## 3 Results and Discussion
### Thermal Conductivity  
The results of thermal conductivity for all samples at ambient temperature are summarized in Table 6. It should be noted that the pellets were held at 500 \({}^{\circ}\)C for 5 h in an electrically heated clean-air muffle-type furnace [53] in order to remove any impurities left after processing. \begin{table}
\begin{tabular}{c c} \hline
**Sample** & **Thermal Conductivity [W/mK]** \\ \hline RWS & 0.267 \(\pm\) 0.02 \\ \hline RRS & 0.260 \(\pm\) 0.02 \\ \hline CB & 0.202 \(\pm\) 0.02 \\ \hline SOS & 0.217 \(\pm\) 0.02 \\ \hline USOS & 0.155 \(\pm\) 0.02 \\ \hline \end{tabular}
\end{table} 
Table 6: Measured bulk thermal conductivity of particulate materials at ambient temperature using KD2-Pro. Figure 4: The condition of USOS after sintering at (a) 800–1000 \({}^{\circ}\)C, (b) and (c) at 1100 \({}^{\circ}\)C.  
The temperature-dependent thermal diffusivity (\(\alpha\)) in [mm\({}^{2}\)/s] of pelletized samples of RWS, RRS, SOS, and CB is presented in Figure 5 over a temperature range of 25 \({}^{\circ}\)C to about 475 \({}^{\circ}\)C. The thermal conductivity (\(k\)) [W/mK] is also presented, which is calculated based on the thermal diffusivity, density, and specific heat, as mentioned in Equations (1)-(3). Note that while measurements of thermal diffusivity and data for the specific heats are available over the entire temperature range, only ambient-temperature density is available. No suitable apparatus for measuring the density change was available; however, the density change is expected to be very small and is estimated to cause less than 1.0% variation in the calculated thermal conductivity. This variation is entirely negligible compared with the approximately \(\pm\)60% variation in conductivity seen in Figure 5.  
Figure 5 illustrates the temperature dependence of the measured thermal diffusivity and the calculated thermal conductivities of the four pelletized samples. The thermal diffusivity values at low temperatures are all grouped from 1.2 to 1.6 mm\({}^{2}\)/s and are mostly grouped from 0.2 to 0.8 at the highest temperature. The diffusivity trends lower with temperature for all samples at similar gradients over most of the range. This trend is most likely caused by the expected decrease in thermal conductivity for solid particles in all these somewhat solidified pellets. The calculated thermal conductivities inferred from the measured diffusivities of all materials do show the expected decrease. Based on a comparison of CB with polycrystalline alumina, the conductivities appear to be about one order of magnitude lower than the conductivity of a fully dense crystalline solid, confirming that the pellets are not overly densified. The uncertainties associated with all experimentally measured quantities were carefully evaluated. For parameters with only  
Figure 5: Thermal diffusivity (\(\alpha\)) from LFD measurements and dependent calculated (\(k\)) thermal conductivities for four pelletized particulates. two available measurements, such as thermal diffusivity, the uncertainty was estimated using the half-range method, calculated as half the difference between the maximum and minimum recorded values. This approach provides a practical estimate of uncertainty when limited data points are available and aligns with the Type B evaluation method described in the _Guide to the Expression of Uncertainty in Measurement_[54]. For thermal conductivity, the uncertainty was determined using uncertainty propagation techniques, taking into account the contributions from the uncertainties in thermal diffusivity, specific heat, and density. The conductivity of the HTM will impact the size and cost of the particle-to-fluid heat exchanger (PFHX) in a CSP system. Since Figure 5 indicates the decrease in thermal conductivity at high temperatures for all the samples, that means a bigger PFHX will be needed to operate at higher temperatures. However, particles in the PFHX will be in a moving bed or other type of flow, and the thermal conductivity in such a bed or flow cannot yet be reliably predicted.