Density Measurements of Molten LiF–BeF2 and LiF–BeF2–LaF3 Salt Mixtures by Neutron Radiography

The densities of eutectic (LiF)2–BeF2 and mixtures of this salt (FLiBe) with LaF3 were measured by dilatometry and by neutron attenuation from 673 K to 1,073 K. Because LaF3 has a limited solubility in FLiBe, it was necessary to determine the amount of LaF3 in solution before the density could be determined. The FLiBe density determination was favorably benchmarked against the literature data. A simple comparison was not available for the LaF3–FLiBe mixtures, so extrapolation of published data was necessary based on analysis using the Molten Salt Thermal Properties Database-Thermochemistry, or MSTDB-TC, developed by the US Department of Energy. Solubilities for LaF3 in FLiBe ranged from 1 to 4 mol % over 673 to 1,073 K. The salt system was heated and cooled over 24 h to evaluate potential changes in composition and hysteresis during the measurement. Changes in the meniscus were observed, and these were included in the correction for density determinations. Salt surface tension may have led to supersaturation of LaF3 in the salt because the solubility curve was nonlinear with respect to the inverse temperature, as would be expected for an ideal system. Surface tension measurements are currently underway to test this hypothesis.


SI-1. Neutron Radiography Data
Figure S1 shows a selection of neutron radiography images taken during the heating and cooling processes.Measurements were collected in increments of 100 K from 773 K to 1,073 K for the heating process, shown in Figures S1 (a)-S1(d), and from 1,073 K to 773 K for the cooling process, shown in Figures S1 (e)-S1 (g).The samples were loaded in FLiBe with 20 wt % LaF 3 or mixture 2 (left) and 10 wt % LaF 3 or mixture 1 (right), and neat FLiBe was measured as a reference (middle).Figure 3 shows the transmission profile at each temperature from Figure S1, with solid and dotted lines indicating the heating and cooling processes, respectively.The neutron radiographs for the FLiBe sample only showed subtle changes during the temperature ramp from 773 K to 1,073 K. Radiographs taken at each temperature are shown in Figure S2.

SI-2. Calculation of FLiBe Density from Volume
To calculate the total volume of the FLiBe, the FLiBe is divided into three regions.Region 1 is the region from the top of the meniscus to the bottom of the meniscus.Region 2 is the region from the bottom of the meniscus to the top of the curved section at the bottom of the V can.Region 3 is the curved portion at the bottom of the can.Each of these regions is defined by the height of the region, h, measured in pixels, and the pixel diameter of the V can, d p .The total volume, in pixels 3 , is then defined by To convert the volume from pixels 3 to cm 3 , the inner diameter of the can was used as a reference.The inner diameter, d 0 , of several vanadium cans were measured at 20⁰C.The diameter of the cans at temperature, T, can then be calculated from the coefficient of thermal expansion by The value of α, in K -1 , as a function of T, in units of K, is given by the following relation [27] The total volume, in cm, is then defined by The density is then the mass divided by volume and can be written as The overall error of the density calculation is defined by the standard error propagation formula for N number of variables, v, each with some error, σ.
Each of the derivative terms in the error propagation formula is given by The measurement or calculation error for each of the variables is shown in Table S1.Height of region 2 (primary cylinder) 5 pixels ℎ 3 Height of region 3 (bottom of the can) 5 pixels

SI-3. Calculation of Mixture Densities
The densities FLiBe and FLiBe + LaF 3 were calculated by arithmetic mean or by the Redlich-Kister model.The end point densities were taken from the Janz compilation for fluoride salts [29].These included the endpoint members LiF, BeF 2 , and LaF 3 .Density of LaF 3 -LiF pseudobinary mixtures are compiled from Janz [28] in Table 1. Figure S3 shows FLiBe density comparison with Cantor's experimental data [39,40] and ideal/RK models calculated by Birri et al. [33].Using values in Table 1, we performed RK modeling on LaF 3 -LiF molten salt pseudobinary.Both the ideal behavior and the RK modeled densities lie within 2% of the Table S1 experimental data.However, is is apparent that the values for pure LiF in Table S1 are not in good agreement with those reported by Cantor [39].Both equations apply to higher temperatures than measured in this work.

Figure S2 .
Figure S2.The mapping of neutron attenuation on the radiographs of the FLiBe sample for the four hold temperatures spaced 100 K apart.

Figure S7 .
Figure S7.Effect of UF 4 on the solubility of CeF 3 in LiF-BeF 2 (62-38 mol %) as reproduced from Ward et al. 1965 [38].The solvent composition was calculated from average values of filtrate analyses.