AND RELATED METHODS

PRIORITY CLAIM

This application claims the benefit of the filing date of United States Provisional

Patent Application Serial No. 62/480,745, filed April 3, 2017, for "Radioactive Tracer Dilution Technique for Determining Molten Salt Mass."

STATEMENT REGARDING FEDERALLY SPONSPORED RESEARCH OR DEVELOPMENT

This invention was made with government support under Contract Number

DE-AC07-05ID14517 awarded by the United States Department of Energy. The government has certain rights in the invention. TECHNICAL FIELD

Embodiments of the disclosure relate to methods for determining the mass of a material. More specifically, embodiments of the disclosure relate to methods for determining the mass of a liquid, such as a molten salt in a container with a non- geometrically shaped cavity and unknown volume.

BACKGROUND

Electrochemical recycling is a group of technologies that has been developed to separate actinide components from spent nuclear fuel. An integral part of the separation process involves electrorefining the spent nuclear fuel in a high temperature molten salt containing the spent nuclear fuel. Electrorefining includes refining a metal in an electrochemical cell containing the molten salt, wherein the impure metal is used as the anode and the refined metal is deposited on the cathode. When electrorefining uranium, the nature of the electrochemical recycling process requires the total concentration of uranium and transuranic isotopes in the molten salt to be up to 9.0 wt%. The transuranic isotopes are mainly plutonium with minor quantities of americium, neptunium, and curium.

Measuring the molten salt mass in an electrorefiner (e.g., the electrochemical cell) is a critical step to safeguard electrochemical recycling plants through nuclear material accountancy. The inventory of transuranic isotopes in the molten salt is an important key measurement point for the International Atomic Energy Agency to conduct nuclear material accountancy for its verification activities essential for international safeguards. Accounting for the nuclear material inventory requires knowing the concentrations of nuclear materials in the molten salt and the mass of the molten salt. A similar mandate by the International Atomic Energy Agency or by others would apply to molten salt nuclear reactors when they become commercially available.

A much-needed measurement technology to determine the molten salt mass is yet to be developed. Presently, determining the molten salt mass in an electrochemical cell, for example, includes measuring the molten salt liquid level, defining the salt volume through the measured liquid level and a pre-established volume calibration curve for the particular electrochemical cell and associated components thereof, and estimating salt density to calculate the salt mass. However, this method results in a high degree of uncertainty in the salt mass determination because of limitations, including challenges in determining the volume of a container with a non-geometrically shaped cavity such as the electrochemical cell, which also usually includes numerous components (e.g., electrodes, sensors, mixers, scrapers, etc.) of unknown volume and non-geometric shapes within the container as well. Another limitation is the development of the volume calibration curve using measurements at room temperature, which would not reflect, for example, the thermal expansion that would occur at the high temperatures at which an electrorefiner operates (for example, 500°C). Furthermore, the salt density varies as the concentrations of actinides and fission products dissolved in the salt changes. In addition, the temperature of the molten salt increases a difficulty of making such measurements.

DISCLOSURE

An embodiment of the invention relates to a method for determining molten salt mass in a container with a non-geometrically shaped cavity using a radioactive tracer dilution technique. The method includes the acts (e.g., steps) of adding a known amount of a radioactive isotope tracer with known activity into the molten salt, mixing the radioactive isotope tracer with the molten salt until homogeneous, obtaining a sample of the resulting mixture, measuring the activity of the sample, and calculating the molten salt mass using radioactive isotope tracer dilution analysis.

An embodiment of the invention may also include using ⁶⁰ Co, ²⁴ Na, ⁵⁸ Co, ⁸² Br, ²² Na, ⁸⁴ Rb, ⁸⁶ Rb, or ¹⁶⁸ Tm as the radioisotope in the radioactive isotope tracer. The compound containing the radioactive isotope tracer may be in a salt such as the fluorides, chlorides, bromides, iodides, and combinations thereof depending on the physical and chemical properties of the molten salt to be measured. In other words, the radioactive isotope tracer may be selected from the group consisting of a fluoride salt, a chloride salt, a bromide salt, an iodide salt, and combinations thereof. For example, C0CI2, KBr, NaCl, RbCl, NaF, NaBr, Nal, or TmCh may be used.

An embodiment of the invention may also include using gamma spectrometry to measure the activity. The gamma-ray spectrometry may be performed using a high purity germanium (HPGe) detector. Other methods may be utilized to measure the activity using chemical analysis, spectroscopy, or another means.

Another embodiment of the invention may also include adding a known amount of a radioactive isotope tracer with known activity into a liquid into which another material has been dissolved, mixing the radioactive isotope tracer with the liquid until homogeneous to form a mixture, obtaining a sample of the resulting mixture, measuring the activity of the sample, and calculating the mass of the mixture using radioactive isotope tracer dilution analysis.

According to other embodiments, a method for determining a mass of a molten salt in a container comprises adding an amount of a radioactive isotope tracer with known activity and known mass into a molten salt in a container, mixing the radioactive isotope tracer with the molten salt to form a mixture, obtaining a sample of the mixture, weighing the sample, measuring the activity of the sample using gamma spectrometry, and calculating the molten salt mass based, at least in part, on the weight of the sample and the activity of the sample.

According to other embodiments of the disclosure, a system for determining a mass of a molten salt comprises an electrochemical cell comprising a molten salt, one or more spent nuclear fuels in the electrochemical cell, and a radioisotope tracer disposed substantially uniformly throughout the molten salt.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a simplified cross-sectional view of a system for electrorefining spent nuclear fuel or another material, in accordance with embodiments of the disclosure;

FIG. 2 is a simplified schematic of a method of determining a mass of a molten salt in a container, in accordance with embodiments of the disclosure;

FIG. 3 is a gamma-ray emission spectrum of a sample containing ²² Na and ¹⁵⁴ Eu; FIG. 4A and FIG. 4B are photographs of the geometry for a GC5019 high-purity germanium gamma-ray detector;

FIG. 5 is a spectrum from of a calibration measurement for an HPGe detector; FIG. 6 is a spectrum from a sample count, in accordance with an embodiment of the disclosure;

FIG. 7 is a plot of a measured ²² Na activity against the mass of a salt using a first detector; and

FIG. 8 is a plot of a measured ²² Na activity against the mass of a salt using a second detector.

MODE(S) FOR CARRYING OUT THE INVENTION According to some embodiments, radioactive isotope tracer dilution analysis is applied to determine the mass of a high temperature molten salt laden with nuclear materials and fission products. The mass of the molten salt can provide information for nuclear material accountancy for the purpose of physical inventory verification (PIV) for safeguarding nuclear materials dissolved in the molten salt. According to embodiments disclosed herein, radioactive isotope tracer dilution analysis may be performed to determine the mass of molten salt within a container, such as a container with a non-geometrically shaped cavity. In addition, the temperature of the molten salt does not influence the determination. In other words, the determination of the mass of molten salt in the container is independent of the temperature of the molten salt. Thus, a method for determining the mass of a molten salt using radioactive isotope tracing and radioactive isotope dilution analysis is disclosed.

The following description provides specific details to provide a thorough description of embodiments of the invention. However, a person of ordinary skill in the art will understand that the embodiments of the invention may be practiced without using these specific details. Indeed, the embodiments of the invention may be practiced in conjunction with conventional systems and methods used in the industry. In addition, only those method components and acts necessary to understand the embodiments of the invention are described in detail. A person of ordinary skill in the art will understand that some components are not described herein but that using various conventional method components and acts would be in accord with the invention. Any drawings accompanying the present application are for illustrative purposes only and are not drawn to scale.

Elements common among figures may retain the same numerical designation.

As used herein, the terms "radioisotope tracer" and "radioactive isotope tracer" are used interchangeably.

As used herein, the terms "container" and "vessel" may be used interchangeably. A container may refer to a structure defining a volume configured to retain one or more materials. A container may include irregular shapes and may not exhibit a substantially uniform cross-sectional area along different portions thereof.

Referring to FIG. 1, a simplified cross-sectional view of a system 100 for electrorefining spent nuclear fuel or another material is shown. The system 100 includes an electrochemical cell 102 including a molten salt 104, such as a molten salt electrolyte. The electrochemical cell 102 may be supported on a support structure 120. The electrochemical cell 102 may exhibit a non-geometrically shaped cavity. Although FIG. 1 illustrates the electrochemical cell 102 having a particular geometry, the disclosure is not so limited. In other embodiments, a cross-sectional shape of the electrochemical cell 102 may not be the same along a length thereof. In some embodiments, the electrochemical cell 102 may have a shape other than a right cylinder. In addition, as will be described herein, the

electrochemical cell 102 may include various components and sensors (e.g., electrodes (anode, cathode, etc.), stirring rod, etc.) that may consume a volume within the

electrochemical cell 102. The presence of such components increases a difficulty of determining a volume, and hence, a mass of the molten salt 104 in the electrochemical cell 102.

The molten salt 104 may include lithium chloride (LiCl), lithium oxide (L12O), a mixture of lithium chloride and lithium oxide, sodium chloride (NaCl), calcium chloride (CaCk), calcium oxide (CaO), a mixture of calcium chloride and calcium oxide, lithium bromide (LiBr), potassium bromide (KBr), cesium bromide (CsBr), calcium bromide (CaBrc), potassium bromide (KBr), strontium chloride (SrCh), strontium bromide (SrBrc), a eutectic salt of lithium chloride and potassium chloride (e.g., LiCl-KCl having about 56 weight percent KC1), uranium tetrafluoride (UF4), uranium tetrafluoride and thorium tetrafluoride (UF4 and ThF4), another molten salt, and combinations thereof. In some embodiments, where the molten salt 104 comprises uranium tetrafluoride, the uranium tetrafluoride may be dissolved in at least one of molten lithium fluoride (LiF), molten beryllium fluoride (BeF2), and molten zirconium fluoride (ZrF4). In some such embodiments, the molten salt 104 may comprise uranium tetrafluoride dissolved in each of molten lithium fluoride, beryllium fluoride, and zirconium fluoride (i.e., LiF-BeF2-ZrF4-UF4). In embodiments where the molten salt 104 comprises uranium tetrafluoride and thorium tetrafluoride, the molten salt 104 may further include at least one of lithium fluoride and beryllium fluoride. In some such embodiments, the molten salt may comprise uranium tetrafluoride, thorium tetrafluoride, lithium fluoride, and beryllium fluoride (i.e., LiF-BeF2-ThF4-UF4). However, the disclosure is not so limited and the molten salt 104 may comprise one or more other materials.

A cathode 106 and an anode 108 may disposed in the molten salt 104. One or more heating elements 110 may be disposed around at least a portion of the electrochemical cell 102 and may be configured to maintain a desired temperature of the molten salt 104. A stirring assembly 112 may be disposed in the molten salt 104 and may be configured to mix the molten salt 104 such that the molten salt 104 exhibits a substantially uniform composition throughout a volume thereof. A heat shield reflector 118, such as a material comprising a thermally insulative material, may be disposed around at least a portion of the electrochemical cell 102 to insulate the electrochemical cell 102 from an external environment. The electrochemical cell 102 may include one or more scrapers configured to scrape materials accumulated at sides, a bottom surface, or both of the electrochemical cell 102.

A basket 116 configured to carry one or more nuclear fuels (e.g., one or more spent nuclear fuels) may be disposed around at least a portion of the anode 108. In some embodiments, the basket 116 is integral with the anode 108. In some embodiments, the basket 116 may include one or more spent nuclear fuels. By way of nonlimiting example, the basket 116 may include spent uranium dioxide, spent uranium oxide (e.g., U3O8), uranium silicide (U3S12), uranium carbide (UC), uranium carbide oxide (UCO), uranium- molybdenum fuels (U-Mo) and alloys thereof, uranium-beryllium (UBe _x ) and oxides thereof (e.g., BeO-UC ), another nuclear fuel, or combinations thereof. In some embodiments, such as where the electrochemical cell 102 comprises a molten salt reactor, the nuclear fuel may dissolve in the molten salt 104. By way of nonlimiting example, one or both of uranium tetrafluoride and thorium tetrafluoride may dissolve in a fluoride molten salt, the fluoride molten salt comprising one or more of lithium fluoride, beryllium fluoride, zirconium fluoride, or another fluoride, as described above. The molten salt 104 may have an unknown mass M _sa it in the electrochemical cell 102 (also referred to herein as "an electrorefiner"), which is an example of a container with a non-geometrically shaped cavity. According to methods described herein, a mass of the molten salt 104 may be determined, independent of the components contained within the electrochemical cell 102 and even if the electrochemical cell 102 exhibits an irregular shape. For example, a radioisotope tracer with a known mass, M _r , and activity, A _r , may be added to the molten salt 104. A sample of the molten salt 104, after being mixed with the radioactive tracer such that the radioactive tracer is substantially uniformly dispersed in the molten salt 104, is obtained. The sample is weighed with weight Ms. The activity of the sample, As, is measured using, for example, an HPGe detector. As will be described herein, in an electrorefiner container (e.g., vessel, such as the electrochemical cell 102) where the mass of molten salt 104 is generally greater than 10 kg, the mass of the radioisotope tracer, Mr, can be ignored. Application of the radioactive tracer dilution technique results in the equation for the mass M _sa it of the molten salt.

In general, according to embodiments disclosed herein, a known mass (Mr) of a radioactive isotope tracer with known or measurable activity (A _r ) is added to a liquid, such as the molten salt 104, in which the mass of the liquid is to be determined. The liquid and radioactive isotope tracer are mixed until homogeneous to form a mixture. A sample, such as a grab sample, of the liquid mixed with radioactive isotope tracer is obtained. The sample is weighed (½), and the activity of the sample (A _s ) is measured. The mass of the liquid M, such as the molten salt 104, may be determined through the following equations:

— -— =— (1)

(M _r +M) M _s M = ^-M _s - M _r (2) wherein, M _r is the mass of the radioactive isotope tracer, and , M _r , M, and A are the same as described above. Where the mass of the liquid is greater than, for example, 50 kg, such as molten salt in an electrorefiner container (e.g., vessel), the value ofM- can be ignored, and equation (2) can be simplified as:

M = _s M _s (3) Since the activity (i.e., the number of disintegrations per second) of a sample is directly proportional to the composition of the sample and the mass of the sample, the mass of a material within a container may be determined by selecting a radioisotope tracer to exhibit an activity at a unique energy relative to other components of the material within the container. For example, by multiplying the mass of the sample by the ratio of the activity of the radioisotope tracer to the activity of the sample according to Equation (3) above, the unknown mass of the material within the container may be determined.

For example, referring to FIG. 2, a method 200 of determining a mass of a molten salt in a container, such as an electrochemical cell used for electrorefining spent nuclear fuel, is shown. The method 200 includes act 202 including adding a radioisotope tracer having a known mass and a known activity to a container including a material; act 204 including mixing the radioisotope tracer with the material in the container; act 206 including obtaining a mixed sample from the container and measuring the mass and activity of the sample; and act 208 including determining the mass of the material in the container based, at least in part, on the mass and activity of the sample.

Act 202 includes adding a radioisotope tracer having a known mass and a known activity to a container including a material. The container may comprise, for example, an electrochemical cell (e.g., the electrochemical cell 102 (FIG. 1)) used in an electrorefining process. The material may include a liquid, such as a molten salt (e.g., the molten salt 104 (FIG. 1)). Spent nuclear fuel from nuclear power plants contains numerous radioactive isotopes, and many of the radioactive isotopes in the spent nuclear fuel can be found in the electrorefiner salt (e.g., the molten salt 104) during the electrochemical recycling process. The radioactive isotope tracer, in some embodiments, may be different from the constituents of spent nuclear fuels, and the activity of the radioisotope tracer may be measurable directly with better than 1% accuracy. Radioactive isotopes that can be used include ⁶⁰ Co, ²⁴ Na, ⁵⁸ Co, ⁸² Br, ²² Na, ⁸⁴ Rb, ⁸⁶ Rb, and ¹⁶⁸ Tm. Additional radioactive isotopes may include ⁷ Be, ² P, ⁵ P, ⁵ S, ⁴⁵ Ca, ⁴⁸ V, ⁴⁹ V, ⁵⁴ Mn, ⁵⁵ Fe, ⁵⁹ Fe, ⁵⁷ Co, ⁶⁵ Zn, ⁶⁸ Ge, ⁷⁵ Se, ⁸ Rb, ⁸⁵ Sr, ⁸⁸ Zr, ⁸⁸ Y, ¹⁰⁹ Cd, ¹¹³ Sn, ¹⁷⁰ Tm, ¹⁷¹ Tm, ¹⁷³ Lu, ¹⁷⁴ Lu, ¹⁷² Hf, ¹⁷⁵ Hf, ¹⁷⁹ Ta, ¹⁸¹ W, ¹⁸⁸ W, ¹⁸² Ta, ²⁰⁴ T1, and combinations thereof. In some embodiments, the radioactive isotopes may be identified and quantified by gamma-ray spectroscopy to determine activity. In some embodiments, the radioactive isotope comprises ²² Na. In other embodiments, a wide range of radioactive isotopes may be utilized as the tracer. The radioactive isotope tracer may be selected based on, among other things, a chemical compatibility of the radioactive isotope tracer with the molten salt 104, the activity of the radioactive isotope tracer, and the half- life thereof. The compounds from which these isotopes could be obtained include salts such as the fluorides, chlorides, bromides, and iodides thereof, depending on the physical and chemical properties of the molten salt to be measured. For example, C0CI2, CoCh, KBr, NaCl, RbCl, NaF, NaBr, Nal, and TmCh may be used.

As two examples, neither ⁶⁰ Co nor ²² Na is present in typical spent nuclear fuel from nuclear power plants, such as in spent nuclear fuel from light water reactors. ⁶⁰ Co is commonly produced by neutron activation of ⁵⁹ Co, a component in stainless steel used for many structural components in a nuclear reaction and is a commercially important radioisotope, used as a radioactive tracer and for the production of high energy gamma rays. ⁶⁰ Co has a half-life of 5.2714 years and a specific activity of 1,132 Ci/gram. ²² Na is a less well-known but also important gamma source. It has a half-life of approximately 2.6 years, specific activity of 6,243 Ci/gram, and a gamma-ray at 1274.5 keV. The half-life of 2.6 years may be an advantage for performing nuclear material safeguards, accountability, and other verification activities. Accordingly, in some embodiments, the radioactive isotope tracer comprises at least one of ⁶⁰ Co or ²² Na.

In some embodiments, the radioactive isotope tracer may be selected to be chemically compatible with the electrorefiner salt (e.g., the molten salt 104 (FIG. 1)). For example, where the material includes a molten salt including a spent nuclear fuel, a tracer of the isotope ²² Na in the form of NaCl may be compatible with a LiCl-KCl eutectic based salt. Cobalt belongs to the noble metal group in the electrochemical recycling process. Based on the thermodynamics of Co ²⁺ , Co ²⁺ in the salt phase can be reduced to cobalt metal by an active metal such as uranium. However, ⁶⁰ Co may be used as a tracer in some embodiments, such as where reduction of Co ²⁺ is not a concern.

The amount of the radioactive isotope tracer added to the material in the container may be related to the quantity of molten salt in the vessel. For example, less than 1 μθί of either ⁶⁰ Co or ²² Na is estimated to be needed to be added to have better than 1% accuracy from a less than 1 gram sample of molten salt. For electrorefiners with larger containers and molten salt content in the tens to hundreds of kilograms, larger quantities of the radioactive tracer may be added to the electrorefiner container to ensure homogeneity of the distribution of the radioactive isotope tracer throughout the electrorefiner container. By way of nonlimiting example, in some embodiments, between about 0.10 μθί and about 2.0 μ¾ such as between about 0.10 μCi and about 0.25 μθ, between about 0.25 μθ and about 0.50 μθ, between about 0.50 μθ and about 0.75 μ¾ between about 0.75 μCi and about 1.0 μ¾ between about 1.0 μCi and about 1.5 μθ, or between about 1.5 μCi and about 2.0 μθί of the radioactive isotope tracer may be added to the container for every estimated about 1.0 gram of the molten salt. However, the disclosure is not so limited and a different amount of the radioactive isotope tracer may be added to the container for every particular amount of the molten salt. In some embodiments, the mass of the radioactive isotope tracer may be selected to be less than about 1.0 weight percent of an estimate mass of the molten salt 104, such as less than about 0.5 weight percent, less than about 0.1 weight percent, less than about 0.01 weight percent, less than about 0.001 weight percent, or even less than about 0.0001 weight percent a mass of the molten salt 104. In some embodiments, the weight percent of the radioactive isotope tracer may be less than about 1.0 ppm. The amount of the radioactive isotope tracer added to the container may be selected based on the composition of the molten salt 104 and a desired accuracy of the activity determination.

Act 204 may include mixing the radioisotope tracer with material in the container. For example, the container may include, a mixer, such as the stirring assembly 1 12 (FIG. 1), configured to substantially uniformly disperse the radioisotope tracer within the material in the container. After a sufficient time has passed and the radioisotope tracer is substantially uniformly dispersed in the material, act 206 may include obtaining a mixed sample from the container and measuring the mass and activity of the sample.

Act 208 may include determining the mass of the material in the container based, at least in part, on the mass and activity of the sample. By way of nonlimiting example, the mass of the material in the container may be determined according to Equation (2) or Equation (3) above, based on the activity of the radioisotope tracer (A _r ), the mass of the radioactive tracer (Mr), the measured mass of the sample (M _s ), and the measured activity of the sample (A _s ). In some embodiments, the mass of the material in the container is determined without knowledge of the mass of the radioactive tracer. Accordingly, the mass of the material in the container may be determined without a knowledge of the geometry of the container.

In some embodiments, the activity of the sample may be determined with a high-purity germanium (HPGe) detector with a gamma-ray spectroscopy system. In some embodiments, the activity of the radioactive isotope tracer exhibits a peak energy at a different wavelength than components of the molten salt 104. In other embodiments, the molten salt 104 may include one or more radioactive isotopes exhibiting an energy peak at one or more energies in the gamma-ray spectrum as the selected radioisotope tracer. In some such embodiments, act 208 may include subtracting the signal (e.g., the energy counts) in the spectrum due to the presence of the one or more radioactive isotopes in the molten salt 104 from the signal (e.g., the energy counts) due to the radioisotope tracer.

As one example, in some embodiments, the molten salt 104 may include ¹⁵⁴ Eu, which exhibits a gamma ray emission at 1,274.46 keV. A gamma-ray emission spectrum of a sample containing ²² Na and ¹⁵⁴ Eu is illustrated in FIG. 3. As shown in FIG. 3, ¹⁵⁴ Eu includes a peak count at a gamma ray emission wavelength of about 1,274.46 keV, which may interfere with the emission energy of about 1,274.54 keV emitted from ²² Na.

Accordingly, where the radioisotope tracer comprises ²² Na, the signal of the ¹⁵⁴ Eu may interfere with the signal of the ²² Na tracer. In some such embodiments, the contribution of the ¹⁵⁴ Eu to the ²² Na peak at 1,274.54 keV may be subtracted from the signal measured at 1,274.54 keV. ¹⁵⁴ Eu has an emission spectrum including several emission energies (e.g., 123.1 keV, 247.9 keV, 591.8 keV, 723.3 keV, 756.8 keV, 873.2 keV, 996.2 keV, 1,004.7 keV, and 1,274.46 keV). Based on the relative decay branching ratio (e.g., the ratio of the intensity at each energy corresponding to ¹⁵⁴ Eu), the contribution of the ¹⁵⁴ Eu to the gamma ray emission peak at 1,274.46 keV may be determined and subtracted from the measured energy at 1,274.54 keV to determine the energy contributed by the ²² Na tracer. Accordingly, in some embodiments, the spectrum may be compensated for other radioactive isotopes in the molten salt that exhibit emission energies close to the emission spectrum of the radioisotope tracer.

Accordingly, in some embodiments, the radioactive isotope tracer may be used to determine a mass of a material without knowledge of a volume of a container in which the radioactive isotope tracer is contained and without knowledge of the density of the material. The container may have an irregular shape. In addition, the mass of the material may be determined independent of the temperature of the material. The method may be used to determine an unknown mass greater than about 10 kg, greater than about 100 kg, greater than about 500 kg, greater than about 1,000 kg, or even greater than about 2,000 kg.

Although FIG. 1 and FIG. 2 have been described as including determining a mass of a molten salt in an electrochemical cell, the disclosure is not so limited. For example, another embodiment of the invention may also include adding a known amount of a radioactive isotope tracer with known activity into a liquid into which another material has been dissolved, mixing the radioactive isotope tracer with the liquid, obtaining a sample of the resulting mixture, measuring the activity of the sample, and calculating the mass of the mixture using radioactive isotope tracer dilution analysis.

Although FIG. 1 and FIG. 2 have been described as including determining a mass of a molten salt in a container having an irregular shape, the disclosure is not so limited. In other embodiments, the method may be used to determine the mass of a material in a container having a shape such as a cylindrical shape, a spherical shape, or any other shape.

Examples

Example 1

Samples of salts with ²² Na activity were prepared and measurements of mass and activity in the salt samples were obtained using a gamma-ray spectroscopy system.

Commercially available radioisotope ²² Na (an amount having an activity of 10.59 μθί) was purchased in the form of a ²² NaCl aquarium solution, which was sealed in a glass ampule. Upon breaking the ampule about 2 mL of the solution was transferred to an empty crucible.

The crucible was put into an oven that had been preheated to 150°C. The crucible was heated in the oven for 20 minutes and then cooled for 20 minutes before being removed from the oven. After being removed from the oven, the liquid on the bottom of the crucible was no longer visible, and the source material (i.e., the ²² Na) appeared as a thin reflective layer on the bottom of the crucible. The crucible was then immediately covered with three layers of plastic food wrap (PVC film). Following these steps, a radiation smear survey of the crucible found no contamination of the laboratory equipment (such as glassware) with radioisotopes.

Prior to preparation of the samples, the total activity of ²² Na deposited in the crucible, which is the total initial activity used for this proof-of-the-concept experiment, was measured using spectroscopy. The activity measured was about 5.49 μθί of ²² Na.

20.00537 grams of LiCl-KCl was added to the crucible with ²² Na. This crucible was then heated to 550°C for 16 hours and the liquid (e.g., molten) salt mixture was intermediately stirred to reach equilibrium. After furnace cooling, the molten salt solidified and portions of the solid salt were moved from the original crucible to other clean crucibles. Three crucibles containing various amounts of salt mixtures were then removed from the glovebox and transported for future use. An alumina crucible, labeled Crucible 1, containing a 5.09 ²² Na source was transported to the lab housing glove box. The food wrap was removed from the top of the crucible, and the crucible was placed within the glovebox via the antechamber. This glovebox was kept at 4.1 ppm of 0 ₂ and 0.2 ppm of H ₂ 0 throughout the sample

preparation.

Initially a 20.00537 ± 0.00001 gram sample of LiCl-KCl, (58 mole % LiCl) was prepared for use. This LiCl-KCl sample was loaded within Crucible 1 for a total crucible weight of 141.4020 ± 0.0001 grams.

Crucible 1 was then loaded into a furnace, and the furnace was set for 550°C. It took 30 minutes for the furnace to stabilize from room temperature to 550°C. At 2 hours, 4.5 hours, and 14.25 hours after initially tuming on the fumace, the salt sample was stirred using a tungsten rod for approximately 1 minute per stirring. The furnace throughout the operation was ± 5°C of the set point.

Sixteen hours after Crucible 1 was loaded in the furnace, the fumace was turned off and the alumina crucible sample was allowed to cool inside the fumace. After

approximately 6 hours, the solidified salt in Crucible 1 had cooled to room temperature.

Because of the difficulty of removing the entire salt sample from Crucible 1, a pick was used to slowly remove small pieces of salt. The pieces of the salt were collected and then distributed to additional crucibles labeled Crucible 2 and Crucible 3.

The three crucibles with salt samples were then removed from the glovebox.

Gamma spectrum analysis was performed on these three crucibles and an empty alumina crucible. The masses of the alumina crucibles and the final masses of salt in each mixture based on the mass measurements of the alumina crucibles is shown in Table I below.

Table I

Sources of error and possible solutions to the error include the inability to remove the entire salt sample from Crucible 1 and the temperature of equilibration, as described herein. For example, one source of error of the experimental procedure was an inability to easily remove the salt sample from Crucible 1 after the furnace had cooled. The method used was to slowly hammer small pieces of salt to be removed. This hammering style of removal led to a larger mass loss (-0.5716 g) of the salt than desired. The mass loss came from the accumulation of small pieces occasionally bouncing out of the crucible upon impact of the pick. However, this loss did not affect the measured mass versus its corresponding activity.

One solution to this result would be to reduce the amount of force from the pick to potentially decrease the number of particles that would leave the crucible. However, this solution would considerably increase the amount of time necessary for sample removal.

Another solution would be to change the crucible from alumina to a glassy carbon crucible. Previous testing in the lab showed that removing an intact salt sample from a glassy carbon crucible is nearly always successful, while removing an intact salt sample from an alumina crucible is nearly impossible. By removing an intact salt sample from the crucible, the mass loss from breaking the salt into pieces could have been reduced.

Another uncertainty in this experiment was the temperature of the salt for which the

NaCl would reach equilibrium with the LiCl-KCl eutectic. While phase diagrams for LiCl- KC1 and KCl-NaCl are plentiful, finding the ternary of LiCl-KCl-NaCl was difficult.

Therefore, the equilibration temperature for the mixing of the LiCl-KCl-NaCl was chosen to be that which was representative of an electrorefiner.

The following is the uncertainty propagation in the values that were not directly measured by the analytical balance. The analytical balance had an uncertainty of 0.0001 grams (except for the initial measurement of the LiCl-KCl which was 0.00001 grams).

Empty Crucible Weight - Crucible 1

Mass Measurement

Crucible 1 Empty weight = Crucible with LiCl-KCl salt - Mass of LiCl-KCl = (141.4020 - 20.00537) grams = 121.3966 grams

Uncertainty Analysis

δ (Crucible 1 empty weight)

= (5(Crucible with LiCl - KC1 salt)) ² + (5 (Mass of LiCl - C1)) ²

5 (Crucible 1 empty weight) = V(0.0001) ² + (0.00001) ²

5 (Crucible 1 empty weight) = 1.005 x 10 ^~4 grams = 0.0001 grams Mass of Salt - Crucible 1

Mass Measurement

Crucible 1 salt = Crucible 1 with salt transported from glovebox

(Mass of crucible initially with LiCl-KCl) - Mass of LiCl-KCl)

Crucible 1 Salt =134.9377 - (141.4020 - 20.00537) grams

Crucible 1 Salt = 13.54107 = 13.5411 grams

Uncertainty Analysis

δ (Crucible 1 salt)

(δ (Crucible removed from glovebox)) + (δ (Crucible 1 initially with LiCl— KC1))

+ (5 (Mass of LiCl - KC1 salt)) ² δ (Crucible 1 salt) = V(0.0001) ² + (0.0001) ² + (0.00001) ²

^(Crucible 1 salt) = 1.4177 x 10 ^"4 grams = 0.0001 grams Mass of Salt - Crucible 2 (applies to Crucible 3 as well)

Mass Measurement

Crucible 2 salt = Crucible 2 with salt - Empty Crucible 2

Crucible 2 salt = 147.2833 - 146.1540 grams

Crucible 2 salt = 1.1293 grams

Uncertainty Analysis

5 (Crucible 2 salt) = / (5 (Crucible 2 with salt)) ^{^} + (5 (Empty Crucible 2))

δ (Crucible 2 salt) = V(0.0001) ² + (0.0001) ²

^(Crucible 2 salt) = 1.414 x 10 ^"4 grams = 0.0001 grams

The three crucibles with the prepared samples were sealed, and an empty crucible was used for calibration-standard measurements. Measurements of the three samples were made using two different detectors in the gamma-ray spectroscopy system.

A gamma-ray spectroscopy system typically consists of an HPGe semiconductor detector, a pre-amplifier, an amplifier, a high-voltage power supply, a multi-channel analyzer (MCA), and a computer-based acquisition and analysis system. In modem systems, many of these components are often combined into integrated units.

Gamma rays emitted from a radioactive source that are absorbed in the HPGe detector produce electrical pulses. The pulse amplitude is proportional to the energy deposited in the detector, which allows for measurement of gamma ray energies. The MCA sorts these pulses by amplitude, and computer software displays a plot of the number of pulses received at each pulse amplitude, corresponding to the energy (e.g., in keV) of the radioactive source. Such a plot is called a spectrum because it shows the spectrum of energies emitted by the source. Comparison of the peaks found in a spectrum against a library of known radionuclide energies and abundances allows identification of the radioactive components of a sample. If the system efficiency is calibrated using a source with traceable activity, the activity of those radionuclides can be quantified. In addition, the library of known radionuclide energies and abundances (e.g., intensity at each energy) may be used to compensate for the energy emitted due to radioisotopes in a sample having an emission energy (e.g., a gamma ray energy) at substantially the same emission energy as the radioisotope tracer.

Data acquisition and control, as well as quantitative analysis of identified radionuclide activity, is performed by a software package (e.g., the software package Genie 2000 from Canberra Industries). The software provides for spectrum acquisition, storage, isotope identification, and activity quantification, as well as detector system energy and efficiency calibration. All files associated with this program (spectra, calibration files, etc.) are stored on the host computer and duplicated to a backup server.

A gamma-ray spectroscopy system may include the computer used for analysis and display as well as the Lynx MCA, a detector shield that minimizes counts from background radiation, and a vacuum dewar filled with liquid nitrogen for keeping the HPGe detector at its operating temperature.

Calibration of a gamma-ray spectrometer involves placing a traceable source, often with emissions at multiple gamma-ray energies, in a repeatable position relative to the detector and acquiring a spectrum. Using the measured spectrum in conjunction with the source activity and date from the source calibration certificate (as well as the half-life of the source, among other things), the analysis software then computes the efficiency of the detector as a function of energy for the source in that position, typically using log-log interpolation between calibration peak energies to create an efficiency curve as a function of energy.

Two gamma-ray spectroscopy system detectors were calibrated for the salt sample measurements using a ⁶⁰ Co point source traceable to the National Institute of Standards and Technology. The first detector is a Canberra GC5019 HPGe, which has an efficiency of 50% relative to a standard 3"x3" Nal detector at 1332 keV, and has a full width at half max of 1.9 keV for peaks measured at 1332 keV. The second detector is a Canberra GC1419 HPGe, which has an efficiency of 14% relative to a standard 3"x3" Nal detector at 1332 keV, and has a full width at half max of 1.9 keV for peaks measured at 1332 keV. ⁶⁰ Co was chosen because of the energy of its emitted gamma rays at 1173 keV and 1332 keV, which bracket the energy of ²² Na at 1275 keV (1,274.54 keV). The calibration source has a stated 2-sigma activity uncertainty (95% confidence) of 2%.

Because the calibration source approximates a point source and the salt samples were distributed sources approximating a disk with a diameter of about 1.25 inches (3.175 cm), a geometry was chosen that placed the sources to be measured at a great enough distance from the detector that the difference in geometry between the calibration source and salt samples is negligible for gamma-ray spectroscopy system measurements. In general, the minimum source-to-detector distance should be at least five times greater than the largest extent of the source, which in this case is the diameter of 1.25 inches

(3.175 cm). A geometry with a distance much greater than this minimum was chosen and it was verified that measurements at this distance would have good signal-to-noise as well as low measurement dead time. In addition, the calibrations were performed with the source in the empty crucible, as gamma rays from the calibration source should be attenuated by intervening material in the same manner as gamma rays from the unknown samples will be. FIGS. 4A and 4B show the chosen geometry for detector GC5019. FIG. 4A shows the detector shield with the measurement platform extending above it, and FIG. 4B shows a top-down view of the crucible above the detector.

Once performed, the calibrations can be used in conjunction with the measured spectra for the salt samples to quantify ²² Na activity. Calculations of sample activity take into account the efficiency of the detector system at the energy of interest, the gamma-ray emission probability for the isotope/energy, and correction for radioactive decay during the count. FIG. 5 shows the spectrum from the calibration measurement, in which peaks at 1173 keV and 1332 keV are seen, as is the Compton continuum at energies below the peak energies.

Each of the three samples, as well as the crucible with the starting source ²² Na source activity, was measured on each of the two detectors calibrated for the experiment. Data collection time was set for each sample to ensure at least 10,000 counts in the photopeak. After completing the count, the spectrum was stored and the analysis software was used to identify peaks and calculate the activity (μθί) of the target radionuclide in the sample. FIG. 6 shows the spectrum from one of the sample counts of one of the crucibles. In addition to the peak at 1275 keV, there is a peak at 51 1 keV, which corresponds to annihilation photons from the positrons that are also emitted from ²² Na.

The uncertainty in the measured activity depends on multiple factors. First, any measurement based on radiation counting systems will have an uncertainty component proportional to the square root of the net number (continuum-subtracted) of counts recorded. This source of uncertainty can be reduced by increasing the count time but eventually reaches a point of diminishing returns. Each sample was counted long enough to ensure at least 10,000 counts in the photopeak, which corresponds to a 1 -sigma uncertainty (68% confidence) of 1 %.

Next, there is the uncertainty in the detector efficiency, which is a function of the number of counts recorded when counting the calibration source for the efficiency calibration, the stated activity uncertainty in the calibration source from its certificate, and the uncertainty associated with assigning an efficiency value to the energy of the gamma ray of interest in the sample. Unless the energy of interest was one of the peaks present in the calibration standard, some form of interpolation is required between energy peaks, which adds to the uncertainty. The calibration source has a stated 1-sigma activity uncertainty (68% confidence) of 1%.

Finally, there are uncertainties in the fundamental physical data - gamma emission probabilities and nuclide half-lives - that also affect the final uncertainty in the measured activity. In practice, an uncertainty floor exists, a minimum uncertainty below which the uncertainty may not be reduced by further counting. This floor can be observed in the data presented in Table II and Table III below, which show some minimum uncertainty applicable to even the samples with the highest activity. In Table II and Table III, the first count of crucible one is prior to removal of any of the salt therefrom into crucible 2 and crucible 3. The second count of crucible 1 is after a portion of the salt is removed from crucible 1 into crucible 2 and crucible 3.

Table II

Table III

The analysis software accounts for each of these components of uncertainty and folds them all into a final uncertainty associated with the measured activity. The activity uncertainty (in μθ) listed in the fourth column of each of Table II and Table III was taken directly from the software output. The relative uncertainty (in %) was calculated by dividing this value by the measured activity. All uncertainties listed (absolute and relative) represent one standard deviation.

The results using the GC5019 detector are summarized in Table II. A plot of the 2 ² Na activity versus the mass of the salt is shown in FIG. 7 for the GC5019 detector.

A least-squares fit of the data to a line through the origin yields an R ² value of 0.9996. The slope of the line is 0.273 ± 0.002 μα/g. The mass of an unknown sample of salt could be calculated by dividing its measured activity by this slope.

The ²² Na activity measurements were also performed on the lower-efficiency GC1419 detector as a check on the GC5019 results. The results using the GC1419 detector are summarized in Table III. A plot of the ²² Na activity versus the mass of the salt is shown in FIG. 8 for the GC 1419 detector.

A least-squares fit of the data to a line through the origin yields an R ² value of 0.9987. The slope of the line is 0.275 ± 0.003 μα/g, which agrees with the results using the GC5019 detector.

Accordingly, a 20.0054 gram sample of LiCl-KCl salt was prepared for use. A total of 5.49±0.07 μθί of ²² NaCl was added to the salt. After melting, mixing, and cooling, four pairs of mass versus activity were measured. Two HPGe detectors were used to eliminate any potential system errors. Results from two detector systems agree with each other very well. From one detector, a least-squares fit of the data yields a line through the origin with an R ² value of 0.9996. The slope of the line, which is the activity of the sample, A _s , divided by the mass of the sample, M _s , is 0.273 ± 0.002 μα/g. The mass, M, of an initial (assumed unknown) sample of salt could be calculated by dividing its measured activity, As, by this slope (i.e., 5.49 μΟί/(0.273 μθ/g)), which yields 20.1099 ± 0.2564 gram. This measured value through activity falls into the mass of the original salt measured with a balance within 1 sig statistical region, validating the radioactive tracer dilution technique. Further studies applying different radioisotopes may be performed because of the interference peaks at the ²² Na photo peak, 1275 keV, from the fission products in an actual molten salt. Example 2

A mixture of ²² Na and ¹⁵⁴ Eu was added to a first crucible (crucible 0) inside a glovebox having conditions of 4.1 ppm C and 0.2 ppm H2O. A eutectic mixture of LiCl- KC1 (45 weight percent LiCl and 55 weight percent KC1) was added to the crucible. The crucible was heated to about 550°C for a duration of about 16 hours, during which the liquid (e.g., molten) salt was stirred. After heating, the crucible and salt were allowed to cool, after which pieces of the salt and tracer were placed in a second crucible (crucible 1) and a third crucible (crucible 3), while a portion of the original salt and tracer remained in the first crucible (labeled crucible 2 in the Table IV and Table V below after a portion of the salt was removed therefrom).

An HPGe detector was used to measure the gamma-ray emission spectrum of the samples in the mixture of ²² Na and ¹⁵⁴ Eu (crucible 0) in Table IV and Table V below, and each of the crucible 1, crucible 2, and crucible 3. The results are reproduced below in Table IV for ²² Na and in Table V for ¹⁵⁴ Eu. Table IV

Table V

The ²² Na activity was determined with it main peak at 1,274.54 keV masked by the interfering ¹⁵⁴ Eu. The intensity and efficiency information for all peaks of the ¹⁵⁴ Eu, and the intensity and efficiency of the 1274.54 keV peak of ²² Na were used to determine the counts at 1274.54 keV attributed to the presence of the ²² Na. Stated another way, the counts at 1274.54 keV attributed to the ¹⁵⁴ Eu were subtracted from the total number of counts at 1274.54 keV to determine the activity attributed to the ²² Na tracer. The mass of salt was determined according to Equation (3) above. Accordingly, the mass of an unknown amount of a molten salt was determined with a tracer exhibiting an activity at an energy overlapping an activity energy of at least one component of the molten salt.

Additional nonlimiting example embodiments of the disclosure are set forth below.

Embodiment 1 : A method for determining the mass of a molten salt in a container comprising: adding an amount of a radioactive isotope tracer with known activity and known mass into the molten salt; mixing the radioactive isotope tracer with the molten salt until homogeneous; obtaining a sample of the radioactive isotope tracer and molten salt mixture; weighing the sample obtained; measuring the activity of the sample obtained using gamma spectrometry; and calculating the molten salt mass using radioactive isotope tracer dilution analysis.

Embodiment 2: The method of Embodiment 1, wherein the molten salt is contained in a container with a non-geometrically shaped cavity. Embodiment 3: The method of Embodiment 1 or Embodiment 2, wherein the molten salt is contained in an electrorefiner.

Embodiment 4: The method of any one of Embodiments 1 through 3, wherein the radioactive isotope tracer is selected from the group consisting of ⁶⁰ Co, ²⁴ Na, ⁵⁸ Co, ⁸² Br, ²² Na, ⁸⁴ Rb, ⁸⁶ Rb, and ¹⁶⁸ Tm.

Embodiment 5: The method of any one of Embodiments 1 through 4, wherein the radioactive isotope tracer comprises a compound containing a radioactive isotope.

Embodiment 6: The method of Embodiment 5, wherein the compound is selected from the group consisting of CoCh, KBr, NaCl, RbCl, NaF, NaBr, Nal, and TmCb.

Embodiment 7: The method of Embodiment 5, wherein the compound is selected from the group consisting of a fluoride salt, chloride salt, bromide salt, and iodide salt.

Embodiment 8: The method of any one of Embodiments 1 through 7, wherein the activity is measured using a high purity germanium detector.

Embodiment 9: A method for using radioactive isotope tracer dilution to determine the mass of a molten salt in a container comprising: adding a known mass {Mr) of a radioactive isotope tracer with a known activity {A _r ) to the molten salt; mixing the radioactive isotope tracer with the molten salt until homogeneous; obtaining a sample of the radioactive isotope tracer and molten salt mixture; weighing the sample obtained (M _s ); measuring the activity of the sample obtained (As) using gamma spectrometry; and

AT AS AT

calculating ^& the molten salt mass ( vMsdi) using & (Mr+M -)=— Ms and Msalt =— As Ms - Mr.

Embodiment 10: The method of Embodiment 9, wherein the molten salt is contained in a container with a non-geometrically shaped cavity.

Embodiment 11 : The method of Embodiment 9 or Embodiment 10, wherein the molten salt is contained in an electrorefiner.

Embodiment 12: The method of any one of Embodiments 9 through 11, wherein the mass of molten salt is greater than 10 kg.

Embodiment 13: The method of any one of Embodiments 9 through 12, wherein the mass of the radioactive isotope tracer (Mr) is ignored and the molten salt mass (Msaii) is

AT

calculated using Msalt =— Ms.

° As

Embodiment 14: The method of any one of Embodiments 9 through 13, wherein the radioactive isotope tracer is selected from the group consisting of ⁶⁰ Co, ²⁴ Na, ⁵⁸ Co, ⁸² Br, ²² Na, ⁸⁴ Rb, ⁸⁶ Rb, and ¹⁶⁸ Tm. Embodiment 15: The method of any one of Embodiments 9 through 14, wherein the radioactive isotope tracer comprises a compound containing a radioactive isotope.

Embodiment 16: The method of Embodiment 15, wherein the compound is selected from the group consisting of CoCh, KBr, NaCl, RbCl, NaF, NaBr, Nal, and TmCh.

Embodiment 17: The method of Embodiment 15, wherein the compound is selected from the group consisting of a fluoride salt, chloride salt, bromide salt, iodide salt, and combinations thereof.

Embodiment 18: The method of any one of Embodiments 9 through 15, wherein the activity is measured using a high purity germanium detector.

Embodiment 19: A method for determining the mass of a liquid in a container comprising: adding an amount of a radioactive isotope tracer with known activity and known mass into the liquid; mixing the radioactive isotope tracer with the liquid until homogeneous; obtaining a sample of the radioactive isotope tracer and liquid mixture; weighing the sample obtained; measuring the activity of the sample obtained using gamma spectrometry; and calculating the mass of the liquid using radioactive isotope tracer dilution analysis.

Embodiment 20: The method of Embodiment 19, wherein the liquid is contained in a container with a non-geometrically shaped cavity.

Embodiment 21 : The method of Embodiment 19 or Embodiment 20, wherein the liquid is a molten salt.

Embodiment 22: The method of any one of Embodiments 19 through 21, wherein the molten salt is contained in an electrorefiner.

Embodiment 23: The method of any one of Embodiments 19 through 22, wherein the radioactive isotope tracer is selected from the group consisting of ⁶⁰ Co, ²⁴ Na, ⁵⁸ Co, ⁸² Br, ²² Na, ⁸⁴ Rb, ⁸⁶ Rb, and ¹⁶⁸ Tm.

Embodiment 24: The method of any one of Embodiments 19 through 23, wherein the radioactive isotope tracer comprises a compound containing a radioactive isotope.

Embodiment 25 : The method of Embodiment 24, wherein the compound is selected from the group consisting of CoCh, KBr, NaCl, RbCl, NaF, NaBr, Nal, and TmCh. Embodiment 26: The method of Embodiment 24, wherein the compound is selected from the group consisting of a fluoride salt, chloride salt, bromide salt, iodide salt, and combinations thereof.

Embodiment 27: The method of any one of Embodiments 19 through 26, wherein the activity is measured using a high purity germanium detector.

Embodiment 28: A method for using radioactive isotope tracer dilution to determine the mass of a liquid in a container comprising: adding a known mass (Mr) of a radioactive isotope tracer with a known activity (A _r ) to the liquid; mixing the radioactive isotope tracer with the liquid until homogeneous; obtaining a sample of the radioactive isotope tracer and liquid mixture; weighing the sample obtained (M _s ); measuring the activity of the sample obtained (As) using gamma spectrometry; and calculating the mass of

AT AS AT

the liquid (M) using- -=— and M =—Ms - Mr.

^M ' ^b {Mr+M) Ms As

Embodiment 29: The method of Embodiment 28, wherein the liquid is contained in a container with a non-geometrically shaped cavity.

Embodiment 30: The method of Embodiment 28 or Embodiment 29, wherein the liquid is a molten salt.

Embodiment 31 : The method of Embodiment 30, wherein the molten salt is contained in an electrorefiner.

Embodiment 32: The method of Embodiment 30, wherein the mass of molten salt is greater than 10 kg.

Embodiment 33: The method of any one of Embodiments 28 through 32, wherein the mass of the liquid (M) is greater than 10 kg.

Embodiment 34: The method of any one of Embodiments 28 through 33, wherein the mass of the radioactive isotope tracer (M _r ) is ignored and the molten salt mass (M) is

AT

calculated using M =— Ms.

^& As

Embodiment 35: The method of any one of Embodiments 28 through 34, wherein the radioactive isotope tracer is selected from the group consisting of ⁶⁰ Co, ²⁴ Na, ⁵⁸ Co, ⁸² Br, ²² Na, ⁸⁴ Rb, ⁸⁶ Rb, and ¹⁶⁸ Tm.

Embodiment 36: The method of any one of Embodiments 28 through 35, wherein the radioactive isotope tracer comprises a compound containing a radioactive isotope. Embodiment 37: The method of Embodiment 36, wherein the compound is selected from the group consisting of CoCh, KBr, NaCl, RbCl, NaF, NaBr, Nal, and TmCh.

Embodiment 38: The method of Embodiment 36, wherein the compound is selected from the group consisting of a fluoride salt, chloride salt, bromide salt, iodide salt, and combinations thereof.

Embodiment 39: The method of any one of Embodiments 28 through 38, wherein the activity is measured using a high purity germanium detector.

Embodiment 40: A method for determining a mass of a molten salt in a container, the method comprising: adding an amount of a radioactive isotope tracer with known activity and known mass into a molten salt in a container; mixing the radioactive isotope tracer with the molten salt to form a mixture; obtaining a sample of the mixture; weighing the sample; measuring the activity of the sample using gamma spectrometry; and calculating the molten salt mass based, at least in part, on the weight of the sample and the activity of the sample.

Embodiment 41 : The method of Embodiment 40, wherein adding an amount of a radioactive isotope tracer with known activity and known mass into a molten salt in a container comprises adding the radioactive isotope tracer in a container with a

non-geometrically shaped cavity.

Embodiment 42: The method of Embodiment 40 or Embodiment 41, further comprising selecting the container to comprise an electrorefiner.

Embodiment 43 : The method of any one of Embodiments 40 through 42, further comprising selecting the radioactive isotope tracer from the group consisting of ⁶⁰ Co, ²⁴ Na, ⁵⁸ Co, ⁸² Br, ²² Na, ⁸⁴ Rb, ⁸⁶ Rb, ¹⁶⁸ Tm, ⁷ Be, ² P, ⁵ P, ⁵ S, ⁴⁵ Ca, ⁴⁸ V, ⁴⁹ V, ⁵⁴ Mn, ⁵⁵ Fe, ⁵⁹ Fe, ⁵⁷ Co, ⁶⁵ Zn, ⁶⁸ Ge, ⁷⁵ Se, ⁸³ Rb, ⁸⁵ Sr, ⁸⁸ Zr, ⁸⁸ Y, ¹⁰⁹ Cd, ¹¹³ Sn, ¹⁷⁰ Tm, ¹⁷¹ Tm, ¹⁷³ Lu, ¹⁷⁴ Lu, ¹⁷² Hf, ¹⁷⁵ Hf, ¹⁷⁹ Ta, ¹⁸¹ W, ¹⁸⁸ W, ¹⁸² Ta, and ²⁰⁴ T1.

Embodiment 44: The method of any one of Embodiments 40 through 43, further comprising selecting the radioactive isotope tracer to comprise a compound containing a radioactive isotope.

Embodiment 45: The method of Embodiment 44, further comprising selecting the compound from the group consisting of CoCh, KBr, NaCl, RbCl, NaF, NaBr, Nal, and TmCh. Embodiment 46: The method of Embodiment 44, further comprising selecting the compound from the group consisting of a fluoride salt, a chloride salt, a bromide salt, iodide salt, and combinations thereof.

Embodiment 47: The method of any one of Embodiments 40 through 46, wherein measuring the activity using gamma ray spectroscopy comprises measuring the activity using a high purity germanium detector.

Embodiment 48: The method of any one of Embodiments 40 through 47, wherein calculating the molten salt mass based, at least in part, on the weight of the sample and the activity of the sample comprises calculating the molten salt mass based on a ratio of the activity of the radioactive isotope tracer to the activity of the sample.

Embodiment 49: The method of any one of Embodiments 40 through 48, wherein calculating the molten salt mass based, at least in part, on the weight of the sample and the activity of the sample comprises calculating the molten salt mass according to the following equation:

AT

Msalt = ^Ms,

wherein Msait is the molten salt mass, A _r is the activity of the radioactive isotope tracer, As is the activity of the sample, md M _s is the mass of the sample.

Embodiment 50: The method of any one of Embodiments 40 through 49, further comprising selecting the mass of the radioactive isotope tracer to be less than about 0.1 percent a mass of the molten salt.

Embodiment 51 : The method of any one of Embodiments 40 through 50, further comprising selecting the radioactive isotope tracer to comprise ²² Na.

Embodiment 52: The method of any one of Embodiments 40 through 51, further comprising determining a number of counts at one or more energies due to the radioactive isotope tracer.

Embodiment 53: The method of Embodiment 52, wherein determining a number of counts at one or more energies due to the radioactive isotope tracer comprises subtracting a number of counts at the one or more energies due to one or more materials of the molten salt.

Embodiment 54: The method of any one of Embodiments 40 through 53, further comprising selecting the container to comprise more than about 10.0 kg of molten salt.

Embodiment 55: The method of any one of Embodiments 40 through 54, further comprising selecting the container to exhibit a shape other than a right cylinder. Embodiment 56: A system for determining a mass of a molten salt, the system comprising: an electrochemical cell comprising a molten salt; one or more spent nuclear fuels in the electrochemical cell; and a radioisotope tracer disposed substantially uniformly throughout the molten salt.

Embodiment 57: The system of Embodiment 56, wherein the radioisotope tracer is selected from the group consisting of ⁶⁰ Co, ²⁴ Na, ⁵⁸ Co, ⁸² Br, ²² Na, ⁸⁴ Rb, ⁸⁶ Rb, ¹⁶⁸ Tm, ⁷ Be, ³² P, ³⁵ P, ³⁵ S, ⁴⁵ Ca, ⁴⁸ V, ⁴⁹ V, ⁵⁴ Mn, ⁵⁵ Fe, ⁵⁹ Fe, ⁵⁷ Co, ⁶⁵ Zn, ⁶⁸ Ge, ⁷⁵ Se, ⁸³ Rb, ⁸⁵ Sr, ⁸⁸ Zr, ⁸⁸ Y, ¹⁰⁹ Cd, ¹¹³ Sn, ¹⁷⁰ Tm, ¹⁷¹ Tm, ¹⁷³ Lu, ¹⁷⁴ Lu, ¹⁷² Hf, ¹⁷⁵ Hf, ¹⁷⁹ Ta, ¹⁸¹ W, ¹⁸⁸ W, ¹⁸² Ta, and ²⁰⁴ T1.

Embodiment 58: The system of Embodiment 56 or Embodiment 57, wherein the radioisotope tracer comprises ²² Na.

Embodiment 59: The system of any one of Embodiments 56 through 58, wherein the molten salt comprises spent nuclear fuel.

Embodiment 60: A method of determining a mass of a molten salt in a container, the method comprising: adding an amount of a radioactive isotope tracer with a known activity and a known mass into a molten salt in a container to form a mixture; obtaining a sample of the mixture; measuring the activity of the sample; subtracting an activity due to the molten salt from the activity of the sample to obtain a compensated activity of the sample; and determining a mass of the molten salt based, at least in part, on a weight of the sample and the compensated activity of the sample.

While embodiments of the disclosure may be susceptible to various modifications and alternative forms, specific embodiments have been shown by way of example in the drawings and have been described in detail herein. However, it should be understood that the disclosure is not limited to the particular forms disclosed. Rather, the disclosure encompasses all modifications, variations, combinations, and alternatives falling within the scope of the disclosure as defined by the following appended claims and their legal equivalents.