## 3 Results and Discussion
The thermal properties are governed by the heat transport within the sample, as well as by the ability of the sample to exchange heat with the surroundings. Loading of Cu particles clearly increased both the material's thermal diffusivity and thermal conductivity, since the heat transport within the modified material occurs through the network of metal particles. Copper is characterized by a higher thermal conductivity compared to TiO\({}_{2}\). For example, the thermal conductivity of Cu is over 40 times higher (\(\sim\)400 W/mK) than the thermal conductivity of TiO\({}_{2}\) (9.4 W/mK, as determined for TiO\({}_{2}\) powders in this work). Therefore, already a small amount of added Cu (0.05%) increased the thermal conductivity of the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & **Thermal Diffusivity,** & **Thermal Conductivity,** & **Carrier** & **Indirect Band** \\  & **mm\({}^{2}\) s\({}^{-1}\)** & **Wm\({}^{-1}\) K\({}^{-1}\)** & **Lifetime, ns** & **Gap, eV** \\ \hline TiO\({}_{2}\) & 7.58 \(\pm\) 0.04 & 9.35 \(\pm\) 0.11 & 382 \(\pm\) 10 & 3.25 \(\pm\) 0.15 \\ TiO\({}_{2}\)/Cu (0.05\%) & 8.05 \(\pm\) 0.11 & 10.15 \(\pm\) 0.22 & 302 \(\pm\) 4 & 2.90 \(\pm\) 0.10 \\ TiO\({}_{2}\)/Zr (1\%) & 7.68 \(\pm\) 0.03 & 9.65 \(\pm\) 0.08 & 362 \(\pm\) 8 & 3.15 \(\pm\) 0.10 \\ TiO\({}_{2}\)/Cu (0.05\%) & 7.80 \(\pm\) 0.04 & 9.95 \(\pm\) 0.21 & 328 \(\pm\) 4 & 2.85 \(\pm\) 0.05 \\ Zr (1\%) & & 95\% CI & & \\ TiO\({}_{2}\) & [7.51; 7.65] & [9.16; 9.54] & & \\ TiO\({}_{2}\)/Zr (0.05\%) & [7.86; 8.24] & [9.78; 10.52] & [295; 308] & [2.83; 2.97] \\ TiO\({}_{2}\)/Zr (1\%) & [7.63; 7.73] & [9.52; 9.78] & [349; 376] & [3.08; 3.22] \\ TiO\({}_{2}\)/Cu (0.05\%) & [7.73; 7.87] & [9.6; 10.3] & [321; 335] & [2.82; 2.88] \\ Zr (1\%) & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Values of the thermal, optical and transport properties for the unmodified and Cu- and/or Zr-modified TiO\({}_{2}\) from the best fits between the experimental and theoretical data. Figure 9: The amplitude (**a**) and phase (**b**) of BDS signal for unmodified and Zr- and/or Cu-modified TiO\({}_{2}\) samples. Points represent the experimental data, whereas continuous lines are the best linear fits to the experimental data by the model presented in [22]. The RSD% for the average of 3 measurements is 1-2%. material. On the other hand, due to the relatively small difference between TiO\({}_{2}\) and Zr (thermal conductivity \(\sim\)23 W/mK), the determined value of thermal conductivity did not change beyond the range of determination error by the addition of 1% Zr when compared to TiO\({}_{2}\) and TiO\({}_{2}\)/Cu (0.05%). It must be stated that the sample preparation process (pressing of nanopowders) changed its original thermal properties. Generally, pressing increases the compactness of a material and thus also increases the thermal conductivity, leaving the optical and transport properties unchanged (band gap and carrier lifetime) since the original structure of the nanomaterial is not changed by the formation of pellets. Comparison of the optical properties determined by BDS for different TiO\({}_{2}\)-based materials showed that the optical absorption properties were significantly affected (95% CI) only in the case of modification by Cu (0.05%), which caused a 9.5-10.8% decrease in the band gap as compared to the pure TiO\({}_{2}\) or Zr-modified TiO\({}_{2}\). It can be also seen that the standard deviations of the measurements in the case of BDS (1-2% RSD) are much lower than for UV-Vis spectrophotometry (6.3-7.8% RSD). This is the consequence of BDS' independence on light scattering, which is not the case for UV-Vis spectrophotometry. Nonetheless, the values of indirect band gaps determined by the BDS and UV-Vis techniques are in good agreement at 95% CI. Still, the differences in band gaps between materials could only be confirmed by BDS.