AsO₄ Remove selected |
| description |
This paper reviews the results of dielectric studies of the proton glass state
in a mixed crystal Rubidium Ammonium Dihydrogen Arsenate (RADA) The
coexistence of paraelectric/proton glass and ferroelectric or antiferroelectric
orders, confirmed by other studies, has been discussed in detail. The
phase diagram of RADA is asymmetric. The proton glass state exists for
ammonium concentration in the range of 0.1 < x < 0.5 . The phase diagram
of deuterated DRADA is presented. The proton glass state region in
DRADA, 0.2 < x < 0.35 is narrower than that for non-deuterated RADA.
The effects of hydrostatic pressure on the dielectric properties in the proton
glass state are presented. The glass temperature Tg decreases with
pressure and is expected to vanish at 5 kbar. Low temperature behaviour
is still an open question, since there is no experimental evidence of Tg(p)
dependence below 4K for proton glass systems.
Ця стаття є оглядом результатів діелектричного вивчення стану протонного скла у змішаних кристалах Rb₁₋x(NH₄)xH₂AsO₄ (RADA).Співіснування впорядкувань параелектричного/протонне скло та сегнетоелектричного чи антисегнетоелектричного, підтверджене іншими дослідженнями, детально обговорюється. Фазова діаграма RADA є асиметричною. Стан протонного скла існує для концентрації аміаку в межах 0, 1 < x < 0, 5 . Представлена фазова діаграма дейтерованого DRADA. Область стану протонного скла в DRADA (0, 2 < x < 0, 35) є вужчою, ніж у недейтерованому RADA. Представлені ефекти впливу гідростатичного тиску на діелектричні властивості кристалу в стані протонного скла. Температура склування Tg спадає з тиском і за оцінками прямує до нуля при 5 кбар. Низькотемпературна поведінка є все ще дискусійною, оскільки немає експериментально підтвердженої Tg(p) залежності нижче 4 К для систем протонного скла.
|
| issn |
1607-324X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/118952 |
| citation_txt |
Coexistence of paraelectric/proton-glass and ferroelectric (antiferroelectric) orders in Rb₁₋x(NH₄)xH₂AsO₄ crystals / Z. Trybuła, J. Stankowski // Condensed Matter Physics. — 1998. — Т. 1, № 2(14). — С. 311-330. — Бібліогр.: 52 назв. — англ. |
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| fulltext |
Condensed Matter Physics, 1998, Vol. 1, No 2(14), p. 311–330
Coexistence of
paraelectric/proton-glass and
ferroelectric (antiferroelectric) orders in
Rb 1−x (NH 4 )xH 2AsO 4 crystals
Z.Trybuła, J.Stankowski
Institute of Molecular Physics, Polish Academy of Sciences,
Smoluchowskiego 17, 60-179 Poznañ, Poland
Received June 17, 1998
This paper reviews the results of dielectric studies of the proton glass state
in a mixed crystal Rubidium Ammonium Dihydrogen Arsenate (RADA) The
coexistence of paraelectric/proton glass and ferroelectric or antiferroelec-
tric orders, confirmed by other studies, has been discussed in detail. The
phase diagram of RADA is asymmetric. The proton glass state exists for
ammonium concentration in the range of 0.1 < x < 0.5 . The phase dia-
gram of deuterated DRADA is presented. The proton glass state region in
DRADA, 0.2 < x < 0.35 is narrower than that for non-deuterated RADA.
The effects of hydrostatic pressure on the dielectric properties in the pro-
ton glass state are presented. The glass temperature Tg decreases with
pressure and is expected to vanish at 5 kbar. Low temperature behaviour
is still an open question, since there is no experimental evidence of Tg(p)
dependence below 4K for proton glass systems.
Key words: domain structure, ferroelasticity
PACS: 77.22.ch, 77.22.gm, 64.70.-p, 74.84.-s
1. Introduction
The studies of the proton glass state in a mixed crystal of Rubidium Am-
monium Dihydrogen Phosphate – Rb1−x(NH4)xH2PO4 (RADP) were launched by
Courtens [1] in 1982. At low ammonium concentration x RADP has a distorted
ferroelectric structure with a typical paraelectric-ferroelectric (P-FE) transition,
while at high ammonium concentration (x close to 1) RADP exhibits a distorted
paraelectric/aniferroelectric transition (P-AFE). Temperature of the phase transi-
tions: Tc of P-FE transition as well as TN of P-AFE transition significantly lowers
with the increase of the concentration of the second component of a mixed crystal.
For NH4 concentration 0.22 6 x 6 0.75 [2], below the “freezing” temperature Tg,
c© Z.Trybuła, J.Stankowski 311
Z.Trybuła, J.Stankowski
the competition between ferroelectric and antiferroelectric orderings leads to frus-
tration of the protonic system and appearance of regions with a local short-range
order but without any evidence of a long-range order (ferroelectric or antiferro-
electric). The proton glass state was also detected in an isomorphous crystal of
Rubidium Ammonium Dihydrogen Arsenate- Rb1−x(NH4)xH2AsO4 (RADA) by
Trybu la et al. [3] in the dielectric study. This paper will focus essentially on the
properties of the RADA crystal. Earlier dielectric studies gave some insight into the
properties of the proton glass state [4-7]. The phase diagram for RADA obtained
by those studies is unlike that for RADP, and reveals the glass state existence in
the range of 0.1 6 x 6 0.5 [4,5].
Further studies showed [8-16] that the phase diagram is more complex, since
paraelectric/proton-glass-ferroelectric or antiferroelectric phases coexist. This pa-
per presents the up to date understanding of the proton-glass state. First, after a
short introduction, dielectric results in the mixed RADA crystal will be reviewed.
Then, the problem of phase coexistence in this crystal based on dielectric studies,
discussion of the phase diagram and the effect of pressure and electric field on the
proton glass state will be presented.
Figure 1. Ordered hydrogen-bonds sys-
tem that gives spontaneous polarization.
Crystals of the KH2PO4 (KDP) fa-
mily were the most extensively stud-
ied ferroelectrics [17,18]. Ferroelectric
properties of these crystals originate
from the ordering of the protons in hy-
drogen bonds linking tetrahedral PO4
or AsO4 units in the crystal structure.
The unit cell is tetragonal. Sponta-
neous polarization is the result of pro-
ton ordering due to the shift along the
c axis of the centre of Rb+ or NH+
4
tetrahedrons with respect to phospho-
rus or arsenium atoms in H2PO4 or
H2AsO4 groups, while hydrogen bonds
are formed almost in (ab) plane (figu-
re 1). In an ordered ferroelectric pha-
se, below Tc, up-down configuration of
hydrogen bonds (figure 3) is favoured.
The change from up to down configu-
ration leads to a switch in the polar-
ization of the crystal. The next-lying
excited state corresponds to lateral con-
figurations - two protons are in a lateral
position. These configurations are called Slater configurations [19]. Higher energies
of the hydrogen bond network correspond to Takagi configurations [20] related to
the ordering of a distorted tetrahedron with one, three, four protons or lack of
protons at all (figure 2). Antiferroelectrically ordered ADP or ADA crystals, be-
312
Coexistence of proton-glass and ferroelectric orders in RADA
low Néel temperature TN , have lateral configurations in the ground state. The first
excited state corresponds to up- down configuration. In mixed crystals of RADP
or RADA there is a small energy difference between the ground and excited states,
so the multiplet ground state is possible, hence the proton glass state can occur
(figure 3).
Figure 2. Configurational energies of 16
types of phosphate PO4 or arsenate AsO4
tetrahedra, represented in the pseudospin
formalism and in terms of Slater energy εo
and Takagi energy ε1 [52].
Figure 3. Proton configuration in ferro-
electric RDA, proton glass RADA and an-
tiferroelectric ADA.
2. Review of dielectric studies of mixed RADA
Since Courtens discovered the proton glass state in RADP [1-2], the tempera-
ture dependence of real ε′ and imaginary ε′′ parts of electric permittivity has been
extensively studied [21-29]. We have contributed to this work with the observation
of the proton glass state in a RADA mixed crystal [3]. First measurements were
carried out in a microwave X-band range for measuring electric field frequency of
9.2 GHz. The methodology of ε′ and ε′′ measurement in a microwave resonator
is described in [33]. As this method does not require to paste electrodes, it is
especially useful for small crystals and polycrystalline samples. The studied crys-
313
Z.Trybuła, J.Stankowski
tal of RADA x = 0.31 was placed in the maximum of electric field in cylindrical
microwave resonator TM010. The c-axis was parallel to electric field lines. The
orientation of the sample in the microwave resonator is shown in figure 4. Thermal
Figure 4. Diagram of the
TM010 resonator: a) configu-
ration of the electromagnetic
field in the resonator, b) res-
onator loaded with a sample
[33].
contact of the sample with the resonator was pro-
vided by special support. The microwave resonator
was mounted to the heat exchanging facility in the
helium flow cryostat. Assuming that the sample
diameter is much smaller than the diameter of the
resonator, ε′ and ε′′ were determined from the fol-
lowing expressions:
ε′ = 1 + 0.539
r20l
r2h
f0 − f
f0
,
ε′′ = 0.269
r20l
r2h
(
l
Q
− l
Q0
)
,
where r0 is the radius of the cylindrical resonator;
r is the radius of the sample; l and h - the height of
the resonator and the sample, respectively; f0- and
Q0 - the frequency and quality factor of the empty
resonator; f and Q are the frequency and quality
factor of the loaded resonator. Figure 5 presents
the results of the temperature dependence of ε′
and ε′′ for RADA, x = 0.31. There is a clear cusp-
like maximum on ε′(T ) dependence around 65 K
and a maximum on losses ε′′(T ) dependence at
Tg = 48 K, typical of proton glass.
In proton glass the electric field Ei and polar-
ization Pi are strongly related to ordering. Local
polarization Pi is given by:
Pi = tanh
[
1
T
(
∑
j
Ji,jPj + Ei
)]
,
where Jij is the interaction energy of pseudospins. There is no long-range order
in proton glass, hence the average value of polarization vanishes, i.e. 〈P 〉 = 0.
According to Edwards-Anderson, there is only a short range order within the
clusters. The order parameter qE−A can be regarded as square of the average
polarization:
qE−A(T ) =
1
N
∑
i
〈pi〉2, (1)
where N is the number of dipoles in the cluster and pi is the polarization of a
single dipole. In the proton glass state qE−A 6= 0. Different models have been
developed to describe the proton glass state. The model of clusters by Prelovs̆ek
314
Coexistence of proton-glass and ferroelectric orders in RADA
and Blinc [51], extended by Matsushita and Matsubara [52], plays an important
role in understanding phase diagrams in proton glass systems. The configuration
Figure 5. Temperature dependence of
the electric permittivity a) ε′; b) ε′′ in
RADA x = 0.31 at 9.2 GHz of the elec-
tric measured field [3,34].
energy is assumed to be given by a
Hamiltonian of the form:
H = −
∑
i>j
Jijσiσj , (2)
where pseudospin σi (i =1, 2, 3, 4) is
+1 or -1 depending on each of the two
possible positions along the hydrogen
bond occupied by i-th proton. For a
ferroelectric crystal the energy differ-
ence between the lateral and up-down
ground states equals ε0 and depends
on J . For an antiferroelectric crystal,
besides the energy difference between
the two configurations, – εo, another
parameter should be introduced. This
extra parameter w accounts for the
interaction between two neighbouring
parallel hydrogen bonds, which is nec-
essary to establish an antiferroelectric
long-range order. For the mixed crystal
RADP, considered as a system of clus-
ters (j is the number of clusters), the
Hamiltonian (2) can be written as [52]:
H =
1
8
∑
j
εjΦj +
J
2
∑
j
Ψj , (3)
Φj = (σj
1 − σj
3) + (σj
2 − σj
4),
Ψj = (σj
1 + σj
2 + σj
3 + σj
4),
εj has a different value for each cluster in RADP. A simple Gaussian distribution
function for random variable εj in the Hamiltonian (3) is assumed:
g(ε) =
1√
π
∆−1 exp
[
−
(
ε− ε̄
∆
)2
]
,
where ε is the average of energy ε depending on the concentration x and ∆ is the
energy parameter:
∆ =
√
2〈(ε− ε̄)2〉.
For the mixed proton-glass crystal RADP ε̄ can take the following values de-
pending on the ammonium concentration x [52]:
ε̄ > 0 for 0 < x < 0.5,
315
Z.Trybuła, J.Stankowski
ε̄ = 0 for x = 0.5,
ε̄ < 0 for 0.5 < x < 1.
The glass transition temperature Tg is given by [52]:
(
kBTg
∆
)
=
1
8
1 + 2y2
(1 + 2y)2
,
where:
y = exp
(
− −ε̄
kBT
)
.
The average of ε̄(x) is given by [52]:
ε̄(x) = εP+(x) + 0 · Po(x) − εP−(x),
where P+(x), Po(x) and P−(x) are three x-dependent probability functions for
finding a cluster in three groups: ferro, neutral and antiferro group, respectively.
This function is plotted in figure 6a. The broken lines are ε(x) dependences for
different RADA crystals.
Figure 6. Concentration de-
pendence of: a) the average
energy between up-down and
lateral; b) (∆/εo)
2 (see equa-
tion 4) [52].
The root mean square as a function of x (figure 6b)
is defined as [52]:
∆2(x)
ε2
= 2{1 − Po(x) − [P+(x) − P−(x)]2}. (4)
The paraelectric-ordered phase transitions of
the components of mixed RADP crystals do not
differ much. RDP has the Curie temperature
Tc = 148 K [30], while for antiferroelectric ADP
the Néel temperature equals TN = 150 K [31].
Thus, for x = 0.5 composition of RADP the aver-
age energy is zero, ε = 0. In the RADA crystal the
temperatures of paraelectric-ordered phase transi-
tions are very different for the both components
(RDA, Tc = 110 K [32], and ADA TN = 216 K
[31]). This difference implies that the RADA phase
diagram should be asymmetric because ε = 0
falls on approximately x = 0.3 concentration. Mi-
crowave dielectric measurements for different NH4
concentrations x, shown in figure 7, support this
conclusion. The phase diagram of RADA, thus de-
termined, (figure 8), differs from that of RADP.
The phase diagram of RADA is asymmetric with
the glass state for NH4 concentration of 0.1 <
x < 0.5. The temperature of the transition to the
proton glass state increases with frequency of the
measured electric field, but is not NH4 concentra-
tion dependent, like for RADP. This asymmetry
of the RADA phase diagram from microwave studies was confirmed by Kim and
316
Coexistence of proton-glass and ferroelectric orders in RADA
Kwun [7] in dielectric measurements at 700 Hz to 1 MHz and the existence of the
proton glass state was limited to the concentration of 0.13 < x < 0.49 (figure 9).
Figure 7. The temperature and concentration x dependence of the electric per-
mittivity ε′c and ε′′c in RADA x=0.31 at 9.2 GHz of the measured electric field [4].
Further studies of the proton glass state in RADA revealed dispersion of electric
permittivity in the transition from the paraelectric to the proton glass phase. The
dielectric properties of the RADA crystal (x = 0.35) were investigated for two
perature to Tf > 70 K. Deviation of ε′(T ) from the Curie-Weiss law determines
317
Z.Trybuła, J.Stankowski
Figure 8. The phase diagram of RADA.
PE, FE, AFE, and PG denote para-
electric, ferroelectric, antiferroelectric and
proton glass phases, respectively. The
open circles and crosses denote maximum
of ε′c and ε′′c , respectively. The full circles
denote the middle of the phase transition
region from the ε′c(T ) dependence [4].
Figure 9. The phase diagram of RADA
done by Kim and Kwun [7] from electric
permittivity ε′a and ε′′a.
Figure 10. Temperature dependence of
the dielectric permittivity in RADA x =
0.35: a) ε′a(T ); b) ε′c(T ). Solid lines present
fits to the Curie-Weiss law [6].
samples [6]: along a and c axis of
the crystal. Figure 10 shows a real
part of electric permittivity data for
both crystal orientations. For the both
directions a typical proton glass be-
haviour is observed. As the temper-
ature lowers from the room temper-
ature to about 40 K, ε′ initially in-
creases. After a cusp-like maximum
ε′ decreases to the value of approxi-
mately 10 at temperature T = 3 K.
Electric permittivity ε′ can be well de-
scribed by the Curie-Weiss law in the
paraelectric phase from the room tem-
318
Coexistence of proton-glass and ferroelectric orders in RADA
temperature Tf . At this temperature a short-range order is established in certain
regions of the crystal – clusters start to be formed. On decreasing the temperature,
the volume of each cluster increases to Vogel-Fulcher temperature To (equation 5),
according to the following equation first applied to proton glass by Courtens [36]:
νc = νo exp
( −Ec
T − To
)
, (5)
where To is Vogel-Fulcher freezing temperature, Ec is a cut-off energy in the tem-
perature unit, νo is an attempt frequency. The temperatures Tg of the freezing
electric dipoles reorientation within the cluster have been determined for each
measuring frequency from the maximum of ε′′(T ). At To, the reorientation of elec-
tric dipoles within the cluster becomes frozen. Dielectric dispersions of ε′(T ) and
ε′′(T ) have been demonstrated for T < 40 K (figure 10). As the frequency of the
measured electric field increases, the maximum of ε′′(T ) shifts to a higher temper-
ature.
The proton glass state was also observed in K1−x(NH4)xH2AsO4 x = 0.40,
(KADA x = 0.40) [35]. The substitution of Rb by K does not influence the prop-
erties of the proton glass state significantly. The temperature dependence of ε′a for
KADA x = 0.40 is very similar to that of RADA.
3. Coexistence of paraelectric/proton-glass and ordered l ong-
range phases
3.1. Undeuterated glass RADA
Detailed dielectric studies of mixed RADA crystals for different x concentra-
tions have shown that for very small, as well as for very large x concentrations
the crystals are exclusively in a ferroelectric /or antiferroelectric phase. The first
evidence of the coexistence of paraelectric, glass and ordered ferroelectric phases
was given by Trybu la , Schmidt and Drumheller [8] for RADA x = 0.12; 0.15
and 0.20. This result was confirmed by Eom et al. [9] in dielectric and laser opti-
cal studies. The latter shows that the orthorhombic symmetry – optically biaxial
characteristic of a ferroelectric phase is preserved up to the lowest temperature at
which the glass state is present. The crystal in the glass state is tetragonal (op-
tically uniaxial), like in a paraelectric phase. It seems that the glass state exists
independently of the ferroelectric one.
Temperature dependences of the real part of electric permittivity ε′a in RADA
for different ammonium concentrations x, revealing the coexistence of glass and fer-
roelectric phases, are shown in figure 11 and 12 [8]. The ammonium concentration
was determined by measuring the rubidium content with flame atomic-absorption
spectroscopy. In contrary to RADP, in RADA the concentration of rubidium (1−x)
in solution equals the concentration in the crystal. The following concentrations
were studied: x = 0, x = 0.12 ± 0.01, x = 0.15 ± 0.01 and x = 0.20 ± 0.01. For
x = 0.12 and x = 0.15 there are two transitions: at Tc to a ferroelectric phase
319
Z.Trybuła, J.Stankowski
Figure 11. Temperature dependence of
the real part of the electric permittivity ε′a
in a) RDA; b) RADA x = 0.12; c) RADA
x = 0.15; d) RADA x = 0.20 [8].
Figure 12. Dielectric dispersion of ε′a in
RADA x = 0.12 in the proton glass regime
[8].
and at Tg to a glass phase. The transition to the ferroelectric phase is not fre-
quency dependent, while that to the glass state displays dispersion both in ε′
and ε′′ (figure 12). The measurements along the a axis of the crystal, perpendic-
ular to ferroelectric axis c, excluded the possibility of dispersion, typical of KDP
ferroelectrics related to the freezing of the dynamics of the domains walls. Such
dispersion does not exist along the a axis. The RADA results in figure 11 clearly
show two phase transitions. In the case of the coexistence of ferroelectric and glass
phases, Tg for the given frequency of the measured electric field is lower than Tg
at the same frequency for RADA exhibiting only the glass state. This observa-
tion suggests that the volume of the cluster with a short-range order in crystals
with phase coexistence is smaller than the volume of the clusters in crystals in
the glass state only. Moreover, because of the shorter correlation length, the dy-
namics of the clusters is less hindered. Howell, Pinto and Schmidt [10] have shown
that the coexistence of ferroelectric / glass phases exists even for lower concentra-
tions, i.e. x=0.05. Recent measurements up to 0.4K by Trybu la et al. [37] reveal
320
Coexistence of proton-glass and ferroelectric orders in RADA
Figure 13. Part of the phase diagram
of RADA: PE- paraelectric phase; FE-
ferroelectric phase; PG- proton glass
regime; F-P-coexistence of paraelectric
and ferroelectric phases; , F-G >coex-
istence of ferroelectric and proton-glass
phases [8,10].
Figure 14. Spontaneous polarization ob-
tained from saturated hysteresis loops in
RDA x=0 (•) and RADA x = 0.08 (N)
as a function of temperature. The open
diamond (♦) symbol represents sponta-
neous polarization obtained from equa-
tion (6) and figure 15 for RADA x = 0.08
[12].
that such coexistence can be observed
even for x = 0.01. The part of
the RADA phase diagram presenting
the coexistence of ferroelectric/glass
phases is shown in figure 13.
The coexistence of ferroelectric and
proton glass states was also ob-
served in other isomorphic ferroe-
lectric-antiferroelectric mixed crystals:
K1−x(NH4)xH2AsO4 x = 0.23 [38],
K1−x(NH4)xH2PO4 [39], and also for
deuterated DRADA [11,13].
The coexistence
of paraelectric/proton glass and ferro-
electric orders below the glass tran-
sition temperature Tg was confirmed
by spontaneous polarization measure-
ments in deuterated DRADA an un-
deuterated RADA crystals by Pinto et
al. [12]. The temperature dependence of
Ps for a ferroelectric crystal RDA and
mixed RADA x = 0.08 was determined
from a saturated hysteresis loop in the
standard Sawer-Tower circuit. Figure
14 presents the results for a nondeuter-
ated crystal. A RDA crystal exhibits
a distinct jump of spontaneous polar-
ization at Tc = 110 K, typical of the
first order phase transition. The spon-
taneous polarization reaches the value
of 3.6 ± 0.5µC/cm−2 at the tempera-
ture far below Tc. For a mixed crystal
RADA x = 0.8, below T = 94 K, there
is a gradual increase of Ps. The max-
imum value of Ps attained in a mixed
c rystal is lower than that of a RDA
crystal. Spontaneous polarization of a
mixed crystal can be thus described by
the following expression [12]:
Psd(T ) = Pso
[
ε′1(T )
ε′1(T ) + ε′2(T )
]
, (6)
where Psd is the spontaneous polariza-
tion of the mixed crystal, Pso is the
321
Z.Trybuła, J.Stankowski
Figure 15. Temperature dependence of
the electric permittivity e>a for RADA
x = 0.08 and x = 0.40 at 1kHz (ε′
∞
is
assumed to be 10) [12].
maximum spontaneous polarization of
the pure crystal RDA well below Tc ;
ε′1 and ε′2 electric permittivity values
marked in figure 15 which gives temper-
ature dependences of ε′ for proton-glass
RADA x = 0.40 and RADA x = 0.08.
Spontaneous polarization of the mixed
crystal is equal to the spontaneous po-
larization in the pure RDA crystal well
below Tc multiplied by the fraction of
the mixed crystal that becomes ferro-
electric below Tc. Similar results were
obtained by Pinto et al. [12] for the
deuterated D-RADA x = 0.08 crys-
tal. The maximum value of the spon-
taneous polarization in mixed RADA
x = 0.8, and its deuterated counterpart is lower than that of the pure crystal. This
indicates that at lower temperatures there are still paraelectric clusters closely
interlocked with ferroelectric clusters.
3.2. Deuterated glass DRADA
Deuteration shifts the transition temperature Tc upward from 110 K for RDA
to 170 K for DRDA or, in antiferroelectrics, the Néel temperature TN from 216 for
ADA to 304 K for DADA and increases the value of the spontaneous polarization
Ps compared with the undeuterated crystal [40]. The studies of deuteron glass
have revealed that, like in a undeuterated crystal, the state of glass may coexist
with the ferroelectric or antiferroelectric order [10-14]. Deuteration leads to the
narrowing of glass existence range to 0.2 6 x 6 0.35 [14-15,41].
Figure 16. Dispersion of electric permit-
tivity ε′a(T, ν) for DRADA x = 0.28.
Figure 17. Dispersion of electric permit-
tivity ε′′a(T, ν) for DRADA x = 0.28.
322
Coexistence of proton-glass and ferroelectric orders in RADA
The complex dielectric permittivity ε′a(T ) and ε′′a(T ) of DRDA for x = 0.28 in
the deuteron glass range, typical of the glass state, are presented in figures 16 and
17. The dielectric permittivity ε′a(T ) of deuterated DRADA for x = 0.39 studied
by Trybu la et al. [11] is shown in figure 18. A typical behaviour attributed to the
transition from the paraelectric to antiferroelectric state is marked at TN = 127 K.
This phase transition takes place at the same temperature for different frequencies
of the measured electric field. Precise measurements for the temperature below 100
K show the occurrence of dispersion of the permittivity ε′a(T ) in the temperature
range from 20 K to 90 K (figure 19). Analysis of the shape of the temperature
Figure 18. Temperature dependence of
the real part of the electric permittiv-
ity e>a for DRADA x = 0.39, at the
frequency of the measuring electric field
ν = 10 kHz [11].
Figure 19. Dispersion of electric permit-
tivity ε′a(T, ν) for DRADA x = 0.39 [11].
Figure 20. The fit of the experimen-
tally obtained ε′′a(T, ν) data for DRADA
x = 0.39 using two Gaussian-shape lines
(at ν = 10 kHz). The contributions of
two different relaxation mechanisms are
marked [11].
dependence of ε′′a(T ) (figure 20) proves
the existence of phases of a short-range
order. In the antiferroelectric phase,
the values of ε′′ do not change with
temperature, as a result of the oppo-
site dipolar moments of the two sub-
lattices of the crystal due to the or-
dering of deuterons in the hydrogen
bond O-D· · ·O and the formation of the
lateral Slater configuration. The tem-
perature and frequency dependence of
ε′′, two orders of magnitude smaller
than those characteristic of the concen-
tration range in which deuteron glass
can exist, provides information that the
regions of the glass state are formed
where a long-range antiferroelectric or-
der disappears. A complex temperature
323
Z.Trybuła, J.Stankowski
Figure 21. Phase diagram of
Rb1−x(NH4)xH2AsO4 (DRADA).
dependence of ε′a(T, ν) indicates two
kinds of electric dipolar relaxation.
One of these mechanisms can be de-
scribed by the Vogel-Fulcher tempera-
ture (equation 5) with the parameters:
T0 = 25.7 K, Ec = 105.6 K and νo =
1.16 · 108 Hz, and is typical of clusters
with a short-range order characteristic
of proton (deuteron) glass. The second
relaxation mechanism is the thermally
activated Arrhenius dipolar reorienta-
tion with activation energy Ec = 1105
K and frequency νo = 1.44 · 1012 Hz.
The Arrhenius-type relaxation is re-
lated to free dipoles which are released
from the melting long-range ordering
but have not managed to form a cluster
yet. Similar behaviour of relaxation, de-
scribed by the Arrhenius equation, was
reported by Hutton et al. [42] for pro-
ton glass which is a mixture of antifer-
roelectric betaine phosphate (BP): (CH)3NCH2COO·H3PO4, and ferroelectric be-
taine phosphite (BPI): (CH)3NCH2COO·H3PO3 and in which the hydrogen bonds
between PO3 or PO4 groups form quasi-one dimensional chains. The Arrhenius-
type relaxation is typical of strong glass [43] characterized by a low density of
configurational states in their potential energy.
Figure 21 presents a new phase diagram of DRADA displaying the coexistence
of paraelectric/proton glass and ferroelectric (antiferroelectric) phases.
4. Pressure dependence of a proton glass phase
The first high-pressure studies in RADP mixed crystals were carried out by
Samara et al. [45-46]. The effect of pressure was expected to influence the glassy
state via the pressure dependence on the hydrogen-bond length. These studies have
led to a much better understanding of the nature of the competing inter-molecular
and intra-molecular interactions which are responsible for the establishment of
a long-range order. Pressure modifies interactions responsible for a short-range
correlation; therefore, the results of pressure dependence provide new insights into
the formation and properties of the glassy state. In the family of KDP crystals
the proton moves in a double-well potential along the hydrogen bond. In the
high- temperature tetragonal paraelectric phase the protons are disordered in the
potential wells leading to an effectively symmetric hydrogen bond. In the glass
state the proton freezes in one or another potential minimum; this results in an
elongated asymmetric hydrogen bond. Pressure reduces the H-bond length and
324
Coexistence of proton-glass and ferroelectric orders in RADA
favours a more symmetric bond with a lower energy barrier, which in turn leads
to a lower glass transition temperature. For a sufficiently high pressure, the H-
bond will become effectively symmetric, so that there will be no order and the
glassy state will vanish. The results of Samara for the RADP with x = 0.48, 72 %
deuterated crystal [45] and RADP with x = 0.50 [46] show the lowering of the glass
temperatures Tg, as presented in figure 22. The results for c and a crystallographic
Figure 22. Temperature-pressure phase
diagram for an RADP crystal. Insert:
comparison of the pressure dependences
of the dynamic glass Tg, ferroelectric Tc,
and antiferroelectric TN transition tem-
peratures for several crystals of RADP.
Curves 1-5 correspond to x = 1; 0; 0.8;
0.48 (72% D); and 0.5, respectively [46].
axes were qualitatively similar. Com-
parison of a pressure-induced suppres-
sion of the glassy state in a RADP
mixed crystal with the suppression of
the ferroelectric state in RDP and the
antiferroelectric state in ADP shows an
important difference between the glassy
transition and ferroelectric or antifer-
roelectric transitions. For pure ferro-
electric or antiferroelectric crystals the
magnitude of slope dTc,N/dp increases
with pressure at high pressure values.
The data strongly suggest that the
transition vanishes at an infinite slope,
i.e. dTc,N/dp → −∞ as Tc,N → 0. The
results of glassy RADP x = 0.5 are dif-
ferent. Glass transition temperature Tg
decreases linearly with pressure up to
temperature 5 K with no hint of any
impending increase in the magnitude of
dTg/dp at a lower temperature. There
are no data below 4 K, and only linear
Tg(p) extrapolation to higher pressures
is given. Samara supposes that the pro-
ton glass phase will disappear at 5 kbar.
Up to this time there is no experimental
evidence of a linear or nonlinear Tg(p)
response below 4 K. Samara believes that this linear dependence is most likely
the evidence of the nonequilibrium nature of the glass transition in RADP glass
crystals. There is a large hydrogen-isotope effect not only on Tg but also on its
pressure derivative. The magnitude of dTg/dp decreases from -3.6 to -2.0 K/kbar
on deuteration. The higher Tg and smaller dTg/dp for deuterated glass are due to
the fact that a deuteron is located deeper in the potential well than a proton, and
there is a much lower probability for tunneling between two potential wells along
the O-D· · ·O bond.
The effects of hydrostatic pressure on the dielectric properties and phase tran-
sitions were investigated in a RADA crystal by Samara and Schmidt [16] for the
compositions in the coexistence region of proton-glass and ferroelectric or antifer-
325
Z.Trybuła, J.Stankowski
Figure 23. Temperature dependence of
the ε′a electric permittivity in RADA x =
0.1 at different applied pressure [16].
roelectric orders. Figure 23 shows that
this crystal is inhomogeneous, contain-
ing a sufficiently large region (about
4 % of the sample’s volume) of pure
RDA, as indicated by Tc1 = 110
K. The second transition at Tc2 =
90 K is related to the presence of
RADA for x = 0.1. Glass transition
temperature Tg is marked at 30 K.
The pressure derivatives of Tc for the
paraelectric-ferroelectric transitions in
RDA (-4.6 K/kbar) are about twice as
large as those of TN for the paraelectric-
antiferroelectric ones in ADA (-1.97
K/kbar). The pressure derivative of Tg
for the paraelectric-proton glass transi-
tion (-2.2 K/kbar) is of about the same
magnitude as for ADA suggesting that
the compressibility of ADA clusters in RADA determines the glass transition. The
Tg is weakly dependent on the composition over most of the region of a proton glass
phase. Samara’s results indicate that pressure derivative dTg/dp is also essentially
independent of the composition. The decrease of Tc, TN , and Tg with pressure
results from an increase in the tunnelling frequency and a decrease in the dipo-
lar interaction which is long-range in the case of ferroelectric and antiferroelectric
phases and short-range (probably antiferroelectric) in proton glass.
5. External dc electric field dependence of electric permitt ivity
in RADA
The temperature dependence of the field-cooled (FC), zero field-cooled (ZFC)
and field-heated (FH) static permittivity ε′ was studied in deuterated DRADP
crystals by Levstik et al. [47] and in Deuterated Rubidium Ammonium Dihydro-
gen Arsenate DRADA x = 0.28 by Pinto et al. [44]. Unlike magnetic spin glass,
where only random-bond type interactions exist [48], proton and deuteron glass
are characterized by the presence of random bonds and a random field [49-50].
The random bias electric field is due to the random sites of the NH4 (or ND4)
groups; this leads to a random freeze-out of the acid proton (or deuteron) in the
hydrogen bonds O-H· · ·O as temperature is lowered below Tg. Because of this field
the Edwards-Anderson order parameter qEA (see equation 1) is nonzero in the
whole temperature range. In magnetic spin glass systems the qEA is zero above
glass transition temperature and nonzero below Tg.
The static dielectric response of deuteron glass to the external dc electric field
depends on the history of the sample. It is important how the low temperature
glass phase (nonergotic) is reached. Above the glass phase the field-cooled ε′FC
326
Coexistence of proton-glass and ferroelectric orders in RADA
and zero field-cooled ε′ZFC electric permittivities are the same, whereas below
Tg, in general ε′FC > ε′ZFC. The DC electric field increases the value of a static
permittivity. The field-cooled electric permittivity ε′FC retains the same value as
temperature is lowered below Tg and is constant at the temperature decrease due
to the gradual freeze-out of the acid proton or deuteron in the hydrogen O-H· · ·O
bond. On switching the external dc field off, remanent polarization is observed
which vanishes as temperature is raised above Tg.
6. Conclusions
Dielectric studies of the proton state have contributed to a better under-
standing of the phenomena in mixed crystals Rb1−x(NH4)xH2AsO4 and deuterated
Rb1−x(ND4)xD2AsO4. After first observation of the glass state in dielectric data
for RADA x = 0.31 in 1986 [3], further measurements in the microwave region
by Trybu la, Stankowski and Blinc in 1988 [4,5] showed that the phase diagram
for RADA is asymmetric. Two years later this result was confirmed by Kim and
Kwun [7]. The dielectric dispersion of ε′ nd ε′′ in the paraelectric-proton glass
transition, described by the Vogel-Fulcher expression, was revealed. Further di-
electric studies led to the discovery of the coexistence of paraelectric/proton glass
and long-range ordered phases. Analysis of the temperature dependence of ε′′a in
deuterated DRADA x = 0.39 exposed the coexistence of antiferroelectric and glass
phases. Two different relaxation mechanisms are involved: the Arrhenius type and
the Vogel-Fulcher kind of relaxation. Thus, the phase coexistence for a mixed
RADA crystal was confirmed.
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Співіснування параелектричного/протонне скло та
сегнетоелектричного (антисегнетоелектричного)
впорядкування в кристалах Rb 1−x (NH 4 ) x H 2 AsO 4
З.Трибула, Я.Станковскі
Інститут молекулярної фізики ПАН,
Польща, 60-179, Познань, вул. Смолуховського, 17
Отримано 17 червня 1998 р.
Ця стаття є оглядом результатів діелектричного вивчення стану про-
тонного скла у змішаних кристалах Rb 1−x (NH 4 ) x H 2 AsO 4 (RA-
DA). Співіснування впорядкувань параелектричного/протонне скло
та сегнетоелектричного чи антисегнетоелектричного, підтверджене
іншими дослідженнями, детально обговорюється. Фазова діаграма
RADA є асиметричною. Стан протонного скла існує для концентрації
аміаку в межах 0, 1 < x < 0, 5 . Представлена фазова діаграма дейте-
рованого DRADA. Область стану протонного скла в DRADA (0, 2 < x <
0, 35) є вужчою, ніж у недейтерованому RADA. Представлені ефек-
ти впливу гідростатичного тиску на діелектричні властивості криста-
лу в стані протонного скла. Температура склування Tg спадає з тис-
ком і за оцінками прямує до нуля при 5 кбар. Низькотемпературна по-
ведінка є все ще дискусійною, оскільки немає експериментально під-
твердженої Tg(p) залежності нижче 4 К для систем протонного скла
Ключові слова: доменна структура, сегнетоелектрики
PACS: 77.22 ch, 77.22 gm, 64.70 -p, 74.84 -s
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