10554 J. Phys. Chem. B, Vol. 107, No. 38, 2003
Janssen et al.
particle of Figure 1 show that the pores are almost straight and
hexagonally ordered. Our eyes interpret the YZ slice in Figure
2 as showing a hexagonal ordering of white pores surrounded
by a black pore wall, just as is expected from a system with
empty pores. In contrast to this, YZ slice 1 in Figure 3 seems
to show a hexagonal ordering of black pores surrounded by
white pore walls. However, we postulate that this is not the
case but rather a contrast effect due to the diffraction contrast
in the original TEM images (below). The white areas in this
YZ slice are still the pores and the black areas are still the pore
walls. When a single pore is followed from 2 to 1 in the XY
slice, the corresponding YZ slices along that trajectory show
the pore always in white. However, going from 2 to 1 in the
XY slice the pore walls become more pronounced in the
reconstruction. In YZ slice 1 these strongly pronounced pore
walls are visible as large black spots, rather than a continuous
black pore wall around the white pores. This is caused by the
assignment of gray areas to belong to either the “white part” or
to the “black part” of the image. Our eyes focus strongly at the
black spots in YZ slice 1 and easily regard the rest as “white”,
which leads to a picture of black spots surrounded by white.
This is shown in Figure 7a, where a threshold has been applied
to the data to show the gray pixels in white. A closer look at
YZ slice 1 in Figure 3 reveals that the white spots are surrounded
by three black spots that are connected to each other with gray
areas. If these gray values are regarded as belonging to the
“black part” of the image, one ends up with white spots
surrounded by black. This is shown in Figure 7b, where a
threshold (with a different value than for Figure 7a) has been
applied to the data. In principle, one would expect the pore walls
to have the same gray value (black) everywhere. This is,
however, not the case. In YZ slice 2 of Figure 3 the pore walls
also differ strongly in gray value, although our eyes interpret
the image as white pores surrounded by gray/black pore walls.
It is not exactly clear why the pore walls are not uniform in
gray value. A likely explanation could be the fact that diffraction
contrast plays a role in the image formation of the original TEM
images. As has been mentioned in the Introduction, the theory
of electron tomography has not been developed for images that
have been formed with diffraction contrast. Although it is not
exactly clear what the effect of the diffraction contrast is on
the final reconstruction, the XY slice of Figure 3 shows
enormous changes in contrast. This is even more clear when
the subsequent XY slices are displayed in a movie (see
Supporting Information). The contrast changes seem to run as
a wave through the reconstruction.
Figure 5. Zirconia particles in SBA-15: (a) conventional TEM image,
(b) three orthogonal slices through the 3D-reconstruction (the black
arrows indicate the same zirconia particle in the three orientations),
(c) slice through the 3D-TEM reconstruction showing U-shaped pores
and zirconia particles inside the mesopores (black arrow).
slice the hexagonal packing of the mesopores is not visible and
the gold particles are elongated.
The conventional TEM image in Figure 5a shows small ZrO2
particles on SBA-15. The ordered nature of the SBA-15 material
is not clear from this image, as the tilt angle of the sample was
chosen such that diffraction contrast was (almost) absent, to
allow imaging of the small zirconia particles. Some of the largest
ZrO2 particles (5-6 nm) are indicated with an arrow. The
ordered nature of the material is evident from a movie of a tilt
series of this material (see Supporting Information). In Figure
5b three orthogonal slices through a part of the 3D-TEM
reconstruction of the SBA-15 particle from Figure 5a are shown.
In these three orthogonal slices the zirconia particles are visible
as small black dots, whereas the mesopores are visible as lighter
regions. The arrows in the three orthogonal slices indicate the
same zirconia particle. In Figure 5c another XY slice through
the reconstruction is given, showing some pores with many
zirconia particles in it, while other pores do not contain zirconia
particles. In this XY slice also the curved nature of the
mesopores (U-shape) can be seen.
In Figure 6 the nitrogen adsorption and desorption isotherms
of the SBA-15 samples with gold and zirconia particles,
respectively, are shown. The isotherm shows a distinct hysteresis
loop with a two-step desorption branch. In contrast, the isotherm
of the parent material corresponds to the one expected for
cylindrical mesopores with a sharp size distribution, i.e., it has
a single capillary condensation step. BJH analysis of the
desorption branch allows one to calculate a size distribution
with the majority of the pores lying between 6.5 and 7.5 nm.
Crystalline materials give rise to diffraction contrast in certain
orientations. Above it was shown that for SBA-15 this can
hamper the interpretation of the 3D-reconstruction. However,
for zeolite samples the reconstructions show a uniform gray
value for the zeolite material.11,12 Although zeolites are crystal-
line and give rise to diffraction contrast in the electron
microscope in certain orientations, the distance between the
lattice planes (in the Å range) is smaller than the resolution of
the TEM images. Instead of lattice planes being visible in certain
orientations, the entire zeolite crystal is imaged somewhat darker
in the orientations where diffraction contrast occurs. In the 3D-
TEM reconstruction this does not result in contrast changes
within the zeolite crystal. For ordered mesoporous materials,
however, the distance between the lattice planes is in the
nanometer range. At the low magnifications used, also the
resolution of the TEM images is in the nanometer range. This
results in the diffraction-based imaging of the lattice planes in
Discussion
3D-Reconstruction of SBA-15. The three orthogonal slices
in Figure 2 through the 3D-reconstruction of the small SBA-15