Neutron diffraction study of ferrielectric phase transition in monoclinic RbD2PO4

Article abstract of DOI:10.1143/JPSJ.76.044606

Crystal structures of monoclinic RbD₂PO₄ were studied at 297K in the ferrielectric phase (phase III) and at 350 K in the paraelectric phase (phase II) by means of the single crystal neutron diffraction. The oxygen and deuterium atoms associated with the hydrogen bonds along the b axis are ordered in phase III and are disordered in phase II. Other atoms are ordered in both phases II and III. There are four kinds of PO4 tetrahedra in phase III. The ferrielectricity of phase III were confirmed in the present neutron structural analysis. The III-II phase transition is caused by an order-disorder of PO ₄ tetrahedra accompanied by the motion of deuterium atoms within the hydrogen-bond chain. Fluctuations of the oxygen and deuterium atoms related hydrogen-bond chains along the b axis give rise to a quasi-one-dimensionality. 2007 The Physical Society of Japan.

Full text of DOI:10.1143/JPSJ.76.044606

Journal of the Physical Society of Japan
Vol. 76, No. 4, April, 2007, 044606
#2007 The Physical Society of Japan
Neutron Diffraction Study of Ferrielectric Phase Transition
in Monoclinic RbD2PO4
ꢀ
1
Eisuke MAGOME , Masaru KOMUKAE, and Mitsuo MACHIDA
Department of Applied Physics, Faculty of Science, Tokyo University of Science,
1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601
1Department of Physics, Faculty of Science, Kyushu University,
6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581
(Received December 14, 2006; accepted February 13, 2007; published April 10, 2007)
Crystal structures of monoclinic RbD2PO4 were studied at 297 K in the ferrielectric phase (phase III)
and at 350 K in the paraelectric phase (phase II) by means of the single crystal neutron diffraction. The
oxygen and deuterium atoms associated with the hydrogen bonds along the b axis are ordered in phase III
and are disordered in phase II. Other atoms are ordered in both phases II and III. There are four kinds of
PO4 tetrahedra in phase III. The ferrielectricity of phase III were confirmed in the present neutron
structural analysis. The III–II phase transition is caused by an order–disorder of PO4 tetrahedra
accompanied by the motion of deuterium atoms within the hydrogen-bond chain. Fluctuations of the
oxygen and deuterium atoms related hydrogen-bond chains along the b axis give rise to a quasi-one-
dimensionality.
KEYWORDS: RbD2PO4, monoclinic system, crystal structure, phase transition, hydrogen bond
DOI: 10.1143/JPSJ.76.044606
phase II, and does not obey the Curie–Weiss law even in
phase I.25,29–31) Such deviations from the Curie–Weiss law
1. Introduction
In the AH2BO4-type crystals [A ¼ K, Rb, Cs, Tl, NH4, were observed also in the case of CsH2PO4 which is
(CH3)2NH2; B ¼ P, As], two kinds of crystal systems can isomorphous to monoclinic RbD2PO4 in phase I.32,33) The
stably be crystallized at room temperature. The crystals of deviation from the Curie–Weiss law has been interpreted
KH2PO4, RbH2PO4 and NH4H2PO4 belong to the tetragonal by the quasi-one-dimensional Ising model. In this model, the
system, whereas the crystals of CsH2PO4, TlH2PO4, short-range intrachain interactions of the dipole moments are
(CH3)2NH2H2PO4 to the monoclinic one.1–7) The tetragonal exactly accounted for, and the long-range interchain inter-
and monoclinic AH2BO4-type crystals differ extremely in actions are approximated by a mean-field.34) Monoclinic
the physical properties associated with the phase transition, RbD2PO4 has dielectric relaxation of Debye type in the
for example the dielectric and thermal properties and the frequency range between 1 and 1000 MHz, and exhibits
pressure effect.7–23)
critical slowing-down near the III–II phase transition point
The RbH2PO4 crystal undergoes the ferroelectric phase as in the case of ferroelectric CsH2PO4.15,29) It is therefore
transition at 147 K.24) The space group changes from the suggested that the III–II phase transition in monoclinic
ꢀ
tetragonal I42d of the paraelectric phase to the orthorhombic RbD2PO4 is of order–disorder type with respect to PO4
Fdd2 of the ferroelectric phase. The tetragonal RbH2PO4 tetrahedra.
crystal is characterized by a three-dimensional network of
The crystal structures of monoclinic RbD2PO4 have been
the hydrogen-bond chains linking the PO4 tetrahedra.2) The reported in phases I, II, and III.27,28,35) X-ray diffraction
hydrogen atoms within the O–H···O bond chains are ordered studies of monoclinic RbD2PO4 indicate that the crystal has
below the ferroelectric transition point and disordered a superlattice structure with the cell doubling along the c
above.2) The dielectric constant follows the Curie–Weiss axis (a0 ꢂ b0 ꢂ 2c0) in phase II and another superlattice
law as in the cases of many ferroelectric crystals.11)
structure with the cell doubling along the a axis (2a0 ꢂ
On the other hand, monoclinic RbD2PO4, in which b0 ꢂ 2c0) in phase III. Here, a0, b0 and c0 are the lattice
deuterium was substituted for hydrogen in RbH2PO4, can parameters in phase I. The PO4 tetrahedra of monoclinic
stably be crystallized at room temperature.25) Monoclinic RbD2PO4 are connected to each other through hydrogen-
RbD2PO4 undergoes successive phase transitions accompa- bond chains exhibiting the layer structure which consists of
nied by a large peak in dielectric constant ꢀb along the the hydrogen-bond chains running along the b axis and
unique b axis at 317 K and a change in the temperature the c axis. Hence monoclinic RbD2PO4 is characterized by
gradient of ꢀbꢁ1 at 377 K.25) Monoclinic RbD2PO4 is ferri- a two-dimensional network of the hydrogen-bond chains
electric below 317 K and paraelectric above.26) Thus mono- parallel to the cleavage (100) plane. It was suggested that the
clinic RbD2PO4 has three phases denoted as I, II, and III in deuterium within O–D···O bond chain along the b axis are
order of descending temperature. The space groups of ordered in phase III and disordered in phases I and II,
monoclinic RbD2PO4 were reported to be P21=m, P21=c and whereas those along the c axis are ordered even in phase I.
P21 in phases I, II, and III, respectively.27,28) Furthermore, However, the position of deuterium of monoclinic RbD2PO4
the static dielectric constant of monoclinic RbD2PO4 shows has not yet been determined in phase III. The structure
a pronounced deviation from the Curie–Weiss law in analysis in phase II by means of X-ray diffraction indicates
that the thermal parameter of the deuterium within O–D···O
ꢀE-mail: magome@rs.kagu.tus.ac.jp
bond along the c axis is small value, and suggests its
044606-1

J. Phys. Soc. Jpn., Vol. 76, No. 4
E. MAGOME et al.
X
"
#
1=2
2
harmonic thermal motion. On the other hand, remarkable
large values for deuterium along the b axis imply their
disordered motion in their associated O–D···O bonds.
wðjFoj ꢁ jFcjÞ
X
Rw ¼
;
ð1Þ
2
wjFoj
However, there is no experimental evidence for the disorder- where the weight is w ¼ 1. The positional parameters
determined by the X-ray structure analysis at T ¼ 297 and
ing of deuterium within the O–D···O bond chains along
the b axis.
It is interesting to solve questions whether the III–II phase
transition in monoclinic RbD2PO4 relates to the orientational
polarization of PO4 tetrahedra or not, and also the deuterium
332 K were used as starting parameters of the least squares
calculation.
3. Results
in phase II is disordered or not. It is, therefore, necessary 3.1 Crystal structure in phase III
to investigate the mechanism of the III–II phase transition
The III–II phase transition is accompanied by a symmetry
in monoclinic RbD2PO4 from the point of view of crystal change from P21=c of phase II to P21 of phase III and the
occurrence of the superlattice structure with the unit cell
constant doubling along the a axis. A refinement of the
crystal structure in phase III was started from the positional
parameters of non-deuterium atoms in the X-ray structure
analysis reported by Suzuki et al. The subsequent refinement
structure. In the present study, neutron structure analysis of
monoclinic RbD2PO4 was performed in phases III and II, to
elucidate the III–II phase transition.
2. Experimental and Analysis
Single crystals of RbH2PO4 were obtained from an referred to the positions of deuterium atoms reported by
aqueous solution containing Rb2CO3 and H3PO4 in the Hagiwara et al. in phase II. The final structure refinement in
molar ratio of 1 : 2. The crystals of RbH2PO4 were phase III converged at Rw ¼ 0:0594 with anisotropic ther-
mal parameters for all the atoms. The positional and thermal
parameters of the crystal structure in phase III are listed
in Table I, and the interatomic distances in Table II. The
recrystallized for the sake of purification. The deuterated
crystals become tetragonal or monoclinic system in different
crystallization condition of temperature. Monoclinic
RbD2PO4 single crystals were grown at 313 K, where is thermal parameters of all the atoms are small value, and
higher than that in the case of tetragonal RbD2PO4, by a suggest their harmonic thermal motion. All constituent
slow evaporation method from 99.8% D2O solution started atoms of monoclinic RbD2PO4 are located at the general
from RbH2PO4 crystals. The deuterium-rich RbD2PO4 positions, and are ordered in phase III. We confirmed that
single crystals were obtained through a several times of the structural parameters of all atoms except deuterium are
almost equal to those reported by Suzuki et al. The structural
parameters of deuterium in phase III were first determined in
the present work.
recrystallization. A single crystal was polished with wet
filter paper to a sphere whose diameter is about 6 mm, and
was used as a specimen for the neutron experiment.
Neutron diffraction measurements were carried out at
The crystal structure projected on the (010) plane is
297 K in phase III and at 350 K in phase II on a four-circle depicted in Fig. 1. The origin in Fig. 1 were selected at
diffractometer 4CND at the Research Reactor Institute, ð0; 0; ꢁ1=4Þ in the coordinates shown in Table I, so as to
Kyoto University. Neutrons, monochromatized by the (220) compare the crystal structure of phase II. The PO4 tetrahedra
plane of a Cu single crystal, were used, where wavelength is are connected to each other through hydrogen bonds in a
˚
two-dimensional network parallel to the b–c plane and
two kinds of networks exist in the unit cell in phase III. The
crystal structure is formed by independent four kinds of
ꢁ ¼ 1:00 A. An ! step-scanning method was used to collect
ꢁ1
˚
independent reflections within the limit sin ꢂ=ꢁ ¼ 0:78 A
in both phases. One standard reflection was also measured at
regular intervals to check the stability of the measurement, RbD2PO4 molecules. Four kinds of PO4 tetrahedra, P(1)–
and no significant variation was noticed in their intensities. O(11)–O(12)–O(13)–O(14),
P(2)–O(21)–O(22)–O(23)–
The lattice parameters reported in the X-ray study were used O(24), P(3)–O(31)–O(32)–O(33)–O(34), and P(4)–O(41)–
for the present structure analysis by means of neutron O(42)–O(43)–O(44), are abbreviated as PO4(1), PO4(2),
diffraction. The unit cell parameters and the number of the PO4(3), and PO4(4), respectively. We examined the atomic
˚
distances of the PO4(1) tetrahedron. The atomic distances of
chemical formula in the unit cell (Z) are a ¼ 15:352ð2Þ A,
ꢃ
˚
˚
O(11)–D(11) and O(14)–D(13), 0.99(1) A and 1.08(1) A, are
˚
˚
b ¼ 6:184ð1Þ A, c ¼ 9:566ð2Þ A, ꢃ ¼ 108:8ð1Þ and Z ¼ 8 at
iv
˚
˚
˚
˚
shorter than those [1.56(1) A, 1.43(2) A] of O(12)···D(41 )
297 K in phase III and are a ¼ 7:683ð1Þ A, b ¼ 6:170ð1Þ A,
c ¼ 9:560ð1Þ A, ꢃ ¼ 109:1ꢃ and Z ¼ 4 at 332 K in and O(13)···D(42vii) (see Table II). Moreover, the P(1)–
˚
phase II.27,28) The crystal structure analyses of monoclinic O(11) and P(1)–O(14) distances which are estimated to
˚
RbD2PO4 in phases III and II were performed by using 1918 be 1.56(1) and 1.56(2) A respectively, are longer than the
˚
and 1091 diffraction intensities satisfying the condition that distances of 1.49(1) and 1.49(1) A for P(1)–O(12) and P(1)–
jFoj ꢄ 3ꢄðjFojÞ, where jFoj is the observed structure factor O(13), reflecting a fact that the D(11) and D(13) atoms are
close to the O(11) and O(14) atoms, respectively.
The P(1) atom deviates from a center of the oxygen atoms
and ꢄ the estimated standard deviation. We refined
the structure using the full-matrix least squares program
assuming an anisotropic secondary extinction effect.36)
within the PO4(1) tetrahedron. The magnitude of deviation
˚
The function minimized in the structure refinement is was estimated to be about 0.10 A, and the b-component of
P
2
˚
ðjFoj ꢁ jFcjÞ , where jFcj is the calculated structure deviation is about 0.06 A. It can be therefore expected that
factor. The coherent scattering lengths used for Rb, P, O, the dipole moment occurs within the PO4(1) tetrahedron.
and D were 7.08, 5.130, 5.805, and 6.674 fm, respectively. The P(2), P(3), and P(4) atoms also deviate from a center of
The discrepancy factor is given by
the oxygen atoms. These deviations differ in the direction
and magnitude. Therefore, there are four kinds of dipole
044606-2

J. Phys. Soc. Jpn., Vol. 76, No. 4
E. MAGOME et al.
2
Table I. Positional parameters x, y, z (fraction) and thermal parameters Uij (10ꢁ2 A ) in phase III of monoclinic RbD2PO4 at T ¼ 297 K.
˚
Atom
x
y
z
U11
U22
U33
U12
U13
U23
Rb(1)
Rb(2)
Rb(3)
Rb(4)
P(1)
0.1321(5)
0.3691(5)
0.6330(5)
0.8668(5)
0.1211(6)
0.3769(6)
0.6234(6)
0.8791(6)
0.2010(5)
0.1650(7)
0.0474(6)
0.0833(7)
0.2975(5)
0.3345(7)
0.4512(6)
0.4167(6)
0.6993(6)
0.6664(7)
0.5495(7)
0.5761(7)
0.8018(6)
0.8339(6)
0.9518(6)
0.9175(6)
0.1838(6)
0.3165(5)
0.6809(6)
0.8180(6)
0.0155(9)
0.4824(5)
0.5106(5)
0.9926(8)
0.25
0.0287(8)
0.4720(8)
0.0346(9)
0.4620(8)
0.2659(8)
0.2334(9)
0.2695(9)
0.2311(8)
0.1993(8)
0.4230(9)
0.1762(10)
0.2446(13)
0.3009(9)
0.0728(9)
0.3205(11)
0.2444(12)
0.1937(9)
0.4274(9)
0.1865(10)
0.2397(13)
0.3052(9)
0.0753(9)
0.3198(9)
0.2488(11)
0.0904(11)
0.4122(8)
0.0839(9)
0.4119(10)
0.2535(11)
0.2521(12)
0.2408(10)
0.2537(13)
3.4(3)
3.2(3)
3.4(3)
3.2(3)
2.6(3)
2.6(3)
2.6(3)
2.6(3)
2.5(3)
4.7(4)
3.3(4)
4.2(4)
2.6(3)
4.4(4)
3.6(4)
2.8(3)
3.0(3)
4.7(4)
4.9(4)
4.0(4)
2.5(3)
3.7(4)
3.6(3)
3.9(3)
5.0(4)
3.8(3)
4.4(4)
4.3(4)
9.1(7)
3.9(3)
3.1(3)
7.5(6)
3.4(3)
3.6(3)
3.6(3)
3.3(3)
2.5(3)
3.2(4)
3.2(4)
2.6(3)
5.8(5)
3.9(3)
3.5(3)
3.1(3)
3.8(3)
8.5(6)
3.9(4)
3.3(3)
4.6(4)
4.6(4)
4.5(4)
3.4(3)
4.7(4)
8.3(6)
3.8(3)
2.5(3)
3.8(4)
5.3(4)
4.7(4)
4.2(4)
3.8(3)
4.7(4)
4.6(4)
4.3(4)
3.1(3)
3.7(3)
4.0(3)
3.4(3)
2.5(3)
2.3(3)
2.5(3)
2.4(3)
2.1(3)
2.5(3)
3.4(4)
7.1(5)
2.9(3)
2.0(3)
3.9(4)
6.5(5)
2.6(4)
2.5(4)
3.8(4)
7.5(6)
2.8(4)
2.1(3)
3.0(3)
5.3(4)
5.1(5)
2.9(3)
3.3(3)
4.4(4)
4.9(4)
6.9(5)
4.8(4)
5.4(5)
0.1(2)
ꢁ0:1ð3Þ
ꢁ0:2ð3Þ
0.2(3)
0.5(2)
0.9(3)
1.2(3)
0.9(2)
1.2(3)
0.7(3)
1.0(3)
1.2(3)
0.8(2)
1.0(3)
0.7(3)
3.3(4)
1.5(3)
1.3(3)
2.0(3)
1.4(3)
1.3(3)
1.3(3)
2.9(3)
3.7(4)
1.1(3)
0.9(3)
0.5(2)
1.5(3)
2.5(4)
1.1(3)
1.1(3)
2.3(3)
1.5(4)
2.2(3)
1.7(3)
0.3(4)
ꢁ0:2ð2Þ
ꢁ0:3ð3Þ
ꢁ0:1ð3Þ
ꢁ0:2ð2Þ
0.2(3)
0.7328(6)
0.2564(18)
0.7290(17)
0.7252(17)
0.2594(18)
0.7531(18)
0.2367(17)
0.7438(20)
0.6584(19)
0.5768(20)
0.9621(20)
0.2531(18)
0.3138(24)
0.4155(20)
0.0239(19)
0.7394(19)
0.6791(20)
0.5768(20)
0.9684(20)
0.2541(19)
0.3011(25)
0.4016(19)
0.0113(20)
0.7581(19)
0.2308(19)
0.7666(19)
0.2213(18)
0.9828(22)
0.0105(20)
0.5183(19)
0.4773(23)
ꢁ0:1ð3Þ
ꢁ0:3ð3Þ
ꢁ0:2ð3Þ
0.2(3)
P(2)
ꢁ0:1ð3Þ
ꢁ0:3ð3Þ
0.1(3)
P(3)
P(4)
O(11)
O(12)
O(13)
O(14)
O(21)
O(22)
O(23)
O(24)
O(31)
O(32)
O(33)
O(34)
O(41)
O(42)
O(43)
O(44)
D(11)
D(21)
D(31)
D(41)
D(13)
D(23)
D(32)
D(42)
ꢁ0:4ð3Þ
0.2(3)
0.4(3)
0.3(2)
ꢁ0:8ð3Þ
0.7(3)
ꢁ0:5ð3Þ
0.8(3)
0.3(2)
0.3(2)
ꢁ0:6ð4Þ
ꢁ1:0ð3Þ
ꢁ0:3ð3Þ
0.7(3)
0.0(3)
ꢁ1:0ð3Þ
ꢁ0:9ð3Þ
0.7(3)
0.1(3)
0.5(2)
ꢁ2:0ð3Þ
1.2(3)
ꢁ1:1ð3Þ
0.8(3)
0.4(3)
0.6(3)
ꢁ0:6ð4Þ
ꢁ0:9ð3Þ
ꢁ0:1ð2Þ
0.6(3)
ꢁ0:3ð3Þ
ꢁ0:2ð2Þ
ꢁ0:1ð2Þ
ꢁ0:2ð3Þ
0.2(3)
ꢁ0:7ð3Þ
ꢁ0:8ð3Þ
0.5(3)
0.0(3)
ꢁ0:4ð3Þ
ꢁ0:4ð3Þ
ꢁ0:5ð4Þ
ꢁ0:7ð3Þ
ꢁ0:1ð3Þ
ꢁ1:5ð4Þ
0.9(3)
ꢁ0:4ð2Þ
0.3(4)
b
a
c
Rb(1)
Rb(3)
O(33)
D(31)
O(22)
D(32)
O(24)
O(42)
D(42)
P(4) O(44)
D(11)
O(11)
O(13)
O(31)
P(2)
P(1)
O(34) P(3)
D(23)
O(14)
D(13)
O(21)
O(41)
O(23)
O(43)
D(41)
D(21)
O(12)
Rb(4)
Rb(2)
O(32)
1 Å
Fig. 1. Crystal structure of monoclinic RbD2PO4 in phase III. Projection on the (010) plane.
044606-3

J. Phys. Soc. Jpn., Vol. 76, No. 4
E. MAGOME et al.
˚
Table II. The interatomic distances (A) calculated from the average
a
c
b
structure of phase III (T ¼ 297 K) given in Table I.
P–O distances
P(1)–O(11)
P(1)–O(12)
P(1)–O(13)
P(1)–O(14)
P(2)–O(21)
P(2)–O(22)
P(2)–O(23)
P(2)–O(24)
1.56(1)
1.49(1)
1.49(1)
1.56(2)
1.55(1)
1.50(1)
1.52(1)
1.57(2)
P(3)–O(31)
P(3)–O(32)
P(3)–O(33)
P(3)–O(34)
P(4)–O(41)
P(4)–O(42)
P(4)–O(43)
P(4)–O(44)
1.56(1)
1.51(1)
1.59(2)
1.50(2)
1.57(1)
1.48(1)
1.55(1)
1.50(2)
µ2
µ4
µ3
µ1
O–D···O distances
O(11)–D(11)···O(42i)
O(21)–D(21)···O(32ii)
O(14)–D(13)···O(44v)
O(24)–D(23)···O(34vi)
2.53(1)
2.52(1)
2.58(2)
2.48(2)
O(31iii)–D(31iii)···O(22)
O(41iv)–D(41iv)···O(12)
2.47(1)
2.55(1)
2.48(2)
2.55(1)
O(33)–D(32)···O(23)
O(43vii)–D(42vii)···O(13)
−0.25 < x < 0.25
0.25 < x < 0.75
D–O and D···O distances
D(11)–O(11)
D(21)–O(21)
D(31iii)–O(31iii)
D(41iv)–O(41iv)
D(13)–O(14)
D(23)–O(24)
D(32)–O(33)
0.99(1)
1.02(1)
1.01(1)
0.99(1)
1.08(1)
0.99(1)
0.98(1)
1.13(2)
D(11)···O(42i)
D(21)···O(32ii)
D(31iii)···O(22)
D(41iv)···O(12)
D(13)···O(44v)
D(23)···O(34vi)
D(32)···O(23)
D(42vii)···O(13)
1.54(1)
1.51(1)
1.47(1)
1.56(1)
1.50(2)
1.50(1)
1.50(1)
1.43(2)
Fig. 2. Schematic drawings of configurations of the pseudo-moments
projected along the a axis in phase III.
D(1), D(2), and D(3) atoms, D(1) atoms are located at the
general positions, whereas D(2) and D(3) atoms at the
inversion center. The D(2), D(3), O(3), and O(4) atoms have
remarkably large and highly anisotropic thermal parameters.
For example, the root-mean-square displacements of the
D(42vii)–O(43vii
)
2
˚
Symmetry code: (i) 1 ꢁ x, y þ 1=2, ꢁz; (ii) 1 ꢁ x, y ꢁ 1=2, 1 ꢁ z; (iii)
1 ꢁ x, y ꢁ 1=2, ꢁz; (iv) 1 ꢁ x, y þ 1=2, 1 ꢁ z; (v) x ꢁ 1, y þ 1, z; (vi) x,
y ꢁ 1, z; (vii) x ꢁ 1, y, z.
O(4) atom are 0.12, 0.04, and 0.02 A along the principal
axes of the thermal ellipsoid. The results suggested a
possibility that D(2), D(3) atoms are disordered within
hydrogen bonds along the b axis, and the O(3) and O(4)
moment corresponding to these deviations. It can be atoms also are disordered in phase II. Subsequent neutron
assumed that the dipole moment is roughly proportional to structure analysis was performed by means of the split-atom
the deviation of P atom from a center of the oxygen atoms method, in order to make clear the disordering for the D(2),
within the PO4 tetrahedron. In order to ascertain ferrielectric D(3), O(3), and O(4) atoms of monoclinic RbD2PO4 in
state in phase III, the pseudo-moments, ꢅ1, ꢅ2, ꢅ3 and ꢅ4, phase II. Then, the D(2) and D(3) atoms within the hydrogen
proportional to the displacements are assumed as the dipole bonds split into two sites related by the inversion center,
moments of PO4(1), PO4(2), PO4(3) and PO4(4). Figure 2 and the O(3) and O(4) atoms into two independent sites.
shows schematically the arrangement of the pseudo-mo- Disordered structure was successfully refined by means of
ments ꢅ1, ꢅ2, ꢅ3 and ꢅ4. The pseudo-dipole moments ꢅ1 the split-atom method. The final discrepancy factor is Rw ¼
and ꢅ4 exist on the hydrogen-bond network in a range of 0:0694. The positional and thermal parameters of mono-
ꢁ0:25 < x < 0:25 and run zigzag along the b axis. The clinic RbD2PO4 are listed in Table III, and the interatomic
pseudo-dipole moments ꢅ2 and ꢅ3 which are on the distances in Table IV. Two split atoms for both the O(3)
hydrogen-bond network in a range of 0:25 < x < 0:75, run and O(4) atoms are discriminated by the a and b symbols.
zigzag in the opposite direction of ꢅ1 and ꢅ4 with respect to The three kinds of hydrogen bond lengths O–D···O are
˚
the b-component. Such an arrangement of the pseudo-dipole about 2.50 A as shown in Table IV.
moments corresponding dipole moments indicates that
Figure 3 shows the disordered structure viewed along the
monoclinic RbD2PO4 is ferrielectric in phase III, and the b axis of monoclinic RbD2PO4 in phase II. The crystal
ferrielectric state consists of four sublattices.
structure has the same hydrogen-bond network of phase III.
It was appreciated in Fig. 3 that the superlattice structure of
phase III along the a axis disappears in phase II. The O(1),
3.2 Crystal structure in phase II
The atomic parameters of all atoms in phase II were O(2), and D(1) atoms associated with the hydrogen-bond
determined on the basis of the average structure model in chains along the c axis are in the ordered state. The O(1)–
advance of the structure analysis of a split-atom method. The D(1)···O(2i) and D(1)–O(1) distances are 2.500(3) and
discrepancy factor converges at Rw ¼ 0:0813 as an average 0.993(3) A, respectively (see Table IV). The D(1)···O(2i)
˚
structure. The positional and thermal parameters of all atoms distance 1.512(3) A is longer than that of D(1)–O(1).
˚
except deuterium atom as a whole are similar to those Therefore, the P–O(1) distance 1.558(3) A is longer than
˚
reported by Hagiwara et al. The structural parameters of the another P–O(2) distance 1.481(3) A, reflecting a fact that the
deuterium atoms are reliably determined more than those D(1) atoms are close to the O(1) atoms (see Table IV). On
obtained by X-ray study. The average structure formed by the other hand, both the O(3) and O(4) atoms are disordered
one RbD2PO4 molecule is satisfied with the symmetry of the between two independent positions. The distances between
space group P21=c in phase II. As for the three independent two positions of oxygen are determined to be 0.26(2) and
044606-4

J. Phys. Soc. Jpn., Vol. 76, No. 4
E. MAGOME et al.
2
Table III. Positional parameters x, y, z (fraction) and thermal parameters Uij (10ꢁ2 A ) in phase II of monoclinic RbD2PO4 at T ¼ 350 K. Anisotropic
˚
ꢀ2
ꢀ2
þ k2b
ꢀ2
þ l2c
U
temperature factor is defined by exp½ꢁ2ꢆ2ðh2a
U
U
22
þ 2hkaꢀbꢀU12 þ 2hlaꢀcꢀU13 þ 2klbꢀcꢀU23Þꢅ.
11
33
Atom
x
y
z
U11
U22
U33
U12
U13
U23
Rb
0.2629(2)
0.2447(2)
0.4019(2)
0.3328(3)
0.1154(2)
0.0991(2)
0.1379(2)
0.1700(2)
0.3662(3)
0.0208(6)
0.0326(1)
0.2581(3)
0.7469(3)
0.7459(4)
0.6950(6)
0.5581(3)
0.5899(3)
0.9646(3)
0.9713(2)
0.7630(4)
0.5176(6)
ꢁ0:0116ð2Þ
0.2787(2)
0.5175(2)
0.4478(2)
0.6763(2)
0.4465(2)
0.4288(1)
0.4692(2)
0.5037(2)
0.3388(2)
0.4949(6)
0.4957(2)
4.07(8)
3.11(7)
3.11(7)
5.33(12)
6.3(7)
4.25(8)
3.70(8)
5.92(11)
9.82(22)
4.7(6)
4.18(8)
2.78(7)
2.95(7)
2.73(8)
7.2(7)
3.1(2)
8.1(8)
7.0(6)
4.58(9)
6.5(6)
6.5(3)
ꢁ0:01ð6Þ
ꢁ0:03ð7Þ
0.22(8)
ꢁ0:08ð12Þ
ꢁ2:4ð5Þ
ꢁ0:9ð2Þ
2.1(4)
1.17(6)
1.29(5)
1.39(5)
1.54(7)
5.0(6)
ꢁ0:20ð6Þ
0.04(7)
0.46(8)
0.34(10)
ꢁ1:6ð5Þ
ꢁ0:1ð2Þ
2.3(5)
P
O(1)
O(2)
O(3a)
O(3b)
O(4a)
O(4b)
D(1)
D(2)
D(3)
4.5(3)
3.7(4)
0.8(2)
4.5(6)
5.1(5)
4.0(7)
3.5(4)
3.0(3)
0.0(3)
1.3(3)
ꢁ0:2ð3Þ
ꢁ0:16ð8Þ
ꢁ0:8ð8Þ
ꢁ0:5ð3Þ
4.75(9)
7.3(17)
7.8(9)
5.16(10)
5.1(11)
4.7(3)
ꢁ0:12ð8Þ
0.5(6)
2.09(7)
0.3(10)
2.2(6)
0.0(5)
˚
Table IV. The interatomic distances (A) calculated from the disordered
b
a
structure of the phase II (T ¼ 350 K) given in Table III.
P–O distances
c
P–O(1)
1.558(3)
1.481(3)
1.54(2)
1.51(2)
1.56(2)
1.49(1)
P–O(2)
i
P–O(3a)
P–O(3b)
P–O(4a)
P–O(4b)
O(2 )
Rb
O(3b)
D(1)
O(1)
D(3)
D(2)
O(3a)
O–D···O distances
P
O(4a)
O(4b)
O(1)–D(1)···O(2i)
O(3b)–D(2)···O(3aii)
O(4a)–D(3iv)···O(4biii)
2.500(3)
2.50(2)
2.49(2)
O(2)
D–O and D···O distances
D(1)–O(1)
0.993(3)
1.512(3)
1.02(5)
1.42(5)
0.97(2)
1.56(2)
D(1)···O(2i)
D(2)–O(3b)
D(2)···O(3aii)
D(3iv)–O(4a)
D(3ii)···O(4b)
1 Å
Fig. 3. Crystal structure of monoclinic RbD2PO4 in phase II. Projection
along the b axis.
2-site distances
O(3a)–O(3b)
O(4a)–O(4b)
D(2)–D(2ii)
D(3ii)–D(3iv)
0.26(2)
0.34(2)
0.42(2)
0.55(6)
a
c
b
D(1)
O(1)
Symmetry code: (i) x, 3=2 ꢁ y, z ꢁ 1=2; (ii) ꢁx, 1 ꢁ y, 1 ꢁ z; (iii) ꢁx,
2 ꢁ y, 1 ꢁ z; (iv) x, y þ 1, z; (v) ꢁx, ꢁy, 1 ꢁ z; (vi) x, 3=2 ꢁ y, z þ 1.
O(3b)
O(3a)
ii
O(4a)
D(3
iv
)
D(2 )
ii
D(3 )
˚
0.34(2) A for O(3a)–O(3b) and O(4a)–O(4b), respectively
D(2)
O(4b)
(see Table IV). The PO4 ion can be decomposed into two
kinds of O(1)–O(2)–O(3a)–O(4a) and O(1)–O(2)–O(3b)–
O(4b) tetrahedra.
Figure 4 depicts the PO4 tetrahedra and the deuterium
atoms viewed along the a axis. For simplicity, the Rb and P
atoms are not shown. Two kinds of PO4 tetrahedra are
represented by solid and broken lines in Fig. 4. Atomic
distances between the P atom and the oxygen atoms
involved in the hydrogen bonds running along the b axis
ii
O(3a )
ii
O(3b )
O(2)
Fig. 4. Crystal structure around the PO4 tetrahedra and deuterium atoms
viewed along the a axis in phase II. Rb and P atoms are not shown. Two
kinds of PO4 tetrahedra are shown by the solid and broken lines.
˚
are 1.54(2), 1.51(2), 1.56(2), and 1.49(1) A for P–O(3a), P–
O(3b), P–O(4a), and P–O(4b), respectively (see Table IV). D(3iv), respectively (see Table IV and Fig. 4). In addition,
˚
˚
Both the D(2) and D(3) atoms are also disordered over two the D(2)–O(3b) length 1.02(5) A is shorter than 1.42(5) A for
equilibrium positions of which the distances are determined the D(2)···O(3aii) length (see Table IV and Fig. 4). It should
ii
ii
˚
to be 0.42(2) A and 0.55(6) A for D(2)–D(2 ) and D(3 )– be note that the hydrogen-bond chain linking two disordered
˚
044606-5

J. Phys. Soc. Jpn., Vol. 76, No. 4
E. MAGOME et al.
tetrahedra along the b axis are O(3bii)–D(2ii)···O(3a) and
O(3b)–D(2)···O(3aii) as shown in Fig. 4. The relation
between O(3bii) and O(3a) within the hydrogen-bond
Acknowledgement
This work was carried out under the Visiting Researcher’s
chain of O(3bii)–D(2ii)···O(3a) is clearly unsatisfied by Program of the Research Reactor Institute, Kyoto Univer-
any symmetry operation. Similarly, the relation between sity.
O(3aii) and O(3b) also is unsatisfied. However, the average
position of O(3a) and O(3b) relates that of O(3aii) and
O(3bii) by the inversion symmetry.
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bond along the b axis. The III–II phase transition is caused
by an order–disorder of PO4 tetrahedra accompanied by the
motion of deuterium atoms within the hydrogen-bond chain.
It was also noted that the oxygen and deuterium atoms
related hydrogen bond along only the b axis have large
fluctuation as disordering state. It was suggested that such
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4. Conclusion
The results obtained in the present study are summarized
as follows.
(1) In phase III, the positional parameters of all constituent
atoms were determined. All constituent atoms of
monoclinic RbD2PO4 are ordered in phase III.
(2) There are four kinds of PO4 tetrahedra with dipole
moment in phase III. An arrangement of the pseudo-
dipole moments corresponding dipole moments indi-
cates the ferrielectricity of monoclinic RbD2PO4 in
phase III.
(3) Disordered structure of RbD2PO4 in phase II was
refined by means of the split-atom method. The oxygen
and deuterium atoms associated with the hydrogen
bonds along the b axis are disordered, and other atoms
are ordered. Therefore, the PO4 tetrahedron is disor-
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by the disordering of deuterium atoms within the
hydrogen-bond chain along the b axis.
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Such fluctuations give rise to a quasi-one-dimension-
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(5) The III–II phase transition in monoclinic RbD2PO4
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Debye type in the microwave range, and exhibits
critical slowing-down near the III–II phase transition
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044606-6