Dynamics of the domain structure in non-uniform ferroelectric crystals
This work presents a study of the domain reversal characteristics related to the internal bias field in nonuniform telluric acid ammonium phosphate (TAAP) crystal. We have shown that there is a direct connection between the defective structure of the crystal and stretched exponential polarization re...
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Інститут фізики конденсованих систем НАН України
2007
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| Цитувати: | Dynamics of the domain structure in non-uniform ferroelectric crystals / K. Matyjasek, R. Rogowski // Condensed Matter Physics. — 2007. — Т. 10, № 1(49). — С. 95-99. — Бібліогр.: 11 назв. — англ. |
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irk-123456789-1180642017-05-29T03:04:50Z Dynamics of the domain structure in non-uniform ferroelectric crystals Matyjasek, K. Rogowski, R. This work presents a study of the domain reversal characteristics related to the internal bias field in nonuniform telluric acid ammonium phosphate (TAAP) crystal. We have shown that there is a direct connection between the defective structure of the crystal and stretched exponential polarization relaxation in ferroelectric crystals. The domain switching was studied by means of the nematic liquid crystal decoration technique. Дана робота представляє дослiдження властивостей оборотних процесiв у доменах, пов’язаних з внутрiшнiм полем змiщення у неоднорiдних кристалах телуровокислого сульфату амонiю. Нами показано, що iснує прямий зв’язок мiж дефектною структурою цього кристалу iз затягнутою експоненцiйною релаксацiєю поляризацiї у сегнетоелектричних кристалах. Перемикання доменiв вивчалось з використанням технологiї нанесення нематичних рiдких кристалiв. 2007 Article Dynamics of the domain structure in non-uniform ferroelectric crystals / K. Matyjasek, R. Rogowski // Condensed Matter Physics. — 2007. — Т. 10, № 1(49). — С. 95-99. — Бібліогр.: 11 назв. — англ. 1607-324X PACS: 77.80.Dj, 77.80.Fm, 77.84 DOI:10.5488/CMP.10.1.95 http://dspace.nbuv.gov.ua/handle/123456789/118064 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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English |
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This work presents a study of the domain reversal characteristics related to the internal bias field in nonuniform telluric acid ammonium phosphate (TAAP) crystal. We have shown that there is a direct connection between the defective structure of the crystal and stretched exponential polarization relaxation in ferroelectric crystals. The domain switching was studied by means of the nematic liquid crystal decoration technique. |
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Article |
| author |
Matyjasek, K. Rogowski, R. |
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Matyjasek, K. Rogowski, R. Dynamics of the domain structure in non-uniform ferroelectric crystals Condensed Matter Physics |
| author_facet |
Matyjasek, K. Rogowski, R. |
| author_sort |
Matyjasek, K. |
| title |
Dynamics of the domain structure in non-uniform ferroelectric crystals |
| title_short |
Dynamics of the domain structure in non-uniform ferroelectric crystals |
| title_full |
Dynamics of the domain structure in non-uniform ferroelectric crystals |
| title_fullStr |
Dynamics of the domain structure in non-uniform ferroelectric crystals |
| title_full_unstemmed |
Dynamics of the domain structure in non-uniform ferroelectric crystals |
| title_sort |
dynamics of the domain structure in non-uniform ferroelectric crystals |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2007 |
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http://dspace.nbuv.gov.ua/handle/123456789/118064 |
| citation_txt |
Dynamics of the domain structure in non-uniform ferroelectric crystals / K. Matyjasek, R. Rogowski // Condensed Matter Physics. — 2007. — Т. 10, № 1(49). — С. 95-99. — Бібліогр.: 11 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT matyjasekk dynamicsofthedomainstructureinnonuniformferroelectriccrystals AT rogowskir dynamicsofthedomainstructureinnonuniformferroelectriccrystals |
| first_indexed |
2025-07-08T13:18:17Z |
| last_indexed |
2025-07-08T13:18:17Z |
| _version_ |
1837084913943183360 |
| fulltext |
Condensed Matter Physics 2007, Vol. 10, No 1(49), pp. 95–99
Dynamics of the domain structure in non-uniform
ferroelectric crystals
K.Matyjasek, R.Rogowski
Institute of Physics, Szczecin University of Technology, Al. Piastow 48, 70–310 Szczecin, Poland
Received September 4, 2006
This work presents a study of the domain reversal characteristics related to the internal bias field in non-
uniform telluric acid ammonium phosphate (TAAP) crystal. We have shown that there is a direct connection
between the defective structure of the crystal and stretched exponential polarization relaxation in ferroelectric
crystals. The domain switching was studied by means of the nematic liquid crystal decoration technique.
Key words: ferroelectric domains, polarization reversal, internal bias field
PACS: 77.80.Dj, 77.80.Fm, 77.84
1. Introduction
Polarization switching in an external electric field has been intensively studied and is described
using classical nucleation and growth concepts of phase transformation (e.g. the Kolmogorov-
Avrami-Ishibashi model [1]). However, relatively less has been reported on the spontaneous reversal
of polarization, which occurs in the absence of an external electric field. The existing literature
is not consistent regarding their origin and explanation for empirical formulas describing various
types of polarization relaxation [2]. In general, retention of polarization in ferroelectrics is related
to depolarization field, resulting from incomplete compensation of the polarization charges and
internal bias field induced by defects.
In this report, the study of dynamics of the domain structure has been carried out in highly non-
uniform TAAP crystal sample. We focus on the investigation of polarization switching dynamics
in dc-fields as well as polarization decay after the removal of the electric field. These effects were
examined by optical imaging of the domain structure. Microscopic observations provide information
on the initial location of the polarization reversal process and its progress as a function of time.
2. Experimental details
The TAAP crystal having a chemical formula Te(OH)6 · 2NH4H2PO4 · (NH4)2HPO4 undergoes
a phase transition at ∼321 K changing its symmetry from the centrosymmetric class 2/m to the
polar class m [3]. The TAAP crystals were grown from aqueous solution at room temperature. The
composition of the solution was the same as described by Nicolau [4,5]. In order to observe the do-
main structure we used the nematic phase of p-methoxybenzylidene-p-n-butylaniline (MBBA) and
p-ethoxy-benzylidene-p-n-butylaniline (EBBA) mixture of liquid crystals (NLC). After supplying
a sample (coated with NLC-layers on its surfaces) with transparent electrodes, the electric field
could be applied and the observation of the domain structure was carried out using a polarizing
microscope. The method for studying the domain kinetics is based on the visualization with NLC
of the moving domain walls. The reversed regions, where reorientation of the domain structure
still occurs, look somewhat darker than the “white” surrounding domains, since in these regions
certain electrohydrodynamic instability, particularly dynamic scattering of NLC molecules, takes
place [6]. It should be emphasized that the thickness of the “visible” walls is not the real physical
thickness of the domain walls, which are usually very thin, of the order of a few lattice constants.
c© K.Matyjasek, R.Rogowski 95
K.Matyjasek, R.Rogowski
3. Results and discussion
Figure 1. Domain pattern in
as-grown TAAP sample at
room temperature, revealed by
etching with water. Polariza-
tion axis is approximately nor-
mal to the image plane (101).
Microscopic observations of the domain structure show that
TAAP crystals, grown at room temperature, are highly inho-
mogeneous; regions may exist that exhibit switchable polariza-
tion and there are parts with more fixed polarization. Figure 1
shows the etched pattern of the domain structure observed on
(101) natural face of the crystal, which is approximately nor-
mal to the polarization direction. Some part of the crystal has
plate-like domains elongated in the b-direction while the other
part is a single domain. The single domain state, observed in
the lower part of the image in figure 1 does not vanish when
heating over a transition temperature, but can still be detected
at room temperature. When polarization was switched to the
opposite direction it was found that this single domain region
was not uniform. This can be seen by observing non-uniform di-
stribution of domain nuclei that arise in external electric field.
For comparison, figure 2 presents the distribution of domain nuclei in various dc electric fields,
observed in a more homogeneous region of the crystal sample (with plate-like domains in as-grown
crystal). In weak dc fields, the plate-like domains elongated in the b-direction were observed on the
crystal surface normal to the polar axis. In higher electric fields circular domains are nucleated (see
figure 2(a)). When electric field increases, the new nuclei appear adjacent to the moving domain
walls. We found the wall to be often of zigzag type, as a result of preferential formation of new nuclei
along the b-direction (see figure 2(b), (c)). In sufficiently high electric fields, the intensive domain
nucleation occurs upon the whole homogeneous fragment of the crystal sample (see figure 2(d)).
Figure 2. Domain configuration at various dc
fields, observed in homogeneous region of TAAP
crystal sample; (a) 125 kV/m, (b) 135 kV/m, (c)
145 kV/m, (d) 160 kV/m.
The domain nuclei which are randomly di-
stributed in weak fields are aligned into nearly
parallel rows (parallel to the b-direction) in hi-
gher electric fields. This indicates the impor-
tance of crystallographic factors in the ordering
of defects (which are nucleation centers) in the
process of crystal growth. With the increase of
an electric field, the density of the domain nu-
clei in each row and the number of chains per
unit length increase, so that they become opti-
cally indistinguishable (as is shown in figure 3).
Figure 3 presents the distribution of domain
nuclei in alternate square pulses of electric field
in the region of the crystal sample in which sin-
gle domain state was observed in as-grown crys-
tal (lower part of the region in figure 1). The
amplitude and frequency were so chosen that
they could only permit a nucleation of domains.
It is shown that the formation of domains is
possible if the amplitude of electric field exceeds some threshold value at a given site of the crystal.
There are parts in which intensive domain nucleation arranged in rows is seen, and parts where the
nucleation process is suppressed. The inhomogeneous distribution of the domain nuclei is a result of
non-uniform internal field distribution within the crystal sample. This can be clearly seen during the
switching process in dc-electric fields. Figures 4(a)–(b) show the series of video frames illustrating
the domain pattern evolution observed in a small (about 1mm2) fragment of the crystal sample in
a region set in frame in figure 3(a). We observed a fast partial switching, by intensive nucleation of
domains arranged in rows, instantaneously after the field application in the upper part of the first
image in figure 4(a). Further switching continues to occur more slowly through the new domains
arising adjacent to the moving domain front, formed after coalescence of domains. The moving
96
Dynamics of the domain structure in non-uniform ferroelectric crystals
domain front goes through smoothly from one part of the crystal to another with a decreasing ve-
locity. Very approximate estimations give values from 6× 10−4 m/s at the initial stage to 2× 10−6
m/s at the end of the switching process. In higher dc fields, the mechanism of the switching process
does not change; only the region with the intensive domain nucleation becomes larger (figure 4(b)).
Figure 3. Distribution of domain nuclei aris-
ing in pulsed electric field at various pulse am-
plitudes: (a) 200 kV/m, (b) 300 kV/m, (c)
400 kV/m; f=100 Hz. The polarization axis is
approximately normal to the image plane (101).
Dark regions in the images represent the sites at
which the reorganization of the domain struc-
ture still occurs.
The experimental results are represented as
sets of switching curves, where for each curve,
the switching polarization is plotted as a func-
tion of time for the fixed electric field, as is
shown in figure 5. There is observed an essen-
tial difference between the domain kinetics ob-
served in inhomogeneous crystal samples and
homogeneous ones. In a homogeneous crystal
sample, the switching curves taken at differ-
ent electric fields typically saturate at the same
value, so that they relate to the complete po-
larization reversal [7]. In the examined inho-
mogeneous region of the crystal sample, the
saturation value of the switching polarization
increases with the electric field increase. This
inhomogeneous crystal sample consists of inde-
pendently switched regions in which polariza-
tion reversal process is limited mainly by nu-
cleation of reversed domains.
After switching the polarization vector under an external electric field, an unstable state of
polarization is created, which then relaxes to the initial single domain state after the removal
of the electric field, as shown in figure 6(a). One can see that the process of spontaneous de-
polarization occurs in reverse order to the switching process; first nucleation of backswitching
domains is observed in the lower part of the image in figure 6(a). It is interesting to note that
the effective field during the spontaneous backswitching process is comprised of the sum of depo-
larization field due to the unscreened portion of the polarization bound charges and an internal
bias field Eb. The fact that the spontaneous backswitching process has not been observed in
the crystal sample with a symmetric switching property for positive and negative polarization
state (without Eb) demonstrates that the polarization relaxation behavior should be dominated
Figure 4. Selected video frames in recording of
domain pattern evolution during the switching
process at two different dc fields: (a) 200 kV/m,
(b) 300 kV/m.
by directional internal field caused by struc-
tural disorder in the examined crystal sample.
The slowing down of the polarization relax-
ation process can be obtained when the exter-
nal field is applied to the opposite direction of
Eb, as shown in figure 6(b). It means that the
strong polarization relaxation could be closely
related to the large Eb, inside the crystal sam-
ple. We could experimentally determine the ap-
proximate local value of Eb from the applied
electric field under which the polarization re-
laxation is stopped at the given site of the crys-
tal. Figure 7 presents the time dependence of
the normalized retained polarization with re-
spect to the initial polarization P(t)/P0) taken
during the backswitching process. The value of
Eb is different in various regions of the crystal
sample. Very approximate estimations give the
values from 20 kV/m in the upper to 240 kV/m
in the lower region of the image in figure 6.
97
K.Matyjasek, R.Rogowski
Figure 5. Temporal dependence of the
switched area for various electric fields
(calculated for domain configurations, as
shown in Fig. 4).
The relaxation of polarization during the
switching process as well as during spontaneous
backswitching process is well described by a
Kohlrausch-Williams-Watts (KWW) stretched ex-
ponential function P (t) = P0 exp(−t/τ)n with 0 <
n < 1. KWW function has been widely used in the
dielectric relaxation studies [8]. The existing liter-
ature is not consistent regarding their origin and
explanations. Theories based on the defect distribu-
tion in disordered systems or on the distribution of
relaxation times have been developed [9].
On analyzing the switching process in a homoge-
neous crystal sample [7], the kinetics of polarization
switching in external electric field has been well de-
scribed by the Avrami function i.e., the expression
of the same form as KWW function, with exponen-
tial coefficient ranging from 1 to 2. In that case the
exponential coefficient could express the spatial dimensionality of the domain growth, which should
take the integer value of 2 for two-dimensional domain growth (circular domains as shown in fig-
ure 2(a)) and the value of 1 for one-dimensional domain growth (as shown in figure 4). The data
analysis has revealed no integer dimensionality of the domain growth, contrary to expectations
from the Avrami equation, due to the dependence of the rate of growth of particular domain on
the state of the crystal (i e. impurities, defects, etc). The Avrami model is a simplification of the
real physical conditions assuming a constant domain growth velocity.
Figure 6. Selected video frames in recoding
of domain pattern evolution during the back-
switching process at: (a) E=0, (b) E=30 kV/m
applied in the direction opposite to Eb.
Figure 7. Slowing down of the domain relax-
ation at the external electric fields applied in
the direction opposite to Eb.
We have shown that the main peculiarities of the non-uniform ferroelectrics are the presence of
an in-built internal field and a broad distribution function for the random field. Hence, we observe
a broad distribution of characteristic domain growth times. Generally, substitutional disorder,
vacancies, and displacement of ions from their equilibrium positions create random fields [10,
11]. In disordered ferroelectric systems, the defects locally modify the depths of the double-well
potential giving rise to spatially varying energy barriers for domain nucleation. Now it is hard
to explain what kind of crystal imperfections or non-uniformities are responsible for stabilization
effects and the broad spectrum of potential barriers for the domain nucleation in TAAP crystals.
The examined crystal sample was obtained from a non-stoichiometric solution. During the crystal
98
Dynamics of the domain structure in non-uniform ferroelectric crystals
growth the defects are built in a preferential alignment. The above results suggest that the defects
can induce a space charge gradient, which in turn generates an internal bias field, causing the
observed preferential orientation of polarization.
4. Conclusions
Imaging measurements confirm the site-specific nature of nucleation of domains in TAAP crys-
tals. The defects present in the crystal sample seem to play the major role in creating an internal
bias field causing the observed preferential orientation of polarization, making the poling procedure
impracticable. Stretched exponential polarization relaxation is observed in highly inhomogeneous
crystals, in which domain wall propagates at a decreasing rate at a spatially inhomogeneous, grad-
ually decreasing internal field. The use of NLC method should offer a relatively simple and rapid
means of quality control in determining the degree of domain alignment in ferroelectric crystals.
Acknowledgements
The authors would like to thank Prof. Z. Czapla from University of Wroclaw for providing
TAAP samples for this study.
References
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3. Guillot Gauthier S, Peuzin J. C., Olivier M, Rolland G. 1984 Ferroelectrics 52, 293.
4. Nicolau Y.F. Ferroelectrics, 1984, 52, 281.
5. Przeslawski J., Kosturek B., Czapla Z., Tomaszewski P.E., Wondre F. Ferroelectrics, 1994, 152, 255.
6. Tikhomirova N.A., Dontsova L.I., Pikin S.A., Shuvalov L.A. JETP Lett., 1979, 29, 34.
7. Matyjasek K., Rogowski R.Z. J. Phys. Condens. Matter, 2006, 18, 7687.
8. Kim K., Epstein A.J. Appl. Phys. Lett., 1995, 67, 2786.
9. Scher H., Shlesinger M.F., Bendler J.T. Phys. Today, 1991, 44, 26.
10. Glinchuk M.D., Stephanovich V.A. J. Appl. Phys., 1999, 85, 1722.
11. Gopalan V., Mitchell T., Furukava Y., Kitamura K. Appl. Phys. Lett., 1998, 72, 1981.
Динамiка доменної структури у неоднорiдних
сегнетоелектричних кристалах
К.Матиясек, Р.Роговскi
Iнститут фiзики, Щецiнський технологiчний унiверситет, ал. П’ястув, 48, 70–310 Щецiн, Польща
Отримано 4 вересня 2006 р.
Дана робота представляє дослiдження властивостей оборотних процесiв у доменах, пов’язаних з
внутрiшнiм полем змiщення у неоднорiдних кристалах телуровокислого сульфату амонiю. Нами по-
казано, що iснує прямий зв’язок мiж дефектною структурою цього кристалу iз затягнутою експонен-
цiйною релаксацiєю поляризацiї у сегнетоелектричних кристалах. Перемикання доменiв вивчалось
з використанням технологiї нанесення нематичних рiдких кристалiв.
Ключовi слова: сегнетоелектричнi домени, переключення поляризацiї, внутрiшнє поле змiщення
PACS: 77.80.Dj, 77.80.Fm, 77.84
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