METHOD FOR DETERMINING THE PHASE TRANSITION TEMPERATURE OF MOLTENED SALTS

Abstract

According to the present disclosure, a method for determining the phase transition temperature using electrical conductivity is provided. More precisely, according to the present disclosure, a method for determining the phase transition temperature using electrical conductivity is provided, comprising the creation of a graph of the change in electrical conductivity of molten salts as a function of temperature and the performance of at least one mathematical analysis in which (i) a first-order differential is performed on the graph, (ii) a second-order differential is performed on the graph; and (iii) the determination of the number (n) of data points and the resolution (ΔT) based on the graph to determine T nderiving from equation (1) below, and performing a linear regression analysis on a linear section to identify an outlier based on a distance from the linear regression equation, Tn = Tmax − ΔT × n where n is the number of data points and ΔT is the interval of the measurement temperature and the average resolution.

Description

CROSS-REFERENCE TO RELATED ANNOUNCEMENT (EN)

[0001] This application claims the priorities of Korean patent application No. 10-2023-0119841, filed on September 8, 2023, and Korean patent application No. 10-2024-0039332, filed with the Korean Intellectual Property Office on March 21, 2024, the full disclosure of which is incorporated herein by reference. BACKGROUND1. AREA

[0002] The present disclosure relates to a method for determining the phase transition temperature using electrical conductivity and to a method capable of quickly and accurately determining the phase transition temperature of a solid solution without the need for expensive, specially manufactured equipment. 2. DESCRIPTION OF THE RELATED STATE OF THE TECHNOLOGY

[0003] Materials undergo a phase change at a specific temperature. The temperature at which liquefied materials solidify is called the freezing point, and the temperature at which solid materials melt is called the melting point. The temperature at which liquefied substances begin to solidify is called the liquidus temperature, and the temperature at which solid substances begin to melt is called the solidus temperature.

[0004] For pure materials without impurities, the temperature does not change during phase transitions, so the temperatures are the same at all four phase changes. As long as a solid transforms into a liquid and a liquid into a solid, the temperature remains constant. However, all materials contain impurities, which can lead to differences in the four phase change temperatures. Since the starting point remains unchanged even as the temperature changes, the liquidus temperature is a constant value. Accordingly, international temperature standards use the liquidus temperature of a given material as the ideal reference point.

[0005] A molten salt reactor (MSR) uses liquid fuel in the form of a molten salt and attracts attention due to its inherent safety characteristics. The molten salt must remain liquid within the desired temperature range and have a relatively low melting point to ensure efficient heat transfer and fluid dynamics within the reactor. Since the selection of a molten salt with a suitable melting point affects the safety, efficiency, and overall performance of the reactor, understanding the phase transition behavior of different molten salt mixtures can be essential for the design of molten salt reactors.

[0006] To assess the safety and material corrosivity of fuel element salts in a molten salt reactor, deriving a phase equilibrium diagram of the fuel element according to composition is essential. The experimentally determined value of the phase transition temperature in high-temperature melts can be crucial for use as reference data for a fuel element phase equilibrium diagram based on computational thermodynamics. In this context, differential scanning calorimetry (DSC), a representative method for experimentally determining the phase transition temperature, faces the challenge of requiring expensive, specialized reactor cells and the installation of large instruments in a small glovebox to analyze molten salts, which are highly sensitive to atmospheric moisture and oxygen.

[0007] Meanwhile, Korean patent no. 10-1412594 B1 discloses a method for measuring the electrical conductivity of a solution. It is therefore expected that Korean patent no. 10-1412594 B1 will find widespread application in related fields, where it is possible to determine the phase transition temperature using electrical conductivity in a way suitable for use at actual process sites. SUMMARY

[0008] One aspect of the present disclosure may provide a method for determining the electrical conductivity and for determining the phase transition temperature based on the determined electrical conductivity.

[0009] According to one aspect of the present disclosure, a method for determining the phase transition temperature using electrical conductivity may include the creation of a diagram of the change in electrical conductivity of molten salts as a function of temperature; and

[0010] Performing at least one mathematical analysis of (i) performing a first-order differential on the graph, (ii) performing a second-order differential on the graph; and (iii) determining the number n of data and the resolution ΔT based on the graph to calculate T n deriving from equation (1) below, and performing a linear regression analysis on a linear section to identify an outlier based on a distance from the linear regression equation, Tn=Tmax−ΔT×n where n is the number of data points and ΔT is the interval of the measurement temperature and the average resolution. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The above and other aspects, features and advantages of the present disclosure will be more clearly understood from the following detailed description in conjunction with the accompanying drawings: Fig. Figure 1 is a diagram that represents a schematic algorithm flowchart for determining the phase transition temperature using electrical conductivity data; Fig. Figure 2 is a diagram that shows the definitions of the algorithm flowchart from Fig. 1 described elements illustrated; Fig. 3 is a diagram that represents first-order differential diagrams ( Fig.3A) and second-order differential diagrams for measuring an electrical conductivity-temperature curve and the phase transition temperature in (0.56LiCl-0.44KCl)-NdCl3 (30 wt.%) molten salts ( Fig. 3B) shows; and Fig. 4 is a diagram that represents first-order differential diagrams ( Fig. 4A) and second-order differential diagrams for measuring an electrical conductivity-temperature curve and the phase transition temperature, which were determined in (0.56LiCl-0.44KCl)-NdCl3 (15 wt%) molten salts ( Fig. 4B). DETAILED DESCRIPTION

[0012] Exemplary embodiments of the present disclosure are described below with reference to the accompanying drawings. However, the exemplary embodiments of the present disclosure can be modified in various other ways, and the scope of the present disclosure is not limited to the exemplary embodiments described below.

[0013] The phase transition behavior of the molten salt is one of the fundamental properties that must be considered when determining the operating temperature, which affects the safety, efficiency, and overall performance of the molten salt reactor. This disclosure provides a new method for determining the phase transition temperature using electrical conductivity data.

[0014] In the method for determining the phase transition temperature using the electrical conductivity of the present disclosure, any material whose electrical conductivity is measured can be used without special restrictions and can be a solid solution or molten salts with electrical conductivity, etc.Examples of the molten salts may include one or more selected from the group consisting of LiPF6, LiF, KF, NaF, RbF, CsF, CaF2, MgF2, SrF2, BaF2, AlF3, UF3, UF4, PuF3, ThF3, ZrF4, NdF3, CeF3, LaF3, LiCl, KCl, NaCl, RbCl, CsCl, CaCl2, MgCl2, SrCl2, BaCl2, AlCl3, UCl3, UCl4, PuCl3, ThCl3, ZrCl4, NdCl3, CeCl3, LaCl3, LiBr, KCBr, NaBr, RbBr, CsBr, CaBr2, MgBr2, SrBr2, BaBr2, AlBr3, UBr3, UBr4, PuBr3, ThBr3, ZrBr4, NdBr3, CeBr3, LaBr3, LiI, KI, NaI, RbI, CsI, CaI2, MgI2, SrI2, BaI2, AlI3, UI3, UI4, PuI3, ThI3, ZrI4, NdI3, CeI3, LaI3, LiI, KI, NaI, LiNO3, KNO3, NaNO3, RbNO3 and CsNO3, and may preferably comprise one or more from the group consisting of LiCl-KCl, NaCl-KCl, NaCl-MgCl2, LiCl-NaCl-CaCl2-BaCl2, NaCl-KCl-BaCl2, CsI, UCl3, UCl4, NdCl3, CeCl3 and LaCl3.

[0015] Specifically, the method for determining the phase transition temperature using the electrical conductivity of the present disclosure comprises the creation of a diagram of the change in the electrical conductivity of molten salts as a function of a temperature change and the performance of at least one mathematical analysis.

[0016] The execution of the mathematical analysis that can be applied to the present disclosure comprises (i) performing a first-order differential on the graph of the change in the electrical conductivity of the molten salts, (ii) performing a second-order differential on the graph of the change in the electrical conductivity of the molten salts, and (iii) determining the number (n) of data points and the resolution (ΔT) based on the graph of the change in the electrical conductivity of the molten salts, in order to determine T nto derive by equation (1) below, and to perform a linear regression analysis on a linear section to identify an outlier based on a distance from the linear regression equation. Tn=Tmax−ΔT×n (In the equation (1) above, n represents the amount of data and ΔT represents an interval of the measured temperature and means resolution).

[0017] As a result of the mathematical analysis, in the case of (i) a point at which a value is highest when processing the first-order differential, in the case of (ii) an inflection point at which the value becomes 0 when processing the second-order differential, and in the case of (iii) the temperature corresponding to the outlier can be determined as the phase transition temperature.

[0018] The phase transition temperature to be measured in the present disclosure is not particularly limited, as long as it is the temperature at which the phase of the material changes, but can, for example, be the liquidus temperature T. L be.

[0019] If the difference between the liquid temperature T L and the solidus temperature T S 25°C or less, i.e., the smaller the difference, the more difficult it can be to distinguish between the liquidus and solidus temperatures. In this case, if (iii) the mathematical analysis is carried out, a relatively accurate liquidus temperature T can be determined. L be determined.

[0020] According to the present disclosure, a diagram of the change in the electrical conductivity of the molten salts as a function of temperature change is first created. In this case, the device or method for determining the electrical conductivity is not restricted, and any known device or method for determining the electrical conductivity can be used.

[0021] When creating the diagram for the change in the electrical conductivity of the molten salt as a function of temperature, the temperature change can be either an increase or a decrease. For example, if the electrical conductivity is measured at a decreasing temperature, the maximum temperature T can be mThe temperature can be chosen to be higher than or equal to the melting point of the molten salt, and the measurement can begin at the maximum temperature. In this case, the maximum temperature is not particularly limited and could, for example, be a maximum temperature that a high-temperature furnace can withstand. However, from a process-economic point of view, the temperature can be reduced from the melting point of the molten salt being analyzed, and from a temperature 50 to 500°C above the melting point, to room temperature. Alternatively, the electrical conductivity can be measured by starting with the solid salt and increasing the temperature to the melting point or higher. However, considering the accuracy of the data, it is preferable that when increasing the temperature and plotting the change in the electrical conductivity of the molten salt as a function of temperature, the temperature rises slowly to 20°C / h or less.In view of the time required for the analysis and the accuracy of the analysis, it is therefore preferable to create the diagram by cooling the temperature from the melting temperature of the molten salts or a temperature 50 to 500°C higher than the melting temperature to room temperature.

[0022] In equation (1) of (iii) above, n is the number of data points, and the range of n is not particularly limited. Considering the reliability of the data, the range of n is preferably 10 or more and may be an integer of 100 or less, e.g., 50 or less or 30 or less. Meanwhile, ΔT may refer to the resolution in the interval of the measured temperature, and this too is not particularly limited and may be adjusted as needed, but considering the reliability of the data and the time required, ΔT is preferably 2 to 10°C.

[0023] If the absolute value of the distance constant, which represents the distance from the linear regression equation, is greater than or equal to the discrimination reference value in Table 1, the outlier can be identified as an outlier based on the distance from the linear regression equation from (iii) above. However, the discrimination reference value can also be adjusted as needed.

[0024] When identifying outliers based on their distance from the linear regression equation, at least one of the following equations A to E can be applied. That is, the distance from the linear regression equation can be determined by selecting at least one of the equations above. Z(A)=ri=yi−y^i Z(B)=hi=1n+(xi−x¯)SSX Z(C)=rsi=riMSEi×(1−hi) Z(D)=ri2(k+1)MSE[hi(1−hi)2] Z(E)=rsihi(1−hi)

[0025] Specifically, the algorithm is based on the discrimination reference value specified in Table 1 below. [Table 1] Formula for deriving the distance constant Reference value for differentiation Equation A 2 Equation B The smaller value of 6 / n and 0.99 Equation C 2 Equation D 1 Equation E If n is less than 30, it is 1; if n is greater than or equal to 30, it is 2 / n. 0.5

[0026] For example, if, when applying equations A to E, the absolute value of the distance constant is less than the discrimination reference value in Table 1, the algorithm proceeds by re-performing the linear regression analysis, adding n as n+1, re-performing the linear regression analysis, and again adding 1 to n, resulting in n+2. In this case, it is not necessary to satisfy all equations A to E and independently check whether the value is below the discrimination reference value according to each equation. If the absolute value of the distance constant according to equations A to E is greater than or equal to the discrimination reference value, the point can be identified as an outlier, and the point's temperature can be determined as the liquidus temperature T. L be performed.

[0027] Meanwhile, outlier detection based on the distance from the linear regression equation in (iii) above ends when the liquidus temperature T L equal to the solidus temperature T S becomes.

[0028] The present disclosure may, for example, include: increasing the temperature of the solid salt melts and creating a diagram of the change in the electrical conductivity of the salt melts according to the temperature increase; determining the solidus temperature T. Sby performing a first- or second-order differential on the graph of the change in electrical conductivity of the molten salts as a function of temperature increase; melting the molten salts by raising the temperature to a temperature 50 to 500°C higher than the melting point of the molten salts; creating a graph of the change in electrical conductivity of the molten salts as the temperature decreases to room temperature; and determining the number n of data points and the resolution ΔT based on the graph of the change in electrical conductivity of the molten salts as the temperature decreases to T nderiving using equation (1), and performing a linear regression analysis on a linear section to detect an outlier based on a distance from the linear regression equation, wherein the detection of the outlier includes applying one or more equations selected from equations A to E, and, based on the distance constant confirmed on the equation(s), repeating the linear regression analysis and adding n as n+1 if an absolute value of a distance constant is less than a distinguishing reference value, and determining as an outlier if the absolute value of the distance constant is greater than or equal to a distinguishing reference value, and determining the temperature at that point as the liquidus temperature T L .

[0029] The present revelation is described in more detail below using specific examples. These examples are provided for illustrative purposes only, to facilitate understanding of the present revelation, and are not limited to the scope of the present revelation. Example 1. Materials and equipment

[0030] To measure the electrical conductivity, a custom-designed glass capillary cell (1.5 mm inner diameter, 3 cm capillary length) was used. A platinum conductor (1 mm diameter) was used to establish electrical contact between the capillary cell and a highly conductive liquid. The electrical conductivity values ​​were determined by measuring a step voltage in microseconds using a potentiometer.

[0031] The cell constant is a coefficient used to convert a measured resistance (or its reciprocal) into conductivity, and the capillary cell is selected so that its cell constant lies within a suitable range. Generally, for highly conductive liquids, cells with values ​​greater than or equal to 300 cm⁻¹ are used. -1 recommended. The cell constant was measured in a water bath at a constant temperature of 291 K by adding a standard KCl solution with known conductivity to the capillary cell, which was determined using the following equation. C=k×R

[0032] Here, C represents the cell constant (cm³). -1 ), k for the electrical conductivity (S cm) -1) of the solution, R for the resistance of the solution, and the value of R was determined from the slope of a current-voltage curve obtained using a method for measuring a step voltage in units of microseconds. 2. Method for determining the phase transition temperature of molten salts

[0033] According to the present disclosure, it is possible to measure a value of the electrical conductivity in the molten salt mixture at regular intervals by using the system described above for measuring the electrical conductivity in the material and in the equipment of 1. while the temperature is lowered, and to determine the phase transition temperature objectively and accurately by applying a series of mathematical algorithms to the measured value. (1) Measurement of electrical conductivity

[0034] To measure the electrical conductivity of the molten salt at high temperature, the molten salt mixture was placed in a quartz vessel and then transferred to a high-temperature furnace inside a glove box (99.999% argon, humidity and oxygen <1 ppm). The temperature of the high-temperature furnace was controlled and monitored using a thermocouple. The thermocouple was positioned as close as possible to the end of the capillary cell to ensure accurate temperature measurement. To determine the phase transition of the molten salt, the electrical conductivity was measured at regular intervals while the temperature was lowered from 300 to 650°C. (2) Determination of the phase transition temperature using a mathematical algorithm1) Second-order differential method

[0035] The measured electrical conductivity-temperature curve can be subjected to a first- and / or second-order differential. The point at which the result of the first-order differential is highest, and the value at which an inflection point in the result of the second-order differential becomes 0, can be determined as the phase transition temperature. This method allows for the differentiation of transition points that are difficult to determine as the intersection point of a simple linear regression equation, and a more accurate temperature can be determined by appropriately adjusting a temperature interval corresponding to a specific resolution.

[0036] However, if, for example, in a system of molten salt of a composition with two phase transition temperatures, namely the solidus temperature T S and the liquid temperature T L , the temperature interval between T S and T LSince the temperature difference is narrow, calculations based on difference values ​​can lead to inaccuracies in some cases. The phase transition temperature can be determined using a phase transition temperature determination procedure based on a mathematical algorithm, as shown below, or by additionally performing this procedure. 2) Analysis algorithm with linear regression and statistical data analysis

[0037] As shown in the algorithm flowchart of Fig. As shown in Figure 1, the phase transition temperature can be determined by a systematic procedure for determining a value according to various statistical evaluation criteria of equations A, B, C, D and E.

[0038] In this case, the definitions of the individual descriptions in the algorithm above are as follows. T0 = ​​T max : Highest temperature at which the measurement of the conductivity value begins. Tn = Minimum temperature in the linear section T max = Maximum temperature T L = Liquidus temperature ΔT = Resolution n = minimum number of data points R 2 = Coefficient of determination Z = distance constant |Z| = Absolute value of the distance constant Z det = Reference value for differentiation

[0039] Furthermore, equations A, B, C, D and E are exemplary statistical equations that can be used to assess how far the data value is from the linear regression equation, which is as follows: Z(A)=ri=yi−y^i Z(B)=hi=1n+(xi−x¯)2SSX Z(C)=rsi=riMSEi×(1−hi) Z(D)=ri2(k+1)MSE[hi(1−hi)2] Z(E)=rsihi(1−hi)

[0040] In this case, the definitions of the elements described in each equation are as follows. n: Number of data points k: Number of independent terms in the regression model (e.g., for a linear model: y = ax + b, i.e., two, a and b) yi: i−th y−value yi^:predicted i-th y-value xi: i−th x−value x¯: mean x−value SSX=∑(xi−x¯)2 SSE=∑(yi−yi^)2 df=n−k−1 MSE=SSEdf MSEi=MSE−ri2(1−hi)×df×dfdf−1 3. Experimental example: Determination of the phase transition temperature

[0041] LiCl-KCl salt melts, which are chloride-based molten salts used for the thermochemical reprocessing of spent nuclear fuel, served as the objects of study. Various physical properties of these salt melts were investigated by several researchers. For example, the melting temperature, which depends on the KCl (or LiCl) composition, was measured in several studies using a thermal analysis method.

[0042] To demonstrate the validity of the method based on electrical conductivity for determining the phase transition temperature, the electrical conductivity-temperature curve was determined from a LiCl-KCl-based salt melt and the solidus temperature (T) was calculated. S : solidus temperature) or liquidus temperature (T L : liquidus temperature).

[0043] Subsequently, all measured temperature values ​​were compared with the previously reported reliable results.

[0044] Fig. Figure 3A shows the electrical conductivity-temperature curve measured in LiCl-KCl-NdCl3 (30 wt%) molten salts, and Fig. Figure 3B shows the first differential and second differential result diagrams for determining the phase transition temperature, and Fig. Figure 4A shows the electrical conductivity-temperature curve measured in LiCl-KCl-NdCl3 (15 wt%) molten salts, and Fig.4B shows the first differential and second differential result diagrams for determining the phase transition temperature. In this case, the wt% is expressed as a percentage of the mass of NdCl3 compared to the mass of the total solution, using the eutectic LiCl-KCl mixture as the solvent.

[0045] In experimental example 1 (Type I) of Fig. 3. The exact transition temperature could be determined on the basis of the first and / or second order differential of the corresponding curve if there is a gap between T. S and T L was sufficiently large. The T measured in this way S was measured at 353°C (first order differential), 352°C (second order differential) and the T L confirmed at 420°C (first order differential) and 417°C (second order differential), which correspond to the values ​​given in the literature (T S : 355°C and T L : 424°C) are very similar.

[0046] If the gap between T S and T L If the temperature is less than 25°C, it can be difficult to determine the inflection point, which is T L to determine unambiguously. Therefore, additional T L,cal -Values ​​that meet the statistical evaluation criteria of the present disclosure, as calculated in Table 1 and compared in Table 2.

[0047] Table 2 shows the results of statistical equations A to E, which assess how much the data values ​​deviate from the linear regression equation. In Table 2 below, column 1 represents n, columns 2 and 3 represent T (absolute temperature, the value obtained by adding 273 to the Celsius temperature) and x-value (1 / T, the reciprocal of the absolute temperature), respectively, and column 4 represents y-value (ln k). Column 5 represents the predicted ŷ value from the linear regression equation. A, B, C, D, and E, shown in columns 6 to 10, show the values ​​calculated by substituting each of the equations mentioned above. [Table 2] n T / K X(1 / T) Y(InK) Previous Y Remaining lever RStudent Cook D DFFITS 1 873 0,00115 0,79416 0,79742 -0,00326 0,11386 -0,05090 0,00017 -0,01825 2 863 0,00116 0,77262 0,77482 -0,00221 0,10505 -0,03428 0,00007 -0,01174 3 853 0,00117 0,74998 0,75171 -0,00173 0,09656 -0.02670 0,00004 -0,00873 4 843 0,00119 0,72810 0,72804 0,00007 0,08843 0,00102 0,00000 0,00032 5 833 0,00120 0,70624 0,70380 0,00243 0,08068 0,03729 0,00006 0,01105 6 823 0,00122 0,67974 0,67898 0,00076 0,07335 0,01166 0,00001 0,00328 7 813 0,00123 0,65621 0,65354 0,00267 0,06648 0,04063 0,00006 0,01084 8 803 0,00125 0,63145 0,62747 0,00398 0,06011 0,06033 0,00012 0,01526 9 793 0,00126 0,60365 0,60075 0,00290 0,05428 0,04386 0,00006 0,01051 10 783 0,00128 0,57528 0,57334 0,00195 0,04905 0,02933 0,00002 0,00666 11 773 0,00129 0,54517 0,54522 -0,00005 0,04446 -0,00071 0,00000 -0,00015 12 763 0,00131 0,51347 0,51636 -0,00289 0,04057 -0,04333 0,00004 -0,00891 13 753 0,00133 0,48213 0,48674 -0,00461 0,03745 -0,06902 0,00010 -0,01361 14 743 0,00135 0,44434 0,45632 -0,01199 0,03515 -0,17944 0,00061 -0,03425 15 733 0,00136 0,40877 0,42507 -0,01630 0,03376 -0,24395 0,00108 -0,04560 16 728 0,00137 0,39532 0,40913 -0,01380 0,03342 -0,20648 0,00076 -0,03839 17 723 0,00138 0,373305 0,39296 -0,01991 0,03334 -0,29806 0,00158 -0,05535 18 718 0,00139 0,35262 0,37657 -0,02395 0,03352 -0,35884 0,00230 -0,06683 19 713 0,00140 0,33624 0,35994 -0,02370 0,03398 -0,35523 0,00229 -0,06663 20 708 0,00141 0,31260 0,34309 -0,03049 0,03473 -0,45784 0,00388 -0,08685 21 703 0,00142 0,28882 0,32599 -0,03717 0,03578 -0,55954 0,00596 -0,10779 22 698 0,00143 0,26925 0,30865 -0,03939 0,03715 -0,59389 0,00697 -0,11665 23 693 0,00144 0,24343 0,29106 -0,04763 0,03884 -0,72084 0,01068 -0,14490 24 683 0,00146 0,19923 0,25510 -0,05587 0,04326 -0,85064 0,01652 -0,18088 25 673 0,00149 0,14710 0,21807 -0,07097 0,04916 -1,09311 0,03067 -0,24855 26 663 0,00151 0,09939 0,17993 -0,08055 0,05667 -1,25382 0,04627 -0,30731 27 653 0,00153 0,06065 0,14062 -0,07997 0,06593 -1,25090 0,05413 -0,33234 28 643 0,00156 -0,06298 0,10009 -0,16307 0,07710 -2,84403 0,26961 -0,82203 29 638 0,00157 -0,13720 0,07935 -0,21654 0,08345 -4,32537 0,52174 -1,30516 30 633 0,00158 -0,20582 0,05827 -0,26410 0,09034 0,85292 -2,06278 31 623 0,00161 -1,22781 0,01512 -1,24292 0,10584 22,90659 32 613 0,00163 -6,44702 -0,02945 -6,41758 0,12380 743,88273 33 603 0,00166 -9,39146 0,07549 -9,31597 0,14444

[0048] For the electrical conductivity-temperature curve measured in (0.56LiCl-0.44KCl)-NdCl3 (15 wt%) salt, the T LValues ​​obtained from the analysis algorithm using linear regression and statistical data analysis are summarized in Table 3 below. [Table 3] T L,cal % Difference Value given in the literature [J.Mol.Liq.382 (2023) 121869] 382 A 350 8,4 B 330 13,6 C 380 0,5 D 360 5,8 E 370 3,1

[0049] As can be seen in Table 3, the electrical conductivity-temperature curve in Fig. 4. A difference of approximately 10% was found between the values ​​given in the literature, which was confirmed in the order C < E < D < A < B.

[0050] To confirm the objectivity and suitability of the evaluation method for equations A to E, the T values ​​for the electrical conductivity-temperature curve with different result values ​​were determined using 0.70LiCl-0.30KCl salts with different compositions. L Values ​​resulting from the analysis algorithm using linear regression and statistical data analysis are summarized in Table 4 below. [Table 4] T L,cal % Difference Value given in the literature (Russ. J.Inorg.Chema. 53 (2008) 1509) 452 A 360 20,4 B 350 22,6 C 450 0,4 D 445 1,5 E 450 0,4

[0051] As shown in Table 4, the percentage differences from the literature values ​​showed differences in the order C, E < D < A < B. In general, it can be observed that methods C and E showed small differences from the literature values, while methods A and B showed relatively large differences.

[0052] It is therefore to be expected that the method of integrating values ​​according to various statistical evaluation criteria based on the present disclosure can offer a degree of objectivity, rationality and sensitivity control to achieve a desired level of uncertainty.

[0053] In other words, the system for determining the phase transition temperature by measuring electrical conductivity, as disclosed herein, is very promising as a new method for measuring the phase transition temperature of various multi-component salt melts, and this technology offers a much simpler and faster measurement system compared to existing thermal analysis methods. At the same time, this analysis algorithm enables a consistent determination of the transition temperature under all conditions and environments.

[0054] According to the method for determining the phase transition temperature using electrical conductivity, it is possible to easily and quickly calculate accurate values ​​for the phase transition temperature by measuring the electrical conductivity of a target and applying a series of mathematical algorithms using the measured electrical conductivity. Therefore, it is expected that experimentally determined values ​​of the phase transition temperature in high-temperature salt melts, etc., can be used as reference data for phase equilibrium diagrams based on computational thermodynamics.

[0055] While exemplary embodiments have been illustrated and described above, it will be obvious to those skilled in the art that modifications and variations can be made without deviating from the scope of the present disclosure as defined by the attached claims. QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents cited by the applicant was automatically generated and is included solely for the reader's convenience. The list is not part of the German patent or utility model application. The DPMA accepts no liability for any errors or omissions. Cited patent literature

[0000] KR 10-2023-0119841

[0001] KR 10-2024-0039332

[0001] KR 10-1412594 B1

[0007] Cited non-patent literature

[0000] J.Mol.Liq.382 (2023) 121869

[0048]

Claims

[1] A method for measuring phase transition temperature using electrical conductivity, comprising: Drawing up a diagram of the change in electrical conductivity of molten salts as a function of temperature; and Carrying out at least one mathematical analysis of(i) performing a first-order differential on the graph, (ii) performing a second-order differential on the graph, and (iii) Determine the number (n) of data and the resolution (ΔT) based on the graph of the derivative of T n according to equation (1) below and performing a linear regression analysis on a linear section to detect an outlier based on a distance from the linear regression equation, Tn=Tmax−ΔT×n where n is the number of data and ΔT is the interval of the measurement temperature and the average resolution. [2] The method according to claim 1, wherein, in the case of (i), a point at which a value is the highest in the first-order differential processing, in the case of (ii), an inflection point at which the value becomes 0 in the second-order differential processing, and in the case of (iii), the temperature corresponding to the outlier are determined as the phase transition temperature. [3] The method according to claim 1, wherein the mathematical analysis according to (iii) is carried out when the difference between the liquidus temperature (T L ) and the solidus temperature (T S ) is 25°C or less. [4] The method according to claim 1, wherein the temperature change refers to cooling the temperature from the melting temperature of the molten salt to be analyzed or a temperature 50 to 500°C above the melting temperature to room temperature or raising the temperature of the solid molten salt to the melting temperature or above. [5] The method according to claim 1, wherein the molten salts comprise at least one component selected from the group consisting of LiCl-KCl, NaCl-KCl, CsCl-KCl, LiCl-NaCl-CaCl2-BaCl2, NaCl-KCl-BaCl2, CaF2, NdCl3, CeCl3 and LaCl3. [6] The process according to claim 1, wherein the phase transition temperature is the liquidus temperature (T L ) is. [7] The method according to claim 1, wherein in equation (1) of (iii) above, n is an integer of 10 to 100, and ΔT is 2 to 10°C. [8] The method according to claim 1, further comprising re-performing the linear regression analysis and adding n as n+1 if an absolute value of a distance constant is smaller than a discrimination reference value, and Determination as an outlier if the absolute value of the lower distance constant is greater than or equal to a discrimination reference value, and determination of the temperature at this point as the liquidus temperature (T L ), when applying one or more of the following equations A to E. Z(A)=ri=yi−yi^ Z(B)=hi=1n+(xi−x¯)2SSX Z(C)=rsi=riMSEi×(1−hi) Z(D)=ri2(k+1)MSE[hi(1−hi)2] Z(E)=rsihi(1−hi) (In this case, the definitions of the elements described in each equation are as follows: n: number of data k: number of independent terms in the regression model yi:i−th y−value yi^:predicted i-th y-value xi:i−th x−value x¯:mean x−value SSX=∑(xi−x¯)2 SSE=∑(yi−yi^)2 df=n−k−1 MSE=SSEdf MSEi=MSE−ri2(1−hi)×df×dfdf−1 [9] The method according to claim 8, wherein in the detection of the outlier based on the distance from the linear regression equation in (iii) above, if the absolute value of the distance constant representing the distance from the linear regression equation is greater than or equal to each of the following discrimination reference values ​​in each derivation equation of the distance constant A to E, it is detected as an outlier. Equation A: 2 Equation B: Smaller value of 6 / n and 0.99 Equation C: 2 Equation D: 1 Equation E: If n is less than 30, it is 1, and if n is greater than or equal to 30, it is 2 / n 0.5 . [10] The method according to claim 8, wherein the detection of the outlier based on the distance from the linear regression equation in (iii) above ends when the liquidus temperature (T L ) is equal to the solidus temperature (T S ) becomes. [11] The method according to claim 1 further comprises: Increasing the temperature of the solid molten salts and creating a graph of the change in the electrical conductivity of the molten salts as a function of the temperature increase; Determination of the solidus temperature (T S ) by performing the first-order differential or the second-order differential on the graph of the change in the electrical conductivity of the molten salt as a function of the temperature increase; Melting the molten salts by raising the temperature to a temperature 50 to 500°C higher than the melting temperature of the molten salts; Drawing up a diagram of the change in electrical conductivity of the molten salt with decreasing temperature during cooling to room temperature; and Determine the number (n) of data and the resolution (ΔT) based on the graph of the change in the electrical conductivity of the molten salts according to the temperature drop to T n using the above equation (1), and performing a linear regression analysis on a linear section to detect an outlier based on a distance from the linear regression equation, where the detection of the outlier includes re-performing the linear regression analysis and adding n as n+1 if an absolute value of a distance constant is smaller than a discrimination reference value, and Determination as an outlier if the absolute value of the lower distance constant is greater than or equal to a discrimination reference value, and determination of the temperature at this point as the liquidus temperature (T L ), using one or more of the following equations A to E. Z(A)=ri=yi−y^i Z(B)=hi=1n+(xi−x¯)2SSX Z(C)=rsi=riMSEi×(1−hi) Z(D)=ri2(k+1)MSE[hi(1−hi)2] Z(E)=rsihi(1−hi) (In this case, the definitions of the elements described in each equation are as follows: n: number of data k: number of independent terms in the regression model yi: i−th y−value yi^:predicted i-th y-value xi: i-th x-value x¯: mean x−value SSX=∑(xi−x¯)2 SSE=∑(yi−yi^) df=n−k−1 MSE=SSEdf MSEi=MSE−ri2(1−hi)×df×dfdf−1, where each discrimination reference value in each derivative equation of the distance constants A to E is as follows: Equation A: 2 Equation B: Smaller value of 6 / n and 0.99 Equation C: 2 Equation D: 1 Equation E: If n is less than 30, it is 1, and if n is greater than or equal to 30, it is 2 / n) 0.5

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