## 2 Protocols for Synchrotron X-Ray Experiments
### Saxs
#### 2.6.4 Interpreting the Results and Validation  
The corrected scattering profiles often display characteristic features that reflect the particle size distribution. For instance, Figure 14 illustrates a typical scattering intensity profile of carbon-supported Pt catalysts recorded at BL40B2, along with simulated profiles of spheres with similar diameters. In the observed curve, a shoulder-like feature around \(Q\approx 1.0\) nm\({}^{-1}\) (the Guinier region) can be seen, representing the average diameter of the Pt particles. A uniform particle size distribution produces clear oscillations in the scattering curve; however, the observed curve in Figure 14 does not show such oscillations, indicating a broad particle size distribution.  
Additionally, in the low-\(Q\) region, the observed curve shows an increase in intensity due to strong scattering from the Pt particles, which is significantly higher than that from  
Figure 14: Measured and simulated scattering intensity profiles of Pt catalysts. The green curve shows experimental data for carbon-supported Pt catalysts (TEC10V30E, supplied by TANAKA Precious Metals), while the blue and red curves represent simulated profiles of Pt catalysts without carbon support, sharing an identical mean particle radius (1.33 nm). Varying the radius distribution (standard deviations of 0.05 and 0.38 nm) illustrates the effect of particle size dispersion on the scattering profile.  
the carbon support. In the example shown in Figure 14, Vulcan 72\({}^{\text{TM}}\) is used as the carbon support, and the scattering slope is smaller than \(-4\) in the log-log plot. This slope suggests that the Pt particles formed a shell-like structure on the surface of the carbon spheres. When mesoporous carbon supports such as CNNovel\({}^{\text{TM}}\) are used, the Pt particles are likely to form solid spheres embedded within the carbon, resulting in a slope closer to \(-4\). Understanding these variations helps clarify the structural relationship between the Pt particles and their carbon supports.  
To further validate the particle size distributions, advanced software tools such as McSAS (version 1.3.1) were used to analyze the scattering data. For example, Figure 15 shows the McSAS output for the scattered data shown in Figure 14. The left panel depicts the measured scattering profile (black) and the fitted curve (red), whereas the right panel shows a histogram of the particle size distribution. In this analysis, a Gaussian distribution fit reveals that the mean particle radius is 1.33 \(\pm\) 0.38 nm, highlighting the utility of SAXS data for precise particle characterization.  
Validation of the SAXS analysis is critical for ensuring reliability. One method is to compare the simulated scattering profiles of the model particles with the experimental results, as shown in Figure 14. Another approach involves cross-referencing SAXS-derived size distributions with transmission electron microscopy (TEM) images. Studies conducted during the NEDO project find good agreement between McSAS fittings and TEM observations [38], thereby confirming the robustness of the SAXS protocol for analyzing Pt catalyst nanoparticles.