Ferroelastic domain wall orientations in the (NH₄)₃H(SeO₄)₂ crystal
Experimental and theoretical studies of the ferroelastic domain structure of the (NH₄)₃H(SeO₄)₂ crystal in phases III and IV are performed. Using the refined structural data the orientations of W - and W′-type domain walls, as well as the temperature evolution of the domain structure are inv...
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Інститут фізики конденсованих систем НАН України
1998
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irk-123456789-1189372017-06-02T03:02:42Z Ferroelastic domain wall orientations in the (NH₄)₃H(SeO₄)₂ crystal Pavlenko, N. Połomska, M. Hilczer, B. Experimental and theoretical studies of the ferroelastic domain structure of the (NH₄)₃H(SeO₄)₂ crystal in phases III and IV are performed. Using the refined structural data the orientations of W - and W′-type domain walls, as well as the temperature evolution of the domain structure are investigated. It is shown that in spite of the fact that the room temperature phase III has a triclinic symmetry with small deviations from monoclinic, the domain structure in this phase differs strongly from the structure in the case of a monoclinic symmetry which has been previously accepted in this temperature range. In the monoclinic phase IV all the W′-type domain walls lie almost in parallel to the (001)-plane which explains the invisibility of W′ walls after III-IV phase transition during the observation of the domain structure in the (001)-plane. В роботі проведено експериментальне й теоретичне вивчення доменної структури кристалу (NH₄)₃H(SeO₄)₂ у фероеластичних фазах III і IV. Використовуючи найновіші структурні дані, досліджено орієнтації доменних стінок типу W та W′. Показано, що незважаючи на те, що при кімнатній температурі кристал має триклінну симетрію з незначними відхиленнями від моноклінної, доменна структура сильно відрізняється від тієї, яка отримується для фази з моноклінною симетрією, що було прийнято раніше для цього температурного інтервалу. У моноклінній фазі IV доменні стінки типу W′ майже паралельні до площини (001), що пояснює факт їх зникнення при оптичних спостереженнях у цій площині. 1998 Article Ferroelastic domain wall orientations in the (NH₄)₃H(SeO₄)₂ crystal / N. Pavlenko, M. Połomska, B. Hilczer // Condensed Matter Physics. — 1998. — Т. 1, № 2(14). — С. 357-364. — Бібліогр.: 15 назв. — англ. 1607-324X DOI:10.5488/CMP.1.2.357 PACS: 77.80.Dj http://dspace.nbuv.gov.ua/handle/123456789/118937 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Experimental and theoretical studies of the ferroelastic domain structure of
the (NH₄)₃H(SeO₄)₂ crystal in phases III and IV are performed. Using
the refined structural data the orientations of W - and W′-type domain
walls, as well as the temperature evolution of the domain structure are
investigated. It is shown that in spite of the fact that the room temperature
phase III has a triclinic symmetry with small deviations from monoclinic,
the domain structure in this phase differs strongly from the structure in
the case of a monoclinic symmetry which has been previously accepted in
this temperature range. In the monoclinic phase IV all the W′-type domain
walls lie almost in parallel to the (001)-plane which explains the invisibility of
W′ walls after III-IV phase transition during the observation of the domain
structure in the (001)-plane. |
| format |
Article |
| author |
Pavlenko, N. Połomska, M. Hilczer, B. |
| spellingShingle |
Pavlenko, N. Połomska, M. Hilczer, B. Ferroelastic domain wall orientations in the (NH₄)₃H(SeO₄)₂ crystal Condensed Matter Physics |
| author_facet |
Pavlenko, N. Połomska, M. Hilczer, B. |
| author_sort |
Pavlenko, N. |
| title |
Ferroelastic domain wall orientations in the (NH₄)₃H(SeO₄)₂ crystal |
| title_short |
Ferroelastic domain wall orientations in the (NH₄)₃H(SeO₄)₂ crystal |
| title_full |
Ferroelastic domain wall orientations in the (NH₄)₃H(SeO₄)₂ crystal |
| title_fullStr |
Ferroelastic domain wall orientations in the (NH₄)₃H(SeO₄)₂ crystal |
| title_full_unstemmed |
Ferroelastic domain wall orientations in the (NH₄)₃H(SeO₄)₂ crystal |
| title_sort |
ferroelastic domain wall orientations in the (nh₄)₃h(seo₄)₂ crystal |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
1998 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118937 |
| citation_txt |
Ferroelastic domain wall orientations in the (NH₄)₃H(SeO₄)₂ crystal / N. Pavlenko, M. Połomska, B. Hilczer // Condensed Matter Physics. — 1998. — Т. 1, № 2(14). — С. 357-364. — Бібліогр.: 15 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT pavlenkon ferroelasticdomainwallorientationsinthenh43hseo42crystal AT połomskam ferroelasticdomainwallorientationsinthenh43hseo42crystal AT hilczerb ferroelasticdomainwallorientationsinthenh43hseo42crystal |
| first_indexed |
2025-07-08T14:56:13Z |
| last_indexed |
2025-07-08T14:56:13Z |
| _version_ |
1837091074353397760 |
| fulltext |
Condensed Matter Physics, 1998, Vol. 1, No 2(14), p. 357–364
Ferroelastic domain wall orientations in
the (NH 4 ) 3H(SeO 4 ) 2 crystal
N.Pavlenko 1 , M.Połomska 2 , B.Hilczer 2
1 Institute for Condensed Matter Physics, Ukrainian National Academy of
Sciences, 1 Svientsitskii St., UA–290011 Lviv–11, Ukraine
2 Institute of Molecular Physics, Polish Academy of Sciences,
Smoluchowskiego 17/19, PL-60179, Poznan, Poland
Received April 3, 1998
Experimental and theoretical studies of the ferroelastic domain structure of
the (NH 4 ) 3 H(SeO 4 ) 2 crystal in phases III and IV are performed. Using
the refined structural data the orientations of W - and W
′ -type domain
walls, as well as the temperature evolution of the domain structure are
investigated. It is shown that in spite of the fact that the room temperature
phase III has a triclinic symmetry with small deviations from monoclinic,
the domain structure in this phase differs strongly from the structure in
the case of a monoclinic symmetry which has been previously accepted in
this temperature range. In the monoclinic phase IV all the W
′ -type domain
walls lie almost in parallel to the (001)-plane which explains the invisibility of
W
′ walls after III-IV phase transition during the observation of the domain
structure in the (001)-plane.
Key words: domain structure, ferroelasticity
PACS: 77.80.Dj
1. Introduction
The (NH4)3H(SeO4)2 crystal belongs to the family of hydrogen disulphates and
diselenates of the chemical formula M3H(XO4)2, where M denotes NH4, K, Rb and
Cs. The crystalline structure of the family is characterized by dimers formed by
XO4 tetrahedra linked with H-bonds. The dynamics of the XO4 groups and the pro-
ton ordering in crystals result in a sequence of phases exhibiting various long-range
orderings. The following phase diagram is now accepted for the (NH4)3H(SeO4)2
crystal:
c© N.Pavlenko, M.Połomska, B.Hilczer 357
N.Pavlenko, M.Połomska, B.Hilczer
Phase Phase transition temperature Point group Reference
I R3̄m [1,2]
328 K
II R3̄ [2]
302 K
III C1̄ [3]
275 K
IV A2/a [4,5]
181 K
V Aa [6]
101 K
VI Aa [6]
At 302 K the crystal undergoes a transition to the superprotonic phase [1,7]
and this transition coincides with the ferroelastic-paraelastic one [1,8]. It should be
noted that the ferroelastic domain structure was observed not only in the triclinic
phase III but also in the monoclinic phase IV [8–12]. Moreover, dilatometric studies
of the crystal [8] revealed drastic changes in the lattice dilatation at 275K. A long
range electric ordering was reported in phase V and the ferroelectric-paraelectric
phase transition took place at 181 K [13]. Here we would like to present the re-
sults of theoretical studies of the ferroelastic domain structure in (NH4)3H(SeO4)2
single crystals and the comparison of the results with the experimentally observed
variations in the domain pattern.
2. Domain structure of phases III and IV
According to the recent structural investigations [3,4] in (NH4)3H(SeO4)2 two
ferroelastic phases occur on cooling. In particular, at room temperature (phase
III) the symmetry of the crystal is triclinic C1̄ with a small deviation from mon-
oclinic. The elementary unit cell shown in figure 1(a) has the following param-
eters at = 15.81Å, bt = 6.052Å, ct = 10.482Å, α = 90.79◦, β = 102.31◦ and
γ = 89.13◦. Only below 279 K the symmetry of (NH4)3H(SeO4)2 changes to
monoclinic C2/c (phase IV) with the unit cell parameters am = 10.44Å, bm =
6.011Å, cm = 15.825Åand β = 103.99◦ (figure 1(b)). Orientations of the crys-
tallographic axes of phases III and IV in the hexagonal setting perpendicular to
the x3-axis are shown in figure 2. Observations of the ferroelastic domain struc-
ture in phases III and IV have revealed a drastic change of the domain wall ori-
entations at the transition III-IV. The domain walls separating ferroelastic do-
mains with different values of the components of the spontaneous strain tensor
can be of two types: three domain walls of the W -type with crystallographi-
cally prominent and independent of temperature directions, and the W ′-type do-
main walls with orientations varying with the temperature change. In our case
both types of boundaries are observed in phase III, whereas in phase IV only
the W-type domain walls were noticed in the plane of observation (figure 3).
358
Ferroelastic domain wall orientations in the (NH 4 ) 3 H(SeO 4 ) 2 crystal
x3
x2
x1
ct
at
bt
(a)
x3
cm
am
bm
x1
IV
x2
IV (b)
Figure 1. The unit cell of the (NH4)3H(SeO4)2 crystal in (a) triclinic phase III;
(x1, x2, x3) is the Cartesian coordinate system and (b) monoclinic phase IV with
the Cartesian coordinate system (xIV
1 , xIV2 , x3).
bt
bm
ct
am
Figure 2. Projection of the lattice
vectors in the triclinic phase III
and the monoclinic phase IV on the
(001)-plane in the hexagonal setting
of phase II.
Theoretical analysis of the domain
structure is based on the theory of Sapriel
[14]. In our case, after transition from the
trigonal prototype phase R3̄m to the ferroe-
lastic phase C1̄, six different orientational
states (domains) can exist [15] and, con-
sequently, 12 permissible domain walls are
predicted [14].
The components of the spontaneous
strain tensor esij(Sk) can be determined as
[15]:
esij(Sk) = eij(Sk)−
1
N
N
∑
l=1
eij(Sl), (2.1)
where N denotes the number of orienta-
tional states, e(Sk) is the strain tensor for
orientational state Sk.
In the case of the 3̄m → 1̄ transition and
with the additional condition that the 3-folded axis is parallel to the Cartesian
coordinate axis x3 and 2-folded axis - to x2 in phase 3̄m, the components es(Sk)
have the following form:
es(S1) =
−a b c
b a d
c d 0
, es(S2) =
−a −b c
−b a −d
c −d 0
, (2.2)
here a = 1
2
(e22 − e11), b = e12, c = e13 and d = e23. The components for the four
remaining domains can be obtained from equation (2.2) by rotation around the
x3-axis through ±2π/3.
359
N.Pavlenko, M.Połomska, B.Hilczer
Figure 3. Thermal evolution of ferroelastic domains in (NH4)3H(SeO4)2. The
pictures present the sample surface in phases I, II-(A), III-(B), IV-(C) and again
III (D). The arrows show the direction of temperature changes.
In particular, in phase III the components a, b, c and d are expressed through
the unit cell parameters of the triclinic phase 1̄ in the following manner:
a =
bt
√
sin2 γ − z2f − ct/
√
3
2br
, b = −bt(ct cos γ sinβ − zf(3at + ct cos β))
6atbr sin β
,
c =
ct + 3at cos β
6at sin β
, d =
bt(3at cos γ + ct cosα)
6atbr sin β
, (2.3)
where zf =
cosα− cos β cos γ
sin β
, br = 6.064Åin phase I, and are evaluated to be:
a = −0.69 · 10−4, b = −0.69 · 10−2, c = 0.399 · 10−2 and d = 0.62 · 10−2.
360
Ferroelastic domain wall orientations in the (NH 4 ) 3 H(SeO 4 ) 2 crystal
The orientations of permissible domain walls between two adjacent domains Sk
and Sl can be determined from the strain compatibility condition [14]:
(es(Sk)ij − es(Sl)ij)xixj = 0. (2.4)
Substituting the spontaneous strain components (2.2) into (2.4), the following
equations for domain walls can be obtained:
x2 = 0 (W1) and
bx1 + dx3 = 0 (W ′
1),
(
√
3a+ b)x1 + (
√
3c+ d)x3 = 0 (W ′
2),
(
√
3a− b)x1 + (
√
3c− d)x3 = 0 (W ′
3).
(2.5)
The rest of the equations for domain walls (two of the W -type and three W ′-type
for each W -type wall) can be derived by rotations of the surfaces (2.5) around
the x3-axis through ±2π/3. Equations (2.5) yield the following angles between the
domain walls W ′
1, W
′
2, W
′
3 and the x3-axis at room temperature:
Θ1 = arctan
(
d
b
)
= −41.8◦,
Θ2 = arctan
(√
3c+ d√
3a+ b
)
= −61.73◦, (2.6)
Θ3 = arctan
(√
3c− d√
3a− b
)
= 5.98◦.
Setting formally α = γ = 90◦ we obtain the monoclinic structure from the
triclinic one, in this case e12 = e23 = 0. Then, from expressions (2.3) one reads:
b = d = 0; a =
bm − cm/
√
3
2br
; c =
cm + 3am cos β
6am sin β
.
Considering equations (2.5) for the determination of the domain walls with the
constraint α = γ = 90◦, we can see that the tilt of the W1-plane is unchanged,
the relation for W ′
1 becomes identity (i.e. W ′
1-wall disappears in this case) and
another two equations for W ′
2, W
′
3 transform into a single one: ax1 + cx3 = 0;
that is, we obtain a single domain wall of the W ′-type with the tilt angle Θ =
arctan(c/a) to the x3-axis, which is to be expected after the transition 3̄m → 2/m.
Using the structural data of the monoclinic phase IV we have: a = −0.138 · 10−2,
c = −0.11 · 10−1 and Θ = arctan(c/a) = 83.03◦. The value of the angle between
the cross-section of the W ′-wall with the bt = 0 plane (domain wall W1 in phase
III) and the x3-axis is Θ′ = arctan(2c/a) = 86.5◦. Thus, the W ′-wall is almost
parallel to the (001)-plane and this fact can be the possible explanation of the
phenomenon that W ′-type walls were not observed in phase IV (figure 3). The tilt
angle of W ′-walls in phase IV differs drastically from the values (2.6) of Θ2 and Θ3
even with small deviations of the structure from monoclinic (∆α = α−90◦ = 0.79◦,
∆γ = γ − 90◦ = −0.87◦), as well as from the results obtained by Kishimoto et al.
in [8] and Schranz et al. in [9].
361
N.Pavlenko, M.Połomska, B.Hilczer
To explain the influence of pseudomonoclinic symmetry on the orientation of
domain walls W ′
2 and W ′
3, let us expand expressions (2.6) for Θ2, Θ3 in the powers
of small deviations of b and d from zero:
Θ2,3 ≈
c
a
− 1
1 + (c/a)2
1√
3
(
∓d
a
± c
a
b
a
)
, (2.7)
for
∣
∣
∣
∣
∣
d
a
∣
∣
∣
∣
∣
,
∣
∣
∣
∣
∣
b
a
∣
∣
∣
∣
∣
≪ 1. (2.8)
Even at slight deviations of α and γ angles from 90◦, conditions (2.8) do not hold
for our structure, since
∣
∣
∣
∣
∣
d
a
∣
∣
∣
∣
∣
,
∣
∣
∣
∣
∣
b
a
∣
∣
∣
∣
∣
∼ 102. Thus, a sharp separation of W ′
2 and W ′
3
domain walls is observed after a phase transition to the triclinic phase III.
3. Conclusions
Despite the fact that the determined in [3] symmetry of the room temperature
phase of the (NH4)3H(SeO4)2 crystal deviates in a small degree from the accepted
in previous investigations monoclinic, the domain structure in this phase differs
drastically from the structure in the case of a monoclinic symmetry. This difference
manifests itself in the number of permissible domain walls (nine W ′-type walls in-
stead of three for the monoclinic phase), as well as in its orientations. In particular,
the slight deviations ∆α, ∆γ from 90◦ induce a significant separation of W ′
2- and
W ′
3-domain walls and the angles between the W ′-walls and the (001)-plane differ
strongly from the previously reported in [8,9] value 47.3◦.
In the case of the monoclinic phase IV, all domain walls of the W ′-type lie
almost parallelly to the (001)-plane. This result confirms disappearance of the
domain walls of the W ′-type in the plane of observation when crystal transforms
into phase IV.
References
1. Merinov B.V., Antipin M.Yu., Baranov A.I., Tregubchenko A.M., Shuvalov L.A.,
Struchko Yu.T. Atomic structure of the superionic phase of (NH4)3H(SeO4)2 crys-
tal. // Crystallografiya, 1991, vol. 36, p. 872–875 (in Russian).
2. Lukaszewicz K., Pietraszko A., Augustyniak M.A. Structure of(NH4)3H(SeO4)2 in
high-temperature phases I and II. // Acta Cryst. C, 1993, vol. 49, p. 430–432.
3. Pietraszko A., Lukaszewicz K., Augustyniak M.A. Structure of phase III of
(NH4)3H(SeO4)2. // Acta Cryst. C , 1992, vol. 48, p. 2069–2071.
4. Pietraszko A., Lukaszewicz K. Crystal structure of (NH4)3H(SeO4)2 in the low tem-
perature phase IV. // Bull. Polish Acad. Sci., 1993, vol. 41, p. 157–162.
5. Fukami T., Tobaru K., Kaneda K., Nakasone K., Furukawa K. Crystal structure of
(NH4)3H(SeO4)2 in phase IV // J. Phys. Soc. Japan, 1994, vol. 63, p .2829–2830.
362
Ferroelastic domain wall orientations in the (NH 4 ) 3 H(SeO 4 ) 2 crystal
6. Lukaszewicz K., Pietraszko A., Augustyniak M.A. Crystal structure of
(NH4)3H(SeO4)2 in the ferroelectric phase V and low temperature phase VI. // Fer-
roelectrics, 1995, vol. 172, p. 307.
7. Pawlowski A., Pawlaczyk Cz., Hilczer B. Electric conductivity in crystal group
Me3H(SeO4)2 (Me: NH4
+, Rb+, Cs+). // Solid State Ionics, 1990, vol. 44, p .17–19.
8. Kishimoto T., Osaka T., Komukae M., Makita Y. Ferroelastic phase transition in
(NH4)3H(SeO4)2. // J. Phys. Soc. Japan, 1987, vol. 56, p. 2070–2079.
9. Schranz W., Dolinar P., Fuith A., Warhanek H. Optical studies of the ferroelastic
phase transitions in Rb3H(SeO4)2, (NH4)3H(SO4)2 and (NH4)3H(SeO4)2. // Phase
Transitions, 1991, vol. 34, p. 189–204.
10. Polomska M., Augustyniak M. Effect of phase transition sequence on the ferroelastic
domain structure of (NH4)3H(SeO4)2 at room temperature. // Ferroelectrics, 1997,
vol. 190, p. 113–117.
11. Chen R.H., Chen T.M. Studies of domain structures and structural phase transition
of (NH4)3H(SeO4)2 crystal. //Phase Transitions, 1997, vol. 60, p. 39–57.
12. Stasyuk I.V., Pavlenko N., Polomska M. Ferroelastic domain structure of
(NH4)3H(SeO4)2 crystal. //Phase Transitions, 1997, vol. 62, p. 167–179.
13. Gesi K. Ferroelectric phase transition in (NH4)3H(SeO4)2 // J. Phys. Soc. Japan,
1977, vol. 43, p .1949–1953.
14. Sapriel J. Domain-wall orientations in ferroelastics. // Phys. Rev. B, 1975, vol. 12,
p. 5128–5140.
15. Aizu K. Determination of the state parameters and formulation of spontaneous strain
for ferroelastics. // J. Phys. Soc. Japan, 1970, vol. 28, p. 706–716.
Орієнтації фероеластичних доменних стінок у
кристалі (NH 4 ) 3 H(SeO 4 ) 2
Н.Павленко 1 , М.Поломська 2 , Б.Хільчер 2
1 Інститут фізики конденсованих систем НАН України,
290011 м. Львів, вул. Свєнціцького, 1
2 Інститут молекулярної фізики ПАН,
Польща, 60179, Познань, вул. Смолуховського, 17/19
Отримано 3 квітня 1998 р.
В роботі проведено експериментальне й теоретичне вивчення до-
менної структури кристалу (NH 4 ) 3 H(SeO 4 ) 2 у фероеластичних фа-
зах III і IV. Використовуючи найновіші структурні дані, досліджено орі-
єнтації доменних стінок типу W та W
′ . Показано, що незважаючи на
те, що при кімнатній температурі кристал має триклінну симетрію з
незначними відхиленнями від моноклінної, доменна структура силь-
но відрізняється від тієї, яка отримується для фази з моноклінною си-
метрією, що було прийнято раніше для цього температурного інтер-
валу. У моноклінній фазі IV доменні стінки типу W
′ майже паралельні
363
N.Pavlenko, M.Połomska, B.Hilczer
до площини (001), що пояснює факт їх зникнення при оптичних спо-
стереженнях у цій площині.
Ключові слова: доменна структура, фероеластичність
PACS: 77.80.Dj
364
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