## 2 Materials and Methods
### Catalysts Characterization  
Powder X-ray diffraction patterns were recorded using a Scintag X1 diffractometer equipped, with a Cu K\(\alpha\) (\(\lambda\) = 1.5418 A) source and the Brag-Brentano \(\theta\)-\(\theta\) configuration in the 2\(\theta\) range 20-80\({}^{\circ}\), with 0.05 step size and 3 s acquisition time. The NiO crystallite sizes were estimated by Scherrer Equation (1), where: \(D\) is the crystallite size in nm, \(K\) is the crystallite-shape factor, \(\lambda\) is the X-ray wavelength, \(\beta_{D}\) is the full-width at half maximum in radians, and \(\theta\) is the Bragg angle. \[D=\frac{K\lambda}{\beta_{D}cos\ \theta} \tag{1}\]  
The lattice constant (\(\alpha\)) of CeO2 was calculated by the following Equation (2):  
\[\alpha=\frac{\lambda}{2 sin\ \theta}\sqrt{h^{2}+k^{2}+l^{2}} \tag{2}\]  
The supports and catalysts XRD patterns were further elaborated by the Williamson plot to obtain the effects of size and strain in the CeO2 crystals. The full width at half maximum \(\beta_{T}\) of the diffraction peak is ascribed to the broadening effect of both the crystallite size \(\beta_{D}\) and the lattice strain \(\beta_{s}\), arising from strain-induced broadening \(\epsilon\), according to the following Equations (3) and (4)  
\[\beta_{T}=\beta_{D}+\beta_{S}=\frac{K\lambda}{Dcos\ \theta}+4\epsilon\ tan\ \theta \tag{3}\]  
\[\beta_{T}cos\ \theta=\frac{K\lambda}{D}+4\epsilon\ sin\ \theta \tag{4}\]  
The N\({}_{2}\) adsorption-desorption isotherms of the samples were obtained at \(-196.1\)\({}^{\circ}\)C using a Micromeritics Gemini V apparatus. Prior to measurement, the samples were heated at 300 \({}^{\circ}\)C for 4 h in He. The specific surface area (SSA) was calculated by the Brunauer-Emmet-Teller (BET) method in the equilibrium pressure range of 0.05 \(<\) p/p\({}^{\circ}\)\(<\) 0.3. The pore size distribution was obtained from the branch of the desorption isotherm using the Barrett-Halenda (BJH) method. The total pore volume was calculated from the maximum adsorption point at p/p\({}^{\circ}\) = 0.98. Temperature-programmed reduction (TPR) and temperature-programmed desorption (TPD) of H\({}_{2}\) were performed using a Thermo Scientific TPDRO1100 flow-through apparatus. Before the experiments, the calcined sample was placed into a quartz reactor, and pre-treated flowing 20 cm\({}^{3}\) min\({}^{-1}\) of 5% O\({}_{2}\)/He gas mixture at 500 \({}^{\circ}\)C for 1 h, and cooled down to 50 \({}^{\circ}\)C. TPR was conducted by flowing 30 cm\({}^{3}\) min\({}^{-1}\) of 5% H\({}_{2}\)/Ar gas mixture, raising the temperature up to 1000 \({}^{\circ}\)C, with a heating rate of 10 \({}^{\circ}\)C min\({}^{-1}\). For TPD experiment, the calcined sample was pre-reduced flowing 30 cm\({}^{3}\) min\({}^{-1}\) of 5% H\({}_{2}\)/Ar gas mixture up to 500 \({}^{\circ}\)C for 1 h, then cooled down to 50 \({}^{\circ}\)C. The H\({}_{2}\) physisorbed was removed flowing 30 cm\({}^{3}\) min\({}^{-1}\) of Ar for 1 h, then the temperature was increased up to 500 \({}^{\circ}\)C, with a heating rate of 10 \({}^{\circ}\)C min\({}^{-1}\). The H\({}_{2}\) consumption/chemisorption was measured by a TCD detector, calibrated by reducing a known amount of CuO (99.99% purity from Sigma Aldrich). A trap removed the H\({}_{2}\)O generated in the reduction before flowing into the TCD detector.