## 2 Methodology
### Thermal Conductivity Measurement & Calculation  
The bulk thermal conductivity of the candidate particulate materials at ambient temperatures was measured using a KD2 Pro thermal conductivity analyzer supplied by Decagon Devices Inc., Pullman, WA, USA [45]. This instrument implements the transient line source measurement. This instrument was calibrated using distilled water at ambient temperature. This test was conducted at ambient temperature. The particulate sample was first filled in a glass cylinder and then a KD2 Pro needle was inserted into the sample. The reading was recorded once the analyzer completed the transient measurement and related calculations. For the accuracy of the results, three measurements were carried out at different times.  
In the case of determining the bulk thermal conductivity at high temperatures, an indirect method was used. The thermal diffusivity of the samples was measured first by the transient laser flash method [46; 47]. This apparatus is not suited for loose particles; so, sintered pellets or discs were used. The pellets, which were agglomerated during the sintering process, were in a state intermediate to the solid material and the loose particles, but these were the best available upper-bound approximation to the conductivity of particle beds in a CSP system. To this effect, particulate samples were slightly sintered at high temperature and pressure in the HFHS, as described above, to obtain a disc-shaped pellet of bonded particles. The sintered samples were then sized to the pan dimensions of the machine by cutting and polishing the samples using a Dremel tool 4000-4/34 by KVM Tools Inc., Cypress, TX, USA [48] and fine-grit SiC abrasive paper, respectively. Bulk density at ambient temperature was measured using an Electronic Densimeter SD 200L by Alfa Mirage Co. Ltd., Osaka, Japan [49] with a density resolution of up to 0.0001 units. Thermal diffusivity was measured using a laser flash apparatus (LFA 457) by [PERSON], Selb, Germany [46; 47]. It was measured at different temperatures starting from ambient temperature up to 475 \({}^{\circ}\)C.  
Thermal conductivity (\(k\)) in W/mK was then calculated as follows:  
\[k=\alpha\;\rho\;C_{p} \tag{1}\]  
where \(\rho\) is the density in kg/m\({}^{3}\), \(\alpha\) is the thermal diffusivity in m\({}^{2}\)/s, and \(C_{p}\) is the specific heat in J/kgK.  
Since silica (SiO\({}_{2}\)) is by far the dominant ingredient of both RRS and RWS, it is assumed that the specific heat for both of them is the same as that of SiO\({}_{2}\). To calculate the specific heat of SiO\({}_{2}\), [PERSON] [50] suggested the following relation:  
\[C_{P_{\text{RWS,RRS}}}=\text{A}+\text{B}T+\text{C}T^{2}+\text{D}T^{3}+\text{E} /T^{2} \tag{2}\]  
where A = \(-\)101.134, B = 4188.707, C = \(-\)5405.677, D = 2805.398, E = 0.042407, and \(T\) is the particulate temperature in Kelvin/1000. \(C_{P_{\text{RWS,RRS}}}\) represents the specific heat of RWS and RRS in J/kgK.  
At Sandia National Laboratories, the specific heat of CB was measured with the application of differential scanning calorimetry. [PERSON] et al. [51] developed the following relation for the calculation of the specific heat of CB:  
\[\text{C}_{PCB}=0.365~{}T^{0.18} \tag{3}\]  
where C\({}_{PCB}\) is in kJ/kgK, and \(T\) is the CB temperature in K, which falls between 50 \({}^{\circ}\)C and 1100 \({}^{\circ}\)C.  
The specific heat of SOS was measured using a STA 409C/CD apparatus by [PERSON], Selb, Germany [52], which is based on differential scanning calorimetry. The measurements were carried out from room temperature to 1200 \({}^{\circ}\)C.  
These measurements and research sources resulted in the needed density, specific heat, and thermal diffusivity data.