## 2 Methodology
### Sintering Test  
Sintering of particles into clumps or larger masses would be detrimental in a CSP system since small clumps of particles can clog the PHR, heat exchanger, or other processes, and any large agglomeration of mass in the high-temperature TES would quickly disrupt and deactivate the entire system. The most likely situations for sintering are in the highest-temperature parts of the PHR and in the highest-pressure lower level of the high-temperature TES. In commercial-scale TES bins, pressures up to 1 MPa or more should be expected. Since sintering is promoted by pressure, the TES conditions are likely the most critical. At present, the actual TES pressures cannot yet be reliably specified, nor can the expected residence time for particles in this TES. In any case, long-duration testing of \begin{table}
\begin{tabular}{c c c c} \hline
**Sample** & **Average Particle Diameter [\(\mu\)m]** & **Shape** & **Chemical Composition** \\ \hline RWS & 500 to 1000 & Irregular & 98\% SiO\({}_{2}\), 1.56\% Al\({}_{2}\)O\({}_{3}\), 0.44\% others \\ \hline RWS & 210 to 425 & Irregular & 98\% SiO\({}_{2}\), 1.56\% Al\({}_{2}\)O\({}_{3}\), 0.44\% others \\ \hline RRS & 210 to 425 & Irregular & 90\% SiO\({}_{2}\), 2.93\% Al\({}_{2}\)O\({}_{3}\), 3.15\% Fe\({}_{2}\)O\({}_{3}\), 2.23\% \\  & & & CaSiO\({}_{3}\), and 1.69\% others \\ \hline SOS * & 200 to 500 & Irregular & 59.32\% O, 22.91\% Mg, 12.91\% Si, 4.87\% Fe \\ \hline USOS & 250 to 400 & Irregular & Al\({}_{2}\)O\({}_{3}\), 0.7\% CaO, <0.1\% Ni \& NiO, 0.1\% Cr\({}_{2}\)O\({}_{3}\) \\  & & & and \textless{}0.1\% Trace Elements \& Compounds \\ \hline CB & 300 & Regular & 75\% Al\({}_{2}\)O\({}_{3}\), 11\% SiO\({}_{2}\), 9\% Fe\({}_{2}\)O\({}_{3}\), 3\% TiO\({}_{2}\), & \\  & & & and 2\% others [42] \\ \hline \end{tabular}  
* Energy-dispersive X-ray analysis (Jeol Limited, Akishima, Tokyo, Japan, EDX), together with a scanning electron microscope (Jeol Limited, Akishima, Tokyo, Japan, SEM) both by Jeol Limited (Akishima, Tokyo, Japan), were used to identify the elemental composition of the SOS materials. Qualitative and quantitative analyses were conducted to identify the types of elements that were present, as well as the percentage of each element’s concentration within the sample.  
\end{table} 
Table 2: Particulate materials’ properties. numerous candidate particles at moderate pressures is not currently feasible. Consequently, the development teams have conducted rapid high-temperature and high-pressure testing to quickly screen candidate HTM materials. To investigate the sintering of particulates, the samples were tested in a High-Frequency Induction Heat Sintering Furnace (HFIHS), as shown in Figure 2. In this device, the samples are heated to a desired temperature and then rapidly compressed to a specified pressure. Since this type of testing is relatively unfamiliar, the apparatus and procedure are described below in some detail. In this apparatus, the test sample is placed in a robust high-temperature- and high-pressure-resistant cylindrical graphite die. The inner diameter is 12.7 mm in this case. Two plungers, one from each end, are utilized to consolidate the tested sample, as shown in Figure 2a). To prepare for testing, a small, 1.0 g sample of the solid particulate is loaded into the die, and the plungers are inserted until they touch the sample. Then, the loaded die is placed in the sintering chamber of the HFIHS, as shown in Figure 2c, and the chamber is evacuated. At this point, the apparatus is ready for testing. In a typical test, the electrically conductive graphite die, along with the sample, is rapidly heated (100-150 \({}^{\circ}\)C/min) by induction from the ambient temperature to the test temperature. To prevent actual melting, the temperature in the chamber is typically kept at less than 75% of the melting point of the material being processed. Subsequently, uniaxial pressure is applied by the piston seen in Figure 2 in 10 kPa steps until the ultimate test pressure, 20-50 MPa, is reached or until sintering is automatically detected.