## 2 Synthesis and Characterization of CeO\({}_{2}\) NPs of Different Morphology  
Concerning the preparation of ceria nanoparticles, numerous synthetic routes have been employed, such as thermal decomposition, precipitation, sol-gel, solution combustion, surfactant or template-assisted method, hydrothermal or alcoholothermal method, microemulsion, sonochemical, microwave-assisted synthesis, etc. [75; 76; 77; 78; 79; 80; 81; 82; 83; 84; 85; 86; 87; 88; 89]. Among the different preparation techniques, the hydrothermal method has been widely employed, owing to the short reaction time, the simple precursor compounds utilized, the homogeneous morphology and the development of nanoparticles with well-defined shapes, such as wires, polyhedra, rods, and cubes [71; 75; 76; 81; 82; 95; 100; 101; 102; 103; 104; 105; 106; 107; 108; 109; 110; 111; 112; 113; 114] (Figure 1). In our recent works [33; 34; 35; 38; 39; 75], the hydrothermal method was successfully used in order to prepare three distinct ceria morphologies of well-defined shape, i.e., nanocubes (NC), nanorods (NR), and nanopolyhedra (NP), which are then employed as supporting carriers for various transition metal catalysts (Fe, Co, Ni, and Cu). Figure 2 schematically \begin{table}
\begin{tabular}{c c} \hline \hline
**Adjusted Parameter** & **Main Implications in Physicochemical Properties** \\ \hline Composition & surface area; \\ (e.g., binary or ternary MOs) & structural characteristics \\ \hline Size & surface area; electronic environment; \\ (e.g., metal particles of nanometer size) & coordination environment; \\  & structural defects \\ \hline Shape & energy formation of anionic vacancies; \\ (e.g., nanorods and nanocubes) & redox features \\ \hline Electronic state & work function; \\ (e.g., alkali addition) & redox characteristics \\ \hline Chemical state & redox properties; structural defects; \\ (e.g., incorporation of rGO) & electronic environment \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Adjusted parameters and their implications in the physicochemical characteristics of metal oxides. Figure 1: **(a)** Model shapes of rods and cubes. Reproduced with permission from Reference [115]. Copyright© 2018, Elsevier. **(b)** Model shapes illustrating an anisotropic growth process starting from a truncated cuboctahedron shape. Protecting the [111] facets by using a capping agent results in the growth of [100] facets until they disappear and only [111] facets remain on the surface (octahedral shape). The opposite would result in cubic nanoparticles NPs with only [100] facets. Reproduced with permission from Reference [116]. Copyright© 2015, Elsevier. illustrates the procedure followed for the preparation of CeO\({}_{2}\)-NP, CeO\({}_{2}\)-NR and CeO\({}_{2}\)-NC. Briefly, suitable amounts of cerium nitrate hexahydrate (Ce(NO\({}_{3}\))\({}_{3}\cdot\)6H\({}_{2}\)O) and sodium hydroxide (NaOH) were firstly dissolved in deionized H\({}_{2}\)O, mixed under continuous stirring for 1 h, and finally aged at 180 \({}^{\circ}\)C for 24 h (for cubes) or at 90 \({}^{\circ}\)C (for rods and polyhedra). The precipitates obtained by centrifugation were washed several times with deionized H\({}_{2}\)O and finally with C\({}_{2}\)H\({}_{5}\)OH, to prevent agglomeration. The obtained precipitate was finally dried and calcined for 2 h, at 500 \({}^{\circ}\)C.  
Ceria-based transition metals, i.e., Fe, Co, Ni, and Cu, were next prepared through wet impregnation, employing the corresponding aqueous nitrate precursors. In all cases the metal/Ce atomic ratio was kept constant at 0.25. Suspensions were dried at 90 \({}^{\circ}\)C and finally calcined for 2 h, at 500 \({}^{\circ}\)C. The as-prepared materials are denoted for convenience as M/CeO\({}_{2}\)-NC, where M = Cu, Co, Ni, and Fe, whereas NX stands for nanorods (NR), nanocubes (NC) and nanopolyhedra (NP).