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.


Main manuscript: ACS, Journal of Physical Chemistry C, doi.org/10.1021/acs.jpcc.1c01221
In this supplementary information, we report further details concerning background information behind the figures in the main manuscript. (i) A statistical pore size analysis to put into context the chosen pores for tomographic analysis, which are confirmed as of "typical" size ( Fig SI-1

) (ii)
A further micrograph confirming the well-facetted nature of pores and their alignment to the main rod axes (Fig SI-2), as well as the formal relationship of pores and building blocks within Oriented Attachment growth. Profile analysis, geometric tomography, and shape-from contour methods applied to ceria nanorods. These results confirm the findings reported throughout the paper. The reconstructions in Figs SI-5 -SI-7 are also meant to present the advantage of using binarized images or even contour methods for efficiency. (v) Example images about TEM sample support, Fig SI-8, carbon vs Si-nitride.
(vi) An extensive Rationale behind the simulations presented in the main manuscript. (Figs SI-9 to Si-12) (vii) A video file of the dynamics of atom motion on the modelled nanorod surface is provided (outside this word-document), to accompany Figs SI-9 to SI-12. The video file is uploaded alongside the supporting information. Each of our facetted voids can be (formally) exchanged for one "building block" of the OA-growth mechanism. Not to scale (regular hexagons used for simplicity).

Supplementary Experimental Figures:
Orange arrows indicate parallelity of rod faces (horizontal blue lines), lattice fringes and void facet direction.

Simulation Rationale and Supplementary Computational Figures:
Most simulations proceed by generating a model structure, which is then used to predict properties. For example, one might generate a model of a nanorod using crystallographic data and manually introduce voids into the rods as seen experimentally. However, real ceria nanorods are never pristine; rather they likely comprise a rich microstructure, such as polar CeO2(100) and non-polar CeO2 (111) surfaces, edges where two surfaces meet, surface steps and corners together with point and extended defects. Such structural features are metastable and intrinsically of high energy compared to the perfect, pristine nanorod. We postulate that voids emanate from high-energy microstructural 'active sites' because the activation energy barriers associated with their evolution is likely lower from a highenergy state compared to evolution from the thermodynamically low energy structural configurations associated with the pristine parent material.
To increase the probability of simulation being able to 'observe' (predict) mechanisms underpinning void formation, one must capture this rich microstructure within the model. However, it is very difficult to 'manually' introduce a complex microstructure that accord with the real material within a single model. Here, we achieve this by simulating, in part, the experimental method of nanorod fabrication. In particular, real ceria nanorods emanate from some kind of crystallisation process during synthesis and it is this process that endows nanorods with rich microstructures. Accordingly, we generate atom level models of nanorods by simulating crystallisation using methods we developed previously 1,2

Generating Atomistic Models
A nanoparticle of CeO2 comprising 15,972 atoms (5324 Ce, 10648 O) was melted at 8000K using Molecular Dynamics simulation, MD, and cooled to 3750K. The nanoparticle was then placed in a simulation box, while imposing periodic boundary conditions. One of the dimensions of the box was then reduced to enable cluster-cluster interactions along one direction. Under MD simulation, performed at 3750K, the nanoparticle agglomerated with its (periodic) neighbour to form an amorphous nanorod. Starting from this amorphous nanorod precursor, MD simulation within an NVT ensemble (constant Number of atoms, Volume and Temperature) was performed for 2 ns at 3400K. At a particular instant in time a crystalline seed spontaneously evolved within the amorphous sea of Ce and O ions. This seed then propagates the crystallisation of the rod as amorphous ions, at the crystalline-amorphous interface, move to lattice positions on the surface of the seed. The model resulting from this procedure is shown in fig. SI-7  • Structural rearrangements to quench the dipole associated with {100} surfaces. All these structural features are observed in real ceria nanorods. In particular, that simulation is able to capture these features, without any a priori information (i.e. starting from an amorphous precursor) by simulating both the kinetics and thermodynamics of the non-equilibrium crystallisation processes that operate, provides strong evidence of its capability. Accordingly, we can have confidence in using the model to simulate processes, such as void evolution and properties including changes in catalytic activity.

Void Evolution Mechanism
The images presented, figs SI 9-12, represent low-temperature model structures of the ceria nanorods. The models were then used to simulate (experimental) annealing by performing MD simulation at high temperature. Analysis of the MD trajectories reveals substantial mobility of both Ce and O ions on {100} and {110} surfaces, steps, edges and corners. In comparison, little ionic mobility was observed on {111} plateau regions. An animation showing the mobility of oxygen (coloured red) and cerium (coloured blue) on the surface of a ceria nanorod is deposited as SI. Ionic mobility is associated with atoms moving off their lattice sites creating vacancies. The vacancy is able to migrate deeper within the nanorod when subsurface atoms migrate to the surface to fill surface vacancies. The mobility is vacancy driven and we observed concerted motion analogous to that we observed previously in BaF2 and CaF2, which also conform to the fluorite structure 7 . Preferential migration of ions on {100}, {110} surfaces and surface steps, compared to {111}, to form a vacancy is expected because the energy required to form a vacancy on {111} surfaces is higher than on {100}, {110} and stepped sites 8 . Additional simulations reveal that ionic mobility increases when cerium is reduced to Ce 3+ (together with charge compensating oxygen vacancies). This accords with experiment, which showed that cationic mobility on ceria {100} surfaces is higher when the surface is reduced compared to when it is fully oxidised 4 . This work will be presented in more detail in a later paper. In summary, our simulations predict that • Ce and O vacancies evolve spontaneously on high-energy ceria nanorod surfaces and steps.
• Vacancy formation is expediated when Ce 4+ is reduced to Ce 3+ .
• Ce and O vacancies diffuse deeper into the nanorod via a concerted mechanism.
• Ce and O vacancies in the nanorod agglomerate to form larger voids.
• Voids in the model evolve into polyhedral morphologies with {111} surfaces truncated by {100} and {110} (internal surfaces) -observed in our experiments in this study.
• {111} (internal) surfaces of voids in the model nanorod align with {111} (external) surfaces of the nanorod -observed in our experiments. Such close accord with experiment increases confidence that the simulation is able to predict the mechanism of void evolution within the rods, which is difficult to elucidate experimentally. Specifically, we predict that, under annealing conditions, voids in ceria nanorods, via spontaneous vacancy formation on high-energy surfaces. The vacancies then diffuse into the nanorod, and agglomerate into voids.

Outlook
In addition to modelling void evolution, we predict a change in catalytic activity as a consequence of the voids. Specifically, we find that the energy required to extract oxygen from the surface, to participate in an oxidative catalytic reaction, is influenced by the presence of the voids, fig 9. Previously, simulation showed that surface stability and vacancy energies are directly linked with catalytic activity 8 and helped establish the concept of 'reactive surfaces'. Although the paper was published over 25 years ago it shows that simulation is able to reliably provide fundamental scientific insight that has remained relevant and insightful today. More recently, Aryanpour and co-workers showed 9 that the "energy for oxygen vacancy formation is a simple yet powerful activity descriptor." We advocate that it is reasonable to use such methods to predict that voids confer catalytic activity changes upon nanorods. Accordingly, mechanistic insight and understanding of void evolution will enable their control, facilitating tuneable properties via structural engineering.  [110] (110 )