## 3 Results and Discussion
Figure 2: Diffraction patterns of ceria nanoparticles in (**a**) TT-25, (**b**) TT-300, (**c**) TT-600, (**d**) TT-900 and (**e**) TT-1100 samples. The results of the SEM measurement can be seen in Figure 4. All pictures were captured with a magnification of 1300x. It is evident that the objects formed by the nontreated nanoparticles (Figure 4a) were finer and looser. With the increasing temperature, the nanoparticles conglomerated, forming bigger aggregates. However, it was difficult and almost impossible to determine the absolute size of the objects. Needless to say, the size of the formed objects was not uniform, but in general, when observing the treated samples, it was almost impossible to find such fine objects as in Figure 4a. Additionally, if we focus on the morphology of the TT-1100 sample shown in Figure 4e, we can see significant differences in comparison with the previous samples. Both of these effects had an impact on the surface area of the nanoparticles, which will be discussed later. Figure 4: (**a**) SEM image of sample TT-25, (**b**) SEM image of sample TT-300, (**c**) SEM image of sample TT-600, (**d**) SEM image of sample TT-900 and (**e**) SEM image of sample TT-1100. Figure 3: Crystallite sizes in directions of the (220), (111) and (200) crystal planes, and their average values. To directly observe the size and morphology of the nanoparticles, a high-resolution transmission electron microscope (HR-TEM) was used. The measurements of selected samples TT-25 and TT-1100 can be seen in Figure 5, while TEM micrographs of all samples are shown in Figure S1 in Supporting Information. Increasing particle sizes with increasing temperatures were clearly visible. It is significant that the results of both the HR-TEM and SAED measurements were in agreement with the XRD measurements. The BET analysis of the data obtained by a sorption analyzer was used for the nanoparticles' surface area determination. In relation to the catalytic activity of nanoparticles, the specific surface area was the most important quantity. The results of the measurements can be seen in Figure 6. The most significant surface area change appeared for sample TT-300. This effect was a bit contrary to the X-ray diffraction measurements, where the changes in crystallite sizes between the low-temperature treated samples were only minimal. We believe that such a significant drop in surface area is due to dehydration of the surface and subsequent agglomeration or aggregation of ceria nanoparticles. After the first drop in surface area, we could see a quite linear decrease with the increasing temperature of the thermal treatment, corresponding to the crystallite size changes. Between samples TT-900 and TT-1100, we could see again a significant reduction in surface area. This nevertheless corresponded to the crystallite size change, which was unusually large in comparison with previous samples. If we focus on the absolute values of the surface area and crystallite sizes, we can see huge irregularities. These irregularities could be caused by the agglomeration and formation of the large clusters, which were observed by SEM. Figure 5: TEM micrographs and selected area electron diffraction (SAED) for samples (**a**) TT-25 and (**b**) TT-1100. Thin ceria layers prepared on alumina underlays (Figure 7a) and roughened silica glass (Figure 7b) were examined. The layers were sufficiently mechanically stable and, in the reverse horizontal position, no powder fell out of the samples. Similarly, the layers were resistant to laminar water flow. Nevertheless, for practical applications, other ingredients for better fixation of the ceria nanoparticles on the layer may be needed. Samples were also investigated by SEM and EDS. The morphology of the prepared layers with EDS maps of ceria can be seen. In both cases, the surface was relatively covered with similar complex ceria aggregates with apparently large surfaces.