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Direct Observation of Ferrielectricity at Ferroelastic Domain
Boundaries in CaTiO3 by Electron Microscopy
Sandra Van Aert,* Stuart Turner, Rémi Delville, Dominique Schryvers,
Gustaaf Van Tendeloo, and Ekhard K. H. Salje
Ever since it has been realized that interfaces and domain
boundaries are not necessarily a simple structural juxtaposition of adjacent bulk materials, but contain novel structural elements which do not exist in the bulk, the chase for such “exotic”
interfaces has begun. Typical examples are superconducting
domain boundaries in insulating materials,[1,2] twin boundaries with high defect mobilities,[3–6] two-dimensional electron
gas at interfaces,[7–10] unusual vortices near twin boundaries,[11]
or multiferroicity and chirality at domain boundaries.[12–14] If
such properties are exclusively related to interfaces or domain
boundaries, then they qualify as objects of the emerging field of
“domain boundary engineering”.[15,16] This name became popular because it embodies the hope that “active” domain boundaries can, one day, be reproduced in an engineering fashion
rather than being simply observed in suitable samples. A typical
example is the IBM racetrack memory based on the controlled
movement of magnetic domain walls. Their movement is registered electromagnetically and their position is used as memory
information. The desired breakthrough is now to use ferroelectric domain walls where the information can be written and
read by simple application of electric fields. The memory is the
location and the ferroelectric spontaneous polarisation of the
domain wall with expected memory densities well above any
current application. The wider industrial consequence of such
local structures as memory devices, conductors, holographic
templates, or as membranes for batteries have motivated significant research efforts during recent years.
One of the first materials, which was identified theoretically for domain boundary applications, was CaTiO3. Two lines
of research come together in this material: first, it was shown
that twin and antiphase boundaries represent sinks for oxygen
vacancies. The stabilization energy for oxygen vacancies was
predicted to be ca. 0.7 eV with a repulsive interaction between
vacancies.[5,17–19] It is expected, therefore, that oxygen vacancies
are rather uniformly distributed within twin walls and depleted
in the bulk.[20] The second prediction is based on the inherent
Prof. S. Van Aert, Dr. S. Turner, Dr. R. Delville, Prof. D. Schryvers,
G. Van Tendeloo
Electron Microscopy for Materials Research (EMAT)
University of Antwerp
Groenenborgerlaan 171, 2020 Antwerp, Belgium
E-mail: [email protected]
Prof. E. K. H. Salje
Department of Earth Sciences
Cambridge University
Downing Street, Cambridge CB2 3 EQ, UK
DOI: 10.1002/adma.201103717
Adv. Mater. 2012, 24, 523–527
instability of regular TiO6 octahedra. Even a cubic oxygen cage
of sufficient size will lead to off-centering of the Ti position so
that it is probable that distorted octahedra will contain Ti located
slightly off the geometrical midpoint of the octahedra.[17] Such
geometrical configurations contain electric dipole moments
which, depending on the nature of the dipole-dipole interaction, will lead to ferroelectric or ferrielectric local centers.
Numerical calculations[17] have shown that domain boundaries in CaTiO3 are mainly ferrielectric with maximum dipole
moments at the wall; a small ferroelectric dipole moment was
found perpendicular to the wall with alternating (antiferroelectric) dipoles between neighbouring walls. The same tendency
for polar layers in CaTiO3, e.g. near surfaces, was also predicted
for CaTiO3/BaTiO3 interfaces.[21]
The great challenge for domain boundary studies is to
observe the described singularities experimentally. Transport studies have made great progress in the understanding
of domain wall conductivity[1–10] and atomic force microscopy
(AFM) has shown that conductivity is, indeed, restricted to the
domain walls.[2,4] However, in contrast to transmission electron
microscopy (TEM), AFM only reveals information about near
surface regions.[4] In this paper, we will show that sufficient
advances have been made using aberration-corrected TEM
imaging[22] in combination with statistical parameter estimation
theory[23–25] to not only visualize atomic displacements directly
inside domain boundaries but also to measure their displacements, atomic layer by atomic layer, with picometer precision.
This opens the door for massive advances in the investigation,
design, and production of active domain boundaries and local
structures that are based on small, local atomic displacements
inside extended crystal lattices. We will argue that the predicted
structural singularities in CaTiO3 exist and that these features
are confined to the domain boundaries. We will show that the
dominant off-centering of Ti can be observed while all other
structural deformations, such as, shifts of the Ca atomic positions, remain too small to be seen.
Twin boundaries in CaTiO3 have been imaged using aberration-corrected TEM in combination with exit wave reconstruction.[26] The insertion of multipole aberration-correcting
elements in the electron optical column has significantly
improved the direct interpretability of TEM images. A FEI
Titan3 50–80 operated at 300 kV has been used in this study
providing direct structural imaging at a sub-Å resolution level.
Further improvement of the resolution up to the information
limit of the microscope can be achieved by reconstructing the
so-called exit wave, which is in fact the complex electron wave
when leaving the specimen. The idea is to invert the image
formation process so that all residual lens aberrations can be
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Figure 1. a) Single twin wall, indicated as standing dark grey plane, with
the chosen (x, y, z) reference system for the definitions of the measured
displacements. The angle of 178.8° is the result of the twinning operation
from the high temperature cubic to the low temperature orthorhombic
phase. b) Atomic configuration on both sides of the (110) twin plane as
seen by the electron beam in Figure 2 and Figure 3 (Ca atoms are marked
by large filled circles, Ti atoms by medium-sized shaded circles, and O
atoms by small circles).
eliminated. This requires post acquisition processing of multiple
images recorded under varying imaging conditions. Here,
we used the through-focal series reconstruction method in
which the exit wave is reconstructed from a set of images taken
at different defocus values.[26] The present observations relate to
a (110) type twin boundary formed in the orthorhombic Pnma
CaTiO3 phase after cooling from the cubic high temperature
phase[17] and imaged along its [001] zone-axis in order to maximize the visibility of any expected atomic displacements. The
imaging conditions are schematized in Figure 1, also noting
the respective definitions for the further discussion. The experimental focal series comprised 20 images separated by a focal
increment of –2.4 nm with the series centred around the zero
defocus condition (starting defocus +27 nm) with a spherical
aberration coefficient of +50 μm (see the Experimental Section
for a full list of experimental parameters). The actual reconstruction of the exit wave is carried out using the TrueImage
software. After reconstruction the residual aberrations are corrected using the standard techniques in TrueImage. The amplitude and phase of the reconstructed exit wave are shown in
Figure 2a and b, respectively, with a resolution equal to 0.8 Å.
An example of a low-magnification image of the relevant area
is given in the Supporting Information (Figure S1) including
a fast Fourier transform (FFT) revealing the spot splitting
confirming the twin nature of the interface.
Although the combination of exit wave reconstruction with
aberration-corrected TEM significantly improves the visual
interpretability, quantitative numbers for the atomic column
positions are still lacking. Therefore, techniques such as
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Figure 2. a) Amplitude of the reconstructed exit wave. The CaTiO3 crystal
is imaged along the [001] zone axis orientation, the (110) twin boundary
is indicated by the horizontal white line. The Ca and Ti column positions are marked by red and green dots, respectively. The angle of 181.2°
reveals the twin relation over the interface (and is the complement of the
178.8° angle indicated in Figure 1a). b) Phase of the reconstructed exit
wave, the region used for the statistical parameter estimation is indicated
by the white rectangle. c) 4 * 4 unit cell magnified from the amplitude
image. d) 4 * 4 unit cell magnified from the phase image. e) 4 * 4 unit
cell structure model (same colour legend as in a., tilted oxygen octahedra
depicted in white shades).
statistical parameter estimation theory need to be included in
order to properly interpret the experimental data. This allows
position measurements of all atomic columns with a precision
of a few picometers without being restricted by the information limit of the microscope.[23,24,27–29] For a further quantitative
analysis we will use the phase of the reconstructed exit wave
since it is directly proportional to the projected electrostatic
potential of the structure. First, the atomic column positions
are estimated using statistical parameter estimation theory.[24]
Therefore, a local region of the reconstructed phase including
the twin wall has been analysed. This region is indicated by
the rectangular box in Figure 2b. The estimated atomic positions are shown as an overlay in Figure 3a. Next, the projected
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Figure 3. a) Reproduction of the boxed region in Figure 2b. The estimated Ca and Ti atomic column positions are indicated in red and green, respectively. The blue horizontal line shows the position of the twin wall. b) Mean interatomic Ca–Ca and Ti–Ti column distances perpendicular to the twin
wall, averaged in the direction parallel with the twin wall, together with their 90% confidence intervals. The vertical red line corresponds to the overall
mean Ca–Ca interatomic distance. Note the deviations from this line for particular Ti–Ti atomic column distances close to the twin wall (arrows).
c) Mean interatomic Ca–Ca and Ti–Ti column distances parallel with the twin wall, averaged in the direction parallel with the twin wall, together with
their 90% confidence intervals. The vertical red line corresponds to the overall mean Ca–Ca interatomic distance. No deviations from this line are
observed for the Ca–Ca or the Ti–Ti atomic column distances. d) Mean displacements of the Ti atomic columns from the center of the four neighbouring
Ca atomic columns and indicated by green arrows. e,f) Displacements of Ti atomic columns in the x- and y-directions averaged along and in mirror
operation with respect to the twin wall together with their 90% confidence intervals.
interatomic column distances between neighbouring Ca–Ca
and Ti–Ti columns are determined. In Figure 3b, the distances
perpendicular to the twin wall are presented in terms of their
mean values, averaged in the direction parallel with the twin
wall, together with their 90% confidence intervals. The corresponding standard deviations range between 1 pm and 2 pm for
the Ca–Ca distances and between 1 pm and 3 pm for the Ti–Ti
distances. By comparing the 90% confidence intervals with the
overall mean Ca–Ca interatomic distance, shown by the vertical
red line, deviations from a constant lattice parameter are clearly
observed for the Ti–Ti distances in the vicinity of the twin wall
whereas no conclusions can be drawn for the Ca–Ca distances.
This indicates a shift of the Ti atomic positions close to the
twin wall. A similar analysis for the Ti–Ti and Ca–Ca distances
parallel with the twin wall is shown in Figure 3c, where no
Adv. Mater. 2012, 24, 523–527
significant deviations from a constant for both types of atomic
columns are observed.
The previous analyses clearly indicate shifts in the Ti atomic
positions whereas any shifts in the Ca atomic positions are too
small to be identified. Therefore, in the following, we will focus
on the off-centering of the Ti atomic positions with respect
to the center of the neighboring four Ca atomic positions. As
these displacements are largely random and small as compared
to the experimental measurement precision, we will extract the
systematic fluctuations related to the twin wall using the following filtering. First, we average all displacements in planes
parallel to the twin wall. Next, we average the results in the
planes above with the corresponding planes below the twin
wall. This second operation identifies the overall symmetry of
the sample with the twin wall representing a mirror plane. The
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resulting displacements along and perpendicular to the twin
wall are shown in Figure 3e and f together with their 90% confidence intervals. In the x-direction (perpendicular to the wall),
we find systematic deviations for Ti of 3.1 pm in the second
closest layers pointing toward the twin wall. A larger displacement is measured in the y-direction (parallel to the wall) in the
layers adjacent to the twin wall. The averaged displacement in
these layers is 6.1 pm. In all layers further away from the twin
wall, no systematic deviations in x- or y-direction are observed.
The significant shifts are schematically shown in Figure 3d.
These results can now be compared with the predictions for
the displacements in the literature. Goncalves-Ferreira et al.[17]
found large displacements of Ti with much smaller values for
Ca. They also showed that the main Ti displacements occur
inside the twin wall, by which displacements parallel to the twin
wall are implied, with only a small component perpendicular
to the wall (their Figure 2). The thickness of the domain wall
is ca. two octahedra, which is the same length scale as in the
present experiments. The displacement pattern can be seen as
a combination of ferroelectric and antiferroelectric/ferrielectric
components. The ferroelectric component is the smaller one
and has effect both parallel as well as perpendicular to the wall.
This is the only component which we can observe in our experiment because the anticipated larger antiferroelectric movement
of Ti atoms displaces pairs of Ti in an antiparallel fashion at
the wall. Averaging over the wall along the viewing direction
thus yields no resulting displacement which would be visible
in the electron microscope. Nevertheless, simulations[17] show
a very strong coupling between the ferroelectric and antiferroelectric movement so that our observations imply that antiferroelectricity concurs with ferroelectricity in the domain walls.
We may now compare the observed and predicted displacement
amplitudes: the theoretical predictions are based on empirical
potentials and vary somewhat with the model parameters. The
largest amplitude of some 2 pm was found along the c-direction
with an antiferroelectric displacement pattern. The ferroelectric
component along the y-axis is anticipated from the simulations
to be slightly below 1 pm amplitude. In the calculations this displacement is not maximum in the centre of the wall but shows
two peaks on either side of the centre; this however might be
an artifact of the model which would lead in Landau coupling
to displacements of some 1.5 pm. All amplitudes depend on
the actual model parameters with variations of 30% within the
same model but different energy minimizing conditions. The
only visible displacement in the y-direction in the present
experiment is 6 pm, i.e., 4 times bigger than the largest value
anticipated by model calculations. Nevertheless, calculations in
their present version can only give rough orders of magnitude
for the displacements but we expect that they predict correctly
that the displacements are finite in the twin wall and lead to ferrielectricity in CaTiO3.
Finally, let us comment on the magnitude of the spontaneous polarization of the wall. In the model calculations it was
found that, depending on the chosen model, the wall polarization is between 0.004 and 0.02 Clb m−2. Using the experimental
value for the displacement of 6 pm we expect the polarization
to be as big as 0.04–0.2 Clb m−2. This value is comparable with
the bulk spontaneous polarization of BaTiO3 (0.24 Clb m−2) and
confirms the tendency of interfacial structures to enhance the
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Table 1. List of experimental parameters.
Parameter
Value
Starting defocus
27 nm
Number of focal images
20
Focal increment
–2.4 nm
Spherical aberration constant
+50 μm
Focal spread
2.9 nm
Convergence angle
0.15 mrad
Pixel size
0.0248 nm
spontaneous polarization.[30] Important progress is presented
in this paper: we do not enhance ferroelectricity, we generate
it! This means that ferroelectricity is indeed confined to twin
boundaries in a paraelectric matrix. In addition, we can now
observe such localized effects experimentally. Moreover, the
density of these defects can be controlled by slow cooling
through the cubic-to-orthorhombic transformation temperature
while their position can be changed by external stress applied
using a micromanipulator. Devices can then be imagined
where each domain wall acts as a memory element, which can
be switched electrically. The pixel density is then as high as the
domain wall density and can surpass all known ferroelectric
devices known so far. Recent developments in electron micro­
scopy have advanced our resolution to the point that we can now
measure small atomic displacements inside domain boundaries
which opens the door for using such domain boundaries as
active elements in such device applications.
Experimental Section
The CaTiO3 single crystals were grown by the floating-zone technique
with powders of CaCO3 and TiO2 (99.9% purity) as starting materials.[31]
All electron microscopy, including through focal series reconstruction
of the complex exit wave of the (110) twin boundary region, was
performed on a FEI Titan3 50–80 microscope operated at 300 kV
acceleration voltage. The parameters used for the through-focal series
reconstruction are summarized in Table 1.
Reconstruction of the complex exit wave was performed using the FEI
True Image software package.[32]
Supporting Information
Supporting Information is available from the Wiley Online Library or
from the author.
Acknowledgements
The authors acknowledge financial support from the Fund for Scientific
Research-Flanders (Reference G.0064.10N and G.0393.11N) and the
Flemish Hercules 3 programme for large infrastructure. Anna Carlsson and
Emrah Yücelen (FEI) are gratefully acknowledged for their help with the
microscopy, through-focal reconstruction and fruitful discussions. G.V.T.
acknowledges funding from the European Research Council under the
7th Framework Program (FP7), ERC grant N 246791–COUNTATOMS.
© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Received: October 6, 2011
Revised: November 16, 2011
Published online: December 20, 2011
Adv. Mater. 2012, 24, 523–527
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Adv. Mater. 2012, 24, 523–527
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