Supplementary Information
Atomic structure of titania nanosheet with vacancies
Megumi Ohwada1,2,*, Koji Kimoto1,*, Teruyasu Mizoguchi3, Yasuo Ebina4& Takayoshi Sasaki4
1
Surface Physics and Structure Unit and 4International Center for Materials Nanoarchitectonics,
National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan
2
Department of Applied Chemistry, Kyushu University, Tsukuba, Ibaraki 305-0044, Japan
3
Institute of Industrial Science, The University of Tokyo, Meguro, Tokyo 153-8505, Japan
1. Preparation of TEM specimen; UV light illumination for self-cleaning
2. TEM observation
2.1. Details of Ti vacancy observation
2.2. Details of TEM imaging parameters
2.3. Beam damage during the TEM observation
3. First-principles calculation of Ti vacancy structure models
4. Charge redistribution and its effect in high-resolution TEM image
References
*Correspondence and requests for materials should be addressed to M.O. or K.K. (emails:
ohwada.megumi@nims.go.jp or kimoto.koji@nims.go.jp).
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1. Preparation of TEM specimen; UV light illumination for self-cleaning
Ti0.87O2 nanosheets are synthesized as negatively charged colloidal sheets surrounded by
tetrabutylammonium (TBA) ions ((C4H9)4N+), which make it difficult to observe the atomic structures
of the nanosheets using transmission electron microscopy (TEM). TEM specimens, which are titania
nanosheets on a holey carbon film, are illuminated by ultraviolet (UV) light in air to decompose the
TBA ions photocatalytically. Figure S1a,b respectively shows a diffraction pattern and a TEM image of
a titania nanosheet without UV light illumination. These data were acquired using a conventional 300
kV transmission electron microscope (Hitachi, HF-3000). The halo in the diffraction pattern and the
amorphous contrast of the TEM image indicate that a substantial number of TBA ions remained on the
nanosheets. Figure S1c,d respectively shows a TEM image and a diffraction pattern of a titania
nanosheet after UV light illumination for 2 h. The amorphous structure on the nanosheet in (d) is almost
nonexistent and the intensity of the halo in the diffraction pattern in (c) is weaker than that in (a). The
TBA ions on the titania nanosheets are considered to be decomposed by the UV light illumination. The
chemical compounds remaining after the decomposition of TBA ions are considered to be H3O+ and/or
NH4+, which compensate the charge balance of titania nanosheets1. Oxygen atoms in the crystal lattice
of the titania nanosheet are not considered to be desorbed through UV light illumination.
2
Figure S1. Effect of UV light illumination on a single titania nanosheet with tetrabutylammonium
(TBA) ions. (a) and (b) show a diffraction pattern and a TEM image from a titania nanosheet without
UV light illumination, respectively. (c) and (d) were obtained from a titania nanosheet after UV light
illumination for 2 h.
2. TEM observation
2.1. Details of Ti vacancy observation
The direct observation of atomic structures using TEM is challenging, particularly for materials
sensitive to electron beam, because the required dose rate is proportional to the square of the
magnification. Here we describe details of our TEM observation.
We used an advanced electron microscope (FEI, Titan-Cubed) equipped with a spherical aberration
corrector and a monochromator. The acceleration voltage of the microscope was set to 80 kV to
decrease knock-on damage. To improve the resolution and contrast of the TEM images, the spherical
aberration was corrected to less than 0.001 mm and the energy spread of the microscope was reduced to
0.1 eV in full width at half maximum. To observe a single titania nanosheet without electron beam
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damage, we applied a low dose rate of 2.5×104 electrons/nm2/s, which is substantially low compared
with those used in previously reported high-resolution TEM observations, for example, 3×106
electrons/nm2/s for BN nanosheets2. We also applied a beam blanking system to reduce the total dose.
The defocus of the objective lens was set at an underfocus of about 4 nm. TEM images were recorded
using a charge-coupled device (CCD) camera of 1024×1024 pixels (Gatan Inc., UltraScan) with an
exposure time of 2 s. Since the microscope was installed on an active vibration-isolation system
(Tokkyokiki Corporation) in a room with a panel-cooling air conditioning system (Nihon Spindle
Manufacturing Co., Ltd.), a high specimen-stage stability of less than 0.2 nm/min was routinely realized.
We acquired ten TEM images at the same focus, and the specimen drift between the ten images was
corrected after their acquisition using cross correlation. Then we obtained an image with a high signalto-noise (SN) ratio by summation of the ten images (Fig. S2). An acquired raw image is shown in Fig.
S3, which indicates that the SN ratio is rather low without summation. Figure S4 shows Ti vacancies in
the same area as Fig. 1a in the main text. Although we summed 28 small images of Ti vacancies to
improve the SN ratio for the structural analysis (Fig. 2a), we can confirm the presence of about 60 Ti
vacancies as indicated by open rectangles. To improve the SN ratio, we also averaged TEM images on
the basis of the projected symmetry of the crystal structure (mm, i.e., two perpendicular mirror
symmetries). Since the TEM specimen was carefully prepared, the surface was clean and the structural
change reported in our previous study3 cannot be seen in Fig. S2. However, very weak extra spots of the
titania nanosheets can be seen, as marked by arrows in the Fourier transform in the inset of Fig. S2. It is
possible that the missing oxygen atoms around Ti vacancies (discussed in the main text) are responsible
for these spots, although it is difficult to confirm the disordered atomic loss from a Fourier transform.
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Figure S2. Relatively low magnification TEM image of a titania nanosheet and its Fourier
transform (inset). The TEM image is the summation of ten images after specimen drift correction. The
square in the TEM image indicates the area shown in Figure 1a in the main text. The spots marked by
arrows in the Fourier transform are kinematically forbidden.
Figure S3. Acquired raw image before summation. The area is the same as the image in Fig. S2. Note
the low SN ratio of the image.
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Figure S4. High-resolution TEM image showing Ti vacancies. The area is the same as the image in
Fig. 1a and the square area in Fig. S2. Rectangles indicate Ti vacancies. Scale bar is 1 nm.
2.2. Details of TEM imaging parameters
To observe atomic arrangements using high-resolution TEM, it is indispensable to optimize
microscope parameters. Here we describe the TEM imaging parameters and contrast transfer function
(CTF).
The major parameters are as follows; the third-order spherical aberration coefficient C3 = 0 mm,
the chromatic aberration coefficient Cc = 1.5 mm, and energy spread ΔE = 0.1 eV at an acceleration
voltage E = 80 kV. We draw a CTF under this condition with a defocus z = 4 nm of underfocus (Fig.
S5a). In comparison with non-monochromated condition (CTF and Kc in blue), the present condition
with a monochromator (those in pink) provides a higher spatial frequency of the information limit, and
it improves the contrast of TEM images, as described in a specialized journal4. Figure S5b shows CTFs
with different defocus values under the same condition of Fig. S5a with ΔE = 0.1 eV. We chose 4 nm of
underfocus to enhance the contrast made of the lattice spacings of the tinania nanosheet (e.g., d200=1.9
Å, d002=1.5 Å).
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Figure S5. Contrast transfer functions (CTFs) of the high-resolution TEM imaging. (a) CTF with
different energy spreads. The CTF with a monochromator (ΔE = 0.1 eV) is indicated in pink, and that
without a monochromator is indicated in blue (ΔE = 0.9 eV). Both the defocus value is set to 4 nm of
underfocus. Kc (broken lines) are chromatic envelope functions. (b) CTFs with different values of
defocus.
2.3. Beam damage during TEM observation
Beam damage such as knock-on damage is critical when observing the intrinsic crystal structure of
nanosheets. The threshold energy of the incident beam for the atomic displacement of a titanium atom
has been reported to be approximately 400 keV5; therefore, the present lower-voltage (80 kV) TEM is
considered to be usable for observing atomic vacancies. Here we experimentally investigate the beam
damage in the nanosheets during TEM observations at acceleration voltages of 80 and 300 kV.
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We first observed the dose dependence at an acceleration voltage of 80 kV. Since we acquired
many TEM images under a low-dose condition, we can investigate the effect of beam irradiation with
atomic resolution. Figure S6 shows TEM images of the same area at total doses of about (a) 2.5×105
electrons/nm2 and (b) 5×105 electrons/nm2, in which the former is a TEM image obtained at the
beginning of the experiment. Rectangles indicate the same Ti vacancy sites in the two images, and the
distribution of the Ti vacancies was found to be almost identical. The titanium atom marked by the
arrow in image (a) disappeared during the TEM observation; however, the estimated ratio of Ti atoms
displaced during the TEM measurement was approximately 1% of the Ti atoms in the crystal lattice.
Since the present analysis was performed under this total dose condition, almost all the Ti vacancies
observed in this study originally existed in the as-prepared titania nanosheets.
Figure S6. TEM image sequences showing effect of electron irradiation on Ti vacancies. The
images are obtained at total doses of about (a) 2.5×105 electrons/nm2 and (b) 5×105 electrons/nm2.
Rectangles indicate common Ti vacancies. The arrows in the two images show the loss of a titanium
atom.
We also investigated the beam damage at 300 kV. Figure S7 shows typical irradiation damage of a
titania nanosheet observed using a conventional microscope (a 300 kV uncorrected microscope with a
cold field emission gun, Hitachi HF-3000) at a dose rate of 2.6×105 electrons/nm2/s, which is low in
comparison with the conventional dose rate. Small holes were produced by electron irradiation at the
beginning of high-resolution observation, and the sheet was torn within a couple of minutes. Thus,
lower-voltage TEM observation is indispensable to investigate the atomic structure of titania nanosheets.
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Figure S7. High-resolution observation of a titania nanosheet using a 300 kV conventional
electron microscope with a cold field emission gun. The nanometer-sized holes marked by arrows
were formed after 2 min observation.
3. First-principles calculation of Ti vacancy structure models
We examined three structure models with different arrangements of oxygen atoms around Ti
vacancies. The optimization of the structure around each Ti vacancy was performed by first-principles
plane-wave basis pseudopotential calculations within the generalized gradient approximation (GGA)
using the CASTEP code6. Ultrasoft pseudopotentials were used and the plane-wave cutoff energy was
taken to be 340 eV. Before the optimization, the theoretical lattice constants of the titania nanosheet
were obtained. The calculation was performed using a unit cell of the titania nanosheet (a = 3.83 Å, c =
3.00 Å), in which each nanosheet is separated from adjacent nanosheets by 17 Å. The calculated lattice
constants are a = 3.762 Å and c = 3.0258 Å, which are in good agreement with the experimental lattice
constants, although the calculation slightly overestimates the lattice constants due to the GGA error. To
introduce vacancies, the calculated unit cell was expanded by 5×1×5 and 150-atom supercells were used.
In the vacancy calculation, the Monkhorst-Pack k point was set to 2×1×2. All atoms were relaxed until
their residual force became smaller than 0.1 eV/Å. During the atomic relaxation, each volume was fixed.
In all cases, neutral vacancies were considered. Figure S8 shows the three structures examined: (a) Ti
vacancy model, (b) Ti+Oc1+Oc2 vacancy model, and (c) Ti+Oa1+Oa2 vacancy model. Each atomic
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arrangement was optimized to minimize the residual forces. Here, we compare the optimized structures
with the non-optimized ones. The non-optimized structures of the three models (Fig. S8) generated
similar TEM simulation images, although the contrasts of oxygen sites around the Ti vacancies
depended on the models. When the structures are optimized, the local structures around the Ti vacancies
are differently relaxed, resulting in changes in the simulation images. From a total energy calculation,
the Ti+Oc1+Oc2 vacancy model was found to be 3.45 eV more stable than the Ti+Oa1+Oa2 vacancy
model, indicating that the Ti+Oc1+Oc2 vacancy model is feasible and that the oxygen atoms c1 and c2
tend to be removed during reduction, which is consistent with the quantitative analyses of TEM image
intensities (Fig. 3d,e in the main text).
Figure S8. The three Ti vacancy structure models before and after optimization and their
simulation TEM images. The structures and simulation images on the left are not optimized, whereas
those on the right are optimized. (a) Ti vacancy model. (b) Ti+Oc1+Oc2 vacancy model. (c) Ti+Oa1+Oa2
vacancy model. The numbers in the structure drawings indicate those of existing oxygen atoms. The
arrows in each optimized structure in a-c indicate the main directions of atomic distortion resulting from
structure optimization (large and small arrows indicate titanium and oxygen atoms, respectively).
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4. Charge redistribution and its effect in high-resolution TEM image
A few advanced studies on high-resolution TEM include the effect of charge distribution on image
contrast7,8. Here we briefly discuss its effect in our monochromated aberration-corrected TEM
observation.
The net charge of each atom can be evaluated by the first-principles calculations as shown in Fig.
S9. The net charge of titanium atoms in a titania nanosheet was found to be 1.32, and that of oxygen
atoms -0.71 or -0.60. Around a Ti+Oc1+Oc2 vacancy, the net charge of titanium atoms ranged from 1.31
to 1.33. That of oxygen atoms was from -0.69 to -0.59. These first-principles calculations indicate that
the charge redistribution near the Ti vacancy is not large. This allows us to use the same atomic
scattering factors for all the oxygen/titanium atoms in TEM image simulation.
Figure S9. Net charge of Ti+Oc1+Oc2 vacancy model. Numbers in the structure drawing indicate
calculated values of the net charge around the vacancy.
Although the charge states of Ti vacancy models were obtained by the first-principles calculations,
the high-resolution TEM image simulation without charge distribution parameters is still usable as
remarked below.
The electron scattering factors for oxygen (O0 and O1-) and titanium atoms (Ti0 and Ti4+) listed in
the literature9 are plotted in Fig. S10. The atomic scattering factors of neutral and ionized atoms differ in
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the low-angle range (sinθ/λ < 0.15-0.20 Å-1). We draw the CTF under the present TEM condition in Fig.
S10. The present high-resolution TEM imaging does not include the low-angle scattering (sinθ/λ < 0.15
Å-1) so much because of the small defocus and the small spherical aberration in the monochromated
aberration-corrected TEM. This implies that the simulation with the parameter of charge distributions
may not induce a significant difference from the simulation with neutral atoms. It would be possible that
the simulation including ionic states more reproduce the contrast of the TEM image.
Figure S10. Atomic scattering factors for titanium and oxygen atoms. CTF under the present TEM
condition (Fig. S5a,b) is displayed with the same scale of the lattice spacing.
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