Tomographic Study of Mesopore Formation in Ceria Nanorods
Porosity in functional oxide nanorods is a recently discovered new type of microstructure, which is not yet fully understood and still under evaluation for its impact on applications in catalysis and gas/ion storage. Here we explore the shape and distribution of pores in ceria in three dimensions using a modified algorithm of geometric tomography as a reliable tool for reconstructing defective and strained nanoobjects. The pores are confirmed as “negative-particle” or “inverse-particle” cuboctahedral shapes located exclusively beneath the flat surface of the rods separated via a sub-5 nm thin ceria wall from the outside. New findings also comprise elongated “negative-rod” defects, seen as embryonic nanotubes, and pores in cube-shaped ceria. Furthermore, we report near-sintering secondary heat treatment of nanorods and cubes, confirming persistence of pores beyond external surface rounding. We support our experiments with molecular modeling and predict that the growth history of voids is via diffusion and aggregation of atomic point defects. In addition, we use density functional theory to show that the relative stability of pore (shape) increases in the order “cuboidal” < “hexagonal-prismatic” < “octahedral”. The results indicate that by engineering voids into nanorods, via a high-temperature postsynthetic heat treatment, a potential future alternative route of tuning catalytic activities might become possible.
Introduction<!><!>Introduction<!>Materials
Preparation<!>Materials Characterization<!>DFT Methodology<!>Classical
Molecular Dynamics Methodology<!>Overview by Two-Dimensional Imaging<!><!>Overview by Two-Dimensional Imaging<!><!>Overview by Two-Dimensional Imaging<!><!>Overview by Two-Dimensional Imaging<!>Three-Dimensional Imaging of Pore Distribution
via Tomography<!>Cross-Sectional
Analysis of Ceria Nanorods<!>Influence
of Heat Treatment on Ceria Nanorods<!>Classical
Molecular Dynamics<!><!>Classical
Molecular Dynamics<!><!>Classical
Molecular Dynamics<!>Density Functional Theory (DFT)<!><!>Computational Prediction of Catalytic Activity<!><!>Computational Prediction of Catalytic Activity<!>Discussion<!>Conclusions<!>
<p>Ceria
has remained one of the most studied nanostructured materials
for many decades.1 Its abundance and versatility
have seen its impact increase steadily. Since 2014, over half of the
publications on nanoceria have concerned uses in catalysis.2 However, cutting-edge applications can be found
across many other disciplines from biomedical3 to energy and environmental4,5 processes. The high
redox activity and structural stability of ceria-based materials make
them particularly appealing for the ever-growing field of heterogeneous
catalysis, where novel structures are constantly being developed and
tested for their catalytic performance.6 Rod-shaped nanoparticles are of particular interest, as they present
higher activity than other ceria nanostructures of similar surface
area.7−9 This is attributed to the presence of exposed planes
and to the number of {100} and {110} surfaces.</p><p>More recently,
there have been reports of porosity in ceria nanorods,
at first for micropores (<2 nm) of nonspecific shape randomly found
as part of the synthesis process.10,11 A hydrothermal
process with systematic postengineering of pores via heat treatment
has been found leading to larger well-faceted pores.12,13 Similar mesopores have been further elaborated and found to enhance
the already high catalytic performance of ceria nanorods.14,15 Electron microscopy has so far been mostly used for 2D structural
imaging of nanoceria, for example,13,16 and in few
cases for electron tomography of ceria particles.17,18 While the tomography of solid and microporous rods10 is also available, there is no exploration into the three-dimensional
shape and distribution of the newer heat-induced mesopore defects
in the shape of "negative particles". We believe that
such a study is essential to understand the growth history and benefits
the design and applications of such sophisticatedly engineered mesoporous
ceria nanorods.</p><p>Figure 1 shows a
schematic classification of different 3D microstructures that could
correspond to images of defective nanorods commonly known. This list
is by no means exhaustive and only aims to present some of the most
likely possible origins for these features. We distinguish (a) patches
of high concentrations of any point defects (vacancies and interstitials),
possibly combined with lattice swelling;19 (b) agglomeration of these defects into clusters of ordered and
neighboring point defects without forming voids;11,20 and (c) micropores of sub-2 nm sized voids of irregular shape randomly
distributed over all the volume.10,13,21,22 (d) corresponds to
internal mesopores of 2–10 nm size with well-faceted geometry,
often termed "negative particles", which are the topic
of the present work;13,23,24,28 (e) refers to surface pores (indents, recesses,
and etch pits);20,25−27 and (f) refers
to through pores (nanochannels and wormhole shapes).14,29,30 While cases (a, b) are commonly
found as result of irradiation experiments, (c–f) more commonly
stem from chemical processes, including etching, phase separation,
reactions, and heat treatments.</p><!><p>Schematic representation of different
propositions of porous structures:
(a) point defects/vacancies, (b) vacancy clusters, (c) microvoids,
(d) mesopores with "negative particle" facet shape,
(e) surface pores, etch pits, and concavities, and (f) through holes,
nanochannels, and wormholes.</p><!><p>Some of those pores, for example, Figure 1e, have been excellently resolved by characterization.27 However, when TEM instead of AFM is needed,
it becomes particularly relevant to note that several of these proposed
porous structures could appear very similar in conventional 2D projection
imaging; therefore, tomographic examination appears as the essential
way forward to resolve the microstructure origin. Here we introduce
a modified version of geometric tomography32−34 applied to
electron tomography of crystalline materials with nonconvex features,
not normally eligible for this technique. These explorations continue
the work presented by Sakthivel et al.,13 which established reproducible annealing methods for the production
of defect patterns in CeO2 nanorods. We seek to resolve
the unanswered questions regarding the structure and morphology of
those defects. We also expand the earlier work by a comparison of
rod- and cube-shaped nanostructures and by increasing the range of
heat treatment right up to the sintering starting temperature.</p><!><p>The detailed synthesis of our
samples has been previously published by Sakthivel el al.12,13 In brief, different morphologies (including rod, cube, and octahedral
particles) of CeO2 were achieved by controlling parameters
(temperature and aging time) in a hydrothermal synthesis using Ce(NO3)3·6H2O as the ceria precursor
and NaOH as reaction agent. Postsynthesis heat treatment was mostly
conducted by conventional furnace heating of powders; however, we
also added to the procedure some heat treatment of small powder samples
suspended on Si/Si3N4 TEM carrier films, annealed
in air with a heating rate of 5 °C/min, held at 800 °C for
3 h, and allowed to cool in the furnace overnight. The second temperature
of 950 °C involved the same heating rate with 1 h holding time
before cooling overnight. This latter procedure allows for TEM samples
of specific powders to be viewed before and after heat treatment without
disturbing intermediate specimen preparation.</p><!><p>Apart from the mentioned
Si3N4 specimens, typical powdered samples were
suspended in deionized water and mounted onto standard copper grids
with continuous or holey carbon film. High-resolution structural analysis
was performed by using a JEOL JEM-F200 and a JEOL JEM-2010F field
emission transmission electron microscope. Electron tomography or
3D-TEM was performed by using a JEOL JEM-3010 coupled with a Gatan
model 912 tomography holder. Tilt series were aligned by using TomoJ.48 Then, they were segmented and binarized to create
paths that precisely tracked the features of interest. The binary
images were processed via Back-Projection algorithm, also in TomoJ.
Finally, the stacks were rendered by using Chimera49 to image and measure the three-dimensional reconstructions.</p><!><p>DFT calculations were performed by
using the VASP 5 code.50,51 Simulations used a plane-wave
basis set, which incorporates relativistic effect core potentials
and the projector augmented wave (PAW) method. The exchange-correlation
functional applied was the Perdew–Burke–Ernzerhof PBE.
The Hubbard U correction, using the Dudarev methodology,
was 5 eV.52,53 The cutoff energy of the plane-wave basis
set was 500 eV. The electronic and ionic convergence criteria were
1 × 10–4 eV atom–1 and 1
× 10–2 eV Å–1. The Brillouin
zone was sampled by using the Γ point. The energy of the void
was calculated by removing the energy of a stoichiometric cubic unit
cell comprising 256 CeO2 from the energy of the structure containing the void and
the energy corresponding to the nanoparticle that was carved out to
leave the void behind (9, 11, and 8 CeO2 units for the
cube-like, hexagon-like, and octahedron-like shaped voids).</p><!><p>Molecular
dynamics (MD) simulations were performed by using the DL_POLY code54 using the Born model of the ionic solid. The
energy of the system is given by1where the
first term represents the Coulombic
interaction between ions i and j of charge Qi and Qj at a distance of rij. The second term represents
the Buckingham form, and potential parameters were taken from ref (55). A rigid ion model representation
was used to reduce computational cost. Model ceria nanorod structures
were generated by using simulated crystallization, following procedures
reported previously.44,56−59 Graphical analysis of the molecular
dynamical trajectories was performed by using Visual Molecular Dynamics
(VMD).60 Calculation of the Madelung energies
was performed by using the METADISE code.61</p><!><p>At first, ceria
nanorod samples before and after heat treatment in air at 800 °C
(mounted onto carbon-coated copper grid) are presented for overview
in Figure 2. The nonheated
rods show overall single crystallinity and homogeneity on the mesoscale
(>2 nm) but a high density of sub-2 nm features, such as strain,
lattice
imperfections, and micropores (Figure 2a). In contrast, after heating, the microimperfections
appear swapped against new mesoscale pores, with the overall lattice
now healed to greater sub-2 nm perfection (Figure 2f).</p><!><p>Crystallography of ceria nanorods. (a) Before
heat treatment; with
insets b and d for magnified lattice planes and insets c and e for
FFT diffraction analysis; segment b is viewed near ⟨110⟩
on a ⟨110⟩ rod axis, while segment d is mainly a ⟨211⟩
rod axis, although the FFT indicates a superposition of two local
grains. (f) After heat treatment; with insets g, h, and i for magnified
lattice planes and inset j for FFT diffraction analysis. Segment g
has a ⟨110⟩ rod axis and is viewed near ⟨110⟩,
and segment i has a ⟨211⟩ rod axis and is viewed along
⟨110⟩, while segment h is near ⟨110⟩.</p><!><p>The three neighboring rods visible represent a
typical diversity,
with aspect ratios varying significantly, for example, diameters ranging
from 20 to 45 nm and lengths from 50 up to 200 nm. The rods show a
continuous single-crystalline cubic structure with one of two growth
directions: the rods highlighted (h) and (i) exhibit growth in the
[211] direction while nanorod (g) has [110] growth direction, consistent
with cited work.35,36 Both types of rods would show
a nonregular hexagon cross section, enclosed by {111}/{110} facets
for the ⟨211⟩ rod axis or {100}/{110} facets for the
⟨110⟩ axis.</p><!><p>Virtually
every single rod examined after heat treatment
shows a number of pores (light patches), much unlike cube samples
discussed later.</p><p>The diameters of pores
are fluctuating much more narrowly
than the size of rods, ranging from 1 to 12 nm with an average of
4–6 nm (as demonstrated in Figure SI-1). That means whatever the diameter of the rod, the pore diameter
remains similar. For example, the voids found throughout Figures 2 and 3 range only from 2 to 11 nm across. The pore size is not proportional
to the varying rod diameters and lengths but appears defined by the
heat treatment.</p><p>Most pores in Figure 2f (and even more
so in Figure 3) are
isotropic (e.g., compatible with regular
octahedra). Their facets are aligned with the crystal lattices of
the rod, as highlighted in Figure 3d.</p><p>However, some of the
newly heat-generated pores show
elongated morphology along the rod direction, not reported previously.
These voids in the shape of "negative rods" rather than
"negative octahedral particles" could be an initiating
stage of a later conversion of rods into hollow ceria nanotubes.37,38 While pore shapes vary, we find a trend that those pores, which
show enclosure by straight facets, e.g., in Figures 2f and 3, have their
straight border lines in projection along lattice fringes showing
consistent faceted geometry, as further detailed in Figure SI-2.</p><p>(a) Bright-field TEM
image of a ceria nanorod with ⟨110⟩
axis, annealed at 800 °C. (b) HRTEM imaging of the same region
showing lattice fringes and clear facets parallel to the {111} plane
orientation. (c) 25 nm nanorod also with ⟨110⟩ axis,
used for profile analysis. For profile-line traces on (a) and (c),
see Figures SI-4 and SI-5. (d) Digital
close-up of (b) showing lattice fringes and inset oriented model cuboctahedron,
enclosed by {111} faces and small caps of {100} and {110} type. Here
the top/bottom void faces are clearly parallel to the lattice fringes.</p><!><p>Figure 3 shows nanorods
at various magnifications with a selection of pores along their length,
suitable and chosen for tomographic analysis in Figures 4 and 5. For preparation
details of the powders see previous work.12Figure 3a shows a
segment of the rod 140 nm long suitable for 3D examination of both
the external rod shape and the internal voids. Figure 3b shows a HRTEM image of the central part
of the rods including four major pores suitable for tomographic reconstruction,
with multiple sets of lattice fringes resolved, corresponding to (111)
planes, as shown in Figure 3d. We can see that the fringes cross the void regions uninterrupted.
This behavior suggests that the single crystalline structure is continuous
in spite of the defects. Together with the absence of moiré
patterns, this suggests that the voids occur within one single crystal
grain, as of Figure 2f. Apart from slight variations of pore morphology (partially due
to 2D-projection effects) we can see a consistency in the orientation
of the features, with two opposite facets maintaining parallelism
of exposed {111} planes, while the shorter sides remain parallel to
the growth direction of the rod.</p><!><p>3D reconstruction of 800 °C-heated
CNR segment containing
four faceted voids. (a, b) Overall rod shape and relative internal
void locations viewed perpendicular and along rod axis. (c) 3D reconstruction
of the shape of individual pores with rod annulated. (d) Crystallographic
index identification for rod (red) and pore (green). (e–g)
A single pore in three viewing directions. All scale bars in (a–g)
are 10 nm. Axes color code: x (red), y (yellow), and z (blue). The electron beam direction
is indicated by the blue axis.</p><p>Occurrence
of defects/micropores in rods before (a, b) and extended
faceted mesopores in rods after HT heat treatment (c, d). Cuboctahedral
model void as inset in (d). Absence of any defects or pores in cubes
before (e, f) and occurrence of extended mesopores in cubes after
HT heat treatment (g, h). Top/bottom represents two examples for each
type of sample.</p><!><p>In Figure 3c another
rod with average lateral size of 25 nm and pore sizes ranging from
4 to 7 nm is shown. This rod appears to have a higher concentration
of pore-type defects per projected area than the one in Figure 3a,b, despite having similar
diameters. This could be attributed to the pores in Figure 3a,b being larger, ranging from
7 to 11 nm.</p><!><p>All three images in Figure 3a–c are the 0° central projections
of tomographic
acquisition series over ±60° angular range in 5° steps.
A total of 13 2D images are underlying each acquisition series. Two
series, at different magnification setting, have been recorded and
are superimposed, as demonstrated in Figure SI-3. This helps benefiting from both high resolution and better alignment
from a larger field of view. Because of various nonlinearities (strain
and lattice contrast, see discussion below), standard computed tomography
is not applicable for bright-field TEM at high resolution, without
special mitigation of scattering contrast artifacts. While EFTEM and
HAADF-STEM have been proposed for this situation,17,39,40 these require extra peripheral equipment
and more complex image acquisition, not always available.</p><p>Heat
treatment of ceria nanorods can result in strain around pores in single-crystalline
nanorods, which contributes imaging artifacts, manifest as dark patches,
through modified Bragg scattering. Electrons are locally removed from
image intensity without the object being thick. These features are
detrimental to electron tomography, as variations in gray values are
interpreted as changes in thickness × density upon reconstruction.
For this reason, ceria nanorods are good candidates for "geometric
tomography" (GT) to reconstruct nanostructures based on binarized
intensities. However, the standard condition for GT of objects being
axially convex is not met here.</p><p>We are therefore exploring an
innovative approach in which we at
first subdivide the image information into multiple images, starting
with the (solid) rod as a whole, followed by selected pores, with
each pore being treated one after another. For each image subseries,
the GT conditions are fulfilled. Following separate reconstruction,
the resulting 3D models are superimposed as if they form one single
reconstruction. The tomographic reconstructions obtained in this work
are therefore innovative 3D models of the mesoporous nanorods and
simultaneously reveal pore-shape information as well as the location
of the pores with respect to the surfaces of the rod.</p><p>On the
other hand, geometric tomography (GT)34 has already been demonstrated as a fast and low-complexity
short-cut to use bright-field TEM for suitable nanoparticles.33 GT is also termed the "shape-from-silhouette"
technique. However, the main applicability condition for GT is that
all objects are shaped in "axially convex" cross sections.
That means each 2D section perpendicular to the rotation axis must
have convex shape, as otherwise any concavities would be filled up
and enlarged into a geometric body called the "convex hull".
For the external nanorod shape we expect axial convexity to be fulfilled.
The same applies for each individual void in isolation, if contrast
is inverted into a "positive particle". However, the
combined object (rod with multiple overlapping voids) would classify
as mixed convex–concave. Here we propose a new strategy, modified
from Saghi et al.:33 First, we separate
the rod-image binarization from the void-image binarization. Then
we apply back-projection two times: first to reconstruct the rod shape
only as if there are no voids and second to reconstruct the voids
one by one (in their original 3D space position relative to each other)
as if there was no finite rod around them. The resulting 3D models
of rod and voids are then intercalated into a combined 3D reconstruction.</p><p>The lower magnification images like Figure 3a allowed us to reconstruct a long enough
representative segment of the rod, while the higher detail in images
like Figure 3b was
used to extract the faceted geometry of the voids. The final reconstructed
volume of interest comprises the outer morphology of the rod along
with four internal features of interest. The 10 nm scale bar can be
used to verify the lateral dimensions of the rod, which is 35 nm wide
by 45 nm tall with defined facets along the (220) and (100) planes.
The distance between the diagonal faces is 40 nm.</p><p>We present
the reconstruction of the rod surface as a transparent
mesh while the pores are inserted as solid surface rendered "particles",
viewed either perpendicular (Figure 4a) or along the rod axis (Figure 4b). The location of the pores within the
rod is accurate, as the locations of pores and rods were not altered
relative to the 3D data space during the separately executed back-projections.
Both views confirm the existence of a preference orientation of the
pores with respect to the faceted sides of the rod and the rod axis:
The smaller flat surfaces at the top and bottom of each pore are parallel
to the top and bottom surfaces of the rod. In a similar way, the longer
diagonal sides of the pores are parallel to the diagonal sides of
the rod. The missing wedge artifact deforms the sides of each feature.
In the view shown in Figure 4c, the pores appear to end in flat surfaces at the top, bottom,
front, and back, while the sides terminate in a point. It is expected
that these sides terminate in (100) surfaces like the others. This
orientation is further confirmed by postprocessing in Figures SI5 and SI6. This orientation relationship
emphasizes the single-crystal nature of the rod and equivalence in
shape equilibration for each facet pore, similar to how octahedral
nanoparticles would adopt a common relationship if grown on a connecting
single-crystal substrate by epitaxy. The void shape also matches the
shape of an "oriented attachment" building block, which
plays a role during hydrothermal growth, as imaged in Figure SI-2.</p><p>When we remove the rod from
view (Figure 4c), we
can appreciate the consistency in
shape and orientation of the pores, which present flat surfaces at
the top and bottom. We can also see that the larger pores, such as
the ones at the top and right in Figure 4c, have more defined geometries than the
smaller pore at the far left of the image. Finally, the bottom row, Figure 4 e–g, shows
the reconstruction of a single pore in isolation.</p><p>The overall
crystallography is indexed for rod and pores in Figure 4d: The geometry is
symmetrical and is composed of smooth surfaces. For reasons of single
crystal geometry the rods and pores must have differing facet distributions
and therefore differing angles relative to the flat {100} type reference
planes which are in common. The diagonal {110} planes for the rod
are well distinguished in the reconstruction from the less steep {111}
facets of the cuboctahedral pores.</p><p>The presence of pores inside
the body of the rod, which do not
reach the surfaces, requires careful definition of functional parameters
in prospective applications, such as the surface area/volume ratio
(see also the Discussion section). The conventional
ratio (Sext/V), using
only external surfaces, remains nearly the same after heat treatment
due to the diameter and volume not changing. However, if we introduce
a total S/V ratio via Stot/V = (Sext + Sint)/V, the formation
of surface significantly increases due to internal surface, e.g.,
for the porous rod shown in Figure 4 by ∼36% compared to its nonporous counterpart.
The applicability of Stot instead of Sext for predicting functional performance depends
on the gas permeation of the very thin separation walls.</p><!><p>A main advantage
of tomography is that the resulting 3D models can be sliced into cross-sectional
planes. At first, we analyze intensity profiles evaluated from Figure 3a, displayed as Figure SI-4. The residual contrast inside the
pores relative to the carbon background clearly confirms that the
light patches are never through pores or holes (as of Figure 1f) but must be internal voids
as proven by the tomography in Figure 4. Next, we construct three cross-sectional tomographic
reconstructions from the tilt series behind Figure 3c, shown in Figure SI-5a–c. The reconstructed cross sections show in white the outer morphology
of the rod. This consists of a six-sided polyhedron of 2-fold rotational
symmetry with prominent {110} facets cut by shorter {100} facets,
with occasional {110} capped edges. These intersections are credited
to host most catalytically active sites.7 The shape is also compatible with previous 3D models for ceria nanorods.10 The tomography results also show the pores as
symmetrical with defined facets consistent with mainly {100}-truncated
{111}-octahedra. The geometry appears to align with the edges of the
rod, coinciding in their shorter {100} sides and their more prominent
{111} facets. As for the location of the pores, the reconstructions
show them to be fully enclosed by the rod. They seem to appear at
random lateral locations within its volume. In Figure 4b, the distance between pore and surface
is never smaller than 1.4 nm.</p><p>Furthermore, it is important to
verify the isotropy and deviations from it: In contrast with other
forms of tomography, electron tomography does not allow a full axial
rotation of the sample. This is limited by the goniometer and the
projected thickness of the specimen at high tilt angles, which impedes
transmission imaging. The missing information results in a "missing
wedge" artifact. To distinguish the effect of the missing wedge
from the morphology of the sample, we include a theoretical reconstruction
of a perfect cylinder simulating the same imaging conditions as our
experimental results (Figure SI-6). We
can see that the top and bottom of the reconstruction present the
expected circular cross section, while the area of missing information
appears elongated and distorted. However, the missing wedge would
not introduce any extra capping of the rod or void shapes on the top
and bottom ({100} facets). There is no facet detected in our work,
which would not be visible in at least one 2D image, although the
missing wedge might lengthen {111} type facets.</p><p>To study the
pore–rod relationship in more detail and to
judge possible influences of incomplete data acquisition (120°
instead of 180° tilt series), we apply another modified GT algorithm:
In Saghi et al.,33 the standard GT algorithm
was contrasted with an even further data-reduced concept, labeled
"shape-from-contour": rather than binarizing object
projections into regions inside vs outside the radiation shadow, each
object surface line in each image is "edge-enhanced"
into a bright line while the areas both inside and outside the objects
are blackened. We show here for the first time that this algorithm
can successfully deal with porous objects, such as a pore inside a
rod, by using the cross section (i) arrowed in Figure 3c. The selected cross section appears as
a 1D line on each image in the tilt series, with only four pixels
retained: the four transition positions from rod/vacuum and rod/pore.</p><p>The advantage of the shape-from-contour method relative to the
earlier GT algorithms lies (apart from data compression) in its ability
to (at least partially) simultaneously process binary objects fully
enclosed inside larger objects, as the thin back-projected lines are
less likely to override inner contour details, which would be completely
wiped clear by the shape-from-silhouette approach. Figure SI-7c is an encouraging result, as it can be safely
interpreted for both rod shape and pore shape from a single cross
section and thereby rendering the applied segmentation optional. We
plan to expand on this reasoning in a forthcoming publication.</p><!><p>Figure 5 shows a selection
of high-resolution TEM images comparing samples of nanorods and nanocubes
as-synthesized and after high-temperature (HT) near-sintering heat
treatment, complementing earlier work in refs (12 and 13). In brief, we observe rounding
and shortening of the nanorods and even more pronounced loss of edges
and corners in the cube morphology. We note the prevalence of a few
sharp corners after heat treatment, e.g., cubes at 950 °C (a).
By comparison of the as-prepared samples, the monocrystallinity of
the rods is more pronounced. This is consistent with the similar comparison
shown in Figure 2.
Such a TEM on furnace-heated samples is typically performed by heating
the powder in a suitable container and then drop some grains afterward
onto a (cool) support film/grid. To evaluate the possibility of heating
the powders on the TEM grid, we trialled an amorphous Si3N4 film. The upper temperature is a challenge due to brittleness
and possible reaction in air. In Figure SI-8 we show that Si3N4 is safe to be utilized
at 950 °C.</p><p>As expected, pores have formed in the rod morphology
upon heat treatment. The size of these pores is similar to the ones
found after heating at lower temperature.13 The shape of the pores does not appear to have lost the facets analyzed
in the previous sections, regardless of the rounding of the rods.
The pores do not appear to be closer to the edges of the rod than
in Figures 2 and 3, which suggests that they have remained inside
the structure. The cube-shaped nanoparticles12,45 also developed pores upon heat treatment to this higher temperature,
which is a new finding. They are not as common as in the rods with
only few pores per cube. However, they tend to be larger in size than
the pores found in the rods.</p><!><p>To complement our experiments
and help rationalize the structure, shape, and evolution of voids
within ceria nanorods, we performed a combination of classical molecular
dynamics (MD) and density functional (DFT) simulations.</p><p>A model
CeO2 nanorod, with [211] growth direction (Figure 6a), was heated under molecular
dynamics simulation to within 90% of its melting point. Analysis of
the nanorod revealed that surface Ce and O vacancies spontaneously
evolved as surface atoms moved off their lattice positions. Occasionally,
the vacancies would migrate toward the center of the nanorod. We hypothesize
that voids in ceria nanorods, observed experimentally, evolve from
the agglomeration of these vacancies in the body of the nanorod. To
test this hypothesis, we introduced 4500 vacancies (1500 cerium and
3000 oxygen), at random positions, into a (15972-atom unit cell) nanorod
with [211] growth direction. The nanorod was then heated, under MD
simulation, to within 90% of its melting temperature. Analysis of
the atom trajectories revealed that both oxygen and cerium vacancies
were mobile within the nanorod and agglomerated to form voids. In
particular, a segment, cut through the nanorod during the MD simulation
(Figure 6b), shows
three voids that have evolved from the agglomeration of vacancies.</p><!><p>Molecular
modeling of porous ceria nanorods. (a) Structure of a
ceria nanorod with [211] growth direction; oxygen atoms are colored
red, and cerium are white. (b) Surface rendered model of a slice cut
through the nanorod in (a) showing voids that have evolved via the
agglomeration of cerium and oxygen vacancies within the nanorod. Single
vacancies and vacancy clusters are also present but are not shown
to reveal more clearly the structures of the (larger) voids. (c–e)
Snapshots of an MD trajectory depicting a segment cut through a model
ceria nanorod with [110] growth direction revealing the gradual annihilation
of voids and vacancy clusters during simulated annealing. The diameter
of the model nanorod is about 4 nm.</p><!><p>The voids within the nanorods (Figure 6b) appear to have octahedral morphologies,
but the voids are small, which makes morphological characterization
difficult. Accordingly, we generated a model of a much larger void.
In particular, a spherical void was generated at the center of a simulation
cell of crystalline ceria by removing a stoichiometric number of Ce
and O atoms. The system was then heated, under MD simulation, to within
90% of its melting point. During the simulation, the spherical void
transformed into a truncated polyhedron with eight {111} surfaces
truncated by six {100} surfaces (Figure 7), in accord with our experimental findings.</p><!><p>Atom level
(model) structure of a void within crystalline ceria.
(a) Sphere model representation of the atoms; cerium is colored white,
and oxygen is red. (b) Surface rendered model of the void revealing
more clearly the truncated polyhedral morphology, to be compared with Figure 4d. (c) Experimental
faceted void with lattice fringes reoriented to match orientation
of (b). The diameter of the (model) void (a, b) is ∼4 nm.</p><!><p>The surface view of the model (Figure 7b) is suitable for direct comparison
to the
projected appearance of experimental voids, as follows: In Figure 7c, the top right
facet of (111} type matches the equivalent top right facet in Figure 7b, while the top
corner in both Figure 7b and Figure 7c is
capped, indicating the {100} occurrence. For a 3D comparison of model
and experiment we point to Figure 4d, which shows tomographic reconstructions oriented
with {111} and {100} suitable for comparison with Figure 7b. Overall, the "negative
particle" concept is confirmed, while also acknowledging the
occasional asymmetry of octahedral facets and cubelike caps as found
in Figure SI-2, leading to distorted octahedra.</p><!><p>DFT calculations of
a supercell comprising 256 CeO2 units were performed to
determine whether there is a difference in energetics of the voids
with respect to shape. A small number of stoichiometric CeO2 units were removed to form cube-like, octahedron-like, and hexagon-like
shapes as shown in Figure 8. It is clear that the stability of the voids is related from
the thermodynamic point of view to the surfaces that are expressed
in the cavity. Cube-like voids are the least stable because they express
{100} surfaces with an energy of 3.14 J/m2. Octahedron-like
voids are more stable as they express {111} surfaces (2.48 J/m2). The hexagonal prismatic-like voids express both {111} and
{110} surfaces and lie between the cube-like and the octahedron-like
voids in terms of energy (2.68 J/m2).</p><!><p>Voids of different shapes
have been introduced in a cube comprising
256 CeO2 units: (a, b) cube-like, (c, d) hexagon-like,
and (e, f) octahedron-like shaped voids.</p><!><p>Nanoceria
can capture, store, and release oxygen from its surfaces. This ability,
named oxygen storage capacity (OSC),41 enables
oxidation/reduction reactions that are central to many applications.
For example, environmental "clean-air" technologies
use nanoceria to release oxygen and catalyze CO to CO2 while
simultaneously (catalytically) reducing harmful NOx emissions by capturing
oxygen.2 Nanoceria can also act as an enzyme
mimetic or "nanozyme" by capturing and releasing oxygen
from its surfaces to modulate concentrations of oxygen species in
cellular environments.42 It is therefore
important to understand how voids within nanoceria might influence
its ability to release oxygen from its surface in catalytic reactions.</p><p>The energy required to extract oxygen from the surface of nanoceria
"is a simple yet powerful activity descriptor".43 Reactivity maps, where oxygen atoms are colored
according to the energy required to extract them from the surface
(calculated via Madelung energies44), are
shown in Figure 9.
The oxygen atoms are colored on a red–white–blue sliding
scale, where red represents oxygen atoms that require the least energy
to extract and oxygen atoms colored blue require the most energy to
extract.</p><!><p>Activity maps of a ceria nanorod, with [211] growth direction,
with and without voids. Only oxygen atoms are displayed and colored
according to their Madelung energy by using a red–white–blue
sliding scale where red indicates oxygen that is energetically easy
to extract and blue indicates oxygen atoms that are difficult to extract.
The nanorod is composed of two large {111} surfaces shown in (a) and
(b) for the nanorod without voids and (c) and (d) for the nanorod
containing voids. (e) and (f) are views of a void close to the surface
shown in (d); atoms were removed to show the void, and ovals indicate
the position of the subsurface void.</p><!><p>Calculated reactivity maps of the nanorod with and without voids
(Figures 9a,b and 9c,d, respectively) show very different surface patterns.
In particular, images reveal that it is (thermodynamically) easier
to extract surface oxygen from a nanorod with voids (oxygen atoms
predominantly colored red) compared to ceria nanorods without voids
(surface oxygen atoms predominantly colored blue). Accordingly, the
simulations predict that voids activate {111} surfaces.</p><!><p>Following the tomographic reconstructions, the "shaped-void"
defects in this study can now be clearly categorized with respected
to speculative alternatives, as sketched in Figure 1. We can safely exclude for our materials
the two cases of through holes and surface pits (Figure 1e,f) as all voids are internal.
The atomic-number contrast between rod and void is also far too large
for oxygen-only vacancy-rich regions. That leaves option Figure 1d, internal faceted
voids, as the only compatible one. Option Figure 1c, a high concentration of subnanometer small
defects, is continued to be believed as the likely precursor situation
before heat treatment, essential to accumulate the high internal energy
which is driving consolidation into fewer but larger and shape-equilibrated
defects. The actually identified preferred octahedral shape for the negative-particle voids is consistent with both molecular
dynamics simulations and DFT calculations, confirming its lowest energy
status and a dynamic pathway to its formation.</p><p>The existence
of such unfilled space in this study is to be seen
with respect to volume loss upon the NaOH triggered conversion of
Ce(NO)3·6H2O to CeO2 with Ce(OH)3 as an intermediate solid phase. However, our results show
that any precursor hydroxide phase expected to exist during the hydrothermal
synthesis does not act via template synthesis to shape future voids.
There is no phase separation followed by dissolution of the more volatile
phase (as e.g. in dealloying of AuAg nanoalloys or in the Vycor process
of glass-in-glass phase separation31).
The void shape is rather an equilibration of surface energy after
the (pure) CeO2 composition is achieved, with the posthydrothermal
heat treatment supplying the mobility to both cations and anions.</p><p>In our atomic modeling calculations, vacancies of O and Ce, preloaded
into a rod model, are found in their majority not to persist through
heat treatment, instead escaping through nearby surfaces. It is therefore
essential that pre-existing internal microvoids (causing the rough
contrast in Figure 5b, also reported by Florea et al.10) are
assumed, which grow by ripening without escaping the rods. However,
it is also found that formation of negative-particle shape voids can
happen spontaneously, well distant from the surface, and therefore
does not require phase separation and chemical impurities, or a sacrificial
spacer phase, if the right conditions are applied, starting from a
pure material enriched in point defects. Modeling confirms that the
shape assumed by the voids is determined by local equilibrium of surface
facets and not via template casting of any earlier phase.</p><p>The
applied heat-treatment temperature of 800 °C is "medium",
in the sense that it is below the known sintering-onset Tsint (expected around 900 °C) for ceria nanostructures
but above routine annealing applied to such nanomaterials (<600
°C). Our comparative high-T experiments at 950
°C thus reveal the differing behavior of external shape and internal
voids: external surfaces start to flow under the influence of surface
tension, assuming rounding, while the internal voids remain trapped
inside the rods and do undergo less rounding or growth.</p><p>Interestingly,
cube samples, which so far have never been reported
to grow negative-particle voids, due to their isotropic growth, have
also been found with at least some voids (much less than for rods),
surviving the 950 °C external rounding of the cubes.</p><p>Images
such as Figure 2f indicate
that some voids are rather elongated, of "negative-rod"
shape rather than "negative-octahedron" shape. The long
axis of those is always aligned with the rod axis, and they tend to
prefer locations central to the rod. It is therefore easy to extrapolate
that further (longer holding time) heat treatment might trigger growth
and merger of these rod voids, which would end up forming ceria nanotubes,
like those reported in refs (37 and 38).</p><p>Some secondary observations referring to strain are of interest
as well, although these had to be suppressed to enable tomographic
reconstructions: Many voids in Figure 3 are enclosed in dark patches, representing modified
Bragg scattering in those bright-field images. This must be residual
strain after formation of the voids from earlier microdefects, not
annealed out at the medium temperatures used. The effect is maximized
near sharp corners enclosing the voids. Apart from those strain effects,
the lattice is however of greater crystalline quality compared to
before any heat treatment (Figure 5a), indicating the absence of microdefects. This strained
neighborhood around pores is also found persisting in 950 °C
heated TEM samples. The bright-field images of the rods (Figure 3) also show a dark
stripe of constant width running along the longitude of the rod. This
is consistent with the pseudohexagonal cross section of the rod and
underpins the flat central surface part found via tomography (Figure 4b). However, this
is pure mass–thickness contrast differentiated from the aforementioned
dark patches encircling the defects, which are strain contrast.</p><p>Apart from inducing pores, it is well-known that heating can induce
transformation of less stable CeO2 surface facets (e.g.,
(110)) via subfacetting and appear in HRTEM as a zigzag edge in projection
(see refs (45 and 46)). While
this phenomenon can be traced in our modeling (see Figure SI-9), the rods selected in the present work have flat
external surfaces. No subfacetting occurs in the modeling of the voids,
while we occasionally see flattened edges at cuboctahedra of {110}
type on micrographs of the ⟨110⟩ viewing direction.</p><p>The location of these cavities inside the body of the nanorods
raises interesting questions as to the performance in applications,
as porosity in similar (but more open) ceria nanostructures has been
found beneficial.14 Here, our simulations
predict that it is easier to extract oxygen from the surfaces of ceria
nanorods, which contain voids, compared to nanorods without voids.
Reduced energetics for oxygen extraction, to create vacancies, impacts
upon the catalytic activity, oxygen storage capacity, and (vacancy-driven)
oxygen transport within ceria.2,43,47</p><!><p>Hydrothermally synthesized ceria nanorods heat-treated
at 800 °C
resulted in development of internal voids of well-faceted "negative
particle" shape, alongside higher crystalline quality with
lower point defects, while external rod morphology remains unchanged.
For the first time, although at lower concentration, cavities are
also found in ceria nanocubes. However, heating to 950 °C results
in surface rounding, onset of sintering of neighboring particles,
while the internal cavities still persist.</p><p>A modified geometric
tomography methodology, adapted to the case
of multiple pores inside a convex rod shaped sample, is presented
to successfully reconstruct the pore shapes and rod cross sections
by using bright-field TEM only. The cuboctahedral shape is confirmed
for most voids, with some of them forming elongated negative rods.
None of the reconstructed voids or cavities have connection to the
surface. However, the separation wall of around 1.5 nm would be well
permeable for atomic oxygen diffusion and would render the internal
voids possibly contributing to catalytic activity.</p><p>Computational
modeling has further elucidated the evidence from
the experiments: first, molecular dynamics revealed that cavity formation
from aggregation of point defects can be a spontaneous process without
the need of a spacer phase to enforce cavities. Second, density functional
theory confirms that the preferred void shape is octahedral (negative-particle)
by using surface energy balance similar to predicting positive particle
shapes. And finally, calculations of multineighbor oxygen coordination
energies from rods with and without cavities confirm that surface
oxygen feels the presence of subsurface cavities and benefits from
lower extraction energy.</p><p>It therefore appears that carefully
chosen intermediate temperature
for heat treatment of known active shapes of nanoceria, e.g., rods
and cubes, can be beneficial to further boost catalytic performance
in those materials.</p><!><p>Statistical analysis of
pore diameters; pore geometries
relative to the nanorods; 3D reconstructions using modified geometric
tomography methods and of a perfect sphere; influence of TEM sample
support; an extensive description of the rationale for modeling (PDF)</p><p>Video S1: dynamics
of atom motion on the modeled nanorod
surface (MP4)</p><p>jp1c01221_si_002.pdf</p><p>jp1c01221_si_001.mp4</p><p>The
authors declare no
competing financial interest.</p>